International Trade and Macroeconomic Dynamics with

International Trade and Macroeconomic Dynamics with Heterogeneous Firms

CitationGhironi, Fabio, and Marc J. Melitz. 2005. International trade and macroeconomic dynamics with heterogeneous firms. Quarterly Journal of Economics 120, no. 3: 865-915.

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INTERNATIONAL TRADE AND MACROECONOMICDYNAMICS WITH HETEROGENEOUS FIRMS*

FABIO GHIRONI AND MARC J. MELITZ

We develop a stochastic, general equilibrium, two-country model of trade andmacroeconomic dynamics. Productivity differs across individual, monopolisticallycompetitive firms in each country. Firms face a sunk entry cost in the domesticmarket and both fixed and per-unit export costs. Only relatively more productivefirms export. Exogenous shocks to aggregate productivity and entry or trade costsinduce firms to enter and exit both their domestic and export markets, thusaltering the composition of consumption baskets across countries over time. In aworld of flexible prices, our model generates endogenously persistent deviationsfrom PPP that would not exist absent our microeconomic structure with hetero-geneous firms. It provides an endogenous, microfounded explanation for a Harrod-Balassa-Samuelson effect in response to aggregate productivity differentials andderegulation. Finally, the model successfully matches several moments of U. S.and international business cycles.

I. INTRODUCTION

Formal models of international macroeconomic dynamics donot usually address or incorporate the determinants and evolu-tion of trade patterns. The vast majority of such macroeconomicmodels take the pattern of international trade and the structureof markets for goods and factors of production as given.1 Thedeterminants of such trade patterns are, in turn, analyzed withinmethodologically distinct models that are generally limited tocomparisons of long-run positions or growth dynamics afterchanges in some determinants of trade. These models do notconsider short- to medium-run business cycle dynamics and theireffect on the pattern of trade over time. This separation betweenmodern models of international macroeconomics and trade theory

* For helpful comments, we thank the editor (Robert Barro), two anonymousreferees, Philippe Bacchetta, Marianne Baxter, Paul Bergin, Lawrence Chris-tiano, Giancarlo Corsetti, Jonathan Eaton, Pierre-Olivier Gourinchas, GeneGrossman, Elhanan Helpman, Hugo Hopenhayn, Andreas Hornstein, Jean Imbs,Paolo Pesenti, Kenneth Rogoff, Kei-Mu Yi, and seminar and conference partici-pants at several institutions. We are grateful to Kolver Hernandez for excellentresearch assistance. Remaining errors are our responsibility. We thank the NSFfor financial support (SES 0417757). Ghironi also acknowledges funding for thisproject from Boston College and the European University Institute, through aJean Monnet Fellowship in the General Programme of the Robert SchumanCentre for Advanced Studies.

1. See Lane [2001] for a survey of the recent literature. We discuss therelation between our work and some exceptions to this trend in internationalmacroeconomics below.

© 2005 by the President and Fellows of Harvard College and the Massachusetts Institute ofTechnology.The Quarterly Journal of Economics, August 2005

865

is somewhat unnatural. Modern international macroeconomicsprides itself on its microfoundations. Yet, it neglects to analyzethe effects of macro phenomena on its microeconomic underpin-nings. Similarly, much of trade theory does not recognize theaggregate feedback effects of micro-level adjustments over time.2

This paper contributes to bridging the gap between interna-tional macroeconomics and trade theory. We use Melitz’s [2003]model of trade with monopolistic competition and heterogeneousfirms as the microeconomic underpinning of a two-country, dy-namic, stochastic, general equilibrium (DSGE) model of interna-tional trade and macroeconomics.3 Firms face some initial uncer-tainty concerning their future productivity when making an irre-versible investment to enter the domestic market. Postentry,firms produce with different productivity levels. In addition to thesunk entry cost, firms face both fixed and per-unit export costs.4

Forward-looking firms formulate entry and export decisionsbased on expectations of future market conditions. Only a subsetof relatively more productive firms export, while the remaining,less productive firms only serve their domestic market. Thismicroeconomic structure endogenously determines the extent ofthe traded sector and the composition of consumption baskets inboth countries. Exogenous shocks to aggregate productivity, orentry and trade costs induce firms to enter and exit both theirdomestic and export markets, thus altering the composition ofconsumption baskets across countries over time. This introducesa new and potentially important channel for the transmission ofmacroeconomic shocks and their propagation over time.

We first introduce this microeconomic structure in a flexible-price model with no international trade in financial assets—andfocus on the role of goods market dynamics. We show that themicroeconomic features of our model have important conse-quences for macroeconomic variables. Macroeconomic dynamics,

2. Baldwin and Lyons [1994] and Dumas [1992] are two notable exceptions.They analyze general equilibrium models that describe the dynamic interactionsbetween costly trade and the real exchange rate. We incorporate microfoundationsinto such a model.

3. Melitz [2003] focuses on the analysis of steady-state effects of trade.4. Recent empirical micro-level studies have documented the relevance of

plant-level fixed export costs. See Bernard and Jensen [2001] (for the UnitedStates), Bernard and Wagner [2001] (for Germany), Das, Roberts, and Tybout[2001] (for Colombia), and Roberts and Tybout [1997] (for Colombia). These fixedcosts include market research, advertising, and regulatory (such as testing, pack-aging, labeling requirements) expenses incurred by plants exporting differenti-ated products.

866 QUARTERLY JOURNAL OF ECONOMICS

in turn, feed back into firm-level decisions, further altering thepattern of trade over time. Our model generates deviations frompurchasing power parity (PPP) that would not exist absent ourmicroeconomic structure with heterogeneous firms. It provides anendogenous, microfounded explanation for a Harrod-Balassa-Samuelson (HBS) effect: More productive economies, or less regu-lated ones (phenomena that affect all firms in the economy),exhibit higher average prices relative to their trading partners.We then show how, under fully flexible prices, deviations fromPPP display substantial endogenous persistence in response totransitory aggregate shocks (for very plausible calibrated pa-rameters).5 Since the micro-level adjustments we analyze occurwithin sectors, our model also explains how these deviations fromPPP are manifested in sector-level prices—even for sectors con-sidered “traded.”

Next, we extend our model to allow for international bondtrading. In this setup, we show that permanently more produc-tive economies, or less regulated ones, also run persistent foreigndebt positions to finance the accelerated entry of firms into therelatively more favorable business environment. A stochastic ex-ercise shows that the model matches several important momentsof the U. S. and international business cycle quite well. In con-trast to benchmark international real business cycle (RBC) mod-els, our setup generates positive GDP correlation across coun-tries; it does not automatically produce high correlation betweenrelative consumption and the real exchange rate; and it substan-tially reduces the “consumption-output anomaly” associated withstandard models.

The rest of the paper is organized as follows. Section IIdiscusses the HBS effect and contrasts our approach to the re-lated literature. Section III describes the benchmark model withfinancial autarky. Section IV presents results on the determi-nants of the real exchange rate in our setup. These results guideour interpretation of the impulse responses in Section V, whichanalyzes the dynamic responses to shocks affecting aggregateproductivity and sunk entry costs (interpreted as changes indomestic market regulation). Section VI introduces internationalbond trading and discusses its implications. It also presents re-

5. More generally, the introduction of micro dynamics motivated by hetero-geneity, and entry and trade costs, significantly improves the ability of our modelto generate endogenously persistent dynamics: a stumbling block for many well-known DSGE macro models.

867TRADE AND MACROECONOMIC DYNAMICS

sults on second-moment properties of the model. Section VIIconcludes.

II. THE HBS LITERATURE AND OUR MODELING APPROACH

Textbook analysis of the HBS effect assumes an exogenouslydefined nontraded sector and some favorable productivity shocksaffecting only the traded sector. These shocks cause the relativeprice of nontraded goods to increase, leading to a real exchangerate appreciation (relative to trading partners). An aggregateproductivity increase (across all sectors) would have no effect onthe real exchange rate. Although the cross-country correlationbetween development (usually measured as GDP per capita) andprice levels is robust and pervasive, the evidence linking thiscorrelation to productivity differentials across traded and non-traded sectors is much weaker and controversial (see Rogoff[1996, sections 6A–B]). Our model explains the former withoutrelying on the latter; it also explains why persistent deviationsfrom PPP also show up in cross-country price differences fortradable goods as documented by Engel [1993, 1999].

One potential problem with the textbook HBS effect is thereliance on the law of one price for traded goods. If these aredifferentiated, then productivity shocks to either the traded ornontraded sectors engender movements in the terms of tradeacross countries. Recently, Fitzgerald [2003] and MacDonald andRicci [2002] have shown how product differentiation within trad-ables affects the measurement of HBS, and have found indirectevidence for such terms-of-trade effects. Our model incorporatesthese effects, but additionally addresses a more fundamentalinconsistency with the textbook HBS effect highlighted by recentmicro-level studies of plant export behavior: most goods in thetradable sector are not traded. Moreover, this division betweentraded and nontraded occurs within narrowly defined sectors (onthe demand side) and substantially evolves over time. For exam-ple, in the United States, only 21 percent of manufacturing plantsexport [Bernard, Eaton, Jensen, and Kortum 2003], and roughly13 percent of plants switch their export status in a given year[Bernard and Jensen 2004].6 It therefore seems improbable—as

6. Similar patterns hold for many other countries. Bernard et al. [2003]further report that the partitioning between exporters and nonexporters is per-vasive across narrowly defined four-digit manufacturing sectors. Bernard and


required for the “textbook” HBS effect—that some productivityshocks only affect the (time varying) proportion of exporting firmswithin each sector.

Our model captures the effects of aggregate shocks on boththe determination of the set of traded goods and their terms oftrade. As previously mentioned, these changes occur within sec-tors and generate persistent deviations in sector-level prices.Although we do not explicitly model multiple sectors, our frame-work nevertheless highlights the micro-level characteristics ofsectors (the level of product differentiation, firm entry and exitrates, levels of sunk costs and trade costs) that would generatedifferences in persistence rates for cross-country sector-levelprice differentials. Imbs, Mumtaz, Ravn, and Rey [2005] andCheung, Chinn, and Fujii [2001] both document that sector-levelprice differentials can be very persistent (across countries), andthat the persistence levels are quite heterogeneous across sectors.Cheung, Chinn, and Fujii further find that sectors with moreintraindustry trade exhibit higher persistence levels—a findingthat is broadly consistent with the forces in our model.

Dornbusch, Fischer, and Samuelson [DFS 1977] first ana-lyzed the endogenous determination of nontraded sectors, andpointed out how aggregate productivity shocks could lead to av-erage price differentials across countries. Bergin and Glick[2003a, 2003b] embed this structure into a dynamic frameworkwhere endogenous nontradability further arises from differencesin trade costs across sectors.7 Whereas this line of research ana-lyzes cross-sectoral variations in tradability, we focus on thewithin-sector determination of “tradedness” based on firm-leveldecisions: all goods are tradable in our model; some are nontradedas a consequence of firm decisions. We believe that the endoge-nous determination of both intrasectoral nontradedness and in-tersectoral nontradability are important, and we view these linesof research as complementary.

Other contributions to the international macroeconomic lit-erature have emphasized the role of trade costs and nontradedintermediate services in the propagation of shocks. Already

Jensen [2004] also document the important aggregate effects of new exporters: inthe United States, 38 percent of the export growth between 1987 and 1992 wasdriven by entry of new exporters.

7. Obstfeld and Rogoff [1996, Ch. 4], Kehoe and Ruhl [2002], and Kraay andVentura [2002] also develop dynamic extensions of the DFS model that capturechanges in the pattern of trade (and tradability) over time.


Backus, Kehoe, and Kydland [1992] showed that the inclusion oftrade frictions improves the quantitative performance of an in-ternational RBC model. Obstfeld and Rogoff [2001] present sim-ple models in which the addition of per-unit trade costs and thepotentially endogenous nature of tradedness help explain a num-ber of puzzles in international macroeconomics. Burstein, Neves,and Rebelo [2003] and Burstein, Eichenbaum, and Rebelo [2002]focus on the role of the nontraded distribution sector and compo-sition effects in the CPI.

Several recent papers study the consequences of firm entry orendogenous nontradedness. Ricci [1997] focuses on the effect ofthe exchange rate regime on the location choice of monopolisti-cally competitive firms under sticky prices and wages. Corsetti,Martin, and Pesenti [2005] explore the implications of entry forthe transmission of monetary shocks in a two-country, sticky-wage model in which all goods are traded. Bergin, Glick, andTaylor [2003] use a model with monopolistic competition, fixedexport costs, and heterogeneous productivity (but an exogenousnumber of producers) in their analysis of the HBS effect. Bettsand Kehoe [2001] introduce heterogeneous, per-unit trade costsin a multicountry, trade and macro model with complete assetmarkets and differentiated goods. Our approach is distinguishedby its focus on fixed costs, heterogeneous productivity, and en-dogenous entry into both domestic and export markets.8

III. THE MODEL

We begin by developing a version of our model under finan-cial autarky.

III.A. Household Preferences and Intratemporal Choices

The world consists of two countries, home and foreign. Wedenote foreign variables by an asterisk. Each country is popu-lated by a unit mass of atomistic households. All contracts andprices in the world economy are written in nominal terms. Pricesare flexible. Thus, we only solve for the real variables in themodel. However, as the composition of consumption baskets in

8. Alessandria and Choi [2003], Ruhl [2003], and Russ [2003] develop modelsthat are closest to ours. In contrast to our model, Alessandria and Choi assumethat firm-specific productivity displays no persistence; Ruhl uses a model thatincludes an exogenously nontraded good; and Russ focuses on foreign directinvestment under nominal stickiness.


the two countries changes over time (affecting the definitions ofthe consumption-based price indexes), we introduce money as aconvenient unit of account for contracts. Money plays no otherrole in the economy. For this reason, we do not model the de-mand for cash currency, and resort to a cashless economy as inWoodford [2003].

The representative home household supplies L units of laborinelastically in each period at the nominal wage rate Wt, denom-inated in units of home currency. The household maximizes ex-pected intertemporal utility from consumption (C): Et [¥s�t

�

�s�tCs1��/(1 � �)], where � � (0,1) is the subjective discount

factor and � � 0 is the inverse of the intertemporal elasticity ofsubstitution. At time t, the household consumes the basket ofgoods Ct, defined over a continuum of goods �: Ct � (��

ct()(�1)/d)/(�1), where � 1 is the symmetric elasticity ofsubstitution across goods. At any given time t, only a subset ofgoods �t � � is available. Let pt() denote the home currencyprice of a good � �t. The consumption-based price index forthe home economy is then Pt � (��t

pt()1�d)1/(1� ), andthe household’s demand for each individual good is ct() �( pt()/Pt)

�Ct.The foreign household supplies L* units of labor inelastically

in each period in the foreign labor market at the nominal wagerate W*t, denominated in units of foreign currency. It maximizesa similar utility function, with identical parameters and a simi-larly defined consumption basket. Crucially, the subset of goodsavailable for consumption in the foreign economy during period tis �*t � � and can differ from the subset of goods that areavailable in the home economy.

III.B. Production, Pricing, and the Export Decision

There is a continuum of firms in each country, each produc-ing a different variety � �. Production requires only one factor,labor. Aggregate labor productivity is indexed by Zt (Z*t), whichrepresents the effectiveness of one unit of home (foreign) labor.Firms are heterogeneous as they produce with different technol-ogies indexed by relative productivity z. A home firm with rela-tive productivity z produces Ztz units of output per unit of laboremployed. Productivity differences across firms therefore trans-late into differences in the unit cost of production. This cost,measured in units of the consumption good Ct, is wt/(Ztz), wherewt � Wt/Pt is the real wage. Similarly, foreign firms are indexed


by their productivity z and unit cost (measured in units of theforeign consumption good) w*t/(Z*tz), where w*t � W*t/P*t is thereal wage of foreign workers.9

Prior to entry, firms are identical and face a sunk entry costof fE,t ( f *E,t) effective labor units, equal to wtfE,t/Zt (w *tf *E,t/Z*t)units of the home (foreign) consumption good. Upon entry, homefirms draw their productivity level z from a common distributionG( z) with support on [ zmin, �). Foreign firms draw their produc-tivity level from an identical distribution. This relative produc-tivity level remains fixed thereafter. Since there are no fixedproduction costs, all firms produce in every period, until they arehit with a “death” shock, which occurs with probability � � (0,1)in every period. This exit-inducing shock is independent of thefirm’s productivity level, so G( z) also represents the productivitydistribution of all producing firms.

Given our modeling assumption relating each firm to anindividual variety, we think of a firm as a production line for thatvariety, and the entry cost as the development and setup costassociated with the latter (potentially influenced by market regu-lation). The exogenous “death” shock also takes place at theindividual variety level. Empirically, a firm may comprise morethan one of these production lines. Our model does not addressthe determination of product variety within firms, but our mainresults would be unaffected by the introduction of multiproductfirms.

Home and foreign firms can serve both their domestic marketas well as the export market. Exporting is costly, and involvesboth a melting-iceberg trade cost t � 1 ( *t � 1) as well as a fixedcost fX,t ( f *X,t) (measured in units of effective labor). We assumethat firms hire workers from their respective domestic labormarkets to cover these fixed costs. These costs, in real terms, arethen wtfX,t/Zt for home firms (in units of the home consumptiongood) and w *tf *X,t/Z*t for foreign firms (in units of the foreignconsumption good). The fixed export costs are paid on a period-

9. We use the same index z for both home and foreign firms as this variableonly captures firm productivity relative to the distribution of firms in that country.Consistent with standard RBC theory, aggregate productivity Zt (Z*t) affects allhome (foreign) labor uniformly. We abstract from more complex technology diffu-sion processes across firms of different vintages. See Caballero and Hammour[1994] and Campbell [1998] for a treatment of this topic.


by-period basis rather than sunk upon entry in the exportmarket.10

All firms face a residual demand curve with constant elastic-ity in both markets, and they set flexible prices that reflect thesame proportional markup /( � 1) over marginal cost. LetpD,t( z) and pX,t( z) denote the nominal domestic and export pricesof a home firm. We assume that export prices are denominated inthe currency of the export market. Prices, in real terms relative tothe price index in the destination market, are then given by

(1) �D,t�z� �pD,t�z�

Pt�

� 1wt

Ztz, �X,t�z� �

pX,t�z�

P*t� Qt

�1 t�D,t�z�,

where Qt � εtP*t/Pt is the consumption-based real exchange rate(units of home consumption per unit of foreign consumption; εt isthe nominal exchange rate, units of home currency per unit offoreign).11 However, due to the fixed export cost, firms with lowproductivity levels z may decide not to export in any given period.When making this decision, a firm decomposes its total profitdt( z) (d*t( z)) (returned to households as dividends) into portionsearned from domestic sales dD,t( z) (d*D,t( z)) and from potentialexport sales dX,t( z) (d*X,t( z)). All these profit levels (dividends)are expressed in real terms in units of the consumption basket inthe firm’s location.12 In the case of a home firm, total profits inperiod t are given by dt( z) � dD,t( z) � dX,t( z), where

dD,t� z� �1

��D,t� z��1�Ct,

dX,t� z� � � Qt

��X,t� z��1�C*t �

wtfX,t

Ztif firm z exports,

0 otherwise.

10. Although a substantial portion of fixed export costs are probably sunkupon market entry, we do not model the sunk nature of these costs explicitly. Wedo this for simplicity, as sunk export market entry costs would complicate thesolution method considerably while leaving the main message of the paper unaf-fected. We conjecture that introducing these costs would enhance the persistenceproperties of our model.

11. Similar price equations hold for foreign firms. Note that �*X,t( z) � p*X,t( z)/Pt � Qt *t�*D,t( z).

12. Note that an exporter’s relative price �X,t( z) (�*X,t( z)) is expressed inunits of C*t (Ct) (the consumption good at the location of sales) but the profits fromexport sales dX,t( z) (d*X,t( z)) are expressed in units of Ct (C*t) (the consumptionbasket in the firm’s location).


Foreign firms behave in a similar way.13 As expected, moreproductive firms earn higher profits (relative to less productivefirms), although they set lower prices (see (1)).14 A firm willexport if and only if it would earn nonnegative profit fromdoing so. For home firms, this will be the case so long asproductivity z is above a cutoff level zX,t � inf{z : dX,t(z) � 0}. Asimilar cutoff level z*X,t � inf{z : d*X,t(z) � 0} holds for foreignexporters. We assume that the lower bound productivity zmin islow enough relative to the export costs that zX,t and z*X,t areboth above zmin. This ensures the existence of an endogenouslydetermined nontraded sector: the set of firms that could export,but decide not to. These firms, with productivity levels betweenzmin and the export cutoff level, only produce for their domesticmarket. This set of firms fluctuates over time with changes inthe profitability of the export market, inducing changes in thecutoff levels zX,t and z*X,t.

III.C. Firm Averages

In every period, a mass ND,t (N*D,t) of firms produces in thehome (foreign) country. These firms have a distribution of pro-ductivity levels over [ zmin, �) given by G( z). Among these firms,there are NX,t � [1 � G( zX,t)]ND,t and N*X,t � [1 � G( z*X,t)]N*D,texporters. Following Melitz [2003], we define two special “aver-age” productivity levels—an average zD for all producing firms (ineach country), and an average zX,t for all home exporters:

zD � ��zmin

�

z�1dG�z��1/��1�

, zX,t � � 11 � G�zX,t� �

zX,t

�

z�1dG�z��1/��1�

.

(The definition of z*X,t is analogous to that of zX,t.) As shown inMelitz, these productivity averages—based on weights propor-tional to relative firm output shares—summarize all the informa-tion on the productivity distributions relevant for all macroeco-nomic variables. In essence, our model is isomorphic to one whereND,t (N*D,t) firms with productivity level zD produce in the home(foreign) country and NX,t (N*X,t) firms with productivity level zX,t( z*X,t) export to the foreign (home) market.

13. A foreign firm earns export profits d*X,t( z) � Qt�1[�*X,t( z)]1�Ct/ �

w*tf *X,t/Z*t if it sells output in the home country.14. We think of firm prices as adjusted for product quality. Our model is

isomorphic to one where firms produce the differentiated goods with differentquality levels.


In particular, pD,t � pD,t( zD) ( p*D,t � p*D,t( zD)) representsthe average nominal price of home (foreign) firms in their domes-tic market, and pX,t � pX,t( zX,t) ( p*X,t � p*X,t( z*X,t)) representsthe average nominal price of home (foreign) exporters in theexport market. The price index at home therefore reflects theprices of the ND,t home firms (with average price pD,t) and theN*X,t foreign exporters to the home market (with average pricep*X,t). The home price index can thus be written as Pt �[ND,t( pD,t)

1� � N*X,t( p*X,t)1�]1/(1� ). This is equivalent to

ND,t(�D,t)1� � N*X,t(�*X,t)

1� � 1, where �D,t � �D,t( zD) and�*X,t � �*X,t( z*X,t) represent the average relative prices of homeproducers and foreign exporters in the home market. Similarequations hold for the foreign price index.

The productivity averages zD, zX,t, and z*X,t are constructedin such a way that dD,t � dD,t( zD) (d*D,t � d*D,t( zD)) representsthe average firm profit earned from domestic sales for all home(foreign) producers; and dX,t � dX,t( zX,t) (d*X,t � d*X,t( z*X,t))represents the average firm export profits for all home (foreign)exporters. Thus, dt � dD,t � [1 � G( zX,t)]dX,t and d*t � d*D,t �[1 � G( z*X,t)]d*X,t represent the average total profits of home andforeign firms, since 1 � G( zX,t) and 1 � G( z*X,t) represent theproportion of home and foreign firms that export and earn exportprofits.15

III.D. Firm Entry and Exit

In every period there is an unbounded mass of prospectiveentrants in both countries. These entrants are forward looking,and correctly anticipate their future expected profits dt(d*t) inevery period (the preentry expected profit is equal to postentryaverage profit) as well as the probability � (in every period) ofincurring the exit-inducing shock. We assume that entrants attime t only start producing at time t � 1, which introduces aone-period time-to-build lag in the model. The exogenous exitshock occurs at the very end of the time period (after productionand entry). A proportion � of new entrants will therefore neverproduce. Prospective home entrants in period t compute theirexpected postentry value given by the present discounted value oftheir expected stream of profits {ds}s�t�1

� :

15. dt and d*t represent average firm profit levels in the sense that dt � �zmin�

dt( z)dG( z) and d*t � �zmin� d*t( z)dG( z). See Melitz [2003] for proofs.


(2) vt � Et �s�t�1

�

��1 � ��s�t�Cs

Ct��

ds.

This also represents the average value of incumbent firms afterproduction has occurred (since both new entrants and incum-bents then face the same probability 1 � � of survival andproduction in the subsequent period). Firms discount futureprofits using the household’s stochastic discount factor, ad-justed for the probability of firm survival 1 � �. Entry occursuntil the average firm value is equalized with the entry cost,leading to the free entry condition vt � wtfE,t/Zt. This conditionholds so long as the mass NE,t of entrants is positive. Weassume that macroeconomic shocks are small enough for thiscondition to hold in every period. Finally, the timing of entryand production we have assumed implies that the numberof home-producing firms during period t is given by ND,t �(1 � �)(ND,t�1 � NE,t�1). Similar free entry condition, require-ment on the size of shocks, and law of motion for the number ofproducing firms hold in the foreign country.

III.E. Parameterization of Productivity Draws

In order to solve our model, we parameterize the distributionof firm productivity draws G( z). We assume that productivity z isdistributed Pareto with lower bound zmin and shape parameterk � � 1: G( z) � 1 � ( zmin/z)k. The assumption of a Paretodistribution for productivity induces a size distribution of firmsthat is also Pareto, which fits firm-level data quite well. k indexesthe dispersion of productivity draws: dispersion decreases as kincreases, and the firm productivity levels are increasingly con-centrated toward their lower bound zmin.16 Letting � � {k/[k �( � 1)]}1/(�1), the average productivities zD and zX,t are givenby zD � �zmin and zX,t � �zX,t. The share of home-exporting firmsis then NX,t/ND,t � 1 � G( zX,t) � (�zmin/zX,t)

k, and the zeroexport profit condition (for the cutoff firm), dX,t( zX,t) � 0, impliesthat average export profits must satisfy dX,t � ( � 1)(��1/k)wtfX,t/Zt. Analogous results hold for z*X,t, N*X,t/N*D,t, and d*X,t.

16. The standard deviation of log productivity is equal to 1/k. The conditionthat k � � 1 ensures that the variance of firm size is finite.


III.F. Household Budget Constraint and Intertemporal Choices

Households in each country hold two types of assets: sharesin a mutual fund of domestic firms and domestic, risk-free bonds.(We assume that bonds pay risk-free, consumption-based realreturns.) We now focus on the home economy. Let xt be the sharein the mutual fund of home firms held by the representative homehousehold entering period t. The mutual fund pays a total profitin each period (in units of home currency) that is equal to theaverage total profit of all home firms that produce in that period,PtdtND,t. During period t, the representative home householdbuys xt�1 shares in a mutual fund of NH,t � ND,t � NE,t homefirms (those already operating at time t and the new entrants).Only ND,t�1 � (1 � �) NH,t firms will produce and pay dividendsat time t � 1. Since the household does not know which firms willbe hit by the exogenous exit shock � at the very end of period t, itfinances the continuing operation of all preexisting home firmsand all new entrants during period t. The date t price (in units ofhome currency) of a claim to the future profit stream of themutual fund of NH,t firms is equal to the average nominal price ofclaims to future profits of home firms, Ptvt.

The household enters period t with bond holdings Bt in unitsof consumption and mutual fund share holdings xt. It receivesgross interest income on bond holdings, dividend income on mu-tual fund share holdings and the value of selling its initial shareposition, and labor income. The household allocates these re-sources between purchases of bonds and shares to be carried intonext period and consumption. The period budget constraint (inunits of consumption) is

(3) Bt�1 � vtNH,txt�1 � Ct � �1 � rt� Bt � �dt � vt� ND,txt � wtL,

where rt is the consumption-based interest rate on holdings ofbonds between t � 1 and t (known with certainty as of t � 1). Thehome household maximizes its expected intertemporal utilitysubject to (3).

The Euler equations for bond and share holdings are

�Ct�� 1 � rt�1� Et��Ct�1�

��,

vt � ��1 � �� Et��Ct�1

Ct��

�vt�1 � dt�1�� .


As expected, forward iteration of the equation for share holdingsand absence of speculative bubbles yield the asset price solutionin equation (2).17

III.G. Aggregate Accounting and Balanced Trade

Aggregating the budget constraint (3) across (symmetric)home households and imposing the equilibrium conditions underfinancial autarky (Bt�1 � Bt � 0 and xt�1 � xt � 1) yields theaggregate accounting equation Ct � wtL � ND,tdt � NE,tvt. Asimilar equation holds abroad. Consumption in each period mustequal labor income plus investment income net of the cost ofinvesting in new firms. Since this cost NE,tvt is the value of homeinvestment in new firms, aggregate accounting also states thefamiliar equality of spending (consumption plus investment) andincome (labor plus dividend) that must hold under financial au-tarky. To close the model, observe that financial autarky impliesbalanced trade: the value of home exports must equal the value offoreign exports. Hence, QtNX,t(�X,t)

1�C*t � N*X,t(�*X,t)1�Ct.

III.H. Summary

Table I summarizes the main equilibrium conditions of themodel. The equations in the table constitute a system of nineteenequations in nineteen endogenous variables: wt, w*t, dt, d*t, NE,t,N*E,t, zX,t, z*X,t, ND,t, N*D,t, NX,t, N*X,t, rt, r*t, vt, v*t, Ct, C*t, Qt.Of these endogenous variables, four are predetermined as of timet: the total numbers of firms at home and abroad, ND,t and N*D,t,and the risk-free interest rates, rt and r*t. Additionally, the modelfeatures eight exogenous variables: the aggregate productivitiesZt and Z*t, and the policy variables fE,t, f *E,t, fX,t, f *X,t, t, *t. Weinterpret changes in fE,t and f *E,t as changes in market regulationfacing a country’s firms in the respective domestic markets andchanges in fX,t, f *X,t, t, and *t as changes in trade policy. SincefX,t and t are trade costs facing home firms, they are best inter-preted as the foreign government’s trade policy instruments.

17. We omit the transversality conditions for bonds and shares that must besatisfied to ensure optimality. The foreign household maximizes its utility func-tion subject to a similar budget constraint, resulting in analogous Euler equationsand transversality conditions.


IV. THE REAL EXCHANGE RATE AND THE

HARROD-BALASSA-SAMUELSON EFFECT

Up to now, we have used a definition of the real exchangerate, Qt � εtP*t/Pt, computed using welfare-based price indexes(Pt and P*t). Under C.E.S. product differentiation, it is well-

TABLE IMODEL SUMMARY—FINANCIAL AUTARKY

Price indexesND,t(�D,t)

1� � N*X,t(�*X,t)1� � 1

N*D,t(�*D,t)1� � NX,t(�X,t)

1� � 1

Profitsdt � dD,t �

NX,t

ND,tdX,t

d*t � d*D,t �N*X,t

N*D,td*X,t

Free entryvt � wt

fE,t

Zt

v*t � w*tf*E,t

Z*t

Zero-profit export cutoffsdX,t � wt

fX,t

Zt

� 1k � � � 1�

d*X,t � w*tf*X,t

Z*t

� 1k � � � 1�

Share of exporting firms

NX,t

ND,t� �zmin�

k�zX,t��k� k

k � � � 1��k/��1�

N*X,t

N*D,t� �zmin�

k�z*X,t��k� k

k � � � 1��k/��1�

Number of firmsND,t � (1 � �)(ND,t�1 � NE,t�1)N*D,t � (1 � �)(N*D,t�1 � N*E,t�1)

Euler equation (bonds)(Ct)

�� (1 � rt�1)Et[(Ct�1)��](C*t)

�� (1 � r*t�1)Et[(C*t�1)��]

Euler equation (shares)vt � ��1 � ��Et��Ct�1

Ct��

�vt�1 � dt�1��v*t � ��1 � ��Et��C*t�1

C*t��

�v*t�1 � d*t�1��Aggregate accounting

Ct � wtL � ND,tdt � NE,tvt

C*t � w*tL* � N*D,td*t � N*E,tv*tBalanced trade QtNX,t(�X,t)

1�C*t � N*X,t(�*X,t)1�Ct

In the equations above, it must be understood that the average real prices and profits/dividends arefunctions of the average productivity levels (as previously defined): �D,t � �D,t( zD), �X,t � �X,t( zX,t), dD,t �dD,t( zD), dX,t � dX,t( zX,t). The same applies for the average foreign real prices and profits/dividends. (2) Thezero-profit export cutoff conditions hold only when fX,t and f *X,t are strictly positive. If all firms export (i.e.,if fX,t � f *X,t � 0), then these conditions must be replaced with zX,t � z*X,t � zD. The same is true in the bondtrading case.


known that these price indexes can be decomposed into com-ponents reflecting average prices and product variety: Pt �Nt

1/(1� )Pt and P*t � (N*t)1/(1� )P*t, where Nt � ND,t � N*X,t

(N*t � N*D,t � NX,t) reflects product variety at home (foreign) andPt (P*t) is an average nominal price for all varieties sold in home(foreign).18 These average prices (Pt, P*t) correspond much moreclosely to empirical measures such as the CPI then the welfare-based indexes.19 Thus, we define Qt � εtP*t/Pt as the theoreticalcounterpart to the empirical real exchange rate—since the latterrelates CPI levels best represented by Pt and P*t. This real ex-change rate deviates from the previously defined welfare-basedmeasure Qt due to relative changes in product variety: Qt �(Nt/N*t)

1/(�1)Qt. The differences between these two exchangerates can best be described using an example: Qt � 1 implies thataverage prices (expressed in a common currency) are higher inthe home market. On the other hand, Qt measures differences ina consumer’s welfare derived from spending a given nominalamount in each market (where the amount is converted at thenominal exchange rates). It is then possible for Qt � 1 even ifQt � 1, which implies that the consumer derives higher utilityfrom spending the same amount in the home market with higherprices. This would be the case so long as product variety in thehome market Nt is sufficiently above that in the foreign marketN*t. Our simulations will highlight such divergences between thereal exchange rate (comparing CPI levels) and the welfare-basedmeasure—driven by the crucial contribution of product varietydifferentials across countries.20

As we highlighted in the introduction, we will analyze ourmodel’s predictions for deviations (both permanent and transi-tory) from PPP in response to aggregate shocks. These will begiven by the impulse responses for Qt. In order to understand

18. Pt is a weighted average of pD,t and p*X,t, the average prices of domesticgoods and imports paid by home consumers, where the weights are proportionalto the relative consumption levels of both types of goods. Similarly, P*t is aweighted average of p*D,t and pX,t.

19. Feenstra [1994] develops a similar decomposition (also allowing for pref-erence asymmetries between varieties) to address empirically the impact of in-creasing product variety. Broda and Weinstein [2003] also use this decompositionfor U. S. import prices and find that increases in imported product varietysignificantly contribute to unmeasured welfare benefits for U. S. consumers.

20. We do not address the growth effects of changes in product variety. Bilsand Klenow [2001] document that these effects are empirically relevant for theUnited States.


how and why Qt may deviate from 1, we use the price indexequations to write it in the following way:

(4) Qt1� � �N*D,t

N*t�TOLt�

1� �NX,t

N*t� t

zD

zX,t� 1��

�ND,t

Nt�

N*X,t

Nt�TOLt *t

zD

z*X,t� 1�� ,

defining TOLt � εt(W*t/Z*t)/(Wt/Zt) as the “terms of labor.”21

TOLt measures the relative cost of effective units of labor acrosscountries. A decrease in TOLt indicates an appreciation of homeeffective labor relative to foreign: if TOLt � 1, a firm with givenproductivity z could produce any amount of output at lower costin the foreign country than in home. Note that, absent trade costs,PPP would always hold: Qt � 1, @t.22

Dropping time subscripts to denote a variable’s level insteady state, we assume that fE � f *E, fX � f *X, � *, L �L* � 1, Z � Z* � 1. In a technical appendix available onrequest, we demonstrate existence and uniqueness of a symmet-ric steady state under these assumptions where Q � Q � TOL �1. Using sans-serif fonts to denote percentage deviations fromthis steady state, log-linearizing (4) yields

(5) Qt � �2sD � 1�TOLt � �1 � sD)[(zX,t�z*X,t� � (tt � t*t )]

�1

� 1 � ND

ND � NX� sD��N*D,t � NX,t) � (ND,t � N*X,t)] ,

where sD is the steady-state share of spending on domestic goods(sD,t � ND,t(�D,t)

1�) and tt(t*t ) denotes the percentage deviationof t ( *t) from the steady state. Equation (5) highlights threeimportant channels for real exchange rate changes: 1) given the

21. This is related to the double factorial terms of trade. The two concepts aredistinct because our measure adjusts for the productivity of all labor, not just theproductivity in the export and import sectors (which are endogenous in ourmodel).

22. When fX,t � f *X,t � 0, all firms export: NX,t � ND,t, and N*X,t � N*D,t. If,in addition, t � *t � 1, it is immediate from (4) that Qt � 1 (and hence Qt � 1).Note that this property does not imply that there can be no movements in theterms of trade. Absent trade costs, balanced trade under financial autarky wouldimply that Tt

�1(Ct/C*t) � ND,t/N*D,t, where Tt � εtpX,t/p*X,t denotes the averageterms of trade. With constant numbers of firms at home and abroad, as in morestandard macroeconomic models, Tt

�1(Ct/C*t) is constant. Hence, shocks thatcause the consumption differential Ct/C*t to increase (such as an increase in homeproductivity) always result in a deterioration of the terms of trade—leaving Qt �Qt � 1, @t. In our model, firm entry dampens this deterioration of the terms oftrade. (We discuss terms of trade dynamics in our model in Section V.)


existence of a nontraded sector under costly trade (which impliesthat sD � 1/ 2), changes in the relative cost of labor (TOLt) leadto relative price differences for nontraded goods across countries.2) Changes in relative import prices. These can happen exoge-nously when tariffs change, but more importantly, these relativeprices endogenously change with relative changes in the exportproductivity cutoffs (driven by entry and exit decisions for theexport market).23 3) An expenditure switching channel. Plausibleparameter values imply that ND/(ND � NX) � sD in the sym-metric steady state. This will be the case whenever average pricespD � p*D, which include the high prices of the least productivefirms that do not export, are higher than average import pricespX � p*X.24 Changes in the relative availability of domestic andimported varieties (ND,t/N*X,t and N*D,t/NX,t) then induce expen-diture switching effects for the real exchange rate.

The endogenous HBS effect mentioned in the introductionoccurs through all three of these channels, reinforcing the realexchange rate appreciation in response to increases in aggregateproductivity or deregulation. Before analyzing the full responsepath of Qt and other key endogenous variables to these shocks, wefirst describe the long-run effects of permanent changes in pro-ductivity and deregulation. These effects also highlight steady-state differences for an asymmetric version of our model.

Consider a permanent increase in home productivity Zt or apermanent decrease in home entry costs fE,t (which we interpretas permanent deregulation as in Blanchard and Giavazzi [2003]).Relative to the old steady state, the home market becomes a moreattractive location for prospective entrants. (When productivityincreases, the home market becomes more attractive due to itsincreased size. The standard “home market effect” of new tradetheory models with trade costs then implies that home attracts abigger share of firms than its relative size in the world econ-

23. Since the average export productivity level zX,t is proportional to thecutoff zX,t, their percentage changes from steady-state levels are identical. Thesame holds for z *X,t and z*X,t. Statistical agencies typically do not adjust priceindexes to reflect differences in the price levels of new goods. Thus, the contribu-tion of the newly imported goods to the aggregate relative price Qt would gounmeasured (except when price hedonics are used). However, this particularchannel is not crucial in generating changes in Qt.

24. This condition is equivalent to zX � zD: the productivity advantage ofexporters is larger than the iceberg export cost.


omy.25) Absent any change in the relative cost of effective labor(TOLt), all new firms would only enter the home market (therewould be no new entrants into the foreign market). Thus, in thenew long-run equilibrium, home effective labor units must appre-ciate (TOLt decreases) in order to keep foreign labor employed.26

This causes the relative price of nontraded goods at home toincrease relative to foreign (the first channel for real exchangerate appreciation). The higher relative labor costs at home reducethe export profitability of home firms, and conversely increasethat of foreign firms. Hence, the export cutoff for home firms, zX,t,rises (only relatively more productive home firms export) and thecutoff for foreign firms, z*X,t, drops (relatively less productiveforeign firms can now profitably export). This induces an increasein the average price of home imports relative to the average priceof foreign imports (the second channel for appreciation).27 Last,the increase in the number of domestic varieties relative to for-eign ones available to home consumers (generated by entry intothe more attractive market) induces those consumers to switchtheir expenditures toward home-produced goods (whose prices, onaverage, are higher than imported goods). This is the third chan-nel for real exchange rate appreciation.28

All three channels generating the endogenous HBS effect inour model critically depend on the incorporation of endogenousentry (and the associated endogenous location of new firms acrosscountries). It is this key feature that generates the appreciation ofhome labor in response to the accelerated entry of firms in therelatively more favorable business environment at home. Withoutthis feature, home effective labor would depreciate in response toa favorable aggregate productivity shock at home (when the num-ber of firms is fixed, the increased demand by home consumers forforeign varieties—whose productivity remains unchanged—leadsto an excess demand for foreign labor). We highlight this property

25. Without trade costs, entry in the home economy relative to foreign in thenew long-run equilibrium would be directly proportional to the change in relativemarket size.

26. Absent entry into the foreign country, the number of foreign producingfirms would steadily decrease with the “death” shock.

27. After an increase in home productivity, the total number of home export-ers NX,t is higher in the new long-run equilibrium (compared with the initialsteady state). However, relatively less productive home exporters have droppedout of the export market.

28. Foreign consumers also switch their expenditures between domestic andimported varieties. The direction depends on the type of shock (productivityincrease versus deregulation) but the effect is always dominated by the expendi-ture switching for home consumers.


in our dynamic simulations. Although our model also captures anadditional channel for real exchange rate appreciation via en-dogenous nontradedness, the appreciation of home effective laboralong with an exogenous nontraded sector is enough to generatereal exchange rate appreciation and the HBS effect.

Our model also provides a new explanation for the pervasiveevidence that real exchange rate appreciations are associatedwith increases in the cross-country relative price of tradablegoods (usually referred to as traded goods). This does not precludethe contribution of the traditional HBS channel. If there areexogenously nontradable sectors whose productivity lags behindthe tradable sector, the traditional mechanism operates, ampli-fying the appreciation.

We conclude this section with two important observations.First, when product variety is endogenous, an appreciation inaverage relative prices (Qt decreases) need not lead to an appre-ciation of the welfare-based real exchange rate Qt: the simula-tions described in the next section show that the relative increasein product variety at home overwhelmingly dominates the in-crease in average prices, leading to a depreciation of this welfare-based index. Second, equation (4) and its log-linear counterpart(5) do not depend on the assumption of financial autarky. Inparticular, these equations still hold when we introduce interna-tional bond trading—and would also hold under other assump-tions on asset markets. The international-bond-trading scenariowill thus feature the same three channels for real exchange ratedynamics.

V. INTERNATIONAL TRADE AND MACROECONOMIC DYNAMICS

We now analyze the full response path of the real exchangerate and other key variables in response to permanent and tran-sitory shocks to productivity, and permanent deregulation.29 Todo so, we log-linearize the system of equilibrium conditions inTable I around the unique symmetric steady state under assump-tions of log-normality and homoskedasticity of exogenous sto-chastic shocks. We calibrate parameters, compute the impliedsteady-state levels of endogenous variables, and numerically

29. We discuss the consequences of worldwide trade liberalization in theAppendix.


solve for the dynamic responses to exogenous shocks using themethod of undetermined coefficients.

V.A. Calibration

We calibrate parameters as follows. We interpret periods asquarters and set � � .99 and � � 2—both standard choices forquarterly business cycle models. We set the size of the exogenousfirm exit shock � � .025 to match the U. S. empirical level of 10percent job destruction per year.30 We use the value of fromBernard, Eaton, Jensen, and Kortum [BEJK 2003] and set �3.8, which was calibrated to fit U. S. plant and macro trade data.BEJK also report that the standard deviation of log U. S. plantsales is 1.67. In our theoretical model, this standard deviation isequal to 1/(k � � 1). The choice of � 3.8 then implies that k �3.4 (this satisfies the requirement k � � 1). We postulate that � 1.3, roughly in line with Obstfeld and Rogoff [2001], and setthe steady-state fixed export cost fX such that the proportion ofexporting plants matches the number reported in BEJK (21 per-cent). This leads to a fixed export cost fX equal to 23.5 percent ofthe per-period, amortized flow value of the entry cost, [1 � �(1 ��)]/[�(1 � �)] fE.31 Changing the entry cost fE while maintain-ing the same ratio fX/fE does not affect any of the impulse re-sponses.32 We therefore set fE to 1 without loss of generality. Forsimilar reasons, we normalize zmin to 1. Our calibration impliesthat exporters are on average 58.2 percent more productive thannonexporters. The steady-state share of expenditure on domesticgoods is .733, and the share of expenditure on nontraded domesticgoods is .176. The relative size differential of exporters relative tononexporters in the domestic market is 3.61.

It may be argued that the value of results in a steady-statemarkup that is too high relative to the evidence. A standardchoice in the macro literature is � 6 to deliver a 20 percent

30. Empirically, job destruction is induced by both firm exit and contraction.In our model, the “death” shock � takes place at the product level. In a multiprod-uct firm, the disappearance of a product generates job destruction without firmexit. Since we abstract from the explicit modeling of multiproduct firms, weinclude this portion of job destruction in �.

31. We tried using different values of (1.1, 1.2, 1.25) and recalculated fXrelative to fE to match the 21 percent of exporting plants. The impulse responseswere very similar in all cases.

32. The total number of firms in steady state is inversely proportional tofE—and the size and value of all firms are similarly proportional to fE. Basically,changing fE for given ratio fX/fE amounts to changing the unit of measure foroutput and number of firms.


markup of price over marginal cost [Rotemberg and Woodford1992]. However, it is important to observe that, in models withoutany fixed cost, /( � 1) is a measure of both markup over mar-ginal cost and average cost. In our model with entry costs, freeentry ensures that, on average, firms earn zero profits net of theentry cost. This means that, on average, firms price at averagecost (inclusive of the entry cost). The markup over average costincreases with firm productivity. The firm with productivity zminalways prices below average cost: the net present value of itsprofits does not cover the entry cost. Thus, although � 3.8implies a fairly high markup over marginal cost, our parameter-ization delivers reasonable markups over average costs.

V.B. Impulse Responses

Figures I and II show the responses (percent deviations fromsteady state) to a permanent 1 percent increase in home produc-tivity and a permanent 1 percent decrease in home entry costs.The number of years after the shock is on the horizontal axis.Consider first the long-run effects in the new steady state. As waspreviously described, the home market becomes a relatively moreattractive business environment, drawing a permanently highernumber of entrants, which translates into a permanently highernumber of producers. This induces the new steady state for TOLtbelow 1. This appreciation of home labor costs (which raises therelative costs of home exporters and decreases those of foreignexporters) leads to a long-run increase in zX,t and a decrease inz*X,t. These effects combine to induce a long-run appreciation ofthe real exchange rate Qt. However, our simulations suggest thatthe increase in product variety for home consumers dominatesthis average price appreciation, leading to a depreciation of thewelfare-based index Qt. Thus, consumers in both countries wouldrather spend a given nominal expenditure in the home market,even though average prices there are relatively higher.33

We now describe the transitional changes in response to thepermanent home productivity increase (summarized by the im-pulse responses in Figure I). Absent sunk entry costs, and theassociated time-to-build lag before production starts, the numberof producing firms ND,t would immediately adjust to its new

33. We have experimented with numerous different parameter choices, andalways obtained this long-run dichotomy between the real exchange rate Qt andits welfare-based counterpart Qt.


FIG

UR

EI

Res

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seto

Per

man

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ZS

hoc

k(F

inan

cial

Au

tark

y)


FIG

UR

EII

Res

pon

seto

Per

man

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f ES

hoc

k(F

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steady-state level. Sunk costs and time-to-build transform ND,tinto a state variable that behaves very much like a capital stock:the number of entrants NE,t represents the home consumers’investment, which translates into increases in the stock ND,t overtime. The immediate impact of the productivity increase on TOLt(which increases) is typical of open economy, macroeconomic mod-els without entry (with or without capital): there is an immediateincrease in demand for all existing goods (domestic and foreign)sold in the home market. The increase in home labor productivitythen translates into an excess supply of home effective labor unitsrelative to foreign—whose productivity is unchanged. The result-ing short-run depreciation of home labor then leads to a short-rundecrease in the home export cutoff zX,t and a short-run deprecia-tion of the real exchange rate Qt. The foreign export cutoff fallsnonetheless, as the short-run increase in the foreign exporters’relative cost is dominated by the increase in home demand (for allexisting goods, including imports). The numbers of home andforeign exporters, NX,t and N*X,t, increase on impact as the exportproductivity cutoffs fall. From this point on, the number of homeproducers ND,t steadily increases; this steadily shifts the increasein home demand toward domestic varieties (and away from for-eign varieties). The effect of endogenous entry is crucial, as thelabor demand generated by a greater number of home firmstranslates into an appreciation of home labor units, reversing theinitial change in TOLt, zX,t, and the real exchange rate Qt. Entryof new domestic firms pushes NX,t upward, but the reversal in thedynamics of zX,t has the opposite effect. The net result is that NX,tsettles at a higher level than in the initial steady state: the largernumber of more productive home firms ensures that NX,t ishigher even if relatively less productive exporters have droppedout. Yet, the long-run response of NX,t is smaller than the short-run effect as the less productive exporters drop out during thetransition.

The path of endogenous variables in Figure I highlights theimportance of the microeconomic dynamics in our model relativeto the standard setup with a constant number of firms: absententry, TOLt would remain depreciated in the long run, as wouldQt.

34 Note that, even though prices are fully flexible, the realexchange rate appreciation takes a long time to unfold, reaching

34. When we allow for international trade in bonds, the accelerated entry offirms in the home market financed by borrowing causes TOLt to appreciate also


less than half of its long-run appreciation within five years of thepermanent productivity increase.

In our model, endogenous entry also crucially affects theevolution of the terms of trade. In models with a constant numberof firms, the induced excess demand for foreign labor and depre-ciation in TOLt are also manifested in a strong deterioration ofhome’s terms of trade. This prediction is hard to square with theempirical evidence that suggests a link between productivitygains and improvements in a country’s terms of trade.35 Ourmodel shows how the entry of new producers and varieties in themore productive economy may dampen or even reverse the dete-rioration in the terms of trade. In particular, for any given homeand foreign exporters with productivity z and z* (whose tradestatus does not change with the productivity shock), the relativeprice Tt � εtpX,t( z)/p*X,t( z*) � ( z*/z)( t/ *t)TOLt

�1 increases(due to the appreciation in TOLt)—except initially.36

We now turn to the transitional changes in response to per-manent deregulation (summarized by the impulse responses inFigure II). In contrast to the previous scenario, deregulation doesnot increase the available supply of effective labor units for pro-duction in the home market. Thus, there is no short-run excesssupply of home effective labor units, and TOLt steadily appreci-ates over time with the increase in home labor demand generatedby entry (the appreciation in TOLt is therefore amplified relativeto the productivity scenario). There is thus no reversal in thepaths of TOLt, zX,t, and Qt. The response in the number of homeexporters NX,t reflects the opposing effects of the increase in thetotal number of producers ND,t and the increase in the exportproductivity cutoff zX,t. The immediate increase in the lattercauses NX,t to fall on impact. Subsequently, since the increase inzX,t is amplified relative to the productivity scenario (due to theamplified appreciation in TOLt), its effect dominates the effect of

in the short run. There is then no reversal in the paths of TOLt, zX,t, and Qt. Wedescribe this in further detail in the following section.

35. For instance, see Corsetti, Dedola, and Leduc [2004].36. The initial deterioration of Tt is much shorter-lived when the productivity

increase is not permanent. The average terms of trade Tt � εtpX,t/p*X,t � ( z*X,t/zX,t)( t/ *t)TOLt

�1 decreases in our exercise due to the dominating effect of thechange in the composition of exports (driven by the changes in the cutoffs zX,t andz*X,t). Nevertheless, as previously mentioned, this deterioration is dampenedrelative to the case where the number of home producers is fixed. Gagnon [2003]finds strong empirical support for the positive effect of entry on the terms of trade,first analyzed by Krugman [1989].


higher ND,t, leading to a further decrease in NX,t. Another majordifference in the current scenario is that home consumption de-creases in the short run, in order to finance the entry of new firms(this requires a much greater reallocation of effective labor unitsaway from production as the supply of these labor units is unaf-fected by deregulation). The initial decrease in home import de-mand leads to an initial increase in the foreign export productiv-ity cutoff z*X,t and an associated decrease in the number of foreignexporters. These changes are reversed as home consumption re-covers. As was the case with the productivity increase, we notethat the real exchange rate appreciation is slow to unfold. Again,less than half of the long-run appreciation occurs within fiveyears of the permanent deregulation shock.

We further illustrate the endogenous persistence propertiesof our model by showing the impulse responses to a transitoryincrease in home productivity. These responses are illustrated inFigure III, where Zt � .9Zt�1, @t � 0. As the responses clearlyshow, the shock has no permanent effect since all endogenousvariables are stationary in response to stationary exogenousshocks. However, the responses also clearly highlight the sub-stantial persistence of key endogenous variables—well beyondthe exogenous .9 persistence of the productivity shock. Approxi-mately 84 percent of the initial increase in productivity has beenreabsorbed ten years after the shock. At that point in time, thereal exchange rate Qt still needs to cover roughly half the dis-tance between the peak appreciation (which happens approxi-mately four years after the shock) and the steady state.37

A large literature has developed in the past few years striv-ing to explain empirical real exchange rate movements withmodels that feature nominal rigidity and local currency pricing(see Chari, Kehoe, and McGrattan [2002] and references therein).The success has been, at best, mixed (especially for models withmonopolistic competition that—like ours—are best interpreted asone-sector models and should thus explain persistence in sectoralrelative prices). Plausible degrees of nominal rigidity and localcurrency pricing (supported by the assumption of market segmen-

37. Although persistence .9 is already low by RBC standards, this result isrobust to lower persistence of the productivity shock. If Zt � .5Zt�1, @t � 0, 99percent of the shock has died out within two years, while Qt still needs to covermore than half the distance to the steady state after five years. Qt is roughlyhalfway to the steady state even five years after a zero-persistence shock. The re-sult also does not depend on the presence of a steady-state iceberg cost � * � 1. A similarly persistent deviation from PPP happens if � * � 1.


FIG

UR

EII

IR

espo

nse

toT

ran

sito

ryZ

Sh

ock

(Fin

anci

alA

uta

rky)


tation) succeed in generating volatile real exchange rates, butonly special assumptions deliver persistence in line with the data.Benigno [2004] highlights inertia in endogenous interest ratesetting by central banks and differences in nominal rigidity assources of real exchange rate persistence. Burstein, Neves, andRebelo [2003] and Corsetti and Dedola [forthcoming] incorporatea nontraded distribution sector, pointing to structural featuresbeyond nominal rigidity that matter for real exchange rate dy-namics. We propose a different mechanism that delivers substan-tial real exchange rate persistence in response to transitoryshocks: firm entry and reallocation in and out of markets in aworld of flexible prices.

VI. INTERNATIONAL TRADE IN BONDS

We now extend the model of Section III to allow for interna-tional trade in bonds. We study how international bond tradingaffects the results we have previously described and how our newmicroeconomic dynamics affect the current account. Since theextension to international borrowing and lending does not involveespecially innovative features relative to the financial autarkysetup, we herein limit ourselves to describing its main ingredi-ents in words and present the relevant model equations in theAppendix.

We assume that agents can trade bonds domestically andinternationally. Home bonds, issued by home households, aredenominated in home currency. Foreign bonds, issued by foreignhouseholds, are denominated in foreign currency. We maintainthe assumption that nominal returns are indexed to inflation ineach country, so that bonds issued by each country provide arisk-free, real return in units of that country’s consumption bas-ket. International asset markets are incomplete, as only risk-freebonds are traded across countries. In the absence of any otherchange to our model, this would imply indeterminacy of steady-state net foreign assets and nonstationarity. The choice of initialconditions would then become a matter of convenience, and allshocks would have permanent consequences via wealth realloca-tion across countries (regardless of the nature of the distur-bances). Such a setup would undermine the reliability of log-linear approximation and the validity of stochastic analysis. (Ghi-roni [2000] discusses the issue in detail.) To solve this problem,we assume that agents must pay fees to domestic financial inter-


mediaries when adjusting their bond holdings. We assume thatthese fees are a quadratic function of the stock of bonds. Thisconvenient specification is sufficient to uniquely pin down thesteady state and deliver stationary model dynamics in responseto temporary shocks. Realistic choices of parameter values implythat the cost of adjusting bond holdings has a very small impacton model dynamics, other than pinning down the steady stateand ensuring mean reversion in the long run when shocks aretransitory.38

We assume that financial intermediaries rebate the revenuesfrom bond-adjustment fees to domestic households. In equilib-rium, the markets for home and foreign bonds clear, and eachcountry’s net foreign assets entering period t � 1 depend oninterest income from asset holdings entering period t, labor in-come, net investment income, and consumption during period t.The change in asset holdings between t and t � 1 is the country’scurrent account. Home and foreign current accounts add to zerowhen expressed in units of the same consumption basket. Thereare now three Euler equations in each country: the Euler equa-tion for share holdings, which is unchanged, and Euler equationsfor holdings of domestic and foreign bonds. The fees for adjustingbond holdings imply that the Euler equations for bond holdingsfeature a term that depends on the stock of bonds—a key ingre-dient delivering determinacy of the steady state and model sta-tionarity. Euler equations for bond holdings in each country im-ply a no-arbitrage condition between bonds. In the log-linearmodel, this no-arbitrage condition relates (in a standard fashion)the real interest rate differential across countries to expecteddepreciation of the consumption-based real exchange rate.

The balanced trade condition closed the model under finan-cial autarky. Since trade is no longer balanced under interna-tional bond trading, we must explicitly impose labor marketclearing conditions in both countries.39 These conditions statethat the amount of labor used in production and to cover entrycosts and fixed export costs in each country must equal laborsupply in that country in each period. The costs of adjusting bond

38. Under financial autarky, introducing costs of adjusting bond holdings ofthe type we consider would have no effect on the system of equilibrium conditionsin Table I, since holdings of bonds are always zero in equilibrium.

39. In the technical appendix we show that, under financial autarky, bal-anced trade implies labor market clearing in each country.


holdings imply zero holdings (of both domestic and foreign bonds)in the unique symmetric steady state. Thus, the extended modelwith international bond trading features exactly the same steadystate as the model under financial autarky. As before, we log-linearize the system and solve it using the method of undeter-mined coefficients.40 We set the scale parameter for the bondadjustment cost to .0025—sufficient to generate stationarity inresponse to transitory shocks but small enough to avoid overstat-ing the role of this friction in determining the dynamics of ourmodel.

VI.A. Impulse Responses

We consider the same productivity and deregulation shocksas under financial autarky. Figure IV shows impulse responses toa permanent 1 percent increase in home productivity. The re-sponse of several key variables to the shock is qualitatively simi-lar to that under financial autarky. The permanent nature of theshock implies that home households do not have an incentive toadjust their net foreign asset position to smooth the effect of atransitory fluctuation in income. The path of C is therefore verysimilar to that in Figure I.

The home economy runs a current account deficit in responseto the shock and accumulates net foreign debt.41 Home house-holds borrow from abroad to finance higher initial investment(relative to autarky) in new home firms. This is apparent in thedifferent responses of NE,t in the initial years after the shock(Figure IV relative to Figure I). The home household’s incentiveto front-load entry of more productive firms is mirrored by theforeign household’s desire to invest savings in the more attractiveeconomy. Although foreign households cannot hold shares in themutual portfolio of home firms (since only bonds can be tradedacross countries), the return on bond holdings is tied to the returnon holdings of shares in home firms by no-arbitrage betweenbonds and shares within the home economy. Therefore, foreign

40. Since steady-state holdings of bonds are zero, the percentage deviationsof bond stocks from the steady state (used in the log-linearization) are normalizedusing the steady-state level of consumption (for instance, Bt�1 � dBt�1/C).Similar normalizations are applied for the current account and the trade balance.

41. In Figure IV, ca denotes the current account. The impulse response of theasset stock a cumulates holdings of domestic and foreign bonds. It shows the levelof a at the end of each period. The response of the trade balance (omitted) issimilar to that of the current account in all the examples we consider.


FIG

UR

EIV

Res

pon

seto

Per

man

ent

ZS

hoc

k(I

nte

rnat

ion

alB

ond

Tra

din

g)


households share the benefits of higher home productivity vialending.42

As in the case of financial autarky, TOL must decrease in thelong run (home effective labor must relatively appreciate); other-wise, all new entrants would choose to locate in the home econ-omy. The accelerated entry of new home firms induces an imme-diate relative increase in home labor demand and TOLt no longerdepreciates in the short run. Thus, the real exchange rate Qt alsoappreciates in the short run—in response to the appreciation ofTOLt and the relative increase in average home import prices(which now occurs also in the short run). The opening of theeconomy to international asset trading does not qualitativelychange the functioning of the endogenous HBS mechanism in ourmodel. As in the case of financial autarky, the welfare-basedrelative price index depreciates due to the dominating effect ofincreased product variety at home (relative to foreign).

Figure V shows impulse responses to deregulation of thehome market. The comparison with the case of financial autarkyin Figure II is similar to what we described concerning a produc-tivity shock. Home households borrow from abroad to front-loadentry of new firms in the more favorable home market. The homecountry runs a current account deficit, and accumulates foreigndebt. Home consumption initially declines and is permanentlyhigher in the long run. Foreign consumption moves by more thanin Figure II as foreign households initially save in the form offoreign lending and then receive income from their positive assetposition. The terms of labor, TOLt, and the real exchange rate Qtappreciate in both the short run and the long run. Again, thewelfare-based relative price index Qt depreciates.

Dynamics in response to a productivity shock with persis-tence .9 are qualitatively similar to those under financial au-tarky; thus, we omit the figure. As in the case of a permanentshock, an important difference is the absence of an initial depre-ciation of the terms of labor, again motivated by faster entry ofnew firms into the home economy. Home households borrow ini-tially to finance faster entry. However, borrowing is quickly re-versed, and home runs current account surpluses for approxi-mately seven years after the initial response. The path of the

42. Note that foreign lending also entails less investment in the foreignmarket, and a consequent larger initial drop in the number of new foreignentrants N*E,t.


FIG

UR

EV

Res

pon

seto

Per

man

ent

f ES

hoc

k(I

nte

rnat

ion

alB

ond

Tra

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g)


current account is such that home’s net foreign assets are actu-ally above the steady state throughout the transition, except inthe initial few quarters. When the shock is not permanent, lend-ing abroad to smooth the consequences of a temporary, favorableshock on consumption becomes the main determinant of net for-eign asset dynamics.

VI.B. International Business Cycles

Backus, Kehoe, and Kydland [BKK 1992] show that intro-ducing trade costs in an international RBC model improves itsability to replicate second moments of U. S. and internationaldata. They specify a resource cost of trade as a quadratic functionof net exports. However, the introduction of such trade costs intheir model does not resolve the counterfactual prediction thatconsumption is more strongly correlated across countries thanaggregate output (the consumption-output anomaly). Backus andSmith [1993] show that international RBC models with completeasset markets tie the cross-country consumption differential tothe real exchange rate through international risk sharing. Con-trary to this prediction of perfect positive correlation betweenrelative consumption and the real exchange rate, they documentthat no clear pattern emerges from the data (the consumption-real exchange rate anomaly). Chari, Kehoe, and McGrattan[CKM 2002] report evidence of negative correlation between rela-tive consumption and the real exchange rate for the United Statesrelative to Europe. Their sticky-price model does better than BKKconcerning the consumption-output anomaly but does not resolvethe consumption-real exchange rate anomaly (and also does notgenerate the empirical persistence of the latter). Obstfeld andRogoff [2001] argue that introducing iceberg trade costs helpsexplain a variety of puzzles in international comovements, includ-ing the BKK consumption-output anomaly. They observe thattrade costs and incomplete asset markets can explain the con-sumption-real exchange rate anomaly.43 Our model featurestrade costs and incomplete asset markets. Here, we investigateits ability to reproduce key features of international businesscycles—including the resolution of the puzzles highlighted above.

The model includes only one source of fluctuations at busi-

43. Benigno and Thoenissen [2003] show that international asset marketincompleteness plays a central role in dealing with the Backus-Smith puzzle in amodel in which intermediate goods are traded and households consume onlynontraded goods.


ness cycle frequency, the shocks to aggregate productivities Ztand Z*t. In this section we assume that the percentage deviationsof Zt and Z*t from the steady state follow the bivariate process:

(6) � Zt

Z*t �� Z �ZZ*

�Z*Z �Z*� � Zt�1

Z*t�1�� t

Z

�tZ* �,

where the persistence parameters �Z and �Z* are in the unitinterval, the spillover parameters �ZZ* and �Z*Z are nonnega-tive, and �t

Z and �tZ* are normally distributed, zero-mean innova-

tions. For purposes of comparison, we use the symmetrized esti-mate of the bivariate productivity process for the United Statesand an aggregate of European economies in BKK and set

� �Z �ZZ*

�Z*Z �Z*� � � .906 .088

.088 .906 � .

This matrix implies a small, positive productivity spilloveracross countries, such that, if home productivity rises duringperiod t, foreign productivity will also increase at t � 1. We setthe standard deviation of the productivity innovations to.00852 (a .73 percent variance) and the correlation to .258(corresponding to a .19 percent covariance), as estimated byBKK. We calculate the implied second moments of endogenousvariables (percent deviations from steady state) using the fre-quency domain technique described in Uhlig [1999], and wecompare the model-generated moments with those of U. S. andinternational data computed in BKK and reported in Table IIfor the reader’s convenience.44 For consistency with BKK andCKM, who focus on the high-frequency properties of businesscycles in the United States and abroad, we report second mo-ments of Hodrick-Prescott (HP)-filtered variables.45

We previously argued that empirical price deflators are bestrepresented by the average prices Pt and P*t in our model (asopposed to the welfare based price indices Pt and P*t). As with thereal exchange rate, we thus focus on the second moments of real

44. Results based on model simulation are similar. Benigno [2004] and CKMare the sources on the empirical properties of the real exchange rate. Benignoreports averages of data in Bergin and Feenstra [2001] and CKM.

45. The productivity process has eigenvalues .994 and .818. A stationaryprocess for productivity and model stationarity imply that all endogenous vari-ables of interest are stationary. However, productivity and key endogenous statevariables, such as the number of firms and asset stocks, are persistent enoughthat model-generated moments calculated without HP filtering pick up low fre-quency fluctuations that are not featured in the HP-filtered data in BKK.


TABLE IIBUSINESS CYCLE DATA

United States Standard deviation

Variable Percentage Relative to output

Output 1.71 1.00Consumption .84 .49Investment 5.38 3.15Capital stock .63 .37Net exports/output .45

Corr(Variablet�j,Outputt), j � �5, . . . , 5

Variable 2 �5 �4 �3 �2 �1 0 1 2 3 4 5

Output �.03 .15 .38 .63 .85 1.00 .85 .63 .38 .15 �.03Consumption .20 .38 .53 .67 .77 .76 .63 .46 .27 .06 �.12Investment .09 .25 .44 .64 .83 .90 .81 .60 .35 .08 �.14Capital

stock �.60 �.60 �.54 �.43 �.24 .01 .24 .46 .62 .71 .72Net exports/

output �.51 �.51 �.48 �.43 �.37 �.28 �.17 .00 .17 .30 .38

International: Contemporaneous cross correlation

Country

with United States

within country

Output Consumption

Saving-investment

rate(Net exports/

output)-output

Austria .31 .07 .29 �.42Finland .02 �.01 .09 �.36France .22 �.18 �.04 �.17Germany .42 .39 .42 �.27Italy .39 .25 .06 �.62Switzerland .27 .25 .38 �.66United Kingdom .48 .43 .07 �.21Europe .70 .46United States 1.00 1.00 .68 �.36

Real exchange rate

SourceFirst-orderautocorr.

Std. dev.(ratio to output)

Corr. withrelative consumption

CKM .83 5.50 �.35BF .80 4.81

Source: Backus, Kehoe, and Kydland [1992] unless otherwise noted.


variables deflated by the average prices Pt and P*t. To obtain suchmeasures, for any variable Xt in units of consumption, we definethe corresponding real variable deflated by the average priceindex as XR,t � PtXt/Pt.

46

As we previously discussed, new entrants embody the invest-ment by households, and the stock of firms represents the capitalaccumulated by such investments. For comparison with the in-vestment and capital variables from BKK, we compute secondmoments for NE,t and ND,t as well as for their overall values interms of average firm valuation deflated by the average priceindex (vR,t

E and vR,tD , where vR,t

E � vR,tNE,t and vR,tD � vR,tND,t).

Consistent with BKK, we define saving (in units of consumption)as the difference between GDP and consumption, yt � Ct, whereGDP yt is defined by yt � wtL � ND,tdD,t. We investigate thecorrelation between the saving rate (1 � CR,t/yR,t) and the in-vestment rate (vR,t

E /yR,t) relative to the data.Table III reports our results. The model underpredicts the

standard deviation of aggregate output (measured by GNP inBKK) and overpredicts that of consumption, although it is suc-cessful at generating less volatile consumption than GDP. Theratio of the standard deviation of CR,t to yR,t is roughly .59, tenpercent higher than the consumption-output volatility ratio inBKK’s data. Like fixed investment in the data, investment in newfirms is substantially more volatile than GDP. The ratio of tradebalance (TBR) to GDP is much more volatile than the net exports/output ratio in the data. The trade costs in our model do notprevent the trade balance/GDP ratio from being quite volatile asthe BKK specification does by penalizing trade balance move-ments directly.47 Instead, the real exchange rate is clearly lessvolatile than in the data. There, it reflects to a large extent thevolatility of the nominal exchange rate, which has no impact onreal variables in the flexible-price setup of this paper.

The model is quite successful at reproducing the autocorre-lation function of key U. S. aggregate variables with output: theautocorrelation functions for output itself, consumption, invest-ment in new firms, the stock of productive firms, and the tradebalance in Table III all reproduce the qualitative pattern in Ta-ble II. In the cases of output, consumption, and investment,

46. Unless noted, the main results are unaffected when we consider secondmoments of variables including the variety effect.

47. Note, however, that the volatility of the trade balance itself is muchsmaller.


success is also reasonable, if not striking, on quantitativegrounds.

The BKK model does not deliver positive correlation betweenhome and foreign output. A puzzling negative cross-country cor-relation of aggregate outputs is a standard result of the interna-tional RBC literature. Our model successfully generates positivecorrelation between foreign and domestic GDPs. However, as theBKK setup, ours does not generate cross-country consumption

TABLE IIIMODEL GENERATED MOMENTS

Standard deviation

Variable Percentage Relative to yR

yR .7950 1.00CR .4681 .5888vR

E 3.5002 4.5754NE 3.6314vR

D .3795 .4773ND .2697TBR/yR 1.0178TBR .2968 .3733Q .0278 .035

Corr(Variablet�j,yR,t), j � �5, . . . , 5

Variable 2 �5 �4 �3 �2 �1 0 1 2 3 4 5

yR �.02 .10 .27 .47 .71 1.00 .71 .47 .27 .10 �.02CR �.08 .03 .18 .37 .59 .87 .66 .48 .32 .19 .08vR

E .08 .18 .31 .46 .65 .86 .49 .22 .02 �.12 �.21NE .07 .17 .29 .44 .62 .84 .49 .23 .04 �.10 �.19vR

D �.34 �.37 �.39 �.39 �.37 �.33 .06 .30 .45 .51 .52ND �.41 �.38 �.31 �.21 �.05 .16 .44 .59 .65 .65 .60TBR/yR �.01 �.13 �.29 �.48 �.71 �.99 �.66 �.41 �.20 �.05 .07TBR �.05 �.13 �.23 �.36 �.50 �.67 �.33 �.10 .05 .14 .18

Corr(Qt�j,Qt), j � �5, . . . , 5

�5 �4 �3 �2 �1 0 1 2 3 4 5

.19 .37 .55 .73 .89 1.00 .89 .73 .55 .37 .19

Contemporaneous cross correlation

y*R, yR C*R, CR 1�CR/yR, vRE/yR CR/C*R, Q C/C*, Q

.21 .86 .95 �.99 .71


correlation that is smaller than the correlation across GDPs forthe same parameterization of productivity. The contemporaneouscorrelation between saving and investment rates is positive, butstronger than in the data. The autocorrelation function for thereal exchange rate Qt displays substantial persistence, with afirst-order coefficient equal to .89 roughly in line with the evi-dence. The correlation between relative consumption spendingand the real exchange rate Qt is negative, as in the CKM data,but too large in absolute value. The correlation between relativeconsumption (including the variety effect) and the consumption-based real exchange rate, which is 1 in Backus and Smith’s [1993]complete markets world, is .71.

To verify robustness, we considered an alternative parame-terization of the productivity process (6) and set �ZZ* � �Z*Z �0 and �ZZ � �Z*Z* � .999, consistent with evidence described inBaxter [1995] and Baxter and Farr [2005]. As in Baxter’s exer-cise, we kept the same variance-covariance matrix of the produc-tivity innovations as in BKK. Several key features of our resultsdo not change in this scenario relative to the BKK productivityprocess.48 In particular, the model continues to perform well onthe persistence dimension. The real exchange rate is somewhatless persistent, but its volatility increases. Most importantly, theconsumption-output anomaly is substantially weaker. The corre-lation between CR and C*R is only slightly larger than that be-tween yR and y*R (.46 versus .44, respectively), and the correlationbetween C and C* becomes smaller than that between y and y*(.30 versus .32, respectively). When productivity spillovers arepresent, the response of foreign consumption to a home shock islarger, as foreign households anticipate that foreign productivitywill rise too. When we remove the spillovers, the increase inforeign consumption following a home shock is muted, signifi-cantly ameliorating the anomaly. The correlation between savingand investment rates is now in the same range as in the data(.47). As in the case of the BKK productivity process, the corre-lation between CR/C*R and Q is negative, but too large in absolutevalue (�.98). Importantly, the correlation between C/C* and Qnow drops to .13.49

Overall, we interpret the results of the stochastic exercise of

48. We omit details, but they are available on request.49. Setting the scale parameter for the costs of adjusting bond holdings to .01

leaves most results unaffected.


this section as supportive of the novel features of our model as amechanism for the propagation of business cycles across coun-tries and over time. Even after HP filtering (and thus removinglow-frequency fluctuations that are arguably important for me-dium- to long-run transmission), the model is successful at gen-erating persistent dynamics of endogenous variables and match-ing several key moments of the data quite well for plausibleparameter values—chosen to match micro-level data—and astandard productivity process. Consistent with Obstfeld and Ro-goff ’s [2001] arguments, the introduction of trade costs and mar-ket incompleteness pushes results in the right direction withrespect to important puzzles in international macroeconomics,although assumptions about the exogenous shock process alsoplay an important role.

VII. CONCLUSIONS

We developed a two-country, stochastic, general equilibriummodel of international trade and macroeconomic dynamics. Rela-tive to existing international macro models, ours has the advan-tage of matching several features of empirical evidence in themicro, trade literature. It does so while preserving substantialtractability and the ability to provide intuitions for the mainresults.

We assumed that firms face some uncertainty about theirfuture productivity when they make the decision whether or notto sink the resources necessary to enter the domestic market.Consistent with overwhelming empirical evidence, we assumedthat firms face fixed costs as well as per-unit costs when theyexport. As a consequence of the fixed export cost, only the rela-tively more productive firms self-select into the export market.Aggregate productivity shocks, changes in domestic market regu-lation, and changes in trade policy cause firms to enter and exitmarkets and generate deviations from PPP that would not existabsent our microeconomic structure.

Our model provides a fully microfounded, endogenous expla-nation for the HBS effect. All goods are tradable in our setup,while some are nontraded in equilibrium: this nontradednessmargin then changes over time. In contrast to the textbook treat-ment of the HBS effect, shocks are aggregate rather than sector-specific. Our model predicts that more productive economies, orless regulated ones, exhibit higher average prices relative to their


trading partners. This real exchange rate appreciation is drivenby entry and endogenous nontradedness, the two key new fea-tures of our setup. Entry also has a positive effect on a country’sterms of trade in response to productivity advantages. The samenew features of our model result in substantial persistence of keyendogenous variables in response to transitory exogenous shocks.In particular, our model results in persistent PPP deviations in aworld of flexible prices.

When we allow for international borrowing and lending, themodel predicts that more productive, or less regulated, economieswill experience HBS real appreciation and run persistent foreigndebt positions to finance faster entry of new firms in the economy.Thus, our framework provides a novel perspective on recent styl-ized facts for the U. S. economy that are broadly in line with thesepredictions. In addition, the model matches several importantmoments of the U. S. and international business cycle quite wellfor reasonable assumptions about parameters and productivity.In particular, it generates positive GDP correlation across coun-tries, it does not constrain the correlation between relative con-sumption and the real exchange rate to being perfect, and itimproves on the standard international RBC setup as far ascross-country correlations of consumption and GDP are con-cerned, confirming Obstfeld and Rogoff ’s [2001] argument thattrade costs help explain international macroeconomic puzzles.

Importantly, our model suggests a dichotomy between thebehavior of relative CPIs as currently measured by the data anda welfare-based measure of the real exchange rate that accountsfor availability of new varieties. Rather than appreciating, thelatter depreciates as a consequence of a productivity advantage orderegulation. This raises the issue of PPP adjustments in inter-national statistics, which may contain substantial biases due tothe omission of variety effects. The policy relevance of this impli-cation is apparent, since international agencies use these PPPadjustments to compare per capita income levels that determinecrucial international policy decisions such as the allocation of aid.

APPENDIX 1: TRADE POLICY

In this Appendix we investigate the effects of changes inexogenous trade costs. We focus on the consequences of tradeliberalization: a symmetric, worldwide decrease in the icebergcosts t � *t or fixed export costs fX,t � f *X,t. The impulse


responses are in Figures VI and VII. Since the shocks are sym-metric, there are no movements in relative, cross-country vari-ables such as the terms of labor, the terms of trade, and the real

FIGURE VIResponse to Permanent � * Shock

FIGURE VIIResponse to Permanent fx � f *x Shock


exchange rate. Thus, only home variables are represented, as theresponses of all foreign variables are identical to their homecounterparts. In both scenarios, trade liberalization induces asubstantial increase in the number of exporting firms, along witha decrease in the export productivity cutoff (exporting becomesmore profitable for all firms). The increased export competitioninduces a small downward adjustment in the number of domesticfirms. However, product variety Nt � ND,t � NX,t increases inboth countries as the increase in the number of exporters domi-nates this small reduction in the number of domestic firms.50 Asexpected, the welfare gains from a decrease in the iceberg cost(which affects the trade costs for all export production) aregreater than those generated from a decrease in fixed cost (whichdoes not affect any marginal trade costs). As documented in manymicro-level studies of trade liberalization, our simulation resultshighlight the feature that a substantial portion of the increase inoverall trade comes from the extensive margin (more exportingfirms).

APPENDIX 2: INTERNATIONAL BOND TRADING

The budget constraint of the representative home household,in units of the home consumption basket, is now

Bt�1 � QtB*,t�1 ��

2 �Bt�1�2 �

�

2 Qt�B*,t�1�2 � vtNH,txt�1 � Ct

� �1 � rt� Bt � Qt�1 � r*t� B*,t � �dt � vt� ND,txt � Ttf � wtL,

where Bt�1 denotes holdings of home bonds, B*,t�1 denotes hold-ings of foreign bonds, (�/ 2)(Bt�1)2 is the cost of adjusting hold-ings of home bonds, (�/ 2)(B*,t�1)2 is the cost of adjustingholdings of foreign bonds (in units of foreign consumption), Tt

f isthe fee rebate, taken as given by the household, and equal to(�/ 2)[(Bt�1)2 � Qt(B*,t�1)2] in equilibrium. For simplicity, weassume that the scale parameter � � 0 is identical across costs ofadjusting holdings of home and foreign bonds. Also, there is no

50. To see this based on the impulse responses for ND,t and NX,t, recall thatthe steady-state ratio of exporting firms is calibrated to the U. S. empirical shareof NX/ND � .21. The impulse responses clearly show that the increase in NX,t ismuch greater than five times (1/.21) the decrease in ND,t.


cost of adjusting equity holdings. The justification for this is that,in equilibrium, bond holdings differ from zero only because oftransactions with a foreign counterpart. As a consequence, inequilibrium, bond-adjustment fees actually capture fees on inter-national transactions, which we assume absent from domestictransactions such as those involving equity to avoid adding un-necessary complication.51

The representative foreign household faces a similar con-straint, in units of foreign consumption:

B*t�1

Qt� B**,t�1 �

�

2�B*t�1�

2

Qt�

�

2 �B**,t�1�2 � v*t N*F,tx *t�1 � C*t

��1 � rt�

QtB*t � �1 � r*t � B**,t � �d*t � v*t � N*D,tx*t � T t

f* � w*t L*,

where B*t�1 denotes holdings of the home bond, B**,t�1 denotesholdings of the foreign bond, and Tt

f* � (�/ 2)[(B*t�1)2/Qt �(B**,t�1)2] in equilibrium.

Home and foreign households maximize the respective inter-temporal utility functions subject to the respective constraints.The first-order conditions for the choices of share holdings inmutual portfolios of domestic firms at home and abroad are un-changed relative to the case of financial autarky. Instead, wehave the following Euler equations for bond holdings. At home,

�Ct��1 � �Bt�1� � ��1 � rt�1� Et��Ct�1�

��,

�Ct��1 � �B*,t�1� � ��1 � r*t�1� Et�Qt�1

Qt�Ct�1�

�� .

Abroad,

�C*t��1 � �B*t�1� � ��1 � rt�1� Et� Qt

Qt�1�C*t�1�

�� ,

�C*t��1 � �B**,t�1� � ��1 � r*t�1� Et��C*t�1��.

51. We also experimented with a specification of the cost of adjusting bondholdings as a function of overall assets: (��/ 2)( At�1)2, where At�1 � Bt�1 �QtB*,t�1. The specification we use has the advantage of pinning down uniquelythe steady-state levels and dynamics of Bt�1 and B*,t�1 as well as of theiraggregate. The alternative specification only pins down the latter. It is possible toverify that the two specifications yield identical log-linear dynamics under theassumptions that the steady-state levels of Bt�1 and B*,t�1 are zero when the cost(��/ 2)( At�1)2 is used and �� (1/2)�.


The presence of the terms that depend on the stock of bondson the left-hand side of these equations is crucial for determinacyof the steady state and model stationarity. It ensures that zeroholdings of bonds are the unique steady state in which the prod-uct of � times the gross interest rate equals 1 in each country, sothat economies return to this initial position after temporaryshocks. If we had perfect foresight and � � 0, Euler equations forbond holdings at home and abroad would imply the no-arbitragecondition (1 � rt�1)/(1 � r*t�1) � Qt�1/Qt. This is the familiarcondition that says that the real interest rate differential must beequal to expected depreciation of the consumption-based realexchange rate for agents to be indifferent between home andforeign bonds. With perfect foresight and � � 0, no-arbitrageconditions for home and foreign households imply

(7)1 � rt�1

1 � r*t�1�

Qt�1

Qt

1 � �Bt�1

1 � �B*,t�1�

Qt�1

Qt

1 � �B*t�1

1 � �B**,t�1.

Equilibrium requires that home and foreign bonds be in zeronet supply worldwide:

(8) Bt�1 � B*t�1 � 0,

(9) B*,t�1 � B**,t�1 � 0.

Home and foreign holdings of each individual bond must add upto zero because each country is populated by a unitary mass ofidentical households that make identical equilibrium choices, andonly the home (foreign) country issues home (foreign) currencybonds. Using (8) and (9) in conjunction with the second equality in(7) makes it possible to show that Bt�1 � B*,t�1 and B*t�1 �B**,t�1 at an optimum under perfect foresight. Since householdsface quadratic costs of adjusting bond holdings with identicalscale parameters across bonds, it is optimal to adjust holdings ofdifferent bonds equally so as to spread the cost evenly. The sameresult holds in the log-linear version of the stochastic model.

Aggregate accounting implies the following laws of motion fornet foreign assets at home and abroad:

(10) Bt�1 � QtB*,t�1 � �1 � rt� Bt � Qt�1 � r*t� B*,t

� wtL � ND,tdt � NE,tvt � Ct,


(11)B*t�1

Qt� B**,t�1 �

�1 � rt�

QtB*t � �1 � r*t � B**,t

� w*t L* � N*D,t d*t � N*E,tv*t � C*t,

where holdings of individual bonds across countries are tied bythe equilibrium conditions (8) and (9). Given these conditions,multiplying (11) times Qt and subtracting the resulting equationfrom (10) yields an expression for home net foreign asset accu-mulation as a function of interest income and of the cross-countrydifferentials between labor income, net investment income, andconsumption:

Bt�1 � QtB*,t�1 � �1 � rt�Bt � Qt�1 � r *t �B*,t �12 �wtL � Qtw *t L*�

�12 �ND,tdt � N*D,tQtd *t � �

12 �NE,tvt � N*E,tQtv*t� �

12 �Ct � QtC*t�.

Current accounts are by definition equal to the changes inaggregate bond holdings in the two countries:

CAt � Bt�1 � Bt � Qt�B*,t�1 � B*,t�,

CA*t �B*t�1 � B*t

Qt� B**,t�1 � B**,t.

It is straightforward to verify that the bond-market clearingconditions (8) and (9) imply that CAt � QtCA*t � 0 (a country’sborrowing must equal the other country’s lending) and Ct �QtC*t � wtL � Qtw*tL* � ND,tdt � N*D,tQtd*t � (NE,tvt �N*E,tQtv*t) (since the world as a whole is a closed economy, worldconsumption must equal world labor income plus world net in-vestment income).

Labor market clearing conditions at home and abroad re-quire

L � � 1

wt�ND,tdD,t � NX,tdX,t� �

1Zt

�NX,tfX,t � NE,t fE,t�,

L* � � 1

w*t�N*D,td*D,t � N*X,td*X,t� �

1Z*t

�N*X,tf *X,t � N *E,t f *E,t�.

We thus have 23 endogenous variables: wt, w*t, dt, d*t, NE,t,N*E,t, zX,t, z*X,t, ND,t, N*D,t, NX,t, N*X,t, rt, r*t, vt, v*t, Ct, C*t, Qt,


Bt, B*,t, B*t, B**,t. Of these, eight are predetermined as of time t:the total numbers of firms at home and abroad, ND,t and N*D,t, therisk-free interest rates, rt and r*t, and the stocks of bonds, Bt,B*,t, B*t, and B**,t. The model features the same eight exogenousvariables as in the financial autarky case. The 23 endogenousvariables above are determined by a system of 23 equations thatis identical to the system in Table I in the following blocks: Priceindexes, Profits, Free entry, Zero-profit export cutoffs, Share ofexporting firms, Number of firms, Euler equation (shares). Thefive equations in Euler equation (bonds), Aggregate accounting,and Balanced trade are replaced by the nine equations in Ta-ble IV.52

BOSTON COLLEGE AND EURO AREA BUSINESS CYCLE NETWORK

HARVARD UNIVERSITY, CENTRE FOR ECONOMIC POLICY RESEARCH, AND NATIONAL

BUREAU OF ECONOMIC RESEARCH

52. Of course, we apply again the functions at the bottom of Table I.

TABLE IVMODEL SUMMARY—BOND TRADING

Euler equations (bonds)

(Ct)��(1 � �Bt�1) � �(1 � rt�1)Et[(Ct�1)��]

�Ct��1 � �B*,t�1� � ��1 � r*t�1�Et�Qt�1

Qt�Ct�1�

��C *t ��1 � �B*t�1� � ��1 � rt�1�Et� Qt

Qt�1�C*t�1�

��(C*t)

��(1 � �B**,t�1) � �(1 � r*t�1)Et[(C*t�1)��]

Net foreign assets

Bt�1 � QtB*,t�1 � (1 � rt)Bt � Qt(1 � r*t)B*,t

� 1⁄2 (wtL � Qtw*tL*) � 1⁄2 (ND,tdD,t

� N*D,tQtd*D,t) � 1⁄2 (NX,tdX,t � N*X,tQt d*X,t)

� 1⁄2 (NE,tvt � N*E,tQtv*t) � 1⁄2 (Ct � QtC*t)

Bond marketequilibrium

Bt�1 � B*t�1 � 0B*,t�1 � B*

*,t�1 � 0

Labor marketequilibrium

L � � 1

wt�ND,t dD,t � NX,tdX,t� �

1Zt

�NX,tfX,t � NE,tfE,t�

L* � � 1

w*t�N*D,t d*D,t � N*X,td*X,t� �

1Z*t

�N *X,t f *X,t � N *E,t f *E,t�


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