real exchange rate fluctuations, endogenous tradability and exchange rate regimes

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doi:10.1016/j.jm

$This paper

Kumhof, Mark

John Carlson,

seminar partici

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Journal of Monetary Economics 55 (2008) 645–663

www.elsevier.com/locate/jme

Real exchange rate fluctuations, endogenous tradability andexchange rate regimes$

Kanda Naknoi�

Krannert Graduate School of Management, Purdue University, West Lafayette, IN 47907, USA

Received 13 July 2006; received in revised form 7 January 2008; accepted 10 January 2008

Available online 20 January 2008

Abstract

The real exchange rate is driven by fluctuations of the relative price of traded goods and the relative price of nontraded

to traded goods. This study explains the variance decomposition of the real exchange rate using a stochastic dynamic

general equilibrium model of comparative advantage with money. Given interest rate shocks, exchange rate stability

reduces the covariance between the two relative prices and raises the contribution of the relative price of nontraded to

traded goods. Productivity shocks do not alter the covariance across exchange rate regimes and let the relative price of

traded goods drive the real exchange rate.

r 2008 Elsevier B.V. All rights reserved.

JEL classification: F41; F42

Keywords: Real exchange rate; Exchange rate regimes; Comparative advantage; Trade costs

1. Introduction

The seminal work on real exchange rate (RER) variance decomposition by Engel (1999) found that theRER of high-income countries is driven by the relative price of traded goods (traded RER). However,Mendoza (2000) found that the contribution of international differences in the price of nontraded relative totraded goods (nontraded RER) to the Mexico–U.S. RER variance is higher in the period of fixed exchangerates than that of flexible exchange rates. Recently, Burstein et al. (2005) found that the nontraded RER drivesthe RER after devaluations. The literature has proposed the following explanations: price stickiness andinvoice currency, pricing to market, trade costs, and endogenous tradability. This paper presents analternative theory with an emphasis on endogenous tradability and exchange rate regimes.

e front matter r 2008 Elsevier B.V. All rights reserved.

oneco.2008.01.004

is based on the first two chapters of my Ph.D. dissertation at Stanford University. I thank Masahiro Kawai, Michael

Wright and Gavin Wright for advice and support. I am indebted to comments from Philippe Bacchetta, Gabriele Camera,

Mario Crucini, Charles Engel, David Hummels, Douglas Laxton, Enrique Mendoza, Slavi Slavov, Asaf Zussman and

pants at Stanford, Purdue, UIUC, New York Fed, IMF, 2004 NBER Summer Institute (IFM) and 2005 SED Annual

5 494 3693; fax: +1 765 494 9658.

ess: [email protected]

www.elsevier.com/locate/jme

dx.doi.org/10.1016/j.jmoneco.2008.01.004

mailto:[email protected]

ARTICLE IN PRESSK. Naknoi / Journal of Monetary Economics 55 (2008) 645–663646

In this study, Mendoza’s (2000) and Burstein et al.’s (2005) findings are confirmed in the data of Europeanand emerging economies. Although the contribution of the nontraded RER is high after some currency crises,it is lower than what it was before devaluations by 31% on average. A similar pattern is also found in a cross-section of 595 RERs. Specifically, the country pairs for which the RER is significantly influenced by thenontraded RER have stable exchange rates. My main contribution is a stochastic dynamic general equilibrium(SDGE) monetary model explaining these stylized facts. The model features heterogeneous productivity, tradecosts, export entry costs and sticky wages. Aggregate consumption is a basket of traded and nontraded goodsproduced by labor. Under perfect competition, heterogeneous productivity and trade costs determine thecomposition of traded and nontraded goods, as in Dornbusch et al. (1977). The short-run fluctuations inwages cause the producers at the margin to switch in and out of exporting. The export entry cost is introducedto keep the rate of switching in line with the estimate in Hummels and Klenow (2005).

The gist of the model is that the switching producers arise from a positive correlation between wages andproductivity in both export and nontraded sectors, because rising wages cause high-cost exporters to quitexporting and join the nontraded sector. In addition, productivity is more volatile in the nontraded sector thanin the export sector. The quitting exporters are less productive and smaller than other exporters, but are moreproductive and larger than the incumbent nontraded industries, as found in the empirics. Hence, the quittingexporters create larger disturbances to productivity in the nontraded sector than in the export sector.1

Since the sectoral prices depend on the competing effects of wages and productivity, the correlation betweenthe traded and nontraded RERs depends on the ranking of volatility of the relative wage and productivity inthe export and nontraded sectors. Under the flexible exchange rate regime, the exchange rate fluctuates inresponse to interest rate shocks and creates more volatility in the relative wage than productivity in bothsectors. Thus, the exchange rate dictates both traded and nontraded RERs and makes them positivelycorrelated, as found by Mendoza (2000) and Burstein et al. (2005). In contrast, under the fixed exchange rateregime the same shocks make the relative wage less volatile than the nontraded-sector productivity but morevolatile than the export-sector productivity. Consequently, the relative wage drives the traded RER butproductivity drives the nontraded RER in the opposite direction. The negative correlation between the tradedand nontraded RER under the fixed regime is supported by Mendoza (2000).

By weakening the correlation, exchange rate stability raises the contribution of the nontraded RER by 31%,as found in the data and Mendoza (2000). Moreover, the cross-regime difference in the RER variance isconsistent with Mussa (1986) and Baxter and Stockman (1989) and partially explained by the correlation. Tobe precise, the negative correlation contributes to the low RER variance under the fixed regime, and thepositive correlation contributes to the high RER variance under the flexible regime.

However, TFP shocks do not create significant differences in the covariance of the traded and nontradedRERs across regimes, and the contribution of the traded RER exceeds 50%. This is because favorable TFPshocks encourage high-cost producers to start exporting, so they mitigate productivity fluctuations and theircross-sector asymmetry, which makes the nontraded and traded RERs uncorrelated. At the same time, TFPshocks sharply change the terms of trade and raise the importance of the traded RER. Thus, TFP shocks andendogenous tradability can explain the finding in Engel (1999).

Finally, this study shows that in the absence of endogenous tradability, the traded and nontraded RERs aresolely driven by the relative wage and have perfect correlation, which contradicts the empirical literature.Thus, endogenous tradability is an essential assumption. Demonstrating the impacts of endogenoustradability on the correlation is a major strength of this study, building on the related work by Betts andKehoe (2001b), Bergin and Glick (2003) and Ghironi and Melitz (2005). This study reconciles both strands ofempirical literature, while the existing work explains only the pattern in Engel (1999).

The model is motivated by the evidence for transitions in and out of exporting by Aitken et al. (1997),Bernard and Jensen (2004), Besedes and Prusa (2006) and Das et al. (2001). The sticky wage assumption issupported by the findings in Liu and Phaneuf (2007), Castellanos et al. (2004), Kahn (1997) and Huang andLiu (2002). Besides endogenous tradability, exchange rate stability reduces volatility of the traded RER whenexporters practice local currency pricing, as documented by Goldberg and Knetter (1997) and Campa andGoldberg (2005). This study presents an alternative to local currency pricing models, such as in Devereux and

1I thank an anonymous referee for this insight.

ARTICLE IN PRESSK. Naknoi / Journal of Monetary Economics 55 (2008) 645–663 647

Engel (2002), to explain departures from purchasing power parity. Moreover, it takes the additional step ofcapturing a new richness in the dynamics of the nontraded RER, and has implications for macroeconomics.

This study lends support to the notion that nominal shocks and nominal rigidities, particularly wagerigidity, are important. Specifically, expansionary nominal shocks expand the consumption demand with abias toward the traded goods under the flexible regime, but toward the nontraded goods under the fixedregime. Hence, the assumption that the nontraded RER drives the RER, such as in Calvo (1986), is useful forstudying the effects of nominal shocks. However, to study the effects of real shocks, deviations from the law ofone price for the traded goods are necessary. This is because expansionary productivity shocks always expandthe consumption demand with a bias toward the traded goods. The finding that endogenous tradabilityweakens the correlation between the traded and nontraded RERs could be useful for solving some puzzles,such as why relative consumption of two countries is not correlated with the RER at business cyclefrequencies.

The next section presents the stylized facts. The model is developed in Section 3. Section 4 discusses thequantitative results, and Section 5 concludes the study.

2. Stylized facts and related literature

RER is defined as the relative price level of two economies, RERt ¼ StP%

t =Pt, where St is the nominalexchange rate and Pt is the consumer price index (CPI). The superscript % denotes the foreign variables. LetPt;T be the traded-goods price index. Define the traded RER as the relative price of the traded-goods baskets,RERt;T ¼ StP

%

t;T=Pt;T . The nontraded RER is the residual RERt;N ¼ RERt=RERt;T , as in Engel (1999) andBetts and Kehoe (2001a,b, 2006). The log of RERs are filtered with the Baxter and King (1999) filterwith 12 leads and lags, passing the cyclical components lasting from 6 to 32 quarters. Let the detrendedseries be denoted by lowercase characters. The RER variance can be decomposed into varðrertÞ ¼

varðrert;T Þ þ varðrert;N Þ þ 2 covðrert;T ; rert;NÞ, where var and cov denote the variance and the covariance,respectively. Define the contribution of the nontraded RER as vN ,

vN ¼varðrert;NÞ þ covðrert;T ; rert;N Þ

varðrertÞ. (1)

vN may take negative values, since the covariance is negative by construction.First, the variance decomposition around the following nine currency crises is studied: Finland, Sweden and

the U.K. in 1992; Mexico in 1994; Korea, Indonesia, Philippines and Thailand in 1997; and Brazil in 1999. TheRERs of Finland, Sweden and the U.K. are defined against Germany, and the rest are defined against the U.S.

The quarterly RERs are constructed from various databases. The exchange rate series are from the WorldCurrency Report provided by Reinhart and Rogoff (2004) and the International Financial Statistics (IFS).The Report tracks the market rates while the IFS records the official rates. However, the IFS covers a longerperiod. This study uses two measures of traded-goods prices: the producer price index (PPI) and a geometricaverage of the import and export unit values (UV). Both are from the IFS and have different strengths. ThePPI is available in a large sample, but partly influenced by the prices of local inputs, creating a downward biasin the contribution of the nontraded RER. The UV series proxy the prices of actually traded goods but thereare no data on the expenditure shares on imports and exports. The shares are assumed to be 0.5. These seriesproduce four data sets. Data set 1 uses the market rates and the PPI. Data set 2 uses the market rates and theUV. Data set 3 uses the official rates and the PPI. Data set 4 uses the official rates and the UV. The number ofcrises in each data set is 3, 3, 9 and 6, respectively.

The RER variance over the course of 12 quarters before and after devaluations are decomposed. Fig. 1 plotsthe contributions of the nontraded RER after devaluations against those before devaluations. Countries areidentified by the letter corresponding to the first initial of the country name. The data set is identified by thenumber succeeding each letter. In Fig. 1, almost all observations lie below the 45� line, indicating that thecontribution of the nontraded RER falls after devaluations. The contribution rises following only twoinstances: the crises of Philippines and Thailand in 1997. On average, the contribution before and afterdevaluations is 50% and 19%, respectively. The 31% difference is in the 30–70% range in Mendoza (2000),

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−1 −0.5 0 0.5 1 1.5−1

−0.5

0

0.5

1

1.5

Before devaluations

Afte

r dev

alua

tions

Fig. 1. The contribution of nontraded RER before and after devaluations. (The letter corresponds to the first initial of the country name.

The number succeeding each letter indicates the data set.)

K. Naknoi / Journal of Monetary Economics 55 (2008) 645–663648

which uses disaggregated price series to study the Mexico–U.S. RER. The Mexico–U.S. RER in mymacrodata is marginally influenced by devaluations.

As in Burstein et al. (2005), the UV in Data sets 2 and 4 results in a higher contribution of the nontradedRER than the PPI in Data sets 1 and 3. Burstein et al. (2005) argue that the UV index is a better measure oftraded-goods prices than the domestic price index, and use a similar UV index to show that the nontradedRER dominates the traded RER after devaluations. This is the case for four out of six observations in Dataset 4. However, they do not compare the periods before and after devaluations.

Second, all data sets are expanded to a broad cross-section of countries. Data sets 1 and 3 are extended to 35countries and 595 RERs, and Data sets 2 and 4 to 22 countries and 231 RERs.2 Data sets 1 and 2 cover fromthe first quarter of 1980 to the end of 1998. Data sets 3 and 4 cover from the first quarter of 1980 to the secondquarter of 2005. The standard deviation of quarterly depreciation is used as a measure of exchange ratevolatility. Fig. 2 plots the contribution of the nontraded RER against the volatility of market exchange rates.Panels A and B use the PPI and the UV, respectively. The contribution of the nontraded RER is higher whencalculated with the UV index than with the PPI, as in Fig. 1. Also, the observations with high exchange ratevolatility have a small contribution from the nontraded RER. The observations with low exchange ratevolatility are more heterogeneous, and some have a large contribution from the nontraded RER. For somecountries, the RER is clearly driven by the nontraded RER. Exchange rate volatility of the observations withlarge nontraded-RER contributions is lower than 10% in both panels. These patterns remain even when theofficial exchange rates are used.

Fig. 2 alone does not relate the exchange rate regime to the variance decomposition, since the exchange ratemay be stable when it is floated. However, Fig. 1 suggests the importance of exchange rate regimes and raises aquestion: what mechanism could cause exchange rate flexibility to suppress the role of the nontraded RER?Devereux and Engel (2002) propose that local currency pricing reduces the degree of exchange rate pass-through to import prices and allows exchange rate movements to raise the volatility of the traded RER.

Recently, some trade economists have found that firms do enter and exit the traded sector. Aitken et al.(1997) found that 10% of Mexican manufacturers change their export status in 3 years. In Das et al. (2001),the annual rate of entry into exporting in Columbia is 9%, and the exit rate is 7%. For the U.S., Bernard andJensen (2004) estimated that the entry and exit rates are 14% and 13%, respectively. Within 3 years, 18% of

2The list of sample countries is available upon request.

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0 0.1 0.2 0.3 0.4 0.5−1.5

−1

−0.5

0

0.5

1

Standard deviation of quarterly depreciation

Con

tribu

tion

of n

on−t

rade

d R

ER

0 0.1 0.2 0.3 0.4 0.5−1

−0.5

0

0.5

1

1.5

2

2.5

3

Standard deviation of quarterly depreciation

Con

tribu

tion

of n

on−t

rade

d R

ER

Fig. 2. Contribution of nontraded RER and volatility of market exchange rates. (A) Producer price index, and (B) geometric mean of

import and export unit values.

K. Naknoi / Journal of Monetary Economics 55 (2008) 645–663 649

nonexporters begin to export and 20% of exporters stop. Besedes and Prusa (2006) also found evidence at theindustry level. They found that the median duration that a country exports a product to the U.S. ranges from2 to 4 years.

The evidence suggests that the dynamics of the exporting decision are relevant to the dynamics of aggregateprices and RER. This idea is not new and dates back to Baldwin (1988), who showed in a partial equilibriummodel that sunk costs produce persistent RERs and hysteresis in the exporting behavior. Betts and Kehoe(2001b) assumed a multi-sector model with heterogeneous trade costs. However, the trade pattern in theirmodel is exogenous. Bergin and Glick (2003) assumed heterogeneous trade costs in a small-open-economymodel. Ghironi and Melitz (2005) assumed sunk costs, monopolistic competition and heterogeneousproductivity as in Baldwin (1988) and Melitz (2003). In these studies, the transitions in and out of exporting inresponse to TFP shocks act as another adjustment channel and dampen the price fluctuations. However, thesestudies overlook the role of exchange rate regimes.

3. The model

This section develops a SDGE model of endogenous tradability with money. The model adopts the theoryof comparative advantage by Dornbusch et al. (1977). It is simpler than the monopolistic competition modelby Ghironi and Melitz (2005), since it uses a Ricardian rather than a probabilistic approach and retains theimportance of productivity for the exporting decision. The other innovation is the introduction of sticky wagesto model exchange rate.

The evidence for sticky wages is documented in the following studies. Liu and Phaneuf (2007) estimated theresponse of U.S. wage inflation to productivity shocks and found that wage inflation responds modestly to


productivity shocks. Kahn (1997) studied the distribution of annual wage and salary changes in the U.S., andfound evidence for wage rigidity due to the cost of changing wages. The evidence in Mexico was documentedby Castellanos et al. (2004). In addition, in the SDGE model by Huang and Liu (2002) sticky wages generatemore persistent price dynamics, as observed in the data, than sticky prices.

There are two countries: home and foreign. There is a continuum of goods indexed by z 2 ½0; 1�. Althoughdifferences in the basket of consumption can influence the RER, the model assumes that all householdsconsume all goods to focus on the composition of trade.

3.1. Firms and the specialization pattern

A large number of homogeneous firms take price as given in each industry z. Let X t be the TFP, and atðzÞ bethe industry-specific productivity. The subscript t denotes the period. Goods prices are fully flexible, hence theinvoice currency is irrelevant. Let the producer price, p

pt ðzÞ, be in the seller’s currency. The representative firm

in each industry produces the output ytðzÞ from the labor input ltðzÞ with the linear technology

ytðzÞ ¼ X tatðzÞltðzÞ. (2)

Let W t be the unit labor cost. The cost minimization gives the marginal-cost pricing

ppt ðzÞ ¼W t=ðX tatðzÞÞ. (3)

Similar equations hold for the foreign firms.There is a cost of beginning to exporting, denoted by Ft;aðzÞ. It represents additional costs such as

distribution costs, and prevents the number of new exporters from exceeding the estimate in Hummels andKlenow (2005). It is an iceberg cost, which reduces productivity and drives up price, atðzÞ ¼ ð1� Ft;aðzÞÞaðzÞ,where the superscript ‘‘�’’ denotes the steady state. The cost is time-variant and increasing in deviations of thelong-run relative productivity of the previously least-competitive industry from that of the current one. Definethe industry-specific relative productivity as AtðzÞ ¼ atðzÞ=a%

t ðzÞ, the set of new home export industries as Znt ,

and the set of disappearing home export industries as Zdt . zl

t and zht denote the endogenously determined least-

competitive industry in the home and foreign country, respectively. fa is a parameter where fa40. The entrycost for the home producers is given by the following:

Ft;aðzÞ ¼fa½Aðz

lt�1Þ=Aðzl

tÞ � 1� for z 2 Znt [ Z

dt ;

0 otherwise:

(A similar cost function applies to the foreign producers.

International trade is subject to the iceberg trade costs melting a fraction t of goods. Define the relativewage as ot ¼W t=StW

%

t , and the relative TFP as wt ¼ X t=X%

t . Dornbusch et al. (1977) showed that ifqAt=qzo0 and 0oto1, then there is a unique solution for zl

t and zht , which characterize the specialization

pattern such that 0ozltozh

to1 and

AtðzltÞwtð1� tÞ ¼ ot ¼ Atðz

ht Þwt=ð1� tÞ. (4)

In equilibrium, the home country produces the goods z 2 ½0; zht � and exports the goods z 2 ½0; zl

t�. The foreigncountry produces the goods z 2 ½zl

t; 1� and exports the goods z 2 ½zht ; 1�. Both produce the nontraded goods

z 2 ðzlt; z

ht Þ for domestic consumption.

In the steady state, Ft;a ¼ 0 for all z. When new home exporters emerge, zlt4zl

t�1, Zdt ¼ ;, and Ft;a40 for

z 2 Znt . When some home exporters quit, zl

tozlt�1, Z

nt ¼ ; and Ft;ao0 for z 2 Zd

t . There are exit benefits, whichcapture the recoverable value of overseas sale operation in the industrial organization literature (Ericson andPakes, 1995). Hence, the entry cost raises the slope of the relative productivity schedule, and productivity ofthe exporters relative to nonexporters at the margin. The cost reduces the range of switching industries, bypushing those on the verge of export entry back into the nontraded sector and throwing those about to quitback into exporting. Since the cost is not a fixed cost but is proportional to the relative productivity at themargin, it does not remove switching even with small shocks. It creates discontinuity in the relativeproductivity schedule, but retains the monotonicity along each segment and the solution for zl

t and zht is

unique.


From the home residents’ perspective, it is possible to classify sectors into the import, export and nontradedsectors, and denote them by i 2 ðF ;H ;NÞ, respectively. Define Zt;F ¼ ½z

ht ; 1�, Zt;H ¼ ½0; zl

t�, and Zt;N ¼ ðzlt; z

ht Þ.

The consumer prices in each location are

ptðzÞ ¼StW

�t =ðX

�t a�t ðzÞð1� tÞÞ for z 2 Zt;F ;

W t=ðX tatðzÞÞ for z 2 Zt;H [ Zt;N ;

(

p�t ðzÞ ¼W �

t =ðX�t a�t ðzÞÞ for z 2 Zt;F [ Zt;N ;

W t=ðStX tatðzÞð1� tÞÞ for z 2 Zt;H :

(If t ¼ 0, then Zt;N ¼ ; and ptðzÞ ¼ StptðzÞ

%. Clearly, trade costs are crucial because they create both thenontraded sector and deviations from the law of one price.

3.2. Price indices and RERs

A large number of wholesalers in each sector i 2 ðF ;H;NÞ bundle goods into the constant-elasticity-of-substitution (CES) composites

Ct;i ¼1

dt;i

� �1=y ZZt;i

ctðzÞðy�1Þ=y dz

" #y=ðy�1Þ,

where dt;i ¼ supðZt;iÞ � infðZt;iÞ. ctðzÞ is the demand for the good z and y (y41) is the intratemporal elasticityof substitution. The CES aggregation is often used in the models of monopolistic competition withdifferentiated products, but the aggregation here takes place across industries. The cost minimization gives theunit cost

Pt;i ¼1

dt;i

ZZt;i

ptðzÞ1�y dz

" #1=ð1�yÞ.

A large number of retailers combine the three baskets into final consumption in two steps. First, they bundlethe export and import baskets into the CES traded basket

Ct;T ¼dt;H

dt;H þ dt;F

� �1=y

Cðy�1Þ=yt;H þ

dt;F

dt;H þ dt;F

� �1=y

Cðy�1Þ=yt;F

" #y=ðy�1Þ.

This assumption is motivated by the evidence that the elasticity of substitution is greater than one (Hummels,2001; Anderson and van Wincoop, 2004). The cost minimization gives the traded-goods price index

Pt;T ¼dt;H

dt;H þ dt;FP1�y

t;H þdt;F

dt;H þ dt;FP1�y

t;F

� �1=ð1�yÞ.

Next, the retailers bundle the traded and nontraded baskets into the Cobb–Douglas final consumption Ct ¼

CsTt;T C

sNt;Nðs

sNN s

sTT Þ�1; where sj, j 2 ðN;TÞ, is the exogenous expenditure share and sN ¼ 1� sT . Fixed shares are

assumed because Stockman and Tesar (1995) found evidence for stable shares at high frequencies. The CPI isthe geometric average of the traded- and nontraded-goods price indices, Pt ¼ P

sTt;T P

sNt;N . Then, the RER is the

product of the following traded and nontraded RERs:

RERt;T ¼StP

%

t;T

Pt;T¼

st;H

sT

1

1� t

� �1�y

þst;F

sT

ð1� tÞ1�y" #1=ð1�yÞ

, (5)

RERt;N ¼P%

t;N

P%

t;T

!sNPt;T

Pt;N

� �sN

. (6)


st;i; i 2 ðF ;HÞ is the expenditure share

st;i ¼dt;i

dt;i þ dt;�i

Pt;i

Pt;T

� �1�y

sT .

The traded RER is the relative price of the traded-goods baskets. It depends on the expenditure shares onexports and imports. Trade costs affect fluctuations in the traded RER when ya1. The nontraded RERdepends on international differences in the price of nontraded relative to traded goods.

3.3. Variance decomposition of RER

Define the sectoral productivity such that the sectoral output is monotonically increasing in the product ofthe productivity, TFP and labor input3:

At;i ¼1

dt;i

ZZt;i

atðzÞy�1 dz

" #1=ðy�1Þ; i ¼ H;N.

Since only relative industry productivities matter for the central results, for simplicity, assume that a%

t ðzÞ ¼ 1.Define the terms of trade as Ot ¼ Pt;H=Pt;F .

Let x denote the percentage deviation of xt from its steady state. Define the long-run home bias within thetraded sector as h ¼ sH=sF . Substituting the equilibrium prices into the terms of trade, (5) and (6), and log-linearizing them around the steady state gives

dRERt;T ¼ �xbOt þx

y� 1bZt, (7)

dRERt;N ¼ sNð bAt;N � bAt;H Þ � sN ð1� xÞbOt þx

y� 1bZt

� �, (8)

where x ¼ h½ð1� tÞ1�y � ð1� tÞy�1�=fð1þ hÞ½ð1� tÞ1�y þ hð1� tÞy�1�g40, which is the elasticity of the tradedRER appreciation with respect to the terms of trade. When xo1, the terms of trade improvement appreciatesthe traded and nontraded RERs, all else equal. Zt is the range of home exports defined relative to the foreigneconomy, zl

t=ð1� zht Þ.

The gist here is that rising relative wage contracts the range of exports, and the contraction has differenteffects on the traded and nontraded RERs. In particular, the contraction appreciates the traded RER andamplifies the effect of relative wage in (7). But it depreciates the nontraded RER and offsets the effect ofrelative wage in (8). Hence, endogenous tradability influences the correlation between the two RERs, denotedby corrTN . Let varT and varN denote the variance of the traded and nontraded RERs, respectively. Eqs. (7)and (8) give the correlation:

corrTN ¼sNxffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

varT varNp ð1� xÞ varðbOtÞ �

x

ðy� 1Þ2varð bZtÞ �

1� 2xy� 1

covðbOt; bZtÞ

��covð bAt;N � bAt;H ; bOtÞ þ

1

y� 1covð bAt;N � bAt;H ; bZtÞ

�. (9)

Proposition 1. If zlt ¼ zh

t ¼ 0, then jcorrTN j ¼ 1.

Proof. If zlt ¼ zh

t ¼ 0, then Zt ¼ At;i ¼ 0. Hence, (7), (8) and (9) give corrTN ¼ 1 if xo1 and corrTN ¼ �1 ifx41. &

According to Proposition 1, without endogenous tradability the traded and nontraded RERs are perfectlycorrelated. The perfect correlation is caused by the terms of trade, or the relative wage in this case.

Proposition 2. If zlt ¼ zh

t ¼ 0, then vN ¼ sNð1� xÞ=ðxþ sN ð1� xÞÞ.

Proof. If zlt ¼ zh

t ¼ 0, then corrTN follows from Proposition 1. The correlations (1), (7) and (8) give vN . &

3It can be shown that Y t;i ¼ dt;i1y ðX tAt;i lt;iÞ

ðy�1Þ=yCw1=yt where Y t;i ¼ P�1t

Rz2Zt;i

ptðzÞytðzÞdz and Cwt ¼ aCt þ ð1� aÞð1� tÞy�1C%

t RERyt .


Proposition 2 states that in the absence of endogenous tradability, the contribution of the nontradedRER is independent of transition dynamics. Proposition 2 is related to Proposition 1. When the tradedand nontraded RERs are perfectly correlated, shocks do not influence their relative volatility. Thus,under perfect competition, endogenous tradability weakens the correlation and allow the transitiondynamics to influence the variance decomposition. Denote the covariance between the traded and nontradedRERs with covTN .

Proposition 3. Suppose zlta0 and zh

t a0. If varN4varT , then qvN=qcovNTo0, and vice versa.

Proof. From (1), vN ¼ ðvarN þ covTN Þ=ðvarT þ varN þ 2 covTN Þ. From Proposition 1, zlta0 and zh

t a0 implythat rTN is not constant, and neither are covTN and vN . Thus, we can differentiate vN with respect to covTN ,and qvN=qcovTN ¼ ðvar� varNÞ=ðvarT þ varN þ 2 covTN Þ

2. Hence, qvN=qcovTNo0 if varN4varT . &

Proposition 3 predicts that with endogenous tradability the contribution of the nontraded RER isdecreasing in the covariance between the traded and nontraded RERs, if the nontraded RER is more volatilethan the traded RER. Intuitively, weak covariance means large deviations between the nontraded and tradedRERs. Large deviations then allow the more volatile component of RER to further dominate the RER.Proposition 3 has an implication for the stylized fact in the previous section. Specifically, the contribution ofthe nontraded RER is higher under the fixed than the flexible exchange rate regime. The fact will be consistentwith the model if exchange rate stability reduces the covariance between the traded and nontraded RERs, andif the nontraded RER is more volatile than the traded RER.

3.4. Sticky wages

The model features a monopolistically competitive labor market, in which the wage-setting households areindexed by k 2 ½0; 1�. The set of home residents is ½0; a�; a 2 ð0; 1Þ. The set of foreign residents is ða; 1�. Thehome residents’ optimization problem is described, and the foreign one is a mirror image. The household k’sutility depends on its consumption Ck

t , its real money balance Mkt =Pt, and its labor supply lk

t , which dependson its wage W k

t . Its lifetime expected utility is

Ukt ¼ Et

X1t¼0

bt ss� 1

Ckt

ðs�1Þ=sþ

km

1� �

Mkt

Pt

� �1��

þkl

mð1� lk

t ðWkt ÞÞ

m

" #0obo1, mo1, s40, �40. km40, and kl40. The household accumulates assets through money and a one-period home-currency international bond F k

t , which pays the interest rate it. Adjusting the bond holdings isassumed to be costly, to prevent the bond holding from becoming infinitely large. Otherwise, the model cannotbe solved by the log-linearization technique (Turnovsky, 1985). The cost is quadratic in deviations of the realvalue of bond holdings from its steady-state, assumed to be zero, FðFk

t =PtÞ ¼12fðFk

t =PtÞ2, f40.

Of most importance, it is costly to adjust wages. The cost is similar to the price adjustments cost inRotemberg (1982). It is quadratic in deviations of the wage inflation from its steady state,hðpw;k

t Þ ¼12f

wðpw;k

t � pw;kÞ2, pw;k

t ¼W kt =W k

t�1 and fw40. Tkt is the government transfer. D is the first

difference. The budget constraint requires that the asset accumulation is the gap between income andexpenditure:

DMkt þ DF k

t ¼ itFkt�1 þW k

t lkt þ Tk

t Pt � ½Ckt þ FðF k

t =PtÞ þ hðpwk

t Þ�Pt.

The aggregate labor supply is a CES index with the substitution elasticity Z,

Lt ¼ ð1=aÞZZ a

0

lkð1�1=ZÞt dk

� �1�1=Z.

The unit labor cost

W t ¼1

a

Z a

0

Wk1�Zt dk

� �1=ð1�ZÞ


is obtained from the cost minimization. The demand for the household k’s labor is then

lkt ¼

1

aW k

t

W t

� ��ZLt.

The household k chooses the stochastic processes fW kt ;F

kt ;M

kt g1t¼0 to maximize its utility subject to its budget

constraint, the demand for its labor and the transversality condition

limj!1

Et Fktþs

,Yj�1s¼0

ð1þ itþsÞ

" #X0,

taking as given the price sequence fPtg1t¼0 and the initial conditions ðW k

�1;Fk�1;M

k�1Þ. All households face an

identical problem. So the index k is dropped from the first-order conditions described in the log-linearizedform below:

pwt ¼ bEtpw

tþ1 þ lw

1

sCt þ ll lt � wt

� �, (10)

1

sðEtCtþ1 � CtÞ ¼ �

{

1þ {{� Etptþ1

� �þ ff t, (11)

mt ¼�

sCt �

�

1þ {{, (12)

lw ¼ ðZ� 1Þwl=ðbfwp2Þ40 and ll ¼ m� 140. wt denotes the real wage W t=Pt. Because of wage rigidity, thewage inflation in (10) rises when the marginal rate of substitution (MRS) between consumption and laborexceeds the real wage. Thus, a consumption boom or an increase in the labor demand raises the wage inflation.The Euler equation and the real money demand in (11) and (12) are standard in the SDGE models.

A foreign-currency bond is assumed to be issued by the foreign government, so that the foreign interest ratei%t is well-defined. The bond is available only to the foreign residents and has zero stock in equilibrium. TheEuler conditions yield the interest rate parity condition

St ¼ EtStþ1 �{

1þ {ð{t � {

%

t Þ þ ff %

t . (13)

3.5. Exchange rate regimes

The stylized facts in Mendoza (2000), Burstein et al. (2005) and Fig. 1 in this study strongly suggest theimportance of exchange rate regimes. Hence, exchange rate variability is formulated as an outcome ofthe exchange rate policy characterized by the home interest rate rule. Under the fixed exchange rate regime, thehome central bank adopts the following rule:

{t ¼ {%

t þ St þ lf f %

t ,

where lf ¼ f{=ð1þ {Þ. St is the deviation from the target exchange rate and f %

t ¼ F%

t =ðStP%

t Þ. Endogenously,this rule and (13) give St ¼ 0. The rule is similar to that in Benigno (2004) and Monacelli (2004), apart fromthe debt term. The debt term exists because of the assumption that debt cannot explode, although its empiricalrelevance has not been investigated. Define the real gross domestic product (GDP) as

Y t ¼ P�1t

Zz2Zt;H[Zt;N

ptðzÞytðzÞ dz,

and the inflation rate as pt. The rule in Chari et al. (2002) is adopted under the flexible exchange rate regime:

{t ¼ li {t�1 þ ð1� liÞ½lpEtptþ1 þ lyY t�.

The foreign central bank adopts the following rule regardless of the exchange rate regime:

{�t ¼ li {�t�1 þ ð1� liÞ½lpEtp

�tþ1 þ lyY

�

t � þ V�t ,


V�t is the foreign interest rate shock, following the process logV�t ¼ rv logV�t�1 þ v�t , where v�t is normallydistributed by Nð0; s2vÞ. Shocks on the domestic interest rate are not assumed, to control the type of shocks foreach exchange rate regime. Since the focus here is the exchange rate policy, the seigniorage revenue is assumedto be simply rebated to the households, Tt ¼ ðMt �Mt�1ÞP

�1t . The quantitative predictions of the model are

in the next section.

4. Calibration

4.1. Parametrization

Table 1 summarizes the baseline parameter values. The most important ones concern the relativeproductivity schedule. Some studies have estimated the relative productivity of manufacturing sectors(Harrigan, 1999; Yi, 2003; Eaton and Kortum, 2002), but there are no estimates of the relative productivity ofthe nontraded sector. However, Hummels and Klenow (2005) estimated that the long-run elasticity of the U.S.set of exports with respect to its per-capita income relative to the rest of the world is 0.85. The elasticity isdriven by various factors besides comparative advantage. Hence, the function aðzÞ ¼ ne�gz is assumed, where n

and g are set so that the long-run elasticity is below 0.85 and higher than the short-run elasticity under theflexible exchange rate regime. The baseline long-run and short-run values are 0.69 and 0.37, respectively. Theentry-cost parameter is 9.

The remaining parameters are symmetric. Hummels (2001) estimated that the freight rate varies from 4% to13% of shipment value. The baseline value is 0.15 and reflects other trade barriers. The expenditure share ofnontraded goods is 0.5, from Falvey and Gemmell (1995). The estimate of the intratemporal elasticity ofsubstitution varies from 3 to 8 in Hummels (2001), and from 5 to 10 in Anderson and van Wincoop (2004).The lowest value 3 is chosen, because the classification of goods in this study is quite broad. Other parametersfollow the business cycle literature, such as Mendoza (1991), Huang and Liu (2002) and Chari et al. (2002).The wage-adjustment parameter is set so that the labor contract period is four quarters. The interest rate rule

Table 1

Benchmark parameter values

Parameters Value

International trade

Country size a ¼ 0:5Relative productivity n ¼ 1:5; g ¼ 1

Entry-cost parameter fa ¼ 9

Trade costs t ¼ 0:15

Households

Intratemporal elasticity of substitution y ¼ 3

Intertemporal elasticity of substitution s ¼ 0:2Discount factor b ¼ 0:99Elasticity of labor supply m ¼ 1� 1=sInterest semi-elasticity of money demand 1=� ¼ 0:39Portfolio adjustment cost f ¼ 0:00074Elasticity of substitution of labor Z ¼ 4

Wage-adjustment cost fw¼ 5:8935

Monetary policy

Steady-state inflation p ¼ p% ¼ 1:03581=4

Interest rate rule li ¼ 0:79, lp ¼ 2:15, ly ¼ 0:93

Interest rate shock

Persistence rv ¼ 0

Volatility sv ¼ 0:02


follows Clarida et al. (2000). The standard deviation of shocks is chosen so that the foreign output has thesame standard deviation as the Baxter–King-filtered series of the U.S. output.

In the steady-state, the aggregate allocation is identical in the two countries. The home country exports 24%of goods, and imports 43% of goods. Thirty-three percent of goods are nontraded. The trade-to-GDP ratio is0.42, which is close to that of the U.K. The terms of trade elasticity of the traded RER appreciation are 0.16.

4.2. Baseline results with foreign interest rate shocks

The log-linearized version of the model is simulated 50 times with foreign interest rate shocks over 100periods. Table 2 reports the statistics averaged over all simulations. The first two columns correspond to theflexible and fixed exchange rate regimes, and the last one indicates their differences. The statistics are inboldface letters when the difference across regimes is significant at the 1% level. The target statistics are fromSection 2. In the first block, the contribution of the nontraded RER is 64% under the flexible and 95% underthe fixed exchange rate regime. The model matches the 31% difference in Section 2, although it overpredictsthe level.

The next block gives the volatility of the RER, traded and nontraded RERs, terms of trade, and ratio oftrade balance to GDP. The measure is the standard deviation relative to that of output. As in Mussa (1986)and Baxter and Stockman (1989), exchange rate flexibility raises RER volatility. In line with the exchange ragedisconnect puzzle in Obstfeld and Rogoff (2000), RER volatility under the flexible regime is over 5 times of

Table 2

Baseline calibration with foreign interest rate shocks

Flexible Fixed Flexible–fixed

Contribution of nontraded RER

Model 0.64 0.95 �0.31

Data 0.19 0.50 �0.31

Standard deviation

RER

Model 5.23 0.11 5.12

Data 5.87 2.66 3.21

Traded RER

Model 2.15 0.11 2.04

Data 5.95 2.61 3.34

Non-traded RER

Model 3.55 0.15 3.40

Data 2.66 1.95 0.71

Terms of trade

Model 5.71 0.12 5.59

Data 6.83 2.53 4.30

Trade balance to GDP

Model 3.63 0.17 3.46

Data 2.05 0.59 1.46

Covariance of traded and nontraded RERs

Model 5.08 �0.01 5.09

Correlation of traded and nontraded RERs

Model 0.66 �0.67 1.33

Data (Mendoza, 2000) 0.28 �0.70 0.98

Persistence of RER

Model 0.32 0.84 �0.52

Data 0.71 0.65 0.06

Notes: The statistics are averages of 50 simulations and statistically different from zero at the 1% level. The covariance is measured

relative to the variance of output. The standard deviations are measured relative to that of output.


output volatility. The model underpredicts the volatility of all variables except for the nontraded RER and theratio of trade balance to GDP under the flexible regime.

In the third block, the covariance between the traded and nontraded RERs is 5.08 under the flexible and�0:01 under the fixed exchange rate regime. It is not meaningful to compare these with those in Section 2,which are negative by construction. The study using disaggregated price series by Mendoza (2000) providesthe sample correlation. It is 0.28 under the flexible and �0:70 under the fixed exchange rate regime. Thecorrelation from the model is 0.66 and �0:67, respectively. The model matches the sign and closely matchesthe magnitude under the fixed exchange rate regime.

Overall, the model correctly predicts the sign of differences in the summary statistics across exchange rateregimes, except for the RER persistence. The persistence with flexible exchange rates is 0.3 and close to 0.4 inChari et al. (2002), although still below 0.7 in the data. The model successfully matches the difference acrossregimes in the RER variance decomposition and the correlation between the traded and nontraded RERs.

As predicted by Proposition 3, exchange rate stability reduces the covariance between the traded andnontraded RER, given that the nontraded RER is more volatile than the traded RER. To understand why, thecovariance can be decomposed using (9) and the specialization pattern in (4). When the relative wage rises,some home exporters quit exporting, so corrðot; bZtÞo0. The quitting exporters raise the aggregateproductivity, because they are less productive than other exporters but more productive than the incumbentnontraded industries. Thus, corrð bZt; bAt;iÞ ¼ �1, corrð bAt;H ; bAt;N Þ ¼ 1 and corrðot; bAt;iÞ40. Let std denote thestandard deviation. These correlations and (9) give

covTN ¼ sNx ½ð1� xÞstdðotÞ � stdð bAt;N Þ�½stdðotÞ � corrðot; bAt;H Þstdð bAt;H Þ�

�þ

stdð bZtÞ

y� 1½�corrðot; bZtÞstdðotÞ � stdð bAt;N Þ�

��2x½�corrðot; bZtÞstdðotÞ � stdð bAt;H Þ� �

xy� 1

stdð bZtÞ

��. (14)

In (14), the sign of covariance depends on the ranking of volatility of the relative wage and the ranking ofsectoral productivities. The calibration gives the following covariance with flexible and fixed exchange rates,respectively:

covflexTN ¼ 0:1ð½ð0:8Þ9� 2�½9� ð0:5Þ1� þ0:5ð8Þ½½ð0:5Þ9� 2� � 0:4½ð0:5Þ9� 1� � 0:1ð8Þ�Þ ¼ 5,

covfixTN ¼ 0:1ð½ð0:8Þ0:19� 0:21�½0:19� ð0:3Þ0:13� þ0:5ð0:8Þ½½ð0:3Þ0:19� 0:21�

� 0:4½ð0:3Þ0:19� 0:13� � 0:1ð0:8Þ�Þ ¼ �0:01.

The underlined term has the largest absolute value and shares its sign with the covariance. The covariance withflexible exchange rates is positive because the volatility of the relative wage is higher than that of productivityin the nontraded and export sectors. However, without exchange rate flexibility, the volatility of the relativewage lies below that of the export-sector productivity but above that of the nontraded-sector productivity. Asa result, the covariance is negative under the fixed regime. The assumption of wage rigidity is crucial for theresults. By definition, the relative wage is increasing in the exchange rate appreciation

ot ¼ ot�1 þ ðpwt � pw%

t Þ � ðSt � St�1Þ. (15)

Eq. (15) indicates that wage rigidity mitigates the relative wage responses in the absence of exchange rateadjustments.

Endogenous tradability is crucial, because it makes the nontraded-sector productivity more volatile than theexport-sector productivity. Intuitively, the nontraded-sector productivity is lower than the export-sectorproductivity in equilibrium, so its percentage increase is larger. Alternatively, the quitting exporters are lessproductive and have smaller production share than other exporters; therefore, their exits create smalldisturbances to the export-sector productivity. In contrast, they are more productive and have largerproduction share than the incumbent nontraded industries so they create large disturbances to the nontraded-sector productivity.


Since productivity and wages are positively correlated, the more volatile variable drives the sectoral prices.Thus, under the flexible regime the relative wage drives the traded and nontraded RERs and makes thempositively correlated. However, under the fixed regime the relative wage drives the traded RER, butproductivity drives the nontraded RER in the opposite direction. The pattern is confirmed by the impulseresponses to one standard deviation reduction in the foreign interest rate in Fig. 3. Panels A and B correspondto the flexible and fixed regimes, respectively. Panels A.1 and B.1 display the paths of traded, nontraded andoverall RERs. Panels A.2 and B.2 display the paths of exchange rate, inverse of relative wage and sectoralproductivities.

Under the flexible regime, the traded and nontraded RERs are strongly correlated with the inverse ofrelative wage, which closely tracks the exchange rate. According to (13), the exchange rate appreciates onimpact and its path lies below the inverse of relative wage, indicating that domestic wage inflation is lowerthan foreign wage inflation. Hence, exchange rate appreciation is critical for the traded and nontraded RERsto appreciate. Why is the wage inflation lower at home? With wage rigidity, the exchange rate appreciationraises the terms of trade, and shifts some expenditures from export goods to import goods. So, labor demandin the export sector falls. In the nontraded sector, consumption and output remains unchanged on impact, butlabor demand falls due to the endogenous productivity gains. The aggregate labor demand reduction thenlowers wages.

0 5 10 15 20−20

−15

−10

−5

0

5x 10−3

A.1

Quarter0 5 10 15 20

−0.05

−0.04

−0.03

−0.02

−0.01

0

0.01A.2

Quarter

0 5 10 15 20−15

−10

−5

0

5x 10−6

Quarter

B.1

0 5 10 15 20−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1x 10−5

Quarter

B.2

x+∗

ox+∗

ox+∗

RERtraded RERnontraded RER

x+∗

RERtraded RERnontraded RER

exchange rate1/(relative wage)export productivitynontraded productivity

exchange rate1/(relative wage)export productivitynontraded productivity

Fig. 3. Impulse responses to one standard deviation reduction of the foreign interest rate. (A) Flexible exchange rate regime, and (B) fixed

exchange rate regime.


Under the fixed regime, the home central bank cuts its interest rate to match the foreign rate cut, andeffectively expands the aggregate demand. The expansion biases toward the nontraded and export goods, sothe nontraded-goods consumption increases more than the traded-goods consumption. Consequently, thehome output and labor demand rise and raise wages. The wage inflation creates persistent appreciation in thetraded RER. However, because of wage rigidity the wage inflation is not high enough to offset the endogenousproductivity gains in the nontraded sector. Thus, the nontraded RER in Panel B.1 depreciates from Period 2and becomes negatively correlated with the traded RER. This is why the inverse of relative wage is morecorrelated with the traded than the nontraded RER.

To summarize, the correlation between traded and nontraded RERs reflects different consumptiondynamics, largely due to the home bias in consumption. Besides trade costs, the fixed expenditure share on thenontraded goods creates the home bias. The fixed share makes the distribution of productivity levelscontinuous only for the most part, and yields a large increase in the nontraded output despite a small increasein the range of nontraded goods. The home bias also exists under the flexible exchange rate regime, otherwisethe nontraded-goods consumption would have fallen on impact. Allowing the share to vary will reduce thehome bias but will not remove it. Quantifying the effect of time-variant share is beyond the scope of this paperand a subject for future research.

4.3. Sensitivity analysis

This section compares the model of endogenous tradability with that of exogenous tradability, in which thespecialization pattern is identical to the baseline steady state. Then the model is simulated with TFP shocksfollowing the processes logX t ¼ 0:95 logX t�1 þ ut and logX �t ¼ 0:95 logX �t�1 þ u�t , where ut and u�t are jointlynormally distributed around zero with standard deviation 0.01 and correlation 0.25, as in Chari et al. (2002).Finally, the model is simulated with the foreign interest rate shocks with a 25% reduction in the intertemporalelasticity of substitution, the wage adjustment parameter and the variance of shocks. Table 3 summarizes thesix results.

First, when the trade pattern is exogenous, the type of shocks and the exchange rate regime are irrelevant tothe variance decomposition, as predicted by Proposition 2. In this case, the traded and nontraded RERs areperfectly correlated, as predicted by Proposition 1. However, Engel (1999), Mendoza (2000) and Burstein et al.(2005) found that the correlation in the data is not perfect. Hence, endogenous tradability is essential forgenerating the observed correlation. Moreover, the signs of correlation match with those in Mendoza (2000)when the trade pattern is endogenous.

Second, as predicted by Proposition 3, the contribution of the nontraded RER is decreasing in thecovariance between the traded and nontraded RERs, given that the nontraded RER is more volatile than thetraded RER. With interest rate shocks, exchange rate stability and endogenous tradability turn the covariancefrom a positive to a negative value.

Third, TFP shocks make the traded and nontraded RERs uncorrelated and let the traded RER dominatethe RER. Let RHS14 denote the right-hand side of (14). The covariance in this case is

covwTN ¼ RHS14þ stdðwtÞsNx ð1� xÞstdðwtÞ þ

1� 2xy� 1

stdð bZtÞ

� �þ corrðwt; bAt;H Þ stdðwtÞsNx½stdð bAt;NÞ � stdð bAt;H Þ þ 2ð1� xÞ½stdðotÞ þ stdð bAt;H Þ�.

The ranking of volatility under both exchange rate regimes is as follows: stdð bAt;H Þostdð bAt;N ÞostdðotÞ. Withthis ranking and x40, all terms except for the last one are positive. The last term is negative, becausecorrðwt; bAt;H Þ � �1 as favorable TFP shocks push a large number of producers in the nontraded sector intoexporting. Overall, the last term cancels out the rest and drives the covariance to zero, as found by Engel(1999).

Like Betts and Kehoe (2001b), Bergin and Glick (2003) and Ghironi and Melitz (2005), my model suggeststhat TFP shocks cause the traded RER to drive the U.S. RERs in Engel (1999). To be precise, the nontradedproducers who begin exporting due to favorable TFP shocks mitigate, but do not remove, the increase inproductivity in the export and nontraded sectors due to rising wages. Thus, productivity gains become small in

ARTICLE IN PRESS

Table 3

Sensitivity analysis

Endogenous tradability Exogenous tradability

Flexible Fixed Flexible Fixed

Contribution of nontraded RER

Baseline 0.64 0.95 0.72 0.72

TFP shocks 0.43 0.47 0.72 0.72

Low wage-rigidity 0.64 0.97 0.72 0.72

Low intertemporal elasticity 0.65 0.99 0.72 0.72

Small variance of interest rate shocks 0.64 0.96 0.72 0.72

Correlation of the traded and nontraded RERs

Baseline 0.66 �0.67 1 1

TFP shocks 0.05 0.01 1 1

Low wage-rigidity 0.68 �0.65 1 1

Low intertemporal elasticity 0.70 �0.61 1 1

Small variance of interest rate shocks 0.66 �0.68 1 1

Covariance of the traded and nontraded RERs

Baseline 5.08 �0.011 9.77 0.01

TFP shocks 0.11 0.02 3.71 3.24

Low wage-rigidity 5.08 �0.013 9.55 0.02

Low intertemporal elasticity 4.77 �0.021 8.76 0.03

Small variance of interest rate shocks 4.96 �0.003 9.73 0.004

Standard deviation of RER

Baseline 5.23 0.11 6.97 0.27

TFP shocks 2.22 1.94 4.19 4.06




Standard deviation of relative wage

Baseline 9.43 0.19 13.81 3.85

TFP shocks 4.45 5.02 3.49 3.28




Notes: The boldface numbers indicate that the null that the statistics are the same across exchange rate regimes is rejected at the 1% level.

The covariance and standard deviations are measured relative to those of output.

K. Naknoi / Journal of Monetary Economics 55 (2008) 645–663660

both export and nontraded sectors under both exchange rate regimes. However, the direct impact of TFPshocks on the terms of trade is large and amplified by rising export-sector productivity. The traded RER thenbecomes more volatile than the nontraded RER, and favorable TFP shocks increase the traded-goodsconsumption more than the nontraded-goods consumption.

Fourth, a fall in the wage-adjustment parameter raises the contribution of the nontraded RER. Lowadjustment cost raises volatility of the wage inflation and that of the relative wage under the fixed exchangerate regime. Under the flexible regime, this is not the case because the relative wage is driven by the exchangerate. High volatility of wage inflation prompts the central banks to quickly reverse their changes in interestrate policy. Thus, the exchange rate volatility falls, and drives down volatility of the relative wage. Overall, thecovariance between the traded and nontraded RER falls under both regimes, and more so under the fixed thanthe flexible regime. As a result, rising wage flexibility allows the exchange rate stability to further raise thecontribution of the nontraded RER.

Fifth, a reduction of the intertemporal substitution elasticity qualitatively has the same impact as areduction of the wage-adjustment parameter. A reduction of the intertemporal substitution elasticity raises theresponses of the MRS between consumption and labor in (10). Hence, the impact on wage inflation, andtherefore on variance decomposition, is the same as an increase in wage flexibility.


Finally, a reduction of the variance of interest rate shocks barely changes the variance decomposition.Although the reduction lowers the absolute volatility of the relative wage, it does not change the differences involatility of productivity across sectors. Small shocks do not shut down endogenous tradability, because theexport entry cost is proportional to productivity so the cost prevents only some industries from switching. Ifthe cost is fixed, very small shocks can prevent all industries from switching.

Note that exogenous tradability produces more volatility in the relative wage and RER than endogenoustradability. Although endogenous tradability raises volatility of the trade-balance-to-GDP, the increase is notextreme and is below 20%. Hence, there is a trade-off between adjustments along the price margin and thecomposition of trade. The trade-off has an implication for the role of exchange rate as follows. Withendogenous tradability, the expenditure shares on export and import goods now depend on the ranges ofexport and import goods, besides their prices relative to the CPI. The trade-off implies that volatility of theseranges rises when the intratemporal substitution elasticity falls. Thus, exchange rate can create a great deal ofexpenditure switching within the traded sector through changes in the ranges of export and import goods. Toillustrate this point, the elasticity y is varied from 1.5 to 5 and the model is simulated with foreign interest rateshocks. The cross-regime difference in the correlation between traded and nontraded RERs is used as ameasure of expenditure switching within the traded sector generated by exchange rate. Fig. 4 plots the measureagainst the elasticity, together with the cross-regime difference in the contribution of the nontraded RER.

In Fig. 4, the expenditure switching within the traded sector is increasing in y for y 2 ½1:5; 2:5Þ, butdecreasing for y 2 ð2:5; 5�. The nonmonotonicity is in contrast with the monotonicity of the correspondingrelationship in Monacelli (2004), which measures the expenditure switching by the ratio of RER volatilityunder the flexible and fixed regimes. He uses this measure, because exchange rate fluctuations create deviationsfrom purchasing power parity due to his assumption of sticky prices. However, the nonmonotonicity in thisstudy remains even after adopting his measure. The difference arises from the absence of trade costs and thenontraded goods in his model. In this study, trade costs and the nontraded goods produce a monotonicrelationship between expenditure switching within the traded sector and the difference in the variancedecomposition across regimes instead. The exchange rate regime has a significant effect on the variancedecomposition even when the elasticity is as low as 1.5, which is often used in the business cycle literature suchas Backus et al. (1994) and Ruhl (2005). With this value, exchange rate stability raises the contribution of the

1.5 2 2.5 3 3.5 4 4.5 5−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

θ

corr TNflex −corr TN

fix

vNflex −vN

fix

Fig. 4. Intertemporal substitution elasticity and the expenditure switching within the traded sector generated by exchange rate flexbility.


nontraded RER by 20%. In contrast, expenditure switching becomes less pronounced as the elasticityapproaches 5, because of a reduction in the entry effects.

5. Concluding remarks

This study shows that the transitions in and out of exporting can amplify expenditure switching amongtraded goods resulting from the exchange rate fluctuations in response to nominal shocks. The effect is so largethat the removal of exchange rate flexibility raises the importance of expenditure switching across the tradedand nontraded sectors and the contribution of nontraded RER to the RER variance. The model hasimportant implications for macroeconomics.

The model highlights the importance of nominal shocks in the presence of nominal rigidities, particularly inwages. In particular, nominal shocks have different effects on the dynamics of consumption across exchangerate regimes. Expansionary nominal shocks expand consumption with a bias toward the traded goods underthe flexible regime, but toward the nontraded goods under the fixed regime. Thus, the assumption that thenontraded RER drives RER, as in Calvo (1986), is appropriate for studying stabilization policy when shocksare predominantly nominal. On the other hand, expansionary productivity shocks always expandconsumption with a bias toward the traded goods. For this reason, deviations from the law of one pricefor traded goods are necessary for studying the effects of real shocks.

The model suggests that the traded and nontraded RERs in the standard SDGE models are perfectlycorrelated and contradict the empirics. The zero correlation generated by TFP shocks in this study implies thatrelative traded-goods consumption is uncorrelated with relative nontraded-goods consumption. This insightcould be useful for explaining why relative consumption and the RER are uncorrelated (Backus and Smith,1993).

Finally, this study is related to the theory of optimum currency area. The theory views similarity ofproduction structure as a condition for forming a currency union, since that implies high cross-countrycorrelation of real shocks. However, my model suggests that a different specialization pattern has astabilization effect, reducing the cost of losing monetary independence. The model can be extended to includecapital accumulation in order to study the impact of exchange rate regimes on economic growth.

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real exchange rate fluctuations, endogenous tradability and exchange rate regimes

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