Macroeconomic Theory

Macroeconomic Theory Francesco Franco Nova SBE

February 4, 2013

Francesco Franco

Macroeconomic Theory

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Macro

A short history of Macro

Francesco Franco


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Growth Once starts to think about economic growth, it is hard to think about anything else Rober Lucas 1988 1

Exogenous growth. The Solow model principal conclusion is that accumulation of physical capital cannot account for either the vast growth over time in output per person ot the vast geographic differences in output per person

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Endogenous growth. Allocation of resources to the creation of new technologies. Important for global growth phenomenon. (not covered in this course)

Francesco Franco


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The Solow Model

The aggregate neoclassical production function

The Solow model focuses on the aggregate produciton function. We need four variables: 1

output Y

2

capital K

3

labor L

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knowledge, effectiveness of labor A Y (t) = F (K (t), A(t)L(t)),

where t denotes time. Remarks: F , Harrod-neutral.

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The Solow Model


F is assumed to have CRS F (cK , cAL) = cF (K , AL) for all c Ø 0. Discuss (Large, Natural resources). Allows to write the production in intensive form y = f (k) where y =

Francesco Franco

Y AL , k

=

K AL , f (k)

= F (k, 1). Intuition.


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The Solow Model


f is assumed to satisfy f (0) = 0, f Õ (k) > 0, f ÕÕ (k) < 0, and the Inada conditions: limkæ0 f Õ (k) = Œ, limkæŒ f Õ (k) = 0. Example: Cobb-Douglas.

Francesco Franco


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The Solow Model Input dynamics

Initial conditions are given and Labor and Knowledge grow at exogenous rates n and g ˙ L(t) = nL(t) ˙ A(t) = gA(t) Remark: natural logs and growth rates. Exponential gorwth L(t) = L(0)e nt ,

A(t) = A(0)e gt .

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The Solow Model Capital dynamics

Output is divided between saving and consumption. Saving is constant at a rate s and one unit of output invested yields one unit of capital. Existing capital depreciates at a rate ”. K˙ (t) = sY (t) ≠ ”K (t). Comments: one good, simplifications...

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Let us derive the key equation of the model (differential equation) ˙ k(t) = sf (k(t)) ≠ (” + n + g)k(t)

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Figure : Solow Model

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Figure : Solow Model Francesco Franco


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The Solow Model

The balanced Growth Path

k converges to k ú . What about the other variables of interest? The Solow model implies that regardless of the starting point the economy converges to a Balanced Growth Path: each variable of the model grows at a constant rate. Furthermore the gorwth of output per capita is equal to the growth rate of technological progress.

Francesco Franco


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The Solow Model

Comparative Statics: the saving rate

An interesting question is what changes when we change the saving rate (taxes, government, ...). To study this question we proceed in a laboratory type of exercise. Start with an economy on the BGP and chang permanently the saving rate.

Francesco Franco


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The Solow Model


Figure : Solow Model Francesco Franco


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The Solow Model


The evolution of each variable on the whiteboard. The main lesson is that a permanent increase in s produces a temporary increase in the growth rate of output per worker and a permanent increase in the level of output per capita.

Francesco Franco


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The Solow Model


Welfare, consumption. c(t) = (1 ≠ s)f (k(t)) and on the BGP c ú = f (k ú ) ≠ (n + ” + g)k ú . The Golden Rule.

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The Solow Model quantitative questions

How fast do we expect an economy to converge to the BGP? Or how long is the transition towards the BGP? How long/short is temporary? How strong are the effects? A technique to evaluate quantitatively a model is to take an approximation around the BGP.

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Long Run impact: s ˆy ú k ú f Õ (k ú )/f (k ú ) –K = = . ú Õ ú ú y ú ˆs 1 ≠ k f (k )/f (k ) 1 ≠ –K

if –K = 0.3, the elasticity is 1/2.

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Speed of convergence around the BGP ˙ k(t) ƒ ≠⁄ [k(t) ≠ k ú ] where ⁄ = [1 ≠ –K (k ú )] (n + ” + g). Calibration suggests ⁄ = 0.04. Slow.

Francesco Franco


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The Solow Model

Extensions: natural resources

Conside Land, T , and Resources R Y (t) = K (t)– R(t)— T (t)“ [A(t)L(t)]1≠–≠“≠— with – < 1, “ < 1, — < 1 and – + — + “ < 1. Assume T˙ = 0 and with b > 0.

Francesco Franco

˙ R(t) = ≠bR(t)


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Readings

(*) David Romer. Advanced MAcroeconomics, 4th Edition Chapter I, pages 6-30 Solow Robert, “A contribution to the theory of Economic Growth”, Quarterly Journal of Economics 70 (February 1956): 65-94. Solow Robert, “Technical Change and the Aggregate Production Function”, Review of Economics and Statistics 39 (1957): 312-320. Swan, T.W, “Economic Growth and Capital Accumulation”, Economic Record 32 (November 1956): 334-361.

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