Jan 12, 2016 - 13.8 Tutorial 8: Equilibrium Unemployment Model . . . . . . . . . . . . . . . . . . . . . . 381 .... http://www.hull.ac.uk/php/ecskrb/Confer/research.html.
ADVANCED MACROECONOMICS (56277) Dr. Keshab Bhattarai University of Hull Business School, Hull, England, UK. January 12, 2016
Abstract This monograph aims to present concisely the major elements of popular macroeconomic models for systematic thinking about the modern economies. It contains detailed derivations of classical, Keynesian, new Keynesian, new classical models and open economy and structural models used for analysing short run ‡uctuations and long run growth. Tutorial problems and assignments are provided for each sector for practice. These models could be used for advanced policy discussions required for greater macroeconomic stability and higher rates of economic growth. JEL Classi…cation: E Keywords: macroeconomic models H U 6 7 R X , H u ll,
U K . e m a il: K .R .B h a tta ra i@ hu ll.a c .u k
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Contents 1 L1: Classical and Keynesian Macro Models 1.1 Background: Seven Classical Macro Models . . . . . . . . . . . . . . . . . . . 1.1.1 A simple version of the classical macroeconomic model . . . . . . . . . 1.1.2 Malthusian model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Two period model of consumption and saving . . . . . . . . . . . . . . 1.1.4 Pure exchange model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.5 Ricardian Trade Model for Comparative Advantage . . . . . . . . . . 1.1.6 Intertemporal balance in budgets of households, government and …rms 1.1.7 Ramsey growth model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Keynesian Model: Hicksian Synthesis . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Soution of the Keynesian Model . . . . . . . . . . . . . . . . . . . . . 1.2.2 Comparative Static Analysis in Keynesian Macroeconomic Model . . . 1.2.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Samuelsonian Multiplier Accelerator Model . . . . . . . . . . . . . . . . . . . 1.4 ISLM equilibrium: a new approach . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Basics of monopolistic competition in a new Keynesian model . . . . . . . . . 1.6 Micro-foundation to the Keynesian Multiplier: Mankiw (1988) . . . . . . . . 1.7 Keynesian Stochastic Macroeconomic Model and Policies . . . . . . . . . . . . 1.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.2 Stylized Facts and Macroeconomic Policies in the UK . . . . . . . . . 1.7.3 Macroeconomic Trends . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.4 Fiscal Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.5 Monetary policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.6 Trade Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.7 Modelling of the UK economy . . . . . . . . . . . . . . . . . . . . . . . 1.7.8 Keynesian Stochastic Macroeconomic Model (KSMM) . . . . . . . . . 1.7.9 Steady State in the KSMM . . . . . . . . . . . . . . . . . . . . . . . . 1.7.10 Transitional Dynamics in KSM Model . . . . . . . . . . . . . . . . . . 1.7.11 Estimation and application of the KSMM Model . . . . . . . . . . . . 1.7.12 Qualitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.13 A Small Model of Unemployment, In‡ation and Growth . . . . . . . . 1.7.14 Solution of the stabilisation model . . . . . . . . . . . . . . . . . . . . 1.7.15 Supply side and rational expectation . . . . . . . . . . . . . . . . . . . 1.7.16 Aggregate Demand and Aggregate Supply Model . . . . . . . . . . . . 1.7.17 Trade Policy Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.18 Structural factors and the volatility of exchange rate . . . . . . . . . . 1.7.19 Monetary model of exchange rate expectation . . . . . . . . . . . . . . 1.7.20 Solving for in‡ation and exchange rate paths simultaneously . . . . . 1.7.21 Exchange rate overshooting under the ‡oating exchange rate system . 1.7.22 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.23 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.24 Identi…cation of the simultaneous equation model (SEM) . . . . . . . 1.7.25 Path of price and exchange rates in the Dornbusch model . . . . . . .
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8 11 11 13 14 19 23 27 30 37 39 41 42 46 50 51 56 58 58 58 58 62 64 65 65 67 68 69 71 74 77 78 80 81 84 85 86 87 88 89 95 95 96
2 L2: 2.1 2.2 2.3 2.4
New Keynesian Model: Fundamentals New Keynesian Model: a prototype example . . . . . . . . . . . . . Two Period Model of Stabilisation: Mankiw and Weinzierl (2011) . A DSGE Model of Macroeconomic Policy in South Asia . . . . . . A Prototype of New Keynesian DSGE model with habit formation 2.4.1 Blanchard and Gali (2013) . . . . . . . . . . . . . . . . . . 2.4.2 Solution Procedure in the DSGE Models . . . . . . . . . . . 2.4.3 Basics of Bhattarai and Trzeciakiewicz (2012) DSGE model 2.4.4 Household problem . . . . . . . . . . . . . . . . . . . . . . . 2.4.5 Fiscal and monetary policies . . . . . . . . . . . . . . . . . 2.4.6 Log-Linearised System of Equations . . . . . . . . . . . . . 2.4.7 Households: . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.8 Firms: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.9 Government: . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.10 General equilibrium conditions: . . . . . . . . . . . . . . . . 2.4.11 Parameterisation of the model . . . . . . . . . . . . . . . . 2.4.12 Results of Hull DSGE model . . . . . . . . . . . . . . . . . 2.5 Critical assessment of the DSGE Models . . . . . . . . . . . . . . . 2.5.1 Blanchard’s New Keynesian DSGE model . . . . . . . . . . 2.5.2 Basic New Keynesian Model in logs . . . . . . . . . . . . . 2.5.3 Extended version of the New Keynesian Model . . . . . . . 2.6 Problem on Open Economy New Keynesian Model . . . . . . . . . 2.7 Stability Analysis: Illustrations . . . . . . . . . . . . . . . . . . . .
3 L3: New Classical Macro Models (Real Business Cycle) 3.0.1 Linear RBC Model . . . . . . . . . . . . . . . . . . . . 3.0.2 New Keynesian Model in relation to the RBC models 3.1 Rational Expectation . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Rational Expectation: Another example . . . . . . . . 3.2 Supply Side and Rational Expectation . . . . . . . . . . . . . 3.3 Aggregate demand and aggregate supply model . . . . . . . . 3.3.1 Estimations . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Trade Policy: Small Open Economy Macro Model . . . . . . 3.4.1 Estimations . . . . . . . . . . . . . . . . . . . . . . . .
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97 97 99 100 104 110 112 113 115 116 117 117 118 118 118 118 121 130 131 132 132 132 134
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143 147 148 151 154 160 161 164 164 168
4 L4: Neoclassical Growth Model 172 4.0.2 Four First Order Conditions for Dynamic Optimisation . . . . . . . . . . . . 173 4.0.3 Transitional dynamics towards steady state . . . . . . . . . . . . . . . . . . . 174 4.1 Standard macromodel of growth, …scal policy and welfare (Bruce and Turnovsky(2007))176 4.1.1 Mechanism for Poverty Alleviation (Bhattarai 2010) . . . . . . . . . . . . . . 179 4.2 Dynamic Computable General Equilibrium Model of Fiscal Policy . . . . . . . . . . 182 4.2.1 Trade arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.2.2 Government sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.2.3 General Equilibrium in a Growing Economy . . . . . . . . . . . . . . . . . . . 185 4.2.4 Procedure for Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 4.3 Exercise 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
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5 L5: Endogenous Growth Model 5.0.1 Human capital and …nal goods sectors . . . . . . . . . . . 5.0.2 Balanced growth . . . . . . . . . . . . . . . . . . . . . . . 5.0.3 Cross country calibration of government bias in education 5.0.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 5.0.5 China, India and SAARC Countries in the Global Growth 5.0.6 Dynamic Panel Data Model of Economic Growth . . . . . 5.0.7 GMM 2-step Estimation of Growth in South Asia . . . . 5.0.8 Dynamic Computable General Equilibrium Model . . . . 5.0.9 Macroeconomic simulation model of South Asia . . . . . . 5.1 Exercise 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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189 189 190 192 194 195 199 199 202 205 206
6 L6: Dynamic Programming for Macro Dynamics 6.1 Exercise 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Money in Growth Models . . . . . . . . . . . . . . . . . . . . . 6.2.1 Friedman Rule with Cash in Advance Constraint . . . . 6.2.2 Dynamic optimisation in CIA Model . . . . . . . . . . . 6.2.3 Steady State in the CIA Model . . . . . . . . . . . . . . 6.3 Money in the Utility Function and Growth . . . . . . . . . . . 6.3.1 Dynamic optimisation in the MIU model . . . . . . . . 6.3.2 Steady state in the MIU model . . . . . . . . . . . . . . 6.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Analysis of Dynamic GE Model of Financial Deepening 6.3.5 Optimal and actual …nancial deepening . . . . . . . . . 6.4 Exercise 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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7 L7: 7.1 7.2 7.3
7.4 7.5 7.6 7.7
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208 212 214 214 216 217 223 224 224 228 230 231 233
Open Economy Model: Exchange Rate and Finance in Macro Small Open Economy Model . . . . . . . . . . . . . . . . . . . . . . . Global Economy model of Two Economies . . . . . . . . . . . . . . . . Two SEctor Static Global General Equilibrium Model with Money . . 7.3.1 Outline of the Model . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4 Monetary Sector . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.5 Government Sector . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.6 External sector . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.7 Analytical Forms and the Solution Procedure . . . . . . . . . . 7.3.8 Parameterisation of the Model . . . . . . . . . . . . . . . . . . 7.3.9 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . 7.3.10 Conclusion from the static two country model . . . . . . . . . . Two Country Dynamic Global Economy Model . . . . . . . . . . . . . 7.4.1 Analytical Results of Optimisation . . . . . . . . . . . . . . . . International macroeconomic policy coordination . . . . . . . . . . . . Nash-VAR Policy Game . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6.1 Estimates for the Nash Policy Game . . . . . . . . . . . . . . . Multicountry macro interaction model . . . . . . . . . . . . . . . . . .
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241 241 244 249 250 251 253 255 256 256 257 258 259 262 262 265 272 273 274 275
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7.7.1 7.7.2 7.7.3 7.7.4 7.7.5 7.7.6 7.7.7 7.7.8
Time path in the multicountry macro interaction model . . . . . . . Parameters of the Macroeconomic model . . . . . . . . . . . . . . . . Results of Macro Nash Policy Game . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Growth Impacts of Foreign Direct Investment in an Open Economy Empirical Literature on FDI and Growth . . . . . . . . . . . . . . . Empirics of FDI in BRICS Countries . . . . . . . . . . . . . . . . . . Empirics of FDI in OECD Countries . . . . . . . . . . . . . . . . . .
8 L8: 8.1 8.2 8.3
Business Cycles Optimising model of business cycle . . . . . . . . . . . . . . . . . . . . . Aggregate Demand-Aggregate Supply (AS-AD) Model of Business Cycle AS-AD Model of Business Cycle . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Role of Shocks in AD-AS Model . . . . . . . . . . . . . . . . . . 8.4 Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Integration of Finance in a Macro Model . . . . . . . . . . . . . . 8.5 Policy Rule versus Optimal Discretion . . . . . . . . . . . . . . . . . . .
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277 277 277 278 279 281 282 283
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291 292 294 294 297 300 304 306
9 L9: Class Test: Past Examples
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10 L10: In‡ation and Unemployment 10.1 Natural rate of unemployment and output . . . . . . . . . . . . 10.2 Wage Price Spiral . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Equilibrium Unemployment: Matching and Bargaining Set Up 10.3.1 Markov Process of Employment and Unemployment . . 10.4 Exercise 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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313 314 315 317 321 325
11 L11: Public Debt: Impact of Taxes, Spending and De…cit on Growth 328 11.1 Classical Ricardian Equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 11.2 Role of debt in the Keynesian model . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 11.3 Growth impacts of public de…cit in the Neoclassical growth model . . . . . . . . . . 333 11.4 Analysis of debt crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 12 Blake-Weale (1994) model of debt 12.1 Cole -Kehoe (2000) model of self ful…lling debt crisis . 12.2 Credibility . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Two Period Overlapping Generation Model . . . . . . 12.4 Empirical Analysis . . . . . . . . . . . . . . . . . . . . 12.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 12.6 International strategic policy coordination models . . . 12.7 Exercise 11 . . . . . . . . . . . . . . . . . . . . . . . .
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335 337 340 342 346 348 352 360
13 Tutorial Problems 13.1 Tutorial 1: Comparative Statics . . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Tutorial 2: Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.3 Tutorial 3: Open Economy DSGE Model . . . . . . . . . . . . . . . . . . . . . 13.4 Tutorial 4: Ramsey to RBC Model . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Tutorial 5: Neoclassical Growth with Hamiltonian . . . . . . . . . . . . . . . 13.6 Tutorial 6: Endogenous growth model . . . . . . . . . . . . . . . . . . . . . . 13.7 Tutorial 7: Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . 13.8 Tutorial 8: Equilibrium Unemployment Model . . . . . . . . . . . . . . . . . . 13.9 Tutorial 9: Money, In‡ation, Business Cycle and OLG Model . . . . . . . . . 13.10Tutorial 10: Small Open Economy Model . . . . . . . . . . . . . . . . . . . . 13.10.1 Monetary Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.10.2 Government Sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.11Tutorial 11: New Keynesian and Newclassical Macro Models . . . . . . . . . . 13.12Tutorial 12: Real Business Cycle Model . . . . . . . . . . . . . . . . . . . . . 13.13Tutorial 13: Global Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.14Tutorial 14: A Study on Housing Markets . . . . . . . . . . . . . . . . . . . . 13.15Tutorial 15: Rational Expectation . . . . . . . . . . . . . . . . . . . . . . . . 13.16Tutorial 16: Overlapping Generation Model: Impact of Taxes on Growth . . . 13.17Other Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.17.1 Problem 1: Keynesian Model . . . . . . . . . . . . . . . . . . . . . . . 13.17.2 Problem 2: Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . 13.17.3 Problem 3: Neoclassical Growth with Hamiltonian . . . . . . . . . . . 13.17.4 Problem 4: Dynamic Programming . . . . . . . . . . . . . . . . . . . . 13.17.5 Problem 5: Money in utility (MIU) and cash in advance (CIA) models
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362 362 369 370 372 373 376 378 381 382 384 385 385 390 391 393 394 396 399 401 401 402 405 406 407
14 Assignment(optional) 14.1 Best twenty articles in 100 years in the American 14.2 Other Articles . . . . . . . . . . . . . . . . . . . . 14.2.1 Useful texts . . . . . . . . . . . . . . . . . 14.2.2 Quality ranking of journals in Economics
Economic Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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409 415 417 422 424
15 Computation and software 15.1 GAMS . . . . . . . . . . . . . . . . . . . . . 15.2 MATLAB . . . . . . . . . . . . . . . . . . . 15.3 Dynare . . . . . . . . . . . . . . . . . . . . . 15.4 R . . . . . . . . . . . . . . . . . . . . . . . . 15.5 Econometric and Statistical Software . . . . 15.5.1 Advanced Texts in Macroeconomics
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16 Sample Class test
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17 Sampel Final Exam
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18 Foundations 18.1 First order di¤erence equation . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 First order di¤erential equation . . . . . . . . . . . . . . . . . . . . . . . . 18.3 Second order di¤erential equation: market example . . . . . . . . . . . . . 18.3.1 Higher Order Di¤erence Equations: Schurr Theorem . . . . . . . . 18.3.2 Ten Best articles in the Journal of European Economic Association 18.3.3 Best 40 articles in the Journal of Economic Perspectives . . . . . .
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461 461 464 467 474 475 475
1
L1: Classical and Keynesian Macro Models
Modern macroeconomics in general is a system of thinking about the growth in the long run and ‡uctuations in macro variables in the short run. Theories of Smith (1976), Ricardo (1817), Walras (1874), Pigou (1917), Keynes (1936), Solow (1956), Friedman (1968), Lucas (1976), Sim (1980), Sargent (1987), Romer (1989) and many other economists represent such thinking about the functioning of the economy as a whole. It has four distinguishing features a) dynamic models b) competitive equilibrium c) micro-foundation d) rational expectation. It is important to have a clear historical perspective on these features to understand what is happening to economic growth as well as to the output, employment, price level, interest rate, echange rate, imports and exports. Macroeconomic models explain determinants of aggregate demand and aggregate supply in an economy or group of economies in the global economy. Classical view Ideas of Adam Smith (1776) in "An Inquiry into the Nature and Causes of the Wealth of Nations" Economy adjusts automatically towards its long run equilibrium if the price system is perfectly ‡exible and government policy is liberal. Division of labour creates productivity. Higher rate of saving and investment are key for capital accumulation and rising living standards and output. The invisible hand, price system, plays a crucial role in allocating resources. Ideas of Ricardo (1817), Say (1817), Malthus (1790) Mill (1844), Marx (1859), Marshall (1922) Pigou (1918). General equilibrium and the real business cycle models are based on these classical principles that inlcude: Invisible hand sets prices to equate demand and supply. No excess demand or no excess supply can persist. No glut or shortages in goods market. No unemployment or labour pressure in the labour market. Money is neutral (quantity theory of money). Prices proportional to money supply. It is a long run view. Balanced budget recommended. Free and open market economy is competitive in the global economy. Laisser faire: minimum government is the best government. Downward sloping aggregate demand and vertical supply curve
8
Keynesian Revolution (Short run analysis) Gaps between supply and demand may persist for a log time. Markets (prices) may not work automatically itself because of de…ciency in demand: massive unemployment labour and under utilisation of capital is possible. Costs of waiting to return to the natural level; irresponsible to do so. Balancing budget is stupid and dangerous policy. Active role by government can mitigate de…ciency in private demand (consumption and investment). Positive role of …scal policy and monetary policy. Multiplier e¤ect of demand on output Aggregate supply is horizontal in the short run. Animal spirits –importance of expectations. Consensus on the IS-LM models (Keynes-Hicks-Hansen) (1940-1970s) Exact speci…cation of relations among economic variables discussed in Keynes; Klein’s macro economic model, MMB, dynamic models of UK economy IS curve thought to be too steep: active …scal policy recommended Theory of consumption: Modigliani-(life cycle), Friedman –permanent income ; importance of expectations Theory of investment (Tobin’s q, user cost of capital) Phillips curve; Okun’s law, Trade-o¤ between unemployment and in‡ation; more empirical models adaptive expectations Theory of unemployment (worker mis-perception, ine¢ cient markets, employer mis-perception, E¤ectiveness of monetary policy Mundel-Flemming open economy model Criticism of IS-LM and new macroeconomics Monetarist approach – Natural rate of unemployment of Milton Friedman (1968) vertical Phillips and aggregate supply curve Lucas critique (1976): rational expectations No money illusion possible, people are clever and process current information to know what the government is doing; government cannot fool people, when prices change –nominal wages change accordingly; no trade-o¤ between in‡ation and unemployment 9
Stag‡ation –no growth and in‡ation simultaneously Revenue may decrease if tax rate increases (La¤er curve) Supply side policies recommended (subsidies, manpower, investment tax credit, technological development, e-commerce, low tari¤) IS-LM are ad-hoc models; need more micro-foundation Real business cycle view: fully ‡exible prices Business cycle are optimal response not due to ‡uctuations in demand Mortensen-Pissarides search and matching theory of equilibrium unemployment New Keynesian view: classical model may be right in the long run but the Keynesian hypothesis still valid because of contracts and staggering wages, menu costs: it takes time for prices to adjust Dynamic stochastic general equilibrium (DSGE) models with nominal and real frictions Development of more powerful mathematical and computing tools being applied to analyse and assess di¤erent versions of policy Growth Theory Ramsey model Harrod-Domar model Solow-Swan Neo-Classical Model (with …xed saving rate) Sources of growth (labour, capital and technology) Analysis of the salanced growth path (steady state) and transitional dynamics of the economy Dynamically e¢ cient savings rate: golden rule Role of human capital in enhancing technology Optimal growth theory (Cass-Koopman) Endogenous growth models (Lucas-Romer) Dynamic computable general equilibrium (DCGE) models for analysis of medium and long term growth and business cycles. Some useful web sites: JSTORE and Econlit database of journal articles http://www.eea-esem.com/eea-esem/2014/prog/list_sessions.asp http://editorialexpress.com/conference/MMF2014/program/MMF2014.html https://www.aeaweb.org/aea/2015conference/program/preliminary.php http://www.webmeets.com/RES/2013/prog/list_sessions.asp
10
http://www.hull.ac.uk/php/ecskrb/Confer/research.html http://www.economicsnetwork.ac.uk/ http://www.aeaweb.org/rfe/ http://www.ssc.upenn.edu/~schorf/research.htm http://www.webmeets.com/RES/2013/prog/ http://editorialexpress.com/conference/GAMES2012/program/GAMES2012.html http://www.eea-esem.com/EEA-ESEM/2012/prog/list_sessions.asp https://editorialexpress.com/cgi-bin/conference/listconfs.cgi
Key macro time series (leading lagging and coincident indicators) Above theories need to be tested by data. Macro data has coincident indicators (move together with the real GDP): GDP and GDP components; leading indicators (moves before the real GDP): inventories, capacity utilisation, stock prices, real money balances; and ; lagging indicators: unemployment rate, in‡ation. Consult ESDS International, Datastream, Navidata and the central banks (http://www.bis.org/cbanks.htm) to construct such data.
1.1
Background: Seven Classical Macro Models
Classical economists believed in the e¢ ciency of the free market mechanism, invisible hand of Adams Smith. Believing in Say’s laws that states "supply creates its own demand" they assumed that markets are perfectly competitive and free adjustments in relative prices guarantee full employment in the economy (Hicks (1937)). Government should create economic and social infrastructure in which the market institutions thrive. Money is super-neutral, it has no real impact but only prices will increase if the government tries to raise the aggregate demand. Keynes criticised the classical assumption of full-employment and ‡exibility of prices and o¤ered demand determined model of an economy. Further research in macroeconomics particularly by the Real Business Cycle (RBC) school reinstated classical theory as relevant and consistent with facts after mid 1970s. Recent developments in the rational expectation, modelling of dynamics in the new Keynesian models have emphasised on both real and nominal rigidities to reinstate validity of Keynesian models. This and next two sections are going to review models underlying these four approaches to macroeconomics. 1.1.1
A simple version of the classical macroeconomic model
Output Y = F (N )
(1)
Labour demand: N = N(
11
W ) P
(2)
Labour Supply L = N(
W ) P
(3)
Full employment L=N
(4)
M = mP Y
(5)
S = S(i)
(6)
I = I(i)
(7)
S=I
(8)
Neutrality of money
Perfectly competitive capital market Saving
Investment
Capital market equilibrium
Capital accumulation process Kt = (1
) Kt
1
+ It
0
d (N ) or 2) Nt+1 < Nt if b < d (N ) 3) Nt+1 = Nt if b = d (N ) Explain transitional diagram in (Nt+1 ; Nt ) space. Criticism of Malthus: too rigid in technology; does not see prospects of better technology of production, health care and birth controls; contribution of human capital in production. However, larger population can be burden if the economy cannot educate and provide health care to its population. 1.1.3
Two period model of consumption and saving
How is the interest rate determined in the classical model? Two period two consumer model gives a good example. M ax
U (C1i ; C2i ) = ln C1i +
Subject to 14
ln C2i
i = A; B
(19)
First period budget constraint: C1i + bi = ! i1
(20)
C2i = bi (1 + r) + ! i2
(21)
Second period budget constraint:
here C1i and C2i are consumption in period 1 and 2 by household i = A; B. ! i1 and ! i2 are endowments in period 1 and 2 of household i = A, B; r is the real interest rate and is the discount factor. From (21) C2i ! i2 1+r 1+r substituting (22) in (20) gives the intertemporal budget constraint bi =
! i2 C2i = ! i1 + 1+r 1+r Lagrangian for constrained optimisation is C1i +
Li = ln C1i +
ln C2i +
! i1 +
! i2 1+r
(22)
(23)
C1i
C2i 1+r
(24)
First order conditions for optimisation: 1 @Li = i i @C1 C1 @Li = i @C2i C2
=0
1+r
(25)
=0
(26)
! i2 C2i @Li = ! i1 + C1i =0 (27) @ 1+r 1+r Now dividing (25) by (26) gives the marginal rate of substitution (MRS1;2 ) between current and future consumption : M U1 Ci = 2i = (1 + r) =) C2i = M U2 C1
(1 + r) C1i
(28)
This is the e¢ ciency condition in consumption; todays consumption is worth more than tomorrows consumption. This is re‡ected in the relative price today of one unit consumption tomorrow, (1 + r) ; pp12 = 1+r 1 = (1 + r) . Budget is balanced for each agent in inter-temporal sense (present value of expenditure equals present value of income). From (27) C2i ! i2 (1+r)C i C1i + 1+r = ! i1 + 1+r Putting (28) in budgent constraint (27) it gives C1i + 1+r 1 = (1 + ) C1i = ! i1 +
! i2 1+r
The demand for consumption in period 1 is 15
C1i =
1 (1 + )
! i1 +
! i2 1+r
(29)
Similarly the demand for consumption in period 2 is obtained by putting (29) in (28) C2i =
(1 + r) C1i =
(1 + r) (1 + )
! i1 +
! i2 1+r
(30)
Consumers are taking the interest rate as given while calculating their optimal demand as shown in above equations. These demands need to be equal to supply for an intertemporal general equilibrium to hold. For simplicity supply of commodities given by endowments of consumers in B a pure exchange economy like this. Here ! A 1 and ! 1 are endowments of each consumers A and B B in period 1 and ! A and ! in period 2. A consumer which has more asset tomorrow borrows 2 2 to smooth consumption today and one who has more today than tomorrow will lend in process of inter-temporal optimisation. This result comes from the market clearing condition in each period: B C1A + C1B = ! A 1 + !1
(31)
B C2A + C2B = ! A 2 + !2
(32)
By the Walras law if one of these two markets clear, another one will automatically clear. Thus for the market clearing interest rate, put (29) and (30) in (31) as:
C1A + C1B
=
1 (1 + )
!A 1 +
!A 2 1+r
+
1 (1 + )
!B 1 +
!B 2 1+r
B = !A 1 + !1
(34)
1 !A !B 2 2 B B !A + ! + + = !A 1 1 + !1 (1 + ) 1 1+r 1+r 1 A B !A + !B 2 = (1 + ) ! 1 + ! 1 1+r 2 1+r =
(33)
B 1 !A 2 + !2 ; A !1 + !B 1
B !A 1 + !1 =
r=
B 1 !A 2 + !2 A !1 + !B 1
(35) B !A 1 + !1
(36)
1
(37)
As can be seen the gross interest rate (1 + r) is determined in terms of preference ( ) and endowment B A B parameters, ! A 1 and ! 1 and ! 2 and ! 2 . The Lagrange multiplier ( ) is value of income in terms of utils =
1 = C1i
1 1 (1+ )
!A 1 +
!A 2 1+r
=
1 1 (1+ )
!B 1 +
!B 2 1+r
(38)
Proof of the Walras Law By the Walras law when one market clears other market automatically clears. This can be proven by equivalence by putting (29) and (30) in (32)
16
C2A + C2B
=
(1 + r) (1 + )
!A 1 +
!A 2 1+r
(1 + r) (1 + )
+
!B 1 +
!B 2 1+r
(39)
B = !A 2 + !2
(40)
(1 + r) A !B !A 2 B !1 + !B = !A + 2 1 + 2 + !2 (1 + ) 1+r 1+r (1 + ) !A + !B 2 (1 + r) 2 1 (1 + ) (1 + r) (1 + r) =
B !A 1 + !1 =
1
(41)
1 !A + !B 2 (1 + r) 2
(42)
B A B !A 2 + !2 = !1 + !1
B B 1 !A 1 !A 2 + !2 2 + !2 ; r= A B A !1 + !1 !1 + !B 1
(43) 1
(44)
QED
Endowments
Table 3: Summary of two period general equilibrium model Individual A Individual B A A B !1 ; !2 !B 1 ; !2 h i
Equilibrium interest rate Life time income
r=
!A 1 +
Consumption in period 1 Consumption in period 2 Saving/borrowing period 1 Saving/borrowing period 2 Life time utility Shadow price
1
!A 2
B !A 2 +! 2 B !A +! 1 1
1
!B 1 +
1+r
!A 1 A 2 (1+ ) ! 1 + 1+r !A (1+r) 2 !A 1 + 1+r (1+ ) S1A = ! A C1A 1 S2A = ! A C2A 2 A A A U (C1 ; C2 ) = ln C1 + ln C2A 1 = C1i = A 1 A + !2 1 ! 1 1+r (1+ )
1 (1+ ) (1+r) (1+ )
!B 2 1+r
!B 2 1+r !B 2 !B 1 + 1+r
!B 1 +
S1 = ! 1 C1 S2 = ! 2 C2 U (C1B ; C2B ) = ln C1B + 1 = !B 1 (1+ )
ln C2B
2 !B 1 + 1+r
Summary of results of the two period model Q2. Extend two period two individual model to a three period economy which is inhibited by the low, middle and high income households. Again inter temporal optimisation by each involves maximising utility subject to its life time budget constraint. M ax
U (C1i ; C2i ; C3i ) = ln C1i +
i 2
ln C2i +
i 3
ln C3i
i = A; B; C
subject to budget constraints while young, adult and old as following:
17
(45)
C1i + bi1 = w1i
(46)
C2i + bi2 = bi1 (1 + r) + w2i
(47)
C3i = bi2 (1 + r) + w3i
(48)
whereC1i ; C2i ; C3i are consumptions for periods 1, 2 and 3 for type i agent and i2 and i3 are subjective discount factors for period 2 and 3 consumptions with their values between 0 and 1. Endowment of agent i for time t is given by wti with endowments for agent A, B and C for periods 1, 2 and 3 are w1A ; w1A ; w1A ; w1B ; w1B ; w1B ; w1C ; w1C ; w1C . Again each household is allowed to borrow and lend at the interest rate r. Markets clear for each good for each period: C1A + C1B + C1C = w1A + w1B + w1C
(49)
C2A + C2B + C2C = w2A + w2B + w2C
(50)
C3A + C3B + C3C = w3A + w3B + w3C
(51)
What is the interest rates and equilibrium allocations in for short, medium and long terms in this economy? State how to extend this model to ten households. An exercise on Ricardian equivalence 1. Consider a two period economy with the preferences of households given by U (C1 ; C2 ) = lnC1 +
ln C2
(52)
endowments for period 1 and 2 are given by fw1 ; w2 g and the public policy is fG1 ; G2 ; T1 ; T2 ; Bg. (a) What are the consumption in periods 1 and 2 if r = 0:01. = 0:95; fw1 ; w2 g = f100; 150g ; fG1 ; G2 g = f20; 30g ; fT1 ; T2 g = f20; ?g : If the budget need to be balanced intertemporally, what should be the tax in period 2 when tax is cut in the …rst period, fT1 ; T2 g = f10; ?g?
(b) Prove the Ricardian Equivalence. Comment what this implies to the expansionary …scal policy observed around the world in the current recession. Is this plausible?
Answer (a) Prove that debt-…nancing is a burden on future generation (show that T2 > T1 when D1 = G1 T1 > 0. L = lnC1 + C1 =
1 1+
(w1
ln C2 +
T1 ) +
C1 +
w2 T2 1+r
C2 1+r
; C2 = 18
(w1
T1 )
(1 + r) 1+
(w1
w2 T2 1+r T1 ) +
(53) w2 T2 1+r
(54)
w2 G2 150 30 Here intertemporal endowment is w1 + 1+r = 100+ 1:01 = 248:52 and G1 + 1+r = 20+ 1:01 = 49:7. Assume budget balance in each period
C1 =
1 1 + 0:95
(100
150 30 1 + 0:01
20) +
; C2 =
0:95 (1 + 0:01) 1 + 0:95
(100
20) +
150 30 1 + 0:01
(55) if T1 = 0 T2 should be very high to meet the goverment expenses. Borrowing will be 20 in the frist period and zero in the second period. T2 = 20 (1:01) + 30 = 50:2: T2 G2 = T1 + 1+r 1+r If G1 rises and T1 falls then either G2 should fall or T2 should rise or both. G1 +
1.1.4
Pure exchange model
Q2. Imagine a world dominated by three large corporations each of which supply three di¤erent products, W1 , W2 and W3 . These corporations are owned by three representative households, indexed by i = A, B and C; their share in company supplies are given by W1i , W2i and W3i . Demands for these products by each household are represented by X1i , X2i and X3i . Each household i maximises its own welfare subject to its own budget constraint. Relative price of a commodity adjusts until its demand equals its supply and thus is consistent with the household optimisation. Households prefer each three goods equally. Preferences and constraints for household type i are given by M ax
U (X1i ; X2i ; X3i ) = X1i X2i X3i
i = A; B
(56)
Subject to the budget constraint: I i = P1 W1i + P2 W2i + P3 W3i = P1 X1i + P2 X2i + P3 X3i
(57)
Markets clear (demand equals supply): X X X X X X X1i = W1i ; X2i = W2i ; X3i = W3i
(58)
Welfare maximising demand functions for given preferences and budget constraints (derive them using Lagrangian constrained optimisation): X1i =
Ii Ii Ii ; X2i = ; X3i = 3P1 3P2 3P3
(59)
Demand-supply equilibrium condition for each market is: 3 3 3 3 3 X X X X X3 X X3 Ii X1i = = W1i ; X2i = W2i ; X3i = W3i 3P 1 i=1 i=1 i=1 i=1 i=1 i=1 i=1
(60)
In the …xed supply and distribution situation as above, endowments W1i ,W2i ,W3i for each agent i is taken as given by ownership agreements. Relative prices can be obtained by solving above three equations. It also determines the income of each consumer-producer household, I i .
19
1 I A + I B + I C = W1A + W1B + W1C 3P1 A
B
C
I +I +I 1 = P1 = 3 W1A + W1B + W1C
3
3 P
(61)
Ii
i=1 3 P
i=1
(62)
W1i
When the price of good 1 is considered as a numeraire: i.e. P1 = 1 then the relative prices of good 2 and 3 can be determined using above conditions 3 3 3 3 X X X X i i i I = 3 W1 = 3P2 W2 = 3P3 W3i i=1
i=1
3 P
P1 = i=1 3 P P2
i=1
i=1
3 P
W2i
(63)
i=1
3 P
W3i
W3i P1 P2 i=1 i=1 ; ; = 3 = 3 P i P3 P i P3 W1i W1 W2 i=1
P1 = 1; P2 =
3 P
i=1
3 P
W1i
i=1 3 P
(64)
W1i
i=1 3 P
; P3 =
W2i
i=1
(65)
W3i
i=1
Now it is easy to evaluate income and demand accurately for each household i:
i
I =
P1 W1i
+
P2 W2i
+
P3 W3i
=
W1i
+
3 P
i=1 3 P
i=1
W1i W2i
+
W2i
3 P
i=1 3 P
i=1
W1i W3i
(66)
W3i
Demand for each household for each of three goods is evaluated as:
X1i =
X2i =
0
1B i Ii = B W + 3P1 3@ 1
1 Ii = 3P2 3
1 3 P
W1i
i=1 3 P
W2i
i=1
0
3 P
W1i i=1 W2i 3 P W2i i=1
B i BW1 + @
20
3 P
+
W1i i=1 W2i 3 P W2i i=1
1
3 P
W1i C i=1 W3i C A 3 P i W3 i=1 +
3 P
i=1 3 P
i=1
W1i W3i
(67) 1
C W3i C A
(68)
X3i =
Ii 1 = 3P3 3
1 3 P
W1i
i=1 3 P
W3i
i=1
0
3 P
3 P
W1i
W1i
1
C B i i=1 BW1 + W2i + i=1 W3i C A @ 3 3 P i P i W2 W3 i=1
(69)
i=1
It is possible now to evaluate the welfare of each household: U (X1i ; X2i ; X3i ) = X1i X2i X3i
U (X1i ; X2i ; X3i )
= X1i X2i X3i =
1 3
1 3 P
W1i
i=1 3 P
W2i
i=1
1 3
1 3 P
W1i
i=1 3 P
W3i
i=1
Parameterisation and solution following table:
0
0
i = A; B; C
3 P
(70)
3 P
W1i
W1i
1
C 1B BW1i + i=1 W2i + i=1 W3i C A @ 3 3 P i P i 3 W2 W3 i=1
3 P
W1i
i=1
3 P
W1i
1
(72)
1
(73)
B i i=1 C BW1 + W2i + i=1 W3i C A @ 3 3 P i P i W2 W3 0
i=1
i=1
3 P
3 P
W1i
W1i
B i i=1 C BW1 + W2i + i=1 W3i C @ A 3 3 P i P i W2 W3 i=1
(71)
i=1
The ownership composition of households were given as in the
Table 4: Endowment Structure of Households W1 W2 W3 A 20 70 60 B 30 50 100 C 50 80 140 Total 100 200 300 Find the equilibrium prices and allocations and utility for each household. With these endowments and the share parameters the relative prices that equate demand and supply in each market from the solution of the model are as given in the following table. Decimals matter. Following observations can be made from above solutions of the model: 1) Given that households prefer each good equally goods with larger amount of supplies have lower price. Relative price of good 3 is 0.33 compared to 0.5 for good 2 and 1 for good one. This 21
Table 5: Market Price and Optimal Allocations Market Goods 1 2 3 Price 1 0.5 0.3333 Supply 100 200 300 Household Demand 1 2 3 A 25.0 50.0 75.0 B 29.444 58.889 88.333 C 45.556 91.111 136.667 Total 100 200 300 Table 6: Income and utilities A B C Income 75 88.333 136.667 Utility 93750 153165.6 567251 price structure would change with di¤erences in preferences of households and the endowments of goods in the economy. 2) Income and expenditure of households is balanced in the equilibrium. 3)Welfare of households under market based allocations depends not only on their endowments and preferences but also that of others in the economy. Economic agents are interdependent, choices of one household a¤ects possibilities of choices by others. 4) How would these prices change if there is a 20 percent tax on the richest household and 60 percent and 40 percent of the collected revenue are distributed to bottom and middle income households. Decimals matter. Who gains and who loses from the tax reform?
22
Table 7: Allocations after tax Household Demand 1 2 A 30.4667 60.9333 B 33.0889 66.1778 C 36.4444 72.8889 Total 100 200
Income Utility 1.1.5
and transfer 3 91.400 99.2667 109.3333 300
Table 8: Income and utilities A B C 91.4 99.267 109.333 169678.2097 217369.0975 290432.5266
Ricardian Trade Model for Comparative Advantage
There are two countries indexed by j, producing two goods, manufacturing and services. Each of them have an option to be self reliant or to trade on the basis of comparative advantage. The exchange rate is determined by the relative prices of two commodities in the global market. Preferences in country j are expressed by its utility function in consumption of good 1 and 2 , C1j and C2j respectively: j
max
U j = C1j
C2j
1
j
(74)
Income of country j is obtained from the wage income in sector 1 and sector 2 plus the transfers to country j I j = w1j Lj1 + w2j Lj2 + T Rj
(75)
where Lj1 and Lj2 are labour employed in sector 1 and sector 2 w1j and w2j are corresponding wages respectively and T Rj is the transfer income. Technology constraints in sector 1 in country j X1j = aj1 :Lj1
(76)
where aj1 is the productivity of labour in sector 1 in country j. Technology constraints in sector 2 in country j X2j = aj2 :Lj2
(77)
aj2
is the productivity of labour in sector 2 in country j. where Resource constraint in country j de…ned by the labour endowment as: Lj = Lj1 + Lj2 Production possibility frontier of country j now can be de…ned as
23
(78)
Table 9: Percentage gains and loses from Tax-Transfer System Compared to No Tax and Transfer Base Case A B C Income 17.9% 11.01% -25.0% Utility 44.7% 29.5% -95.3%
Lj =
1 aj1
:X1j +
1
:X2j
aj2
(79)
Given above preferences the demand for good 1 in country j is j
:I j P1
C1j =
(80)
the demand for good 2 therefore is: j
1
C2j =
:I j
(81)
P2
Theoretically two trade arrangements are possible in this model. First one is an autarky equilibrium in which each country is separate and isolated from another. It produces just for its own consumption and no trade take place between these two countries. Such autarky solution is close to the production arrangement when countries were adopting ISI trade strategy. Proposition 1 Autarky solution is Pareto dominated by trade equilibrium for reasonable parameters of preferences and technology. This is proven below by analytical and numerical solutions. A Lagrangian function is used to express how each country j maximises welfare subject to its production possibility frontier constraint under the autarky equilibrium as: " # 1 1 (1 j j) $j = X1;j X2;j + Lj X1;j X2;j (82) aj1 aj2 First order conditions with respect to X1j and X2j and @$j = @X1;j
j
j X1;j
@$j = (1 @X2;j @$j = Lj @
1
(1
X2;j
j)
aj1
( j j ) X1;j X2;j
1 aj1
X1;j
(1
24
=0
j)
1 aj2
aj2
(83)
=0
(84)
X2;j = 0
(1 ) X2;j j ( j) j j )X1;j X2;j
j j X1;j
From the …rst two …rst order conditions
as:
(85)
1
=
j
(1
j)
X2;j X1;j
=
aj2 aj1
X2;j =
(1
j)
aj2
X1;j (86) aj1 is found now putting this condition in the production possibility frontier j
optimal value of X1;j constraint.
1 1 1 (1 X1;j + j X2;j = j X1;j + j j a1 a2 a1 a2
aj2
j)
1
aj1
j
X1;j =
1 aj1
X1;j 1 +
(1
j)
j j a1 Lj
X1;j =
= Lj
(87)
j
(88)
Similarly the optimal value of X2;j is found by (1
j)
aj2
(1
j)
aj2
j j (89) j a1 Lj = (1 j ) a2 Lj a1 aj1 j For each of j country amount produced depends on productivity and preferences parameters and the endowment of its labour input. The autarky welfare level is:
X2;j =
j
U j = (X1;j )
j
X1;j = j
(X2;j )
1
j
=
j
j j a1 Lj
(1
j j ) a2 Lj
(1
j)
(90)
Thus the level of welfare in country j is determined in terms of its preferences for consumption of good 1 and 2 as re‡ected by j and its own production technology as re‡ected in aj1 and aj2 . Numerical version of this model is applied to China and the US taking the population as rough indicator of its resource in production. US has 365 million population and China has 1200 million population. US is more productive in producing services goods X2 whereas China has more advantage in producing manufacturing goods X1 . Preferences are similar but technologies are di¤erent. These parameters are set out in Table 1. Table 10: Parameters of the Autarky Model a1 a2 L US China
0.6 0.6
2 5
5 2
365 1200
Under the autarky equilibrium these two economies are completely isolated and produce only for domestic consumption. The optimal production and consumption and employment of labour for both sectors, prices of commodities and labour, and utility for the representative household are as given in Table 2. In per capita terms citizens of the US and China have welfare of 1.46 and 1.76 respectively. Table 11: Parameters of the Autarky Model X1 X2 L1 L2 U p2 US China
438 3600
730 960
219 720
146 480
537.3 2121.7
1.67 0.27
Each country produces both goods in no trade equilibrium which as explained here is very ine¢ cient. Welfare can be improved by making these countries trade. 25
Analytical Solutions for Trade Equilibrium A representative household in each country maximises its welfare subject to its budget constraint. Demand for goods are derived by standard constrained optimisation on supply side for each country j . Under trade equilibrium it is optimal for each country to specialise in goods in which it has comparative advantage. The optimisation problem and the …rst order conditions for constrained optimisation are given as follows: (1
j)
$j = X1;jj X2;j
+ [Ij
P1 X1;j
P2 X2;j ]
(91)
First order conditions: @$j = @X1;j
j
j X1;j
@$j = (1 @X2;j
j
(1
1
(1
X2;j
P1 X1;j
(1
( j ) X1;j X2;j
X2;j =
=
j)
(1
j) j
j
(1 j)
X1;j =
P1 P2 X1;j j Ij
P2 = 0
P2 X2;j = 0
j (1
P1 = 0
j)
j)
X2;j j
P1 X1;j + P2 X2;j = P1 X1;j + P2
j)
( j j ) X1;j X2;j
@$j = Ij @ j X1;j
1
X2;j P1 = P2 j ) X1;j
P1 X1;j P2
(92) (93) (94)
(95)
(96)
= Ij
; X2;j =
(1
j ) Ij
P1 P2 Global market clearing conditions for goods 1 and 2 are
(97)
N X
X1;j = X1
(98)
N X
X2;j = X2
(99)
j
j
Prices adjust until this equilibrium condition holds. Under complete specialisation, country 1 US specialises in services X2 and produces 1825 units of it. China specialises in manufacturing X1 goods and produced 6000 units of it. It is easy to determine China’s income if we choose good 1 as numeraire setting P1 = 1. I c = P1 X1 = 1
6000 = 6000
(100)
Relative price of good 2, P2 need to be determined to …nd the level of income in the US. This can be done using the global market clearing condition c c :I :I u + = 0:6 (1825 P1 P1
u
26
P2 ) + 0:6 (6000) = 6000
(101)
6000 3600 = 2:192 1095 Now it is easy to determine the income of the US as: P2 =
I u = P2 X2 = 365
5
P2 = 1825
(102)
P2 = 1825
2:192 = 4000:4
(103)
Since income level for both China and the US are determined, it is now easy to determine the level of demand in both countries: X1;u =
X2;u =
(1
u Iu = 0:6 (4000:4) = 2400:2; X1;ch = P1
u ) Iu
P2
=
(1 0:4 (4000:4) = 730; X2;ch = 2:192
ch Ich
= 0:6 (6000) = 3600
P1 ch ) Ich
P2
=
0:4 (6000) = 1094:9 2:192
(104)
(105)
Solutions of both autarky and trade equilibria are given in Table 3 and 4. Given the preferences and technology speci…cations, with complete specialisation both countries gain from trade. Comparative static analysis of trade can be done changing the preference or technology parameters. Table 12: Comparing Specialisation and Autarky Regimes Production Autarky Trade US China
Consumption Autarky Trade
X1
X2
X1
X2
C1
C2
C1
C2
438 3600
730 960
0 6000
1825 0
438 3600
730 960
2400.2 3600
730 1094.9
Table 13: Comparing Employment and Welfere under Specialisation and Autarky Employment Autarky Trade
US China
Uitlity Autarky Trade
L1
L2
L1
L2
U
U
219 720
146 480
0 1200
365 0
537.7 2121.7
1490.9 2236.3
Gains from trade may be distributed di¤erently across countries (Bhattarai and Whalley (2006)). Further there are opportunities for bargaining on the share of those gains particularly from dynamic strategic considerations and the basic elements required for such dynamic model is provided in the next section. 1.1.6
Intertemporal balance in budgets of households, government and …rms
Classical model depends on economic disciplines by not only households but by governments, …rms and economy as a whole; it is subject to No-Ponzi conditions for each agent (that means not default and no bankrupcy in the entire model horizon).
27
Household accumulates debt whenever more debt f(Bt servicing (rBt 1 ) is above current saving (Yt Ct ). Bt Bt
1
=
Bt Bt
1
= Yt
Bt
Ct + rBt
1)
> 0g if the amount for debt
1
(106)
Yt + Ct Ct Yt Bt = + 1+r 1+r 1+r
(107)
Ct+1 Yt+1 Bt+1 Yt+1 + Ct+1 = + 1+r 1+r 1+r
(108)
By successive iteration forward Bt =
Bt+1 Bt+2
Bt+1 =
(109)
Bt+2 Ct+2 Yt+2 Ct+1 Yt+1 + + 2 2 1+r (1 + r) (1 + r)
(110)
Ct+1 Yt+1 Bt+n Ct+2 Yt+2 + :::: + + n 2 1+r (1 + r) (1 + r)
(111)
Bt = Bt =
Yt+2 + Ct+2 Ct+2 Yt+2 Bt+2 = + 1+r 1+r 1+r
For the budget balance over the life time 1 X Ct+2 t=1 (1
+ r)
i
= B0 (1 + r) +
1 X Yt+2 t=1 (1
i
+ r)
; )
Bt+n Lim =0 t ! 1 (1 + r)n
(112)
The life time budget should balance, though the household is free to borrow and lend in the …nancial markets. The present value of expenditure should equal the present value of income (endowments). When productive …rms are included this life time budget set is slightly modi…ed 1 P t+1 and includes value of the …rm V = which is derived from the Tobin’s q. (1+r)i t=1
1 X Ct+2 t=1 (1
i
+ r)
= B0 (1 + r) +
1 X Yt+2 t=1 (1
+ r)
i
+V;
Bt+n Lim =0 t ! 1 (1 + r)n
(113)
Similar logic applies for the governments debt dynamics: Dt Dt Dt =
1
=
Dt Dt
1
= Tt
1
Tt + Gt Gt Tt Dt = + 1+r 1+r 1+r
Gt+1 Tt+1 Dt+1 + ; 1+r 1+r
Dt+1 =
Gt+2 Tt+2 Dt+2 + 1+r 1+r
(114) (115) (116)
Gt+1 Tt+1 Gt+2 Tt+2 Dt+2 + + 2 2 1+r (1 + r) (1 + r)
(117)
Gt+1 Tt+1 Gt+2 Tt+2 Dt+n + + :: + n 2 1+r (1 + r) (1 + r)
(118)
Dt = Dt =
Gt + rDt
28
1 X Gt+2 t=1 (1
i
+ r)
= D0 (1 + r) +
1 X Tt+2 t=1 (1
i
+ r)
;
Dt+n Lim =0 t ! 1 (1 + r)n
(119)
Tobin’s q and investment For …rms investment decisions are guided by inter temporal optimisation. It depends on the ratio of market value to the cost of capital assets (Tobin’s q): 1
I1 = K 1 No investment occurs if q
(q
1) ;
I1 = 0 if q
1
(120)
1. Here qt represents excess return on investment:
Lt (It ; Kt ; qt ) =
1 X
t
t=0 (1
t
+ r)
1 X
qt t [Kt+1 t=0 (1 + r)
(1
) Kt
It ]
(121)
In multisectoral and multi-household model the inter-temporal balance conditions usually are explained as following: Households: prevent value of expenditure = present value of income N T X X
h Pi;t 1 + thci Ci;t =
t=0 i=1
T X
rt (1
tk ) Kth + Rth + wh Lh
(122)
t=0
Firms: Present value of revenue = present value of cost " # T T H X X X h h Pi;t Yi;t = rt (1 tk ) Ki;t + wt Li;t t=0
t=0
Government: present value of public spending = present value of revenue ! H T T X X X Rth RVt + Gt = G= t=1
(123)
h=i
t=1
(124)
h=1
where RVt is the total tax revenue from direct and indirect taxes: RVt =
T X N h X X h Pi;t thci Ci;t + rt tk Kth + wh Lh t=0 i=1
(125)
h=1
Economy: present value of exports = present value of imports T X N X
P Ei;t Ei;t
t=0 i=1
T X N X = P Mi;t Mi;t
(126)
t=0 i=1
For any period: current account de…cit (surplus) = capital in‡ow (out‡ow) N X P Ei;t Ei;t i=1
N X
P Mi;t Mi;t =
F
(127)
i=1
Exchange rate appreciation (depreciations) should follow trade surplus (de…cit) but not all countries follow this rule. 29
1.1.7
Ramsey growth model
In Ramsey (1928), a benevolent social planner or a representative household optimises the lifetime utility from consumption in each period and his saving equals investment in equilibrium. Investment generates additional capital stock and enhances the productive capacity of the economy. The basic Ramsey model can be expressed in …ve functions expressing the utility of a representative household, production of a …rm, the process of capital accumulation, conditions for market clearing and the initial state of the economy: The solutions for optimal consumption from this in…nite horizon problem can be obtained by substituting the consumption term from the market clearing condition in the utility function and using the standard …rst order conditions for utility maximisation and by analysing optimal conditions for any two periods in terms of control and state variables that apply to all other periods in the model as illustrated below. max
Uo =
Ct
1 X
t
ln (Ct )
(128)
t=0
Subject to production technology:
Yt = At Kt ; 0
0
(281)
"
(282)
Elasticity of labour demand to the real wage is thus: Wi =P @Li = @ (Wi =P ) Li
Y nA
"
(1 Y nA
)A mp "
"
( (1
)
)A mp
" 1 Wi P " " Wi P
Wi =P =
"
(283)
Thus higher marp up by …rms results in lower demand for labour. Hence lower employment and output. The expansionary monetary policy can still have any positive impacts when prices or nominal wages are sticky. See: Blanchard O. and J. Galí (2013) Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment American Economic Journal: Macroeconomics 2 (April 2010): 1-30 Smet F. and R. Wouters (2003) An estimated dynamic stochastic general equilibrium model of the Euro Area, Journal of European Economic Association, Sept, 1(5):1123-1175. See: website of Dynare programs a number of applications of DSGE models http://www.douglaslaxton.org/dynare.html. Gri¤oli TM (2007) Dynare v4 - User Guide: An introduction to the solution & estimation of DSGE models. Collard F and M Julliard (2009) Stochastic simulations with DYNARE: A practical guide. Wickens M. (2012) How Useful Are Dsge Macroeconomic Models For Forecasting? CEPR Discussion Paper No. 9049.
Programming Exercises 1) Practice Example0.m, EX0_Hand.m from the Herold Uhlig’s toolkit for macroeconomic analysis. http://www2.wiwi.hu-berlin.de/institute/wpol/html/toolkit.htm 2) Practice some dynare programs. http://www.douglaslaxton.org/dynare.html 3) Write some GAMS and MPSGE programs to compute dynamic models. http://www.gams.com/ and http://www.mpsge.org/mainpage/mpsge.htm
52
See how applied general equilibrium models are constructed using the input-output table. Particularly study static and dynamic multisectoral models for UK, India, China, Germany, France and Hull. Exercise 2 1. Consider the Keynesian model with the production function as following Y = F (K; N )
Fk > 0; FN > 0; Fkk < 0; FN N < 0:
(284)
Consumption C = c Y d ; Y d = (1 Labour demand
)Y
(285)
W = FN (N; K) P
(286)
W = W0 + W (N )
(287)
Labour supply
W (N ) =
Z
0 for N 5 N
(288) +for N > N
money market equilibrium conditions: M = M (Y; r) P
My > 0; Mr < 0
(289)
Equilibrium condition Y =C +I +G+X
IM
(290)
derive the income tax multiplier for this model and determine its sign. derive the income tax multiplier for this model when the money demand depends upon the disposable income and determine its sign. Linearise the model for comparative static analysis and determine the employment and output impacts of changes in the government spending, tax rates the …xed nominal wage rate. 2. Multiplier accelerator model of Samuelson (1939) applies the second order di¤erence equation for analysis of the business cycle. 2 Solve the complex root case of this model ( 2 (1 + ) < 4 ): Yt = Ct + It + Gt Ct = Yt It =
(Ct
(292)
1
Ct
(291)
1)
(293)
[Hint: use De Moivre and pythagorian theorems.] Comment on applicability of this model to analyse macroeconomic event in the current context. 3. What is the mark up if demand of a …rm is given by: 53
p = 130
5q
(294)
and its cost function is: c = 10q
(295)
How much does this …rm charge and how much is the mark up? monopolistic competition perfect competition
p 70 10
q 12 24
c 120 240
m 60 0
720 0
What causes entry barrier and price rigidity here? How should a regulator react? Q1. Consider and contrast classical and Keynesian macro models expressed in terms of equations as given below. Classical model Output (Y ) Y = F (N )
(296)
Labour demand (N ) : N = N(
W ) P
(297)
Labour Supply (L) : W ) P Labour market equilibrium condition as a function of real wage rate ( W P ): L = L(
W W ) = N( ) P P Neutrality of money (M ) to price level (P ) with given velocity of circulation (m) : L(
(298)
(299)
M = mP Y
(300)
S = S(i)
(301)
I = I(i)
(302)
S=I
(303)
Savings (S)
Investment (I)
Capital market equilibrium
Capital (K) accumulation process Kt = (1
) Kt
1
+ It 54
0
0; Fkk < 0; FN N < 0; FkN > 0:
(305)
Labour demand (real wage function of marginal productivity of labour): W = FN (N; K) P
(306)
Consumption: C = c Y d ; Y d = (1
)Y
(307)
Investment: I = I(r)
(308)
Nominal wage(W ) and labour supply (N ): W = W0 + W (N ) W (N ) =
Z
(309)
0 for N 5 N
(310) >0 for N > N
where N is the labour supply at the full employment. Money market equilibrium conditions with supply of real balances M equal to money demand P M (Y; r): M = M (Y; r) My > 0; Mr < 0 (311) P Net exports as a di¤erence between exports (X) and imports (IM ): NX = X
IM
(312)
Goods market equilibrium condition: Y =C +I +G+X
IM
(313)
1. Determine the level of employment, output and price level in the classical model. 2. Determine the tax and government spending multipliers in the Keynesian model. 3. Assess the impacts of changes in government spending and taxes on the output, consumption and price level in the Keynesian model using comparative static analysis. 4. Assess strengths and weakness of the classical and Keynesian models based on above analysis. [Hints: Linearise the model for comparative static analysis and determine the corresponding multipliers.]
55
1.6
Micro-foundation to the Keynesian Multiplier: Mankiw (1988)
Mankiw (1988) tried to rescue the Keynesian multiplier analysis against critics who disbelieved in them due to lack of micro-foundation in the Keynesian model. He provides utility maximising set up for households and labour markets on the supply side providing a simple Walrasian model for comparative static multiplier analysis. The structure of this model is as follows: max u =
log C + (1
) log L
subject to (with L as a numeraire and L as time endowment): PC = L PC + L = L +
T.
L +
T
With the Cobb-Douglas preference; the demand for consumption is: PC =
L+
T
Government gets revenue from the lump sum taxes (T) and spends it in purchasing public goods and payings public employees T =G+W Aggregate expenditure (Y) is sum of private and public spending L+
Y = PC + G =
T +G
Output in the economy (Q) is given by aggregate demand divided by the price level. Y P There are N number of …rms each producing q output and the total cost is sum of …xed and marginal costs as: Q=
T C(q) = F + cq Pro…t margin of a …rm shows how much the market prices above the …rm’s cost of production: p
=
c p
This implies p = 1 c ; therefor Q = 1 c Y: Pro…t of …rms in the economy equal = PQ
= =
c 1 c 1
Q
NF
NF
1 c
Y
cQ
cQ =
c 1
NF = Y
56
Q NF
NF
Labour market clearing: LS = L
(1
) L+
T = L
(1
)[
T]
(1
)[
Now the labour demand should equal to this labour supply: LD
=
N F + cQ + W = (Y
=
L+
T +G
) + (T + (T
G) G) = L
T]
In aggregate the labour demand equals labour supply. Now the multiplier analysis follows: L+ T + G as above Given = Y N F and Y = P C + G = Y = @Y @G
=
1 1
L+
T +G= @Y @T
and
=
1
L+ Y
NF
T + G; Y =
L
NF 1
T +G
This implies:
@Y 1 @Y + = @G @T 1
1
=
1 1
The degree of market power (or imperfect competition) as measured by is very crucial in this multiplier analysis. If there is no market power ( = 0) this multiplier stops at the initial iteration. If ( = 1) the multiplier is 1. When the competition is in between (0 < < 1) then the net multiplier is 11 : Welfare analysis: Take the budget constraint P C + L = L + T . substitue the demand for consumption assuming P =1 in P C = L+ T ; This become L+ T +L = L+ T . This means L+ T = LS + T. L+ T = (Y ) + (T G) + T = (Y G) = 1 c Q G This should mean [ T ] = (1 c ) Q G L = cQ (1 (1 )G) (1 )L @[
T] @G
=
(1 ) (1 )
This means increase is government spending reduces welfare of households by (1 1
)
(1 ) (1 ) :
[note this
derivation is as printed in Mankiw (1988)]. Main point of the analysis is that marginal propensity to consume and share in consumption in the utility function linked to the Keynesian multiplier in a similar way. This provides micro-foundation to the Keynesian multiplier analysis. Mankiw G N (1988) Imperfect Competition And The Keynesian Cross, Economics Letters 26 (1988) 7-13 Two period model of Mankiw and Weinzierl (2011) more comprehensive in analysing impacts of …scal and monetary polcies in stabilisation.
57
1.7
Keynesian Stochastic Macroeconomic Model and Policies
"The General Theory of Employment is a useful book; but it is neither the beginning nor the end of Dynamic Economics." J. R. HICKS (1937) "No rule is likely to remain optimal for long" Mervyn King (2004); "Monetary stability means stable prices and con…dence in the currency." MPC (2014). 1.7.1
Introduction
UK economy growing at around 2.2 percent annually since 1967 suddenly entered into the deepest recession in the last quarter of 2008, resulting in a …ve percent decline in GDP in 2009. Labour government brought a heavy …scal stimulus package to …ght recession in the last quarter of 2008 …nanced by borrowing £ 175 billion (13% GDP) in the budget of 2009. The Bank of England brought £ 200 billion package (£ 375 billion now) for quantitative easing (QE). The coalition government formed after the general election of May 2010 continued this stimulus slightly toning down the de…cit to 11 percent of GDP. These measures were very consistent to the concept of cyclical …ne tuning of the economy and macroeconomic stabilisation role of …scal policy as proposed in Keynes (1936) and Hicks (1937). Process of recovery has been very slow. With a high liquidation rates of companies, the unemployment rate had increased up to 8.1 percent; rates of saving and investment have fallen. Flow of credits to private sector dwindled. It took long time to restore con…dence in the British …nancial and business services sector, which is almost one third of the GDP (32 percent). Pound Sterling, that depreciated by almost 25 percent since January 2008 took time to gain strength. Despite great moderations in macroeconomic volatilities after the independence of the Bank of England the general level of prices rose well above the stipulated 2 percent target mainly due hike in prices of fuel, food and commodities and imported products. Real wages fell and were below the pre-crisis level in 2014 causing deteriorating living standards of the majority of people. When will the UK economy be out of slow growth and high unemployment situation is a question bothering all concerned. The ongoing process of globalisation has further added volatility and constraints on the trade of goods and services. How should these challenges of …scal, monetary and trade policies be analysed and solved using a stochastic Keynesian model and wisdom in tradition of Hicks-Stone–Meade-MirrleesPissarides in this situation? This paper aims to provide some empirical evidence based analysis of this issue. 1.7.2
Stylized Facts and Macroeconomic Policies in the UK
This section aims to provide a basic idea on stylized facts and trends in the UK economy. These show how the …scal, monetary and trade policies interact to the underlying structural features of the economy and what sort of policy options are available to the policy makers to …nd solutions to macroeconomic problems. This sets a nice background of four distinct empirical macro modelling exercises in the coming sections. 1.7.3
Macroeconomic Trends
Quarterly GDP was £ 382 billion in the 3rd quarter of 2013. Among its components, the consumption, public expenditure, exports have been growing faster than investment as presented in Fig.1. This is one of the cause of lower growth rate of the UK economy (Fig. 2).
58
F ig u re 1 : G D P a n d its c o m p o n e nts in U K
F ig u re 2 : G row th ra te o f G D P in U K
Fluctuations in aggregate demand impacts on unemployment and in‡ation. When economy is depressed unemployment rises (Fig. 3). In‡ation has strong seasonal as well as cyclical components (Fig.4). Relationship between unemployment rate and in‡ation, Phillips curve, has changed over time (see Figures 27 and 28). PPI in‡ation is slightly more volatile than the CPI in‡ation.
F ig u re 3 : U n e m p loy m e nt ra te in U K
F i g u r e 4 : I n ‡a t i o n o f C P I a n d P P I
Fiscal policy aims to stabilise the economy and smooth the economic growth by manipulating the size and components of revenue, spending and de…cit. In general the sizes of revenue and spending have grown with the economy (Fig. 5). Government’s e¤orts to …ne tune the economy is clear from the ‡uctuations in the amount borrowed over time (Fig. 6).
59
F ig u re 5 : G ove rn m e nt re ve nu e a n d sp e n d in g
F ig u re 6 : C e ntra l G ove rn m e nt N e t B o rrow in g : £ m C P N S A
Ratio of outstanding public debt to the GDP rises as government borrows more from the central bank or the private sector to …nance its de…cit as shown in Fig. 7. It is a matter of concern as it may reduce the capability of government to …ne-tune,redistribute or reallocate resources ultimately making the economy less competitive and ine¢ cient in coming years.
F ig u re 7 : R a tio o f d e b t to G D P in U K
The Bank of England uses monetary policy to regulate the economy more e¤ectively by actively changing the baseline interest rate according to how the aggregate demand and supply situations are away from the steady state capacity level of the economy. Generally accommodative monetary policy means lower interest rates during the …scal austerity and higher rates during the …scal expansions. This is clear from the path of the interest rates in Fig. 8. By changing the discount factor between the current and the future periods, the interest rate impacts on the accumulation and composition of the …nancial assets and stock of money in the economy (Fig. 9).
60
F ig u re 8 : T h re e m o nth s tre a su ry b ills ra te in U K
F ig u re 9 : M 4 a n d G D P in U K (M illio n £ )
Interest policy plays discernible impacts not only in the ‡ow of domestic credits but also in the ‡ow of international assets mainly through its impacts on the exchange rates. It is clear from the trends of exchange rate of Sterling pounds with respect to the Euro and the US dollars as given in Figures 10 and 11. These two rates do not seem to move in tandem as the o¤setting changes in exchange rates (Fig. 12) also re‡ects the movements in the domestic prices of these economies (Fig. 13).
Figure 10: Exchange rate Pound Sterling to Euro
61
Figure 11: Exchange rate Pound Sterling to US dollars
F ig u re 1 2 : E x ch a n g e ra te s o f S te rlin g to E u ro a n d U S D o lla rs
Figure 13: Domestic and foreign price indices
Changes in domestic demands due to such changes in the interest and exchange rates impact on the volume of exports and imports and resulting imbalances in the current account, which normally are between 2 to 3 percents in the UK (Figure 12).
F ig u re 1 2 : Va lu e o f im p o rts a n d e x p o rts in U K
1.7.4
Fiscal Challenges
Challenges of the …scal policy in the UK are clear from the ratios of revenue, spending, de…cit and debt in Table 1. Public debts and de…cits are becoming more acute than what Prest (1968) or Pain, Weale and Young (1997) observed earlier. These problems add dilemmas that are much more serious than any political business cycle models justify for it (Price (1997)). Cutting public spending under the austerity reduces aggregate demand severely but the collection of revenue cannot increase unless GDP growth rates are up. Full con…dence of consumers and producers to generate 62
adequate demand is key for it (Hicks 1990). Excessive de…cit …nancing has raised the debt/GDP ratio. Alarmed by this the government has put forward a de…cit reduction plan in place so that the UK does not become as insolvent as Greece, Ireland, Portugal and Spain in recent years (OBR). A long run view like this is essential not only because the direct and indirect sources of revenue have already been stretched to the limit of public tolerance (Tables 2) but also for the fact that the ‡exibility on spending side is limited as UK is committed to maintain generous social security system, in provision of universal health care, good standards in education and other public services (Table 3). UK remains one of the high tax-spend economy in the global economy already making …rms here less competitive to their global counterparts, a great deviation from the Ramsey-Mirrlees optimal tax rules (Ramsey (1927), Mirrlees (1971), Mirrlees et al. (2010)). Table 19: Ratios of Revenue, Speding and De…cit to GDP 2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
R evenue/G D P
3 7 .2
3 6 .0
3 7 .0
3 7 .2
3 7 .4
3 7 .0
3 7 .0
3 7 .4
3 7 .8
3 8 .0
3 8 .1
S p e n d in g / G D P
4 4 .1
4 7 .0
4 6 .2
4 4 .8
4 4 .7
4 3 .5
4 2 .5
4 1 .6
4 0 .2
3 8 .8
3 7 .8
D e …c t/ G D P
-6 .9
-1 1 .0
-9 .2
-7 .6
-7 .3
-6 .5
-5 .5
-4 .2
-2 .4
-0 .8
0 .3
D ebt/G D P
5 2 .8
6 0 .5
6 7 .5
7 0 .1
7 0 .1
7 3 .6
7 7 .4
7 9 .7
7 9 .6
7 8 .1
7 5 .7
S o u rce: O B R , M a rch 2 0 1 4
Excessive de…cit is dangerous but the raising tax rates during the period of weak economic growth is an unpleasant and infeasible task. Reducing budget de…cit from currently 11 percent of GDP to a surplus of 0.3 percent by 2018-19 (Table 1), as proposed by the O¢ ce of the Budget Responsibility (OBR) is not an easy task. The optimal taxes and growth concept of Ramsey (1927, 1928) or Mirrlees (1971) need further attention2 . Table 20: Source of Revenue in UK (St. Pounds, Billion) Sources of R evenue
2009
2010
2011
2012
2013
2014
In co m e ta x
1 4 6 (0 .2 7 )
1 5 0 (0 .2 7 )
1 5 8 (0 .2 7 )
1 5 0 (0 .2 7 )
1 5 5 (0 .2 7 )
1 6 7 (0 .2 6 )
N a tio n a l in su ra n c e
9 7 (0 .1 8 )
9 9 (0 .1 8 )
1 0 1 (0 .1 8 )
9 9 (0 .1 7 )
1 0 7 (0 .1 7 )
1 1 0 (0 .1 7 )
C o rp o ra tio n ta x
4 2 (0 .0 8 )
4 3 (0 .0 8 )
4 8 (0 .0 8 )
4 3 (0 .0 8 )
3 9 (0 .0 8 )
4 1 (0 .0 6 )
E x c ise ta x
4 6 (0 .0 9 )
4 6 (0 .0 8 )
4 6 (0 .0 8 )
4 6 (0 .0 8 )
4 7 (0 .0 8 )
4 7 (0 .0 7 )
VA T
7 8 (0 .1 4 )
8 1 (0 .1 5 )
1 0 0 (0 .1 5 )
8 1 (0 .1 7 )
1 0 3 (0 .1 7 )
1 1 1 (0 .1 7 )
B u sin e ss ta x
2 5 (0 .0 5 )
2 5 (0 .0 5 )
2 5 (0 .0 5 )
2 5 (0 .0 4 )
2 7 (0 .0 4 )
2 7 (0 .0 4 )
C o u n c il ta x
2 6 (0 .0 5 )
2 5 (0 .0 5 )
2 6 (0 .0 5 )
2 5 (0 .0 4 )
2 7 (0 .0 4 )
2 7 (0 .0 4 )
O ther
8 1 (0 .1 5 )
7 9 (0 .1 4 )
8 5 (0 .1 4 )
7 9 (0 .1 4 )
1 0 7 (0 .1 7 )
1 1 8 (0 .1 8 )
541
548
589
548
548
648
To ta l
S o u r c e : B u d g e t R e p o r t ( M a r c h 2 0 1 4 ) H M T r e a s u r y, h t t p : / / w w w . h m - t r e a s u r y. g o v ; ; % i n ( ) .
2 Taxes can be optimal instrument for transferring resources from one generation to the next (Samuelson (1954), Modigliani (1961), Diamond (1965), Atkinson and Stern (1974), Feldstein (1985, 1982), Auerbach and Kotliko¤ (1987) ) or for correcting ine¢ ciencies due to negative or positive externalities (Buchanan (1958)). Public debt rightly used could help the government to maintain the intertemporal balance in resources available to it (Meade (1956), Barro(1974), Besley (2001), Ni Shawn and Wang (1995), Basu (1996), Burnside, Eichenbaum and Fisher (2004), Brauninger (2005), Fisher and Ryan (2010)).
63
Table 21: Elements of Public Expenditure in UK (St.Pounds, Billion)) E x p e n d itu re Ite m s
2009
2010
2011
2012
2013
2014
S o c ia l p ro te c tio n
1 9 0 (0 .2 8 )
1 9 4 (0 .2 8 )
2 0 0 (0 .2 8 )
1 9 4 (0 .2 8 )
2 2 0 (0 .3 1 )
2 2 2 (0 .3 0 )
2 9 (0 .0 4 )
3 2 (0 .0 4 )
3 2 (0 .0 5 )
3 2 (0 .0 4 )
3 1 (0 .0 4 )
3 1 (0 .0 4 )
1 1 9 (0 .1 8 )
1 2 2 (0 .1 8 )
1 2 6 (0 .1 8 )
1 2 2 (0 .1 8 )
1 3 7 (0 .1 9 )
1 4 0 (0 .1 9 )
E d u c a tio n
8 8 (0 .1 3 )
8 9 (0 .1 3 )
8 9 (0 .1 3 )
8 9 (0 .1 3 )
9 7 (0 .1 3 )
9 8 (0 .1 3 )
Tra n sp o rt
2 3 (0 .0 3 )
2 2 (0 .0 3 )
2 3 (0 .0 3 )
2 2 (0 .0 3 )
2 1 (0 .0 3 )
2 3 (0 .0 3 )
D efen ce
3 8 (0 .0 5 )
4 0 (0 .0 6 )
4 0 (0 .0 6 )
4 0 (0 .0 6 )
4 0 (0 .0 6 )
3 8 (0 .0 5 )
I n d u s t r y, A g r , E m p l o y m e n t
2 1 (0 .0 3 )
2 0 (0 .0 3 )
2 0 (0 .0 3 )
2 0 (0 .0 3 )
1 9 (0 .0 2 )
1 7 (0 .0 2 )
H o u sin g a n d E nv iro n m e nt
3 0 (0 .0 4 )
2 7 (0 .0 4 )
2 4 (0 .0 3 )
2 7 (0 .0 4 )
2 3 (0 .0 3 )
2 5 (0 .0 3 )
P u b lic o rd e r a n d s a fe ty
3 6 (0 .0 5 )
3 5 (0 .0 4 )
3 3 (0 .0 5 )
3 3 (0 .0 5 )
3 3 (0 .0 4 )
3 2 (0 .0 4 )
D e b t a n d inte re st
4 3 (0 .0 6 )
4 4 (0 .1 1 )
5 0 (0 .0 7 )
5 0 (0 .0 7 )
5 0 (0 .0 7 )
5 3 (0 .0 7 )
O thers
7 4 (0 .1 1 )
7 4 (0 .1 0 )
7 3 (0 .1 0 )
4 3 (0 .1 0 )
5 3 (0 .0 7 )
5 3 (0 .0 7 )
704
696
711
696
720
732
P e rso n a l so c ia l se rv ic e s H e a lth
To ta l
S o u r c e : O B R M a r c h 2 0 1 4 ; H M T r e a s u r y, h t t p : / / w w w . h m - t r e a s u r y. g o v . ; % i n ( ) .
The fact that both taxes and spending policies have wide ranging reallocative as well as redistributive implications as the taxes create distortions in consumption, production and trade is well recognised in the literature (Meade et al. 1971 and Mirrlees et al. (2010), IFS (2014)). There is a perception that over the years these public policies have led to the disparity in income not only among rich and poor households but also across and within the regions of England, Scotland, Wales and Northern Ireland (Sawyer 2003). These regions are facing a situation of two speed economy as the households in the lower income deciles are lagging far behind those in the upper income groups and the regional and sectoral disparities exist in allocation of public resources. Ricardian equivalence of public debt as proved in Barro (1974, 1989) does not seem to apply in credit constrained and regionally imbalanced economies like this (Spencer 1998, Besley 2001). 1.7.5
Monetary policy
Price stability is the most important role of the monetary policy (Friedman (1968), Goodhart (1989), Bernanke and Mishkin (1997)). Interest rates are raised during the booms and reduced during the recessions as guided by an interest rate rule. The BOE’s has …xed the bank rate at 0.5 percent, lowest bank rate in the Bank’s history (Fig. 3) and remained at that rate for more than four years now. However, it is less clear whether 0.5 percent rate was optimal in the recession as the impacts of such move are unclear for three reasons. First, the …rst, second or tertiary rounds of transmission mechanisms of monetary policy as stated in Monetary Policy Committee (1999) becomes less clear when interest rates are very low in this way. When in‡ation rose above 4 percent, higher than the 2 percent target (Fig. 4), the In‡ation Report of the Bank of England (BOE) attributed it to rising energy, food and commodity prices and increase in VAT. Secondly these are severely a¤ecting the rate of saving and the UK economy is in a situation of liquidity trap. Thirdly when there are uncertainties in the demand side of the economy, the lower cost of capital is not able to restore con…dence among investors at the desirable level despite more than three years of historically low interest rate and Fund for Lending Schemes being in operation (BOE 2012). Uncertainties of future not only deter businesses to invest but policy makers are not sure about the future state of the
64
economy. In the Ely lecture the Governor Mervyn King (2004) had stated that "we cannot fully describe an optimal monetary arrangements because we do not know all possible states of the world and hence the policy rule to which we would like to commit". Households do not …nd remunerative enough to save and lenders are reluctant to advance at a lower interest rate. This has squeezed the credit market. The unexpectedly sluggish growth realised in last three years suggests that under the "constrained discretion" the actual shocks hitting the supply and demand sides of the economy are much bigger than policy measures taken to raise the ‡ows of credit aiming to mitigate the consequences of such crises3 . Given "sustained period of tight credit conditions" the MPC predicts that the level of output is less likely to "surpass pre-crisis level till 2014" (BOE 2012). 1.7.6
Trade Issues
Trade is essential for growth and stability. No country is self su¢ cient in producing goods and services that it needs. Ideas of free and liberal trade originated from the UK as the Ricardian theory of comparative advantage is still one of the most important concepts guiding trade practices around the world. External demand can mitigate consequences of reduction in the internal demand. Opening the economy also makes it easier to transmit problems originated elsewhere in the world. The process of globalisation has added further challenges to the UK economy as in the majority of other advanced economies (Haskel and Slaughter (2001), Monacelli and Perotti (2010)). Trade balance deteriorates when exportable goods and services become more expensive than imports. The trade creation and trade diversion e¤ects increased due to regional blocks such as European Union and NAFTA, ASEAN and Mercosur impact on comparative advantage of British …rms. The emergence of global multinational corporations after the revolutions in transport and communications and development of emerging markets including China and India, Russia, Brazil and South Africa in recent years have put further pressures in the trade policies of the UK (Miller and Spencer (1977)). Firms in these new countries can supply goods and services at lower costs than by home …rms. Modelling frameworks and arguments found in Mundell (1962), Dornbusch (1976), Krugman (1979), Taylor (1995) and Gali and Monacelli (2005) are far from complete to handle complications arising from a need to comply to global environmental agreements such as the Kyoto protocol, WTO regulations on fair trade or migration of skilled and unskilled workers, tari¤ and non-tari¤ barriers in movement of goods and services. 1.7.7
Modelling of the UK economy
The tradition of economic modelling for policy analysis started with the pioneering ideas of classical economists including Smith, Ricardo, Malthus, Pigou and Marshall in UK believing that the market system is dynamically stable. They argued for policies that would promote the free enterprise economy under the competitive markets where the ‡exible relative prices of commodities would guarantee full employment equilibrium. Keynesian and New Keynesian economists prefer to stick to the macro-modelling framework that Keynes (1936) had proposed in which rigidities in prices of 3 While the crisis in the monetary general equilibrium contexts analysed in Diamond, Douglas and Dybvig (1983), Rankin (1992), Altig, Carlstrom and Lansing (1995), Ghosal and Miller (2003) Angelopoulou and Gibson (2009) provide useful frameworks to think about the real side causes of …nancial disturbances, the new Keynesian solutions to the problems are provided by Barro and Gordon (1983), Pain, Weale and Young (1997, 2000),Clarida, Gali and Gertler (1999, 2001), Dri¢ ll and Snell (2003), Martin and Milas (2004), Christiano, Eichenbaum and Evans (2005), Rudebusch (2006), Chadha and Nolan (2007), Blinder et al. (2008), Johnson (2009), Tillmann (2009)) or new classical models like King and Plosser (1984), Wickens (1995), Holland and Scott (1998) which assume super-neutrality of money and ignore the modelling of the monetary sector.
65
commodities cause de…ciencies in aggregate demand. Wallis (1989) mentions that macroeconometric models of the UK improved substantially under the auspices of ESRC’s Macroeconomic Modelling Bureau that coordinated research activities across research and policy institutions in the UK including the Bank of England, the HM-Treasury, the LBS, the Liverpool, Edinburgh, Cambridge, Oxford or Exeter. Modelling activities for policy analysis of UK economy became more comprehensive and realistic after modelling innovations following from ability to compute (Church et al. (1997)). For instance Hendry and Doornik (1994) formulated "a linear dynamic system, noting closed, open, complete and incomplete systems for both stationary and integrated l(1) data.. adopting general to simple modelling of the joint data density function . . . ”. In the meanwhile the latest new classical models in works of Kydland and Prescott (1977) or Prescott (1986) or Plosser (1989) resurrected almost all elements of the classical general equilibrium models to explain growth and ‡uctuations simultaneously attributing ‡uctuations in macroeconomic activities to shocks to the preferences and technology of production. For them the collapse of consumer and investor con…dence are root causes of instability and active …scal and monetary policies are required to restore con…dence as in Hicks (1937, 1990). Dynamic Stochastic General Equilibrium (DSGE) and Dynamig Computatble General Equilibrium (DCGE) models have been developed in UK in recent years (Den Haan and Marcet (1990), Holland and Scott (1998) Bhattarai (2007) and Gai, Kapadia, Millard and Perez (2008), Liu and Mumtaz (2011), Bhattarai and Dixon (2014)). Despite that the big slump started in 2008 proved to be a big challenge to both theoreticians and practitioners. Impossibility and undesirability to predict the future state of the economy might have been the main cause of failure of the popular macro models in analysing economic choices available in the context deep contraction (King (2004)). Controversies among di¤erent paradigms (Dixon(1988)) made it further complex. Progress in macro economic theory from the classical to Keynesian to New Keynesian and rational expectation to the real business cycle theories has been quite extra-ordinary and so has been the modelling technology including on the issue of coordination of budgetary and monetary policies (Wilson(1949), Meade (1956), Diamond (1965), Blake and Weale (1998), Turnovsky and Miller (1984), Woodford (2011), Nordhaus (1995)). These analysis underpin the decisions that made the independence of the Bank of England in 1997 producing greater stability by reducing the volatility of in‡ation, unemployment and growth rate as illustrated by trends of volatilities in Figures 13 and 14 as observed by Bean (1998, 2009).
F i g u r e 1 3 : V o l a t i l i t y o f i n ‡a t i o n a n d u n e m p l o y m e n t
66
F ig u re 1 4 : Vo la tility o f g row th ra te
Given above experiences and controversies the main objective here is to apply simple macroeconomic models that are easy enough to understand but generate scenarios that are helpful to analyse ways out of the challenges that the economy is facing today. We formulate, empirically estimate and apply the Keynesian Stochastic Macroeconomic Model (KSMM), Stochastic Phillips curve model, AS-AD with rational expectation model and small open economy macro model in line of theoretical "deconstruction" and "reconstruction" approaches taken by Wren Lewis et al. (1996) in analysing above issues in the UK economy in the next sections4 . 1.7.8
Keynesian Stochastic Macroeconomic Model (KSMM)
Let us consider a version of dynamic Keynesian stochastic macroeconomic model (KSMM) to assess impacts of shocks in the consumer and producer con…dences. It also includes shocks in trade as well as to …scal and monetary policy instruments as anticipated by Meade (1951). The structural features of the stochastic dynamic Keynesian economy are given by following six equations for the consumption (F.589), investment (315), tax revenue (316), imports (317), macro balance (318) and the money market equilibrium (319). Ct =
+
1
It =
0
0
(Yt
Tt
1)
+
2 Xt
+ "C ;
+ Yt
1
+ "I ;
"I
1
1 Rt
Tt = T0 + t1 Yt + t2 Mt + "T ;
"T
"C
N 0; N 0;
M t = m0 + m1 Yt + m2 Rt + m3 Tt + m4 Et + "M Yt = Ct + It + Gt + Xt Rt =
b0 b2
1 b2
MM P
+ t
N 0;
2 C
(314)
2 I
(315)
2 T
(316)
"M
N 0;
2 M
Mt = Ct + Tt + St
b1 Yt + "M P b2
"M P
N 0;
(317) (318)
2 MP
(319)
This interest rate is solution to the money market equilibrium condition given by: MM P
= b0 + b1 Yt
b2 Rt
(320)
t
4 Pain, Weale and Yong (1998) had attributed de…cit problems to increasing commitments of UK government for social securities and transfer programmes rather than to slow growth of revenue. Contributions by Cook, Holly and Turner (2000) on monetary policy, Greensdale, Hall, Henry and Nixon (2000) on natural rate of unemployment, Mellis and Whittaker (2000) on forecasting, Leith and Wren-Lewis (2000) on in‡ation, Blake, Weale and Young (2000) on optimal monetary policy in Holly and Weale (2000) show how monetary policy could be designed taking account of structural changes and unemployment in‡ation trade o¤ existing in the UK economy. Analyses of Church, Mitchel, Sault and Wallis (1997) on the role of technology in the economy, Hendry and Clement (2000) on failures of forecast, Garratt, Lee,Pesaran and Shin (2003) and Bernanke et al. (2005) on structural and VAR models focused on forecasting capability of models. General equilibrium models have been developed to complement above analysis with explicit introduction of the hetorogeniety of …rms and households in the economy for analysis of growth and redistribution the UK (Bhattarai and Whalley (2000) in Holly and Weale (2000) and Bhattarai (2012)).
67
1.7.9
Steady State in the KSMM
Steady state equilibrium in goods and money markets from this IS-LM analysis, is given by (322) and (323) respectively, where mean of idiosyncratic shocks are zero, E ("i ) = 0: Yt =
1 T0
0
+ 1
0
m0 + Gt + Xt + m2 Et 1 + 1 t1 + m1
1
1
1
+
1 t1
+ m1
Rt
(321)
For economy wide equilibrium use the h money market steadyistate condition in the IS curve Yt = b0 1 MM 1 T0 + 0 m0 +Gt +Xt 1 + bb21 Yt to …nd output and the interest rate 1 1 b2 b2 P 1 + 1 t1 +m1 1 + 1 t1 +m1 t at equilibrium as: 0
Yt
=
1
1 T0
0
Rt
=
1
b1 + t + m 1 b2 1 1 1 1
b0 b2
1 b2 0
+ 1
0
MM P 1 T0
+ 1
m0 + Gt + Xt + m2 Et 1 + 1 t1 + m1
+ t 0
(322)
b1 b2
b0 b2
b1 + t + m b 1 2 1 1 1
1 b2
MM P
t
1
1
1
m0 + Gt + Xt + m2 Et 1 + 1 t1 + m1
b0 b2
(323) 1 b2
MM P
t
Exogenous policy variables Gt ; Xt ; MPM and Et along with the behavioral parameters 0 ; 1 T0 ; 0 ; m0 ; t1 ; m1 ; m2 ; b0 ; b1 and b2 determine endogenous variables Yt ; Rt ; Ct ; It ; Tt and Mt (see Peacock and Shaw (1979), McCallum and Nelson (1999) for this type of models). For parameters in Table 4, this model generates the steady state as given in Table 5. Table 22: Parameters Parameters 0 1 Values 600 0.65 Parameters b0 b1 Values 10000 0.15
of the dynamic stochatic Keynesian model T0 m0 m1 0 1 8000 4000 0.1 10000 0.2 b2 M4 X G P 30000000 2157.3 123.50 879.87 1.2
m2 -50 E 1.5
Parameters in a Keynesian macroeconomic simulation model like this should be chosen so that they generate the steady states of output, consumption, investment, revenue and imports. Values of these endogenous variables should be close enough to current levels in the economy.
Variables Values
Table 23: Macro Variables in the steady state C I T M Y R 64072 26639 53278 40111 150928 0.00102805
These steady state values implied in the current model are close to the actual quarterly values of the UK economy. 68
1.7.10
Transitional Dynamics in KSM Model
The next step is to explain how this economy ‡uctuates around that steady state due to exogenous shocks in consumer and investor con…dences or to imports or revenues or to the interest rate. Stochastic assumptions are similar to Den Haan and Marcet (1990), Holland and Scott (1998) and Gai, Kapadia, Millard and Perez (2008), Liu and Mumtaz (2011) but the Keynessian structure here di¤ers from the new Keynesian or the RBC frameworks in those models. Underlying structural parameters are assumed to be stable though it is possible to update them each period using a Bayesian MCMC algorithm as in the fashion of Benati (2008). Schocks to Keynesian models generate as intuitive results as in any other classes of models. First consider impacts of stochastic positive shock to the consumer con…dence. This makes consuers more optimistic exerting expansionary impacts that raises the overall demand in the economy shown in Figure 15. Increase in consumption raises the levels of investment and output and revenue. It also raises the rate of interest via increase in demand for money. C
I
C
0.1
0.01
0.02
0.05
0.005
0.01
0
5
10
15
0
20
5
10
T
15
0
20
I 0.05
5
10
M
15
0
20
0.01
0.02
0.01
0.01
0.005
0.01
0.005
0
0
0
10
15
20
5
10
-10
Y 0.05
4
15
20
5
10
R
x 10
15
0
20
5
10
15
0.05
5
-3
C 0
10
15
20
5
20
15
20
15
20
R
10
15
0
20
5
10
F ig u re 1 6 : Im p u lse s o f a sh o ck to inve sto r c o n …d e n c e
I
x 10
C
-2
-0.02
10
x 10
4
0
F ig u re 1 5 : Im p u lse s o f a sh o ck to c o n su m e r c o n …d e n c e
0
15
2
0
20
5 -10
Y
2 0
10 M
0.02
5
5
T
I
0
0
-0.02
-0.01
-4 -0.04
5
10
15
20
5
T
10
15
-0.04
20
5
M
10
15
20
-0.02
0
0
0.1
0
-0.005
-0.02
0
5
10
15
20
-0.01
5 -10
Y 0
0 -0.5
-0.02
x 10
10
15
-0.04
20
5
R
10
15
20
-0.1
5 -10
Y
-1
10
15
20
15
20
15
20
M
0.1
-0.1
5
T
0
0
-0.05
-2
x 10
10 R
-1.5 -0.04
5
10
15
20
5
10
15
-0.1
20
F ig u re 1 7 : Im p u lse s o f a sh o ck to ta x re ve nu e
5
10
15
20
-4
5
10
F ig u re 1 8 : Im p u lse s o f a sh o ck to im p o rts
Macro impacts of shocks to investment, shown in 16, are of similar magnitute on economic 69
activities as those from shocks in consumption despite the size of investment demand being less than one third of the demand for consumption. The investment demand is a lot more volatile than any other components of aggregate demand as more con…dent investors drive the rate of capital accumulation and growth process in the economy causing more expansionary impacts than a similar increase in con…dence of consumers. Bad news lowers the level of investment more than similar negative shock in consumption (Blanchard and Kiyotaki, 1987). The long run equilibrium point where the marginal e¢ ciency of capital equals the user cost of capital is disturbed by these positive or negative shocks in investment. Taxes are designed to achieve a number of social and economic objectives. As mentioned above government is bound to change taxes to meet expenditure plans that need to be optimal for voters (Meade et al. (1978), Mirrlees et al. (2010)). While the ‡exibility of government to raise or lower the level of taxes either to …nance more public consumption or in order to redistribute income are political economic questions (Price 1997) these decisions can themselves be cause of business cycles as they in‡uence the optimal conditions of consumers and producers and search and matching processes in labour markets (Pissarides,1985). While the net e¤ects of …scal policy in consumption and investment are obtained by deducting the contractionary impact of taxes from the positive multiplier e¤ects of public spending, shocks to policies can alter magnitudes of these multipliers. Thus changes in policy regimes create shocks that disturb and distort the system (Woodford (2011)). Negative …scal shocks depress output, consumption, investment and imports and the interest rate as shown in Figure 17 and these results are consistent to stories of Fisher and Whitley (2000), Fisher and Ryan (2010) or Feldstein (1982). External demand can create expansionary impacts in the UK but an increase in the level of imports causes leakage of resources from the economy and hence reduces the multiplier impacts from net exports as is evident from the response of consumption, investment, output tax and interest rate to a unit shock in imports as shown in Figure 18. Increase in the interest rate raises the cost of investment and consumption and thus contributes to a reduction in demand as shown by responses of macro variables to interest rate shocks in Figure 19. -3
0
C
x 10
I 0
-2
-0.005
-4
5 -3
0
10
15
20
-0.01
x 10
0
-2 -4
5 -3
T
10
15
20
15
20
15
20
M
x 10
-1
5
10
15
20
-2
5
Y
10 R
0
0.2
-0.005
0
-0.01
-0.2
5
10
15
20
5
10
F ig u re 1 9 : Im p u lse s o f a sh o ck s to inte re st ra te (M P )
Let us move to estimation of the KSMM model taking dataset on the exogenous policy variables Gt ; Xt ; MPM ; Et and endogenous variables Yt ; Rt ; Ct ; It ; Tt ; and Mt . The behavioral parameters of the model 0 ; 1 T0 ; 0 ; m0 ; t1 ; m1 ; m2 ; b0 ; b1 ; and b2 can be retrieved from the reduced form estimates when this system is identi…ed by order (K k > m 1) and rank ( (A) > (M 1) (M 1)) 70
conditions. As each equation of above the system is identi…ed (see appendix for details of identi…cation) we take the quarterly time series data from 1967:1 to 2011:1 available from the ONS to estimate the model empirically. Details on estimation and application of this model for analysis of …scal, monetary and exchange rate policies is provided in the next section. 1.7.11
Estimation and application of the KSMM Model
The reduced form parameters of the KSMM model estimated using the full or limited information likelihood method in Table 45 . As these empirically estimated structural parameters of the model are signi…cant and have theoretically expected sings, these are used to assess the impacts of changes in government spending, money supply, exchange rates, exports. The multiplier e¤ects of …scal and monetary policies in the economy are computed with these parameters which along with hypothetical predicted paths of exogenous policy variables Gt ; Xt ; MPM ; Et forecast the path of endogenous variables Yt ; Rt ; Ct ; It ; Tt ; Mt in the model. Table 24: Macro simultaneous equation model of UK (1967:1-2011:1) Consumption Investment Imports Tax t-prob t-prob t-prob t-prob G 1.87 0.00 0.684 0.00 0.310 0.00 1.210 0.00 E 1221.6 0.39 665.0 0.27 2827.0 0.00 -952.5 0.53 M4 -0.017 0.00 -0.011 0.00 -0.001 0.29 -0.013 0.00 X 1.171 0.00 0.280 0.00 0.900 0.00 0.637 0.00 Const -4262.4 0.17 -1057.4 0.426 -7713 0.00 2745.7 0.39 F(20,554) = 247.032 [0.000] **; N =176; R^2(LR) 0.99; R^2(LM) 0.36
Treasury bills rate t-prob 0.0002 0.01 -1.91 0.00 -3.2 6 0.00 -0.0001 0.00 13.76 0.00
Main points emerging from the estimates of the simultaneous equation presented in Table 6 are as follows: 1. The government spending (G) has positive and signi…cant e¤ect in consumption, investment, imports, tax revenue and the interest rate. The sign and the magnitude of multipliers are as one would expect from a Keynesian model. There is very small crowding out e¤ect due to increase in the interest rate following an increase in public spending. 2. Increase in money supply (M4) had negative and signi…cant impacts in consumption, investment, tax revenues and treasury bills rate but did not have signi…cant e¤ect on imports. These must have been due to the in‡ationary impacts of increase in money supply and consequences in QE policies. 3. On the trade front only imports and the interest rates are signi…cantly in‡uenced by the exchange rate (E ) depreciation; its e¤ect in consumption, investment and tax revenue were not statistically signi…cant though with expected signs. Impacts of expansion in exports were similar to that of government spending but smaller in magnitude for consumption, investment, imports and tax revenue. It had small but negative impacts on the interest rates as more export earnings takes o¤ some pressure from the …nancial system. 5 PcGive is used for estimations and forecasting (see Wallis (1989), Hendry (1997), Church et al. (1997) and Holly and Weale (2000) for more extensive analysis of macroeconometric forecasting).
71
Under the current structure of the model, whether the future of the economy is pessimistic or optimistic depends upon the trajectory of …scal, monetary or trade policies. Let us consider three di¤erent policy options for macroeconomic …ne tuning. In the …rst scenario government spending, exports and exchange rates decrease by 1 percent each quarter but the money supply increases by 2 percent. This gives a very pessimistic forecast, all model variables have downward trend as in Figure 21. Second option is to promote export to compensate for decrease in domestic demand. If exports could increase by 1 percent per quarter it slightly modi…es the declining trend as in Figure 22. Thirdly, the forecast of the economy becomes very optimistic when there is inertia in the treasury bills rate. If the monetary policy ties the current interest rate to the previous quarter by one autoregression then consumption, investment, imports and revenue all have positive growth rates (Figure 23). Interest rate rises slowly but steadily. Performance of the model is judged by studying how well the historical simulations for consumption, investment, imports, revenue and treasury bills rate match to past trends. Current model does it well in picking up the trends as well as the turning points of variables (Figure 20). This gives con…dence in using model for forecasting. Histoical Simulation of the UK Economy CONS_HH
Fitted
GFCF
200000
50000
100000
25000
1970 Imports
1980
1990
2000
Fitted
2010 150000
100000
1970 Revenue
Fitted
1980
1990
2000
2010
1990
2000
2010
Fitted
100000 50000
50000 1970
15
Treasury
1980
1990
2000
2010
1990
2000
2010
1970
1980
Fitted
10 5 1970
1980
Figure 20: Hostorical simulation
Figure 21: Pessimistic Forecasts
72
Optimistic Forecasts of UK Economy 275000
Forecasts
CONS_HH
Forecasts
80000
GFCF
70000 250000
60000 50000
225000 2010 140000
2011
Forecasts
2012
2013
2014
2015
2010
Imports
2011
Forecasts
2012
2013
2014
2015
2013
2014
2015
Revenue
160000
130000 120000
140000
110000 2010
2011
Forecasts
2012
2013
2014
2015
2013
2014
2015
2010
2011
2012
Treasury
5
0
2010
2011
Figure 22: Intermediate forecast
2012
Figure 23: Optimistic forecast
The simulation results demonstrate that good coordination between the …scal and monetary policies is essential for smooth functioning of the economy (Blake, Weale (1998)) to avoid noncooperative Nash results rather than cooperative outcome in the policy games between …scal and monetary authorities engaged in the least-square learning process. Model estimated so far implicitly assumes that the policy makers are free to choose …scal, monetary and trade policy measures such as the level of public spending, exports, money supply or the exchange rate in order to achieve desired or optimal values of target variables like consumption, investment, revenue, interest rate or imports. In fact the policy makers are not free to choose but are constrained by the level of GDP, money supply, tax revenue or imports that are acceptable to the general public in the country. As King (2004) states, "no rule is likely to remain optimal for long" applies in this context. It is sensible to re-specify the above simultaneous equation model by endogenising …scal and monetary policy instruments as the function of macro target variables including the levels (or growth rates) of GDP, imports, money supply and revenue. Tinbergenian matching of instrument and policy targets elaborated by Meade (1951, 1956) in the form of targeting nominal GDP or imports to achieve internal or external balance as in Bean (1998, 2009). The simultaneous equation model discussed here is used to estimate policy response parameters, presented in Table 7, necessary to achieve target values of macro variables.
Table 25: Macro simultaneous equation model of UK (1967:1-2011:1)
GDP Imports M4 Revenue Const
Government Expenditure t-prob 0.460 0.00 0.108 0.07 -5.072 0.00 0.517 0.05 -16606.4 0.00
= 1804
In‡ation t-prob -2.253 0.00 5.164 0.006 0.001 0.00 7.284 0.351 1.353 -0.061
= 0:5479
Exports t-prob -0.121 0.00 1.008 0.00 10.054 0.00 -0.018 0.38 18356.0 0.00
= 1455:7
Investment t-prob 1.122 0.00 -0.011 0.53 -10.093 0.00 0.0184 0.00 -18408.6 0.39
= 1464:86
F(20,554) = 247.032 [0.0000] **; N =176; R^2(LR) 0.999502; R^2(LM) 0.364715
73
Interest rate t-prob 9.6 6 0.05 3.9 5 0.31 -0.006 0.00 4.760 0.77 19926 0.00 =1.161
Model …ts to the past series (Fig. 24) and predicts these policy instruments quite well (Fig. 25).
Figure 24: Histoical simulations of policy instruments.
Figure 25: Forecasting of policy instruments.
The de…cit forecasts implied by above parameters is given in Fig. 26.
Figure 26: Forecsting public borrowing 1.7.12
Qualitative analysis
Hicks (1937) had suggested comparative static analyses to measure the impacts of exogenous variables in the employment (N ), price level (P ) and interest rate (r) using three equations showing goods (324), labour (325) and money market(G.653) equilibrium conditions while synthesising the Keynesian model to supply side in the classical system. F (N; K ) = c (1
) F (N; K) + I (r) + G + N X 74
(324)
W = FN (N; K) P
(325)
M = M (F (N; K ) ; r) P Implicit solution of the model requires linearising by the total di¤erentiation as: FN dN + FK dK = c (1
) FN dN + c (1 dW P
) FK dK
(326)
cd F (N; K) + Ir dr + dG + d (N X) (327)
W dP = FN N dN + FN K dK P2
(328)
M dM dP = My FN dN + My FK dK + Mr dr (329) P P2 By further expansion and rearrangement for endogenous variable labour (dN ), price (dP ) and interest rate (dr), this model is succinctly written as: FN dN
c (1
) FN dN
Ir dr = c (1
My FN dN +
) FK dK
cd F (N; K)
M dM dP + Mr dr = 2 P P
W dW dP = P2 P Or this can be written in a matrix notation: FN N dN +
2 4 2
(1
c (1 )) FN My FN FN N
c (1
= 4
) FK dK
0 M P2 W P2
FK dK + dG + d (N X) (330)
My FK dK
(331)
FN K dK
(332)
3 32 Ir dN Mr 5 4 dP 5 dr 0
(333)
3 cd F (N; K) FK dK + dG + d (N X) dM 5 My FK dK P dW FN K dK P
This matrix can be solved for changes in the employment (dN ), price level (dP ) and the interest rate (dr) if the determinant of the coe¢ cients of endogenous variables in the left side (Jacobian matrix) is non-singular; the determinant of this matrix should be non-zero: (1
= = =
c (1 )) FN 0 Ir M My FN M 2 r P W FN N 0 P2 W M My FN 2 Ir + FN N 2 Ir Mr (1 c (1 P P W M Mr 2 [1 c (1 )] FN + FN N 2 Ir P P 75
(334) )) FN
W P2
The …rst term of the determinant (334) is positive since slope of money demand function Mr is negative FN is positive. The second term also is positive since the slope of the investment function Ir is negative, the production function is subject to the diminishing returns, FN N < 0. This means that determinant is non-vanishing and it is possible to …nd a solution for this model. The Cramer’s rule can be applied to …nd out the solution for each endogenous variable.
dN =
1
c (1
) FK dK
2 1 4 dN =
cd F (N; K) FK dK + dG + d (N X) dM My FK dK P dW FN K dK P
dM P
My FK dK
W P 2 Ir
+
dW FN K dK P ) FK dK
0 M P2 W P2 M P 2 Ir
c (1 cd F (N; K) FK dK + dG + d (N X)
Mr PW2
Ir Mr 0 3 5
(335)
(336)
As can be seen the change in the employment (335) depends upon the monetary (My ) and …scal policy variables ( ; G) as well as the structural parameters of the model. Impact on output can be found using the total derivative of the production function, dy = FN dN + FK dK: But the capital stock is constant in the short run, dK = 0. The above value of dN can be used to solve for the change in output, dy.
dy =
dM P
dN Mr PW2
fc (1
My FK dK PW2 Ir + dW FN K dK PM2 Ir P ) FK dK cd F (N; K) FK dK + dG + d (N X)g
(337)
This equation (337) can be used to …nd the output multiplier of change in tax, or money supply or the government expenditure, or the because of the changes in the structural features of the economy. For instance a multiplier e¤ect of the change in the marginal income tax is given by dy = @
cd F (N; K)
Mr
W P2
(338)
Thus increase in the tax rate will reduce the level of income. The size of such reduction depends upon the value of c, Mr and PW2 . Price changes can be computed similarly. Ir Mr 0 (339) Estimates of the parameters for empirical comparative static analysis are made applying the generalised unrestricted model (GUM) estimation routine of Castle, Doornik and Hendry (2011) in the PcGive on macro quarterly time series for 1997:1 to 2012:1 of the UK. This model determines the changes in employment, price level and the interest rate (dN , dP and dr (333)) endogenously in terms of changes in net exports (DN X) and net investment (DInv) as shown in Table 8. Changes in government consumption or change in money supply were insigni…cant and were automatically deleted by the GUM system. dp =
1
(1
c (1 )) FN My FN FN N
c (1
) FK dK
cd F (N; K) FK dK + dG + d (N X) dM My FK dK P dW FN K dK P
76
Table 26: Comparative Static: GUM analysis 1997(2) - 2011(2) Change in employment t-prob DN X 0.0203 2.05 DInv 0.0221 4.49 Const -3.882 -0.195 = 98 F(6,104) = 13.5931 [0.0000]**; T
Change in price level Treasury bills rate t-prob t-prob 0.0002 5.19 -3.129 05 -0.613 8.5 05 4.68 7.670 05 3.02 0.257 3.49 -0.348 -3.39 = 0.363 =0.508 =52; R2 (LR)= 0.686; R2 (LM )=0.263
There are two main criticisms against the analysis above. First by assuming rigidity of nominal wages it overestimates the impact of changes in public spending in output and employment. Secondly it does not provide a good transitional dynamics. Under perfect ‡exibility of wages and prices as one …nds in the classical and new classical system, aggregate demand management policies do not have real impacts in the economy. Growth and employment are only driven by the accumulation of capital, TFP and growth in the labour force. New Keynesian economists equipped with the Phillips curve and rational expectation argue that expansionary monetary policies by raising aggregate demand can have a signi…cant role in reducing unemployment (Dixon (1988), Dixon and Rankin (1994)) because of rigidities. Prices adjust at slower rate than the wage rates, breaching the homogeneity of degree zero in output and input prices required for the classical system, after the launch of an expansionary programme (Wilson (1949), Phillips (1958), Phelps (1968), Taylor (1977), Ball (1999), Ball and Romer (1990), Mankiw (1989) Blanchard and Summers (1986) and Rankin (1992)). Their arguments are tested using a simple stochastic stabilisation model of unemployment rate and in‡ation and growth rates of output and money in UK in the next section. 1.7.13
A Small Model of Unemployment, In‡ation and Growth
The basic mechanism of stabilisation program can be explained by a simple model that involves use of stochastic versions of the Phillips curve, Okun’s law and the growth rate of money supply (gm;t ) with given natural growth rates of output (gy;n ) and natural rate of unemployment (un ). ut
ut
t
1
=
t 1
a (gy;t
=
gy;n ) + bgm;t + "u
b (ut
gm;t = gy;t +
ut t
1)
+ "m
+ "p N 0;
N 0;
N 0; 2 m
2 p
2 u
(340)
(341) (342)
Okun’s law (340) establishes link between unemployment (ut ) and output gap (gy;t gy;n ) : Then the expectation augmented Phillips curve (341) shows a trade-o¤s between in‡ation ( t ) and unemployment rate (ut ) linking the nominal to the real side of the economy. Third equation (342) is an identity, equivalent to the classical quantity theory of money relating growth of money supply (gm;t ) to the growth rates of output (gy;t ) and in‡ation. In‡ation should be lower than the growth rate of money supply when the economy is growing. Despite a signi…cant reduction in the volatility of unemployment rate, in‡ation and the growth rate of output in UK as shown in Figures 13 and 14 after the independence of the Bank of England, events after the …nancial crisis of 2008 is creating
77
doubts in such claims. For instance a closer look at the cross plot between the unemployment rate and in‡ation shows some trade-o¤ in line of the Phillips curve over 1967:1 to 2011:1(Fig.27) but this negative relation has turned to be positive after 1997, as shown in Fig.28. This stabilisation model does not seem to work well when the e¢ ciency of matching of vacancies to jobs and productivity growth are weak as in the current recession. E¢ ciency of job search and matching process that determines the ins and outs of unemployment not only depends on economic activities (Smith (2011)) but also in the way taxes, subsidies and transfers are used on wages, employment or job creating enterprises (Pissarides (1984)).
Figure 27: Phillips’curve for the full sample
1.7.14
Figure 28: Phillips curve after 1997
Solution of the stabilisation model
This small stabilisation policy model is handy in linking four macro variables relating to the stability in the real and nominal sides of the economy. When in‡ation is up to 5 percent, above the 2 percent target the central bank should raise basic interest rate to release pressure o¤ the demand but that is likely to cut in demand and raise the cost of production causing increase in the unemployment rate as households postpone purchasing expensive items and …rms will layo¤ workers due to a fall in the demand for products. In stable scenario given the in‡ation target the central bank should equate the growth rate of money supply to the growth rate of output plus in‡ation. Once the equilibrium is disturbed the transition paths of these variable, shown in Fig.29 and Fig.30, are found by simulation using the realistic values of parameters of the model as given in Table 9.
Table 27: Estimated parameters of the stabilisation model a b un gy;n u1 1 values -0.3 -0.09 0.05 0.022 0.051 0.02 0.08 The stabilisation model is simulated to trace the path of in‡ation during the stabilisation period starting from 5.1 percent in‡ation that was observed in the fourth quarters of 2011. In‡ation is reduced by 0.2 percent each quarter until it reaches it target 2 percent. This lowers demand and raises unemployment rate above its natural rate of …ve percent till the in‡ation target is met as shown in Fig. 29 with implied growth rates of money and output as given in Fig.30. 78
F i g u r e 2 9 : S i m u l a t e d p a t h o f i n ‡a t i o n a n d u n e m p l o y m e n t r a t e
F ig u re 3 0 : S im u la te d p a th o f g row th ra te s o f o u tp u t a n d m o n e y
The transitional path suggested above can be subject to shocks to the Okun, Phillips or money supply equations. These would create impulses to above four variables as shown in Figures 31 to 33. -4
5
-3
u
x 10
3
0
2
-5
1
-10
0
-15
-1
pi
x 10
-3
5
u
x 10
0 -5
2
4
6
8
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
pi 5 -3
15
10
15
20
5 -3
gm
x 10
0.01
15
10
15
20 0
gy
x 10
-0.01 10
10
5
5
0
0
0
-5
-0.01
10
15
20
4
6
8
10 gy
-5
5
2
0.01
5
10
15
20
Figure 31: Impulses of Okun shocks
2
4
6
8
10
Figure 32: Impulses of Phillips’curve schocks
79
-3
1
u
x 10
0 -1
2
4
6
8
-3
2
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
pi
x 10
0 -2
2
4
6
8
10 gy
0.01 0 -0.01
2
4
6
8
10
Figure 33: Impulses of money supply shocks
1.7.15
Supply side and rational expectation
Keynesian economists argue that increase in demand has real e¤ect on output and employment because of rigidity in prices and wages in the short run. Increase in the aggregate demand either by increase in the government spending or by a reduction in the interest rate (increase in money supply) would have permanent impacts on output and employment (Bean (2009), Rudebusch(2006), Greensdale at al. (2000)). The price level would not increase when an economy is below full employment6 . Under the rational expectation, workers are fully informed, nominal wage rate rises according to the expected in‡ation. Workers demand higher wage rate to compensate fully for higher anticipated changes in prices. Thus there is no real impact of an increase in demand even in the short run as it is anticipated by workers. Only unanticipated policy measures can have real impacts as explained above in the short run7 . Higher aggregate demand puts upward pressure in prices and …rms can reduce their markups without altering market prices. Additional workers could be hired to supply additional output without changing prices when there is a pool of unemployed workers (Boinet and Martin (2008), Johnson (2009), Monacelli and Perotti (2010), Nelson (2009), Fisher and Ryan (2010)). Thus an expansionary monetary policy can raise the level of output and employment in the economy in the short run though the economy tends to return to its natural rate in the long run. Despite criticism on the stability of parameters set as above (Lucas critique), it is di¢ cult to 6 In contrast to this, the classical or the new classical proposition remains that the prices and wages are perfectly ‡exible and economy is always in full equilibrium (Kydland and Prescott (1982)). Consequently it is impossible to arti…cially increase real output by increasing demand. Real drivers of the economy are capital accumulation and increase in human capital and increase in work hours and technological progress. Monetary policy is super neutral. Price system that guarantees general equilibrium in goods and factor markets matter for the e¢ cient allocation of resources (Bhattarai and Whalley (1999)) and should be dynamically e¢ cient in terms of growth and redistribution (Bhattarai (2012)). 7 New Keynesian synthesis …nds a more realistic middle path between the Keynesian and real business cycle schools (Arestis et al. (2010), Gali and Monacelli (2005), Kirsanova, Leith and Wren-Lewis (2009)). These features rest on the monopolistic competition and staggering wage contracts (Taylor (1972), Rankin (1992)). Firms with market power under the monopolistically competitive markets are able to absorb demand shocks (Dixon and Rankin (1994), Nickel (1990), Dixon (1988), Blanchard and Kiyotaki (1986)). These issues are further assessed in Angelopoulou and Gibson (2009), Arnold et al. (2011), Gemmell et al. (2011), Beetsma and Giuliodori (2011) in recent years.
80
get an alternative framework of analysis that is as transparent as this one and would provide a benchmark scenario for policy analysis. Rational expectation models developed in Sargent and Wallace (1976) are theoretically very convincing but di¢ cult to implement as correct expectation formation under uncertain economy is a very challenging task. Unanticipated policy changes are likely to have macroeconomic impacts. These issues are better analysed by aggregate demand and aggregate supply models with rational expectation under the new Keynesian framework developed by Lucas (1973) and Mankiw (1989). In fact the another way to study the unemployment in‡ation problem in UK is to consider a popular version of aggregate supply aggregate demand model in line of Lucas (1973), Taylor (1973), Bean (1998), Woodford and Taylor (1999) and Sorensen and Whitta-Jacobsen (2010). It relates output gap to in‡ation instead of the unemployment rate. 1.7.16
Aggregate Demand and Aggregate Supply Model
The AS-AD is our third model to study the impacts of …scal, monetary and trade policies in output and price level in the economy. From the Fisher equation the real interest rate (rt ) is the nominal interest rate (ipt ) adjusted for the risk ( t ) and the expected in‡ation et+1 as: rt = ipt +
t
e t+1
(343)
Aggregate demand (yt ) is subject to the …scal policy shock (gt ) and monetary policy (rt the demand shock (vt ). yt
y=
1
(gt
g)
2
(rt
r) + vt ;
vt v N 0;
2 v
;r = r +
r) and
(344)
Nominal interest rate is set by the monetary authority to close the in‡ation and output gap in a policy rule of the form: ipt = r +
e t+1
+ h(
t
) + b (yt
y)
(345)
The aggregate supply function with the supply shock (st ) is given by: t
=
e t+1
+ (yt
y) + st ; st v N 0;
2 s
(346)
With a backward looking in‡ation expectation as et = t 1 the aggregate demand equation could be derived using the Fisher equation and the interest rate rule in the demand function with rt e e ) + b (yt y) or rt r = t + h( t ) + b (yt y) : The t + t+1 = r + t+1 + h ( t aggregate demand yt y = 1 (gt g) [ + h ( ) + b (y y)] + v 2 t t t t could be written as yt y = 1+2 h2 b ( ) + z . t t yt
y=
(
t)
+ zt ;
=
2h
1+
2b
(347)
Where zt term includes …scal policy shock (gt ), risks ( t ) and random shocks (vt ); zt = 1+ 12 b (gt g) 2 ) + 1+vt 2 b : Aggregate demand is downward slopping; higher rate of in‡ation requires 1+ 2 b ( t central bank to increase the interest rate, that raises the cost of capital, thus causes lower investment and hence lower output. After putting the in‡ation expectation into the supply function, it becomes: t
=
t 1
+ (yt
81
y) + st
(348)
It is upward slopping; larger output requires employers to hire more workers, that lowers the productivity of labour. The cost of production rises resulting in in‡ation. Term st includes trade, exchange rate, technology or other shocks. De…ne deviation from the steady state as bt = t and ybt = yt y when there are no further shocks zt = 0 and st = 0. Then the aggregate demand is bt+1 = 1 ybt+1 :The aggregate supply (by iterating forward and di¤erencing) can be written as bt+1 = bt + ybt+1 =) bt = ybt . There is empirical evidence for such relation in the UK time series (1967: 3 to 2011:1): bt = 0:001096 + 0:6241 ybt (SE) : (0:00193) (0:877)
The estimated b is slightly higher than 0.48 contained in Bean (1998). Equilibrium in terms of the …rst di¤erences of output and in‡ation can be found by equating AD and AS curves: 1
ybt+1 =
1
bt+1 = bt + (
ybt + ybt+1 =) ybt+1 = bt+1 ) =) bt+1 =
1 1+
ybt =) ybt+1 = ybt
1 1+
bt =) bt+1 = bt
(349) (350)
Starting from initial states yb0 and b0 both ybt and bt converge to their stationary state as 1 < 1 < 1. This condition is essential for stabilisation of output and in‡ation. 1+ t
ybt = yb0
t
and bt = b0
for t = 0; 1; 2; :::::
=
(351)
The parameters ; and could be calibrated from the time series to study the impulse responses from demand and supply shocks, zt and st respectively when they are not zero, zt 6= 0 and st 6= 0. Setting demand equals to supply equilibrium condition the stochastic time paths of ybt in (357) and bt in (361) result in autoregressive processes as following: yt
y=
t)
AD :
bt =
ybt =
1
=) ybt +
1 1+
ybt =
bt = bt
1
ybt
(zt
ybt = zt 1
ybt
1
bt = bt
AS : AD = AS
+ zt =) ybt =
(
+ 1
1
ybt ) = zt
1 1+
+
(zt
+ ybt + st = bt 82
zt 1
(zt
+ ybt
(zt
(zt
ybt )
+ ybt + st 1
1
bt + zt
zt
1)
+ (
1
1)
(353) (354)
ybt
1)
st
1
(352)
1+
+ ybt + st
st
st bt + zt ) + st
(355) (356) (357) (358) (359)
bt =
1 1+ bt =
bt
1
bt
+ 1
zt +
1+ +
1 1+
st
zt + st
(360) (361)
Thus solutions of the dynamic aggregate demand and aggregate supply model results in a …rst order autoregressive time path of output ybt and in‡ation bt which are subject to demand and supply shocks, zt and st . This theoretical justi…cation for using AR(1) model is similar to that one would get under the rational expectation models of Sargent and Wallace (1975) , Calvo (1983), Taylor (1987), Dri¢ ll and Schultz (1992). Either the DSGE models of Uhling (1995),Blanchard and Perotti (2002), Smet and Wouters (2003), Nelson (2009), Iacoviello and Neri (2010) or the RBC models of Wickens (1995), Minford and Peel (2002) generate such impulse responses from demand, supply or TFP shocks in the economy. Empirically autoregressive terms are not only signi…cant but also explain 82 percent of the growth rate and 97 percent of in‡ation in the UK (see estimates in Table 10). While the AR(1) coe¢ cients measure persistency, the intercept terms indicate to other regular structural features including …scal, monetary and trade factors.
Table 28: AR(1) model of growth rate and in‡ation in UK
Intercept AR(1) term R2 F DW 2
N
Growth equation Coe¢ cient T-value 0.410 2.93 0.817 18.7 0.67 381( 0.00) 1.97 87.1(0.00) 176:q11967-q12011
In‡ation equation Coe¢ cient T-value 0.172 1.19 0.972 54.7 0.95 2292(0.00) 1.02 102.6(0.00) 176:q11967-q12011
The impulse responses to demand and supply shocks output and in‡ation in a VAR are as shown in Fig. 34.
83
Figure 34: Impulse responses of output and price shocks
1.7.17
Trade Policy Model
Net exports represent the external demand for domestic products, particularly helpful when the other domestic components of aggregate demand as in the previous recession. When growth rate of the UK economy was negative 5 percent at the end of 2009 policy makers thought about creating more external demand to compensate de…ciencies in internal demand. On the face of it this appears to be a plausible and sensible strategy considering the trends of exports and imports, exchange rate, growth rates of money and output, in‡ation and the interest rate in the UK. Three fundamental questions arise in this context: 1) Is there any cause-e¤ect relation between the net exports and the exchange rate? 2) What are the determinants of the exchange rate? 3) Are the economic e¤ects of the exchange rate predictable? The …rst issue has been extensively discussed in the literature since the seminal works of Meade (1951, 1955). Second issue were analysed in Mundell (1962), Flemming (1962), Krugman (1979), Taylor (1995, 2010), Holly and Weale (2000), Clarida, Gali and Gertler (2001), and Gali and Monacelli (2005) with a small open economy or a global economy model of interdependent economies. Thirdly Dornbusch (1976), Taylor (1995) and Taylor (2010) have discussed reasons for the overshooting of exchange rate, lack of PPP relation and unpredictability of spill over e¤ects of it in modern economies. Our empirical …ndings suggests two things. First there is a very thin relation between the trade and exchange rate in recent years. Secondly the export promoting e¤ects of changes in the exchange rates are very unreliable due not only to overshooting of the exchange rate but also because of violations of PPP and UIP fundamentals in the short run. Thus income and employment generating e¤ects of additional external demand are unpredictable. In theory the price of foreign currency relative to the domestic currency relates essentially to the relative prices of goods at home and abroad determined by real factors including preferences of consumers, technology of producers and endowments of factors of production in these economies (Obstfeld and Rogo¤ 1996, Eaton and Kortum 2002). In practice adjustment towards
84
such equilibrium takes longer as shown by empirical …ndings in PPP (Taylor 2010). 1.7.18
Structural factors and the volatility of exchange rate
In theory total output of an economy produced from employing labour and capital can either be consumed (C) domestically or exported (E) as in (363). The level of exports in (364) not only depends on the real exchange rate e P P
with the nominal exchange rate (e), indices of domestic (P )
and foreign P prices but also in the elasticity of exports ( ). Imports in (365) similarly depend on the elasticity of imports ( ), exchange rate (e) that mingles with price indices of domestic (P ) and imported commodities, (Pm ). Any discrepancy between the domestic income P Y and total expenses (P C + ePm M ) is met by external lending or borrowing eB as in (366). A set of structural features underpin the trade and the exchange rate relationship (Johnson 195354). In the classical Ricardian theory, the terms and patterns of trade are based on comparative advantage, expressed in terms of ratio of domestic to foreign prices. In the Mundell-Fleming set up of the Keynesian model such exchange rate (e) can be …xed or ‡exible policy instrument used to determine the volume of net exports (N X = a0 a1 e) and the net ‡ows of capital. Net exports are larger when the home currency depreciates and lower when it appreciates. N X = a0
a1 e; a0 > 0; a1 > 0
(362)
Y = f K; L = C + E E = E0 e
(363)
P P
(364)
C P = K0 e m M P P Y + eB = P C + ePm M =) eB = ePm M
(365) PE
(366)
In an Armington set-up the elasticities of exports ( ) and imports ( ) are crucial parameters that measure the ‡exibility of trading system and indicate the impact of nominal exchange rate (e) on next exports. Putting all these together implicitly the exchange rate is function of trade elasticity and other parameters of the trading system of the economy as: e = f X0 ; C; K0 ; ; ; K; L; Y ; P ; P; B
(367)
Thus the endogenous variables of this trade sub-model C; E; M; P; e depend on the parameters of the model E0 ; K0 ; ; ; K; L; Y ; ; B and Pm but the exchange rate and the prices are the main variables determining the distribution of gains from trade from this model. The rapid space of globalisation has caused swift changes in these parameters, particularly export and import elasticities, and ; which have become larger making UK very vulnerable to the international economy. Depreciation lowers the foreign price of domestic goods P , it raises supply of exports (E), makes foreign goods more expensive and reduces the amount of imports (M ) and raises the production of import substitute goods at home. Depreciation thus can raise both domestic and foreign demand for home products. The Marshall-Lerner condition implies that depreciation is expansionary when the elasticity of exports to the exchange rate is higher than the elasticity of imports. Positive growth rate of exports during the current recession in UK provides support for this theory. 85
If the exchange rate overshoots in‡ation as in Dornbusch (1976) it may cause greater volatility in net exports. It is often di¢ cult to disentangle the impacts of global shocks using the exchange rate instrument as the relation of next exports and exchange rate are unreliable when fundamentals of PPP or UIP do not hold (Taylor 2010). Free monetary policy, ‡oating exchange rate and free capital in‡ow and out‡ow are three pillars that charaterise the exchange rate, trade and balance of payment system in the UK. Change in exchange rate not only re‡ects the underlying changes in trade ‡ows and capital movements but also is an adjustment mechanism of the economy towards rapidly changing system of global trade and payments. Since London is one of the most important …nancial centre of the global economy a steady and stable exchange rate of Sterling Pound to major currencies is in the interest of the UK economy. Available evidence suggests that UK has been quite successful in maintaining stable but with depreciating Pound in recent years (Figures 10 to 12 and 35) tolerating greater volatilities in net exports (Figures 13 and 36). In welfare terms quick adjustments of exchange rates bu¤er consumers and producers from large swings in real variables in order to adjust to the external shocks8 . Mundell (1962) and Gali and Monacelli (2005) open up the basic Keynesian model for trade where net exports (N X) are larger and when the nominal exchange rates (e) of home currency depreciates as in (362). We adopt Dornbusch (1976) and empirical evidence from UK to illustrate this point in this section.
F i g u r e 3 5 : R e d u c e d v o l a t i l i t y o f i n ‡a t i o n a n d e x c h a n g e r a t e
1.7.19
F i g u r e 3 6 : I n c r e a s i n g ‡u c t u a t o n s i n t r a d e ( n e t e x p o r t s )
Monetary model of exchange rate expectation
It is important to understand the dynamic path of in‡ation and exchange rate while assessing the role of external sector in the economy. Under Dornbusch (1976) and Taylor (1987) monetary model of exchange rate with rational expectation swiftly adjusting exchange rate overshoots price level 8 While
the Keynesian trade multipliers can provide a preliminary estimate on the impact of external shocks to the real and BOP conditions in the UK, it is important to consider standard classical comparative advantage arguments of Ricardo and subsequent theories of trade developed in Meade (1951), Miyazawa (1960), Mundell (1962), Dornbusch (1976), Krugman (1979), Wilson (1979) and Taylor (1995) in studying bilateral and multi-lateral relations of trade to get more precise understanding of the impact of external sector in the economy.
86
because of inertia in prices. Under the uncovered interest parity conditions (370) in style of Hoy et al. (2001) the change in the exchange rate equation is obtained with the money demand function (368) the money market equilibrium condition (G.657), interest rate parity (370) and the exchange rate expectation ( e = E e ) as: mD = m
ar + by
p=
(368)
ar + by
(369)
r =r +E e e =
p by m + a a
(370) r
(371)
yD yS ; > 0; the aggregate While in‡ation is positively related to the excess demand p = demand is determined by the real exchange rate (e p) and other demand factors (u) y D = u + v (e
p)
(372)
S
Assuming the steady state supply y = y to be equal to the demand, the in‡ation can be expressed as: p = vp + ave + a (u y) (373) 1.7.20
Solving for in‡ation and exchange rate paths simultaneously
The dynamic system of in‡ation and exchange rates relate to the monetary policy instrument, foreign interest rate and the supply capacity as: ! a (u y) v v p p = + (374) by m 1=a 0 e r e a The explicit time path of price and exchange rate thus is given by: p(t) = C1 exp e(t) = With
p e
!
=
0 0
1
+ v C1 exp v
1t
+C2 exp
1t
+
2
2t
(375)
+p
+ v C2 exp v
2t
+e
(376)
condition, the steady state price level is obtained when e = 0 as p =
1 m by + ar and steady state exchange rate when p = 0 as e = p y) : The constant v (u terms C1 and C2 can be evaluated with initial conditions p0 and e0 and the initial speed p1 and e1 . Qualitatively above results could be presented using a phase diagram in in (e, p) space for p = vp + ave + a (u y) and e = ap + by a m r equations as presented in Figure A1 in the appendix.
87
1.7.21
Exchange rate overshooting under the ‡oating exchange rate system
Analysis of quarterly time series of UK reveals three empirical facts to justify above model. Firstly there is a good evidence of exchange rate overshooting in UK. Sterling dollar exchange rate responds immediately to any shocks in the market (but is less volatile compared to that with Euro in recent years) but the in‡ation is more rigid (less volatile) as shown by conditional volatility of GARCH (1,1) models of the exchange rate and in‡ation in Fig. 37. Secondly the interest rate seems to Granger cause changes in both in‡ation and exchange rates but there is no signi…cant causality from in‡ation to the exchange rate. In fact exchange rate seems to be more persistent as shown by the coe¢ cient of its lagged term in Table 11. Thirdly there is a good empirical support for the long run relationship between in‡ation and the exchange rate; they are cointegrated on the basis of trace test at 3 percent level of signi…cance as shown in Table 13 (at 7.6 percent by the max test). Perhaps this long run should mean to be the time span for the entire business cycles.
Figure 37: Conditional volatility of exchange rate and in‡ation
Table 29: Simultaneous equation model of in‡ation and exchange rate In‡ation Exchange rate Exogenous variables Coe¢ cient tvalue prob Coe¢ cient tvalue prob In‡ation (-1) 0.952 49.4 0.00 -0.0002 -0.176 0.861 Exchange rate (-1) 0.733 2.53 0.01 0.951 45.1 0.00 Constant -1.06 -2.10 0.04 0.086 2.33 0.02
In fact exchange rate seems to be explained by growth of money supply and its lagged term. These empirical facts imply that ‡oating exchange rate system is optimal for the UK as it lowers
88
Table 30: Correlation among residuals of in‡ation and exchange rate equations (standard deviations on diagonal) Correlation among errors In‡ation Exchange rate In‡ation 1.266 0.095 Exchange rate 0.095 0.0921 Table 31: Cointegration between in‡ation and exchange rate rank-order Trace test [prob] max-test [prob] 0 16.69 [0.031]* 13.03 [0.076] 1 3.65 [0.056] 3.65 [0.056] the real side adjustments due to external shocks to the economy. These …ndings are consistent to theoretical analysis of Miller and Weller (1991) that the exchange rates and the impacts of exchange rates in the economy are very unpredictable. Therefore greater reliance should be in creating internal demand to combat the sluggish growth problem. 1.7.22
Conclusion
Deepest recession since the World War II in 2009 has created serious challenges to …scal, monetary and trade policies in UK. While the government is struggling to implement debt reduction plan that aims to reduce de…cit that rose to 13 percent of GDP in 2009 to 2 percent by 2018-19, options available on revenue and spending sides are very limited. With the lowest 0.5 percent bank rate in the history, the Bank of England is facing a liquidity trap and credit ‡ows to private sectors are very slow but the in‡ation went up to 5 percent, well above the target rate of 2 percent. Challenges in trade appear as the Ricardian comparative advantage gradually is in more favour of emerging economies including Brazil, China, India and South Korea though around 25 percent devaluation of Sterling Pound has contributed a bit in growth of exports. With econometric estimation of parameters based on time series data of the closed and open economy models with the basic Keynesian models this paper tries to provide answers to questions relating to appropriate models of business cycles and impulse response analyses in the short run of real and nominal shocks for analysing the dynamics of output, in‡ation, exchange rate and other macro variables in the UK economy. Stochastic Keynesian IS-LM, stabilisation, AS-AD and open economy models are found signi…cant and e¤ective in evaluating the impacts of …scal, monetary and trade policy shocks in macro variables in the UK. They are simpler and more transparent than equivalent DSGE or RBC models and should be complemented by dynamic general equilibrium models in Hicks-Stone– Meade-Mirrlees-Pissarides tradition that takes account of heterogeneity of …rms and households for analysing challenges of stability and slow recovery facing the UK economy after the slump that started with the …nancial crisis 2008.
References [1 ]
A i y a g a r i S . R a o , A l b e r t M a r c e t , T h o m a s J . S a r g e n t , J u h a S e p p ä l ä ( 2 0 0 2 ) O p t i m a l T a x a t i o n w i t h o u t S t a t e - C o n t i n g e n t D e b t , Journal of P olitical E conom y, 1 1 0 : 6 : D e c . , 1 2 2 0 - 1 2 5 4
[2 ]
A l t i g D E , C . T . C a r l s t r o m a n d K . L . L a n s i n g ( 1 9 9 5 ) C o m p u t a b l e G e n e r a l E q u i l i b r i u m M o d e l s a n d M o n e t a r y P o l i c y A d v i c e , Journal of M oney C redit an d B an kin g, 2 7 : 4 : N o v . : 1 4 7 2 - 1 4 9 3 .
89
[3 ]
A n g e lo p o u lo u E ., H . D . G ib so n (2 0 0 9 ) T h e B a la n c e S h e e t C h a n n e l o f M o n e ta ry P o lic y Tra n sm issio n : E v id e n c e fro m th e U n ite d K in g d o m , E conom ica, 7 6 : 3 0 4 : O c t . : 6 7 5 - 7 0 3 .
[4 ]
A r e s t i s P a n d M . S a w y e r ( 1 9 9 8 ) K e y n e s i a n E c o n o m i c P o l i c i e s f o r t h e N e w M i l l e n n i u m , E conom ic Journ al, 1 0 8 , 4 4 6 , 1 8 1 - 1 9 5
[5 ]
A r e s t i s P , G . C h o r t a r e a s a n d J D T s o u k a l a s ( 2 0 1 0 ) M o n e y a n d i n f o r m a t i o n i n a N e w N e o c l a s s i c a l S y n t h e s i s F r a m e w o r k , E conom ic Journal, 1 2 0 : 5 4 2 : F e b r u a r y.
[6 ]
A r n o l d J . M . , B . B r y s , C . H e a d y, C . S c h w e l l n u s a n d L V a r t i a ( 2 0 1 1 ) T a x p o l i c y f o r E c o n o m i c R e c o v e r y a n d G r o w t h , E conom ic Journal, 1 2 1 :5 5 0 :F 5 9 -F 8 0
[7 ]
A s h J . C . K a n d D . J . S m y t h ( 1 9 7 3 ) F o r e c a s t i n g t h e U n i t e d K i n g d o m E c o n o m y, S a x o n H o u s e , L o n d o n .
[8 ]
A t k i n s o n A . B . a n d N . H . S t e r n ( 1 9 7 4 ) P i g o u , T a x a t i o n a n d P u b l i c G o o d s , Review of E con om ic Studies, 4 1 : 1 : 1 1 9 - 1 2 8 .
[9 ]
A u e r b a c h A . J . a n d L . K o t l i k o ¤ ( 1 9 8 7 ) D y n a m i c F i s c a l P o l i c y, C a m b r i d g e U n i v e r s i t y P r e s s .
[1 0 ]
B a n k o f E n g l a n d ( 2 0 1 2 ) I n ‡a t i o n R e p o r t , A u g u s t , 2 0 1 2 .
[1 1 ]
B a r r o , R . J . ( 1 9 7 4 ) , A r e G o v e r n m e n t B o n d s N e t W e a l t h ? , Journal of P olitical E con om y, 8 2 , 1 0 9 5 - 1 1 1 7 .
[1 2 ]
B a r r o R . J . ( 1 9 8 9 ) T h e R i c a r d i a n A p p r o a c h t o B u d g e t D e … c i t s , Journal of E con om ic P erspectives, 3 , 2 , 3 7 - 5 4
[1 3 ]
B a r r o R . J . a n d G o r d o n ( 1 9 8 3 ) A P o s i t i v e T h e o r y o f M o n e t a r y P o l i c y i n a N a t u r a l R a t e M o d e l , Journal of P olitical E con om y, 9 1 : 4 : 5 8 9 - 6 1 0 .
[ 1 4 ] B a s u P . ( 1 9 9 6 ) P r o p o r t i o n a l I n c o m e T a x a n d t h e R i c a r d i a n E q u i v a l e n c e i n a N o n - E x p e c t e d U t i l i t y M a x i m i z i n g M o d e l S outhern E conom ic Journal, 6 3 , 1 , 2 3 3 - 2 4 3 . [1 5 ]
B e a n C . ( 2 0 0 9 ) T h e m e a n i n g o f i n t e r n a l b a l a n c e ’ T h i r t y y e a r s o n , E conom ic Journ al, 1 1 9 ( N o v e m b e r ) , F 4 4 2 –F 4 6 0 .
[1 6 ]
B e a n C . ( 1 9 9 8 ) T h e N e w U K M o n e t a r y A r r a n g e m e n t s : A V i e w f r o m t h e L i t e r a t u r e , E conom ic Journ al, 1 0 8 , 4 5 1 , 1 7 9 5 - 1 8 0 9
[1 7 ]
B e e t s m a R . a n d M . G i u l i o d o r i ( 2 0 1 1 ) T h e E ¤ e c t s o f g o v e r n m e n t p u c h a s e s s h o c k s a n d e s t i m a t e s f o r E U , E conom ic Journ al, 1 2 1 : 5 5 0 : F 4 - F - 3 2
[1 8 ]
B e n a t i , L u c a . ( 2 0 0 8 ) “ T h e ‘G r e a t M o d e r a t i o n ’ i n t h e U n i t e d K i n g d o m . ” Journal of M on ey,C redit an d B an king, 4 0 , 1 2 1 –4 7 .
[1 9 ] B e r n a n k e B e n S ., J . B o iv in a n d P. E lia s z ( 2 0 0 5 ) M e a s u r in g t h e E ¤ e c t s o f M o n e t a r y P o lic y : A Fa c t o r -A u g m e n t e d Ve c t o r A u t o r e g r e s s iv e ( FAVA R ) A p p r o a c h , Q uarterly Journ al of E conom ics, 1 2 0 , 1 , 3 8 7 - 4 2 2 . [ 2 0 ] B e r n a n k e B . S a n d F . S . M i s h k i n ( 1 9 9 7 ) I n ‡a t i o n T a r g e t i n g : A N e w F r a m e w o r k f o r M o n e t a r y P o l i c y ? Journal of E con om ic P erspectives, 1 1 2 , 9 7-11 6 [2 1 ]
B e r n h e i m B . D . ( 1 9 8 9 ) A N e o c l a s s i c a l P e r s p e c t i v e o n B u d g e t D e … c i t s , Journal of E con om ic P erspectives, 3 : 2 S p r i n g : 5 5 - 7 2
[2 2 ]
B e n a s s y J . P . ( 2 0 0 2 ) T he m acroeconom ics of Im perfect C om petition an d N on clearin g M arkets, M I T P r e s s .
[2 3 ]
B e s l e y T . ( 2 0 0 1 ) F r o m m i c r o t o m a c r o : p u b l i c p o l i c i e s a n d a g g r e g a t e e c o n o m i c p e r f o r m a n c e , F iscal S tudies, 2 2 , 3 , 3 5 7 –3 7 4 .
[2 4 ] B h a tta ra i K a n d H . D ix o n (2 0 1 4 ) E q u ilib riu m U n e m p loy m e nt in a G e n e ra l E q u ilib riu m M o d e l w ith Ta x e s, T h e M a n ch e ste r S ch o o l, fo rth c o m in g . [ 2 5 ] B h a t t a r a i K ( 2 0 1 2 ) F i s c a l p o l i c y g r o w t h a n d i n c o m e d i s t r i b u t i o n i n U K , paper for the A E A an d E E A /E S E M conferences, U n i v e r s i t y o f H u l l , B u sin e ss S ch o o l. [ 2 6 ] B h a t t a r a i K ( 2 0 1 1 ) E c o n o m e t r i c a n d S t o c h a s t i c G e n e r a l E q u i l i b r i u m M o d e l s f o r E v a l u a t i o n o f E c o n o m i c P o l i c i e s , In tern ation al Journ al of Trade and G lobal M arkets, 4 : 2 : 2 1 2 - 2 4 1 . [2 7 ]
B h a t t a r a i , K . ( 2 0 0 8 ) A n E m p i r i c a l S t u d y o f I n t e r e s t D e t e r m i n a t i o n R u l e s , A pplied F in an cial E con om ics, 1 8 : 4 : 3 2 7 - 3 4 3 .
[ 2 8 ] B h a t t a r a i K . a n d J . W h a l l e y ( 2 0 0 0 ) G e n e r a l E q u i l i b r i u m M o d e l l i n g o f U K T a x P o l i c y, i n H o l l y S a n d M W e a l e E d s . " E conom etric M odel ling: Techniques an d A pplications " , p p . 1 3 2 - 1 5 7 , C a m b r i d g e U n i v e r s i t y P r e s s . [ 2 9 ] B h a t t a r a i K . a n d J . W h a l l e y ( 1 9 9 9 ) R o l e o f l a b o u r d e m a n d e l a s t i c i t i e s i n t a x i n c i d e n c e a n a l y s i s w i t h h e t e r o g e n e i t y o f l a b o u r , E m pirical E conom ics, 2 4 ( 4 ) . 5 9 9 - 6 2 0 . [3 0 ]
B l a k e A . P . , M . W e a l e ( 1 9 9 8 ) C o s t s o f S e p a r a t i n g B u d g e t a r y P o l i c y f r o m C o n t r o l o f I n ‡a t i o n : A N e g l e c t e d A s p e c t o f C e n t r a l B a n k I
[3 1 ]
n d e p e n d e n c e , O xford E conom ic P apers, 5 0 , 3 , 4 4 9 - 4 6 7
[3 2 ]
B la ck b u r n K e it h a n d M o r t e n O . R a v n ( 1 9 9 2 ) B u s in e s s C y c le s in t h e U n it e d K in g d o m : Fa c t s a n d F ic t io n s , E c o n o m ic a , 5 9 , 2 3 6 , 3 8 3 -4 0 1
[ 3 3 ] B l a k e A . P . , M . W e a l e a n d G . Y o u n g ( 2 0 0 0 ) O p t i m a l m o n e t a r y p o l i c y i n H o l l y S a n d M W e a l e E d s . " E conom etric M odel lin g: Techn iques and A pplications " , p p . 2 0 9 - 2 3 6 , C a m b r i d g e U n i v e r s i t y P r e s s . [3 4 ]
B l a n c h a r d , O a n d C . M . K a h n ( 1 9 8 0 ) , T h e S o l u t i o n o f L i n e a r D i ¤ e r e n c e M o d e l s u n d e r R a t i o n a l E x p e c t a t i o n s , E conom etrica 4 8 , 1 3 0 5 - 1 3 1 3 .
[ 3 5 ] B l a n c h a r d O . J . a n d N . K i y o t a k i ( 1 9 8 7 ) M o n o p o l i s t i c c o m p e t i t i o n a n d t h e e ¤ e c t s o f a g g r e g a t e d e m a n d , Am erican E conom ic Review , 7 7 : S e p t . : 6 47-6 6. [3 6 ] B la n ch a rd , O . a n d P e ro tti, R . (2 0 0 2 ). A n e m p iric a l ch a ra c te riz a tio n o f th e d y n a m ic e ¤ e c ts o f ch a n g e s in g ove rn m e nt sp e n d in g a n d ta x e s o n o u t p u t , Q uarterly Journ al of E conom ics, 1 1 7 ( 4 ) : N o v . : 1 3 2 9 –6 8 .
90
[ 3 7 ] B l a n c h ‡o w e r , D . G a n d A . B r y s o n ( 2 0 1 0 ) T h e W a g e I m p a c t o f T r a d e U n i o n s i n t h e U K P u b l i c a n d P r i v a t e S e c t o r s , E conom ica, 7 7 , 3 0 5 , 92 -10 9 [3 8 ] B lin d e r A .S ., M . E h r m a n n , M . Fr a t z s ch e r , d e H a a n J ., D . J . J a n s e n ( 2 0 0 8 ) C e n t r a l B a n k C o m m u n ic a t io n a n d M o n e t a r y P o lic y : A S u r v e y o f T h e o r y a n d E v i d e n c e , Journal of E con om ic L iterature, 4 6 : 4 : 9 1 0 - 9 4 5 . [ 3 9 ] B o i n e t V . , C . M a r t i n ( 2 0 0 8 ) , T a r g e t s , Z o n e s , a n d A s y m m e t r i e s : A F l e x i b l e N o n l i n e a r M o d e l o f R e c e n t U K M o n e t a r y P o l i c y, O xford E con om ic P apers, 6 0 , 3 , J u l . , 4 2 3 - 4 3 9 . [4 0 ]
B u c h a n a n , J . , ( 1 9 5 8 ) P ublic prin ciples of public debt ( I r w i n : H o m e w o o d , I l l i n o i s ) .
[4 1 ]
B u rn s, A a n d W . M ich e ll, (1 9 4 6 ), “M e a su rin g B u sin e ss C y c le s” N B E R , N e w Yo rk .
[4 2 ]
B u r n s i d e , C . , E i c h e n b a u m , M . a n d F i s h e r , J . D . ( 2 0 0 4 ) . F i s c a l s h o c k s a n d t h e i r c o n s e q u e n c e s , Journal of E con om ic T heory, 1 1 5 : 8 9 –1 1 7 .
[4 3 ]
B r a u n i n g e r M . ( 2 0 0 5 ) T h e b u d g e t d e … c i t , p u b l i c d e b t , a n d e n d o g e n o u s g r o w t h , Journal of P ublic E con om ic T heory, 7 ( 5 ) , 2 0 0 5 , p p . 8 2 7 –8 4 0 .
[4 4 ]
C a l v o , G . ( 1 9 8 3 ) S t a g g e r e d c o n t r a c t s i n a u t i l i t y - m a x i m i z i n g f r a m e w o r k , Journal of M on etary E con om ics, 1 2 , 3 8 3 - 9 8 .
[4 5 ] C a u c u tt E .M , S . Im ro h o ro g lu a n d K . B . K u m a r (2 0 0 6 ) D o e s th e P ro g re s s iv ity o f In c o m e Ta x e s M a tte r fo r H u m a n C a p ita l a n d G row th ? Journal of P ublic E con om ic T heory, 8 : 1 : 9 5 - 1 1 8 [ 4 6 ] C a s t l e , J . L . , D o o r n i k , J . A . , a n d H e n d r y, D . F . ( 2 0 1 1 ) . E v a l u a t i n g a u t o m a t i c m o d e l s e l e c t i o n , Journal of T im e S eries E con om etrics, 3 : 1 : 1 9 4 1 1928. [ 4 7 ] C l a r i d a R . , G a l i J . , a n d G e r t l e r M . ( 1 9 9 9 ) T h e S c i e n c e o f M o n e t a r y P o l i c y : A N e w K e y n e s i a n p e r s p e c t i v e , Journal of E con om ic L iterature ; 3 7 (4), 1 66 1-70 7. [ 4 8 ] C l a r i d a R . , G a l i J . , a n d G e r t l e r M . ( 2 0 0 1 ) O p t i m a l M o n e t a r y P o l i c y i n C l o s e d V e r s u s O p e n E c o n o m i e s : A n i n t e g r a t e d a p p r o a c h . Am erican E conom ic Review , 9 1 ( 2 ) ; M a y ; 2 4 8 - 2 5 2 . [ 4 9 ] C h a d h a , J . S . a n d C . N o l a n ( 2 0 0 7 ) O p t i m a l S i m p l e R u l e s f o r t h e C o n d u c t o f M o n e t a r y a n d F i s c a l P o l i c y, Journal of M acroecon om ics, D e c , 2 9 :4 : 6 6 5 -8 9 . [ 5 0 ] C h r i s t i a n o , L , M . E i c h e n b a u m a n d C . E v a n s ( 2 0 0 5 ) N o m i n a l r i g i d i t i e s a n d t h e d y n a m i c e ¤ e c t s o f s h o c k s t o m o n e t a r y p o l i c y, Journal of P olitical E conom y, 1 1 3 : 1 : 1 - 4 5 . [ 5 1 ] C h u r c h K . B . , P . M i t c h e l , J . S a u l t a n d K . W a l l i s ( 1 9 9 7 ) C o m p a r a t i v e p r o p e r t i e s o f m o d e l s o f t h e U K e c o n o m y, N ation al In stitute E conom ic Review , 1 6 1 : 9 1 - 1 0 0 . [ 5 2 ] C o b h a m D . ( 1 9 9 7 ) T h e P o s t - E r m F r a m e w o r k f o r M o n e t a r y P o l i c y i n t h e U n i t e d K i n g d o m : B o u n d e d C r e d i b i l i t y, E conom ic Journal, 1 0 7 , 4 4 3 : J u l.:1 1 2 8 -1 1 4 1 . [5 3 ] C o o k S . S . H o lly a n d P. Tu rn e r ( 2 0 0 0 ) T h e c o n d u c t o f m o n e t a ry p o lic y w h e n t h e b u s in e s s c y c le is n o n -lin e a r in H o lly S a n d M W e a le E d s . ( 2 0 0 0 ) E conom etric M odel ling:Techniques an d A pplications, C a m b r i d g e U n i v e r s i t y P r e s s . [5 4 ]
D a v i d s o n P . ( 1 9 8 8 ) P o s t K e y n e s i a n E m p l o y m e n t A n a l y s i s a n d t h e M a c r o e c o n o m i c s o f O E C D U n e m p l o y m e n t , E conom ic Journ al, M a y 8 1 7 - 8 3 1 .
[ 5 5 ] d e n H a a n W . J . a n d A M a r c e t ( 1 9 9 0 ) S o l v i n g t h e s t o c h a s t i c g r o w t h m o d e l b y p a r a m e t e r i s i n g e x p e c t a t i o n s , Joun ral of B usin ess and E conom ic S tatistics, 8 : 1 : 3 1 - 3 4 . [5 6 ]
D e s a i M . , a n d G . W e b e r ( 1 9 8 8 ) A K e y n e s i a n M a c r o - E c o n o m e t r i c M o d e l o f t h e U K : 1 9 5 5 - 1 9 8 4 , Journal of A pplied E con om etrics, 3 , 1 1 - 3 3 .
[5 7 ]
D i a m o n d , P . A . , ( 1 9 6 5 ) , N a t i o n a l d e b t i n a n e o c l a s s i c a l g r o w t h m o d e l , Am erican E con om ic Review , 5 5 , 5 , 1 2 2 6 - 1 1 5 0 .
[5 8 ]
D i a m o n d , D o u g l a s W . a n d D y b v i g , P h i l i p H . ( 1 9 8 3 ) B a n k R u n s , D e p o s i t I n s u r a n c e , a n d L i q u i d i t y, Journal of P olitical E con om y, 4 0 1 - 4 1 9 .
[5 9 ]
D i x o n H . ( 1 9 8 8 ) C o n t r o v e r s y : t h e m a c r o e c o n o m i c s o f u n e m p l o y m e n t i n t h e O E C D , E conom ic Journ al, 1 0 8 : 7 7 9 - 7 8 1 , M a y
[6 0 ]
D i x o n H a n d N R a n k i n ( 1 9 9 4 ) I m p e r f e c t C o m p e t i t i o n a n d M a c r o e c o n o m i c s : A S u r v e y, O xford E conom ic P apers, 4 6 , 2 , 1 7 1 - 1 9 9 9 .
[6 1 ]
D o r n b u s c h R . ( 1 9 7 6 ) E x p e c t a t i o n s a n d E x c h a n g e R a t e D y n a m i c s , Journal of P olitical E con om y, 8 4 : 6 : 1 1 6 1 - 1 1 7 6
[6 2 ]
D r i ¢ l l J . , A . S n e l l ( 2 0 0 3 ) W h a t M o v e s O E C D R e a l I n t e r e s t R a t e s ? Journal of M on ey, C redit and B an king, 3 5 : 3 : J u n . : 3 7 5 - 4 0 2
[6 3 ]
D r i ¢ l l J . , C . S c h u l t z ( 1 9 9 2 ) W a g e S e t t i n g a n d S t a b i l i z a t i o n P o l i c y i n a G a m e w i t h R e n e g o t i a t i o n , O xford E conom ic P apers, 4 4 , 3 , 4 4 0 - 4 5 9 .
[6 4 ]
E a t o n J a n d S K o r t u m ( 2 0 0 2 ) T e c h n o l o g y, G e o g r a p h y a n d T r a d e , E conom etrica, 7 0 : 5 : 1 7 4 1 - 1 7 7 9 .
[6 5 ]
E l l i s o n M . a n d J . P e a r l m a n ( 2 0 1 1 ) S a d d l e p a t h l e a r n i n g , Journal of E con om ic theory 1 4 6 , 1 5 0 0 - 1 5 1 9 .
[ 6 6 ] G a i P . , S . K a p a d i a , S . M i l l a r d , A . P e r e z ( 2 0 0 8 ) F i n a n c i a l I n n o v a t i o n , M a c r o e c o n o m i c S t a b i l i t y a n d S y s t e m i c C r i s e s , E conom ic Journal, 1 1 8 , 5 27, 40 1-42 6 [ 6 7 ] G a l i J . a n d T . M o n a c e l l i ( 2 0 0 5 ) . M o n e t a r y P o l i c y a n d E x c h a n g e R a t e V o l a t i l i t y i n a S m a l l O p e n E c o n o m y, Review of E con om ic Studies ; 7 2 ( 3 ) : 7 07-7 34 [ 6 8 ] G a r r a t t A . , K . L e e , M . H . P e s a r a n a n d Y . S h i n ( 2 0 0 3 ) A S t r u c t u r a l C o i n t e g r a t i o n VA R A p p r o a c h t o M a c r o e c o n o m e t r i c M o d e l l i n g , E conom ic Journal, 1 1 3 : 4 8 7 : 4 1 2 - 4 4 5 . [ 6 9 ] G h o s a l S . a n d M . M i l l e r ( 2 0 0 3 ) C o - O r d i n a t i o n F a i l u r e , M o r a l H a z a r d a n d S o v e r e i g n B a n k r u p t c y P r o c e d u r e s , E conom ic Journal, 1 1 3 , 4 8 7 : A p r.: 2 7 6 -3 0 4
91
[7 0 ]
G ilh o o ly R ., M . W e a le a n d T . W ie la d e k (2 0 1 2 ) D isa g g re g a tin g th e inte rn a tio n a l b u sin e ss c y c le , D isc u ssio n P a p e r N o . 3 7 , B a n k o f E n g la n d .
[7 1 ]
G o o d h a r t C . ( 1 9 8 9 ) T h e C o n d u c t o f M o n e t a r y P o l i c y, E conom ic Journ al, 9 9 , 3 9 6 , 2 9 3 - 3 4 6 .
[ 7 2 ] G o o d h a r t C . ( 1 9 9 4 ) W h a t S h o u l d C e n t r a l B a n k s D o ? W h a t S h o u l d B e T h e i r M a c r o e c o n o m i c O b j e c t i v e s a n d O p e r a t i o n s ? E conom ic Journal, 1 0 4 , 4 2 7 ,1 4 2 4 -1 4 3 6 [7 3 ]
F e l d s t e i n M ( 1 9 8 5 ) D e b t a n d t a x e s i n t h e t h e o r y o f p u b l i c … n a n c e , Journal of P ublic E con om ics, 2 8 : 2 3 3 - 4 6
[7 4 ]
F e l d s t e i n M ( 1 9 8 2 ) G o v e r n m e n t d e … c i t s a n d a g g r e g a t e d e m a n d , Journal of M on etary E conom ics 9 , 1 , 1 - 2 0 .
[ 7 5 ] F i s h e r P . a n d J . W h i t l e y ( 2 0 0 0 ) M a c r o e c o n o m i c m o d e l s a t t h e B a n k o f E n g l a n d i n H o l l y S a n d M W e a l e E d s . E conom etric M odel lin g: Techn iques an d A pplication s, C a m b r i d g e U n i v e r s i t y P r e s s . [7 6 ]
F i s h e r J . D . M . a n d R y a n P . ( 2 0 1 0 ) U s i n g S t o c k R e t u r n s t o I d e n t i f y G o v e r n m e n t S p e n d i n g S h o c k s , E conom ic Journ al, 1 2 0 : 5 4 4 , M a y : 4 1 6 - 4 3 6 .
[7 7 ]
F l e m i n g , J . M . ( 1 9 6 2 ) D o m e s t i c … n a n c i a l p o l i c i e s u n d e r … x e d a n d u n d e r ‡o a t i n g e x c h a n g e r a t e s , IM F S ta¤ P apers, N o v . , 9 , 3 6 9 - 7 9 .
[7 8 ]
F r i e d m a n , M . ( 1 9 6 8 ) , T h e R o l e o f M o n e t a r y P o l i c y, Am erican E con om ic Review , 5 8 : M a r c h , 1 - 1 7 .
[7 9 ] G e m m e ll N ., R . K n e lle r a n d I. S a n z (2 0 1 1 ) T h e tim in g p e rsiste n c e o f …sc a l p o lic y im p a c ts o n g row th : E v id e n c e fro m O E C D , c o u ntrie s, E conom ic Journ al, 1 2 1 : 5 5 0 : F 3 3 - F - 5 8 [8 0 ] G re e n sd a le J . V ., S . H a ll, S .G .B . H e n ry a n d J N ix o n (2 0 0 0 ) U n e m p loy m e nt, th e n a tu ra l ra te a n d stru c tu ra l ch a n g e in H o lly S a n d M W e a le E d s . " E conom etric M odel ling: Techn iques and A pplication s " , p p . 1 3 2 - 1 5 7 , C a m b r i d g e U n i v e r s i t y P r e s s . [8 1 ]
H a s k e l J . a n d M . J . S l a u g h t e r ( 2 0 0 1 ) T r a d e , T e c h n o l o g y a n d U . K . W a g e I n e q u a l i t y, E conom ic Journ al, 1 1 1 , 4 6 8 , 1 6 3 - 1 8 7
[8 2 ]
H e n d r y D . F . ( 1 9 9 7 ) T h e E c o n o m e t r i c s o f M a c r o e c o n o m i c F o r e c a s t i n g , E conom ic Journ al, 1 0 7 , 4 4 4 . , 1 3 3 0 - 1 3 5 7 .
[ 8 3 ] H e n d r y D . F . a n d M . P . C l e m e n t ( 2 0 0 0 ) E c o n o m i c f o r e c a s t i n g i n t h e f a c e o f s t r u c t u r a l b r e a k s , i n H o l l y S a n d M W e a l e E d s . E conom etric M odel lin g: Techniques an d A pplications, C a m b r i d g e U n i v e r s i t y P r e s s . [8 4 ]
H e n d r y D . F a n d J . A . D o o r n i k ( 1 9 9 4 ) M o d e l l i n g L i n e a r D y n a m i c E c o n o m e t r i c S y s t e m s , S cottish Journ al of P olitical E conom y, 4 1 , 1 - 3 3
[8 5 ]
H i c k s J o h n ( 1 9 9 0 ) T h e U n i … c a t i o n o f M a c r o - E c o n o m i c s , E con om ic Journ al, 1 0 0 , 4 0 1 , 5 2 8 - 5 3 8
[8 6 ]
H i c k s , J . R . ( 1 9 3 7 ) M r . K e y n e s a n d t h e “ C l a s s i c s ”; A S u g g e s t e d I n t e r p r e t a t i o n s , E conom etrica 5 : 1 4 7 - 1 5 9 .
[8 7 ]
H M Trea su ry (2 0 1 1 ) B u d g et R ep o rt, M a rch 2 0 1 1 , L o n d o n .
[8 8 ]
H o l l a n d A . a n d A . S c o t t ( 1 9 9 8 ) D e t e r m i n a n t s o f U K B u s i n e s s C y c l e , E conom ic Journal, 1 0 8 : 4 4 9 : 1 0 6 7 - 1 0 9 2 .
[8 9 ]
H o y M . , J L i v e r n o i s , C M c K e n n a , R R e e s a n d T . S t e n g o s ( 2 0 0 1 ) M athem atics for E conom ics, 2 n d e d . , M I T P r e s s
[ 9 0 ] I a c o v i e l l o , M . , a n d S . N e r i ( 2 0 1 0 ) H o u s i n g M a r k e t S p i l l o v e r s : E v i d e n c e f r o m a n E s t i m a t e d D S G E M o d e l , Am erican E con om ic Journ al M acro, (A p ril), 1 -4 4 . http :/ / w w w 2 .b c .e d u / ~ ia c ov ie l/ [9 1 ]
In s t it u t e o f F is c a l S t u d ie s ( 2 0 1 4 ) T h e IF S G r e e n B u d g e t , Fe b r u a r y 2 0 1 4 , IF S L o n d o n .
[9 2 ]
J o h n s o n H . G . ( 1 9 5 3 - 5 4 ) O p t i m a l t a r i ¤ s a n d R e t a l i a t i o n , Review of E con om ic Studies, 2 1 ( 2 ) , p p . 1 4 2 - 4 3 .
[9 3 ]
Johnson T . C .
[9 4 ]
K e y n e s J . M . ( 1 9 3 7 ) T h e G e n e r a l T h e o r y o f E m p l o y m e n t , Q uarterly Journ al of E conom ics, 5 1 , 2 , F e b . , 2 0 9 - 2 2 3 .
( 2 0 0 9 ) L i q u i d C a p i t a l a n d M a r k e t L i q u i d i t y, E conom ic Journal, 1 1 9 , . 5 4 0 : O c t . : 1 3 7 4 - 1 4 0 4 .
[9 5 ] K irs a n ova T ., C . L e ith a n d S . W re n -L e w is ( 2 0 0 9 ) M o n e ta ry a n d …s c a l p o lic y in te ra c tio n : T h e c u rre n t c o n s e n s u s a s s ig n m e n t in th e lig h t O f r e c e n t d e v e l o p m e n t s , E conom ic Journ al, 1 1 9 , N o v , F 4 8 2 –F 4 9 6 . [ 9 6 ] K l e i n , L . ( 1 9 7 1 ) ‘F o r e c a s t i n g a n d p o l i c y e v a l u a t i o n u s i n g l a r g e s c a l e e c o n o m e t r i c m o d e l s ’, i n I n t r i l i g a t o r , M . D . ( E d . ) : Fron tiers of Q uan titative E conom ics, N o r t h H o l l a n d . [9 7 ] K o ch e rla ko ta N . R . a n d K . M Y i (1 9 9 6 ) A sim p le tim e se rie s te st o f e n d o g e n o u s a n d e x o g e n o u s g row th m o d e ls: a n a p p lic a tio n to th e U n ite d S t a t e s , Review of E con om ic Studies, 7 8 : 1 : 1 2 6 - 1 3 4 [9 8 ]
K r u g m a n P . ( 1 9 7 9 ) A M o d e l o f B a l a n c e o f P a y m e n t C r i s i s , Journal of M on ey C redit an d B an kin g, 1 1 , 3 , 3 1 1 - 3 2 5 .
[ 9 9 ] K y d l a n d F . E a n d E . C . P r e s c o t t ( 1 9 7 7 ) R u l e s r a t h e r t h a n d i s c r e t i o n s : t h e I n c o n s i s t e n c y o f O p t i m a l P l a n s , Journal of P olitical E conom y, 8 5 : 3 : 4 73-4 91 . [1 0 0 ]
K i n g M e r v y n ( 2 0 0 4 ) T h e I n s t i t u t i o n s o f M o n e t a r y P o l i c y, Am erican E con om ic Review - P r o c e e d i n g s , 9 4 , 2 , 1 - 1 3
[1 0 1 ]
K i n g R . G . a n d P l o s s e r C . I . ( 1 9 8 4 ) M o n e y C r e d i t a n d P r i c e s i n a R e a l B u s i n e s s C y c l e , Am erican E con om ic Review , 6 4 ( J u n e ) 2 6 3 - 3 8 0 .
[ 1 0 2 ] L e i t h C . B a n d S . W r e n - L e w i s ( 2 0 0 0 ) H o w t o u g h m o n e t a r y p o l i c y b e i f i n ‡a t i o n i s f o r w a r d l o o k i n g , i n H o l l y S a n d M W e a l e E d s . E conom etric M odel lin g: Techniques an d A pplications, C a m b r i d g e U n i v e r s i t y P r e s s . [1 0 3 ]
L i m G . C . a n d M c N e l i s ( 2 0 0 8 ) , C o m p u t a t i o n a l M a c r o e c o n o m i c s f o r t h e O p e n E c o n o m y, M I T P r e s s .
[1 0 4 ] L iu , P h ilip H . M u m ta z (2 0 1 1 ) E vo lv in g M a c ro e c o n o m ic D y n a m ic s in a S m a ll O p e n E c o n o m y : M o d e l f o r t h e U K , J ournal of M on ey, C redit, an d B ankin g, 4 3 , 7 , 1 4 4 3 - 7 4 .
92
A n E stim a te d M a rkov S w itch in g D S G E
[1 0 5 ]
L u c a s R . E . ( 1 9 7 3 ) S o m e I n t e r n a t i o n a l E v i d e n c e o n O u t p u t I n ‡a t i o n T r a d e - O ¤ s , Am erican E con om ic Review , 6 3 : 3 : 3 2 6 - 3 3 4 .
[1 0 6 ]
M a n k i w N . G . ( 1 9 8 9 ) R e a l B u s i n e s s c y c l e : A N e w K e y n e s i a n P e r s p e c t i v e , Journal of E con om ic P erspectives, 3 , 3 : 7 9 - 9 0 .
[1 0 7 ]
M a r t i n , C . a n d M i l a s , C . ( 2 0 0 4 ) M o d e l l i n g m o n e t a r y p o l i c y : i n ‡a t i o n t a r g e t s i n p r a c t i c e , E conom ica, 7 1 , 2 0 9 - 2 1 .
[ 1 0 8 ] M c C a l l u m , B . a n d N e l s o n , E . ( 1 9 9 9 ) A n o p t i m i z i n g I S - L M S p e c i … c a t i o n f o r m o n e t a r y p o l i c y a n d b u s i n e s s c y c l e a n a l y s i s , J o u r n a l o f M o n e y, C re d it, a n d B a n k in g , 3 1 , 2 9 6 -3 1 6 . [ 1 0 9 ] M e a d e J . E . , a n d I r o n s i d e , J o n e s , B e l l , F l e m m i n g , K a y, K i n g , M a c d o n a l d , S a n d f o r d a n d W h i t t i n g t o n , W i l l i s . ( 1 9 7 8 ) . T he Structure and Reform of D irect Taxation. I F S , L o n d o n : G e o r g e A l l e n a n d U n w i n . [1 1 0 ]
M e a d e , J .E . (1 9 5 1 ), T h e T h e o ry o f In te ra n tio n a l E c o n o m ic P o lic y : B a la n c e o f P ay m e n ts , L o n d o n : O x fo rd U n ive rs ity P re s s .
[1 1 1 ]
M e a d e , J . E . ( 1 9 5 8 ) , I s t h e n a t i o n a l d e b t a b u r d e n ? O xford E conom ic P apers, 1 0 , 2 , 1 6 3 - 1 8 3 .
[ 1 1 2 ] M e l l i s C a n d R W h i t t a k e r ( 2 0 0 0 ) T h e T r e a s u r y ’s f o r e c a s t s o f G D P a n d t h e R P I : h o w h a v e t h e y c h a n g e d a n d w h a t a r e u n c e r t a i n t i e s i n H o l l y S a n d M W e a l e E d s . ( 2 0 0 0 ) E conom etric M odel ling: Techn iques and A pplication s, C a m b r i d g e U n i v e r s i t y P r e s s . [ 1 1 3 ] M i l l e r , M . H . ; J . E . S p e n c e r ( 1 9 7 7 ) T h e S t a t i c E c o n o m i c E ¤ e c t s o f t h e U K J o i n i n g t h e E E C : A G e n e r a l E q u i l i b r i u m A p p r o a c h , Review of E conom ic S tudies, 4 4 , 1 , 7 1 - 9 3 . [1 1 4 ]
M i l l e r M . a n d P . W e l l e r ( 1 9 9 1 ) E x c h a n g e R a t e B a n d s w i t h P r i c e I n e r t i a , E conom ic Journ al, 1 0 1 : 4 0 9 : 1 3 8 0 - 1 3 9 9 .
[ 1 1 5 ] M i r r l e e s J . , a n d S . A d a m , T . B e s l e y, R . B l u n d e l l , S . B o n d , R . C h o t e , M . G a m m i e , P . J o h n s o n , G . M y l e s , J . P o t e r b a . 2 0 1 0 . D im en sion s of tax design : the M irrlees review , O x f o r d : O x f o r d U n i v e r s i t y P r e s s . [1 1 6 ]
M i r r l e e s , J . A . ( 1 9 7 1 ) A n e x p l o r a t i o n i n t h e t h e o r y o f o p t i m u m i n c o m e t a x a t i o n , Review of E con om ic Studies, 3 8 : 1 7 5 - 2 0 8 .
[1 1 7 ]
M i n f o r d P . a n d D . P e e l ( 2 0 0 2 ) Advan ced M acroeconom ics: A P rim er, E d w a r d E l g a r P u b l i s h i n g .
[ 1 1 8 ] M i y a z a w a K . ( 1 9 6 0 ) F o r e i g n T r a d e M u l t i p l i e r , I n p u t - O u t p u t A n a l y s i s a n d t h e C o n s u m p t i o n F u n c t i o n , Q uarterly Journal of E conom ics, 7 4 , 1 , 5 3-64 [ 1 1 9 ] M o d i g l i a n i , F . , ( 1 9 6 1 ) , L o n g r u n i m p l i c a t i o n s o f a l t e r n a t i v e … s c a l p o l i c i e s a n d t h e b u r d e n o f t h e n a t i o n a l d e b t , E conom ic Journ al 7 1 , 7 28-7 55 . [1 2 0 ]
M o n a c e l l i T a n d R . P e r o t t i ( 2 0 1 0 ) F i s c a l P o l i c y, t h e R e a l E x c h a n g e R a t e a n d T r a d e d G o o d s , E conom ic Journal, 1 2 0 ( M a y ) , 4 3 7 - 4 6 1 .
[ 1 2 1 ] M u n d e l l R . A ( 1 9 6 2 ) C a p i t a l m o b i l i t y a n d s t a b i l i s a t i o n p o l i c y u n d e r … x e d a n d ‡e x i b l e e x c h a n g e r a t e s , C anadian Journal of E con om ic and P olitical S cien ce, 2 9 , 4 7 5 - 8 5 . [1 2 2 ]
M o n e t a r y P o l i c y C o m m i t t e e B a n k o f E n g l a n d ( 1 9 9 9 ) T h e T r a n s m i s s i o n M e c h a n i s m o f M o n e t a r y P o l i c y, w w w . b a n k o f e n g l a n d . c o . u k .
[1 2 3 ]
N e l s o n E . ( 2 0 0 9 ) A n O v e r h a u l o f D o c t r i n e : T h e U n d e r p i n n i n g o f U K I n ‡a t i o n T a r g e t i n g , E conom ic Journal, 1 1 9 : 5 3 8 , F 3 3 3 - F 3 6 8 .
[1 2 4 ]
N e l s o n , E d w a r d , a n d K a l i n N i k o l o v . ( 2 0 0 4 ) , M o n e t a r y P o l i c y a n d S t a g ‡a t i o n i n t h e U K , Journal of M on ey, C redit an d B an king, 3 6 , 2 9 3 –3 1 8 .
[1 2 5 ]
N i c k e l S ( 1 9 9 0 ) U n e m p l o y m e n t S u r v e y, E conom ic Journ al, 1 0 0 : 4 0 1 : J u n e : 3 9 1 - 4 3 9 .
[ 1 2 6 ] N i S h a w n a n d X W a n g ( 1 9 9 5 ) B a l a n c e d g o v e r n m e n t b u d g e t s v e r s u s d e … c i t … n a n c e i n a g r o w t h e c o n o m y, C anadian Journal of E conom ics, 2 8 , 4 b ,1 1 2 0 -1 1 3 4 . [1 2 7 ] N o rd h a u s W .D . (1 9 9 5 ) P o lic y G a m e s: Activities 2 : 1 9 9 4 : 1 3 9 - 2 1 6 .
C o - o r d i n a t i o n a n d I n d e p e n d e n c e i n M o n e t a r y a n d F i s c a l P o l i c e i s , B rookin gs P apers on E con om ic
[1 2 8 ]
O b s t f e l d M . a n d K . R o g o ¤ ( 1 9 9 6 ) E x c h a n g e r a t e d y n a m i c s r e d u x , Journal of P olitical E con om y, 1 0 3 : 3 : J u n e : 6 2 4 - 6 6 0 .
[1 2 9 ]
O ¢ c e o f N a tio n a l S ta tistic s (2 0 1 0 ) In p u t-O u tp u t Ta b le o f U K , http :/ / w w w .sta tistic s.g ov .u k / sta tb a se / .
[1 3 0 ]
P a i n N i g e l ; M a r t i n W e a l e ; G a r r y Y o u n g ( 1 9 9 7 ) B r i t a i n ’s F i s c a l P r o b l e m s , E conom ic Journ al, 1 0 7 , 4 4 3 , 1 1 4 2 - 1 1 5 6 .
[1 3 1 ]
P e a c o c k A . a n d G . K . S h a w ( 1 9 7 9 ) T he E con om ic T heory of F icals P olicy, G e o r g e A l l e n a n d U n w i n .
[1 3 2 ]
P h e l p s , E d m u n d S . ( 1 9 6 8 ) , M o n e y - W a g e D y n a m i c s a n d L a b o r - m a r k e t e q u i l i b r i u m , Journal of P olitical E con om y, 7 6 : 6 7 8 - 7 1 0 .
[1 3 3 ] P h illip s , A . W . (1 9 5 8 ) T h e R e la tio n B e tw e e n U n e m p loy m e n t a n d th e R a te o f C h a n g e o f M o n e y W a g e R a te s in th e U n ite d K in g d o m , 1 8 6 1 - 1 9 5 7 , E conom ica, 2 5 : N o v . : 2 8 3 - 2 9 9 . . [1 3 4 ]
P i s s a r i d e s C . A . ( 1 9 8 5 ) : T a x e s , S u b s i d i e s a n d E q u i l i b r i u m U n e m p l o y m e n t , Review of E con om ic Studies, 5 2 , 1 , J a n . , 1 2 1 - 1 3 3
[1 3 5 ]
P l o s s e r C . I . ( 1 9 8 9 ) U n d e r s t a n d i n g R e a l B u s i n e s s C y c l e , Journal of E con om ic P erspectives, 3 , 3 , 5 1 - 7 7 .
[1 3 6 ]
P r e s c o t t , E . C . ( 1 9 8 6 ) , T h e o r y A h e a d o f B u s i n e s s C y c l e M e a s u r e m e n t , F e d e r a l R e s e r v e B a n k o f M i n n e a p o l i s , Q uarterly Review ; F a l l , 9 - 2 2 .
[1 3 7 ]
P r e s t A . R . ( 1 9 6 8 ) S e n s e a n d N o n s e n s e i n B u d g e t a r y P o l i c y, E conom ic Journ al, 7 8 , 3 0 9 , 1 - 1 8
[1 3 8 ]
P r i c e S i m o n ( 1 9 9 7 ) P o l i t i c a l B u s i n e s s C y c l e s a n d M a c r o e c o n o m i c C r e d i b i l i t y : A S u r v e y, P ublic C hoice, 9 2 , 3 / 4 , 4 0 7 - 4 2 7
[1 3 9 ]
R a m s e y, F . P . ( 1 9 2 8 ) A M a t h e m a t i c a l T h e o r y o f S a v i n g , E conom ic Journ al 3 8 , 1 5 2 , D e c , 5 4 3 - 5 5 9 .
[1 4 0 ]
R a m s e y, F r a n k P . ( 1 9 2 7 ) A C o n t r i b u t i o n t o t h e T h e o r y o f T a x a t i o n , E conom ic Journ al 3 7 ( 1 4 5 ) : 4 7 - 6 1 .
93
[1 4 1 ]
R a n k i n N . ( 1 9 9 2 ) I m p e r f e c t c o m p e t i t i o n , e x p e c t a t i o n s a n d t h e m u l t i p l e e ¤ e c t s o f m o n e t a r y g r o w t h , E conom ic Journ al 1 0 2 : 7 4 3 - 7 5 3 .
[1 4 2 ]
R o m e r P . ( 1 9 9 0 ) E n d o g e n o u s T e c h n o l o g i c a l C h a n g e , Journal of P olitical E con om y, 9 8 : 5 : 2 : . s 7 1 - s 1 0 2 .
[1 4 3 ]
R u d e b u s c h , G . ( 2 0 0 6 ) M o n e t a r y p o l i c y i n e r t i a : f a c t o r … c t i o n ? In tern ation al Journ al of C en tral B ankin g, 2 , 8 5 - 1 3 5 .
[ 1 4 4 ] S a m u e l s o n P . A . ( 1 9 3 9 ) I n t e r a c t i o n B e t w e e n t h e M u l t i p l i e r A n a l y s i s a n d t h e P r i n c i p l e o f A c c e l e r a t i o n , Review of E conom ics and S tatistics, 2 1 : 2 : 7 5 - 7 8 , M a y. [1 4 5 ]
S a m u e l s o n P . A . ( 1 9 5 4 ) P u r e T h e o r y o f P u b l i c E x p e n d i t u r e , Review of E con om ic Statistics, 3 6 : 3 8 7 - 9 /
[1 4 6 ] S a rg e nt, T .J . a n d N . W a lla c e (1 9 7 5 ) " R a tio n a l" E x p e c ta tio n s, th e O p tim a l M o n e ta ry In stru m e nt, a n d th e O p tim a l M o n e y S u p p ly R u le , Journal of P olitical E con om y, 8 3 : 2 : 2 4 1 - 2 5 4 . [1 4 7 ]
S a w y e r M ( 2 0 0 3 ) E m p l o y e r o f L a s t R e s o r t : C o u l d I t D e l i v e r F u l l E m p l o y m e n t a n d P r i c e S t a b i l i t y ? Journal of E con om ic Issues, 3 7 , 4 , 8 8 1 - 9 0 7
[ 1 4 8 ] S m e t F . a n d R . W o u t e r s ( 2 0 0 3 ) A n e s t i m a t e d d y n a m i c s t o c h a s t i c g e n e r a l e q u i l i b r i u m m o d e l o f t h e E u r o A r e a , Journal of E uropean E con om ic A ssociation , S e p t , 1 ( 5 ) : 1 1 2 3 - 1 1 7 5 . [1 4 9 ]
S m i t h J . C . ( 2 0 1 1 ) T h e i n s a n d o u t s o f U K u n e m p l o y m e n t , E conom ic Journal, 1 2 1 , 4 0 2 –4 4 4 .
[1 5 0 ]
S o r e n s e n P B a n d H . J . W h i t t a - J a c o b s e n ( 2 0 1 0 ) In troducin g Advan ced M acroecon om ics, M c G r a w H i l l .
[ 1 5 1 ] S p e n c e r P e t e r D . ( 1 9 8 4 ) T h e E ¤ e c t o f O i l D i s c o v e r i e s o n t h e B r i t i s h E c o n o m y –T h e o r e t i c a l A m b i g u i t i e s a n d t h e C o n s i s t e n t E x p e c t a t i o n s , E conom ic Journ al, 9 4 , 3 7 5 , 6 3 3 - 6 4 4 [1 5 2 ]
S t o n e R i c h a r d . 1 9 4 2 - 4 3 . N a t i o n a l I n c o m e i n t h e U n i t e d K i n g d o m a n d t h e U n i t e d S t a t e s o f A m e r i c a , Am erican E con om ic Review , 1 0 ( 1 ) : 1 - 2 7 .
[1 5 3 ]
T a y l o r M . P . e d . ( 2 0 1 0 ) , P urchasin g P ow er P arity an d Real E xchange Rates, L o n d o n : Routledge.
[1 5 4 ]
T a y l o r M . P . ( 1 9 9 5 ) T h e E c o n o m i c s o f E x c h a n g e R a t e s , Journal of E con om ic L iterature, M a r c h , 3 3 : 1 : 1 3 - 4 7 .
[1 5 5 ]
T a y l o r M P ( 1 9 8 7 ) O n t h e l o n g r u n s o l u t i o n t o d y n a m i c e c o n o m e t r i c e q u a t i o n s u n d e r r a t i o n a l e x p e c t a t i o n , E conom ic Journ al, 9 7 : 3 8 5 : 2 1 5 - 2 1 8 .
[1 5 6 ]
T i l l m a n n P . ( 2 0 0 9 ) R o b u s t M o n e t a r y P o l i c y w i t h t h e C o s t C h a n n e l , E conom ica, N e w S e r i e s , 7 6 : 3 0 3 : 4 8 6 - 5 0 4 .
[ 1 5 7 ] T u r n o v s k y S . J . , M . H . M i l l e r ( 1 9 8 4 ) T h e E ¤ e c t s o f G o v e r n m e n t E x p e n d i t u r e o n t h e T e r m S t r u c t u r e o f I n t e r e s t R a t e s , Journal of M oney, C redit an d B an kin g, 1 6 : 1 : F e b . : 1 6 - 3 3 [1 5 8 ] U h lin g H . (1 9 9 5 ) A to o lk it fo r a n a ly z in g n o n lin e a r e c o n o m ic d y n a m ic m o d e ls e a sily : M AT L A B Reserve B ank of M inn eapolis, M i n n e s o t a , U S A .
p r o g r a m s , d i s c u s s i o n p a p e r 1 0 1 , Federal
[1 5 9 ] W icke n s M . (1 9 9 5 ) R e a l B u sin e ss C y c le A n a ly sis: A N e e d e d R e vo lu tio n in M a c ro e c o n o m e tric s (in C o ntrove rsy : B u sin e ss C y c le E m p iric s) E conom ic Journ al, 1 0 5 , 4 3 3 . , 1 6 3 7 - 1 6 4 8 . [1 6 0 ]
W a l l i s K . F . ( 1 9 8 9 ) M a c r o e c o n o m i c F o r e c a s t i n g : A S u r v e y , E conom ic Journ al, 9 9 , 3 9 4 . , 2 8 - 6 1
[1 6 1 ]
W i l s o n J . S . G . ( 1 9 4 9 ) I n v e s t m e n t i n a M o n e t a r y E c o n o m y, E conom ica, 1 6 , 6 4 , 3 2 1 - 3 3 5
[1 6 2 ]
W i l s o n C . A . ( 1 9 7 9 ) A n t i c i p a t e d S h o c k s a n d E x c h a n g e R a t e D y n a m i c s , Journal of P olitical E con om y, 8 7 , 3 , 6 3 9 - 6 4 7 .
[1 6 3 ]
W o o d f o r d , M . ( 2 0 1 1 ) S i m p l e A n a l y t i c s o f t h e G o v e r n m e n t E x p e n d i t u r e M u l t i p l i e r , Am erican E con om ic Journ al: M acroecon om ics, 3 ( 1 ) : 1 –3 5 .
[1 6 4 ]
W o o d f o r d M . a n d J . T a y l o r ( 1 9 9 9 ) H andbook of M acroeconom ics, E l s e v i e r , N o r t h - H o l l a n d .
[ 1 6 5 ] W r e n - L e w i s S . , J . D a r b y, J . I r e l a n d , O . R i c c h i ( 1 9 9 6 ) T h e M a c r o e c o n o m i c E ¤ e c t s o f F i s c a l P o l i c y : L i n k i n g a n E c o n o m e t r i c M o d e l w i t h T h e o r y, E conom ic Journ al, 1 0 6 , 4 3 6 , 5 4 3 - 5 5 9
94
1.7.23
Appendix
1.7.24
Identi…cation of the simultaneous equation model (SEM)
Each equation in the SEM is identi…ed by both order and rank conditions. For instance, with nine exogenous variables in the model including the intercept term the consumption function has only two exogenous variables. It is over identi…ed by order condition, K k > m 1 =) 9 k > 5 1: All other equations similarly satisfy order conditions, which is a necessary but not su¢ cient condition for identi…cation. Each equation is identi…ed by the rank condition when a rank of the coe¢ cients of the matrix of dimension of (M 1) (M 1) order exists for that equation in a model with M endogenous variables. This matrix is formed from the coe¢ cients in the model for both endogenous and exogenous variables excluded from that particular equation but included in other equations of the model. Here the rank condition, (A) > (M 1) (M 1) = 4 is used to …nd out whether a particular equation is identi…ed or not and involves following steps (Bhattarai (2011)): . 1. Write down the system in the tabular form. 2. Strike out all coe¢ cients in the row corresponding to the equation to be identi…ed. 3. Strike out the columns corresponding to non-zero coe¢ cients in that particular equation. 4. Form matrix from the remaining coe¢ cients. It will contain only the coe¢ cients of the variables included in the system but not in the equation under consideration. Table 32: Identi…cation in macro simultaneous equation model of UK const Y C M I R T G X (M M=P ) C
0
T M I R Y
1
1
0
0
0
t0
t1
0
t2
0
0
1
0
m0
m1
0
1
0
m2
m3
0
0
0
1
1
0
0
0
0 b0 b2
0
-
b1 b2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1 b2
0
0
0
0
0
1
0
Yt
1
2
1
1
From these coe¢ cients form all possible A matrices of order (M 1) (M 1) and ascertain that determinant of order (M 1) (M 1) exist for each equation in this system. If at least one of these determinants is non-zero then that equation is identi…ed. Model is identi…ed when all equations are identi…ed. For consumption function: 2 3 t1 t2 0 0 6 1 0 0 0 7 7 ; jAc j = 1 t2 6= 0; (Ac ) = 4: Ac = 6 b2 4 0 5 0 0 1 0 0 0 b2 Tax function: 2 3 1 0 0 0 6 1 7 m2 0 0 7 ; jAT j = 1 m2 6= 0; (AT ) = 4: AT = 6 b2 4 0 5 1 0 1 1 0 0 0 b2 Import function: 95
2
3 1 0 0 0 2 6 0 t3 0 0 0 7 7 ; jAM j = 1 t2 2 6= 0; (AM ) = 4: AM = 6 b2 4 0 1 0 0 - 5 1 0 0 0 0 b2 Investment function: 2 3 0 0 1 1 6 t1 t2 1 0 7 7 ; jAI j = 1 t2 1 + 1 t2 m1 6= 0; (AI ) = 4: AI = 6 b2 b2 4 m1 1 m3 0 5 b1 1 0 0 b2 b2 Interest 2 rate function: 3 1 0 0 0 6 0 t 0 0 7 2 7 ; jAR j = t2 6= 0; (AR ) = 4: AR = 6 4 0 1 1 0 5 0 0 0 Thus each of above equations are identi…ed by order and rank conditions and model is identi…ed. Estimates of the model could be used for policy analysis. 1.7.25
Path of price and exchange rates in the Dornbusch model
First …nd roots for stability analysis using two di¤erential equations: p tr(A) 1 2 ; = tr(A) 4 jAj; tr(A) = (a11 + a22 ) ; jAj = (a11 a22 a12 a21 ) 1 2 2 2 The roots of the equation depend on the behavioral parameters , v and a These values determine the path of price level and the exchange rate consistent to the demand and supply sides of the economy. v v Here A = ; tr(A) = v and jAj = av . 1=a 0 r tr(A) 1 p v 1 v 2 tr(A) 4 jAj = ( v)2 + 4 (A.1) 1; 2 = 2 2 2 2 a p p v v 1 v 1 v 2 2 p(t) = C1 exp( 2 + 2 ( v) +4 a )t +C2 exp( 2 2 ( v) +4 a )t +p (A.2) v
e(t)
2
=
+
1 2
v
+
2
p
p v)2 + 4 av + v v 1 C1 exp( 2 + 2 ( p v 1 p ( v)2 + 4 av + v v 1 2 C2 exp( 2 2 ( v (
As can be seen below when p = 0; p = e + it; when e = 0; p =p =m
by
(u y) v ,
)t
v)2 +4
v a
)t +e
(A.3)
p rises above p = 0 isocline and falls below
ar here e rises and falls.
96
v a
v)2 +4
2
L2: New Keynesian Model: Fundamentals
New Keynesian models have all features of modern macroeconomics. These are a) dynamic models b) have competitive equilibrium c) based on micro-foundation d) have rational expectation. Most new Keynesian models include consumption saving decision in Ramsey type intertemporal dynamics, include leisure/labour supply decisions, have money/bonds as …nancial assets and include nominal rigidities - Calvo type price setting mechanism. By putting nominal and real rigidities in the RBC models the new Keynesian dynamic stochastic general equilibriums (DSGE) are able to generate Keynesian features in otherwise standard RBC models of modern economies.
2.1
New Keynesian Model: a prototype example
New Keynesian business cycle model in which output equal employment Qi = Li
(B.4)
(This example is based on Romer D. (2008) Advanced Macroeconomic Theory, McGraw Hill). Utility is positive from consumption and negative from work: 1
Ui = Ci
Li ;
>1
(B.5)
Consumption equals real income: Ci =
Pi Qi P
(B.6)
In terms of labour input: max Ui =
Pi Qi P
Pi @Ui = @Li P
1
Li
1
Li =
P i Li P
1
Li
Pi P
= 0 =) Li =
(B.7) 1 1
(B.8)
In logs: li =
1 1
(pi
p)
(B.9)
labour supply and production depends on relative price. Demand with shock qi = y + zi
n (pi
mean: q i = y; z i ; pi = p: output y = m Equilibrium supply equals demand: 1 1
(pi
p) ;
n>0
(B.10)
p
p) = y + zi
97
n (pi
p)
(B.11)
Solve for pi 1 1
1
pi + npi = y + zi +
1+n
n
1
1+n
pi = (y + zi ) +
1
1
pi =
1+n
p + np
(B.12)
n
p
1
(y + zi ) + p
n
(B.13) (B.14)
Given Y = 1; devition from the steady state y = 0 =) m = p: Consumer has pro…t and labour income: 1
Ui = Ci
Li =
* qi = y n (pi p) =) Qi = Y Choice variables are Pi and Li :
Pi P
n
n (pi
Pi P
=n
=Y
Pi P
1
n 1 1 P
Pi P
w) Y p
w @Ui = @Li P w P
+ wLi
=
Li
(B.15)
=0
(B.16)
n
nw =) p
Price set by the …rm depends on the markup
Labour supply Li = Qi :
n
Pi P
w) Y
p
Pi P
Pi P
Y @Ui = @Pi
(pi
1
Li
Pi P
n n 1
n
=
n
w 1p
(B.17)
. 1
w P
= 0 =) Li =
1
(B.18)
1
n n
Pi P
w =) 1p
=
n n
1
Y
1
(B.19)
Taking logs pi
p = ln
n n
1
+(
if pi = p =) Y =
1) ln Y = c + y n
1 n
(B.20)
1 1
(B.21)
Y should be 1 but equilibrium output is less than optimal when producers have mark up power n 1 < 1. n If the aggregate demand equals the real money balances, then Y = M P then price level os proportional to stock of money and inversly related to the market power of the …rm: as
P =
M = Y
98
M n 1 n
1 1
(B.22)
2.2
Two Period Model of Stabilisation: Mankiw and Weinzierl (2011)
This is a basic new Keynesian monetary model in which consumers and producers have horizon of two periods. It explores analysis of …scal and monetary policy under …xed and ‡exible price set up. It is simple analytically tractable and easier to compute policy scenarios. Representative households maximise utility subject to intertemporal budget constraint as: M ax
U = fu (C1 ) + v (G1 )g +
fu (C2 ) + v (Gv )g
(B.23)
Subject to the intertemporal budget constraint: P1 [
1
T1
P2 [
C1 ] +
T2 1 + i1
2
C2 ]
=0
(B.24)
Representative …rms maximise pro…t subject to technology constraint as: max P1
1
+
P2 2 1 + i1
(B.25)
subject to 1
= Y1
I1 ; K2 = I1 given K1
Yt = At Kt ;
(B.26)
At > 0
Money: M t = P t Ct ; M t = A high implies high velocity of money and Fiscal policy:
Mt
= Pt Ct
! 0 implies a cashless economy.
gt =
Gt At Kt
and the government budget constraint: P1 [T1
G1 ] +
P2 [T2 C2 ] =0 1 + i1
(B.27)
Macrobalance: Yt = Ct + It + Gt Demand is less or equal to the capacity: Yt
At Kt
max P1 (A1 K1
K2 ) +
Firms problem can be restated as:
99
P2 A2 K2 1 + i1
(B.28)
Firm chooses capital stock for period two K2 to maximise pro…t: P1 +
P2 A2 = 0 =) 1 + i1
(1 + i) =
P2 P1
(B.29)
Lagrangian for the household problem:
L = fu (C1 ) + v (G1 )g +
fu (C2 ) + v (Gv )g +
P1 [
T1
1
C1 ] +
P2 [
T2 1 + i1
2
C2 ]
(B.30)
Consumer chooses C1 and C2 to maximise consumption (FOC): u0 (C1 ) u0 (C2 )
P1 = 0 P2 =0 1 + i1
u0 (C1 ) P1 = (1 + i) u0 (C2 ) P2
(B.31)
Market clearing: Y1 = C1 + I1 + G1 = A1 K1 Y2 = C2 + G2 = A2 K2 C1 = A1 K1 Solve C1 , C2 , K2 and
P2 P1
I1
G1 ;
C2 = A2 K2
G2
(B.32)
by using (B.29), (B.31) and (B.32). C
1
1
1
2 Now specialise the utility function to U (C1 ) = 11 1 and 1) solve for C1 , C2 , K2 and P P1 2) study the impacts of …scal and monetaries policis on allocation under the ‡exible price system 3) show how the …scal and monetary policies a¤ect the economy under the …xed price system. Study the following paper carefully to answer these questions. Mankiw N.G., M. Weinzierl, O. Blanchard and G. Eggertsson (2011) An Exploration of Optimal stabilization Policy [with Comments and Discussion], Brookings Papers on Economic Activity, Spring, 209-272
2.3
A DSGE Model of Macroeconomic Policy in South Asia
Micro-foundations, dynamics and rational expectations, stochastic shocks to preferences, technologies and policies along with the nominal and real rigidities underpin the business cycle analyses in DSGE models. Analysis of short or long run multipliers, variance decompositions and impulse responses to changes in policies and shocks on the deviations of model variables from the steady state is often the focus of such analysis. Computations have become easier for such models after development of Sim’s BVAR algorithm in the MATLAB and dynare.
100
Let us consider a DSGE model of growth in India (I) and neighbouring (n) countries. We consider stochastic shocks eg_I;t and eg_n;t for growth in two countries as a function of relative prices, exchange rates, trade balance and relative interes trates: gI;t = b0 + b1 gn;t =
0
+
1
pI;t pn;t
+ b2
eI;t en;t
+ b3
iI;t in;t
+ b4
pn;t pI;t
+
en;t eI;t
+
in;t iI;t
+
2
3
T BI;t T Bn;t
4
T Bn;t T BI;t
+ eg_I;t + eg_n;t
(B.33) (B.34)
Adjustment in the relative price lags by one period pI;t pn;t eI;t en;t
=
=
p
(gn;t
r
iI;t in;t
gI;t ) +
pI;t pn;t
Global growth rate is gt = gI;t + gn;t Relative interest rate responds to the global iI;t in;t
=
pI;t pn;t
+ gt
We apply the Metropolis-hasting algorithm of the Bayesian VAR methodology (in dynare 4) to compute this BVAR DSGE with the quarterly dataset for advanced and emerging economies (based on Bhattarai and Mallick (2014)). Initial values of parameters are assinged to simulate the model as in Table
Param eters
b0
Va lu e s
0 .0 1
Table 33: Parameters of the DSGE Model b1 b2 b3 b4 1 0 1 2 0 .3
0 .4
0 .5
0 .0 3
0 .4
0 .1
0 .3
0 .6
3 0 .2
4 0 .0 3
DSGE model of growth in India and neighbouring SAARC countries: priors
101
2 0 .8
b va r_ d c a d v _ d s g e _ In d ia _ P rio rs 1 .e p s S E _eg_a
P rio rs a n d p o ste rio rs
S E _eg_d
150
SE_eg_I
b1
80
4
60
3
40
2
20
1
SE_eg_n
b1 4
100 50 0
0
0.02
0.04
0.06
0
0
0.1
g2 4
3
3
2
2
1 0
0.5
0
-0.5
0
0.5 1 1.5 2 2.5
0.5
0
0.05
g2
6
4
4
2
2
0 -1
1
0
0 -0.8-0.6-0.4-0.2 0 0.2
0.1
b3
rho1
rho1
1 0
-0.5
b3
4
50 2
0 -1
0.2
100
0
0
0.5
5 10
0 0
0.5
0 -0.6
0.2 0.4 0.6 0.8 1
-0.4
-0.2
0
0
0 0.2 0.4 0.6 0.8
rho2
1
rho2
4
6
2
4
0
2 0 0.5
1
0.4 0.6 0.8 1 1.2 1.4
1.5
DSGE model of growth in India and SAARC countries: shocks b va r_ d c a d v _ d s g e _ In d ia _ S m o o th e d S h o ck s 1 .e p s
b va r_ d c a d v _ d s g e _ In d ia _ H is to ric a lA n d S m o o th e d Va ria b le s 1 .e p s
eg_a
g_a
15
15
10
10
5
5 0
0
-5
-5
-10
20
40
60
-4
1.5
80
100
20
120
40
60
eg_d
x 10
80
100
120
80
100
120
g_d 10
1
8
0.5
6
0
4 2
-0.5 -1
0
-1.5
-2
-2
-4 20
40
60
80
100
20
120
40
60
DSGE model of growth in India and SAARC countries: Impulses b va r_ d c a d v _ d s g e _ In d ia _ IR F _ e g _ I.e p s
b va r_ d c a d v _ d s g e _ In d ia _ IR F _ e g _ n -3
0
g_ a
g_I
x 10
1.4 1.2
-2
1
-4
0.8 0.6
-6
0.4
-8
0.2 0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
10
6
7
8
9
10
10
g_n 0.01
g_ d 0
-0.5
0.005
-1
-1.5
-2
0 1
2
3
4
5
6
7
8
9
1
2
3
4
5
10
DSGE model of growth in India and SAARC countries: estimation of time varying parameters
102
b va r_ d c a d v _ d s g e _ In d ia _ u d ia g 1 .e p s
b va r_ d c a d v _ d s g e _ In d ia _ u d ia g 2 .e p s -3
g2 (Interv al) SE_ e g _ a (In te rv a l )
SE_ e g _ a (m 2 )
0 .7 0 .6 0 .5
0.26
SE_ e g _ a (m 3 )
0 .0 6 0 .0 5
0 .0 2
0 .0 4
0 .0 1 5
0 .0 3
0 .0 1
0.24 0.22
SE_ e g _ d (In te rv a l ) 6
-4 x 1 0 SE_ e g _ d (m 2 )
1 .5
0 .0 4
4
1
0 .0 2
2
0 .5
0 1000 2000 3000 4000 5000
0 1000 2000 3000 4000 5000 -3
b 1 (In te rv a l ) 0 .3
12
0 .2 8
-3
g2 (m 2)
x 10
1.6
x 10
8
1.2
x 10
g2 (m 3)
1
6 1000 2000 3000 4000 5000 -4
0.05 5
4.5
0.8 1000 2000 3000 4000 5000 -5
b3 (m 2)
x 10
1.5
3.5 0.04 5
x 10
b3 (m 3)
1
3
0.04 1000 2000 3000 4000 5000
1000 2000 3000 4000 5000 -3
rho1 (In terv al )
b 1 (m 3 )
x 10
4
0.05
-3
2
1.4
b3 (Interv al)
-5 x 1 0 SE_ e g _ d (m 3 )
0 1000 2000 3000 4000 5000
b 1 (m 2 )
9
7
0.2 1000 2000 3000 4000 5000
0 .4 0 .0 2 0 .0 0 5 1000 2000 3000 4000 5000 1000 2000 3000 4000 5000 1000 2000 3000 4000 5000 0 .0 6
10
0 .0 2 5
x 10
0.5 1000 2000 3000 4000 5000 -3
rho1 (m 2)
0.35
12
0.3
10
2
0.25
8
1
0.2
6
0.5
x 10
rho1 (m 3)
1.5
10
0 .2 6
1 .5 8
0 .2 4 0 .2 2 1000 2000 3000 4000 5000
6 1000 2000 3000 4000 5000
1 1000 2000 3000 4000 5000
1000 2000 3000 4000 5000
4 1000 2000 3000 4000 5000
0 1000 2000 3000 4000 5000
DSGE model of growth in India and SAARC countries: historical and smoothed variables b va r_ d c a d v _ d s g e _ In d ia _ H is to ric a lA n d S m o o th e d Va ria b le s 1 .e p s
b va r_ d c a d v _ d s g e _ In d ia _ S m o o th e d S h o ck s 1 .e p s eg_I
g_a
10
15
5 10
0 5
-5 0
-10 -5
20
40
60
80
100
20
40
60
80
100
120
80
100
120
120 -4
2
g_d
eg_n
x 10
10 5
0
0 -5
-2
-10 -15
-4
20
-20 -25
20
40
60
80
100
40
60
120
DSGE model of growth in India and SAARC countries : variance decomposition Va ria n c e d e c o m p o sitio n r
Va ria n c e d e c o m p o sitio n g t
15 10
10
Initial values
5
5 Initial values
0
0
-5
-5
eg_n -10 -15
-15
-20 -25
eg_d
-10
-20
eg_I
0
20
40
60
80
100
120
eg_a -25
140
0
20
40
60
80
100
120
140
see data and code for the South Asia model. Study MATLAB programme DSGEM.m with chapter2_netfun.m. This is based on Lim G. C. and McNelis (2008), Computational Macroeconomics for the Open Economy, MIT Press.
103
2.4
A Prototype of New Keynesian DSGE model with habit formation
The new Keynesian models introduce nominal and real frictions in the standard RBC models. Real frictions can be habit formation in consumption or cost of investment or …scal or monetary policy rules. Nominal frictions occur through price and wage rigidities. Habit formation h (for a represenative houshold and …rm case) is in the form of:
Uth here
=U
t
Cth ; lth
=
h (Ct
(1 1)
hCt
)
(1
1
Lt )
c
i1
c
1 (B.35)
is the preference shock h Uc;t =
t
(1
h UL;t =
) (Ct
t
(Ct
hCt 1 ) (Ct hCt
(1
)(1
Ct
(1 1)
Euler equation (with nominal interest rate,Rt " h Uc;t
1
(1
Lt )
(
(
1) 1
c
1)
1)
)(1
(1
c)
c)
(1
Lt )
c
Lt )
1)
:
Rt
=
t
1 h Uc;t
#
Marginal rate of substitution: h UL;t h Uc;t
=
Wt Pt
Stochastic discount factor: t
h Uc;t h UL;t 1
=
!
wholesale retail sector relation: Yt =
c) YtW
(1
(B.36)
t
Price dispersion: t
=
t 1
+ (1
)
Whole sale production function: YtW =
(At Lt ) Kt1 t
FOC for the labour market:
104
1
J H
PtW YtW Wt = Lt Pt Yt = Ct + It + Gt Kt = where
t
t It
(1
(B.37)
2
(Xt
1) + (1
) Kt
(B.38)
1
is the investment shock. z1t = 2:0 Qt
t
(1
x Xt
2 x ) (Xt 1 )
z2t =
(1
2
(Xt ) Qt
2:0
x Xt
t
(Xt
1)
) PtW YtW + (1 Kt 1 Rt
=
t+1
(B.39)
t
+ z1t+1 = 1
) Qt
z2t+1 Qt
Budget of the government: Gt =
w Wt Lt
Real interest rate rt =
Rt t
Then in‡ation dynamics: h e t+1 = Yt UL;t H
Ht Jt
Jet+1 = (1= (1
et Taylor rule:
1
h )) Yt UC;t mc; mc = PtW = 1
e t+1 = e(t H
1)
Ht
Jet+1 = et Jt
+ (1
et =
Jt Ht
)
t t 1
105
(1
)
=1
1
ln
Rt Rt 1
=
r
ln
Rt 1 R
+ (1
r)
t
ln
+ (1
r)
y
ln
Yt Y
+
m
Processes of shocks to technology, public spending, preference and investment: log At
log At =
A (log At 1
log At ) +
A t
log Gt
log Gt =
G (log Gt 1
log Gt ) +
G t
log
t
log
t
=
(log
t 1
log
t
t
log
t
=
(log
t 1
log
log
Variables in the deviation form: t ; it = yt = YYt ; kt = K K
It I
; ct =
(1
)
Ct C
; wpt =
t)
t)
+
+
t
W Pt WP
; lt =
Lt L
; rrt =
rt r
;
Rt = RRt : Steady state ratios iy =
1
; iy = 1
iy
gy
1+
A typical parameterisation Parameters gy c h c x values 0.2 0.7 0.7 7.0 1/ 0.9871 0.025 2 2 .75 0:7 0.5 Parameters on Taylor rule and persistency of shocks Parameters Ass r y r y I Values 0.7 1.5 0.3 1 0.7 0.7 0.7 0.7 Model is computed in the dynare. The impulse responses to technology, investment, public spending and preference shocks presented in the following diagrams. Literature Wickens M. (2012) Macroeconomic Theory: A Dynamic General Equilibrium Approach, 2nd edition,Princeton University Press. Levine P, J. Pearlman, G. Perendia and B Yang (2013) Endogenous persistence in an estimated DSGE model under imperfect information, Economic Journal, 122 (December), 1287–1312.
Practical work: More extensieve literature on this topic can be found on the web http://economics.sas.upenn.edu/~schorf/research.htm. NK_hab.mod RBCInvcost.mod and RBCSummer.mod.which includes habit formation A simple model from the CIMS Univeristy of Surrey.
106
Figure 5: A1
107
108
109
2.4.1
Blanchard and Gali (2013)
Blanchard and Fisher (1990) and Blanchard and Gali (2013) consider provide a more extensive version of the new Keynesian model as: Problem of Households i "( 1 ) # X Mit+k+1 k Q (Nit+k ) = t max E U (Cit+k ) + V (B.40) P t+k t=0 Subject to:
Cit =
Z
1
0
and the budget constraint Z
1
1
Cijt dj
;
Pt =
Z
1
0
1 Pjt
1
dj
1
(B.41)
L
Pjt Cijt + Mit+1 + Bit+1 = Wt Nit + (1 + it ) Bit + Mit +
it
+ Xit
(B.42)
0
Cit+k is consumption, Mit+k money, Nit+k labour supply P t aggregate price, Pjt price of sector j , Bit+1 bonds, it pro…t from …rms Xit public transfer. First order conditions of household optimisation Pjt Pt
Cijt =
Cit
(B.43)
U 0 (Cit ) = E [f (1 + rt+1 ) U 0 (Cit+1 )g = V0
Mit+1 0 =U (Cit ) Pt
=
t]
(B.44)
it+1 1 + it+1
(B.45)
Wt 0 U (Cit ) = Q0 (Nit ) Pt
(B.46)
Firms’problem assuming a linear production technology Yjt = Zt Njt Pjt Pt
Cijt =
(B.47)
Cit
(B.48)
Firms take wage rates as given and set prices a la Calvo with probability of changing it every period. Then Yjt is solution to the …rms pro…t mamimization problem max E
kU
0
(Ct+1 ) (1 U 0 (Ct )
k
)
Pjt Yjt+k Pt
Subject to:
110
Wt+K Yjt+k P t+1 Zt+1
=
t
(B.49)
Pjt Pt
Yjt+k =
Yt+1
(B.50)
FOC of …rm implies E Pjt = Pt =
1
hX
t+k = A (k) W Zt+1 hkX i E A (k) = t
t
i
(B.51)
k
kU
0
(Ct+1 ) (1 U 0 (Ct )
A (k) =
k
1
) P t+k Yt+k
(B.52)
Aggregate price level is CES of prices of t and t-1 with probability h P t = (1
1
)Pt
1
1
+ Pt
i11
(B.53)
General equilibrium implies clearing of goods, labour and money markets Cit = Ct ; Nt = Mit = Mt ; Above equations now give the IS and LM curves as: IS: demand for goods depends on expected future income and the real interest rate U 0 (Yt ) = E [f (1 + rt+1 ) U 0 (Yt+1 )g =
t]
Yt Zt ;
(B.54)
LM: the …nancial market determines the equilibrium interest rate V0
Mit+1 Pt
=U 0 (Cit ) =
it+1 1 + it+1
(B.55)
LS: Real wage is determined by the marginal productivity of labour Wt 0 U (Cit ) = Q0 Pt
Yt Zt
= Q0 (Nt )
(B.56)
Price settings E Pjt = Pt =
1
hX
t+k = A (k) W Zt+1 k hX i E A (k) = t
t
i
(B.57)
k
A (k) =
kU
0
(Ct+1 ) (1 U 0 (Ct )
k
1
) P t+k Yt+k
(B.58)
Aggregate price level is CES of prices of t and t-1 with probability h P t = (1
1
)Pt
Derivation of market clearing wage rate Production function: Nt =
1
1
+ Pt
Yit Zt
111
i11
(B.59)
(B.60)
When there are no nominal rigidities Wt 1 Zt
Pt =
(B.61)
Yt Q0 Z Wt t = = 0 U (Yt ) Pt
1
Zt
(B.62)
This can implicitly determine the output as a result of technological shocks. Y Q0 ( t ) In a logarithmic utility function U 0 (YZtt ) = 1 Zt implies Q0
Yt Zt
Yt = Q0 Zt
Yt Zt
Nt =
1
(B.63)
Employment remains constant function of the elasticity of markets. Output varies one to one with Zt : Q0
Yt Zt
Yt =
1
Zt
(B.64)
Current output (deviation from the steady state) is just a function of the shock. The RBC model also generates the same result, only di¤erence is that RBC model has technological shock (See Blanchard and Fisher (1990) Lectures on Macroeconomics, MIT Press). 2.4.2
Solution Procedure in the DSGE Models
Most DSGE models are solved using the log-linearization procedure discussed in Campbell (1994) and Uhlig (1995). Deviation of actual capital (Kt ) from steady state capital (K) equals: ^ t = ln Kt K
ln K
(B.65)
where K without subscript t denote steady state value; Kt with subscript t is the actual value ^ t with subscript t and hat above denote log deviations of particular variable of capital at time t; K from steady state. ^t ln Kt = ln K + K (B.66) Taking out log both sides one gets: ^
^
eln Kt = eln K+Kt = eln K eKt
(B.67)
Thus: ^
^
Kt = KeKt ) eKt =
Kt K
(B.68) ^
Next step is to take the …rst order Taylor approximation of eKt around the steady state thus ^ t = 0, though we get: K ^
^t eKt = e0 + e0 (K thus: 112
^t 0) = 1 + K
(B.69)
^t = 1+K
Kt ^ t) ) Kt = K(1 + K K
(B.70)
^ t = Kt K
(B.71)
or: K K
^ t multiplied by 100 informs by what percentage capital at time t diverges from The variable K ^ t is equal 0:2 we interpret that capital is 20% above the steady the steady state. So for example if K state. Apply this method to all equations to log-linearize a model. Then log-linearized system is solved by means of Method of Undetermined Coe¢ cients (Uhlig 1995). In order to do so, log-linearized system has to be transformed to the following form: 0 = Et [F F xt+1 + GGxt + HHxt z(t+1) = N N z +
t+1 ; and
1
+ LLzt+1 + M M zt ]
Et [
(t+1) ]
= 0;
(B.72) (B.73)
Using method of undetermined coe¢ cients the following recursive law of motion is estimated: xt = P xt
1
+ Qzt
(B.74)
so that the equilibrium solution is stable. Following Uhlig (1995) matrix P satis…es the following equation: 0 = F F P 2 + GGP + HH
(B.75)
Subsequently denoting V as: V = NN0
F F + Ik
(F F P + G)
(B.76)
Q can be obtained from VQ=
vec (LLN N + M M )
(B.77)
where ’vec’denotes vectorization. Quadratic equation is solved as proposed by Uhlig (1995). Read Uhlig, H. (1995). A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily. 2.4.3
Basics of Bhattarai and Trzeciakiewicz (2012) DSGE model
DSGE models are used by the New Keynesian (NK) macroeconomists in analysing and explaining causes and consequences business cycles and to assess the role of policy instruments used for stabilising ‡uctuations in macro variables. While the micro-foundations to the macro model and inter-temporal optimisation of households and …rms, and shocks to technology, preferences and …scal policy instruments are similar to those in the real business cycle models in tradition of Kydland and Prescott (1992), the NK models show important roles that economic policies play in containing such ‡uctuations. They integrate nominal rigidities in prices and real rigidities in institutional setup such of Calvo (1993), Rankin (1992), Mankiw (2000) or Campbell Mankiw(2003), to generate Keynesian features of …scal and monetary policies on output, employment and prices. Starting from
113
DSGE exercises of Smets and Wouters (2003), Christiano, Eichenbaum and Evans (2005) and Iacoveillo (2005), these models have become increasingly popular in analysing causes of volatilities in prices and output particularly among the Federal Reserve System in the US, the Bank of England, the European Central Bank, the IMF and other central banks around the world. Many studies based on DSGE models have appeared in the literature in recent years. The new Keynesian DSGE models became more popular after the 2008 crisis as these models could justify large …scal stimulus and credit or quantitative easing (QE) by accommodating nominal and real rigidities in the economic system (Benati (2008), Zanetti (2010), Blanchard and Galí (2012), Levine, Pearlman,Perendia and Yang (2012)). These models are applied also to analyse consequences of search and matching frictions in the labour market, frictions in the …nancial and commodity markets (Blanchard and Gali (2013), Faccini, Millard and Zanetti (2013)). These have also been extended to study open economic issues From policy perspective most of the DSGE models have focused on how monetary policy could be designed to mitigate the consequences of rigidity on wages and prices (Ascari and Rankin (2013)). Very few studies were designed to evaluate the role of …scal policy in the business cycle ). This thesis aims to contribute this lacuna in the literature by introducing a structure of …scal policy rules to enrich existing DSGE models. It also contains a simple form of the monetary policy rule appropriate to study interaction between the …scal and monetary policies ((Blake and Weale (1998), Bouakez and Rebei (2007), Mirrlees et al. (2010), Woodford (2011), Coenen, Straub and Trabandt (2013), Coenen, Erceg, Freedman, Furceri, Kumhof, Lalonde, Laxton, Linde, Mourougane, Muir, Mursula, de Resende, Roberts, Roeger, Snudden,Trabandt and in’t Veld (2012)). While the dynamic general equilibrium models aim to …nd out the dynamically e¢ cient and equitable paths for the allocation of resources in an economy, the DSGE models focus mainly on measuring the short and long run multipliers and impulse responses of various shocks in the economy. They show the pattern of deviations macroeconomic variables from the steady state originating from stochastic shocks in preferences, technology or the policy instruments. Results from these models have short run rather than long-run focus. These models are computationally intensive as they have rich Bayesian statespace for model parameters generated from the application of Metropolis-Hastings algorithm (Gibbs sampling) in traditions of Sims (1980) or Doan, Litterman, and Sims (1984; see also Collard and Juillard (2001)). This is a DSGE model with two types of households with and without the borrowing constraints. Households and …rms solve inter-temporal optimisation problems subject to those constraints. Model constains all …rst order conditions requited for optimisation of economic agents, the revenue and spending structure of the government, a set of …scal policy rules and a monetary policy rule. It discusses calibration and computation procedure. The model is applied in order to assess the present value multipliers of six tax instruments (taxes on consumption, labour and capital income, transfer, public consumption and investment). Then it shows impulse responses to other …ve structural shocks. It provides some discussions on the Metropolis-Hestings algorithm (as given below). Application of DSGE model in computing multipliers, variance decompositions and impulse responses of …scal policy instruments in the context of the UK economy is speci…c to this model as Batini, Harrison and Millard (2003) Harrison and Oomen (2010) to Faccini, Millard and Zanetti (2013), Krause and Lubik (2007), Zanetti (2010), Woodford (2011), Ravn, Schmitt-Grohé and Uribe (2012), Levine, Pearlman, Perendia and Yang (2012) have not considered the analysis of …scal policy explicitly in this manner. Early version of this paper is avialable at http://www.hull.ac.uk/php/ecskrb/Confer/Dawid_May_2012.pdf.
114
2.4.4
Household problem
Households maximize utility subject to the ‡ow budget constraint, capital accumulation function and the demand for labour they faced from labour unions. Lagrangian takes the following form:
L
where:
t
=
X "B t
(Ct
t
hCt 1
t=0
+
t
+
k t
Rt
1 bt t
(1
1
1)
1
"L t 1+
c
c
+ 1 a(! t )Kt
))Kt
1
Lc;t
L
l t
k t
wt Lt + 1 bt 1 + divt + tt
+ 1
"It It It 1
S k t
denotes marginal utility of income;
It
1+
L
!
rk;t ! t Kt It Ct
1
!
(B.78)
Kt
stands for the shadow price of capital; and
Wt Wt
Lt = Nt . The wages are set to balance the productivity marginal utility from work and disutility of working as: ( ) 1 X ~ t Xtl W Ul;t+l l ( $W ) Lt+l t+l =0 (B.79) l Pt+l (1 ) Uc;t+l 1 t+l l=0 When wages are ‡exile i.e. when all households are able to negotiate their wages each period, ~t Ul;t $W = 0, wage then becomes: W l : Pt = ( 1) Uc;t (1 t) Index of wages is given by: 1
Wt = (1
1
~t $W ) W
+ $W (
Pc;t Pc;t
1
w
1
Wt
1 1)
(B.80)
2
Final goods are produced using di¤erentiated intermediate goods: Yt = in new Keynesian supply function Pt {{ 1 Yt ) Yj;t = ( Pj;t
hR 1 0
1 { Y;j;t dj
i{
. It results (B.81)
These intermedate goods are used using private and public capital and labour as: Yj;t = At (! t Kj;t
1)
1 G Nj;t Kj;t
(B.82)
1
where K G is the public capital, and At is a total factor productivity shock and follows a …rstA order autoregressive process: ln At = ln At 1 + A N 0; 2A : The …rst order t , where t conditions yield to: Kj;t = Nj;t (1
Wt ) ! t Rk;t
(B.83)
Nominal marginal costs become: Pt mct = (
1 1
)1
1 ( ) At 1 Kj;t 115
1 (Wt )
G
1
(Rk;t )
(B.84)
Marginal cost increases as wages and return on capital increase. Higher amount of government’s capital along with positive TFP shock along with an increase in public capital will lead to a decrease in marginal costs. 1 { R 1 1 1{ is derived dj Calvo(1983) pricing rules apply to this economy the priceindex Pt = 0 Pj;t as: "
1
1
b $) P t
Pt = (1
1
Pt Pt
{
+$
p
1
1
Pt
1
2
{
#1
{
(B.85)
This economy is subject to the market clearing conditions: Yt
a(! t )Kt
1
= Ct + Gt + It + ItG
R1 Ct = 0 ct d = (1 ) Ctr + Ctnr R1 ) Lrt + Lnr Lt = 0 Lt d = (1 t R1 R1 Kt = 0 Kt d = Ktr It = 0 It d = Itr R1 Bt = 0 Bt d = Btr R1 T Rt = 0 T Rt d 2.4.5
Fiscal and monetary policies
Model evaluates the impact of …scal and monetary policy shocks that a¤ect the government budget constraint: c t Ct
+
l t wt Lt
+
k t rk;t ! t Kt 1
+ bt
trt =
(1 + Rt 1 ) bt 1+ t
1
+ gt + ItG
(B.86)
where b denotes public borrowing, g stands for government spending, and I g stands for government investment. Public capital follows according to the following law of motion: G G k ))Kt 1
KtG = (1
+ ItG
(B.87)
In setting the …scal rules we follow Leeper (2010). Fiscal shocks a¤ect the revenue and spending sides of the government. All shocks follow a …rst-order autoregressive process: ex;t = x ex;t 1 + x;t where x;t N 0; 2x :are i:i:d:- normally distributed errors. Government spending and government investment respond to the output and public borrowing (hats over variables denote deviations from the steady state): ^
g;y Yt 1
^
ig;y Yt 1
g^t =
b;g bt 1
ct = Ig
b;ig bt 1
^
+ eg;t
^
+ eig;t
(B.88) (B.89)
Tax rates respond positively to the debt to output ratio: ^ct =
b;
c
^bt
1
+
y;
116
c
Y^t
1
+e
c ;t
(B.90)
^lt =
b;
^kt =
b;
l
^bt
1
+
y;
l
k
^bt
1
+
y;
k
Y^t
1
+e
l ;t
(B.91)
Y^t
1
+e
k ;t
(B.92)
Finally transfers in this model are de…ned as lump sum taxes minus transfers. Transfers respond to the output public debt and hours worked: ^
bt = tr
^
b;tr bt 1
^ + etr;t
y;tr Yt 1
l;tr Lt
(B.93)
Nominal interest rate follows a Taylor rule version given by: ^t = R ^t R where 2.4.6
m t
2 m
N 0;
1
+ (1
)
^
^t +
y Yt
m t
+
is an i:i:d:- normally distributed error.
Log-Linearised System of Equations
This model is solved by a log-linearised system of equations. The capital letters without subscript t denote the steady state values, whereas a hat over a variable denotes its log-deviations from the steady state. 2.4.7
Households: ^ ^ ^t = Et Ct+1 + hC t 1 C 1+h 1+h
^t= Q
^ t +Et ^ t+1 + R
1
1 + (1
k) r
u ^t =
w ^t
1+
c
k
1
"
k
r^k;t
wL (1 + c ) Cnr
=
1
k
^ )K t
1+
l
1
w
1+
^t
1
l
^lt
^kt
k
^"It+1
k
r^k;t+1
117
1
k
^kt+1
c
^ct
^"It
#
I^t +
c TR d T Rt c (1 + ) Cnr 1+
1+ w 1 w ^t 1 + Et ^ t+1 ^t 1+ 1+ 1+ $w ) (1 $w ) 1 (1 (Xtw +"w t ) (1+& w ) l 1+ w 1+ & w $
Et w ^t+1 +
1+ +
^t w ^ t +L
(^ct Et ^ct+1 ) +^"B "B t+1 ^ t
^ +rk 1 )Q t+1
Et (1
^ t = (1 K l
^ t+1 +
^t I^t 1 E t I^t+1 1 Q + + + Et (1 + ) 1 + 1+ 1+
I^t =
^nr;t = 1 C
c
1 1 h Et Rt c 1+h
1
^
Xtw = w ^t
l Lt
1
l
^t bC ^t C
b
1
c
^ c;t = ^ t +
2.4.8
Firms:
h ^ Y^t = 'y ^"A t + Kt
1+
c
1+ (^ct ^ct
^t=
2.4.9
1+
Et ^ t+1 + p
p
^t
1+
(1
p
c CT
Y
^ T;t + ^ct +C
^ rev;t = R b G Y
^t R
1
l wL
Y
^ g;t = (1 K
1
c t
^ g Kg;t
1
i
^
g Kg;t 1
$) (1 $ 1+
$) p
k rk K
(mc c t +^"pt )
^t ^kt +^ rk;t +^ ut +K
Y
1
b ^ G ^ IG c T R d bt + Gt + IGt + T Rt Y Y Y Y
^ )K g;t
General equilibrium conditions:
1+
ct IG
CT ^ I G ^ IG c Y^t = CT;t + I^t + G IGt +(1 t+ Y Y Y Y CT C^T;t = (1
c
1+
w ^t
^t + ^lt +w ^ t +L
^ t +^bt
c
1)
Government: ^ rev;t = G
2.4.10
1
)w ^t + r^t ^"A t
1+
^lt +^"L t
^t+ )L
^t + (1 1+ u
^t= u ^t L ^t +^ r t +K mc c t = (1
l
k
)
rk K u ^t Y
) C C^ t + C nr C^nr;t
The above equations plus the equations specifying …scal and monetary policy in the text above (which are already in the log-linear form) comprise the system of equations which is subsequently solved and estimated using Dynare routine for a DSGE model. 2.4.11
Parameterisation of the model
Parameters of this model are calibrated from the time series data as follows:
118
Table 34: Steady state ratios and calibrated parameters Discount factor 0.990 Private capital depreciation rate
0.025
Puplic capital depreciation rate
0.020
Share of capital in production function
0.31
Steady-state wage markup parameter
0.15
Capital tax rate
40.71%
Labour tax rate
28.44%
Consumption tax rate
20.08%
Transfer to GDP ratio
0.14
Private investment to GDP ratio
0.15
Private consumption to GDP ratio
0.63
Gov. consumption to GDP ratio
0.20
Gov. investment to GDP ratio
0.02
Gross nominal interest rate
1.0101
Return on capital
0.0518
Gov. debt to GDP ratio
0.6
Note on Bayesian Estimation Applied in this Model The Bayesian VAR became popular after seminal works of Sim (1980) and Doan, Litterman and Sims (1984). In the context of DSGE models the Bayesian estimation can be perceived as a combination of maximum likelihood estimation and calibration. Calibration because of presence of priors, which comprise weights on likelihood function so more importance is given to particular areas in parameters subspace. According to An and Schorfeide (2007), Smets and Wouters (2003) and Mancini (2010) …rst the prior probability distribution is denoted by p ( ), where denotes parameters of the model and p ( ) stands for probability distribution function, likelihood function as L jY T ; where Y T denotes the complete sample of data, and …nally p jY T , as a posterior distribution. Secondly the likelihood T Q can be formulated as: L jY T = p Y T j = p (Y0 j ) p (Yt jYt 1 ; ). Finally the Bayes’theorem t=1
is used in order to get posterior, p jY T , which can be derived from the de…nition of conditional probability: p( ;Y T ) p( ;Y T ) p Y T j = p( ) ; p jY T = p(Y T ) ; ) p ; Y T = p jY T p Y T Thus: p jY T = p(Y T j )p( ) . p(Y T ) Since p Y T is constant, Bayes’ theorem can be written as: p jY T / p Y T j p ( ) | jY T where p Y T j stands for maximum function and p ( ) stands for prior probability distributions, and | jY T stands for posterior kernel. Likelihood function is estimated with help of 119
the Kalman …lter. Estimation of Likelihood Function of the Model The state space representation of the solution to the model can be rewritten in the following way: x ^t+1 = A^ xt + Bvt+1 y^t = C x ^t + wt where …rst equation is the equation comprising the solution of the model (measurement equation) and the second equation is the observation equation (transition equation) i.e. y^ is an observable variable, and wt is an measurement error. Hats over variables denote that the solution is in the deviation from the steady state form in case of model solution, and in case of observable variable 0 vt vt Q V it means that data are detrended by a linear trend. Moreover, E = , vt wt wt V R and wt are uncorrelated and orthogonal to yt . Kalman …lter recursion is the following: b y~t+1 = y^t+1
Et x ^t+1 = AEt
CEt x ^t+1 ^t 1x
+ Kt b y~t
Kt = (APt C 0 + BV ) (CPt C 0 + R) Pt+1 = APt A0 + BQB 0
1
0
Kt (APt C 0 + BV )
Subsequently from the Kalman …lter recursion log-likelihood is derived. With the assumption of 0 b y~t b y~t 1 exp normal distribution which has the probability distribution function: p (Yt j ) = p (CPt C 0 +R) ; 0 2 (CPt C +R)
the log-likelihood is given by: L
jY T =
T ln (2 ) 2
T h X
(CPt C 0 + R)
t=1
0 b y~b y~ (CPt C 0 + R)
1
i
(B.94)
The log posterior kernel then becomes: ln | jY T = ln L jY T + ln p ( ). Subsequently, maximizing the above log posterior kernel with respect to the mode of the posterior distribution is found. Derivation of the Posterior Distribution At this stage only the mode of posterior distribution is known. In order to simulate posterior distribution a particular version of Markov Chain Monte Carlo (MCMC) algorithm i.e. Metropolis algorithm is employed and involves follwoing steps: 1. Choose a starting point - posterior mode. P P 2. Draw from the distribution f j i = N i ; c m , where m is the inverse of the Hessian matrix computed at the mode of the posterior distribution. is a candidate for i+1 with the probability of q i+1 j i , and i is a candidate for i+1 with probability of p( ;Y T ) p( ;Y T ) 1 q i+1 j i , where q i+1 j i = min 1; p i ;Y T , where p i ;Y T is an acceptance ratio. ( ) ( ) 120
3. Accept, or discard the proposed
:
4. Update mean of the drawing distribution, retain value of the parameter. 5. Repeat steps 2,3, and 4 for a chosen number of times. 6. Plot histogram of the retained values. According to An and Schorfeide (2007), Smets and Wouters (2003) and Mancini (2010) the Bayesian estimation process involves search through the space of using appropriate size of steps. This is why the variance of and in particular the scaling parameter are of special interest. Increase in the scaling parameter will cause acceptance rate to decrease and decrease in it will that to increase. In case of too high acceptance ratio the Metropolis algorithm would never visit the tails of the distribution and in case of too low acceptance ratio it would take long time to converge since it can easily get stuck in the local subspaces. Literature proposes acceptance ratio in a range of 0.2-0.4 (Roberts, Gelman and Gilks (1997) get an optimal acceptance rate of 0.234). 2.4.12
Results of Hull DSGE model
Results of this Bayesian DSGE model for UK is calibrated to quarterly timeseries data of the UK economy. It generates interesting results on multipliers. Impact investment shocks output multiplier of 0.96 that of government spending is 0.8225. Increase in consumption tax has long run multiplier -0.8277. Model also is applied to compute the imulse responses to 11 di¤erent shocks in the model. Table 35: Prior and posterior distributions of estimated parameters P rio r d istrib u t
E st m a x p o ste rio r
P o ste rio r d istrib u tio n M H
P a r a m e t e r ’s n a m e
ty p e
m ean
st. error
m ode
st. error
m ean
5%
95%
p ro d u c tiv ity s h o ck
inv _ g
0 .0 1
0 .0 1
0 .0 0 7 8
0 .0 0 0 6
0 .0 0 8 0
0 .0 0 6 9
0 .0 0 9 0
p referen ces sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 0 4 8
0 .0 0 1 4
0 .0 0 6 5
0 .0 0 3 2
0 .0 0 9 8
w a g e m a rk u p sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 0 3 2
0 .0 0 0 3
0 .0 0 3 2
0 .0 0 2 7
0 .0 0 3 6
p ric e m a rk u p sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 0 8 0
0 .0 0 0 8
0 .0 0 8 0
0 .0 0 6 8
0 .0 0 9 2
c o n su m p tio n ta x sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 3 2 9
0 .0 0 2 4
0 .0 3 3 5
0 .0 2 9 6
0 .0 3 7 4
c a p ita l ta x sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 5 1 3
0 .0 0 3 7
0 .0 5 2 4
0 .0 4 6 0
0 .0 5 8 5
la b o u r ta x sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 1 4 9
0 .0 0 1 1
0 .0 1 5 4
0 .0 1 3 5
0 .0 1 7 3
inve stm e nt sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 4 7 1
0 .0 2 0 1
0 .0 9 3 4
0 .0 2 8 6
0 .1 6 1 6
tra n sfers sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 4 8 8
0 .0 0 3 6
0 .0 5 0 2
0 .0 4 3 8
0 .0 5 6 0
g ov . inve stm e nt sh o ck
inv _ g
0 .0 1
0 .0 1
0 .3 0 6 4
0 .0 2 3 3
0 .3 1 2 8
0 .2 7 2 5
0 .3 5 1 6
m o n e ta ry p o lic y sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 0 4 3
0 .0 0 1 0
0 .0 0 4 9
0 .0 0 3 0
0 .0 0 6 7
g ov . c o n su m p tio n sh o ck
inv _ g
0 .0 1
0 .0 1
0 .0 0 9 5
0 .0 0 0 7
0 .0 0 9 8
0 .0 0 8 6
0 .0 1 1 0
A R (1 ) p ro d u c tiv ity s h o ck
b eta
0 .8
0 .1
0 .6 6 2 9
0 .0 8 5 2
0 .6 7 3 6
0 .5 3 7 9
0 .8 1 7 0
A R (1 ) p referen ces sh o ck
b eta
0 .8
0 .1
0 .7 6 3 0
0 .1 0 9 6
0 .7 2 8 9
0 .5 5 5 2
0 .9 0 2 2
121
Table 36: Priors and posteriors of estimated parameters P rio r d istrib u t
E st m a x p o ste rio r
P o ste rio r d istrib u tio n M H m ean
5%
95%
P a r a m e t e r ’s n a m e
ty p e
m ean
st. error
m ode
st. error
A R (1 ) inve stm e nt sh o ck
b eta
0 .8
0 .1
0 .2 7 9 0
0 .0 8 0 8
0 .2 9 1 5
0 .1 6 6 4
0 .4 0 9 4
A R (1 ) n o m . inte re st ra te
b eta
0 .8
0 .1
0 .6 1 8 4
0 .0 7 5 5
0 .6 0 0 4
0 .4 6 4 1
0 .7 3 3 0
i n ‡a t i o n r e s p o n s e
norm al
1 .5
0 .1
1 .5 2 7 2
0 .0 9 7 6
1 .5 3 4 4
1 .3 7 1 0
1 .6 8 8 4
output resp onse
norm al
0 .1 2 5
0 .1
0 .0 7 2 3
0 .0 3 8 4
0 .0 7 7 9
0 .0 2 0 0
0 .1 3 4 5
inve st. a d j. c o st
norm al
4 .0
1 .5
0 .9 0 5 8
0 .4 3 7 3
1 .9 6 5 6
0 .4 8 9 4
3 .5 5 4 7
c a p ita l u til. a d j. c o st
norm al
0 .2
0 .1
0 .6 8 0 5
0 .0 7 9 8
0 .6 7 6 8
0 .5 6 0 3
0 .8 0 4 5
inv . e la st. o f la b o u r
norm al
2 .0
0 .2
2 .0 2 2 1
0 .1 9 6 5
2 .0 1 0 9
1 .6 8 9 9
2 .3 4 0 1
C R R A co e¤.
norm al
0 .6 6
0 .1
0 .6 7 5 5
0 .0 8 7 3
0 .6 9 0 0
0 .5 4 4 9
0 .8 3 3 0
p ric e in d e x .
b eta
0 .5
0 .1 5
0 .1 4 5 3
0 .0 6 9 8
0 .1 7 0 6
0 .0 5 4 9
0 .2 7 9 3
w a g e in d e x .
b eta
0 .5
0 .1 5
0 .1 6 9 6
0 .0 6 9 0
0 .1 9 0 1
0 .0 7 9 1
0 .2 9 9 7
c a lvo p ric e s
b eta
0 .7 5
0 .1
0 .7 4 1 2
0 .0 4 0 6
0 .7 5 1 0
0 .6 8 2 8
0 .8 1 5 8
c a lvo w a g e s
b eta
0 .7 5
0 .1
0 .4 5 4 4
0 .0 6 4 8
0 .5 0 2 2
0 .3 8 8 7
0 .6 1 4 4
h a b it
b eta
0 .7
0 .1
0 .4 7 5 1
0 .0 6 7 7
0 .5 0 8 4
0 .3 9 6 2
0 .6 2 4 3
…x e d c o st
norm al
1 .4
0 .1
1 .5 6 6 0
0 .0 8 7 6
1 .5 7 1 5
1 .4 3 3 0
1 .7 1 4 6
Impulse responses to the government spending shock -3
0
x 10
-3
c 0
x 10
-4
cr 5
x 10
-4
cnr 4
x 10
-4
R 2
-0.5
-0.5
0
2
1
-1
-1
-5
0
0
5 -3
2
x 10
10
15
5 -3
y 0
x 10
10
15
5 -4
I 0
x 10
10
15
5 -4
w 5
x 10
10
15
x 10
-4
pi 2
5
mc
10
15
0
-1
0
0.005
0
-2
-5
0
-0.01
10
15
L 5
5
10
15
-4 x 10 omega
5 -3
1
x 10
10
15
5 -3
ro 0
x 10
10
15
5 -3
Ig 0
x 10
10
15
1
0
0
0.5
-2
-2
0
-5
0
-4
-4
-1
10
15
5
10
15
5
10
15
5
10
15
Impulse responses to the government investment shock
122
5
10
5 -3
trans
-2
5
15
10
15
0.01
-4
5
10 g
0.01
-2
-3
5
b
0
x 10
pip
1
-2
2
x 10
15
x 10
5
g_rev
10
15
Table 37: Priors and posteriors of estimated parameters parameters P rio r d istrib u t
-3
1
x 10
E st m a x p o ste rio r
P o ste rio r d istrib u tio n M H m ean
5%
P a r a m e t e r ’s n a m e
ty p e
m ean
st. error
m ode
sh a re o f n o n -R ic a rd ia n
b eta
0 .5
0 .1
0 .1 4 9 5
0 .0 3 3 9
0 .1 6 4 0
0 .1 0 3 8
0 .2 1 8 9
A R (1) gov. sp en d .
b eta
0 .8
0 .1
0 .7 4 3 9
0 .0 7 9 0
0 .7 8 0 5
0 .6 6 3 9
0 .9 0 4 0
A R (1 ) g ov . inv .
b eta
0 .8
0 .1
0 .3 7 1 2
0 .0 8 2 2
0 .3 7 8 2
0 .2 4 2 8
0 .5 1 3 2
A R (1) gov. tr.
b eta
0 .8
0 .1
0 .4 1 6 0
0 .0 7 9 0
0 .4 4 0 2
0 .3 1 0 3
0 .5 7 6 4
A R (1) cap. tax.
b eta
0 .8
0 .1
0 .6 0 4 7
0 .0 7 0 5
0 .6 0 8 0
0 .4 8 9 1
0 .7 1 8 3
A R (1 ) la b . ta x .
b eta
0 .8
0 .1
0 .4 8 1 2
0 .0 8 0 9
0 .5 1 1 6
0 .3 7 0 3
0 .6 5 1 2
A R (1) con. tax.
b eta
0 .8
0 .1
0 .6 0 5 6
0 .0 7 5 4
0 .6 2 6 8
0 .5 0 0 2
0 .7 5 0 0
gov. sp en d to ou tp u t.
norm
0 .1 5
0 .1
0 .1 7 6 6
0 .0 9 6 5
0 .1 6 9 9
0 .0 1 1 6
0 .3 3 5 4
g ov . inv to o u tp u t.
norm
1 .5
0 .1
1 .5 0 8 1
0 .1 0 0 0
1 .5 1 0 6
1 .3 4 3 1
1 .6 7 6 1
gov. tran s. to ou tp u t.
norm
1 .5
0 .1
1 .5 1 4 4
0 .0 9 9 0
1 .5 1 8 4
1 .3 6 2 0
1 .6 8 3 8
cons. tax to output.
norm
0 .5
0 .1
0 .5 3 6 3
0 .0 9 9 3
0 .5 3 0 6
0 .3 7 1 3
0 .6 9 4 0
cap. sp end to output.
norm
1 .5
0 .1
1 .5 4 3 0
0 .0 9 9 5
1 .5 3 9 6
1 .3 6 7 9
1 .7 0 0 7
la b . sp e n d to o u tp u t.
norm
0 .5
0 .1
0 .4 7 2 7
0 .0 3 3 9
0 .4 8 0 5
0 .3 2 3 9
0 .6 3 2 0 0
-3
c 1
x 10
-3
cr 2
x 10
cnr
-4
5
x 10
st. error
-4
R 5
x 10
-4
pi 2
0
0
0
0
0
0
-1
-1
-2
-5
-5
-2
5
10
15
5 -3
y 0.01
2
x 10
10
15
2
0
0
0
-0.01
-2
-2
5 -3
5
x 10
10
15
5 -3
L 2
x 10
5 -4
I
10
15
x 10
4
15
5 -3
2
x 10
10
15
5
x 10
10
15
5
ro
10
15
0
0
-0.5
-0.01 15
5
10
15
5
10
15
x 10
-4
10
15
10
15
g
10
5
10
5 -3
2
0
0
15
5
4
2
10
5 -4
trans
0
5
15
0.01
-2
15
10 b
0
Ig 0.5
0
10
x 10
pip
-2
-2
-5
5
5 -3
mc
0
5 -3
omega
10 w
x 10
95%
15
x 10
0
g_rev
5
10
15
10
15
10
15
Impulse responses to the transfer shock -3
2
x 10
-4
c 5
x 10
cr
-4
cnr 0.02
2
x 10
-4
R 4
0
0
0
1
2
-2
-5
-0.02
0
0
5 -3
1
x 10
10
15
5 -3
y 1
x 10
10
15
5 -4
I 0
x 10
10
15
5 -4
w 5
x 10
10
15
0
0.01
-4
-5
0
10
15
L 0
5
10
15
-4 x 10 omega
-2
0
5 -3
1
x 10
10
15
5
ro
10
15
5
Ig
0
15
0
pip
5 -3
-0.5
-2
5
10
0
0
-3
5
0.02
-1
x 10
0.5
b
0
x 10
-4
pi 1
mc
-1
1
x 10
10
15
x 10
-1
5 -3
trans
0
0.05
1
-0.005
0
0.5
x 10
g
g_rev
-4 -1
5
10
15
5
10
15
-1
5
10
15
-0.01
123
5
10
15
-0.05
5
10
15
0
5
10
15
Table 38: Priors and posteriors of estimated parameters P rio r d istrib u t
E st m a x p o ste rio r
P o ste rio r d istrib u tio n M H m ean
5%
95%
P a r a m e t e r ’s n a m e
ty p e
m ean
st. error
m ode
st. error
gov. sp en d to d eb t
norm
0 .2
0 .1
0 .0 4 9 5
0 .0 2 6 1
0 .0 7 0 9
0 .0 1 2 6
0 .1 3 2 0
g ov . inv to d e b t
norm
0 .4
0 .1
0 .4 2 5 2
0 .0 9 4 8
0 .4 2 9 7
0 .2 7 1 4
0 .5 8 1 9
gov. tran s. to d eb t
norm
0 .2
0 .1
0 .0 4 7 3
0 .0 5 0 4
0 .0 6 9 0
-0 .0 1 4 2
0 .1 5 6 2
cons. tax to debt
norm
0 .2
0 .1
0 .0 9 7 9
0 .0 4 7 7
0 .1 0 7 7
0 .0 2 3 4
0 .1 9 5 2
cap. tax to debt
norm
0 .2
0 .1
0 .0 2 6 1
0 .0 6 2 0
0 .0 2 4 7
-0 .0 7 6 5
0 .1 2 3 2
la b . ta x to d e b t
norm
0 .2
0 .1
0 .0 0 7 0
0 .0 1 7 1
0 .0 1 1 4
-0 .0 2 1 5
0 .0 4 5 3
g ov . sp en d to d ef.
norm
0 .1 5
0 .1
0 .1 5 0
0 .0 8 3 1
0 .1 0 1 8
-0 .0 3 4 4
0 .2 3 8 0
g ov . inv to d e f.
norm
0 .1 5
0 .1
0 .1 5 8 7
0 .0 9 9 7
0 .1 6 2 4
-0 .0 0 9 4
0 .3 1 6 9
g ov . tra n s. to d ef.
norm
0 .1 5
0 .1
0 .1 3 6 9
0 .0 9 2 5
0 .1 4 6 2
-0 .0 0 5 8
0 .3 0 2 6
co n s. ta x to d ef.
norm
0 .2
0 .1
0 .2 0 2 4
0 .0 9 2 0
0 .2 1 7 4
0 .0 6 1 1
0 .3 6 7 5
ca p . sp en d to d ef.
norm
0 .2
0 .1
0 .2 0 1 6
0 .0 9 6 5
0 .2 0 1 7
0 .0 4 5 3
0 .3 6 0 4
la b . sp e n d to d e f.
norm
0 .2
0 .1
0 .2 2 9 7
0 .0 6 2 8
0 .2 3 2 4
0 .1 2 6 6
0 .3 4 5 7
tr. resp to hours
norm
1 .5
0 .1
1 .5 2 0 1
0 .0 9 9 2
1 .5 1 8 5
1 .3 6 2 9
1 .6 9 0 0
Table 39: Present Value Government Consumption Multiplier Variable
Impact
4 quarters
8 quarters
12 quarters
PV ( PV ( PV ( PV ( PV ( PV (
0.8225
0.5252
0.3288
0.2130
-0.1211
-0.2678
-0.3330
-0.3652
-0.0719
-0.1797
-0.2890
-0.3579
Y) G) C) G) I) G)
Impulse responses to the consumption tax shock -3
5
x 10
-3
c 5
0
-3
cr 5
0
-5
5 -3
5
x 10
x 10
10
15
5 -3
5
-3
cnr 5
0
-5
y
x 10
x 10
10
15
x 10
R
0
-5
5
I
10
15
-5
5
w
10
5
0
0
-0.01 15
5 -3
mc
0.01
-4
pi 0.01
0.01
5
x 10
10
15
-5
5
0
0
0
0
0
0
-5
-0.01 15
-0.01
-5
-5
5 -3
x 10
10
15
5 -3
L 5
x 10
10
5 -3
omega 5
x 10
10
15
5 -3
ro 5
x 10
10
15
0
0
0
-5
-5
-0.01 15
5
10
15
5
10
15
Impulse responses to the labour tax shock
124
5
10
5
10
x 10
5 -3
-0.5
0 -5
15
15
0
0
10
10 trans
0.01
-2
5
5
Ig
15
-1
pip
5 -4
b
-5
2
x 10
x 10
5
10
15
10
15
g
g_rev
10
15
Table 40: Present Value Government Investment Multiplier Variable
Impact
4 quarters
8 quarters
12 quarters
PV ( PV ( PV ( PV ( PV ( PV (
0.9591
0.7282
0.6584
0.6646
-0.0463
-0.1600
-0.1601
-0.1332
-0.0242
-0.0794
-0.1173
-0.1195
Y) Ig) C) Ig) I) Ig)
Table 41: Present Value Transfers Multiplier
-3
1
Impact
4 quarters
8 quarters
12 quarters
PV ( PV ( PV ( PV ( PV ( PV (
0.1275
0.0045
-0.1179
-0.2065
0.1516
0.1182
0.1165
0.1298
-0.0096
-0.0341
-0.0564
-0.0620
-4
c
x 10
Variable
2
Y) tr) C) tr) I) tr)
-3
cr
x 10
5
x 10
-5
cnr 5
x 10
-5
R 5
x 10
-5
pi 5
0.5
1
0
0
0
0
0
0
-5
-5
-5
-5
5
10
-4
5
15
2
0
10
15
5
10
-4
0
5 -4
0
x 10
10
15
x 10
10
15
0
5 -4
5
x 10
10
15
x 10
10
-2
15
5 -3
ro 0
x 10
5
mc
10
15
10
0.01
0
0.005
-2
0
15
5 -3
Ig 0
x 10
10
0
-2
0
-2
-1
0
-4
-5
-4
-2
-5
10
15
5
10
15
5
10
15
5
10
15
5
10
15
x 10
10
15
10
15
g
5 -3
5
-5
5
x 10
-4
15
trans
pip
5 -4
b
-1
-4
omega
5 -4
w
-2
-2
15
L
x 10
5 -4
I
x 10
0
-5
5
5 -4
y
x 10
x 10
g_rev
5
10
15
Impulse responses to the capital tax shock -3
1
x 10
-3
c 2
0
1
-1
0
-3
cr
x 10
0
x 10
-4
cnr 5
-2
x 10
-3
R 1
x 10
-3
pi 1
0
0
0
-5
-1
-1
x 10
pip
-4 5 -3
5
x 10
10
15
5 -3
y 4
10
15
5 -4
I
x 10
5
x 10
10
15
5
w
10
15
0
-0.005
0.01
0
-5
-0.01
0
0
10
15
L
5
10
15
5
omega
-2
10
15
5
ro
10
15
5 -3
Ig 2
x 10
5 -3
-1
2
5
15
0
0
-3
10 b
0.02
-5 x 10
5
mc 0
10
15
-2
x 10
5
trans
10
15
10
15
g
g_rev
0.02
0
0
0.01
0
-0.02
-0.005
0
0
-0.02
-0.04
-0.01
-2
-0.01
-4 5
10
15
5
10
15
5
10
15
5
10
15
5
10
15
5
10
15
Smoothed shocks 2000:Q1 until 2011:Q1 Model is then applied to compute the variance decomposition. The private and public investment accounts for around 50 per cent of the ‡uctuations, in‡ation and monetary shocks account for around 30 per cent and taxes account for around 8 per cent.
125
Table 42: Present Value Consumption Tax Multiplier Variable
Impact
4 quarters
8 quarters
12 quarters
PV ( PV ( PV ( PV ( PV ( PV (
-0.8277
-0.7001
-0.4347
-0.3417
-0.6369
-0.5624
-0.3852
-0.3520
-0.0936
-0.0809
0.0026
0.0552
Y) tc) C) tc) I) tc)
Table 43: Present Value Capital Tax Multipliers Variable
Impact
4 quarters
8 quarters
12 quarters
PV ( PV ( PV ( PV ( PV ( PV (
-0.1382
-0.0708
-0.0127
0.0380
-0.1607
-0.1616
-0.1891
-0.2122
0.0020
-0.0004
-0.0150
0.0306
Y) tc) C) tc) I) tc)
0.06 Initial values tr 0.04 ig it 0.02
wt pit
0
tl tk
-0.02
tc vt nt
-0.04
lt -0.06
at 0
20
40
60
80
100
References [1] An,S., Schorfheide, F.,(2007) Bayesian analysis of DSGE models, Econometric Reviews, 30, 889-920. [2] Ascari, G., Rankin, N. (2013) The e¤ectiveness of government debt for demand management:Sensitivity to monetary policy rules, Journal of Economic Dynamics and 126
Table 44: Present Value Capital Tax Multipliers Variable
Impact
4 quarters
8 quarters
12 quarters
PV ( PV ( PV ( PV ( PV ( PV (
-0.2242
-0.2643
-0.2606
-0.2337
0.0086
-0.0313
-0.0515
-0.0614
-0.0139
-0.0408
-0.0649
-0.0746
Y) tc) C) tc) I) tc)
Table 45: Variance Decomposition in Percents tfp .
wage
p ref.
g_ sp.
c_ tx.
k_ tx.
l_ tx .
in f.
R.
p r_ inv .
g _ inv .
tr.
y
3 .0 5
1 .6 3
1 .5 8
0 .9 1
4 .4 3
3 .8
0 .0 7
1 5 .5
1 6 .5
4 4 .2 4
7 .6 2
0 .6 7
c
5 .9 9
1 .6 7
1 0 .3 5
0 .6 5
8 .3 2
0 .5 4
0 .2 1
2 1 .7 7
2 0 .2 7
2 8 .8 9
0 .5 4
0 .8 1
I
1 .8 4
0 .8 1
1 .6 6
0 .2 7
0 .2 2
0 .2 1
0 .0 0
1 .0 4
1 .9 9
9 1 .8 5
0 .0 8
0 .0 3
L
3 2 .8 5
2 .4 8
1 .3 4
0 .7 3
2 .0 7
9 .4
0 .0 8
6 .6 6
1 1 .9
2 5 .1 7
6 .9 6
0 .3 7
w
1 .7 4
1 2 .7 8
0 .4 4
0 .3 6
1 4 .1 1
0 .2 7
0 .2 2
4 2 .7 7
5 .0 4
2 1 .6 3
0 .0 9
0 .5 4
R
5 .0 4
1 .5 9
0 .9 7
0 .2 6
1 6 .8 2
0 .5 0
1 .0 1
3 3 .7 1
3 3 .9 1
6 .4 8
0 .5 5
0 .1 6
pi
3 .6
1 .5
0 .3
0 .0 9
3 6 .4 2
0 .6 8
0 .0 0
5 4 .0 9
0 .9 6
2 .4 9
0 .2 1
0 .1 1
b
0 .7 8
1 .7 9
0 .7 6
1 .4
0 .3 5
4 .7 8
0 .6 7
1 5 .2 6
2 1 .7 4
4 8 .0 0
0 .3 2
4 .1 5
Control,37(8),1544-1566. [3] Batini, N., Harrison, R., Millard, S. P. (2003) Monetary policy rules for an open economy, Journal of Economics Dynamics and Control, 27(11-12), 2059–2094. [4] Basu, P., Kollmann, R. (2013) Productive Government Purchases and the Real Exchange Rate, Manchester School, 81(4), 461-469. [5] Basu, P., (1987) An adjustment cost model of asset pricing. International Economic Review 28 (3), 609–621. [6] Benati, Luca. (2008) “The ‘Great Moderation’in the United Kingdom.”Journal of Money,Credit and Banking, 40, 121–47. [7] Bhattarai K. (2011) Econometric and Stochastic General Equilibrium Models for Evaluation of Economic Policies, International Journal of Trade and Global Markets, 4:2: 212-241 [8] Bhattarai K. (2007) " Welfare Impacts of Equal-Yield Tax Experiment in the UK Economy, Applied Economics, 39,1545-1563. [9] Blanchard O. and Jordi Galí (2012) Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment, American Economic Journal: Macroeconomics 2:1–30 [10] Blake A. P., M. Weale (1998) Costs of Separating Budgetary Policy from Control of In‡ation: A Neglected Aspect of Central Bank Independence, Oxford Economic Papers, 50, 3, 449-467
127
tfp
transfers
gov. inv
0.02
0.5
5
0
0
0
-0.02
20 priv. inv
40
0.2
-0.5
20 40 monet. policy
0.02
-5
0
0
0
-0.02
-0.02
40
20 cap. tax
40
0.05
0.2
0.2
0
0
0
-0.05
20 40 gov. spend
-0.2
20 pref.
40
-0.2
0.05
0.01
0.01
0
0
0
-0.05
20
40
-0.01
40
20 con. tax
40
20 wages
40
0.02
-0.2
20 lab. tax
20 inflation
20
40
-0.01
0
50
[11] Bouakez, H., Rebei , N. (2007) Why Does Private Consumption Rise After A Government Spending Shock?, Canadian Journal of Economics, 40(3), 954–979. [12] Campbell, J. Y., Mankiw, N. G. (1989) Consumption, income, and interest rates: reinterpreting the time series evidence, NBER Macroeconomics Annual 1989, 4, 185–216. [13] Calvo, G. A. (1983) Staggered prices in a utility-maximizing framework, Journal of Monetary Economics, 12(3), 383-398 [14] Chadha, J. S. and C. Nolan (2007) Optimal Simple Rules for the Conduct of Monetary and Fiscal Policy, Journal of Macroeconomics, Dec, 29:4: 665-89. [15] Clarida R., Gali J., and Gertler M. (1999) The Science of Monetary Policy: A New Keynesian perspective, Journal of Economic Literature; 37 (4), 1661-707. [16] Coenen, G., Straub, R., Trabandt, M. (2013) Gauging the e¤ects of …scal stimulus packages in the euro area, Journal of Economic Dynamics and Control, 37(2), 367-386. [17] Coenen, G., Erceg, C. J., Freedman, C., Furceri, D., Kumhof, M., Lalonde, R., Laxton, D., Linde, J., Mourougane, A., Muir, D., Mursula, S., de Resende, C., Roberts, J., Roeger, W., Snudden, S., Trabandt, M., in’t Veld, J.,(2012) E¤ects of …scal stimulus in structural models, American Economic Journal: Macroeconomics, 4(1), 22–68. [18] Christiano, L., Eichenbaum, M., Rebelo, S. (2011) When is the government spending multiplier large?, Journal of Political Economy, 119(1), 78- 121. [19] Christo¤el, K.,Linzert,T.,2010.Theroleofrealwagefrictionsandlabormarketfrictionsforin‡ationpersistence.Journal of Money,Credit,and Banking 42,1435–1446. 128
[20] Collard, F. and M. Juillard (2001) Accuracy of stochastic perturbation methods: The case of asset pricing models, Journal of Economic Dynamics and Control, 25, 979–999. [21] Doan, T, R. Litterman, and C. Sims (1984) Forecasting and Conditional Projections Using Realistic Prior Distributions", Econometric Reviews, 3, 1-100 [22] Ellison M. and J. Pearlman (2011) Saddlepath learning, Journal of Economic theory 146, 1500-1519. [23] Faccini. R, S. Millard and F. Zanetti (2013) Wage rigidities in an estimated dynamic stochastic general equilibrium model of the UK labour market, Manchester School, 81, 66-99. [24] Harrison, R., Oomen, O. (2010) Evaluating and estimating a DSGE model for the United Kingdom, Bank of England Working Paper, no. 433, Bank of England. [25] Iacoviello, M. (2005) House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle. American Economic Review, 25(3), 739-764. [26] Iacoviello, M., Neri, S. (2010) Housing Market Spillovers: Evidence from an Estimated DSGE Model, American Economic Journal: Macroeconomics, 2(2), 125-164. [27] Koop G and D. Korobilis (2010) Bayesian Multivariate Time Series Methods for Empirical Macroeconomics, now Publishers Inc., Hanover MA, USA [28] Gary Koop, Dale J. Poirier, Justin L. Tobias (2010) Bayesian Econometric Methods, Cambridge University Press. [29] Krause, M. and Lubik,T. (2007).The(ir)relevance of real wage rigidity in the new Keynesian model with search frictions.Journal of Monetary Economics 54, 706–727. [30] Levine P, J. Pearlman, G. Perendia and B. Yang (2012) Endogenous Persistence in an estimated DSGE model under imperfect information, Economic Journal,122,1287–1312 [31] Mirrlees J., and S. Adam, T. Besley, R. Blundell, S. Bond, R. Chote, M. Gammie, P. Johnson, G. Myles, J. Poterba.2010. Dimensions of tax design: the Mirrlees review, Oxford: Oxford University Press. [32] Monacelli, T., Perotti, R. (2010) Fiscal Policy, The Real Exchange Rate and Traded Goods,The Economic Journal, 120, 437–461. [33] Pissarides, C. A. (2013) Unemployment in the Great Recession, Economica, 80: 385–403 [34] Pissarides, C. A. (2011) Equilibrium in the Labor Market with Search Frictions, American Economic Review, 101(4): 1092-1105. [35] Ramey, V. A. (2011) Can government purchases stimulate the economy?, Journal of Economic Literature, 49(3), 673-685. [36] Rankin N. (1992) Imperfect competition, expectations and the multiple e¤ects of monetary growth, Economic Journal 102 (1992): 743-753. [37] Ravn, M. O., Schmitt-Grohé, S. and Uribe, M. (2012) Consumption, government spending, and the real exchange rate, Journal of Monetary Economics, 59(3) 215-234. 129
[38] Rotemberg, J.J.,(1982) Sticky prices in the United States. Journal of Political Economy 90,1187–1211. [39] Sim C.A (1980) Macroeconomics and Reality, Econometrica, 48:1 Jan.1 -45. [40] Sims, C.A. and T. Zha (1999) Error Bands for Impulse Responses, Econometrica, 67 (5): 1113-1155 [41] Smets, F., Wouters, R. (2007) Shocks and frictions in US business cycles: a Bayesian DSGE approach, American Economic Review, 97(3), 586-606. [42] Smet F. and R. Wouters (2003) An estimated dynamic stochastic general equilibrium model of the Euro Area, Journal of European Economic Association, Sept, 1(5):1123-1175. [43] Wickens M. (1995) Real Business Cycle Analysis: A Needed Revolution in Macroeconometrics (in Controversy: Business Cycle Empirics, Economic Journal, 105, 433., 1637-1648. [44] Woodford, M. (2011) Simple Analytics of the Government Expenditure Multiplier, American Economic Journal: Macroeconomics, 3(1): 1–35. [45] Zanetti, F. (2010), ‘Labor market institutions and aggregate ‡uctuations in a search and matching model’, European Economic Review, 55,644-658.
2.5
Critical assessment of the DSGE Models
Bhattarai and Dixon (2013) opine that for almost …ve decades economists have tried to incorporate unemployment as a feature of the equilibrium process in the modelling of an economy. Job matching and search models developed by Phelps (1968), Mortensen (1970), Lucas and Prescott (1974), Pissarides (1979, 1985, 1986), Mortensen and Pissarides (1994, 1999) have signi…cantly contributed to the analysis of unemployment dynamics based on bargaining and matching for wages and work by workers and …rms. In the last decade, the new Keynesian DSGE model has been extended to assess the impacts on in‡ation dynamics of both …rm-union bargaining (Zanetti (2007), Gertler, Sala and Trigari (2008), Gertler and Trigari (2009)) and search-matching a la Mortensen and Pissarides (see for example Kraus and Lubik (2007), Christo¤el and Kuester (2008), Trigari (2009), Christo¤el and Kuester (2008), Krause, Lopez-Salido and Lubik (2008), Christo¤el, Kuester and Linzert (2009), Zanetti (2011)). However, whilst these recent non-Walrasian developments are very much to be welcomed, in standard DSGE models the focus is on short run "business cycle" ‡uctuations around a steady-state in a representative household setting (for an evaluation of these models in this context, see Christo¤el et al. (2009)). Bhattarai and Dixon (2014) observe that the DGSE framework is lacking in certain key dimensions. First, these models shed little or no light on the long run general equilibrium impacts of tax-transfer policies on equilibrium unemployment, growth, capital accumulation among various sectors of the economy and the utility, wages and labour supply of households into the future. Secondly, the micro-foundations are very simple and abstract from diversity across households and sectors, with no role for relative prices and wages by sectors of production and skill categories of labour They extend the computable general equilibrium (CGE) framework to allow a full analysis of equilibrium unemployment in a dynamic general equilibrium model with heterogenous households and …rms, providing the structural details required for more realistic analysis of the allocation
130
mechanism in the economy. They provide a medium and long-term framework for evaluating and understanding economic policy as opposed to the short-run focus of standard new Keynesian DGSE models. They also assess the full impacts of the equilibrium rate of unemployment on labour supply, consumption and saving behavior of households, alongside the investment and capital accumulation behavior of …rms and the resulting relative prices of commodities and factors of production in the broader economy. 2.5.1
Blanchard’s New Keynesian DSGE model
Problem of household i that maximises expected utility from consumption (Cit+k ), accumulation of money (Mit+k+1 ) and labour supply (Nit+k ) taking account of all information ( t ) available up to period t is given as: "1 # X Mit+k+1 k Q (Nit+k ) j t max E U (Cit+k ) + V (B.95) P t+k t=0 subject to: a) CES aggregation of consumption (Cit ) and price level P t over j commodities: Cit =
Z
0
1
1
1
Cijt dj
;
Pt =
Z
1
0
1 Pjt
1
dj
1
(B.96)
b) the budget constraint Z
1
Pjt Cijt + Mit+1 + Bit+1 = Wt Nit + (1 + it ) Bit + Mit +
it
+ Xit
(B.97)
0
where Bit , it and Xit denote bonds held, pro…ts earned and transfer received by the household i ; Wt is wage earned for supplying labour (Nit ) : c) demand for a product Cijt relates to composite demand as: Cijt =
Pjt Pt
Cit
(B.98)
Firms take wage rates as given and set prices a la Calvo with probability of changing it every period. Then Yj;t is the solution to the …rms’pro…t maximization problem: # " X U 0 (Ct+1 ) Pjt Wt+k Yjt+k k k max E (1 ) Yjt+k j t (B.99) U 0 (Ct ) P t+k P t+k Zt+k k
subject to: a) a linear production technology
Yjt = Zt Njt
(B.100)
b) supply Yjt+k =
Pjt P t+k 131
Yt+k
(B.101)
1. Write …rst order conditions for optimisation by households and …rms in this model. 2. Solve for the price level, employment and output at the steady state. 3. Prove that volatility of output is generated from the technological shock. Comment on how does it compare to a standard RBC model. 2.5.2
Basic New Keynesian Model in logs
IS: goods market equilibrium (demand) yt = Eyt+1
art+1 ;
rt+1 = it+1
E
(B.102)
t+1
LM: money market equilibrium (…nancial markets) pt = b yt
mt+1
c:it+1
(B.103)
Phillips curve (Supply) t
2.5.3
= E
t+1
+ d:xt ;
ybt ; xt = yt
xt = yt
zt ;
(B.104)
Extended version of the New Keynesian Model
IS: goods market equilibrium (demand) yt = (1
) yt
1
+ Et yt+1
rt+1 = it+1
art+1 ; E
rt+1 = it+1 it+1 =
t+1
E
t+1
(B.105) (B.106)
t
LM: money market equilibrium (…nancial markets) mt+1
pt = b yt
c:it+1
(B.107)
Phillips curve (Supply) t
= E
t+1
+ d:xt ;
xt = yt
Zt =
2.6
Zt
1
+ "zt
ybt ; xt = yt
zt ;
(B.108) (B.109)
Problem on Open Economy New Keynesian Model
1. Consider a standard open economy optimal growth model with Household problem: max
U = E0
1 X
t
Ut (Ct ; Lt )
t=0
132
0
0
(B.162)
yS
= u + v (e
p)
(B.163)
yS = y p = p = p e
!
=
v 1=a
(u + v (e
(B.164) p)
y)
vp + ave + a (u v 0
p e
+
(B.165)
y)
(B.166) a (u by m a
y) r
(B.167)
p(t) = C1 er1 t + C2 er2 t + p
(B.168)
r1 + v r2 + v e(t) = C1 er1 t + C 2 e r2 t + e v v
(B.169)
138
p e
Steady state is obtained when
!
=
0 0
; From the exchange rate equation given above
when e = 0 steady state price level is p=m
by
ar
(B.170)
Similarly when p = 0 from the price equaution e=p
1 (u v
y)
(B.171)
For dynamics solve pthe transitional dynamics tr(A) 1 tr(A)2 4 jAj; tr(A) = (a11 + a22 ) ; jAj = (a11 a22 a12 a21 ) r1; r2 = 2 2 v v Here A = ; tr(A) = v and jAj = av . 1=a 0 r tr(A) 1 p v 1 v 2 r1; r2 = tr(A) 4 jAj = ( v)2 + 4 2 2 2 2 a p p v v v v 1 1 2 2 p(t) = C1 e( 2 + 2 ( v) +4 a )t + C2 e( 2 2 ( v) +4 a )t + p v
e(t)
2
=
+ v
+
2
1 2
p
v)2 + 4 av + v C1 e( v p 1 ( v)2 + 4 av v 2 C 2 e( v (
v 2
v 2
+ 21 1 2
p
p
(
(
v)2 +4
v)2 +4
v a
v a
(B.172) (B.173)
)t
)t + e
(B.174)
Given the initial conditions p(t = 0) and e(t = 0) the constant terms C1 and C2 can be evaluated. For phase diagram from p = vp + ave + a (u y) when p = 0; p = e + (u v y) , p rises above p = 0 isocline and falls below it. From e = ap + by a m r when e = 0; p =p =m space. b) Markov model of employment and Layo¤ et+1 = (1
by
=
(1
(B.175)
) ut
(B.176)
) (1
et ut
)
1. Apply r2 )r + (1
tr(A)r + jAj = 0 r2 (2 )r + (1 )=0 p 1 tr(A)2 4 jAj; r1; r2 = (2 2 r1; r2 = tr(A) 2 2 p (2 ) 1 r1; r2 = ( + )2 2 2 r1; r2 = 1
( + ) 2
1 2(
now explain the diagram in (e, p)
) et + ut
ut+1 = et + (1 et+1 ut+1
ar
+ ); r1 = 1; r2 = (1
(B.177)
) (1 )
1 2
p
) (2
= 0 ; r2 )2
4 (1
(2 );
)
By rule yt = C1 r1t + C2 r2t + y 139
(B.178)
xt =
r1
a11 r2 a11 C1 r1t + C2 r2t + x a12 a12
et = C1 + C2 (1 xt =
C1
)
t
C2 (1
)
(B.179) (B.180)
t
(B.181)
De…nitising the solution using initial conditions the time path of …nding jobs and unemployment are: e0 u0 t et = + (1 ) (B.182) ( + ) ( + ) xt =
e0 u0 (1 ( + )
( + )
)
t
(B.183)
c) Model of price war
yt+1 xt+1 r1 = 1; r2 = (1
yt+1 = yt
(yt
xt )
(B.184)
xt+1 = xt
(xt
yt )
(B.185)
(1
)
(1
=
)
yt xt
) yt = C1 + C2 (1 C1
xt =
)
C2 (1
(B.186)
t
)
t
(B.187)
De…nitising the solution using initial conditions the time path of …nding jobs and unemployment are: y0 + x0 y0 x0 t yt = + (1 ) (B.188) 2 2 y0 + x0 y0 x0 t xt = (1 ) (B.189) 2 2 d) Entry adjustment model qD
p = p =
(a + bp
N =
qS
mN )
(p
(B.190) >0
c)
(B.191)
>0
(B.192)
Applying y1 (t) = C1 er1 t + C2 er2 t + y 1 r1 a11 r2 a11 y2 (t) = C 1 e r1 t + C2 er2 t + y 2 a12 a12
(B.193) (B.194)
Solution to this problem is: p N
!
=
b
m 0 140
p N
+
a c
(B.195)
P (t) = C1 er1 t + C2 er2 t + p N (t) =
r1
b m
r2
C1 er1 t +
b m
(B.196)
C 2 e r2 t + N
(B.197)
Now draw the phase diagram for stability analysis. Reference: Hoy et al. (2001) Mathematics for Economics, MIT Press. Exercise 4: Stability Analysis 1. Solve the following system of di¤erential equations. y = Ay where a) A =
4 4
1 4
; b) A =
1
3 3
1 4
(B.198)
;c) A =
[Hint: for a second order di¤erence equation r2 p 1 tr(A)2 4 jAj] 2
2 2
5 4
tr(A)r + jAj = 0 ; or r1; r2 =
tr(A) 2
2. Solve the following system of equations and represent solutions in a phase diagram a) y1 =
2y1 + 2
y2 =
3y1 + 6
(B.199)
y1 =
2y1
(B.200)
b) 2
y2 = 3y1
6
(B.201)
y1 = y2
2
(B.202)
y1 4
1 2
(B.203)
y2 + 2
(B.204)
c)
y2 = d) y1 = y2 = y1
y2 + 1
(B.205)
3. Apply above techniques to a) Dornbusch model of exchange rate overshooting e =E e
(B.206)
r =r +E e
(B.207)
141
mD = m
ar + by
p=
(B.208)
ar + by
(B.209)
) et + ut
(B.210)
b) Markov model of employment and Layo¤ et+1 = (1
ut+1 = et + (1
) ut
(B.211)
yt+1 = yt
(yt
xt )
(B.212)
xt+1 = xt
(xt
yt )
(B.213)
c) Model of price war
d) Entry adjustment model p = p =
(a + bp
N =
(p
qD
qS
(B.214)
mN ) c)
>0 >0
(B.215) (B.216)
References [1] Hoy et al. (2001) Mathematics for Economics, MIT Press. [2] Mankiw N.G. (1989) Real Business cycle: A New Keynesian Perspective, Journal of Economic Perspectives, vol. 3, no. 3 pp. 79-90. [3] Phelps E. S. (1968) Money wage dynamics and labour market equilibrium, Journal of Political Economy, 76 , 678-711. [4] Plosser Charles I (1989) Understanding Real Business Cycle, Journal of Economic Perspectives, vol. 3, no. 3 pp. 51-77. [5] Cooly Thomas F (1995) Frontiers of Business Cycle Research, Princeton. [6] Romer D. (2006) Macroeconomics, McGraw Hill. [7] Minford P. and D. Peel (2002) Advanced Macroeconomics: A Primer, Edward Elgar Publishing. [8] Sorensen PB and H. Jl Whitta-Jacobsen (2010) Introducing Advanced Macroeconomics, McGraw Hill. [9] Simon and Blume (1994) Mathematics for Economists, Norton. [10] Shone Ronald (2002) .Economic Dynamics, Cambridge.
142
3
L3: New Classical Macro Models (Real Business Cycle)
Neither Keynesian nor the rational or adaptive expectation models include explicit optimisation by households and …rms. Prices in those models are either sticky or have a very limited role in economic allocation. New classical models have tried to overcome this short coming by introducing alternative models in which demand and supply functions for goods and services are derived explicitly from the optimising behaviour of economic agents as in a Walrasian general equilibrium system. These are dynamic and stochastic general equilibrium models with perfect ‡exibility in prices. Recently more development has taken place on decentralised applied general equilibrium economy with multiple consumers, producers and traders. Simple speci…cation of a real business cycle (RBC) model is similar to the perfect foresight models but it includes stochastic technology to explain macro ‡uctuations of output and employment that is observed in real economy. These technological shocks a¤ect productivity and income and result in intertemporal and intratemporally substitutions (Prescott and Kydland (1982), Prescott (1986)) by households and …rms. Prices are ‡exible clear markets in Walrassian way. Demand and supply in goods, factor and …nancial markets re‡ect optimising behaviour of households and …rms. Stochastic process of technology or public policy such as the government spending causes ‡uctuations of output employment and prices around the trend. More recent versions of RBC models includes non-Walrassian features, such as imperfect competition, externalities, assymetric information, departure from rationality and failure of market to clear- while explaining economic ‡uctuations (Black (1995), Cooley (1995)). Technical innovation (Shumpetarian) leads to a productivity shock, investments become profitable. Demand for investment goods rises along with output and interest rates and savings. Economy slows down with slow down in productivity. A simple RBC model can be illustrated as follows. Output 1
Yt = Kt (At Lt )
0
" T l X k s X X X s=1 l=1 k=1
R R t (s; l; k) t u
ytR (s; l; k)
T X TtR (s; l; k) + t
t
#
(D.457)
Mechanism for Poverty Alleviation:Proposition 4 Proposition 4: Growth requires that income of both poor and rich are rising over time: p p p (s; l; k) (s; l; k) < Tt+1 (s; l; k) < ::::: < Tt+T Ttp (s; l; k) < Tt+1
(D.458)
p p p Ytp (s; l; k) < Yt+1 (s; l; k) < Yt+1 (s; l; k) < ::::: < Yt+T (s; l; k)
(D.459)
R R R YtR (s; l; k) < Yt+1 (s; l; k) < Yt+1 (s; l; k) < ::::: < Yt+T (s; l; k)
(D.460)
Mechanism for Poverty Alleviation:Proposition 5 Proposition 5: Termination of poverty requires that every poor individual has at least the level of income equal to the poverty line determined by the society. When the poverty line is de…ned one half of the average income this can be stated as: Ytp (s; l; k)
1 > 2
N
1X h Yt (s; l; k) N h=1
181
!
(D.461)
Above …ve propositions comprehensively incorporate all possible scenarios in the poverty game mentioned above. Propositions 2-5 present optimistic scenarios for a chosen horizon T . Mechanism for Poverty Alleviation: Tests Testing above propositions in a real world situation is very challenging exercise. It requires modelling of the entire state space of the economy. Moreover in real situation consumers and producers are heterogeneous regarding their preferences, endowments and technology and economy is more complicated than depicted in the model above. In essence it requires a general equilibrium set up of an economy where poor and rich households participate freely in economic activities taking their share of income received from supplying labour and capital inputs that are a¤ected by tax and transfer system as illustrated in the next section.
4.2
Dynamic Computable General Equilibrium Model of Fiscal Policy
Most ot the models reviewed so far abtract away from more complex relations of productions and consumption in the economy and thus are of limited use in formulating economic policies at sectoral and household levels. Dynamic Computable General Equilibrium (DCGE) Models developmed in the last two decades have been phenomenal in creating an analytical and modelling structure that contains consumption, production and trade as in the real economies. These models are applied to assess the impact of tax, transfer, spending and trade policies not only on e¢ cient economic growth but also for evaluating the distribution of income over time. How can a set of policies be more e¢ cient in terms of welfare to one household rather than to another is evaluated with a social welfare function. Model is good for analysing available alternatives for long run growth prospects from the accumulation of physical and human capital or for evaluating the e¢ ciency gains from inter-temporally balanced budget or from the tax-transfer system or welfare reforms or from the low-carbon growth strategy. Short run ‡uctuations often studied in the Keynesian or the new Keynesian type economy could be introduced incorporating stochastic shocks to the production or the consumption sides of the economy (see Stern 1992 for desirable properties of this type of model). The comparative static frameworks in the pioneering work of Whalley (1975) has been improved signi…cantly in recent years. The general features of these models from Bhattarai (2007 and 2013) stated in this section as a brief introduction to this topic. Preferences Model adopts a standard Ramsey (1928) type time separable constant elasticity of substitution (CES) utility function to measure the welfare of households in each period. They 182
engage in the intra-period and inter-temporal substitution between consumption and leisure on relative prices, interest rate, wage rate, tax rates and spending allocations in the economy. It contains AIDS demand similar to that in Deaton and Muellbauer (1980) and has multiple nests. h The …rst stage of it is the aggregation at the level of goods and services Ci;t , next stage of the
nest is the choice between that composite goods and leisure Cth ; lth and …nally choice is over consumption-saving decisions across various periods based on Euler conditions. Thus the problem of household h is: max U0h =
1 X
t;h
Uth Cth ; lth
(D.462)
t=0
Subject to an intertemporal budget constraint of the form: "1 X
Pi;t 1 +
tchi
h Ci;t
+ wj;t 1
twih
h li;t
t=0
#
"
1 X h wi;t 1
twih
h Li;t
+ rj;t (1
h tki ) Ki;t
t=0
#
(D.463)
here tax rates on consumption and income tchi ; twih ; tki are set by the policy makers who aim for optimality and revenue neutrality in process of tax reform. Production Technology Each …rm in the model has a unit pro…t function (
i;t )
which is the
di¤erence between aggregate composite market price - the composite of prices of domestic sales (P Di;t ) and exports (P Ei;t ), and prices of primary inputs (P Yi;t ) and intermediate inputs (Pi;t ). Thus the problem of a …rm i is:
1
y
max
i;t
=
(1
i ) P Di;t
y
+
i P Ei;t
1 y 1
1
y y
i P Yi;t
d i
1 X ai;t Pi;t
(D.464)
t=0
Subject to production technology: 1
p
Yj;t = (1
i ) Ki;t
p
1
p
+
i Li;t
p
1 p 1 p
(D.465)
Sector speci…c capital (Ki;t ) accumulation: Ii;t = Ki;t Here
i
and
i
are share parameters,
y
(1
and
) Ki;t p
1
(D.466)
are elasticities of substitution in trade and
production, ai;t are the input-output coe¢ cients giving the economy wide forward and backward linkages.
183
The real returns (rj;t ) from investments across sectors are determined by the marginal productivity of capital that adjust until the net of business tax returns are equal across sectors. The nominal interest rates set by the central bank should converge to these real rates in the long run. Wage rate of household h; wth , equals its marginal productivity (Becker et al. 1990, Meyer and Rosenbaum 2001). 4.2.1
Trade arrangements
Economy is open for the trade. Domestic …rms supply products di¤erentiated from corresponding foreign goods. Traders decide on how much to buy (Di;t ) in the domestic markets and how much to import (Mi;t ) while supplying goods (Ai;t ) to the economy. Choice of consumers between imports and domestic consumption depend on the elasticity of substitution (
m)
between domestic supplies
and imported commodities in line of Krugman (1980) and Armington (1969). UK exports products that she produces at lower cost and imports products in which she has no comparative advantage. m
Ai;t = 1 X t=0
d m i Di;t
1
+
P Ei;t Ei;t =
m 1 m
m i Mi;t
1 X P Mi;t Mi;t
m y 1
(D.467)
(D.468)
t=0
UK economy, being one of the most liberal economies in the world, has almost no tax on exports and has very minimal tari¤s and non-tari¤ barriers on imports. 4.2.2
Government sector
Government receives revenues from direct and indirect taxes and tari¤s. These taxes are distortionary and a¤ect the marginal conditions of allocation in consumption, production and trade causing widespread shifts in the demand and supply functions of commodities.Which ones of these tax instruments are optimal sources of revenue and which ones are the most ine¢ cient for it and in generating growth process of the economy is a very important question but could be set following the logic of micro level incentive compatible mechanism of Mirrlees (1971, 2011) or in DiamondMirrlees (1971). It can adopt a balanced budget or a de…cit budget or a cyclically balanced budget or inter temporally balanced budget or it may simply peg de…cit to a …xed debt/GDP ratio. Which one of these strategies is adopted may depend on circumstances of the economy, policy debates and rules based on conventions and international commitments made in the treaties or agreements (i.e. EU or G20).
184
Rt =
H X N X
h tchi Pi;t Ci;t
h=1 i=1
H X N N X X h h h + twi wj;t LSi;t + tki ri Ki;t h=1 i=1
Gt
(D.469)
i=1
Ideally people’s preference for public good should decide the degree of freedom the government is given in determining the size public sector relative to the aggregate economic activities (Devereux and Love 1995, Barro (1990), Jensen and Rutherford (2002)). 4.2.3
General Equilibrium in a Growing Economy
General equilibrium is a point of rest, where the opposing forces of demand and supply balance across all markets in each period and over the entire model horizon. It is given by the system of prices of commodities and services, wage rate and interest rate in which demand and supply balance for each period (Hicks 1939). When a model is properly calibrated to the benchmark micro-consistent data set, such prices re‡ect the scarcity for those goods in the economy. Cost bene…t analysis or economic decisions can be based on real level of welfare for a set of alternatives available to the households, …rms and the government. Theoretically there has been much work, since the time of Walras, in …nding whether such equilibrium exists, or is unique or is stable (Scarf 1973, Feenberg and Poterba 2000, Feldstein 1985, Friedman 1962, Lee and Gordon 2005, Hines and Summers 2009, Naito 2006, Lockwood and Manning 1993, Bovenberg and Sørensen 2009). Uniqueness is guaranteed by the properties of preferences, technology and trade, such as continuity, concavity or convexity or twice di¤erentiability of functions. Explicit analytical solutions are possible only for very small scale models that are instructive but hardly representative of the economy (Heckman, Lochner and Taber 1998,García-Peñalosa and Turnovsky 2007). It is common to apply numerical methods to …nd the solutions of these models for a realistic policy analysis.
Yi;t =
H X
h Ci;t + Ii;t + Ei;t + gi;t
(D.470)
h=1 h
h
Lt = L0 en
h
Gt =
;t
= LSth + lth
N X gi;t
(D.471)
(D.472)
i=1
Markets for goods clear but the economy may not always be in equilibrium. Imperfections either in goods or input markets are common giving rise to monopolistic or oligopolist situations. Such imperfections in the markets are often represented by appropriately designed mark-up schemes (Dixit and Stiglitz 1977). These mark ups may be sensitive to strategic interactions between consumers and producers, …rms and government or between the national economy and the Rest of 185
the World. With widening gap between number of vacancies and unemployed workers it is possible to incorporate the equilibrium unemployment features of Mortensen and Pissarides (1994) in the model. 4.2.4
Procedure for Calibration
Computation and calibration of dynamic models like this are discussed in greater details in the literature (Blanchard and Kahn 1980, Sims 1980, Rutherford 1995, Smet and Wouters 2003, den Haan and Marcet 1990, Sims 1980, Kehoe 1985, Taylor and Uhlig 1990, Harrison and Vinod 1992). This model is calibrated to the reference path of the economy using the arbitrage condition in the capital market: k t Pi;t = Ri;t
t Ri;t = (r +
k Pi;t+1 k Pi;t
(1
i ) Pi;t
=
k i ) Pi;t+1
= (r +
1 1 + ri
(1
(D.473)
k i ) Pi;t+1
i)
(D.474)
(D.475)
This helps to calibrate the capital stock and the level of investment in equilibrium path: V i;t = (r +
k i ) Pi;t+1 Ki;t ;
Ki;t =
V i;t ; ri + i
k Pi;t = Pi;t+1
(D.476)
gi + i V i;t (D.477) ri + i Even a small reform in the public policy of a sector can have a large impact on the welfare and Ii;t =
growth over time if such policy has larger knock on e¤ects in the wider economy and removes the root source of the distortions that can have a detrimental impact on output, employment and investment levels in the economy. Most important aspect of DCGE model is that these provide an evolution of the economy along with essential structures that we observe in the real economies. Paths of the relative prices are such that all households and …rms are making optimal choices regarding their economic decisions. Model simulations based on the solutions with these parameters are compared for alternative policies under considerations. These provide basis for selecting the best policy that are dynamically prudent on for growth across sector and more equal distribution of income across households. See GAMS/MPSGE programmes and solutions in excel spreadsheets for a general understanding of the evolution of economies over time. 186
4.3
Exercise 6
1. An economy has to decide how much to consume today and how much save and invest to add into the capital stock that can help produce goods for future consumption. The optimal capital stock maximises the present value of utility from consumption. Problem of this economy is:
M ax U0 =
Z
T
e
rt
C (t) dt
(D.478)
0
subject to the production technology:
Q = Q(K)
(D.479)
Capital accumulation constraint: Kt =
@K =Q @t
C
K
(D.480)
Write the current value Hamiltonian for dynamic optimisation in this model. Discuss …rst order conditions and the terminal conditions required for dynamic optimisation Use a phase diagram to determine the convergence process towards the optimal capital stock. Apply this model for determining the optimal pricing strategy for exhaustible resources (nonrenewable resources) such as oil and gas in a competitive economy. 2. Consider a dynamic economy with Preference: M ax U0 =
Z
T
e
0
(1
Technology: Yt = At Kt Nt
)
1 t Ct
1
dt
(D.481)
assume At = 1 and Nt = 1
Capital accumulation: K t = Yt
Nt C t
Kt
All of the above notations have usual meaning. Write the current value Hamiltonian for this problem. Give four …rst order conditions for the dynamic optimisation in this economy. Characterise the balanced growth path using those conditions for this economy. Discuss the transitional dynamics in space when and when . 187
(D.482)
References [1] Acemoglu D. (2009) Introduction to Modern Economic Growth, Princeton. [2] Aghion P. and P. Howitt (1998) Endogenous Growth Theory, MIT Press, Cambridge MA. [3] Barro R. J. and Sala-I-Martin (1995) Economic Growth, McGraw Hill. [4] Bhattarai K. (2007) Welfare Impacts of Equal-Yield Tax Experiment in the UK Economy, Applied Economics, 39, 10-12, 1545-1563, June-July. [5] Cass, D. (1965): Optimum Growth in Aggregative Model of Capital Accumulation, Review of Economic Studies, 32:233-240. [6] Maddison A. (1991) Dynamic of Capital Accumulation and Economic Growth, Oxford. [7] Solow, R. M.(1956) A Contribution to the Theory of Economic Growth, Quarterly Journal of Economics, 70:1:65-95.
188
5
L5: Endogenous Growth Model
(This model is based on Basu and Bhattarai (2012) that has adapted Lucas-Uzawa (Lucas, 1988) model for analyis of government bias in on economic growth). Issues The e¤ect of public expenditure on educational attainment and growth is an unresolved issue. in majority of the cases, the active involvement of the government in the education sector is deemed to be a failure. If the government involvement in education has such questionable e¤ects on pupil’s educational attainment, the spillover e¤ect of this on economic growth thus also becomes debatable. Two E¤ects First is a positive complementarity e¤ect that arises because of the government provision of intermediate inputs in the form of teachers and other school aids. Second is a distortionary e¤ect that comes into play when the government taxes resources away from the non-education sector to …nance education spending. Such a spending based public education policy could fail if the latter negative e¤ect is stronger. Thus contrary to conventional wisdom, a blanket increase in government spending on education may not necessarily promote growth and welfare in all countries. 5.0.1
Human capital and …nal goods sectors
Human capital sector ht+1 = (1
h )ht
+ AH gt (lHt ht )1
(E.483)
Final goods sector yt = AG kt (lG ht )1
(E.484)
Capital accumulation kt+1 = (1 Financing education
189
k )kt
+ ikt
(E.485)
gt =
t yt
(E.486)
Social Planners Problem M ax
1 X
t
ln(ct )
t=0
subject to the resource constraint:
ct + it = (1
t )yt
(E.487)
and (E.483) through (E.485). Proposition 2 Along the balanced growth path, the optimal share of public spending in GDP is given by:
=
1 1
1+
: 1 1
lH lG
:
(E.488)
lH lG
In economies where private schooling e¤orts (lHt ) are higher, it is optimal to tax the goods sector more. Balanced Growth Properties the steady state government spending share in GDP is given by: gt = yt 5.0.2
(E.489)
Balanced growth
De…ne the gross balanced growth rate as : There are three key balanced growth equations. Based on the …rst order condition for the physical capital stock we get: =
[(1
)( yt =kt ) + 1
k]
(E.490)
Based on the …rst order condition for the human capital stock, one gets: = [1
h
+ AH (1
)
lH (yt =ht ) ]
(E.491)
Finally, using the human capital technology (E.483), we get a third balanced growth equation: =1
h
+ AH
(1
1 lH AG lG
190
)
(kt =ht )
(E.492)
Return to Schooling It is easy to verify that this value of human capital is the same as the ratio of the shadow price of consumption to that of investment in schooling. In other words, t
qth = where
t
and
t
(E.493)
t
are the Lagrange multipliers associated with the schooling technology (E.483) and
the ‡ow resource constraint (see E.487). Using the Euler equation for human capital (see (E.506), one gets the following valuation equation for the human capital:
h qth = mt+1 [fqt+1 f1
)(1 lGt+1 )1
h +AH gt+1 (1
ht+1
g+fAG (1
t+1 )(1
1 )kt+1 ht+1 lGt+1 g]
where mt+1 is the intertemporal marginal rate of substitution in consumption given by
(E.494)
t+1 = t :
Next verify from (E.504) in the appendix that qth =
(1
G t )M P Ht E M P Ht
(E.495)
Return to Schooling Rewrite (E.494) as h qth = mt+1 qt+1 (1
h
E + lHt+1 M P Ht+1 ) + lGt+1 (1
G t+1 )M P Ht+1
(E.496)
h The return to schooling (Rt+1 ) is thus given by:
h Rt+1 =
h qt+1 (1
h
E + lHt+1 M P Ht+1 ) + lGt+1 (1 qth
Rh = 1
h
G t+1 )M P Ht+1
+ M P HE
(E.497)
(E.498)
Using (E.498) one can rewrite the balanced growth equation (M.1196) as follows: 1 + g = Rh
(E.499)
Comparison of (M.1195) with (E.499) immediately reveals a familiar arbitrage condition that the return on human capital must balance the after tax return on physical capital. In other words, Rh = (1
)( y=k) + 1
191
k
(E.500)
Table 51: Cross country steady state distribution of the education technology lH AH k=y Mean
0.47
0.15
0.07
1.91
Std Deviation
0.07
0.02
0.03
0.21
Table 52: Regional Features of the Government Bias in Education Asia 0.057
5.0.3
Europe 0.078
Latin America and
Middle East
Carribean
and North Africa
0.068
OECD
0.063
0.08
North
South
America
Asia
0.096
0.036
Africa 0.077
Cross country calibration of government bias in education
Cross country calibration of government bias in education Let
First order conditions
t;
t ;be
the Lagrangian multipliers associated with the ‡ow budget
constraint (N.1408), human capital technology. The Lagrange is: 1 1 P P t L= U (ct ) + t=0 1 P
+
t=0
t [AG (1
t )kt
t=0
t [(1
(lGt ht )1
+ AH gt (lHt ht )1
h )ht
+ (1
k )kt
ct
kt+1 ]
ht+1 ]
First order conditions are: t
ct :
kt+1 :
ht+1
:
t
t
=
+
lGt :
t (1
+
t+1 [(1
t+1 [1
:
t yt
=
yt+1 +1 kt+1
t (1
1 t
192
k]
)ht+1
=0
(E.502)
1 lHt+1 ]
(E.503)
1 )kt+1 ht+1 lGt+1 ]
kt h1t
t AH
(E.501)
t
+ AH gt+1 (1
t+1 )(1
t )AG lGt
t
t+1 )
h
t+1 [AG (1
)(1
U 0 (ct ) =
(ht lHt )1
)gt AH h1t
yt
lHt = 0
(E.504)
(E.505)
Table 53: Cross country correlations of the key macroeconomic varaibles lH AH k=y Rh lH
1
AH
0.92
1
-0.64
-0.39
1
-0.94
-0.96
0.35
1
-0.14
0.12
0.81
-0.19
1
0.93
0.99
-0.46
-0.95
0.01
1
0.93
0.99
-0.46
-0.95
0.01
1
k=y
R
h
1
The expression for the optimal tax rate in proposition 1 immediately
Proof of Proposition 1
follows after substituting out
t= t
from (E.504) and (E.505). One gets the optimal tax rate:
t
=
1 1
1+
: 1 1
lHt lGt Ht : llGt
Next, we exploit the fact that along the balanced growth path, the time allocations to goods and schooling (lGt and lHt ) are constants. Unless the time allocations are constant, a constant balanced growth rate does not exist because the marginal product of capital will be time varying (see (E.502)). Since lGt is a constant, this means that the optimal tax rate
t
is also stationary.
Derivation of the Balanced Growth Equations Hereafter we drop time subscripts for variables which are stationary along the balanced growth path. To prove (M.1195), use (E.501) and (E.502). To get (M.1196), rewrite (E.503) as:
t
t+1
=
t
t+1
:
t+1
+
t+1 t
t
t+1 t
h
fAG (1 t+1
Using (E.501), check that balanced growth condition
[1
t
=
+ AH gt+1 (1 )(1
ct ct+1 :
)(1
lGt+1 )1
ht+1
]
(E.506)
1 t+1 )kt+1 ht+1 lGt+1 g
Use (E.505) to substitute out
t t
and also use the
= =(1 + g) which upon substitution in (E.506) yields:
= [1
h
+ AH (1
)
To get (M.1197) use (E.483), (N.1405) and (M.1192). Proposition
193
lH (yt =ht ) ]
(E.507)
Proposition 3 The tax rate that maximizes growth also maximizes the long run welfare. Proof. The steady state welfare can be written as:
Wt
=
1 X
j
ln ct+j
j=0
= =
ln ct ln + 1 (1 )2 ln kt ln(ct =kt ) + + 1 1 (1
(E.508) )2
ln
Use the resource constraint (N.1408) and the balanced growth condition to very that Proposition ct (1 )yt = + (1 kt kt Proof. Next plug (M.1195) into (E.509) to …nd 1 ct = kt which upon substitution in (??) yields
(1
k)
)(1
(E.509)
)
ln kt 1 + ln( (1 )) + ln + ln 2 1 (1 ) This shows that the steady state welfare is positively related to growth rate. Wt =
(E.510)
(E.511)
Thus the growth maximizer tax rate is also a welfare maximizer. 5.0.4
Conclusion The e¤ect of public education spending on growth is an empirically unsettled issue.
A
plethora of studies document that public education spending does not help promote growth. Our cross country stylized facts also support this …nding. Growth and schooling returns are in fact lower in countries with a higher ratio of public spending to GDP except for very high education spenders. In this paper, we reopen this issue and investigate this within an endogenous growth framework. Public spending on education appears directly in the human capital technology. The relative intensity of public and private spending on education in the human capital production, which we call government bias in education, appears to be a fundamental determinant of cross country dispersion in long run growth and schooling returns. 194
Conclusion A higher government bias has con‡icting e¤ects on growth. On the one hand, it lowers growth by crowding out private schooling e¤orts. On the other hand, it promotes growth through the complementarity channel. The latter e¤ect is stronger in countries which have historically a greater government bias in education. Based on our growth model, we estimate this government bias parameter for a wide range of countries and …nd that the government bias in education is generally higher in rich countries. The policy implications of our analysis is that an increase in public spending on education without adequate infrastructural support may not necessarily be bene…cial for the society. For the complementarity e¤ect of public spending to dominate, a nation may need a greater educational infrastructure. This infrastructural role of the government in education is an area worth exploring in future research. see: Basu P. and K. Bhattarai (2012) 1) Cognitive Skills, Openness and Growth, the Economic Record, 88: 280: 18-38, March; 2) Government Bias in Education, Schooling Attainment and Long-run Growth, Southern Economic Journal, 79(1), 127-143.
See dynare programme:BB_Er_…nal.mod and GAUSS programme growth.g and data…le EDU_GDP_EXP_IMP_gr_panel.cs
5.0.5
China, India and SAARC Countries in the Global Growth Competition
The process of convergence and divergence has been going on in the global economy in the last three hundred years after the scienti…c discoveries and technical innovations that have fundamentally changed the nature of production, exchange and consumption. Industrialisation came to the current stage going through stages of development from 18th to the last quarter of 20th century. This process has further intensi…ed in the last six decades. Every country in the world wants to achieve a higher rate of growth of GDP per capita. While the countries in the West were successful in achieving higher growth till 1980s the growth pole has now gradually shifted towards the countries in developing Asia including India in the South Asia. Stylized facts of growth and economic development presented here are based on the data sets from the World Economic Outlook of the IMF and World Bank Development Indicators (WBDI). Economists generally agree on the factors that lead to economic growth as above based on experienced of Western Europe, North America, Japan and other advanced economies. Policies that raise the rate of accumulation of physical and human capital and advancement in the production
195
technology lead to higher economic growth (Madison (1995)). Classical, neoclassical and endogenous growth models have been constructed to show the precise relationships among these factors and economic growth. Early versions of South Asian growth models used by the Planning Commission of these nations were based on basic Harrod-Domar set up where given the capital output ratio increasing growth required just increasing the rate of national saving. Then there were various sectoral decomposition exercises aimed to …t the aggregate target. Big gaps remained between targets and accomplishments. Levels of per capita income were similar across all SAARC countries till 1980 but these started to di¤er substantially following the economic reforms and liberalisations that started in India in late 1980s (after the success of similar trend in China). Kotwal, Ramaswami and Wadhwa (2011) explain how the recent growth in India was spurred by exports of high tech services rather than manufacturing products as in China. The average growth rate in developing Asia has been 7 to 8 percent in the last 30 years, twice the global average and three times or more of that in the EU economies. After decades of sluggishness, growth rates in South Asian countries have been higher than those in other regions of the world; particularly very impressive in India (5.5 to 7.0 percents) and china (8.5 to 10.3 percents). Bosworth and Collins (2008) provide growth accounting at aggregate and sectoral levels of the extraordinarily growth occurring in China and India, residence of over one third of the global population; less than 20 percent population reside now in advanced countries. Thus a higher growth rate in China and India in next two three decades is likely to tranform the structure of the global economy. Table 1: GDP growth rates around the globe ASEAN-5
ADV Econ
5.30 5.03 4.87 5.61
3.12 2.78 1.78 1.88
1980-89 1990-99 2000-09 2010-14
CIS
CE Europe
-4.26 5.98 3.72
2.11 1.70 3.90 3.30
DevAsia EmDevEcon.
6.79 7.36 8.31 7.37
EuroA
3.51 3.67 6.15 5.66
1.97 1.35 0.68
EU Majadv (G7)
2.15 2.16 1.75 0.93
3.03 2.55 1.45 1.87
MENA
MENAP
OthAdv
SSA
WestHm
World
1.47 4.35 5.42 3.99
1.99 4.37 5.34 3.94
4.73 4.33 3.37 3.28
2.60 2.23 5.53 5.39
2.12 2.97 3.18 3.86
3.24 3.09 3.62 3.75
Table 2: Average annual growth rate of GDP in SAARC countries (%) Afghanistan 1980-89 1990-99 2000-09 2010-14
9.23 6.72
Bangladesh 3.28 4.80 5.82 6.15
Bhutan 9.37 5.33 8.10 8.66
China 9.76 10.00 10.29 8.46
India 5.54 5.63 7.00 5.81
Maldives 10.52 6.61 7.10 4.33
Nepal Pakistan Sri Lanka 4.10 6.59 4.21 4.87 4.50 5.61 4.14 4.69 4.64 4.25 3.34 7.13
Table 2: GDP per capita, current prices ($) Afghanistan 1980 1990 2000 2010 641 2014 641
Bangladesh 236 284 355 703 1006
Bhutan 321 544 802 2063 3042
China 307 341 946 4423 7138
India 277 386 461 1432 1389
Maldives 413 1092 2967 6668 7501
Nepal Pakistan Sri Lanka 138 374 301 215 483 509 247 581 917 596 1034 2429 703 1234 3360
By maintaining average 8 percent growth, it is possible that India will catch up the advanced countries in the West and the East in per capita income within a generation. Other SAARC (South
196
Asian Assotiation for Regional Cooperation) member countries, may be able to converge to India in per-capita income taking appropriate actions to create stable institutions and socioeconomic conditions required for growth. By the size of the economy and manpower-strength, India is the centre of the economic gravity with seven smaller economies surrounding it. Considering the growth success story of China since 1980s, which is in the eastern neighbor of this region, it is very essential and bene…cial to India to have an integrated approach for the development of these countries in South Asia. Modi’s recent proposal for HIT-ways9 (highways, information technology and transmission ways) for the region is a timely and visionary proposal for growth. In an address on the Independence Day 2014 he has proposed new strategies including i) "no defect" and "zero e¤ect" approach to manufacturing, ii) a model village in each constituency iii) new initiative for expanding bank accounts to million of poor households, iv) massive investment on skills and sanitation iv) …ght against poverty in all SAARC countries and v) an open approach to the foreign direct investment or "make in India". Several strategic points for growth emerging from the analysis of facts in this paper are worth considering in this context. These are as follows: 1. Given the 20 percent population residing in South Asia this region should push for growth and increase its share of global GDP up to 20 percent from roughly 6.5 percent in 2014. 2. Such growth requires increasing the ratio of saving and investment about 10 percent above the current averages around 35 percent. 3. Process of structural transformation should continue so that output and employment increases substantially in industrial and services sectors and till both output and employment in the agriculture sector are less than 5 percent from around 17 and 50 percent in recent years. 4. Such transformation will occur as this region moves towards urbanisation so than about 90 percent of the population starts living in urban area with facilities. Building mega cities like this will create not only employment but also income. It also will gradually free up rural lands for more scienti…c cultivations and other meaningful economic uses. 5. On manpower issues it is important to reduce the student teacher ratio from 40 to close to 16 to raise the quality of education and cognitive skill among children. This is essential for human capital required for science and technology and for improving the PISA scores. 6. Revenue and spending of government should balance at least in the medium term and debt to GDP ratio should not increase over 50 percent of GDP; the size of the public sector is not over 30 percent of GDP. 9 It
is very appropriate for India’s new government to take extra initiative on forming growth links with China
(including Xi Jinpin’s announcement for building industrial parks Gujarat and improving railnetworks in South India), Japan (making Varanasi a smart city) and other advanced countries including Germany and United states.
197
7. Trade ratio should increase to around 100 percent from the 50 percent at this time. Free trade regimes can enhance both the supply and demand side of the economy. 8. Liquidity of the …nancial system need at least to treble to have a smooth ‡ow of credits required for new and existing enterprises. 9. Free convertibility of currency is essential to protect this region from international shocks. 10. A high 8 percent growth strategy is consistent with all above and requires …rm commitment, e¢ cient and strong public administration. Gini coe¢ cient should not be above 35 percent for social integrity and cohesion. Size of the SAARC region has increased to around 7 percent of global GDP in PPP which more has more than doubled since 1980. However this growth in global share pales when compared to China which raised its global share to 16.5 in 2014 percent compared to 6 percent of India. Srinivasan (2005) reports on TFP growth rates underlying these trends. Economic integration of the South Asian region must base on the strength of its members. India is stable, dynamic and economic power of the region. Bhutan and Maldives two tiny countries of the region are doing better economically by pursuing strategies appropriate to the vastly growing production sectors and middle classes in India. Bhutan is bene…ting by proximity of India by developing a number of hydro power stations generating electricity to sell to India. Maldives is developing fast by tourism aiming at individuals in the growing middle income class in India. Bangladesh is achieving higher growth rates than before by exporting textiles but still caught in natural disasters and political problems. War torn Afghanistan and Pakistan could not emerge above the ethnic con‡icts to focus on economic growth. Despite uprooting the age old monarchy and being able to restore the peace with Maoists it is an irony that Nepal is yet struggling to form a political consensus to draft a new constitution for the republic of Nepal. Given above potentials and absurdities a systematic study, particularly focusing on the role that India can play in development of the South Asia region has become an interesting topic of research, apparently very little is found on this in the existing literature. There is no single economic model that is perfect and …t for analysis of all important issues relating to growth and development. Each type of model has its strength and limitations. Since the overall objective is having a comprehensive understanding of underlying factors that in‡uence on growth and development it is essential to consider each of these models and appreciate how it can contribute to our understanding of the economy. We illustrate this by applying a panel data model of growth, dynamic CGE model with …nancial deepening, macroeconometric model for macroeconomic forecastging and a policy coordination model to analyse gains from cooperation to enhance growth and development in India and SAARC countries in this section. 198
5.0.6
Dynamic Panel Data Model of Economic Growth
Growth models show how the output per capita increases over time with accumulation of physical and human capital and improvement in technology (Solow (1956), Lucas (1988), Romer (1990)). However the growth rates di¤er signi…cantly by countries and the degree of convergence in per capita income varies substantially across nations. Frustrated from the dismal growth performance from 1950-1980s Malenbaum (1982) even stated pessimistically that "decades of slow growth lie ahead before either nation emerges as a modern industrial state of developed-nation status". Fortunately there occurred a structural break in the growth process around mid 1980s in India motivating Rodrik and Subramanian (2005) to assess policy and structural factors that caused a surge from "Hindu growth" to productivity surge. These surges occurred because of the reforms of the labour market giving freedom in hiring and …ring of workers to …rms, end of reservation in small scale industries, reforms of the banking sector, simpli…cation of FDI rules, improvement in infrastructure and reduction of debt. These policy factors accelerated growth in India starting in early 1990s (Kaur (2007)). Agrawal (2010) empirically establishes causality between savings and economic growth in India. Bosworth and Collins (2008) provided growth accounting at aggregate and sectoral levels of the extraordinarily growth occurring in China and India. From the panel data analysis and endogenous growth models Basu and Bhattarai (2012a) found that cognitive skill and openness to be factors of higher economic growth. Shocks to the technology sectors caused more macroeconomic ‡uctuations than the total productivity shocks in the short run in their models. Education is the key for growth but it is the joint responsibility of public and private sectors to educate children. Public bias to education does not produce desired results (Basu and Bhattarai (2012b)). South Asia forms the part of global economy in both of these endogenous growth models. We estimate coe¢ cient the dynamic panel data model of growth for the South Asian economies report results in Table 14. This shows in general trade ratio and investment ratios contribute signi…cantly and positively on the growth rates of per capita income but the higher population growth rates reduced output growth rates signi…cantly. However there are country and time speci…c factors at play as growth rate vary signi…cantly across countries and time years. 5.0.7
GMM 2-step Estimation of Growth in South Asia
Consider a dynamic panel data model of the form where growth rate of output of country i at time t, yi;t is explained by its lagged values and a set of exogenous explanatory variables xi;t . Here individual speci…c e¤ects and
t
i
is
represents the time speci…c e¤ects.
yi;t = yi;t
1
+
i
+
i xi;t
+
t
+ +ei;t
@Pj;t ). Term of trade is in favour of the home country. Higher domestic wage rate makes home country less competitive causing a fall in the exchange rate but it rises
when wage rate increases in the foreign country, (@Ei;t # if @wi;t > @wj;t ). Similar arguments apply to the interest rate. Higher domestic interest rate pushes exchange rate up by raising the the cost
of capital at home but higher interest rate abroad makes the foreign country less competitive and raises the value of home currency (@Ei;t # if @ri;t > @rj;t ). Increase in labour and capital at home
lowers the price of commodity and hence puts downward pressure on the exchange rate but these are sensitive to productivity of labour and capital inputs, (@Ei;t " if @Li;t > @Lj;t or @Ki;t > @Kj;t ). Table 1: Theoretical Predictions from Dynamic Two Country Trade Model
Pi;t
Pj;t
wi;t
wj;t
ri;t
rj;t
Yi;t
Yj;t
Li;t
Lj;t
Ki;t
Kj;t
Ei;t
Ci;t
Mi;t
Ei;t
+
-
-
+
-
+
+
-
-
+
-
+
+
-
1
-
+
Yi;t
+
-
-
+
+
-
1
+
+
-
+
-
-
+
+
-
+
ri;t
-
+
+
-
1
+
+
-
+
-
-
+
+
-
-
+
-
wi;t
-
+
1
+
+
-
+
-
-
+
+
-
-
+
-
+
-
Ci;t
-
+
+
-
+
-
-
+
+
-
+
-
-
+
-
1
+
+
1
i;t
j;t
Mi;t + + + + + + + + Similar arguments can be made to other model variables including the GDP (Yi;t ) ;wage rate (wi;t ) ;interest rate (ri;t ) ; consumption (Ci;t ) ; and imports (Mi;t ) as illustrated in Table 1. The model solutions can di¤er remarkably when two countries di¤er in productivites of capital i;t ;
j;t
or interest rates (ri;t ; rj;t ) or the wage rates (wi;t ; wj;t ) or in the stock of capital
(Ki;t ; Kj;t ) or endowments of labour (Li;t ; Lj;t ) or in tari¤s and tax rates (tmi;t ; tcj;t ) or in the 268
preferences and technologies ( i ;
i;
i) :
Cooperation in policies of home and foreign countries can
result in mutually bene…cial in‡ows and out‡ows or the retaliation could result in the collapse of trade as seen in 2008-09 recession when international demand or supply shocks had reduced global trade by up to 14 percent. How such structural features of the real exchange rates underpin the patterns of the nominal exchange rates is well explained in the studies of Mundell (1957), Meade(1978), Miller and Spencer (1977), Eaton (1987), Neary (1988), Taylor (1995), and Eaton and Kortum (1999). In short, the long run equilibrium real exchange rate is a consequence of the balancing forces of the demand and supply for home and foreign products.
References [1] Ahn J.B, M. Amity and D.E. Weinstein (2011) Trade …nance and the greate trade collapse, American Economic Review, 101:3:298-302. [2] Baak, S.J. (2008) The bilateral real exchange rates and trade between China and the U.S., China Economic Review, 19 (2): 117-127. [3] Bahmani-Oskooee, M., and A. Ratha (2010), S-Curve dynamics of trade between U.S. and China, China Economic Review, 21 (2): 212-223. [4] Bahmani-Oskooee, M. and Wang, Y. (2007), United States-China Trade at the Commodity Level and ther Yuan-Dollar Exchange Rate. Contemporary Economic Policy, 25: 341–361. [5] Balassa Bela (1967) Trade Creation and Trade Diversion in the European Common Market, Economic Journal, 77:305:Mar.:1-21 [6] Baldwin R. E. (1992) Measurable Dynamic Gains from Trade, Journal of Political Economy, 100:1 :Feb: 162-174 [7] Bergin, P.R., and R.C. Feenstra (2009) Pass-Through of Exchange Rates and Competition between Floaters and Fixers, Journal of Money, Credit and Banking, 41 (s1): 35-70. [8] Bhagwati J. (1964) The Pure Theory of International Trade: A Survey, Economic Journal, 74:293:1-84. [9] Bhattarai K. (2011) Econometric and stochastic general equilibrium models for evaluation of economic policies, Int. J. Trade and Global Market, 4:2:212-241. [10] Bhattarai, K.R. and J. Whalley (2006) Division and Size of Gains from Liberalization of Trade in Services, Review of International Economics, 14 (3): 348-361, August.
269
[11] Bhattarai K. and S. Mallick (2013) Impact of China’s currency valuation and labour cost on the US in a trade and exchange rate model. North American Journal of Economicsand Finance, 25:40-59. [12] Corden, W.M. (2009), China’s Exchange Rate Policy, Its Current Account Surplus and the Global Imbalances. The Economic Journal, 119: F430–F441. [13] Dekle R, J. Eaton, and S. Kortum (2007) New approaches to international trade: Unbalanced Trade, American Economic Review, 70:2:351-355. [14] Eaton J. (1987) Dynamic speci…c factor model of international trade, Review of Economic Studies, 54:2: 325-338, April. [15] Eaton J and S. Kortum (2002) Technology, Geography, and Trade, Econometrica, 70: 5:Sep:1741-1779 [16] Frenkel J. A. and M. L. Mussa (1981) Monetary and …scal policies in an open economy, American Economic Review, 71:2:PP:May 253-258. [17] Fry R. and A. Pagan (2011) Sign restrictions in structural vector autoregressions: a critical survey, Journal of Economic Literature, 49:4:938-960. [18] Gopinath G., P.O Gourinchas, C.T Hsieh and N. Li (2011) International prices, costs and markup di¤erences, American Economic Reivew, 101 (6): 2450-2486. [19] Granville, B., S. Mallick, and N. Zeng (2011), Chinese exchange rate and price e¤ects on G3 import prices, Journal of Asian Economics, 22 (6): 427-440. [20] Grosssman G.M. and E. Helpman (1990) Comparative Advantage and Long-Run Growth, American Economic Reivew, 80:4:796-815. [21] Imbs, J.M., Mumtaz, H., Ravn, M.O., Rey, H. (2010), One TV, One Price? Scandinavian Journal of Economics, 112 (4): 753-781. [22] Johnson H. G. (1951-1952). Optimum welfare and maximum revenue tari¤s, Review of Economic Studies, 19:1:28-35. [23] Krugman P. (1980) Scale Economies, Product Di¤erentiation and the Pattern of Trade, American Economic Review, 70:5:950-959. [24] Krugman P. and A. J. Venables (1995) Globalization and the Inequality of Nations, Quarterly Journal of Economics, 110:4: Nov: 857-880.
270
[25] Markusen J. R. and L. E. O. Svensson (1985) Trade in Goods and Factors with International Di¤erences in Technology, International Economic Review, 26:1:Feb:175-192. [26] Melitz M. T. (2003) The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity, Econometrica, 71:6:1695-1725. [27] Marquez, J. and Schindler, J. (2007), Exchange-rate E¤ects on China’s Trade. Review of International Economics, 15: 837–853. [28] Meade, James (1978) The Meaning of Internal Balance, Economic Journal, 88 (351): Sep 423-435. [29] Mehrotra, A.N. (2007) Exchange and interest rate channels during a de‡ationary era— Evidence from Japan, Hong Kong and China, Journal of Comparative Economics, 35 (1): 188-210. [30] Miller, M. H.; Spencer, J. E. (1977)The Static Economic E¤ects of the UK Joining the EEC: A General Equilibrium Approach Review of Economic Studies, 44:1: 71-93, Feb [31] Mundell R. A. (1957) International Trade and Factor Mobility, American Economic Review, 47: 3:Jun: 321-335. [32] Naylor R (2000) Trade and Wages When the Trade Regime is Determined Endogenously, Review of International Economics, 8:3:556-565. [33] Neary P.J. (1988) Determinants of the Equilibrium Real Exchange Rate, American Economic Review, 78:1:Mar.: 210-215. [34] Norman V. D. and A. J. Venables (1995) International trade, factor mobility and trade costs, Economic Journal, 105:433:1488-1504. [35] Ra…q, M.S. and S.K. Mallick (2008) The e¤ect of monetary policy on output in EMU3: A sign restriction approach, Journal of Macroeconomics, 30 (4): 1756-1791. [36] Sim C.A (1980) Macroeconomics and Reality, Econometrica, 48:1 Jan.1 -45. [37] Sims, C.A. and T. Zha (1999) Error Bands for Impulse Responses, Econometrica, 67 (5): 1113-1155 [38] Stock, J.H., and M.W. Watson (2001). Vector Autoregressions, The Journal of Economic Perspectives, 15 (4): 101-115. [39] Turnovsky S. (1999) International Macroeconomic Dynamics, MIT Press.
271
[40] Taylor, M. (1995) The Economics of Exchange Rates, Journal of Economic Literature, March, 33,1: 13-47. [41] Ventura, J. (1997) Growth and Interdependence, Quarterly Journal of Economics, 112 (1): 57-84. [42] Xu Chenggang (2011) The fundamental Institutions of China’s reforms and Development, Journal of Economic Literature, 49:4:1076-1151. [43] Xu, Zhenhui (2008), China’s Exchange Rate Policy and Its Trade Balance with the US, Review of Development Economics, 12 (4): 714-727. [44] Witte, M.D., (2009) Pricing to Market: Chinese Export Pricing to the USA after the Peg, China & World Economy, 17 (2): 65-78.
7.5
International macroeconomic policy coordination
Basics of the Nash policy game Let us consider three countries aiming for a policy coordination with the Nash utility frontier Nt = U1;t U2;t U3;t
(G.714)
Each receive utility from consuming products produced in each country: Ui;t = F (y1;t; y2;t ; y3;t )
(G.715)
Goods supply process is determined simultaneously as y1;t =
1;0
+
1;2
y2;t +
1;3
y3;t +
1;1
y1;t
1
+
1;2
y2;t
1
+
1;3
y3;t
1
+ e1;t
(G.716)
y2;t =
2;0
+
2;1
y1;t +
2;3
y3;t +
2;1
y1;t
1
+
2;2
y2;t
1
+
2;3
y3;t
1
+ e2;t
(G.717)
+
3;1
y1;t +
3;2
y2;t +
3;1
y1;t
1
+
3;2
y2;t
1
+
3;3
y3;t
1
+ e3;t
(G.718)
Nash to VAR y3;t =
3;0
272
0
1
B B @
3;1
B = B @
1;0 2;0 3;0
1;3
1
2;1
0
7.6
1;2
2;3
1
3;2
0
1
C B C+B A @
10
1;1
1;2
2;1
2;2
3;1
3;2
y1;t
1
C CB CB y C A @ 2;t A y3;t 10 1;3
2;3
3;3
y1;t
CB CB y A @ 2;t y3;t
0
e1;t
10
y1;t
1
1
C C B C+B e C A @ 2;t A e3;t
1 1 1
(G.719)
Nash-VAR Policy Game 0
=
1
y1;t
C B B y C @ 2;t A y3;t 0 1 B B 2;1 @ 3;1
0 B B @
1
B +B @
2;3
1
3;2
C C A
2;3
1
3;2
1 2;1
1
1;3
1
3;1
C C A
1;3
1
1;2
2;1
0
1;2
1
1;2
1;3
1
3;1
3;2
2;3
1
Paramters of Nash Policy Game
1
1
1
0
1
C C+ A
B B @
1;0
B B @
1;1
1;2
1;3
2;1
2;2
2;3
3;2
3;3
2;0 3;0
0 1
C C A
0
3;1
1
CB CB y A @ 2;t y3;t
e B 1;t C B e C @ 2;t A e3;t
1 1 1
1 C C A (G.720)
In common meetings or summits they decide policies given by
1;0
;
2;0 ;
3;0
but each of them
face idiocyncratice shocks e1;t ; e2;t ; e3;t Then each country determine its action yi;t taking account of actions taken by others yj;t and such response patterns are given by parameters
1;2
;
1;3 ;
2;1
;
2;3
;
3;1
;
3;2
,
1;2
;
1;3 ;
2;1
;
and shocks e1;t ; e2;t ; e3;t : Each would like to get more utility and this opens the bargain. The optimal solution of this game should ful…ll four properties of Nash bargaining game. This must be symmetric, e¢ cient, linear invariance and IIA. 273
2;3
;
3;1
;
3;2
7.6.1
Estimates for the Nash Policy Game
Estimates for the Nash Policy Game between Advanced and BRIC Countries Table 68: Interdependence in Economic Growth between US, EU and BRIC Countries USGR
EUGR
JPGR
CHGR
INGR
BRGR
RUGR
USGR_1
0.903 (10.1)
0.222 (1.06)
0.323 (1.81)
-0.153 (-1.39)
-0.203(-1.26)
0.004(0.02)
0.184(0.58)
EUGR_1
-0.049 (-0.45)
0.388(1.54)
-0.241 (-1.22)
0.118 (0.89)
0.167(0.86)
-0.046(-0.20)
-0.358(-0.94)
JPGR_1
0.187 (1.91)
0.538(2.34)
0.682 (3.48)
0.153(1.27)
-0.023(-0.13)
0.084(0.40)
0.880(2.54)
CHGR_1
0.071 (0.79)
0.543(2.59)
0.194 (1.09)
0.645(5.84)
0.138(0.85)
0.027(0.18)
0.798(2.52)
INGR_1
0.072(1.07)
-0.052(-0.34)
0.167(1.24)
0.251(3.01)
0.562(4.60)
0.479(3.11)
-0.193(-0.81)
BRGR_1
-0.135 (-1.91)
-0.356(-2.14)
-0.031 (-0.22)
-0.095(-1.08)
-0.052(-0.40)
0.479(3.11)
-0.543(-2.16)
RUGR_1
-0.499(-0.76)
0.086(-0.56)
0.117(0.88)
-0.095(-1.17)
-0.077(-0.64)
0.060(0.42)
0.719(3.08)
Constant
-0.270(-0.36)
-2.323(-1.28)
-2.322(-1.28)
2.119(2.22)
2.137(1.53)
-2.675(-1.60)
-2.706(-0.99)
RSq (Adj)
0.84
0.75
0.61
0.71
0.45
0.55
0.69
F-stat
45.9
24.9
13.5
20.7
7.6
10.7
18.7
T-values are in the parentheses.
Impulse Responses in Growth between US, EU and BRIC Countries Estimates for the Nash Policy Game between Advanced Country Club Table 69: Rich Country Growth Club USGR EUGR JPGR
CHGR
USGR_1
0.961(12.8)
0.287 (1.06)
0.242 (1.67)
-0.103(-1.06)
EUGR_1
-0.103(-2.39)
0.617(1.54)
-0.046(-0.55)
-0.038(-0.68)
JPGR_1
0.045(0.57)
0.130(2.34)
0.624(4.13)
0.067(0.66)
CHGR_1
0.085(1.19)
0.336(2.59)
0.235(1.70)
0.813(8.73)
Constant
-0.401(-0.54)
-2.425(-1.32)
-2.473(-1.72)
2.147(2.21)
RSq (Adj)
0.84
0.71
0.61
0.65
F-stat
77.1
37.4
23.9
28.3
T-values are in the parentheses.
274
US-EU and Japan Growth Club Accumulated Response to Cholesky One S.D. Innov ations ± 2 S.E. Accumulated Response of USGR to USGR
Accumulated Response of USGR to EUGR
Accumulated Response of USGR to CHGR
12
12
12
8
8
8
8
4
4
4
4
0
0
0
0
-4
-4
-4
-4
-8
-8 1
2
3
4
5
6
7
8
9
-8
10
1
Accumulated Response of EUGR to USGR
2
3
4
5
6
7
8
9
10
-8 1
Accumulated Response of EUGR to EUGR
2
3
4
5
6
7
8
9
10
1
Accumulated Response of EUGR to JPGR
15
15
15
10
10
10
10
5
5
5
5
0
0
0
-5 1
2
3
4
5
6
7
8
9
1
Accumulated Response of JPGR to USGR
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
1
Accumulated Response of JPGR to JPGR
12
12
12
8
8
8
8
4
4
4
4
0
0
0
-4 1
2
3
4
5
6
7
8
9
1
Accumulated Response of CHGR to USGR
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
1
Accumulated Response of CHGR to JPGR
8
8
8
6
6
6
6
4
4
4
4
2
2
2
0
0
0
0
-2
-2
-2
-2
-4
-4
-4
-4
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
8
9
10
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
Accumulated Response of CHGR to CHGR
8
1
7
-4 1
Accumulated Response of CHGR to EUGR
6
0
-4
10
5
Accumulated Response of JPGR to CHGR
12
-4
4
-5 1
Accumulated Response of JPGR to EUGR
3
0
-5
10
2
Accumulated Response of EUGR to CHGR
15
-5
[Figure]
Accumulated Response of USGR to JPGR
12
2
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Estimates for the Nash Policy Game in the BRIC Club Table 70: BRIC Country Growth Club CHGR INGR BRGR
RUGR
CHGR_1
0.679(6.35)
0.170(1.08)
0.409(2.23)
0.790(2.34)
INGR_1
0.272(3.36)
0.597(5.02)
0.025(0.18)
-0.247(-0.97)
BRGR_1
-0.014(-0.21)
-0.034(-0.33)
0.504(4.19)
-0.255(-1.15)
RUGR_1
-0.009(-0.31)
-0.013(-0.30)
0.053(1.03)
0.750(7.88)
Constant
1.225(1.62)
1.440(1.30)
-2.820(-2.17)
-3.822(-1.60)
RSq (Adj)
0.71
0.45
0.57
0.62
F-stat
35.9
12.6
19.7
24.3
T-values are in the parentheses.
7.7
Multicountry macro interaction model Yi;t = Ci;t + Ii;t + N Xi;t + Gi;t
(G.721)
Consumption function for this country is
Ci;t =
i Yi;t 1 ;
275
0
0
(H.823)
In‡ation and output (Supply or Phillips curve) (
t)
t
= c yt
yt
1
1
;
c>0
(H.824)
a > 0; b > 0
(H.825)
Interest rate determination rule it = i + a (yt
yt ) + b (
t
t);
yt ) + b (
t
Solution of the Interest Rate Rule Model
it
= i + a (yt
t)
= i
ad (it
1
i ) + cb yt
= i
ad (it
1
i )
1
cbd (it
yt
1
i )
(H.826)
= i + ad:i + cbd:i
(H.827)
it+2 + ad:it+1 + cbd:it = i + adi + cbdi
(H.828)
2
Collecting terms it + ad:it
1
+ cbd:it
2
Iterating forward by two periods
Long run natural rate of interest: steady state it = it
1
= it
2
= bi
(H.829)
(1 + ad + cbd)bi = i (1 + ad + cbd)
(H.830)
bi = i
(H.831)
it+2 + ad:it+1 + cbd:it = 0
(H.832)
Fluctuations around this long run interest rate depends on homogenous part of the second order di¤erence equation
Transitional dynamics (replace it = A A
t+2
t
in homogenous equation).
+ ad:A
t+1
301
+ cbd:A
t
=0
(H.833)
2
+ ad: + cbd = 0
(H.834)
Three Cases in Samuelsonian Multiplier Accelerator Model Cycle depends on roots of the quadratic equation
1;
2
q
ad
=
2
(ad)
4cbd
(H.835)
2
Distinct real root case (no cycle) 2
(H.836)
2
(H.837)
2
(H.838)
(ad) > 4cbd Repeated real root case (no cycle) (ad) = 4cbd Complex root case (cycle) (ad) < 4cbd Complete solution t 1
it = A1 it = A1 Rt (cos
t + i sin
t) + A2 Rt (cos
+ A2 t
t 2
+ bi
i sin
Parameters and solutions of the model
(H.839) t) + bi
Table 87: Parameters of the Interest Rate Rule Model a b c d i0 i y0 0 values
1.5
0.25
0.4
-0.25
0.010
0.0575
0.02
0.02
yt
-0.05
Solution of the Interest Rate Rule Model Example of Complex Root Case: Example Preliminaries: Exponential forms and polar coordinates
sin =
p
h2 + v 2 = bcd
(H.840)
v =) v = R:sin R
(H.841)
R=
302
cos =
h =) h = R:co R
ei = cos + i Si n
h @ sin @
= cos ;
@ cos @
vi = R:co =
e
i
(H.842)
= cos
R:i sin = R: (co
i Si n
(H.843)
i sin ) = Re
i
(H.844)
sin ; 2
Example of Complex Root Case: Example (ad) < 4cbd Need to consider the algebra for the imaginary number and some trigonometric functions in this case. Using Pythagorean in an imaginary axis is used to derive the roots of the characteristic equation.
1;
2
Yt = A1
= (h
v i) =
t 1
t 2
+ A2
ad 2
s
i
2
4cbd (ad) 2
t
(H.845)
t
(H.846)
t) for Rht > 0:
(H.847)
= A1 (h + v i) + A2 (h
v i)
Using DeMoivre’s theorem (h
v i) = Rht (cos
t
i sin
Imaginary axis (Pithagorus Theorem) R=
it = A1 Rht (cos
it = A1 Rht cos
2
p
t + i sin
t + i sin
2
h2 + v 2 = bcd
(H.848)
t) + A2 Rht (cos
t + A2 Rht cos
t
2
i sin
t
i sin
t)
2
(H.849)
t
(H.850)
Three possibilities: i) Rht > 1; bcd > 1 ii) Rht = 1
bcd = 1 and ii) Rht < 1 bcd < 1 Only the bcd < 1 case is
convergent other two cases are divergent. Principles of Finance Maximisation of return and minimisation of risk given the arbitrage opportunities in the economy.
303
Essence: discounting and net present value, capital asset pricing (CAPM) model, e¢ cient market hypothesis -arbitrage, life cycle decisions, options. Intertemporal balance, mobilisation of saving and investment; borrowers and lenders. Risk pooling and sharing by the economy as a whole. Bad …nancial system very harmful for the economy: bubbles and crises. E¢ ciency of the …nancial system is important for real economic growth. Mechanism required to correct moral hazard and adverse selection: e¢ cient regulation. Miles, D. (2014), Monetary Policy and Forward Guidance in the UK. The Manchester School, 82: 44–59 James H. Stock and Mark W. Watson (2005) Understanding changes in international business cycle dynamics,Journal of European Economic Association, 3:5:968-1006. 8.4.1
Integration of Finance in a Macro Model
Technology Yt = At Kt
(H.851)
Capital Accumulation It = Kt+1
Yt = Ct + St with
I Y
=
S Y
(1
) Kt
It = St
(H.852)
0 < 0 b>0
(H.864)
Subject to y = y + c(
E ( )) ;
c>0
(H.865)
where y is actual output y is the natural level of output and (y
y ) is the output gap and
is the actual in‡ation rate. Aggregate Supply: Output responds to higher level of in‡ation Using the value of from the constraint in the objective function M in S ( ) = bc (
E ( ))
a
2
(H.866)
E ( ))
a
2
(H.867)
Optimal In‡ation Under the Policy Rule M in S ( ) = bc (
Let in‡ationary expectation of people,E ( ) to be a constant. Policy maker have two choices: stick to a policy rule or use optimal discretion If they stick to policy rule; people know this, actual in‡ation equals expected in‡ation. = E ( );;y = y
S( )=
a
2
@S = @
2a
(H.868)
Optimal In‡ation in the policy rule: =0
(H.869)
Optimal In‡ation Under the Discretion M in S ( ) = bc (
E ( ))
a
2
(H.870)
Policy makers choose the in‡ation rate to minimise the loss function . First order condition of wrt @S = bc @
2a = 0;
Conclusion:
306
=
bc >0 2a
(H.871)
In‡ation rate under discretion is higher than the in‡ation under the policy rule; it depends on a, b and c, the parameters of the loss function (a, b) and the slope of the supply (c). This is the main reason for the argument for central bank independence and the policy rule. These conclusions are for normal times. However,many economists agree that recession like 2008-2009 requires …scal stimulus and quantitative easing. Minford P and Zhirong Ou (2013) Taylor Rule or optimal timeless policy? Reconsidering the Fed’s behavior since 1982,Economic Modelling 32 (2013) 113–123
307
9
L9: Class Test: Past Examples
Questions are given in sections A and B. Answer two questions, at least one from each section. Each question is worth 100 marks. Each subquestion within a question is of equal value. Use diagrams to illustrate your answers. Section A Q1 Consider the basic IS-LM model as given in the following equations
Y = C +I +G
(I.872)
C = C (Y
(I.873)
Consumption function T)
Investment I = I(r)
(I.874)
M s = M (Y; r)
(I.875)
Money Market
where Y is output, C consumption, I investment and G public spending, T tax revenue, M money and r the interest rate. 1. Derive separate equations to demonstrate the equilibrium in goods and money market. 2. Take the total di¤erentiation of the system of those two equations and …nd out how changes in the output and interest rate could be determined in terms of the structural features of the economy. 3. Find the expression of total change in output 4. Solve the equation to …nd the total change in the interest rate. 5. What are the multipliers with respect to the government spending and taxes? 6. What is the multiplier with respect to changes in the money supply? 7. How can this model be applied to analyse impacts of …scal and monetary policies in an economy? 308
Q2. Consider a Markov model of employment and layo¤ et+1 = (1
) et + ut
ut+1 = et + (1
(I.876)
) ut
(I.877)
Where et and ut are the levels employment and the unemployment. 1) What is the level of employment and unemployment in the steady state. 2) Find the transitional path towards the steady state. Q3. Consider a version of the Brock-Mirman type dynamic programming problem
max
U=
1 X
t
ln(Ct )
0
0 , 0 < b < 1
Assume that tax (T ) is collected lump sum and de…cit (G
(K.992)
T ) is …nanced by borrowing (B)
when tax is not enough to meet expenses (G). G=T +B
(K.993)
C =I +T +B
(K.994)
Rearrange for a matrix: Y
bY + C = a
Y C
!
=
"
1 b
1 1
#
bT 1
(K.995)
I +T +B a
bT
!
(K.996)
Using Cramer’s rule Y =
C=
Y =
(I + T + B) + (a 1 b (a
bT )
bT ) + (I + T + B) 1 b
a + I + (1 b) T B + 1 b 1 b
331
(K.997)
(K.998)
(K.999)
Thus the budget de…cit will have direct impact on output and consumption by the Keynesian multiplier,
@Y @B
=
1 1 b
> 0 or
@C @B
=
1 1 b
> 0:; in this set up
@Y @T
= 1 and
@C @T
= 1 a balanced budget
multiplier e¤ect is achieved when budget is exactly balanced, B = 0. By log di¤erentiation it can be shown that growth rate of GDP depends on the percentage change in the public borrowing: gY =
+
1
2 gB
(K.1000)
This model can be extended to an open economy model by adding exports and imports in the aggregate demand function. It can include in‡ation making the interest rate subject to the real interest rate and using the Fisher equation. With these modi…cations the model becomes: Y = C + I (r) + G + X
r=
IM
(K.1001)
i
(K.1002)
IM = mY
(K.1003)
Y =C +I(
i) + T + B + CA
(K.1004)
Central bank determines the nominal interest rate and then the in‡ation is determined from the money market where the demand for money for money equals the supply of money, which is in…nitely elastic given the central bank’s commitment to a certain interest rate. M = kL ( i) + f Y (K.1005) P Taking log di¤erentiation of this function in‡ation is the di¤erence between the growth rate of money supply and the sum of growth rate of output and liquidity as: = gm
gy
gL
(K.1006)
From this equation one could link in‡ation, current account de…cit and de…cit to the growth rate of the economy. gY = X
IM = Y
1
C
+
2 gB
I (r)
+
2
+
G=Y
2 gCA
C
+e I (r)
(K.1007) T
B
If the private sectors investment and savings are balanced this simply becomes: 332
(K.1008)
X
IM =
(T + B)
(K.1009)
From this equation one could argue that higher government de…cit will lead to larger current account de…cit.
11.3
Growth impacts of public de…cit in the Neoclassical growth model
Growth impacts of public de…cit in a neoclassical growth model could be based on studies of Feldstein (1974), Whalley (1975), Boadway (1979), Summer (1980), Blomquest (1985), Bovenberg (1989), Rankin (1992) Ni and Wang (1995), Benabou (2002). Larger public sector de…cit is found to be harmful for long term growth in neoclassical growth models where households choose the 1
optimal path of consumption and accumulation of capital fct ; kt gt=1 in response to public policy that 1
includes plan of taxes and public expenditure f ; ggt=1 . Particularly the household’s optimisation
problem is:
max
1 X
t
U (ct )
(K.1010)
t=0
subject to ct + kt+1 = (1
Uc ((1
t) f
(kt )
kt+1 ) = Et (1
t) f
t+1 ) Uc
(kt )
((1
0
t
t+1 ) f
(kt+1 )
(K.1011)
kt+2 ) f 0 (kt+1 ) (K.1012)
When government is forced to operate a balanced budget every period the link between tax revenue and public spending is given by: tf
(kt ) = g
(K.1013)
When government is allowed to operate a structural balance it is permitted to intertemporally balance the budget bt+1 =b+g 1 + rt Balancing the budget in the entire model horizon would imply f (kt ) +
f (k0 )
g+
8
1 > < X t=1
> :
tf t 1 t=0
333
(kt )
9 > g=
> (1 + rt ) ;
=0
(K.1014)
(K.1015)
Uc ((1
t) f
(kt )
kt+1
g) = Et (1
t+1 ) Uc
((1
t+1 ) f
(kt+1 )
kt+2
g) f 0 (kt+1 ) (K.1016)
In steady sate ) f 0 (k) = 1
(1
g f 0 (k)
1
f 0 (k) = 1
(K.1017)
(K.1018)
g 1 f 0 (k) = (K.1019) (k) Positive e¤ect of public sector …nances is possible only when ratio of tax rates to the marginal G(k) =
1
productivity of capital is less than one, 1
11.4
f0
g f 0 (k)
> 0:
Analysis of debt crisis
Let R be the risk free payo¤ for investors and R be the return on government bonds. Let
be the
probability of default. Then an arbitrage condition implies (1
)R = R
(K.1020)
Some arrangement yields: =
R
R R
334
(K.1021)
As the probability of default rises the government need to pay higher interest rate, as shown by line D in the graph. Then the government retire debt if T = RD . This implies
T D
= R. When the interest rate is
low, as at point R, the collected tax revenue is likely to be enough to serve the debt and therefore probability of default ( ) on public debt is zero. Then
0
g. Taylor approximation: g
b+
1+g ( dt g r
g) +
dt =
1 g
+
r
(rt
1+r dt 1+g
r) +
1
+
K 1
1 (et B
K
(tt
et
Ktt ) +
k) ' et
dt
1
1 rt 1+g
(L.1040)
(L.1041)
Stochastic optimal control method and learning
12.1
Cole -Kehoe (2000) model of self ful…lling debt crisis
Cole and Kehoe (2000) use a dynamic stochastic general equilibrium model in which self-ful…lling crisis may arise. They say that "Because of the government’s need to roll over its debt, a liquidity crunch induced by the inability to sell new debt can lead to a self-ful…lling default" and "if fundamentals like the level of the government’s debt, its maturity structure, and the private capital stock, lie within a particular range (the crisis zone), then the probability of default is determined by the beliefs of market participants." It is "also related to the literature on how the government’s inability to commit to future policy choices can generate multiple equilibria." Household: E
1 X
t
(Ct + V (gt )))
(L.1042)
t=0
ct + kt+1 < (1
)at f (kt )
(L.1043)
Banker: E
1 X
t
xt
(L.1044)
t=0
xt 5 x + zt bt
337
qt bt+1
(L.1045)
Government budget constraint: gt + zt Bt 5 at t f (kt ) + qt Bt+1
(L.1046)
Timing. The timing of actions within each period is the following. 1. The sunspot variable
t
is realized, and the aggregate state is st = (Bt ; Kt ; at
1; t)
2. The government, taking the price schedule qt = q(st ; Bt+1 ) as given, chooses Bt+1 . 3. The international bankers, taking qt as given, choose bt . 4. The government chooses whether or not to default, zt , and how much to consume, gt 5. The consumers, taking at as given, choose ct and kt+1 . Consumer’s dynamic problem: Vc (k; s; B0; g; z) = max c + v(g) + EVc (k0; s0; B0(s0); g0; z0) c;k0
(L.1047)
subject to c + k0 5 (1
)a(s; z)f (k)
(L.1048)
c; k0 > 0
(L.1049)
s = (B0; K0(s; B0; g; z); a(s; z); c0);
(L.1050)
g0 = g(s0; B0(s0); q(s0; B0(s0)));
(L.1051)
z = z(s0; B0(s0); q(s0; B0(s0)))
(L.1052)
The representative banker’s value function is de…ned by the functional equation Vb (b; s; B0) = max x + z(s; B0; q(s; B0))b b0
q(s; B0)b0 + EVb (b0; s0; B0(s0));
(L.1053)
subject to q(s; B0)b0 5 x b0 >
A;
s = (B0; K0(s; B0; g; z); a(s; z); c0) 338
(L.1054)
(L.1055)
(L.1056)
The government’s value function is de…ned by the functional equation Vg (s) = max c(K; s; B0; g; z) + v(g) + EVg (s0);
(L.1057)
g = g(s; B0; q(s; B0));
(L.1058)
z = z(s; B0; q(s; B0))
(L.1059)
s = (B0; K0(s; B0; g; z); a(s; z); c0)
(L.1060)
B0
subject to
Later in the period, the government makes its default choice z, which in turn determines the level of productivity a and, through its budget constraint, the level of government spending g. Given the government’s initial value function, Vg (s), they de…ne the policy functions g(s; B0; q) and z(s; B0; q) as the solutions to the problem max c(K; s; B0; g; z) + v(g) + EVg (s0)
(L.1061)
g + zB 5 a(s; z)f (K) + qB0;
(L.1062)
z = 0 or z = 1
(L.1063)
g>0
(L.1064)
s0 = (B0; K0(s; B0; g; z); a(s; z); 0)
(L.1065)
g;z
subject to
De…nition of an equilibrium. An equilibrium is a list of value functions Vc for the representative consumer, Vb for the representative banker, and Vg for the government;policy functions c and k0 for the consumer, b0 for the banker, and B0, g, and z for the government; a price function q; and an equation of motion for the aggregate capital stock K0 such that: 1. Given B0, g, and z, Vc is the value function for the solution to the representative consumer’s problem, and c and k0 are the maximizing choices; 2. Given B0, q, and z, Vb is the value function for the solution to the representative banker’s problem, and the value of B0 chosen by the government solves the problem whenb = B; 339
3. Given q; c; K0; g; and z; Vg is the value function for the solution to the government’s …rst problem (), and B0 is the maximizing choice. Furthermore, given C; K0; Vg ; and B0; g and z solve the government’s second problem (); 4. B0(s) 2 b0(B; s; B0);
5. K0(s; B0; g; z) = k0(K; s; B0; g; z). Cole H. L. , T. J. Kehoe (2000) Self-Ful…lling Debt Crises, Review of Economic Studies, 67, 1, 91-116.3. Given q; c; K0; g; and z; Vg is the value function for the solution to the government’s …rst problem (), and B0 is the maximizing choice. Furthermore, given C; K0; Vg ; and B0; g and z solve the government’s second problem (); 4. B0(s) 2 b0(B; s; B0);
5. K0(s; B0; g; z) = k0(K; s; B0; g; z). Cole H. L. , T. J. Kehoe (2000) Self-Ful…lling Debt Crises, Review of Economic Studies, 67, 1, 91-116. Tamai, T.,(2013) The macroeconomic e¤ects of …scal policy in a stochastically growing economy, EconomicModelling (2013), Economic Modelling 35 xxx–xxx
12.2
Credibility
Two types of time protocol: 1. Chooses sequence of
t+j
once and walks away
2. Chooses sequence of
t+j
in each period
this requires ideas of game in the modelling. Can reputation be subject to ability to commit. Need to form a strategy space that is history dependent. Reputation could be based on the rational expectation. Credibility is based on beliefs and it leads to the theory of government. They will do as this is in their interest and feasible. Motives of the government is included in the model. Model speci…cation Household h chooses consumption
2 X and the private sector average x 2 X. The public
sector chooses y, e.g. in‡ation. Utility is ( ; x; y) ;
when x = Q
y=
t+j
Choice problem: max ( ; x; y) 2X
where choice of household depends on average choice
= f (x; y)
Rational expectation equilibrium is equivalent to competitive equilibrium: REE s CE; f (x; y) Set of competitive equilibrium C =) f(x; y) ; X = h (g)g 340
x=
Ramsey problem: Government chooses y knowing x = ln (y) max u (h (y) ; h (y) ; y) = max y2Y
(x;y)2C
u (x; x; y) =) V R ; y R
Nash equilibrium X N ; y N satis…es that: 1. X N ; y N 2 C
2. G, X N , u X N ; X v ; y G = max u (x0 ; x0 ; ) =) V N ; y N and V N < V R 2Y
Example
u (l; c; g) = l + lg ( + c) + lg ( + g) ;
l+g = 1+l ;
l ( ) = f11 History
t
if
Vg x ; y
1 2
( ; g) s y
if 2(0;1 >1
=
1
1 X
t
r (xt ; yt ) ;
t=0
x; y
0;
)
2 X 8t ; xt 2 X 8t ; yt 2 X 8t for t 1 1 ! !
! !
2
2 (0; 1)
1
= f(xt ; yt )gt=0
Reputation means choice at t is a function of t-1 yt = X t
1
;Y t
1
Dynamic programming square Let V be the value to government in the …rst period of following the policy that the private sector had expected. Let V1 be the continuation value of known policy. Let V2 be the continuation value if the private sector believes that the government choice is not what they expect. V = (1
) u (x; x; y) + V1
>
(1
(x;y)2C
) u (x; x; ) + V2 ; 8
2Y
A strategy pro…le implies a trajectory of outcome (x; y) and a value function Vg ( ) = Vg [x ( ) ; y ( )]
341
and continuation pro…le j(x;y) ; j(x
;y ) :
A strategy pro…le is a subgame perfect equilibrium (SPE) of in…nitely repeated economy if 8
t > 1 and 8 (xt ; yt ) 2 X t a) xt = b) 8
h t
Xt
1
;Y t
1
1
;Y t
1
is consistent with the competitive equilibrium where
g t
Xt
1
;Y t
1
2Y (1
) (xt ; yt ) + Vg
j(x;y)
>
(1
) (xt ; ) + Vg
(x;y)2C
j(x;
)
Ljungqvist L. and T. J. Sargent (2012) Recursive Macroeconomic Theory, 3rd ed. MIT Press.
12.3
Two Period Overlapping Generation Model
Impacts of de…cit spending on individuals vary by the age group they belong to. Overlapping generation models as in Samuelson (1958) and Auerbach and Kotliko¤ (1987) provide framework to evaluate such age speci…c impacts. For instance consider an economy, inhibited by two generations, young and old. Young ones work, earn , consume and save and old ones stay at home in retirement and consume out of their past savings. Economy is continuum of generations such as gi;t where i = 1; 2; ::::N refers to the generations and t = 1; 2; ::::T refers to the time period. Each agent is assumed to live for two periods - as a young worker …rst and then as an old retiree. For instance, person in generation 1, g1;1 is born and young in t = 1 and becomes old in t = 2 and is succeeded by g2;1 who is young in t = 2 , becomes old one in period t = 3 and dies at the end of that period. In this manner new generations continuously replace the old generations but the economy continues without any interruption with these two types of people forever. Behavior of each type is similar to their types in earlier periods; young ones work, earn, save part of their income and make families and get children and old ones retire and consume their savings and leave some bequest to their children. Production is function of capital, labour and technology and is subject to constant return to scale with here
+
= 1: Yt = AKt Lt
(L.1066)
In terms of income per e¤ective worker: yt = Ak Market clears in each period, whatever is produced is either consumed or invested.
342
(L.1067)
Yt = Ct + It
(L.1068)
Equilibrium conditions in overlapping generation model requires aggregate consumption be total of the consumption of young and old Ct = N cyt + N cot
(L.1069)
Net of tax wage income is given by the labour share in production (1
l )Wt
= AKt Lt
(L.1070)
Net of tax interest rate equals the marginal product of capital (1 Agents consume
k )rt
estate tax
v)
(L.1071)
Lt
fraction of their income in period 1 and pay a VAT rate at cyt = (1
Young save (1
1
= AKt
wt
v
(L.1072)
) share of wt and invest it in assets for consumption at the old age subject
A:
at = (1
A ) (1
cot = at (1 + rt ) = (1 +
) wt
A ) (1
) wt (1 + rt )
(L.1073)
(L.1074)
Law of accumulation of capital stock, with no depreciation is: Kt+1 = Kt + It
(L.1075)
From L.1068 and L.1066 Ct = AKt Lt
It
(L.1076)
Kt+1 + Kt
(L.1077)
Then substituting L.1075 and L.1069 in L.1076 N cyt + N cot = AKt Lt
343
Capital Accumulation in Overlapping Generation Model Further substituting ?? and ?? for consumption of young and old
N (1
v )(1
l)
wt +N (1
v )(1
l )(1
k ) (1
) wt (1 + rt )+g = AKt Lt
Kt+1 +Kt (L.1078)
substituting L.1070
AKt Lt
Kt+1 +Kt = (1
v )(1
l)
AKt Lt +(1
v )(1
l )(1
k ) (1
) (1
) AKt Lt (1 + rt ) (L.1079)
By further re-arrangement
Kt+1 Kt = AKt Lt
(1
v )(1
l)
AKt Lt
(1
v )(1
l )(1
k ) (1
) (1
) AKt Lt (1 + rt ) (L.1080)
Parameters and results in Overlapping Generation Model
Table 89: Parameters of the Two Period OLG Model K 0 k0 N l k
Parameter Value
0.5
0.5
0.5
300
3
100
0.35
0.28
Table 90: Results of the Two Period OLG Model k K Y w r cy c0
Variables
v
0.2
S=I
Solution without tax Initial condition
1.5
150
1129.3
7.90
2.26
3.95
4.9
245.3
Steady State
1.78
178.5
1189.8
8.3
2.0
4.16
5.8
191.8
Solution with tax Initial condition
1.5
150
1129.3
6.3
1.8
3.2
4.2
166.2
Steady State
1.78
178.5
1189.8
6.7
1.6
4.2
5.4
0
Larger de…cits raise consumption of old generation but lower the consumption of younger generations if such de…cit is used mainly for transfer but can improve living standards of young if spent on creation of physical and human capital. 344
Three types of people exist every year in the economy: young ones, adults and old ones. Young ones go to the school, adults work, and old ones stay at home in retirement. In g11, …rst subscript refers to the generation and second subscript to the period. Person in g11 is born in period 1, becomes adult in period 2 and becomes old in period3 and dies at the end of period 3. Economy continues with these three types of people forever. It never stops. new generations continuously replace the old generations Behavior of each type is very di¤erent. 1. Young ones borrow to fund their education; 2. adult ones work, earn and save part of their income and make families and get children; 3. old ones retire and consume their saving and leave some bequest to their children. Three Period Overlapping Generation Model
Summary of the OLG model First order di¤erential equation in Kt and can be solved iteratively using a numerical method starting from initial condition where K0 is given. System converges to the steady state when Kt+1 = Kt . A numerical method is adopted to solve the model using Excel for tax and no tax scenarios. Labour income and capital income taxes distort the …rst order conditions (1 AKt
1
Lt and (1
l )Wt
= AKt Lt .
345
k )rt
=
This raises the cost of capital and labour to the producer and reduces the capital stock and output as the level of welfare of the households. Net investment and savings are zero in the steady state. Solutions of the model for parameter values given in Table 9 is given Table 10. As expected capital and labour income taxes have signi…cantly reduced the capital stock, output, wage rate, saving and investment and consumption of young and old in the model.
12.4
Empirical Analysis
Economic and political believes and circumstances keep changing in response to new opportunities and di¢ culties which augment theoretical controversy regarding the relationship between growth and public debt. As the public decisions a¤ect millions of households and …rms and their reactions to announced or anticipated policies vary the empirical analysis of the link becomes of great public interest. Here data on growth,de…cit, current account and several macroeconomic variables are obtained for advanced countries from the World Economic Outlook database of the IMF from 2000 to
2010 including the IMF forecasts for up to 2015. ( http://www.imf.org/external/pubs/ft/weo/2010/01/weodata/index.asp This data set is used here to examine whether the public de…cit helpful or harmful for economic growth and whether de…cit stabilises or destabilises an economy in terms of its impact on in‡ation and current account de…cit. Regression coe¢ cients of de…cit or a set of variables including de…cit multiple explanatory variables are estimated using the OLS or GLS models and examining their validity on the basis of t; F ,
2
and R2 tests. These estimates are tested for heteroskedasticity,
autocorrelations and any restrictions as appropriate. Regresses growth rate of output (Yi ) on net borrowing (Xi ) as: Yi =
1
+
2 Xi
+ ei
i = 1 :::T
Following the OLS technique to …nd estimators of b 1 and b 2 . b = (X 0 X)
1
X 0Y
(L.1081)
These estimates are subject to standard OLS assumptions on error terms normality ei N 0;
2
, homoskedaticity, non- autororrelation (E ("i "j ) = 0)and independence of errors from
the dependent variables, (E ("i Xi ) = 0).
"
b b
1 2
#
==
"
N P Xi
P
P
Xi Xi2
#
1
"
b
b
1 2
#
=
"
12 51:92
346
51:92 413:52
#
1
"
21:3 26:23
#
=
"
3:283
#
0:349 (L.1082)
Table 91: Testing overall signi…cance by F-test Source of Variance Sum Degrees of freedom Mean Total sum square (TSS)
56.597
12
5.145
Regression Sum Square (RSS)
22.967
1
22.967
Sum of square error
33.629
10
3.737
F-value 6.147
Where k = number of parameters in the regression; N = number of observations Table of results summarising all above calculations are presented as: Table 92: Growth on net borrowing Coe¢ cient Standard Error
t-value
Intercept
3.283
0.783
4.191
Net borrowing
0.349
0.133
2.613
2
R = 0.406 , F = 6:147 ;
N = 12:
Coe¢ cients as well as t-statistics are signi…cant. Autocorrelation is positive because d = 1:74 < 2 but that autocorrelation is not statistically signi…cant. The calculated DW value, d = 1:74 is clearly out of the inconclusive region as it does not fall in the range of [0:971; 1:331] of the Durbin-Watson table. White test or ARCH and AR test suggest there is slight problem of heteroskedasticity in the errors in this model. However, heteroskedasticity is more serious for cross section than for time series. Therefore conclusion of above model are still valid. One way is to regress predicted square 2 errors eb2 in predicated square of y, Yb 2 . The test statistics for normality of errors is nR2 with i
i
df
df =1.
eb2i =
eb2i = 0
+
1 X1;i
+
0
+
b2 1 Yi
2 X2;i
+
+ vi ; n:R2 = 6:089
2 3 X1;i
+
2 4 X2;i
+
(L.1083)
5 X1;i X2;i
Null hypothesis of homoskedasticity is rejected as nR2 = 6:089 >
2 df
+ vi
= 2:7055.
Table 93: Price index on net borrowing Coe¢ cient Standard Error t-value Intercept
102.5
1.603
63.9
Net borrowing
-1.85
0.273
-6.76
2
R = 0.82 , F = 45:7 [0:00] ;
347
N = 12 ; DW = 1:09
(L.1084)
Table 94: Current account balance on net borrowing Coe¢ cient Standard Error t-value Intercept
-2.44
0.225
-10.8
Net borrowing
-0.008
0.038
-2.20
2
R = 0.33 , F = 4:9 [0:05] ;
N = 12 ; DW = 1:03
Prices were relatively stable despite …scal expansion during the study period as the monetary policy mainly concerned in achieving the target in‡ation, had been complementary to the …scal policy in UK in the period of study as shown in above Tables. However higher borrowing had caused slight deterioration in the current account, as both consumers and producers tend to import more in response to higher income they received from …scal expansion. There is weak evidence on simultaneity between growth and de…cit in UK in last ten years. Past records like this may or may not apply for projecting the impacts of current debt reduction plans in the future years; these require analysis of the impacts of such de…cit in the path of economy under dynamic general equilibrium system or under the DSGE or VAR frameworks. These tasks have been analysed in my other papers.
12.5
Conclusion
There is a controversy in the literature about the economic contribution of public de…cit. Keynesian economists generally argue that by spending more on goods and services and infrastructure possible, the public de…cit is helpful to create more jobs, reduce unemployment rate and raise the economic growth rate of the economy. Neoclassical economists are worried about the adverse consequences of public de…cit on capital accumulation and the long run growth rate. Classical Ricardian equivalence proposition does not match well with the empirical evidences on adverse consequences of budget de…cit on in‡ation, current account balances and redistribution of income. In practice this is essentially an empirical issue, evidence suggests that the role of de…cit largely depends on economic circumstances. Empirical estimates in this paper show that de…cit has contributed for growth in UK; 1 percent increase in net borrowing would raise growth rate by 0.34 percent between 2000 and 2010. In other words statistical and econometric evidence clearly suggests that reducing de…cit will lower the growth rate; proposed de…cit reduction plan will clearly slow down the growth rates.
348
References [1] Aiyagari S. Rao, Albert Marcet, Thomas J. Sargent, Juha Seppälä (2002) Optimal Taxation without State-Contingent Debt, Journal of Political Economy, Vol. 110, No. 6 Dec., pp. 1220-1254 [2] Atkinson A. B.and N. H. Stern (1974) Pigou, Taxation and Public Goods, Review of Economic Studies, 41:1:119-128. [3] Atkinson A. B. (1971) Capital Taxes, the Redistribution of Wealth and Individual Savings ,The Review of Economic Studies, 38: 2: 209-227. [4] Auerbach A.J.and L. Kotliko¤ (1987) Dynamic Fiscal Policy, Cambridge University Press. [5] Bank of England (2010) In‡ation Report, August, 2010. [6] Barro, R. J. (1974), Are Government Bonds Net Wealth?, Journal of Political Economy, 82: Nov., 1095-1117. [7] Barro Robert J. (1989) The Ricardian Approach to Budget De…cits, Journal of Economic Perspectives, 3: 2: Spring, 37-54 [8] Bean Charles (2009) the meaning of internal balance’Thirty years on, Economic Journal, 119 (November), F442–F460. [9] Bean Charles (1998) The New UK Monetary Arrangements: A View from the Literature Economic Journal, 108:451: Nov. 1795-1809 [10] Beetsma R and M. Giuliodori (2011) The e¤ects of government purchanges shocks: review and estimates for the EU, Economic Journal, 121-550: F4-F32. [11] Bernheim B. Douglas (1989) A Neoclassical Perspective on Budget De…cits, The Journal of Economic Perspectives, 3:2:Spring:55-72 [12] Besley Tim (2001) From micro to macro: public policies and aggregate economic performance, Fiscal Studies, 22: 3: September. [13] Bhattarai K. (2012) Advanced Macroeconomics, University of Hull, Business School. [14] Bhattarai K (2010) Taxes, public spending and growth in OECD countries, Problems and Perspective in Management, 8:1: 14-30. [15] Bhattarai K. (2007) Welfare Impacts of Equal-yield Tax Reforms in the UK Economy, Applied Economics, 39:10-12: 1545-1563. 349
[16] Blanchard, O. and Perotti, R. (2002). _An empirical characterization of the dynamic e¤ects of changes in government spending and taxes on output_, Quarterly Journal of Economics, 117(4) : Nov.:1329–68. [17] Boadway Robin (1979) Long-Run Tax Incidence: A Comparative Dynamic Approach The Review of Economic Studies, 46:3:505-511. [18] Bovenberg L.A. (1989) The E¤ects of Capital Income Taxation on International Competitiveness and Trade Flows, The American Economic Review, 79,: 5 :1045-1064. [19] Buchanan, J., 1958, Public principles of public debt (Irwin: Homewood, Illinois). [20] Burnside, C., Eichenbaum, M. and Fisher, J. D. (2004). Fiscal shocks and their consequences, Journal of Economic Theory,115: 89–117. [21] Brauninger Michael (2005) The budget de…cit, public debt, and endogenous growth ,Journal of Public Economic Theory, 7 (5): 827–840. [22] Caucutt E.M, S. Imrohoroglu and K. B. Kumar (2006) Does the Progressivity of Income Taxes Matter for Human Capital and Growth? Journal of Public Economic Theory, 8:1:95-118 [23] Diamond, P.A., 1965, National debt in a neoclassical growth model, American Economic Review 55, 112551150. [24] Diamond P, Douglas W. and Dybvig, Philip H. (1983) Bank Runs, Deposit Insurance,and Liquidity, Journal of Political Economy, 401-419. [25] Fisher Jonas D.M. and Ryan Peters (2010) Using Stock Returns to Identify Government Spending Shocks, Economic Journal, 120: :544: May, [26] Feldstein M (1985) Debt and taxes in the theory of public …nance, Journal of Public Economics, 28:233-46 [27] Feldstein M (1982) Government de…cits and aggregate demand, Journal of Monetary Economics 9 (1982) 1-20 [28] Fullerton, D., J. Shoven and J. Whalley (1983) Dynamic General Equilibrium Impacts of Replacing the US Income tax with a Progressive Consumption Tax, Journal of Public Economics 38, 265-96. [29] Holly S and M Weale (Eds.) Econometric Modelling: Techniques and Applications, pp.69-93, the Cambridge University Press, 2000.
350
[30] HM Treasury (2010) Pre-Budget Report, October 2010. [31] Kirsanova Tatiana, Campbell Leith and Simon Wren-Lewis ( 2009) Monetary and …scal policy interaction: The current consensus assignment in the light Of recent developments, Economic Journal,119:Nov,F482–F496. [32] Kydland F.E and E.C. Prescott (1977) Rules rather than discretions: the Inconsistency of Optimal Plans, Journal of Political Economy, 85:3: 473-491. [33] Meade, J.E. (1958), Is the national debt a burden? Oxford Economic Papers IO, 1633183. [34] Mendoza E. G and V. Z. Yue (2012) A general equilibrium model of sovereign default and business cycles, Quarterly Journal of Economics 127, 889–946. [35] Mirlees, J.A. (1971) An exploration in the theory of optimum income taxation, Review of Economic Studies, 38:175-208. [36] Modigliani, F., 1961, Long run implications of alternative …scal policies and the burden of the national debt, Economic Journal 71, 728755. [37] Monacelli T and R. Perotti (2010) Fiscal Policy, the Real Exchange Rate and Traded Goods, Economic Journal, 120(May), 437-461. [38] Ni Shawn and X Wang ( 1995) Balanced government budgets versus de…cit …nance in a growth economy, Canadian Journal of economics, XXVIII: 4b:1120-1134. [39] Obstfeld, Maurice, Jay C. Shambaugh and Alan M. Taylor. (2010) Financial Stability, the Trilemma, and International Reserves, American Economic Journal: Macroeconomics: 2:2, April , [40] Perroni, C. (1995), Assessing the Dynamic E¢ ciency Gains of Tax Reform When Human Capital is Endogenous, International Economic Review 36:907-925. [41] Phelps, Edmund S. (1968), Money-Wage Dynamics and Labor-market equilibrium, Journal of Political Economy, 76: 678-710. [42] Rankin Neil (1992) Imperfect competition, expectations and the multiple e¤ects of monetary growth, Economic Journal 102: 743-753. [43] Rebelo S. (1990) Long run policy analysis and long run growth, Journal of Political Economy vo. 99 no. 3 pp. 500-521.
351
[44] Samuelson P. A. (1954) Pure Theory of Public Expenditure, Review of Economic Statistics, 36:387-9/ [45] Sargent, T. J. (2011), Where to Draw Lines: Stability Versus E¢ ciency. Economica, 78: 197– 214. [46] Schmitt-Grohe´ S.,M. Uribe, Balanced-budget rules,distortio nary taxes and aggregate instability, [47] J. Polit. Econ. 105 (1997) 976–1000. [48] Sorensen PB and H. Jl Whitta-Jacobsen (2010) Introducing Advanced Macroeconomics, McGraw Hill. [49] Tekin-koru Ayc a and Erdal O¨ zmen (2003) Budget de…cits, money growth and in‡ation: the Turkish evidence, Applied Economics, 35, 591–596 [50] Whalley J. (1975) “A General Equilibrium Assessment of the 1973 United Kingdom tax reform”, Economica, 42:166:139-161.
12.6
International strategic policy coordination models
Economic crisis very often is contegious. It transmits from one economy to another. Policy coordinations can mitigate adverse consequences of these crisis. This requires studying how one economy is linked to the another in the regional or global economy settings. Interdependence among economies and interactions could be studied using bargaining, signalling and mechanism designing concepts. Cooperative and non-cooperative games with complete and incomplete information among nations, households and …rms could be used to conceptualize the issues and solutions to the problems of growth and development in these economies. There are three generations of literature in the policy coordination. First generation models include studies such as Kydland and Prescott (1977), Dri¢ l (1988), Currie and Levine (1986) and Obstfeld and Rogo¤ (2000). These had found gains from coordination to be small. Cooper (1969) and Hamada (1976) and Kydland (1975) showed inferiority of the non-cooperative Nash equilibrium compared to a cooperative solution. Lucas (1976), and Kydland and Prescott (1977) used rational expectations and argued for the advantage of rule-based policies to create rational expectations equilibrium solution. Petit (1989) used di¤erential games as did the studies of Obstfeld (1994), Sutherland (1996), Senay (1998), Martin and Rey (2000). Obstfeld (2001) and Rogo¤ (2002) provide an excellent review of some of the models used for policy coordination with Mundell-Fleming-Dornbush type models with little gains from coordination. Second generation models of policy coordination in Pappa (2004),
352
Canzoneri, Cumby and Diba (2005), Clerc, Dellas and Loisel (2011), Juillard and Villemot (2011) and Goyal (2007) …nd pay o¤ from monetary and …scal policy coordination to be bigger. Supply and strategic modelling has much improved in recent literature on the policy coordination showing more gains from coordination as stated by Conzoneri et. al.(2005), Evans and Hnatkovska (2007), Douglas and Laxton in dynare. Aarle et.al. (2002) examine the coalition formation in EMU. Recent models such as Kempf and von Thadden (2013), Dedola et al. (2013) add asymmetric information and commitment where the welfare gains can be bigger as the number of countries increase in such deals. Given this literature let us consider three countries aiming for a policy coordination with the Nash utility frontier: Nt = U1;t U2;t U3;t
(L.1085)
Each receive utility from consuming products produced in each country: Ui;t = F (y1;t; y2;t ; y3;t )
(L.1086)
Goods supply process is determined simultaneously as: y1;t =
1;0
+
1;2
y2;t +
1;3
y3;t +
1;1
y1;t
1
+
1;2
y2;t
1
+
1;3
y3;t
1
+ e1;t
(L.1087)
y2;t =
2;0
+
2;1
y1;t +
2;3
y3;t +
2;1
y1;t
1
+
2;2
y2;t
1
+
2;3
y3;t
1
+ e2;t
(L.1088)
y3;t =
3;0
+
3;1
y1;t +
3;2
y2;t +
3;1
y1;t
1
+
3;2
y2;t
1
+
3;3
y3;t
1
+ e3;t
(L.1089)
Coe¢ cient of a VAR model estimated from the time series data provides information on interactions among model economies as: 0 B B @ 0
B = B @
1
1;2
2;1 3;1
1;0 2;0 3;0
1
1
2;3
1
3;2
0
C B C+B A @
10
1;3
1;1
1;2
2;1
2;2
3;1
3;2
y1;t
1
C CB CB y C A @ 2;t A y3;t 10
353
1;3
2;3
3;3
y1;t
CB CB y A @ 2;t y3;t
1 1 1
1
0
e1;t
1
C B C C+B e C A @ 2;t A e3;t
(L.1090)
0
=
1
y1;t
C B B y C @ 2;t A y3;t 0 1 B B 2;1 @ 3;1
0 B B @
1
1
1 1;2
2;1 3;1
C C A
2;3
3;2
1
1
1;3
1
3;1
B +B @
2;3
3;2
1 3;2
1
C C A
1;3
1
1;2
2;1
0
1;2
1
1;3 2;3
1
1
1
0
1
B B @
1;0
B B @
1;1
1;2
1;3
2;1
2;2
2;3
3;2
3;3
2;0 3;0
0 1
C C A
0
3;1
C C+ A
1
e B 1;t C B e C @ 2;t A e3;t
10
y1;t
CB CB y A @ 2;t y3;t
1 1 1
1 C C A (L.1091)
Paramters of VAR could be interpreted in the context of Nash Policy Game as:1) In common meetings or summits they decide policies given by
1;0
;
2;0 ;
3;0
but each of them face idiocyn-
cratice shocks e1;t ; e2;t ; e3;t ; 2) Then each country determine its action yi;t taking account of actions taken by others yj;t and such response patterns are given by parameters ,
; 1;2
1;3 ;
; 2;1
; 2;3
; 3;1
3;2
1;2
;
1;3 ;
2;1
;
2;3
;
3;1
;
3;2
and shocks e1;t ; e2;t ; e3;t ; 3)Each would like to get more utility and this
opens the bargain; 4) The optimal solution of this game should ful…ll four properties of Nash bargaining game; 5) This must be symmetric, e¢ cient, linear invariance and IIA. Extention of this model for the many countries case is very obvious. Beetsma R. M.W.J. and H. Jensen (2005) Monetary and …scal policy interactions in a microfounded model of a monetary union Journal of International Economics, 67, 2, 320-352 Bullard J and ASingh (2008) Worldwide macroeconomic stability and monetary policy rules Journal of Monetary Economics, 55, S34-S47 Chang, Roberto. (1997) Financial integration with and without international policy coordination ,International Economic Review, 38, 3, 547. 18p. Canzoneri M. B., R. E. Cumby and B.T. Diba (2005) The need for international policy coordination: what’s old, what’s new, what’s yet to come? Journal of International Economics, 66, 2, 363-384 Clerc L, H. Dellas, O. Loisel (2011) To be or not to be in monetary union: A synthesis Journal of International Economics, 83, 2, 154-167 354
Clarida R, Jordi Galí and M. Gertler (2002) A simple framework for international monetary policy analysis, Journal of Monetary Economics, 49, 5, 87–904 Conconi P and Carlo Perroni (2009) Do credible domestic institutions promote credible international agreements? Journal of International Economics, 79, 1, 160-170 Cooper, R, D. DeJong , R Forsythe and T. W. Ross(1992) Communication in coordination games, Quarterly Journal of Economics. 107 2, p739. 33p. Currie D and P Levine (1986) Time inconsistency and optimal policies in deterministic and stochastic worlds Journal of Economic Dynamics and Control, 10, 1–2,191-199 D. Luca , P Karadi and G. Lombardo (2013) Global implications of national unconventional policies Journal of Monetary Economics, 60, 1, 66-85 Fratzscher M (2009) How successful is the G7 in managing exchange rates? Journal of International Economics, 79, 1, 78-88 Goodfriend, M.; R. G. King (1997) The New Neoclassical Synthesis and the Role of Monetary Policy NBER/Macroeconomics Annual (MIT Press). 12 1, 231-283. Juillard M, S. Villemot (2011)Multi-country real business cycle models: Accuracy tests and test bench Journal of Economic Dynamics and Control, 35, 2„178-185 Levine P, A. Brociner (1994) Fiscal policy coordination and EMU: A dynamic game approach Journal of Economic Dynamics and Control, 18, s 3–4, 699-729 Hansen L. P. and T. J. Sargent (2003) Robust control of forward-looking models Journal of Monetary Economics, 50, 3, 581-604 Kempf H. and L. von Thadden (2013) When do cooperation and commitment matter in a monetary union? Journal of International Economics, 91, 2, 252-262 Liu Z and E. Pappa (2008) Gains from international monetary policy coordination: Does it pay to be di¤erent? Journal of Economic Dynamics and Control, 32, 7, 2085-2117 Marquez J (1988) International policy coordination and the reduction of the US trade de…cit, Journal of Economic Dynamics and Control, 12, 1, 19-25 Gar…nkel M.R. (1989) Global macroeconomics: Policy con‡ict and cooperation: A review essay Journal of Monetary Economics, 23, 2, 345-352
355
Pappa E. (2004) Do the ECB and the fed really need to cooperate? Optimal monetary policy in a two-country world Journal of Monetary Economics, 51, 4, 753-779 Kose Ayhan K.M, C. Otrok and C. H. Whiteman (2008) Understanding the evolution of world business cycles Journal of International Economics, 75, 1, 110-130 Je¤rey S. (1992) International monetary and …scal policy cooperation in the presence of wage in‡exibilities: Are both counterproductive? Journal of Economic Dynamics and Control, 16, 2, 359-387
References [1] Barro R.J. and D. B. Gordon (1983) Rules, Discretion and Reputation in a Model of Monetary Policy, Journal of Monetary Economics, 12: 101-121, North-Holland. [2] Bhattarai K. (2014) Money and economic growth, Journal of Economic Asymmetries 11, 8–18 [3] Bhattarai K. and S. Mallick (2013) Impact of China’s currency valuation and labour cost on the US in a trade and exchange rate model. North American Journal of Economics and Finance, 25, 40-59. [4] Bhattarai K and J Whalley (2006), Division and Size of Gains from Liberalization of Trade in Services, Review of International Economics, 14:3:348-361, August. [5] Breitner M. H. (2005) Genesis of Di¤erential Games in Light of Isaac’s Contributions, Jounral of Optimisation Theory and Applications, 124:3:529-559 [6] Burda M. and C. Wyplosz (2010) Mundell-Flemming model, Macroeconomics, Oxford University Press. [7] Canzoneri M. B. and J A Gray (1985) “Monetary Policy Games and the Consequences of NonCooperative Behaviour”, International Economic Review, 26:3:1985, pp. 547-567. [8] Canzoneri M. B., R. E. Combey and B. T. Diba (2005) The need for International monetary policy coordination,: what is old, what is new and what is yet to come, Journal of International Economics, 66:363-384 [9] Canzoneri Matthew B. , Robert E. Cumby, Behzad T. Diba (2005) The need for international policy coordination: what’s old, what’s new, what’s yet to come? Journal of International Economics, 66, 2, 363-384
356
[10] Conconi P, Carlo Perroni (2009) Do credible domestic institutions promote credible international agreements? Journal of International Economics, 79, 1,160-170. [11] Currie D, P. Levine (1985) Simple Macropolicy Rules for the Open Economy The Economic Journal, 95, 60-70. [12] Currie D adn P Levine (1986) Time inconsistency and optimal policies in deterministic and stochastic worlds Journal of Economic Dynamics and Control, 10, 1–2,191-199 [13] Chakravarty S. (1965) Optimal Programme of Capital Accumulation in a Multi-Sector Economy, Econometrica, 33, 3 ,Jul. 557-570 [14] Cooley T. and Hansen (1989) The in‡ation tax in real business cycle models, American Economic Review, 79,3:733-748 [15] Cooper R. N. (1969) Macroeconomic Policy Adjustment in Interdependent Economies, Quarterly Journal of Economics, 83: 1:Feb.:1-24 [16] Corden W.M. (1985) Macroeconomic Policy Interaction under Flexible Exchange Rates: A Two-Country Model, Economica, New Series, 52:205:Feb. 9-23 [17] Cruz J.B. (1975) Survey of Nash and Stackeberg equilibrium strategies in dynamic games, Annals of Economic and Social Measurement, 4:2:339-344. [18] Cruz J.B. and Chen (1971) Series Nash Solution of Two Person Non-Zero-Sum Linear Quadratic Di¤erential Games, Jounral of Optimisation Theory and Applications, 7:4:240-257 [19] Ellsberg D. (1968) Theory and practicel of blackmail, Rand Corporation. [20] Datt G, Martin Ravallion (2011) Has India’s Economic Growth Become More Pro-Poor in the Wake of Economic Reforms? World Bank Economic Review, 25, 2 ,157-189 [21] Dedola Luca , Peter Karadi, Giovanni Lombardo (2013) Global implications of national unconventional policies, Journal of Monetary Economics, 60, 1, 66-85 [22] Dri¢ l J. (1988) Macroeconomic Policy Games with Incomplete Information: A Survey, European Economic Review, 32 (2-3) 513-41. [23] Evans, M. D., and V. V. Hnatkovska (2007): “Financial Integration, Macroeconomic Volatility, and Welfare,”Journal of the European Economic Association, 5(2-3), 500–508. [24] Frankel J. (1992) Obstacles to the macroeconomic policy coordination with an analysis of international policy targets, UC, Berkley. 357
[25] Frankel J. A., K. E. Rockett (1988) International Macroeconomic Policy Coordination When Policymakers Do Not Agree on the True Model, American Economic Review, 78, 3,Jun.,: 318-340. [26] Freiling Jank and Abou-Kendill (1996) On global existence solutions to coupled matrix Riccati equations in closed loop Nash games, memio? [27] Goyal A (2007) Tradeo¤s, Delegation, and Fiscal-Monetary Coordination in a Developing Economy, Indian Economic Review,42, 2,141-164 [28] Hamada K (1976) Strategic Analysis of Monetary Interdependence, Journal of Political Economy, 84 August. [29] Ivanov I. G. (2008) A method to solve discrete time coupled algebraic Ricaati equations, Applied Mathematics and Computations, 206, 34-41 [30] Jank G and Kremer ( ) Open loop Nash games and positive systems: solvability conditions for non-symmetric Riccati equations, memio? [31] Jorgenson D. W. (1961) Stability of a Dynamic Input-Output System Stability of a Dynamic Input-Output System, Review of Economic Studies, 28,2, Feb., 105-116 [32] Kehoe P.J. (1989) Policy Cooperation Among Benevolent Governments May Be Undesirable ,The Review of Economic Studies, 56, 2, Apr., 289-296 [33] Kawai M (2011) G-20 Financial Reforms and Emerging Asia’s Challenges, in Asia and Policymaking for the Global Economy, Asian Development Bank. [34] Kempf Hubert , Leopold von Thadden (2013) When do cooperation and commitment matter in a monetary union? Journal of International Economics, 91, 2, 252-262 [35] Kotwal A, Bharat Ramaswami, and Wiliam Wadhwa (2011) Journal of Economic Literature 2011, 49:4, 1152–1199. [36] Krugman Paul (1979) A Model of Balance of Payment Crisis, Journal of Money Credit and Banking, 11,Aug. [37] Kumar T. K. (1969) The Existence of an Optimal Economic Policy Econometrica, 37:4 :Oct.: 600-610. [38] Kydland F. (1975) Equilibrium Solutions in Dynamic Dominant Player Models, Journal of Economic Theory, 15:307-324
358
[39] Kydland F. (1975) Non-cooperative and dominant player solutions in dynamic discrete games, International Economic Review, 16:2:321-335 [40] Kydland F.E and E.C. Prescott (1977) Rules rather than discretion: the Inconsistency of Optimal Plans, Journal of Political Economy, 85:3: 473-491. [41] Li M., J.B. Cruz, M. A. Simaan (2002) An approach to discrete-time incentive feedback stackelberg games, IEEE Transactions on System, Man and Cybernatics- Part A: Systems and Humans, 32:4:472-481. [42] Martin, P., and H. Rey (2000): “Financial integration and asset returns,”European Economic Review, 44(7), 1327–1350. [43] Miller M, Mark Salmon (1985) Dynamic Games and the Time Inconsistency of Optimal Policy in Open Economies, Economic Journal, 95, Conference Papers:124-137. [44] Miller, Marcus; Salmon, Mark When Does Coordination Pay? Journal of Economic Dynamics and Control, July-Oct. 1990, v. 14, iss. 3-4, pp. 553-69 [45] Mundell R. A (1962) Capital mobility and stabilisation policy under …xed and ‡exible exchange rates,Canadian Journal of Economic and Political Science, 29, 475-85. [46] Mukaidani H. (2004) Proceedings of the American Control Conference, Boston [47] Nordhaus W.D. (1995) Policy Games: Co-ordination and Independence in Monetary and Fiscal Policeis, Brookings Papers on Economic Activity 2:1994: 139-216. [48] Obstfeld M. (2001) International macroeconomics: beyond the Mundell-Flemming model, Cebter for International and Development Economics Research, UC Berkeley. [49] Obstfeld, M. (1994): “Risk-Taking, Global Diversi…cation, and Growth,” American Economic Review, 84(5), 1310–29. [50] Oudiz G. and J Sachs (1984) Macroeconomic policy coordination among industrial economies, Brookings papers in economic activities, 1:1-64 [51] Papavassiloupoulos G. P. and Olsder (1984) On the linear-quadratic, closed loop, no-memory, Nash game, Journal of Optimisation Theory and Applications, 42:4:551-560 [52] Parikh A. (1979) Forecasts of Input-Output Matrices Using the R.A.S. Method The Review of Economics and Statistics, 61, 3 Aug., 477-481.
359
[53] Petit M. S. (1989) Fiscal and Monetary Policy Co-Ordination: A Di¤erential Game Approach,Journal of Applied Econometrics, 4:2:Apr. - Jun.:161-179 [54] Rogo¤ K. (2002) Dornbusch’s Overshooting Model After 25 Years, IMF Sta¤ Papers, 49:1-35. [55] Senay, O. (1998): “The Ex oects of Goods and Financial Market Integration on Macroeconomic Volatility,” Manchester School of Economic & Social Studies, 66(0), 39–61. [56] Sutherland, A. (1996):
“Financial Market Integration and Macroeconomic Volatil-
ity,”Scandinavian Journal of Economics, 98(4), 521–39. [57] Starr A. W. and Y. C. Ho (1969) Non-zero sum di¤erential games, Jounral of Optimisation Theory and Applications, 3:3:184-206 [58] Taylor J (1993) Discretion versus policy rules in practice, Carnegie Rochester Conference,Series on Public Policy 29 Amsterdam. [59] Turnovsky S.J., T. Basar and V. d’Orey (1988) Dynamic Strategic Monetary Policies and Coordination in Interdependent Economies,The American Economic Review, 78, 3,Jun., 341-361 [60] Van Long N. and G. Sorger (2009) A dynamic principle agent as a stacklebege di¤erential game, working paper 0905, Department of Economics, University of Vienna. [61] Van Aarle B, J. Engwerda and J. Plasmann (2002 ) Monetary and Fiscal policy interaction in the EU: A Dynamic Game Approach, Annals of Operation Research, 109, 229-264 [62] Van Aarle B, J. Engwerda and J. Plasmann (2001) Monetary and Fiscal policy interaction in the EU: A Dynamic Game Approach, Open Economies Review, 12:1, 29-60 [63] van de Klundert T. and F. van der Ploeg (1989)Fiscal Policy and Finite Lives in Interdependent Economies with Real and Nominal Wage Rigidity, Oxford Economic Papers, New Series, Vol. 41, No. 3 (Jul., 1989), pp. 459-489 [64] Xu C (2011) The Fundamental Institutions of China’s Reforms and Development Journal of Economic Literature 2011, 49:4, 1076–1151
12.7
Exercise 11
1. Consider the macroeconomic system in two interdependent economies, i.e. Europe and the ROW Economy 1 Y1 = C1 + I1 + G1 + N X1 360
(L.1092)
C1 = a1 + b1 (Y1
T1 )
(L.1093)
I1 = k1 + d1 r1
(L.1094)
N X1 = Y2
(L.1095)
Y2 = C2 + I2 + G2 + N X2
(L.1096)
Economy 2
C2 = a2 + b2 (Y2
T2 )
(L.1097)
I2 = k2 + d2 r2
(L.1098)
N X2 = Y1
(L.1099)
(a) Solve for the national income of both economies simultaneously. (b) Determine how public spending of economy 1 would impact economy 2. (c) How would the monetary policy one economy a¤ect the monetary policy of another economy?
361
13
Tutorial Problems
13.1
Tutorial 1: Comparative Statics
Q1. Keynesian Model: Hicksian Synthesis Y = C +I +G
(M.1100)
C = C (Y
(M.1101)
Consumption function T)
Investment I = I(r)
(M.1102)
M s = M (Y; R)
(M.1103)
Money Market
Reduced form for goods and money markets Y
C (Y
T)
I(r) = G
(M.1104)
M s = M (Y; R)
(M.1105)
Y and r are implicit functions of G, T and Ms Derive comparative static equations for for dY and dr. Find the expression to analyse the impacts of …scal and monetary policy instruments in output and the interest rate. Hint: Take total de¤erentition of these two equations dY
C 0 (Y
T ) dY
I(r)dr = dG + C 0 (Y
T ) dT
(M.1106)
@M @M dY + dr = dM s (M.1107) @Y @r Using the time series contained in the Workhours.csv …le estimate this Keynesian model and use it for policy analysis. Be able to execute the programmes written in MATLAB, dynare, GAMS, Oxmetrics 7 and Eviews 8. Find the absolute and relative standard deviation of growth rate of output, consumption, investment and hours worked observed in the data. Test the validity of the quantity theory of money MV = PY with appropriate data. 362
Table 95: Percentage standard deviation of macro variables GDP
Consumption
Investment
Hours worked
% standard deviation Relative % standard deviation Table 96: Lag, contemporaneous and lead correlations among macro variables GDPt ; xt
GDPt ; xt
1
GDPt ; xt+1
GDP Consumption Investment Hours worked
Q2. Hicks (1937) had integrated Keynesian ideas nicely like this. Output Y = F (K; N )
Fk > 0; FN > 0; Fkk < 0; FN N < 0:
(M.1108)
Consumption C = c Y d ; Y d = (1
)Y
(M.1109)
Investment I = I(r)
(M.1110)
W = FN (N; K) P
(M.1111)
W = W0 + W (N )
(M.1112)
Labour demand
Labour supply
W (N ) =
Z
0 for N 5 N
(M.1113) +for N > N
money market equilibrium conditions: M = M (Y; r) P
My > 0; Mr < 0 363
(M.1114)
Net exports NX = X
IM
(M.1115)
Equilibrium condition Y = C + I (r) + G + N X
(M.1116)
Q3. Samuelsonian Multiplier Accelerator Model (1939) provides good dynamics in the system. Macro balance Yt = Ct + It + G0
(M.1117)
Consumption function Ct = Yt
1;
0
4
2
(1 + ) = 4
2
(1 + ) < 4
Repeated real root case (no cycle)
Complex root case (cycle)
Complete solution
364
Yt = A1 bt1 + A2 bt2 + Y
(M.1124)
Practice with stochastic Keynesian and Samuelsonian models. Q4.Imagine an economy inhabited by rich, middle income and poor households, indexed by i = A, B and C. There are three types of goods in the economy. Endowments of these three goods to three categories of households are W1 , W2 and W3 respectively. Each household prefers to consume all three goods, j = 1; 2;and 3. The demand of household i for good j , is denoted by Xji ; i.e. X1i ; X2i and X3i . Each household i maximises its own welfare subject to its own budget j P constraint, I i = Pj Wji , where I i is the total income of the household, Pj is the relative price j=1
of a commodity and Wji is the endowment of commodity j of household i. Price of good j adjusts until demand for it equals its supply. For simplicity assume that each household is endowed only with one type of good but prefers to consume each of three goods equally. Thus preferences and constraints for household type i are given by following equations: U (X1i ; X2i ; X3i ) = X1i X2i X3i
M ax
i = A; B; C
(M.1125)
subject to Ii =
j X Pj Wji = P1 X1i + P2 X2i + P3 X3i
(M.1126)
j=1
Markets clear (only A is endowed by W1 ; only B is endowed by W2 and only C is endowed by W3 ) X
X1i = W1A ;
X
X2i = W2B ;
X
X3i = W3C
(M.1127)
The endowments of households were as given in Table 1.
Table 97: Endowment Structure of Households W1 W2 W3 A
100
0
0
B
0
200
0
C
0
0
300
100
200
300
Total supply
a. Derive demand functions, X1i ; X2i and X3i consistent with utility maximisation by each household. Find equilibrium prices, optimal allocations and utility for each household.
365
Table 98: Optimal Consumption of Households X1 X2 X3 U A B C Total
100
200
300
Price
b. Record the quilibrium solutions of the model in respective cells of Table 2. c. How would these prices change if there is a 20 percent tax on income of each household and all revenue collected are distributed equally among them. Q5. Three period model of consumption Extend two period two individual model to a three period economy which is inhibited by the low, middle and high income households. Again inter temporal optimisation by each involves maximising utility subject to its life time budget constraint. M ax
U (C1i ; C2i ; C3i ) = ln C1i +
i 2
ln C2i +
i 3
ln C3i
i = A, B,C
(M.1128)
subject to budget constraints while young, adult and old as following: C1i + bi1 = w1i
(M.1129)
C2i + bi2 = bi1 (1 + r) + w2i
(M.1130)
C3i = bi2 (1 + r) + w3i
(M.1131)
whereC1i ; C2i ; C3i are consumptions for periods 1, 2 and 3 for type i agent and
i 2 and
i 3 are
subjective discount factors for period 2 and 3 consumptions with their values between 0 and 1. Endowment of agent i for time t is given by wti with endowments for agent A, B and C for periods 1, 2 and 3 are w1A ; w1A ; w1A ; w1B ; w1B ; w1B ; w1C ; w1C ; w1C . Again each household is allowed to borrow and lend at the interest rate r. Markets clear for each good for each period: C1A + C1B + C1C = w1A + w1B + w1C
366
(M.1132)
C2A + C2B + C2C = w2A + w2B + w2C
(M.1133)
C3A + C3B + C3C = w3A + w3B + w3C
(M.1134)
What is the interest rate and equilibrium allocations in this economy? State how to extend this model to ten households. Q6. Consider a New Keynesian business cycle model in which Qi = Li
Ui = Ci
(M.1135)
Li ;
>1
(M.1136)
Consumption equals real income Ci =
Pi Qi P
(M.1137)
with demand shocks as given by qi = y + zi
n>0
(M.1138)
Prove that equilibrium output is less than optimal when producers have mark up power. Q7. Consider a new Keynesian structure with are i:::n …rms each with technology Yi = AL1i
M P Li =
;
0
0
y D = u + v (e
(M.1158)
p)
(M.1159)
yS = y
(M.1160)
b) Markov model of employment and Layo¤ et+1 = (1
) et + ut
ut+1 = et + (1
(M.1161)
) ut
(M.1162)
Reference: Hoy et al. (2001) Mathematics for Economics, MIT Press.
13.3
Tutorial 3: Open Economy DSGE Model
Q1 Consider a standard open economy optimal growth model with Household problem: max
U = E0
1 X
t
Ut (Ct ; Lt )
0
0
(M.1366)
y D = u + v (e
p)
yS = y
(M.1367) (M.1368)
b) Markov model of employment and Layo¤ et+1 = (1
) et + ut
ut+1 = et + (1 403
) ut
(M.1369) (M.1370)
1. c) Model of price war
yt+1 = yt
(yt
xt )
(M.1371)
xt+1 = xt
(xt
yt )
(M.1372)
d) Entry adjustment model qD
p = p =
(a + bp
N =
(p
qS
(M.1373)
mN )
>0
c)
>0
(M.1374) (M.1375)
Reference: Hoy et al. (2001) Mathematics for Economics, MIT Press. Q3. Consider a standard version of Ramsey’s optimal growth model max
U=
1 X
t
ln(Ct )
0
0
(P.1427)
6) aggregate demand y D = u + v (e
p)
(P.1428)
7) demand supply balance yS = y
(P.1429)
1. What are the steady state values of exchange rate and price level in this economy? 2. Find the time paths of the exchange rate and price level solving di¤erential equations simultaneously. Explain the convergence or divergence properties of the system. 3. Illustrate the transitional dynamics in a phase diagram in (e; p) space. 4. Discuss why the exchange rate overshoots in the short run using the above derivations and analysis. Q2. Imagine an economy inhabited by rich, middle income and poor households, indexed by i = A, B and C. There are three types of goods in the economy. Endowments of these three goods to three categories of households are W1 , W2 and W3 respectively. Each household prefers to consume all three goods, j = 1; 2;and 3. The demand of household i for good j , is denoted by Xji ; i.e. X1i ; X2i and X3i . Each household i maximises its own welfare subject j P to its own budget constraint, I i = Pj Wji , where I i is the total income of the household, Pj j=1
is the relative price of a commodity and Wji is the endowment of commodity j of household i. Price of good j adjusts until demand for it equals its supply. For simplicity assume that each household is endowed only with one type of good but prefers to consume each of three goods equally. Thus preferences and constraints for household type i are given by following equations:
M ax
U (X1i ; X2i ; X3i ) = X1i X2i X3i
subject to
443
i = A; B; C
(P.1430)
i
I =
j X
Pj Wji = P1 X1i + P2 X2i + P3 X3i
(P.1431)
j=1
Markets clear (only A is endowed by W1 ; only B is endowed by W2 and only C is endowed by W3 ) X
X1i = W1A ;
X
X2i = W2B ;
X
X3i = W3C
(P.1432)
The endowments of households were as given in Table 1.
Table 107: Endowment Structure of Households W1 W2 W3 A
100
0
0
B
0
200
0
C
0
0
300
100
200
300
Total supply
a. Derive demand functions, X1i ; X2i and X3i consistent with utility maximisation by each household. Find equilibrium prices, optimal allocations and utility for each household. b. Record the quilibrium solutions of the model in respective cells of Table 2. Table 108: Optimal Consumption of Households X1 X2 X3 U A B C Total
100
200
300
Price c. How would these prices change if there is a 20 percent tax on income of each household and all revenue collected are distributed equally among them. Q3. A representative household in a economy has to decide on how much to consume today and how much to save and invest to add to the capital stock to produce more goods for future consumption. The optimal capital stock maximises the present value of utility (U0 ) from consumption (C (t)). Problem of this representative household is: 444
M ax U0 =
Z
T
e
rt
C (t) dt
(P.1433)
0
subject to:
1) the production technology relates how output (Q) relates to capital stock (K) as: Q = Q(K)
(P.1434)
The …rst and the second order derivatives of output w.r.t capital (K) are:
@Q @K
@2Q @K 2
> 0 and
0 a1 > 0;
t
2
N 0;
(P.1448)
Actual output (yts ) deviates from the natural rate of output when actual prices are not equal to expected prices pt 6=Et
1
pt as:
yts = yn + b1 pt
Et
1
p t + vt ;
a1 > 0 ;
t
N 0;
2
(P.1449)
Demands equals supply in equilibrium as: ytd = yts = yt
(P.1450)
Consider a money supply rule given by: mt
mt
1
=
(P.1451)
1. Use rational expectation method to solve for equilibrium output and prices in this model. 2. Show that under the rational expectation average in‡ation equals growth rate of money supply but only the unanticipated shocks to demand or supply in‡uence the level of output. Q7. Consider a two sector endogenous growth model in which output (yt ) is produced using physical capital (kt ) and human capital (ht ). This output is either consumed (ct ) or exported (xt ). Part of the human capital (lG share, 0 < lG < 1) is used in producing …nal goods and remaining (1
lG ) of it is used to produce more human capital. The technical progress in the
…nal goods sector is AGt and that in the human capital sector is Aht . The physical capital depreciates at
k
rate and the human capital at
purchase investment goods
ikt ,
xt =
pkt ikt
where
pkt
h:
Proceedings from exports are used to
is the price of capital good. International
borrowing (bt ) is permited at the interest rate r but being a small open economy it faces 448
borrowing constraints, it can borrow only up to its physical capital, bt
kt :More speci…cally
the optimization problem faced by the benevolent social planner of this economy is:
M ax
1 X
t
U (ct );
0
4 + +
+ n
+ n i
#
(R.1572)
: (R.1573)
It requires two initial conditions for de…nite solution
P t = A1 e
1 2
m n
q
In case of repeated root
(m n )
2
4(
m 2 n
+ n
=
)
t
+ A2 e + n
4
q
1 2
m n +
2
(m n )
+4(
parts as:
h
m 2 n
4a2 II. Repeated real root if a21 = 4a2 III. Complex real root a21 < 4a2 This requires use of the imaginary number, De Moivre theorem and trigonometry. These cases is illustrated below by two examples: 468
Consider a market price adjustment model where it takes time for demand and supply to adjust towards equilibrium. Starting from an initial point, does market prices converge to the long run equilibrium or not depends on the roots of the equations. These provide stability conditions for the system: Preliminaries
Example of Complex Root Case: Example Exponential forms and polar coordinates p
h2 + v 2
(R.1582)
sin n =
v =) v = Rsin R
(R.1583)
cos =
h =) h = Rco R
(R.1584)
R=
ei = cos + i Si n
h @ sin @
= cos ;
@ cos @
vi = Rco =
e
i
= cos
Ri sin = R (co
i Si n
i sin ) = Re
(R.1585)
i
(R.1586)
sin ;
Thus the Cartesian coordinates of the complex numbers have been transformed to polar coordinates R and
and also expressed as exponential form Re
i
:
Give the Cartesian form of the complex number 5e
3i 2
R (co
i ( 1)) =
i sin ) = 5 cos 3 2
i sin 3 2 = 5 (cos 0
: Here R = 5, 5i = h
= 32 vi
By De Moivre’s theorem n
(h + vi) = Rn ein
and
n
(h
vi) = Rn e
in
(h
vi) = Rn (cos n
n
i sin n )
(R.1587)
Solving a di¤erential equation with complex roots Table 109: Values of Trigonometric Ratios 0 300 450 600 900 1200 1800 2700 0
0 sin cos
0 1
6 1 2 p
3 2
4 p1 2 p1 2
3 p
3 2 1 2
2
1 0
469
3 4 p1 2 - p12
3 2
0 -1
2 1
0
3600 0 1
Example of Complex Root Case: Example An Example y + 2y + 17y = 34
(R.1588a)
34 b = =2 a2 17
(R.1589)
Steady state yp =
This is a complex root case because (a1 = 2; a2 = 17; b = 34) a21
4a2 = 22
4
17 = 4
68 =
64 < 0
Use the formula explained above h h=
vi = Rco 1 2 a1
=
Ri sin = R (co i sin ) = Re i p p p 1 v = 12 4a2 a21 = 21 4 (17) 22 = 12 64 =
1 2
(8) = 4
In case of the complex root
yc
=
eht A1 evit + A2 e
vit
=
eht [A1 (cos vt + i sin vt) + A2 (cos vt
(R.1590) i sin vt)]
(R.1591)
For this problem complementary solution
yc
=
eht A1 e4it + A2 e
=
e
yt = yc + yp = e
t
yt = e
t
(R.1592)
[A1 (cos 4t + i sin 4t) + A2 (cos 4t
[A1 (cos 4t + i sin 4t) + A2 (cos 4t t
[(A1 + A2 ) cos 4t + (A1
yt = e where A5 = (A1 + A2 )
4it
t
A6 = (A1
i sin 4t)]
i sin 4t)] + 2
A2 ) i sin 4t] + 2
[A5 cos 4t + A6 sin 4t] + 2
(R.1593)
(R.1594)
(R.1595)
(R.1596)
A2 ) i
Use two initial conditions to de…nitize the values of A5 and A6 . y0 = 3 and y = 11: When t = 0 y0 = 3 = e
t
[A5 cos 4t + A6 sin 4t] + 2 = [A5 cos 0 + A6 sin 0] + 2 = A5 + 2 470
(R.1597)
Thus A5 = 1 take the …rst derivative of with respect to time
y y
= =
@y e t [A5 cos 4t + A6 sin 4t] + 2 @t e t [A5 cos 4t + A6 sin 4t] + e t [ 4A5 sin 4t + 4A6 cos 4t]
(R.1598) (R.1599)
Evaluated when t = 0 y=
e
t
[A5 cos 0 + A6 sin 0] + e
t
[ 4A5 sin 0 + 4A6 cos 0]
11 =
(A5 + 0) + [0 + 4A6 ]
(R.1600)
A6 = 3 Thus the complete solution of this equation is: t
yt = e
[cos 4t + 3 sin 4t] + 2
(R.1601)
The …rst trigonometric function gives the cycle and second part is the steady state. Numerical example 1 for SODE demand
QD = 42
Supply
QS =
4P + 4P 0 + P 00
6 + 8P
(R.1602)
(R.1603)
Initial conditions P0 = 6 and P 0 (t = 0) = 4: Let market …nd its equilibrium in each period QD = QS : This implies 42
4P + 4P 0 + P 00 =
The steady state equilibrium like before is : Pp = For homogenous solution rearrange P
00
P 00
4P
0
4P 0
471
46 12
6 + 8P
(R.1604)
=4
4P + 42 =
8P = 0
6 + 8P to
(R.1605)
Numerical example 1 for SODE Corresponding quadratic equation is given by ( 4)
r1 ; r2 =
q 2 ( 4)
4:1:( 12)
2
=
4
p
16 + 46 = 6; 2 2
Pt = Pc + Pp = A1 er1 t + A2 er2 t + 4 = A1 e6t + A2 e
2t
+4
(R.1606)
(R.1607)
Use two initial conditions for the complete solution P0 = 6 = A1 e6:0 + A2 e
P 0 = 4 = 6A1 e6:0
2:0
+ 4 = A1 + A2 + 4
2:0
2A2 e
= 6A1
(R.1608)
2A2
(R.1609)
+4
(R.1610)
Solving these equations A1 = 1 and A2 = 1: Pt = A1 er1 t + A2 er2 t + 4 = e6t + e
2t
This path is dynamically unstable because of r1 = 6: This gives divergent Oscillations. Numerical example 2 for SODE demand
QD = 40
QS =
Supply
2P 0
2P
P 00
(R.1611)
5 + 3P
(R.1612)
Initial conditions P0 = 12 and P 0 (t = 0) = 1: Let market …nd its equilibrium in each period QD = QS : This implies 40
2P 0
2P
P 00 = 45 5
The steady state equilibrium like before is : Pp = For homogenous solution rearrange 40
2P
p
22 4:1:5 2 = r1 ; r2 = 2 This is complex root case with h + vi = 2
p 2 1
2P 4
20
0
5 + 3P =9 P 00 =
1 ( 2 2 2i where h = =
(R.1613)
5 + 3P toP 00 + 2P 0 + 5P = 45 4i) =
1
2i
(R.1614)
1 and v = 2
The general solution of this model is Pt = Pc + Pp = e
t
[A5 cos (2t) + A6 Si n (2t)] + 9 472
(R.1615)
Using the initial conditions 0
P0 = 12 = e
Pt0 =
t
e
[A5 cos (0) + A6 Si n (0)] + 9 = A5 (1) + A6 :0 + 9 = A5 + 9
[A5 cos (2t) + A6 Si n (2t)] + e
0 Pt=0
=
t
[ 2A5 sin (2t) + 2A6 Cos (2t)]
(R.1616)
(R.1617)
1 e
0
[A5 cos (2:0) + A6 Si n (2:0)]
+e
0
[ 2A5 sin (2:0) + 2A6 Cos (2:0)]
=
= A5 + 0 + 0 + 2A6
(R.1618)
Solving A5 + 9 = 12 and A5 + 2A6 = 1 we get A5 = 3 and A6 = 2. Thus the de…nite solution path of the system is t
Pt = e Pt ‡uctuates in each period of
2 v
=
[3 cos (2t) + 2 Si n (2t)] + 9
(R.1619)
= 3:1452. when t increases 3.1452 the Pt completes one
cycle. This cycle is damped because of the multiplicative term e t . That means this path Pt starts at 12 and gradually converges to 9 in a cyclical fashion. Generic Di¤erential Equations In a higher order di¤erential equation Routh theorem is applied to …nd whether time path converges to long run equilibrium: Take a polynomial of the form a0 rn + a1 rn
1
+ a2 rn
2
+ ::: + an 1 r + an = 0
the real parts of all the roots of nth degree polynomial are negative when …rst n sequence of determinants are positive. Therefore above equation is convergent. Routh Theorem
Routh Matrix is formed by letting odd coe¢ cients head a row and succes-
sively reducing the subscripts and writing zero for negative coe¢ cients (Samuelson (1947) Foundations of Economic Analysis).
ja1 j ;
a1
a3
a0
a2
a1
a3
a5
; a0
a2
a4
0
a1
a3
a1
a3
a5
a7
a0
a2
a4
a6
0
a1
a3
a5
0
a0
a2
a4
473
000
00
0
Numerical example y 4 (t) + 6y (t) + 14y (t) + 16y (t) + 8y = 24 a0 = 1; a1 = 6; a2 = 14; a3 = 16; a4 = 8; a5 = 0; a6 = 0; 0
= ja1 j = j6j > 0;
6
16
0
0
1
14
8
0
0
6
16
0
1
=
a1
a3
a0
a2
=
6
16
1
14
6
16
0
= 84 16 = 68 > 0; 1
14
8
0
6
16
= 800 > 0;
= 6400 > 0
0 1 14 8 The …rst n sequence of determinants are positive, the real parts of all the roots of nth degree polynomial are negative . Therefore the time path of y(t) in above equation is convergent. Higher Order Di¤erence Equations: Schurr Theorem Checking convergence of a di¤erence equation (Schur determinants approach) 1 Yt+2 + Yt 6 This is a second order di¤erence equation a0 = 1; a1 = 16 ; a2 = ;
1
2
18.3.1
=
=
a0 a2
a2 a0
1 Yt = 2 6
1
(R.1620)
1 6
> 0;
a0
0
a2
a1
a1
a0
0
a2
a2
0
a0
a1
a1
a2
0
a0
1
1 6
1 =
1 6
1
=
1 6
1 1 6
1 1 6
1 1 6
1
=
35 36
>0 1 6
1 1 6
1 1 6
1 1 6
= 0907407 > 0
1
Higher Order Di¤erence Equations: Schurr Theorem
Divide the matrix in four parts: A
B
C
D
Start with a0 in diagonal at the upper left matrix (A), put zeros above the diagonal and successively higher subscripts down the column (A) Matrix at the southeast corner (D) is the transpose of the northwest corner (A’); Put an in the diagonal of the south west corner (C) and zeros above the diagonal and successively smaller subscripts down the column of (C) The matrix at northeast corner (B) is transpose of matrix at the southwest corner (C)
474
Roots of the polynomial are less than unity when Schur determinants are positive. Therefore above di¤erence equation gives a convergent path. Routh theorem used for di¤erential equations. 18.3.2
Ten Best articles in the Journal of European Economic Association
1. Frank Smets and Raf Wouters (2003) An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area", Journal of European Economic Association, 1:5:1123-1175.
2. Jean-Charles Rochet and Jean Tirole (2003) Platform Competition in Two-Sided Markets" Journal of European Economic Association, 1:4:990-1029.
3. Daron Acemoglu, Philippe Aghion and Fabrizio Zilibotti (2006) Distance to Frontier and Economic Growth",Journal of European Economic Association, 4:1:37-74.
4. Alberto Alesina, Filipe R. Campante and Guido Tabellini (2008) Why is …scal policy often procyclical?Journal of European Economic Association, 6:5:1006-1036.
5. Richard Blundell, Monica Costa Dias and Costas Meghir, (2004) Evaluating the employment impact of a mandatory job search program,Journal of European Economic Association, 2:4:569-606.
6. Ernst Fehr and John List,(2004) The hidden costs and returns of incentives— trust and trustworthiness among CEOs, Journal of European Economic Association, 2:5:743-771.
7. Jordi Galí, J. David López-Salido and Javier Vallés (2007) Understanding the e¤ects of government spending on consumption, Journal of European Economic Association, 5:1:277-270.
8. Thomas Laubach New Evidence on the Interest Rate E¤ects of Budget De…cits and Debt, Journal of European Economic Association, 7:4:858-885.
9. James H. Stock and Mark W. Watson (2005) Understanding changes in international business cycle dynamics,Journal of European Economic Association, 3:5:968-1006.
10. Guido Tabellini (2010) Culture and institutions: economic development in the regions of Europe,Journal of European Economic Association, 8:4:677-716.
18.3.3
Best 40 articles in the Journal of Economic Perspectives
David Autor (2012) The Journal of Economic Perspectives at 100, Journal of Economic Perspectives, 26, 2,Spring, 3–18
1. Porter, Michael E.;van der Linde,Claas 1995 Toward a New Conception of the Environment-Competitiveness Relationship 9(4) 657
475
2. Kahneman, Daniel; Knetsch, Jack L.; Thaler, Richard H. 1991 Anomalies: The Endowment E¤ect, Loss Aversion, and Status Quo Bias 5(1) 572
3. Diamond, Peter A.; Hausman, Jerry A. 1994 Contingent Valuation: Is Some Number Better than No Number? 8(4) 524
4. Fehr, Ernst; Gächter,Simon Fairness and Retaliation: The Economics of Reciprocity 2000 14(3) 490 5. Katz, Michael L.; Shapiro, Carl 1994 Systems Competition and Network E¤ects 8(2) 448 6. North, Douglass C. 1991 Institutions 5(1) 395 7. Koenker, Roger; Hallock, Kevin F. 2001 Quantile Regression 15(4) 375 8. Markusen, James R. 1995 The Boundaries of Multinational Enterprises and the Theory of International Trade 9(2) 375
9. Bernanke, Ben S.; Gertler, Mark 1995 Inside the Black Box: The Credit Channel of Monetary Policy Transmission 9(4) 365
10. Romer, Paul M. 1994 The Origins of Endogenous Growth 8(1) 365 11. Brynjolfsson, Erik; Hitt, Lorin M. 2000 Beyond Computation: Information Technology, Organizational Transformation and Business Performance14(4) 350
12. Nickell, Stephen 1997 Unemployment and Labor Market Rigidities: Europe versus North America 11(3) 344
13. Machina, Mark J. 1987 Choice under Uncertainty: Problems Solved and Unsolved 1(1) 338 14. Hanemann, W. Michael 1994 Valuing the Environment through Contingent Valuation 8(4) 332 15. Camerer, Colin; Thaler, Richard H. 1995 Anomalies: Ultimatums, Dictators, and Manners 9(2) 316 16. Ostrom, Elinor 2000 Collective Action and the Evolution of Social Norms 14(3) 313 17. Smith, James P. 1999 Healthy Bodies and Thick Wallets: The Dual Relation between Health and Economic Status 13(2) 311
18. Jarrell, Gregg A.; Brickley, James A.; Netter, Je¤ry M. 1988 The Market for Corporate Control: The Empirical Evidence since 1980 2(1) 295
19. Andrade, Gregor; Mitchell, Mark; Sta¤ord, Erik 2001 New Evidence and Perspectives on Mergers 15(2) 290
476
20. Scotchmer, Suzanne 1991Standing on the Shoulders of Giants: Cumulative Research and the Patent Law 5(1) 280
21. Simon, Herbert A. 1991 Organizations and Markets 5(2) 278 22. Bikhchandani, Sushil; Hirshleifer,David; and Welch, Ivo 1998 Learning from the Behavior of Others: Conformity, Fads, and Informational Cascades 12(3) 273
23. Elster, Jon 1989 Social Norms and Economic Theory 3(4) 272 24. Feenstra, Robert C. 1998 Integration of Trade and Disintegration of Production in the Global Economy 12(4) 272
25. Frank, Robert H.; Gilovich, Thomas; Regan, Dennis T. 1993 Does Studying Economics Inhibit Cooperation? 7(2) 272
26. Kirman, Alan P. 1992 Whom or What Does the Representative Individual Represent? 6(2) 272 27. Jensen, Michael C. 1988 Takeovers: Their Causes and Consequences 2(1) 268 28. Przeworski, Adam; Limongi, Fernando 1993 Political Regimes and Economic Growth 7(3) 268 29. Newhouse, Joseph P. 1992 Medical Care Costs: How Much Welfare Loss? 6(3) 265 30. Dixit, Avinash 1992 Investment and Hysteresis 6(1) 259 31. Oliner, Stephen D.; Sichel, Daniel E.2000 The Resurgence of Growth in the Late 1990s: Is Information Technology the Story? 14(4) 257
32. Cutler, David M; Glaeser, Edward L.; Shapiro, Jesse M. 2003 Why Have Americans Become More Obsese? 17(3) 250
33. Milgrom, Paul 1989 Auctions and Bidding: A Primer 3(3) 242 34. Portney, Paul R. 1994 The Contingent Valuation Debate: Why Economists Should Care 8(4) 239 35. Babcock, Linda; Loewenstein,George 1997 Explaining Bargaining Impasse: The Role of Self-Serving Biases 11(1) 231
36. Grossman, Gene M.; Helpman, Elhanan 1994 Endogenous Innovation in the Theory of Growth 8(1) 225
37. Palmer, Karen; Oates, Wallace E.; Portney, Paul R. 1995 Tightening Environmental Standards: The Bene… t-Cost or the No-Cost Paradigm 9(4) 222
477
38. Angrist, Joshua D.; Krueger, Alan B. 2001 Instrumental Variables and the Search for Identi… cation: From Supply and Demand to Natural Experiments 15(4) 221
39. Pritchett, Lant 1997 Divergence, Big Time 11(3) 209 40. Dawes, Robyn M.; Thaler, Richard H. 1988 Anomalies: Cooperation 2(3) 206 41. Lundberg, Shelly; Pollak, Robert A. 1996 Bargaining and Distribution in Marriage10(4) 206
Reading for policy coordintion Beetsma R. M.W.J. and H. Jensen (2005) Monetary and …scal policy interactions in a microfounded model of a monetary union Journal of International Economics, 67, 2, 320-352 Bullard J and ASingh (2008) Worldwide macroeconomic stability and monetary policy rules Journal of Monetary Economics, 55, S34-S47 Chang, Roberto. (1997) Financial integration with and without international policy coordination ,International Economic Review, 38, 3, 547. 18p. Canzoneri M. B., R. E. Cumby and B.T. Diba (2005) The need for international policy coordination: what’s old, what’s new, what’s yet to come? Journal of International Economics, 66, 2, 363-384 Clerc L, H. Dellas, O. Loisel (2011) To be or not to be in monetary union: A synthesis Journal of International Economics, 83, 2, 154-167 Clarida R, Jordi Galí and M. Gertler (2002) A simple framework for international monetary policy analysis, Journal of Monetary Economics, 49, 5, 87–904 Conconi P and Carlo Perroni (2009) Do credible domestic institutions promote credible international agreements? Journal of International Economics, 79, 1, 160-170 Cooper, R, D. DeJong , R Forsythe and T. W. Ross(1992) Communication in coordination games, Quarterly Journal of Economics. 107 2, p739. 33p. Currie D and P Levine (1986) Time inconsistency and optimal policies in deterministic and stochastic worlds Journal of Economic Dynamics and Control, 10, 1–2,191-199 D. Luca , P Karadi and G. Lombardo (2013) Global implications of national unconventional policies Journal of Monetary Economics, 60, 1, 66-85
478
Fratzscher M (2009) How successful is the G7 in managing exchange rates? Journal of International Economics, 79, 1, 78-88 Goodfriend, M.; R. G. King (1997) The New Neoclassical Synthesis and the Role of Monetary Policy NBER/Macroeconomics Annual (MIT Press). 12 1, 231-283. Juillard M, S. Villemot (2011)Multi-country real business cycle models: Accuracy tests and test bench Journal of Economic Dynamics and Control, 35, 2„178-185 Levine P, A. Brociner (1994) Fiscal policy coordination and EMU: A dynamic game approach Journal of Economic Dynamics and Control, 18, s 3–4, 699-729 Hansen L. P. and T. J. Sargent (2003) Robust control of forward-looking models Journal of Monetary Economics, 50, 3, 581-604 Kempf H. and L. von Thadden (2013) When do cooperation and commitment matter in a monetary union? Journal of International Economics, 91, 2, 252-262 Liu Z and E. Pappa (2008) Gains from international monetary policy coordination: Does it pay to be di¤erent? Journal of Economic Dynamics and Control, 32, 7, 2085-2117 Marquez J (1988) International policy coordination and the reduction of the US trade de…cit, Journal of Economic Dynamics and Control, 12, 1, 19-25 Gar…nkel M.R. (1989) Global macroeconomics: Policy con‡ict and cooperation: A review essay Journal of Monetary Economics, 23, 2, 345-352 Pappa E. (2004) Do the ECB and the fed really need to cooperate? Optimal monetary policy in a two-country world Journal of Monetary Economics, 51, 4, 753-779 Kose Ayhan K.M, C. Otrok and C. H. Whiteman (2008) Understanding the evolution of world business cycles Journal of International Economics, 75, 1, 110-130 Je¤rey S. (1992) International monetary and …scal policy cooperation in the presence of wage in‡exibilities: Are both counterproductive? Journal of Economic Dynamics and Control, 16, 2, 359-387
479
