real rigidities and real exchange rate volatility

Journal of International Money and Finance 28 (2009) 135–147

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Journal of International Moneyand Finance

journal homepage: www.elsevier .com/locate/ j imf

Real rigidities and real exchange rate volatility

William D. Craighead*

Department of Economics, Farmer School of Business, Miami University, 208 Laws Hall, Oxford, OH 45056, USA

JEL classification:E1F4

Key words:Real exchange ratesIntersectoral adjustment costsDistribution costs

* Tel.: þ1 513 529 2849; fax: þ1 513 529 8047.E-mail address: [email protected]

0261-5606/$ – see front matter � 2008 Elsevier Ldoi:10.1016/j.jimonfin.2008.08.012

a b s t r a c t

This paper shows that certain real rigidities can help explain highvolatility of real exchange rates relative to other macroeconomicaggregates. An international real business cycle model is used todemonstrate that real exchange rate volatility increases if (i) it iscostly to move labor between sectors and (ii) the consumption oftradable goods requires distribution services. Model dynamics aregenerated by shocks to productivity and preferences based onsectoral output, employment and consumption data from G-7countries. The introduction of intersectoral adjustment anddistribution costs substantially increases the real exchange ratevolatility generated by the model.

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1. Introduction

Real exchange rates are highly volatile relative to other macroeconomic variables. Table 1 reportsthe average annual percentage standard deviation of real exchange rates relative to output for the G-7for the period 1970–2004. On average, the real effective exchange rate is 3.15 times as volatile asoutput. Economists have struggled to account for this ‘‘excess volatility.’’ In the words of Obstfeld andRogoff (2000, p. 380), ‘‘exchange rates are remarkably volatile relative to any model we have ofunderlying fundamentals such as interest rates, outputs and money supplies.’’ Chari et al. (2002, p. 533)describe the volatility and persistence of real exchange rates as ‘‘the central puzzle in internationalbusiness cycles.’’

One approach to this issue, pioneered by Dornbusch’s (1976) ‘‘overshooting’’ model, emphasizesnominal rigidities and monetary shocks. Chari et al. (2002) implement this idea in a calibrated, two-

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Table 1Standard deviations relative to output, 1970–2004a.

REER RER vs. US

Canada 2.52 2.76France 2.02 11.20Germany 1.99 7.83Italy 4.36 9.84Japan 3.57 5.22United Kingdom 3.24 4.63United States 4.36 –G-7 average 3.15 6.91

a Data: OECD main economic indicators. All data are HP-filtered.

W.D. Craighead / Journal of International Money and Finance 28 (2009) 135–147136

country dynamic general equilibrium model with sticky prices. They are able to match the volatility ofthe real exchange rate, but only by assuming a high degree of risk aversion.

This paper explores an alternative approach based on real rigidities. It demonstrates that realexchange rates become considerably more volatile when it is costly to move factors of productionbetween sectors, and when consumption of tradable goods requires nontradable distributionservices.

The international real business cycle framework developed by Backus et al. (1992) and extended byStockman and Tesar (1995) is used to examine the effect of distribution costs and intersectoral labormobility costs on the real exchange rate. Since the intuition is based entirely on relative prices and realcosts, money and nominal rigidities are ignored, but the ideas explored here may be viewed ascomplementary to theories that rely on nominal rigidities. In addition to the standard productivityshocks, preference shocks are introduced to allow consideration of the effects of changes on thedemand side of the economy in a nonmonetary framework.

Introducing intersectoral labor mobility and distribution costs causes the standard deviation of thereal exchange rate to more than double, increasing from 2.14% to 5.17%. The channels through whichreal exchange rate movements are affected by real rigidities are investigated by decomposing theminto the portions due to the relative price of tradable goods between countries and the relative price ofnontradable goods within each country. The effects of the individual shocks are examined byconsidering the impulse response functions generated by sectoral productivity and relative demandshocks.

The intuition motivating the introduction of costly intersectoral factor movements is relativelysimple. Real exchange rates are functions of relative prices. If it is costly to change quantities byreallocating inputs, relative prices will move more. To illustrate, consider a shock that increases thedemand for tradable goods. The change in demand raises the relative price of tradables. In the absenceof adjustment costs, factors of production would instantly move from the nontradable sector into thetradable sector, increasing the relative supply of tradables, and lowering the price. With adjustmentcosts, supply does not respond as much and the relative price of tradables remains elevated.

Distribution costs also amplify relative price movements in an intuitively straightforward manner.With distribution costs, when consumers purchase goods, they are also purchasing nontradableservices, like retailing. The retail price reflects both the good and service inputs. In order to achievea given change in retail relative prices, the relative prices of the goods will need to change by a largeramount.

Several strands of empirical research suggest that costs of reallocating labor between sectors maybe substantial. The cost of adjusting labor inputs is reflected in the procyclical behavior of laborproductivity known as ‘‘labor hoarding.’’ Based on surveys of employers, Fay and Medoff (1985) findthat four percent of blue-collar hours should be classified as hoarded during downturns. Fair (1985)provides econometric estimates on aggregate US data consistent with Fay and Medoff’s evidence.Burgess and Dolado (1989) and Pfann and Palm (1993) estimate models of sluggish adjustment of laborinputs on UK data. Both find statistically significant adjustment costs. On the labor supply side, Lee andWolpin (2006) estimate a dynamic model using survey data on individuals and find significant costs ofmoving between sectors.

W.D. Craighead / Journal of International Money and Finance 28 (2009) 135–147 137

Two interesting applications of intersectoral adjustment costs in the international trade literatureare Mussa (1978) and Davidson and Matusz (2004). Mussa (1978) analyzes the dynamics of theHecksher–Ohlin–Samuelson model when it is costly to reallocate capital between sectors in responseto a change in relative prices, which are taken as exogenous in his model. Davidson and Matusz (2004)examine the benefits of trade liberalization in the presence of intersectoral adjustment costs. Theyshow that a significant portion of the benefits of liberalization may be offset by the costs associatedwith worker retraining.

Several papers have examined real exchange rates in small open economy models with inter-sectoral adjustment costs. Gavin (1990) examines the dynamic response to a terms of trade shockin a model with nontradable goods and costs to reallocating capital. Capital adjustment costs playthe same role of amplifying movements the price of tradable relative to nontradable goods as laboradjustment costs in this paper. Morshed and Turnovsky (2004) show that costs to moving capitalbetween sectors generate persistent real exchange rate and current account dynamics in responseto shocks to government expenditures and technology. de Cordoba and Kehoe (2002) employintersectoral adjustment costs to help explain the movements of the real exchange rate and tradebalance that occurred as Spain lifted restrictions on capital inflows after entering the EuropeanCommunity.

Unlike those papers, the model presented here specifically addresses the standard deviation of thereal exchange rate, and does so in the context of a two-country general equilibrium system wherefluctuations in the terms of trade are generated endogenously from technology and preference shocks.

Distribution costs are the other key feature of the model presented here. Burstein et al. (2003)argue that the nontradable components of tradable goods consumption are large. They use severalsources of data to calculate the ‘‘distribution margin,’’ the difference between the retail and producerprice, as a percentage of the retail price. For US personal consumption expenditures on tradablegoods, they find a distribution margin of 43.4% using the input–output tables for 1997. For the otherG-7 countries, the margin ranges from 35% (France) to 50% (Japan). In a model calibrated to matchArgentina’s 1991 currency board, they show that accounting for distribution costs can help under-stand the movement of real exchange rates and relative prices following an exchange ratestabilization.

Corsetti et al. (2008) use distribution costs to address the negative correlation between the termsof trade and relative consumption, which is contrary to international risk-sharing. They introducedistribution costs as a mechanism for reducing the share of imports in consumption and theelasticity of substitution between domestic and imported tradables. This allows their model tomatch the negative correlation between the terms of trade and relative consumption observed inthe data.

2. Model

Stockman and Tesar (1995) show that incorporating nontradable goods and taste shocks into a two-country real business cycle model improves its ability to match certain empirical regularities such ascross-country output correlations and the correlation between trade balances and output. The modelpresented below builds on their framework by incorporating intersectoral labor adjustment costs anddistribution costs.

Two countries, ‘‘home’’ and ‘‘foreign,’’ each produce tradable and nontradable goods. Foreignvariables are denoted with an asterisk. Capital letters denote consumption bundles and price indexes,and lower-case letters represent consumption and prices of specific goods. For simplicity, the prefer-ences and technology for home are presented here; foreign is symmetric.

Each country has a representative household that maximizes expected lifetime utility fromconsumption and leisure. The utility function has the form

EXNt¼0

bt 11� g

C1�gt ð1� NtÞ1�m; (1)

Table 2Baseline parameterization.

Parameter Value Definition

b 0.96 Discount factorg 2 Intertemporal elasticity of substitution (consumption)m 4.17 Intertemporal elasticity of substitution (labor)q 0.44 Elasticity of substitution between tradables and nontradabless 1.5 Elasticity of substitution between domestic and imported tradablesu 0.55 Share of tradables in consumption bundleh 0.69 Share of domestic goods in tradable consumptionaN 0.44 Capital share (nontradable sector)aT 0.39 Capital share (tradable sector)d 0.1 Depreciation rate


where N denotes labor and the consumption bundle, C, is a constant elasticity of substitution aggregateof tradable and nontradable goods,

C ¼hð1� uÞ1=qcðq�1Þ=q

N þ u1=qCðq�1Þ=qT

iq=ðq�1Þ: (2)

Tradable goods consumption, CT, is an aggregate of home-produced and imported tradable goods

CT ¼hh1=scðs�1Þ=s

T þ ð1� hÞ1=scðs�1Þ=sT�

iðs�1Þ=s: (3)

The elasticity of substitution between tradable and nontradable goods is q; s is the elasticity ofsubstitution between domestically produced and imported tradables; u is the weight on tradables inthe consumption bundle; h is the weight on domestically produced tradables.

The representative household allocates fractions sT and sN of its labor respectively to the tradableand nontradable sectors, with sTþ sN¼ 1. Output in each sector is produced according to the function

yjt ¼ zj

t

�kj

t

�aj�

sjtNt

�1�aj�y

2

�sj

t � sjt�1

�2

sjt

; j ¼ T;N; (4)

where z is technology, k is capital and sN is the total labor employed in the sector. The second termrepresents the cost of reallocating labor between sectors, with y governing the degree of costliness.1

The cost takes the form of lost output when the share of labor allocated to the sector is changed. Notethat the cost is associated with changing the sectoral allocation rather than the overall amount of labor.

Capital is sector-specific and each sector produces its own capital. Capital is accumulated according to

kjtþ1 ¼ ijt þ ð1� dÞkj

t ; j ¼ T;N; (5)

where i is investment and d is the depreciation rate.Distribution costs are introduced by assuming tradable consumption is a combination of a goods

input produced by the tradable sector, and a service input produced by the nontradable sector.Distribution services take place in the same country as consumption. Home’s tradable sector produces

1 The functional form is chosen to be consistent with the existence of a large number of identical competitive firms in eachsector. If there are M identical firms indexed by i,

XMi¼1

y

2

�si

t � sit�1

�2

sit

¼ y

2ðst � st�1Þ2

st:

Table 3Share of tradable goods in consumptiona.

Beginning End Average

Canada, 1970–2003 0.59 0.49 0.54France, 1978–2004 0.66 0.53 0.59Germany, 1991–2004 0.61 0.53 0.56Italy, 1970–2004 0.68 0.50 0.61Japan, 1980–2003 0.56 0.43 0.50United Kingdom, 1970–2001 0.70 0.52 0.61United States, 1970–2003 0.55 0.40 0.47

a Data: OECD annual national accounts.


goods for domestic and foreign consumption and the home nontradable sector produces nontradableconsumption goods as well as the service input into home consumption of home- and foreign-produced tradables. One unit of tradable consumption is comprised of 4 units of goods and 1� 4 unitsof services. The market-clearing conditions can be rewritten as

yT ¼ 4cT þ 4c�T (6)and

yN ¼ cN þ ð1� 4ÞcT þ ð1� 4ÞcT� : (7)

A complete set of state-contingent claims is assumed to be available for international asset trade,allowing the model to be solved as a social planner’s problem.

3. Parameterization

The parameters used are reported in Table 2. The capital share parameters for the tradable andnontradable sectors and the depreciation rate are taken from Stockman and Tesar (1995). The levelsof the technology parameters, z, are normalized so that all relative prices are unitary in the steadystate.

The discount factor and the utility curvature parameters are also taken from Stockman andTesar (1995); the curvature on leisure, m, is set so that 20% of the time endowment is devoted tolabor in the steady state. The consumption bundle includes two elasticities. The elasticity ofsubstitution between tradables and nontradables is estimated by Stockman and Tesar (1995) to be0.44. Based on an examination of relevant empirical literature, Backus et al. (1994) choose a valueof 1.5 for the elasticity between domestic and imported tradables; this value is also used by Chariet al. (2002).

The weighting parameters in the consumption bundles are chosen based on OECD annual nationalaccounts data. This database includes household final consumption broken into services, durable andnondurable goods components. Table 3 reports the shares of tradable goods in consumption for the G-7; the average share is 0.55, which is used for the weighting parameter u. The share of imports intradable consumption is proxied by multiplying imports of goods by the share of GDP devoted tohousehold consumption and dividing by total household consumption of durable and nondurablegoods. The average of the import shares reported in Table 4 is 0.31; h is set to 0.69 to match this in themodel. 2

A process for the demand shocks is derived using some properties of the CES structure of theconsumption bundles. The functional form implies that total home expenditure on imported tradablegoods, xT� , is

2 The share of tradables (i.e. durable and nondurable goods) in consumption has fallen while the import share has risen.Because the model is stationary, these dynamics are not accounted for here, but the effects of these trends may meritconsideration in future research.

Table 4Share of imports in tradable goods consumptiona.

Beginning End Average

Canada, 1970–2003 0.27 0.59 0.45France, 1978–2004 0.24 0.39 0.32Germany, 1991–2004 0.38 0.55 0.43Italy, 1970–2004 0.18 0.39 0.28Japan, 1980–2003 0.22 0.19 0.15United Kingdom, 1970–2001 0.23 0.46 0.36United States, 1970–2003 0.07 0.29 0.19

a Data: OECD annual national accounts.


xT� ¼ ð1� hÞ�

pT�

PT

�1�s

XT; (8)

where XT is total expenditure on tradables. Log-linearization gives

bxT� ¼h

1� hbh þ ð1� sÞ

�bpT� � bPT

�þ bXT; (9)

where the carets denote percentage deviations. This can be rearranged to yield an equation for thedeviation in the share of domestic goods in the tradable bundle,

bh ¼ 1� h

h

hbxT� � ð1� sÞ�bpT� � bP�� bXT�

i: (10)

Similarly, expenditure on nontradable goods, xN, is related to total consumption expenditure, X, by

xN ¼ ð1� uÞ�pN

P

�1�qX: (11)

This can be log-linearized and rearranged to give

bu ¼ 1� u

u

hbxN � ð1� qÞ�bpN � bP�� bXi: (12)

Expenditure on durable and nondurable goods is used for XT. Nontradable expenditure, xN, isexpenditure on services, xT� is imports of goods, and X is household final consumption expenditure.Prices are the corresponding deflators. The data are from the OECD annual national accounts. The seriesare HP-filtered and the percentage deviations from trend are applied to the above formulas. Data areavailable to estimate preference shock processes for Canada and the US for the period 1970–2003, Italy(1970–2004)3 and France (1978–2004). The average estimated process is� butbht

¼�

0:494 0:279�0:019 0:459

" but�1bht�1

#þ 3t ; (13)

where

3twN�½0�; 1

1000

�0:069 �0:034�0:034 0:605

�: (14)

In the model, home and foreign preference shocks are assumed to be independent and to behaveaccording to this process.4

3 Several outlier observations at the beginning of the series were discarded.4 It would be preferable to jointly estimate a US and European process; however, the requisite data are not available for two

of four European G-7 economies.

Table 5Standard deviations of selected aggregates, 1970–2004a.

Canada France Germany Italy Japan UK US

Output 2.57 1.45 2.17 1.51 2.54 2.42 2.12Labor 1.91 1.23 1.43 1.44 1.11 2.19 1.69Consumption 2.79 1.66 2.36 2.04 2.32 3.18 2.09Investment 6.37 5.46 5.24 4.50 6.51 6.55 6.70Tradable output 7.43 2.81 3.24 4.13 4.19 4.36 3.92Tradable labor 3.41 1.84 3.33 2.15 1.96 3.62 3.19Tradable consumption 3.86 1.99 – 2.51 2.53 – 1.84Nontradable output 2.08 1.69 1.76 1.51 2.42 3.32 2.33Nontradable labor 1.67 1.11 1.08 1.86 1.23 2.16 1.53Nontradable consumption 2.10 1.45 – 1.14 1.81 – 1.39Terms of trade 3.41 3.75 3.74 5.37 10.01 4.03 3.82REER 6.50 2.93 4.31 6.59 9.08 7.83 9.25RER vs. US 7.09 16.24 16.99 14.59 13.02 10.63 –

a Data: OECD annual national accounts (output, consumption, investment, tradable consumption, nontradable consumption,terms of trade), OECD STAN database (labor, tradable output, tradable labor nontradable output, nontradable labor), OECD maineconomic indicators (real effective exchange rate, real exchange rate vs. US).


The technology shock process is estimated using annual data from the OECD STAN database forindustrial analysis for 1978–2003. The two countries are US and Europe, where Europe is a weightedaverage of Germany (0.31), France (0.23), Italy (0.23) and the UK (0.23). The tradable sector is proxiedby total manufacturing (ISIC 15–37) and total services (ISIC 50–99) is used to represent non-tradables.The productivity shock for each sector is

bz ¼ bY � ð1� aÞbL: (15)

Volume indexes of value added are used for output. Labor is total employment in each sector.5

Capital stock data are not available for all countries, so they are omitted.6 The technology shock processis estimated on HP-filtered data. Terms of the estimated process are averaged to give the symmetricprocess used in to generate the moments of the model:2666664

bzTtbzNtbzT�

tbzN�

t

3777775 ¼2664

0:494 0:035 �0:113 0:0990:085 0:503 �0:359 0:029�0:113 0:099 0:494 0:035�0:359 0:029 0:085 0:503

37752666664bzT

t�1bzNt�1bzT�

t�1bzN�

t�1

3777775þ 3t ; (16)

where

3twN

0BB@½0�; 11000

26640:452 0:092 0:132 0:0110:092 0:123 0:011 �0:0180:132 0:011 0:452 0:0920:011 �0:018 0:092 0:123

37751CCA: (17)

4. Results

The steady state is found numerically and the first-order conditions of the social planner’s problemare log-linearized around it. The resulting system of 28 linear difference equations7 is solved using the

5 Data on hours worked are not available for all countries.6 Backus et al. (1992) also omit capital from the calculation of technology shocks. They argue that this ‘‘is probably not

a serious problem. Experience indicates that the short run variability of the capital stock is small and orthogonal to the cycle’’(p. 759).

7 A technical appendix with the complete system is available from the author upon request.

Table 6Model standard deviations.

Data (G-7 average) 4¼ 1, y¼ 0 4¼ 1, y¼ 24 4¼ 0.572, y¼ 0 4¼ 0.572, y¼ 24

Output 2.11 3.02 3.06 2.91 2.96Consumption 2.35 2.37 2.43 2.27 2.39Labor 1.57 1.93 1.96 1.84 1.89Investment 5.90 5.54 5.56 5.18 5.25Tradable output 4.30 4.12 3.78 4.22 3.86Tradable labor 2.79 2.93 2.21 3.60 2.63Tradable consumption 2.54 3.19 3.14 2.81 2.90Nontradable output 2.16 2.59 2.63 2.74 2.82Nontradable labor 1.52 2.58 2.03 1.96 1.84Nontradable consumption 1.58 2.66 2.69 2.98 3.01Terms of trade 4.87 3.32 3.38 6.43 6.42Real exchange rate 6.64 2.14 2.71 4.65 5.17


method of King and Watson (2002). This algorithm automates the process of reducing a large, singularsystem to a solvable nonsingular system in a subset of the variables and solving it. For a givendistribution of the exogenous variables – the technology and preference shocks – the moments of theendogenous variables as well as other variables that are functions of them can be found from the state-space form of the solution.

Table 6 reports selected moments of the model. For comparison, Table 5 reports moments fromannual data from the G-7 countries, over the period 1970–2004. Model moments are reported for fourcases: (i) no labor mobility or distribution costs, (ii) labor mobility costs only, (iii) distribution costsonly and (iv) both labor mobility and distribution costs.

There is no obvious empirical counterpart to y, the parameter governing labor mobility costs. Thevalue used to generate the results in Table 6 (y¼ 24), is based on Lee and Wolpin’s (2006) estimate thatthe cost to a worker of changing sectors is $9655, in 1983 dollars (the midpoint of their sample). In1983, US per capita GDP was approximately $20,300, which implies a cost to an individual of changingsectors of 48% of a year’s income. Using the data on sectoral employment, the OECD average standarddeviation of the fraction of the labor force in the tradable sector is 1.8%. If 1.8% of the population ischanging sectors on average, this implies an overall annual loss of output of 0.855%, which is replicatedin the model when y¼ 24.8

With no distribution or labor mobility costs, the model generates a standard deviation of the realexchange rate of 2.14%, which is significantly less than the model’s output volatility of 3.02%. Intro-ducing the labor mobility cost increases the volatility of the real exchange rate by 27%, to 2.71%,without significantly changing the behavior of the other aggregates. With distribution costs only, thestandard deviation of the real exchange rate is 4.65%, and with both distribution and labor mobilitycosts, it is 5.17%, which is 1.75 times the volatility of output.

More insight into the effects of these costs can be gained by examining the behavior of thecomponent parts of the real exchange rate, which depends on several relative prices. Engel (1999)proposes the decomposition

bq ¼ bx1 þ bx2; (18)

where x1 is the relative price of tradable goods between the two countries,

bx1 ¼ be þ bP�T � bPT; (19)

and x2 is proportional to the difference between countries in the relative price of nontradables,

8 Because of the uncertainty about this parameter, a much higher value is used in a robustness check below.

Table 7Standard deviations of real exchange rate components.

4¼ 1, y¼ 0 4¼ 1, y¼ 24 4¼ 0.572, y¼ 0 4¼ 0.572, y¼ 24

x1 1.26 1.28 3.77 3.97x2 1.28 2.22 0.96 1.38


bx2 ¼ ð1� uÞh�bp�N � bP�T�� bpN � bPT

�i: (20)

Engel (1999) argues that movements in real exchange rates are primarily due to movements in x1.Burstein et al. (2005) point out that Engel’s measures fail to separate the distribution cost component oftradable goods prices. When import and export price indexes are used to remove the influence ofdistribution costs in traded goods prices, they find that roughly 50% of real exchange movements atcyclical frequencies are attributable to x2.

The results reported in Table 7 show that labor mobility costs increase real exchange ratevolatility by increasing the volatility of the cross-country difference in relative price of non-tradables (x2). The distribution costs act on the relative price of tradables between countries (x1).When both costs are present, both components contribute to real exchange rate volatility, butthe contribution of the x1 component is larger. Introducing distribution costs actually dampensmovements in x2, the component associated with the price of nontradable relative to tradablegoods. This is because distribution costs introduce a nontradable component into the tradablegoods price.

To examine the sources of real exchange rate movements in response to particular shocks, theresponses over 10 periods of the real exchange rate, x1 and x2 to each type of shock are presented inFigs. 1–4. In each figure, the upper left-side panel represents the case of no costs, the upper right-sidepanel is intersectoral adjustment costs only, the lower left-side panel is distribution costs only and thelower right-side panel is both costs.

-0.050.000.050.100.150.200.25

Case 1: No Costs Case 2: Intersectoral Adjustment

Costs Only

0.000.050.100.150.200.250.30

Case 3: Distribution Costs Only

-0.100.000.100.200.300.400.50

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

Percen

tP

ercen

t

Perce

nt

Pe

rcen

t

Case 4: Intersectoral Adjustment

and Distribution Costs

0.000.100.200.300.400.50

q x1 x2

Fig. 1. Response to 1% home tradable sector productivity increase.

-0.050.000.050.100.150.200.25

0.000.100.200.300.400.50

Percen

tP

ercen

t


Costs Only

0.000.050.100.150.200.25

Case 3: Distribution Costs Only

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

Percen

tP

ercen

t

Case 4: Intersectoral Adjustment


0.000.100.200.300.400.50

q x1 x2

Fig. 2. Response to 1% home nontradable sector productivity increase.


Fig. 1 presents responses to a one-percent home tradable sector productivity increase. In theabsence of adjustment costs, home will reallocate some labor to nontradable goods production,since tradable and nontradable goods are complements. When adjustment costs impede thereallocation of resources, the relative price movement is larger, generating a larger movement inx2, which can be seen by comparing the left-side panels to the right-side panels. Comparing upper

-0.020.000.020.040.060.080.100.120.14

0.000.020.040.060.080.100.120.14

0.16

0.000.020.040.060.080.10

-0.050.000.050.100.150.200.25

Percen

tP

ercen

t

Percen

tP

ercen

t

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year

1 2 3 4 5 6 7 8 9 10Year


Costs Only

Case 3: Distribution Costs Only Case 4: Intersectoral Adjustment


q x1 x2

Fig. 3. Response to 1% home tradables relative demand (u) shock.

-0.15-0.10-0.050.000.050.10

-0.15-0.10-0.050.000.050.10

0.15

-0.08-0.06-0.04-0.020.000.020.04

-0.08-0.06-0.04-0.020.000.020.04 0.06

0.08


Costs Only

Case 3: Distribution Costs Only Case 4: Intersectoral Adjustment


1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10

Year Year

YearYear

Percen

tP

ercen

t

Percen

tP

ercen

t

q x1 x2

Fig. 4. Response to 1% home domestic tradables relative demand (h) shock.


with lower panels shows that distribution costs amplify the change in the relative price oftradable goods between countries (x1) and this is the main source of the real exchange ratemovement.

The responses to a one-percent home nontradable sector productivity increase are shown in Fig. 2.Without distribution costs, the main source of real exchange rate dynamics is the movement in x2

because the relative price of nontradables falls in home. Introducing distribution costs leads to anincrease in x1 because the change in the relative price of home nontradables affects the distributioncomponent of the home tradables. Distribution costs nearly double the magnitude of the real exchangerate response to the shock.

Fig. 3 shows that, without distribution costs, the increase in the real exchange rate followinga one-percent increase in the weight on tradables (u) in the home consumption bundle is driven byx2. The movement in x2 due to the larger relative demand change when it is costly to reallocate laborbetween sectors. Comparing upper to lower panels shows that the effect of distribution costsdampening the movement in x2 is strong enough to reduce the overall response of the real exchangerate to the shock.

The real exchange rate movement resulting from a one-percent increase in the weight ondomestic tradables (h) in the home tradable consumption aggregate is quite small, as shown inFig. 4. The main effect of the increase in demand for the home tradable good is to increase the priceof tradables in home. The negative effect of this on x1 and the positive effect on x2 partially cancel

Table 8Model standard deviations, productivity shocks only.

4¼ 1, y¼ 0 4¼ 1, y¼ 24 4¼ 0.572, y¼ 0 4¼ 0.572, y¼ 24

Output 2.99 3.03 2.89 2.95Consumption 2.36 2.42 2.25 2.38Labor 1.92 1.95 1.83 1.88Real exchange rate 2.07 2.59 4.59 5.13x1 0.98 0.91 3.69 3.92x2 0.95 1.76 0.93 1.25

Table 9Model standard deviations, s¼ 3.

4¼ 1, y¼ 0 4¼ 1, y¼ 24 4¼ 0.572, y¼ 0 4¼ 0.572, y¼ 24

Output 2.95 3.02 2.77 2.90Consumption 2.30 2.39 2.00 2.24Labor 1.89 1.94 1.73 1.83Real exchange rate 1.57 2.42 3.44 4.53x1 0.71 0.71 2.68 3.23x2 1.18 2.20 0.83 1.39


each other out. Note that the presence of distribution costs does lead to a bigger movement in bothcomponents.

5. Robustness

Dynamics in real business cycle models are traditionally generated with productivity shocks. Table 8reports some of the standard deviations of the model without the preference shocks. Since the tech-nology shocks generate most of the model dynamics, the results are similar when the preferenceshocks are excluded.

There is little consensus in the literature regarding the elasticity of substitution between domesticand imported tradables (s). A value of 1.5 was used above, following earlier literature. However, asdiscussed in Anderson and van Wincoop (2004), estimates at a less aggregated level generally finda higher elasticity. To test the effect of increasing the elasticity, the model properties are reexaminedwith s¼ 3. The results reported in Table 9 show that increasing the elasticity reduces real exchange ratevolatility, but does not alter the basic result regarding the effects of intersectoral labor mobility costsand distribution costs.

As discussed above, it is unclear how costly it is to reallocate labor between sectors. Table 10 reportsmodel moments with a much higher degree of intersectoral adjustment costs (y¼ 1000). This changeresults in a significant increase in real exchange rate volatility.

6. Conclusion

The volatility of real exchange rates has acquired the status of a ‘‘puzzle’’ in macroeconomics. Thispaper demonstrates that a two-country general equilibrium model generates substantially more realexchange rate volatility when two plausible types of rigidity – intersectoral adjustment costs anddistribution costs – are included. The examination of impulse responses for productivity and prefer-ence shocks illustrates that the mechanism depends on the type of shock. It is beyond the scope of thisresearch to take a position on the true nature of the shock process driving the economy. Certainly,a natural extension would be to incorporate intersectoral adjustment and distribution costs intoa framework which includes monetary shocks. The significant increase in real exchange rate volatilitywhen the costs are included suggests that real exchange rate volatility may be less puzzling thanpreviously thought.

Table 10Model standard deviations, y¼ 1000.

4¼ 1 4¼ 0.572

Output 3.09 3.05Consumption 2.54 2.64Labor 2.00 1.98Real exchange rate 3.48 6.22x1 1.21 4.40x2 3.10 1.97


Acknowledgements

This paper is based on a chapter of my Ph.D. dissertation at the University of Virginia. It benefitedfrom numerous suggestions by my advisors, Christopher Otrok and Eric van Wincoop. I am also gratefulto Marco Cagetti, George Davis, Ben Keen, Norm Miller, Gregor Smith, Frank Warnock and an anony-mous referee as well as seminar participants at Miami University, Ohio Wesleyan University, Sewanee,the U.S. Treasury Department, the University of Virginia, Western Washington University and theSouthern Economic Association for their comments. Any errors are my own, of course. Financialsupport from the Bankard Fund for Political Economy at the University of Virginia is gratefullyacknowledged.

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real rigidities and real exchange rate volatility

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