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Exchange rate policy and the role of non-traded goods prices in real exchange rate fluctuations

  • Nestor Azcona EMAIL logo
Published/Copyright: July 18, 2017
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 17 Issue 2

Abstract

This paper uses a DSGE model of two small open economies to explain certain features of real exchange rate cyclical fluctuations in countries with fixed and flexible exchange rates, focusing on the role of traded and non-traded goods prices. In particular, the model illustrates why the relative price of non-traded goods and the relative price between domestic and foreign traded goods are more volatile than the real exchange rate under a fixed exchange rate but not under a flexible exchange rate, why deviations from purchasing power parity for traded goods prices can be more volatile under a fixed exchange rate than under a flexible exchange rate, and why there is no correlation between the volatility of the real exchange rate and its variance decomposition.

Keywords: fixed exchange rate; non-traded goods; purchasing power parity; real exchange rate; variance decomposition
JEL Classification: F31; F41; F45

Appendix

This Appendix briefly describes the main equations in the log-linearized model. Lower-case variables represent percentage deviations of the variables from their steady-state values. The symbol ∼ indicates that the nominal variable has been divided by the consumer price index to become stationary. For example, w~H,t denotes the percentage deviation of WH,t/Pt from its steady-state value. An asterisk indicates the corresponding variable in the Foreign small open economy. W indicates that the variable is related to the rest of the world (ROW).

The demand for non-traded inputs depends on the price of non-traded goods and domestic spending:

(17)yN,t=−ζp~N,t+CYct+IYit+GYgt

where aggregate investment is a weighted average of investment spending in each sector.

(18)it=YNYiN,t+YHYiH,t

The demand for Home traded inputs depends on domestic demand and export demand:

(19)yH,t|T=−ζp~T,t−ζT(p~H,t−p~T,t)+CYct+IYit+GYgt
(20)yH,t|EX=−ζT(−rerW,tT+p~H,t−p~T,t)−ζ(pT,tW−ptW)+ζyytW
(21)yH,t=κyH,t|T+(1−κ)yH,t|EX

The demand for imports is given by:

(22)imt=−ζp~T,t−ζT(p~IM,t−p~T,t)+CYct+IYit+GYgt

Domestic output consists of traded and non-traded inputs, which are produced according to Cobb-Douglass production functions:

(23)yt=γyN,t+(1−γ)yH,t
(24)yN,t=aN,t+αkN,t−1+(1−α)nN,t
(25)yH,t=aH,t+αkH,t−1+(1−α)nH,t

The hybrid New Keynesian Phillips curves in each sector are:

(26)πN,t=11+βπN,t−1+(1−βθ)(1−θ)θ(1+β)(mc~N,t−p~N,t)+β1+βEtπN,t+1
(27)πH,t=11+βπH,t−1+(1−βθ)(1−θ)θ(1+β)(mc~H,t−p~H,t)+β1+βEtπH,t+1
(28)πIM,t=11+βπIM,t−1+(1−βθIM)(1−θIM)θIM(1+β)(rerW,tT+p~T,t−p~IM,t)+β1+βEtπIM,t+1

where the marginal cost and the rental cost of capital in each sector are determined by:

(29)mc~N,t=αq~N,t+(1−α)w~N,t−aN,t
(30)mc~H,t=αq~H,t+(1−α)w~H,t−aH,t
(31)q~N,t=p~N,t+aN,t+(α−1)(kN,t−1−nN,t)
(32)q~H,t=p~H,t+aH,t+(α−1)(kH,t−1−nH,t)

The equations describing the evolution of the capital stocks and the investment decision rules are:

(33)δiH,t=kH,t−(1−δ)kH,t−1
(34)δiN,t=kN,t−(1−δ)kN,t−1
(35)rt−Etπt+1+ϕ(kH,t−kH,t−1)=ϕβ(EtkH,t+1−kH,t)+(1+β(δ−1))Etq~H,t+1
(36)rt−Etπt+1+ϕ(kN,t−kN,t−1)=ϕβ(EtkN,t+1−kN,t)+(1+β(δ−1))Etq~N,t+1

The inflation rates for domestic spending and for traded goods prices are:

(37)πt=γπN,t+(1−γ)πT,t
(38)πT,t=κπH,t+(1−κ)πIM,t

The Euler equation, money demand, and labor supplies are:

(39)λt=Etλt+1+rt−Etπt+1
(40)m~t=−Π+Rϖrt−1ϖλt
(41)ωnH,t=−λt+w~H,t
(42)ωnN,t=−λt+w~N,t
(43)λt=−(ct−ηct−1)(σ/(1−η))

where λt is the marginal utility of consumption.

The central bank’s monetary policy rule (under a flexible exchange rate) is:

(44)rt=λrrt−1+(1−λr)(λπEtπt+1+λyyt)

Under a fixed exchange rate, the bilateral nominal exchange rate is constant:

(45)Δst=0

The real interest rate parity equation (relative to ROW) is:

(46)EtrerW,t+1−rerW,t=rt−Etπt+1−(rW,t−EtπW,t+1)

The interest paid or received on ROW bonds is determined by the world interest rate and the country-specific risk premia/discounts:

(47)rW,t=rtW−ψbyt+zt

Assuming that net foreign assets in the steady state are zero, the evolution of the net foreign assets to income ratio can be approximated by the difference between exports and imports:

(48)byt=byt−1+EXY(p~H,t+yH,t|EX)−IMY(p~IM,t+yIM,t)

Combining (46) with the corresponding real interest parity condition in the Foreign economy we obtain the bilateral real exchange rate between the Home and Foreign economies:

(49)rert=rerW,t−rerW,t∗

The bilateral nominal depreciation can be obtained from the definition of the real exchange rate:

(50)Δst=Δrert+πt−πt∗

The two components of the bilateral real exchange rate are:

(51)rertN=p~T,t−(pT,tW−ptW)
(52)rertT=rert−rertN

The exogenous variables (aH,t, aN,t, gt, zt, aF,t∗, aN,t∗, gt∗,zt∗, ytW, ptW, pT,tW, rtW) evolve following AR(1) processes. For example, traded sector productivity evolves according to:

(53)aH,t=ρHaH,t−1+εtH

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Published Online: 2017-7-18

©2017 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/bejm-2015-0185
Keywords for this article
fixed exchange rate; non-traded goods; purchasing power parity; real exchange rate; variance decomposition

Articles in the same Issue

  1. Advances
  2. Does microfinance reduce poverty? Some international evidence
  3. Exchange rate policy and the role of non-traded goods prices in real exchange rate fluctuations
  4. Democracy and income: taking parameter heterogeneity and cross-country dependency into account
  5. Pass-through of imported input prices to domestic producer prices: evidence from sector-level data
  6. Economic policy uncertainty and household inflation uncertainty
  7. Corruption, fiscal policy, and growth: a unified approach
  8. Monetary policy and energy price shocks
  9. Government education expenditures and economic growth: a meta-analysis
  10. Has the forecasting performance of the Federal Reserve’s Greenbooks changed over time?
  11. Life-cycle consumption, precautionary saving, and risk sharing: an integrated analysis using household panel data
  12. Can removing the tax cap save Social Security?
  13. A non-monotonic relationship between public debt and economic growth: the effect of financial monopsony
  14. The Euler equation around the world
  15. Structural change and non-constant biased technical change
  16. Contributions
  17. Trade and growth in a model of allocative inefficiency
  18. Macroeconomic Shocks and Corporate R&D
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