t - EPI

International macroeconomics#1 Monetary models of exchange-rate determination 1. The monetarist model 2. The Dornbusch overshooting model 3. Empirical validation

1 Bénassy-Quéré - International Macroeconomics 2012-13

Prologue: nominal exchange-rate volatility Effective exchange rate of the euro

Source: ECB.

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Prologue: exchange-rate models • Real exchange rate: – PPP: constant – Balassa-Samuelson: catch-up effect – Balance-of-payment equilibrium • Static: Marshall-Lerner-Robinson • Dynamic: Obstfeld-Rogoff.

• Nominal exchange rate: – – – –

RER+inflation differential Monetary approach (PPP) Overshooting model (sticky prices) Portfolio-balance model (risk aversion)


1. The monetarist model Frenkel, J. (1976), “A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence,” Scandinavian Journal of Economics, May. Bilson, J. (1978), “The Monetary Approach to the Exchange Rate: Some Evidence,” IMF Staff Papers, March.

Germany, Feb. 1920-Nov. 1923 Source: Frenkel (1976) Jakob Frenkel, 1943-

John Bilson, 19484 Bénassy-Quéré - International Macroeconomics 2012-13

A repetition of history Brazil, 1991-94 (yoy growth rates in percent) Source: IMF.


The model

Small open economy: Money market: mt - pt = α yt - β it α, β > 0 Uncovered interest parity: it = it* - (st,t+1e - st) Purchasing power parity: pt = pt* - st Exogenous real output: yt = 0 Exogenous world price: pt* = 0 Exchange-rate expectations: st,t+1e

• • • • • • • •

p domestic price p* : world price s : nominal exchange rate m : money supply y : real output i : domestic interest rate i* : world interest rate se: expected exchange rate


Resolution with static expectations Resolution: mt + st = - β (it* - set+1 + st) Static expectations: st,t+1e = st Hence st = -mt –βi*t If i* exogenous, we have ∆st = -∆mt


Resolution with rational expectations mt + st = - β

(it*

-

set+1

+ st) with

set+1=Etst+1

β

mt + β it* Et st +1 − ⇒ st = 1+ β 1+ β

Denote by zt the ‘fundamental’ exchange-rate determinant: The exchange rate writes: Et st +1 = β Et st + 2 + Et zt +1 1+ β  β ⇒ st =  1+ β

2

  β  Et st + 2 +   1+ β

∞

  Et zt +1 + zt 

∞  β   β  Et st + ∞ + ∑  st =  k =0  1 + β 1+ β  ∞  β  Transversality condition:  1 + β  Et st + ∞ = 0  

Finally:

 β stf = ∑  k =0  1 + β ∞

k

  Et zt + k 

m t + β it* zt = − 1+ β

k

  Et zt + k  t

Fundamental exchange rate

The exchange rate at time t depends on the expected future path of zt Bénassy-Quéré - International Macroeconomics 2012-13

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Consequence: the exchange rate is forward looking

Source: Reuter.


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Speculative bubbles Coming back to: st = Let bt =

β

β 1+ β

Et st +1 + zt

Et bt +1

1+ β + bt is also a solution of the exchange-rate equation: β f s = Et stf+1 + zt if t then stf + bt = β (Et stf+1 + Et bt +1 ) + zt 1+ β 1+ β

st f

Problem: this solution is explosive:

∞

Solution with bubble

∞  β   β  Et bt + ∞ + ∑  st =  k =0  1 + β 1+ β 

k

  Et zt + k 

Solution: to meet the transversality condition, markets must be assumed to attribute a probability of burst at each period. Cumulated probabilities prevent the expected exchange rate to diverge in the long run. 10 Bénassy-Quéré - International Macroeconomics 2012-13

Case study: the euro/dollar, 1980-2009


The monetarist model under criticism • Rational expectations – Models with non-rational expectations – ex. Frankel & Froot 1990: fundamentalists and chartists

• Uncovered interest parity – Portfolio choice model

• Price flexibility – Dornbusch model: exchange-rate overshooting

• Perfect competition – Pricing to market: exporters do not pass the whole exchange rate variation on export prices (Betts & Devereux, 1996).

• Exogenous output – Long-lasting impact of exchange-rate variations on output (Baldwin & Krugman, 1989). 12 Bénassy-Quéré - International Macroeconomics 2012-13

2. The Dornbusch overshooting model Puzzle: nominal exchange rate much more volatile than its macroeconomic determinants (Flood and Rose, JME 1995).

Rudiger Dornbusch 1942-2002 Sources : ECB and Fed. Ref. Dornbusch, R. (1976), “Expectations and Exchange Rate Dynamics,” Journal of Political Economy, 84, pp. 1161–76. Bénassy-Quéré - International Macroeconomics 2012-13

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The model Exogenous real output: Demand: Exogenous world price: Money market: UIP + rational expectations: Sticky prices (λ > 0):

y=0 yd = -ε(p + s - p*), ε > 0 p* = 0 m- p = α y- β i α, β > 0

i + s& = i * p& = λ y d − y

(

)

p& = λ (− ε ( p + s ) − y ) = −λε ( p + s ) Long-run solution :

• • • • • • • •

p : domestic price p* : world price s : nominal exchange rate m : money supply y : real output yd : aggregate demand i : domestic interest rate i* : world interest rate.

s& = p& = 0 p = m + β i* s = −p

s = − p = −(m + β i * )

x& = dx / dt


Dynamics Short run:

(

p = m + β i = m + β i * − s&

Long run

)

p = m + β i*

s = −p

p& p& = −λε ( p + s ) ⇔ s = − p −

λε

Difference between short run and long run: 1 p − p = − β s& ⇔ s& = − ( p − p ) p& β ⇔ p& = −λε [(s − s ) + ( p − p )] s − s = −( p − p ) − λε

 s&   0  p&  = − λε    X&

−1/ β  s − s  − λε   p − p  A

λε 0: two real eigenvalues v1 = 2 2) ∆ = 0: one real eigenvalue 3) ∆ < 0: two conjugated complex eigenvalues Here: ∆ = λ2ε 2 + 4 λε > 0 β

v1v2 = −

λε 0

(s − s ) < −( p − p ) ⇒ p& > 0

Impact of a monetary shock

p p = p = m + β i* ∆m > 0

s

E1 E0’ s0 ’


E0 s1

s0

s 17

Time dynamics Impact of a permanent increase in money supply p ' = m + ∆m + β i

p

Short run: *

p = m + β i*

s = − p = −m − βi*

s ' = − p ' = −m − ∆m − β i *

s

s& > 0

• rise in real money supply (fixed prices); fall in domestic interest rate. • domestic currency depreciates until markets can rationally expect an appreciation at a pace corresponding to the interestrate differential. Then:

i = i*

i

i = i * − s& < i *

• price level increases; real money supply falls back; domestic interest rate rises; domestic currency appreciates.

t 18 Bénassy-Quéré - International Macroeconomics 2012-13

The Dornbusch model: empirical evidence • Exchange-rate instability • But exchange rates do not seem to overshoot following monetary shocks – Domestic currency depreciates on impact, but then it continues to depreciate – Gourinchas and Tornell (2004): learning effect

• Variants of the model – Flexible prices, fixed asset stocks in the short run: portfolio model

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3. Empirical validation • Meese, R. et K. Rogoff (1983), “Empirical exchange rate models of the seventies. Do they fit out of sample?”, Journal of International Economics, 14, pp. 3-24. • Cheung, Y.W, Chinn M.D et A. Garcia Pascual (2005), « Empirical exchange rate models of the nineties: Are any fit to survive?”, Journal of International Money and Finance, 24, 1150-1175. • Methodology: – Estimate reduced forms – Perform out-of-sample forecasts – Compare with random walk: st = st-1 + εt


Reduced forms (Cheung et al. 2005)

• • • • •

PPP Sticky price model Balassa-Samuelson Composite model UIP


Estimation (Cheung et al. 2005)

• • • • •

USA, Canada, UK, Japan, Germany, Switzerland 1973Q2-2000Q4 Rolling regressions+out-of-sample forecasts Error-correction model First difference specification


Forecast accuracy (Cheung et al. 2005)

• Mean Squared Error (MSE) – H0: MSE/MSE0 = 1 (MSE0: MSE of random walk). Diebold-Mariano (1995) test

• Direction of change (DoC=1 if direction correctly predicted, 0 otherwise) – H0: DoC=0.5. Diebold-Mariano (1995) test

• Consistency (cointegration between ŝ and s with unitary coefficient) • Error-correction model • First difference specification


PPP significantly worse than random walk

Results (MSE)


PPP significantly better than random walk

Results (Direction of change)

PPP significantly worse than random walk

Better for yen/dollar and long horizons. 25 Bénassy-Quéré - International Macroeconomics 2012-13

Conclusion • Limitations of the empirical methodology – Reduced, linear forms – Time series (not panel data) estimations

• Still, exchange rates are difficult to forecast – But they can be explained – Robust long-run relationships yielding normative analysis – Explain exchange rates as they should be? Non-refutable theories.

• Dornbusch’s legacy – Rogoff (2007), “Dornbusch’s overshooting model after 25 years”, IMF Staff papers 49, 134. – Overshooting can arise from rational expectations (i.e. without ‘animal spirits’). – Interaction between sluggish real world and hyperactive financial markets – Extensions: endogenous GDP, debt accumulation… 26 Bénassy-Quéré - International Macroeconomics 2012-13