The International Elasticity Puzzle

Transcription

1 Marc 2008 Te International Elasticity Puzzle Kim J. Rul* University of Texas at Austin ABSTRACT In models of international trade, te elasticity of substitution between foreign and domestic goods te Armington elasticity determines te beavior of trade flows and international prices. International real business cycle models need low elasticities, in te range of 1 to 2, to matc te quarterly fluctuations in trade balances and te terms of trade, but static applied general equilibrium models need ig elasticities, between 10 and 15, to account for te growt in trade following trade liberalization. To reconcile tese contradictory findings, we construct a model in wic cyclical fluctuations are caused by temporary socks, as in business cycle models, but tariff canges are permanent. In te model, firms do not cange export status in response to temporary socks, wile tariff decreases induce some non-exporters to export. In a calibrated model, te entry of new exporters increases te measured elasticity wit respect to a tariff cange to 6.4, wile te elasticity in response to temporary socks is 1.2. *I would like to tank Timoty Keoe for is advice and encouragement. I also tank V.V. Cari, Patrick Keoe, Sam Kortum, Erzo G.J. Luttmer, Edward Prescott, and Kei-Mu Yi elpful discussions and comments. I tank te National Science Foundation for financial support under grant number

2 1. Introduction A common feature of many international trade models is national product differentiation: countries produce and trade differentiated goods tat are to some extent substitutable for eac oter. In tese models, te elasticity of substitution between ome and foreign produced goods te Armington elasticity, after Armington (1969) is te critical parameter for determining te beavior of trade flows and international prices. Te importance of tis parameter as manifested in two of te leading brances of international economics: te international business cycle literature tat seeks to understand te ig frequency fluctuations in macroeconomic aggregates, and te static applied general equilibrium literature tat focuses on explaining te patterns of trade and te effects of trade policy. Tese two disciplines, owever, ave very different views on te value of te Armington elasticity. International real business cycle (IRBC) models need small values of te elasticity to generate te volatility of te terms of trade and te negative correlation between te terms of trade and te trade balance tat are found in te data. IRBC models commonly use Armington elasticities around 1.5, toug sensitivity analysis suggests values even lower tan tis may be appropriate. (See for example, Backus, Keoe and Kydland (1994), Zimmermann (1997), or Heatcote and Perri (2002).) Not surprisingly, wen empirical researcers ave estimated te Armington elasticity from ig frequency data tey find small estimates tat range from about 0.2 to 3.5. In contrast, applied general equilibrium (GE) models need large Armington elasticities to explain te growt in trade volumes tat result from a cange in tariffs. As sown in Yi (2003), tese models need elasticities of 12 or 13 to generate te large growt in trade found in te data. Empirical work on trade liberalizations, as well as cross country regressions relating trade patterns to tariff and non-tariff barriers, find Armington elasticities tat range from about 4 to 15, similar to te ones needed in applied GE models. Te key to understanding tese two different measurements of te Armington elasticity is to realize tat te source of variation in te prices and quantities being measured is different. Te ig frequency variation in te time series data is likely caused by transitory socks to supply or demand. Tese are exactly te transitory socks 2

3 used in te business cycle models tat need small Armington elasticities. Trade liberalization, owever, can be tougt of as a permanent cange. Wen agents react differently to temporary and permanent canges, te measured Armington elasticities will differ. In tis paper we sow tat a model combining elements of te real business cycle and te applied GE frameworks can reproduce bot te low elasticities estimated from te time series data and te ig elasticities implied by te growt in trade following a decrease in tariffs. Te model features an entry cost of exporting and eterogeneous firms, as in Melitz (2003), but adds aggregate productivity socks, as found in te IRBC models of Backus, Keoe and Kydland (1994) and Stockman and Tesar (1995). As in Melitz (2003), entry costs interact wit firm level eterogeneity to partition firms into exporters and non-exporters. A firm decides weter to become an exporter by comparing te expected future value of exporting to te cost of entry. If te expected gain from exporting is larger tan te cost of entry, te firm becomes an exporter. Te movement of firms into and out of exporting in response to temporary canges in productivity or permanent canges in tariffs drives te two very different elasticities measured in te model. Since temporary canges in productivity cange expected future profits from exporting little, few firms coose to cange teir exporting status. Tus, temporary canges in productivity tend to sow up as price canges in te goods already being traded, and consumers substitute between goods at te low true elasticity specified as a parameter in te model. We call tis cange in te amount of goods tat were already being traded a cange on te intensive margin. Wen all cange occurs on te intensive margin, as it does in most trade models, estimating te elasticity from aggregate trade flows will recover te true elasticity. In our model tere is a small number of firms entering and exiting te export market in response to productivity socks, but te trade from tese firms is small compared to aggregate trade. Tus, wen we estimate te Armington elasticity in te model in response to productivity socks, we find small values tat are close to te true elasticity specified by te parameters. Te estimated elasticity is not exactly equal to te true elasticity because te price indices constructed for use in te estimation do not incorporate te canging set of goods being traded. As 3

4 sown in Feenstra (1994), not including tese newly traded goods imparts a bias to te indices. We discuss tis mismeasurement and its implications in Section 6. In contrast, a permanent cange, suc as lower tariffs, raises te profit from exporting in all states of nature and increases te expected future gain from exporting more tan a temporary productivity sock. Tis induces more firms to begin exporting, resulting in large trade flows. We call te increase in trade flows from newly traded goods an increase on te extensive margin. Te increase in te extensive margin is te key to understanding te large elasticities measured in response to trade liberalization. Following a decrease in tariffs, trade increases for two reasons: consumers buy more of te goods tey already import, since te delivered price is now lower, and tey buy new imports tat were not previously available. Te first kind of growt is intensive margin growt, wile te second is extensive margin growt. If te cange in aggregate trade is mistakenly assumed to be all intensive margin growt, te small canges in tariffs appear to induce large canges in imports on te intensive margin, wic implies a large elasticity of substitution. Wen we make a similar measurement in our model after a decrease in tariffs, we find an Armington elasticity tat is more tan 3 times te true value. Wen we sut down te extensive margin in our model, owever, our measured elasticity is te same as te true elasticity. Tere is growing evidence tat te extensive margin, wic drives te central result of tis paper, is an important facet of te data. Empirically, Hillberry and McDaniel (2002) find evidence of extensive margin growt for te U.S. following te implementation of te Nort American Free Trade Agreement (NAFTA). Keoe and Rul (2002) document extensive margin growt in a study of trade liberalizations and lay out a simple Ricardian model to igligt te forces at work. In a test of several firmlevel models of exporter beavior, Bernard, Jensen and Scott (2003) study data on U.S. manufacturing plants and find strong evidence tat new plants coose to enter te export market as trade costs fall. 1 In a cross sectional study, Hummels and Klenow (2005) find tat larger and ricer countries ave larger extensive margins. Te larger, ricer, countries also tend to be te countries wit te most liberalized trade policy. Broda and 1 Bernard, Jensen et al. (2003) test te predictions of te plant-level models of Bernard, Eaton, Jensen and Kortum (2003), Melitz (2003), and Yeaple (2005). 4

5 Weinstein (2006) document te increase in te number of imported goods available in te U.S. and compute an import price index, based on Feenstra (1994), wic corrects for tese newly imported goods. Tey find significant gains in welfare from tese new imports. Earlier teoretical work on export entry costs and uncertainty as focused on ysteresis in exporting. Baldwin (1988), Baldwin and Krugman (1989), and Dixit (1989) sow ow temporary increases in profitability (tey considered excange rates) could increase exports as firms enter te export market, but tat ig levels of exports would persist even as excange rates appreciated. Te firms tat ad incurred te sunk cost to export would continue to do so, even faced wit a less attractive excange rate, since tey ad already incurred te start-up cost. In more recent work, Melitz (2003) incorporates export entry costs into a model of monopolistic competition, as in Dixit and Stiglitz (1977), in an environment wit no aggregate uncertainty. His analysis focuses on te reaction of an industry to canges caused by trade liberalization. Te model presented ere as a structure of production similar to tat in Melitz (2003), but focuses on te effects of industry structure on aggregate trade in te presence of aggregate uncertainty. In Alessandria and Coi (2007a) export entry costs are imbedded in a standard international real business cycle model to study te effects of exporter entry and exit on international correlations of consumption and output. Tey find, as do we, tat te extensive margin is not important for aggregate quantities at business cycle frequencies. Gironi and Melitz (2005) model fixed but not sunk export costs, in a real business cycle model to generate endogenous persistent deviations from purcasing power parity. Teir models are conceptually similar to te one presented ere, in tat tey involve aggregate uncertainty modeled as socks to productivity. Teir analysis, owever, is focused on te caracteristics of international business cycles, wile we are concerned wit te different beavior of trade flows in response to different sources of variation. Empirical justification for te export entry costs tat are central to tis model, and te literature cited above, as come as te result of plant-level dynamic models of export entry decisions. Te seminal work in tis literature is Roberts and Tybout (1997), wo develop an econometric model of a plant s decision to enter te export market. Using 5

6 panel data on te Colombian manufacturing sector, tey reject te null ypotesis tat entry costs are unimportant. In a study of German plants, Bernard and Wagner (2001) find evidence of substantial sunk costs in export entry. Using a detailed data set on U.S. manufacturing plants, Bernard and Jensen (2004) find tat export entry costs are significant and tat plant eterogeneity is important in te export decision. Te next section reviews te evidence on te elasticity of substitution as estimated by different autors using different tecniques. Section 3 lays out evidence tat te extensive margin is active during times of policy canges, but not during business cycles. Section 4 presents a model of te extensive margin: firms coose weter or not to export in te presence of fixed costs and uncertainty about future productivity. Section 5 discusses computational issues and calibration of te model. Section 6 presents te model results, and Section 7 concludes. 2. Measuring Import Price Elasticities In tis section we review previous estimates of te Armington elasticity. Based on our ypotesis tat transitory canges in profitability lead to different responses tan permanent canges, we divide te literature into two subsections. We find tat studies tat use ig frequency price variation to estimate te Armington elasticity find low values, wile studies tat use data on trade barriers or data from trade liberalizations, tend to find muc iger values Incorporating Substitution into Models In Armington (1969), it is posited tat goods produced by different countries are intrinsically different goods. Te utility tat consumers derive from tese nationally differentiated goods is represented by a constant elasticity of substitution utility function, 1 ρ ρ ( 1 ρ ω ω) f (1) U = C + C were C is te consumption of te good produced in country k. Maximizing tis k function wit respect to te standard budget constraint and rearranging te first order conditions yields C C f Pf = P σ ω, (2) 1 ω 6

7 were P is te price of te good produced in te ome country and P f is te price of te good produced in te foreign country. It is easy to see from (2) tat σ 1 ( 1 ρ ) = is te elasticity of substitution between te goods. Wen te two goods are differentiated by country of origin, as in tis case, tis elasticity is commonly referred to as te Armington elasticity. An alternative way of incorporating national product differentiation is to assume tat countries produce intermediate goods tat are combined to produce an aggregate consumption-investment good. In tese models, te feasibility condition is were 1 ρ ρ ( 1 ρ ω ω) f, (3) C+ X = q + q C is consumption, X is investment, is te intermediate good produced in te q ome country, and q f is te intermediate good produced in te foreign country. Wen using tis specification, te constant elasticity function on te rigt-and side of (3) is commonly called te Armington aggregator. Minimizing te cost of producing one unit of te aggregate good implies te same first order condition as (2). In trade models tat feature imperfect competition and differentiated goods, suc as tose in Helpman and Krugman (1985), consumers are frequently modeled as aving constant elasticity of substitution preferences over varieties of goods witin an industry, were (), j ρ ρ U j = ω c, j() ι dι+ ( 1 ω) cf, j() ι dι Ι ι Ι ι f, (4) c ι is consumption of domestically produced variety ι, and c ( ) 1 ρ f, j ι is consumption of te foreign produced variety in industry j. Te set Ι k is te set of varieties tat te consumer as available for purcase. Maximizing (4) subject to a standard budget constraint yields te familiar condition, were ( ) f, j c c () ( ), j f, j ( ) () ι p ι ω = ι p ι ω, (5) f, j, j 1 p ι and p () ι are, respectively, te price of te foreign and ome goods. For example, (, j ), j c ι could be a sirt made domestically, wile c ( ) σ f, j ι is a sirt made 7

8 abroad and imported. Te empirical literature we survey below uses data collected at a level of aggregation iger tan te variety level used in (5) so, it is common to write te first order condition in terms of industry level aggregate quantities and prices, were C, j C C P ω = ω, j f, j f, j P, j1 is te aggregate amount of domestic consumption of goods in industry σ (6) j and P, j is an aggregate price index for te domestically produced goods. C f, j and f, j P are similarly defined for te goods imported into te ome country. Note tat in contrast to te Armington model, goods in tis specification are not different because tey are made in different countries. Here goods are different by teir very nature; tese are te differentiated goods found in models of monopolistic competition suc as Dixit and Stiglitz (1977). Tat te goods are made in different countries matters only to te consumer troug te ome bias parameter, ω. Wat is te same about te two models, owever, is te implication of te first order conditions, (2) and (6). Tese equations are te basis for te estimation of Armington elasticities Estimates from Price Variation We begin by reviewing te Armington elasticities used in te IRBC literature. Te Armington elasticities used in te IRBC literature range from 0.5 to 2.0. In Backus, Keoe, and Kydland (1994) eac country produces a tradable intermediate good wic is combined using an Armington aggregator, as in (3), to produce an aggregate consumption-investment good. Te autors baseline coice of te Armington elasticity is 1.5, but tey perform sensitivity analysis to tis parameter. Tey find tat te model wit a smaller elasticity (0.5) can better account for te volatility of te terms of trade and te negative correlation between te terms of trade and te trade balance, tan can te model wit a larger (2.5) elasticity. Heatcote and Perri (2002) use a similar twointermediate-goods environment to study business cycles under different degrees of financial market completeness. Beginning wit a baseline value of 1.0, tey find tat te volatility of te terms of trade, te cross-country correlation of investment, and te cross- 8

9 country correlation of consumption and output are closer to tose in te data wen lower values of te elasticity are used. In addition to te low elasticities needed for IRBC models to matc te features of te ig frequency data, low elasticities are also found wen tey are directly estimated from ig frequency data on prices. Te estimating equations are derived from te first order conditions, suc as tose in (2) or (6). Taking te logaritm of (6) yields te basic equation estimated by several autors, log ( C, C, ) log ( P, P, ) = α + σ + ε, (7) f jt jt j j jt f jt jt were C f, jt is te real quantity of imports in industry j, C, jt is te real consumption of domestically produced goods in industry j, and P, jt and P f, jt are price indices for domestic sales and imports. To estimate tis equation, quarterly data on imports and domestic consumption of te industry s good, as well as data on te relative prices is collected. Typically, te price data take te form of a unit price index for imports, and a producer price index for domestic goods. Reinert and Roland-Holst (1992) estimate an equation similar to (7) for 163 industries and find elasticities tat range from 0.02 to 3.49, wit an average value of Blonigen and Wilson (1999) estimate elasticities for 146 sectors, and find an average elasticity of 0.81, wit a maximum value of Similar estimates are found in Reinert and Siells (1993) and in te sort run elasticities reported in Gallaway, McDaniel and Rivera (2003). Te elasticities found by estimating (7) on ig frequency time series data are fairly robust. Adjustments ave been made for, among oter tings, serially correlated errors, differing levels of aggregation, and seasonal effects. Te elasticities estimated using tese expanded tecniques still find low values. Te most complete study of trade elasticities to date is Broda and Weinstein (2006), in wic te autors estimate tens of tousands of elasticities for te United States. Using a teoretical model wit tree tiers of goods: a composite imported good, imported goods, indexed by g, and varieties of a good, m gc, were c indexes te country of origin, te autors extend te metodology developed in Feenstra (1994) and estimate a demand equation for varieties, ( s ) ϕ ( σ ) ( p ) Δ log = 1 Δ log + ε, (8) t 1, t gct gt g t 1, t gct gct 9

10 were s gc is te expenditure sare of variety gc in good g, ϕgt is a random effect, and Δ is te difference operator. Te demand equation is estimated wit an export supply equation to allow for upward sloping supply curves, ( p ) ψ ω log ( s ) Δ log = + Δ + δ. (9) t 1, t gct gt g t 1, t gct gct Tese equations are differenced wit respect to a reference county, eliminating te random effects, and te resulting system of equations is estimated using a general metod of moments estimator. Identification comes from te cross country variation in prices (te between estimator). Broda and Weinstein (2006) define a 10-digit Harmonized System code or 7-digit Tariff System of te U.S.A. code from a particular country as a variety. Wen defining a good as a HS code, tey report good specific elasticities wit a median value of Te median elasticity is iger tan te oters found in tis section, but it is important to note tat unlike te oter studies in te section, te elasticities are restricted to be greater tan one. Broda and Weinstein (2006) estimate some large elasticities as well te maximum elasticity in te HS data is but te estimated values vary wit te good type in ways one migt expect. For example, goods tat are commodities ave iger elasticities tan goods tat are considered a priori differentiated. Wat is clear, from bot te calibration based literature and te empirical estimates, is tat te cyclical fluctuations in prices and quantities seem to imply tat te Armington elasticity is small. We now turn to te estimates of te Armington elasticity tat use data from trade liberalizations to identify te elasticity of substitution Estimates from Trade Policy and Geograpy In tis subsection we consider estimates of te Armington elasticity tat are derived from variation in geograpy and tariffs. In contrast to te ig frequency data used in te studies above, te main sources of variation considered in tese studies are permanent in nature. In te studies of specific trade liberalization episodes, te trade policy being analyzed is typically not a temporary policy to be reversed later. In te cross section regressions, cross-country variation in trade barriers, suc as transportation costs, tends to be permanent. Toug per-mile transportation costs may be falling, distances between countries are not; te relative transportation cost of importing a good from two different 10

11 countries stays about te same. Te eterogeneity in bilateral trade policy, wic is also an important source of variation, may cange, but again, te canges are likely permanent. Before turning to te empirical estimates, we consider te model-based estimates of te Armington elasticity. Applied general equilibrium models ave been used in te past to predict te consequences of trade policy, but tese models can also be used ex post to study trade flows. Tis metod uses te observed cange in trade flows and tariff rates to back out values for te elasticity of substitution between foreign and domestic goods. Yi (2003) performs tis exercise for tree workorse models: a Ricardian model, as in Dornbusc, Fiscer, and Samuelson (1977), a model wit differentiated goods as in Krugman (1980), and a model wit an Armington aggregator, as in Backus, Keoe, and Kydland (1994). He finds tat te Armington elasticity needs to be at least 12 for any of te models to generate te observed trade flows in response to te observed tariffs rates. Similarly, in a calibration-as-estimation exercise, Anderson, Balistreri, Fox, and Hillberry (2005) find tat te Armington elasticities needed to matc te world bilateral trade pattern are, on average, 17. Wen Armington elasticities are econometrically estimated from trade policy episodes, te results support te ig elasticities found in te model-based exercises like Yi (2003). Elasticities derived from natural experiments, like policy canges, are typically computed from te canges in imports and domestic consumption given te observed canges in tariff rates. Comparisons are made over two points in time, typically several years, as liberalization is usually a gradual process. A simple version of te calculation is C j Δ t, t+ Tlog = α j+ σ jδ t, t+ Tlog ( 1+ τ j) + ε j t T C, +, (10) fj were τ is te ad valorem tariff rate and Δ tt, T is te T year difference operator. Te subscript j indexes te industry; te equation specified in (10) can be estimated as a panel. Calculating te elasticity tis way assumes tat te cange in tariff is te only cange in relative prices, altoug various adjustments are typically made to control for oter sources of variation. + 11

12 Using tis metodology, Clausing (2001) finds a price elasticity of 9.6 in a study of te Canada-U.S. Free Trade Agreement. 2 Head and Ries (2001) find elasticities tat range from 7.9 to 11.4 in a regression relating trade sares to bot tariff and non-tariff barriers between Canada and te United States. In a detailed study of NAFTA and te Canada U.S. Free Trade Agreement tat features data on tousands of goods, Romalis (2007) estimates elasticities tat range between 4 and 13. Tese estimates are based on te substantial variation in tariff rates across partners and goods tat is a feature of te disaggregated data. Furter evidence of ig Armington elasticities can be found in cross sectional studies, were te identification comes from differences across countries, suc as distance or tariff levels. In a model of economic geograpy wit explicit consideration of transportation costs, Hummels (2001) uses data from Argentina, Brazil, Cile, New Zealand, Paraguay, and te United States to estimate te elasticity of substitution between varieties in a model wit preferences similar to (4). Te estimation produces elasticities ranging from 3 to 8. Baier and Bergstrand (2001) estimate a panel model over 16 OECD countries and find tat trade flows are about 16 times more responsive to canges in tariffs tan canges in relative prices. In tis section we ave seen ow estimates of te Armington elasticity differ considerably wen te underlying source of variation differs. Elasticities measured by studying te ig frequency canges in prices and quantities are likely capturing responses to transitory socks, and range between 0.2 and 3.5. Estimates based on canges in trade policy, oter trade costs, or cross country variation are likely capturing te response of trade flows to more permanent factors, and usually range between 4 and 15. Te large differences in tese estimates suggest tat trade flows are more sensitive to permanent canges ten to temporary socks. 3. Wen is te Extensive Margin Important? Te estimates surveyed above imply tat different kinds of variations in import prices drive different measured elasticities. In te model presented below, we use te extensive 2 In models based on (4), te elasticity of substitution and te price elasticity of demand are equal. In models wit a finite number of varieties te price elasticity converges to te elasticity of substitution as te number of varieties approaces infinity. 12

13 margin to generate te different response to temporary and permanent canges. In tis section we review te evidence on wen te extensive margin is most important. Keoe and Rul (2002) use disaggregated trade flow data to determine wen te extensive margin is important for trade growt. Using data on about digit Standard International Trade Classification (SITC) codes, tey construct a set of least traded goods goods wit no trade plus goods wit very little trade and study ow tis set of goods grows during trade liberalization episodes and over te business cycle. To construct te set of least traded goods for a particular trade flow, tey order te SITC codes by te value of trade in a base year. Tey cumulate te ordered codes to form 10 sets of codes, eac representing one-tent of total exports. Te first set is constructed, starting wit te smallest codes, by adding codes to te set until te sum of teir values reaces one-tent of total export value. Te next set is formed by summing te smallest remaining codes until te value of te set reaces one-tent of total export value. Tis procedure produces 10 sets of codes, eac representing one-tent of total trade in te base year. Te first set consists of te least traded goods: te codes wit te smallest export values, including all te SITC codes wit zero trade value. If goods tat were previously not traded, or traded very little, begin being traded tis will sow up in te data as growt in te set of least traded goods, tat is, growt on te extensive margin Trade Liberalization and te Extensive Margin Keoe and Rul (2002) find substantial growt in te set of least traded goods following trade liberalization. As an example, consider te Nort American Free Trade Agreement s impact on exports from Mexico to Canada, te results of wic are reproduced in Figure 1. Taking 1989 as te base year, te goods are partitioned into 10 sets: eac bar in Figure 1 represents a set of goods tat makes up 10 percent of total trade in Te number above te bar is te number of SITC codes in te set. Te first bar is te set of least traded goods: of te least traded SITC codes tat account for 10 percent of trade in Te eigt of te bar represents te sare of tose same goods in Te extensive margin growt is striking; te set of goods tat accounted for 10 percent of trade in 1989 accounts for 23 percent of trade in Furter evidence of te impact of te NAFTA can be seen in Figure 2. Tis figure focuses on te timing of te 13

14 growt of te extensive margin. For eac year, te least traded goods sare of total Mexican exports to Canada is plotted. Te extensive margin decreases sligtly prior to te NAFTA and grows as te agreement is implemented. Keoe and Rul (2002) study various liberalization episodes and find extensive margin growt to be a robust feature of te data Business Cycles and te Extensive Margin Keoe and Rul (2002) sow tat wile te extensive margin is active during trade liberalization, it is does not cange muc over te business cycle. Take te United States exports to te United Kingdom from as an example; te U.K. is one of te top trading partners of te U.S. during tis time period. Trade policy between te two countries did not cange significantly, but te period encompasses bot a recession and an expansion. As in te previous example, trade between te U.S. and te U.K. is partitioned into 10 sets of goods. Te results are plotted in Figure 3. Te least traded goods, wic make up 10 percent of trade in 1989, make up 11 percent of trade in In fact, te tere is little cange in te composition of goods being traded; no set of goods canges by more tan four percentage points. In Figure 4 te evolution of te least traded goods is plotted. Wile tere is some variation in te sare of trade accounted for by te least traded goods, te variation is small compared to tat in Figure 2. Estimates of te elasticity of substitution between domestic and foreign goods sow tat trade flows are more sensitive to permanent canges, like trade liberalization tan tey are to cyclical fluctuations. Te data from disaggregated trade flows reveals tat te extensive margin is active during tese trade policy episodes, but not during business cycles. In te next section we specify a model tat ties tese two ideas togeter. Te model produces temporary canges troug productivity socks and permanent canges troug trade policy. It is ten possible to study te effects of temporary and permanent canges on trade flows and te extensive margin. 4. Model Te model is designed to incorporate te major elements of standard applied general equilibrium models into an environment wit aggregate uncertainty as in IRBC models. Consumers derive utility from consuming differentiated goods sold in markets 14

15 caracterized by monopolistic competition. Te economy departs from te standard framework by requiring firms to pay a one-time entry cost before exporting and by subjecting te economy to aggregate productivity socks. Tis structure of production is similar to Melitz (2003), but ere te economy is subject to uncertainty about future productivity. Tese elements create an economy in wic firms respond differently to temporary socks to productivity, tan tey do to permanent canges in policy. Te economy consists of two countries, denoted as ome ( ) and foreign ( f ). Eac country is endowed wit L k units of labor, wic is te only factor of production. Eac country produces two types of goods: a non-traded, omogeneous good, q, wic is sold in a competitive market, and a continuum of tradable differentiated goods, indexed by ι, wic are produced by monopolistically competitive firms. A differentiated good f produced in country and consumed in country f is denoted by c () ι. For clarity, only te ome country variables and maximization problems are described. Te foreign country faces analogous problems. At eac date t, one of Η possible events, η t, occurs. Eac event is associated ( ) wit a vector of economy-wide productivity socks, z z ( η ), z ( η ) t t f t =, and te initial event η 0 is given. We assume η follows a stationary first-order Markov cain wit transition matrix Λ. An element of given event η appened today, is ληη pr ( ηt 1 η + ηt η) Λ, te probability of event η appening tomorrow, = = =. A key feature of tis economy is tat differentiated good firms are eterogeneous in teir productivity and in te entry cost tey must pay in order to export. A firm is indexed by its idiosyncratic productivity, φ F, its entry cost, κ K, and weter or not it is an exporter. Te firm s values of φ and κ are constant for te life of te firm. A firm is an exporter if and only if it as paid te entry cost κ. Te distribution of firms tat begin te period as exporters is represented by a measure over ( φ, κ ), (, ) μ φκ, wic as support F K. Plants tat begin te period as non-exporters are tracked by a similar measure, μ ( φκ,. Since firms ave market power, tey will coose teir prices d ) taking into account te consumer s demand function. In order to compute te x 15

16 ouseold s demand, te firm needs to know wic firms are selling in a market, so te measures over exporters and non-exporters are state variables. Denoting te vector of firm distributions as μ = ( μ, μ, μ, μ, te aggregate state variables for te d x fd fx ) economy can be represented by ( η, μ ). Te agents in te economy take as given te laws of motion for μ, ) ( φκ, ) (,, ) μ =Μ φκημ (11) d d, x ( φ, κ ) (,,, ) μ =Μ x φ κ ημ, wit similar laws of motion for te distributions in te foreign country. For notational ( simplicity, define Μ as te law of motion over te distribution of all firms, 4.1. Houseolds μ =Μ( ημ, ). (12) Te economy is populated by a unit measure of identical ouseolds. It is assumed tat eac ouseold owns an equal sare in all domestic firms in operation. We do not allow countries to borrow and lend wit eac oter, but witin a country, ouseolds can trade a complete set of Arrow Securities. Given tese assumptions, and te omoteticity of preferences, te ouseolds can be represented by a stand-in ouseold. Te ouseold s period utility function is γ u( c, c, ) log ρ ρ f q () ι dι cf () ι dι = c + + ( 1 γ) log( q ρ ), (13) Ι ι ( μ) Ι ι f ( μ) j were c () ι is te differentiated good ι made in country k and consumed in country j. k We denote te pre-tariff price of differentiated good ι made in country in country k and consumed j j as p () ι. Imports are subject to an ad valorem tariff, τ, wic is modeled k as an iceberg transportation cost for simplicity. Important objects in tis model are te sets of good available for consumption in te period, Ι ( μ ) and Ι ( μ ). ( μ ) f Ι is te set of goods produced in te ome country tat are available to consume in te ome country. Since firms do not pay an entry cost to sell to te domestic market, tis set is te entire set of domestically produced goods, regardless of te state of te economy. Te 16

17 set of imported varieties tat are available, Ι ( μ ) f, will generally be a strict subset of te varieties produced in te foreign country. Tis set consists only of te goods wose firms ave paid te entry cost to set up exporting operations. Tis set of varieties varies wit te state of te economy. As is common, we can define an artificial composite good, ρ ρ C = c () ι dι+ cf () ι dι Ι ι ( μ) Ι ι f ( μ) 1 ρ, (14) wose price can be found by minimizing te cost of producing one unit of C, subject to P ( η, μ) = min p ( ι ; η, μ) c ( ι) dι+ p ( ι ; η, μ)( 1 + τ) c ( ι) dι, (15) f f c() ι, cf () ι Ι ι ( μ) Ι ι f ( μ) C = 1. Solving tis minimization problem yields te familiar expressions for te price of te composite good, P(, ) p ( ; ) ρ ( 1 ) ρ pf ( ;, ) ρ ρ ρ ρ ημ = ιημ, dι+ + τ ιημ dι, (16) i Ι( μ) Ι ι f ( μ) demand functions for eac of te differentiated varieties produced in te ome country, ( ημ, ) ( ιη ;, μ) 1 1 ρ P c ( p () ι ;, ιη, μ) = C( η, μ ) p, (17) and demand functions for eac of te differentiated varieties produced in te foreign country, P ( ημ, ) ( ιη ;, μ) ( 1+ τ) c f ( pf () ι ;, ιη, μ) = C( η, μ ). (18) p f Te stand-in ouseold in eac country inelastically supplies labor to firms and cooses consumption of te domestically produced varieties, te available imported varieties, and te non traded good to maximize utility. Te ouseold s value function can be written as 1 1 ρ ρ 1 ρ 17

18 W ( ημ, ) = max γlog( C) + ( 1 γ) log ( q) + β W( η, μ ) λ ηη, (19) η subject to te budget constraint, P( η, μ) C + pq( ημ, ) q + Q( ηημ, ) B( ηη ) = L +Π ( ημ, ) + B( η) (20) η and te laws of motion over te distribution of firms, (12). Te price of te non-traded good in te ome country is p q. Aggregate profits, Π, are returned to te ouseold, and te ome country wage is normalized to 1. As te ouseolds witin a country are identical, tere will be no borrowing and lending witin te country. Te existence of tese securities, owever, allows us to compute ( ημ, ) C( ημ, ) ( η, μ ) C ( η, μ ) P Q ( η ημ, ) = β λ P so tat firms value future profits in a consistent way Differentiated Good Producers Tere is a continuum of differentiated good firms indexed by teir idiosyncratic productivities, φ, and export entry costs, κ. A firm s marginal cost of production consists of two parts: te idiosyncratic, non-stocastic productivity, φ, and te economy wide, stocastic productivity, z ( η ). Te production function for a firm of type ( φ, κ ) in aggregate state ( η, μ ) is linear, ( φ κ ημ) ( ) ηη (21) y,,, = z ηφl. (22) Wen a firm cooses to begin exporting, it must pay te entry cost, κ. Tis cost must be paid before te realization of η and can not be recovered afterward. After paying tis entry cost, te firm faces no furter costs associated wit exporting. An incumbent firm enters te period as eiter an exporter or a non-exporter. After aggregate productivity is revealed, firms coose ow muc labor to ire and ow muc to produce. After production, a mass of entrants, ν, arrives wo ave not paid te fixed cost to export. Te joint distribution of idiosyncratic productivity and entry costs over tese entrants as p.d.f. Φ. At te end of te period, non-exporters decide weter to continue as non-exporters, or to pay κ and begin exporting. In addition, firms face an 18

19 exogenous probability of deat, δ. Exporting decisions, along wit te exogenous deat of firms, determine te next period s distributions of exporters and non-exporters, and μ d μ x. Te timing of decisions and te evolution of te distributions over firms are displayed in Figure 5. Te firm s problem can be broken up into two sub-problems. Te first problem is a static maximization of period profits. Te second is te dynamic decision of exporter status. We turn to te static problem first. Plants are monopolistic competitors wo coose prices to maximize profits, taken as given te aggregate price index and te wage. Te firm realizes, owever, tat te ouseold s demand is downward sloping, and tus te demand functions defined in (11) and (12) appear in te firm s problem. For clarity in te firm s dynamic problem, it is useful to define te value of maximized profits from selling domestically for a firm of type ( φ, κ ) in aggregate state (, ) (, κη,, ) max ( ;,,, ) π φ μ = c p φκημ p l d p, l ( η) φ = ( φ κ η μ) s. t. z l c p ;,,, η μ as (23) and maximized profits from exporting as (,,, μ ) = max ( ;,,, ) π φκη c p φκημ p l f f f x f p, l f f ( η) φ = ( φ κ η μ) s. t. z l c p ;,,,. (24) Optimization implies tat firms set prices as a constant markup over marginal costs, p = = 1 ρφz, (25) f ( φκ,, η, μ) p ( φκημ,,, ) ( η) f and determines te labor demand functions, l ( φ, κημ,, ) and l (,,, ) φ κημ. Having defined te maximized values from te static problem, te firm s dynamic problem is reduced to coosing only exporting decisions. As tere are no export continuation costs, an exporter will always coose to stay an exporter; monopolistic competition ensures tat te firm always earns a positive profit. An exporter s value function is defined by ( φ, κημ,, ) = π ( φκημ,,, ) + π x ( φκημ,,, ) + ( 1 δ) ( ηημ, ) ( φκη,,, μ ) V Q V x d x η ( η μ) s. t. μ =Μ, (26) 19

20 were Μ ( ) is te law of motion for te aggregate state variable μ. Te term ( 1 δ ) reflects te probability of exogenous deat tat te firm faces. Te summation represents an expected value calculation were te transition probabilities are included in Q, as defined in (21). A non-exporter must decide weter to remain selling only to te domestic market, or to enter te export market. Te non-exporter s problem can be written as V d ( φκημ) ( ) + ( ) Q( ) Vd ( ) πd φκημ,,, 1 δ ηημ, φκη,,, μ, η,,, = max π d ( φκημ,,, ) κ+ ( 1 δ) Q( ηημ, ) Vx( φκη,,, μ ). (27) η s.t. μ =Μ, ( η μ) Te two terms in te maximization correspond, respectively, to te expected future profit from continuing as a non-exporter and te expected future profit from becoming an exporter. Tis coice is te crucial one for te results presented ere. Te small, temporary productivity socks cange te future expected profits from exporting little, and tus few firms are willing to sink te cost of becoming exporters. A permanent cange, suc as a tariff decrease, increases a firm s profit in every realization of η, and tus as a larger effect on te expected future profits from exporting. Tis larger effect induces more firms to enter te export market, and increases te amount of goods being traded. Tus, in tis model, permanent canges in tariffs ave larger impacts on trade tan do temporary socks to productivity. Solving te non-exporter s problem yields te decision rule over next period s export status, d (,,, ) φ κημ, wic is equal to 1 if te firm cooses to export next period and is equal to 0 if te firm cooses to continue as a non-exporter in te next period Nontraded Good Producers Te non-traded good, q, is produced by a constant returns to scale firm and is sold in a competitive market. Te firm s problem is ( ημ) max pq, q l l, (28) s.t. q = z l ( η ) were te price of good q is p q. 20

21 4.4. Market Clearing Goods market clearing conditions are standard. Te labor market clearing condition is κφ, κφ, k, φ (,,, ) (, ) L = l φκημ μd φκ dφdκ f (,,, ) (,,, ) (, ) + l φ κημ + l φκημ μx φκ dφdκ ( )( d( ) ( )) + κ d φ, κ, η, μ μ φ, κ + νφ φ, κ dφdκ. (29) Te first term on te rigt and side is te use of labor for production by non-exporting firms, te second is te use of labor for production by exporting firms and te tird term is te use of labor in exporter entry, some of wic is paid by newly created firms. Aggregate profits are te sum of gross profits earned by firms minus te costs of entry, Π ( ημ, ) = πd( φκημ,,, ) μd( φκ, ) dφdκ κφ, + π d ( φκημ,,, ) + πx ( φκημ,,, ) μx ( φκ, ) dφdκ κφ, k, φ ( )( d ( ) + Φ( )) κ d φ, κ, η, μ μ φ, κ ν φ, κ dφdκ. (30) Te model is closed by assuming tat trade is balanced eac period, 4.5. Equilibrium f f p ( ιημ ;, ) c ( ιημ ;, ) dι pf ( ιημ ;, ) cf ( ιημ ;, ) dι = 0. (31) f Ι ι ( μ) Ι ι ( μ) Equilibrium is defined recursively. For simplicity, only te ome country equilibrium objects are enumerated; te agents in te foreign country solve problems analogous to tose in te ome country, and ave te corresponding decision rules. f A recursive equilibrium in tis economy is value functions, V (,,, ) V (,,, ) d x φ κ ημ and f φ κημ, decision rules, d ( φ, κημ,, ), l ( φ, κημ,, ), (,,, ) l φ κημ, f p ( φ, κ, η, μ ), and p ( φ, κημ,, ), te sets of goods available for consumption 21

22 Ι ( μ ) and Ι ( μ ), decision rules c ( ι, ημ, ) for eac ι ( μ ) ι f Ι ( μ), and q ( ημ, ), te price function, p (, ) f distribution of firms, Μ ( η, μ ) and Μ ( η, μ ) 1. te ouseold s problem, (19), d x q f Ι, c ( ι, ημ, ) for eac ημ, and te laws of motion for te, suc tat tese functions satisfy: 2. te firm s problems for eac type ( φκ, ) F K, (26) and (27), 3. te consistency of aggregate and individual decisions, ( + φκημ ) ( φκημ, ) ( Μ x ( φ, κ) = μx ( φκημ,,, ) + νφ( φκ, ) μd (,,, ) d,, 1 δ) ( ) and ( φ, κ) 1 d ( φ, κ, η, μ) μd ( φ, κ, η, μ) + ν Φ( φ, κ) ( 1 δ) Μ d =, for all ( φκ, ) F K, 4. te goods and labor market clearing conditions, 5. te balanced trade condition, (31) Equilibrium Properties Te equilibrium in tis economy is caracterized by a cut-off rule, ˆ φ ημκ,,, tat is a function of te aggregate state and te value of te entry cost. Tis is te productivity level at wic te non-exporting firm wit idiosyncratic productivity ˆ (,, ) cost ( ) φ ημκ and entry κ is indifferent between continuing as a non-exporter, and entering te export market wen te aggregate state is ( ( η, μ ). Te cutoff productivity satisfies (,, κ, η, μ ) V ( ˆ (,, κ ), κ, η μ ) d φ η ) κ = ( 1 δ) Q( η η, μ) V ˆ x φ ( η, μ κ) μ,. (32) η Te rigt-and-side of (32) is te discounted expected future gain from exporting: it is te difference in future profits if te firm exports rater tan only selling domestically. Te left-and-side of (32) is te cost of entering te export market. Plants wit productivity below ˆ φ η, μ, κ ( ( ) ) sell only to te domestic market, wile firms wit productivity above ˆ φ ημκ,, sell to bot te domestic and te exports markets. As te aggregate state of te economy canges, te expected future profits of te firms cange; tis sifts te cutoff firms, generating te entry and exit of firms in te export market. It 22

23 is easy to sow tat, for a given ( η, μ ), ˆ φ is increasing in κ. Tat is, te larger is te entry cost, te more productive a firm needs to be in order to break even in te export market. Plants moving into and out of exporting play te crucial role in explaining te different responses of aggregate exports to canges in trade policy and productivity. If te socks to productivity are small, or not very persistent, tere will be little movement of firms into or out of exporting. Tus, productivity socks induce incumbent exporting firms to cange prices, and ouseolds react to te cange in prices by substituting according to te elasticity of substitution implied by ρ. Tis is growt on te intensive margin. Wit only a few firms entering te export market, extensive margin growt is small. If transitory socks are te dominant source of te variation measured in time series regressions suc as Reinert and Roland-Holst (1992) or Blonigen and Wilson (1999), tey would mostly affect te intensive margin, and te low elasticities estimated in tese studies would reflect a low true elasticity of substitution. A permanent cange, suc as te lower tariffs tat accompany free trade agreements, increases te profit from exporting for all realizations of future productivity, and tus as a larger impact on te expected future profits from exporting. Te larger increase in expected future profits induces some firms tat were only selling in te domestic market to enter te export market. Tese newly traded goods create growt on te extensive margin. Tese extensive margin effects increase trade flows by more tan tat implied by te fall in tariffs and te elasticity of substitution. Tis mecanism contributes to te seemingly large estimated elasticities found wen regressing trade volumes on tariff canges or transportation costs as in Clausing (2001) or Hummels (2001). In Figure 6 we plot te components of (32): te expected gain from exporting for different productivity types and te value of a particular entry cost. Te intersection of tese two lines defines ˆ φ : te cutoff productivity for firms wit a particular entry cost κ. All te firms wit productivity less tan ˆ φ do not export, wile firms wit productivity greater tan ˆ φ do. To see ow te model responds to temporary socks compared to permanent canges, consider two scenarios. In te first scenario, te economy is subject 23

24 to a positive productivity sock. Tese socks are persistent, but not permanent. In response to te sock, te expected future value of exporting sifts up; for any level of idiosyncratic productivity, te gain from exporting is larger wen productivity is ig. Tis sift lowers te cutoff productivity to ˆbc φ and te firms between ˆbc φ and ˆ φ enter te export market. A typical conditional distribution over firm productivity types is sown in Figure 7. As te cutoff productivity moves to te left, te amount of new firms entering can be inferred from te slope of te distribution. If te slope is steep, te mass of firms entering from even a small cange in te cutoff productivity can be large. Te slope of tis distribution near te marginal exporter is a function of te model s parameters, wic will be determined in te calibration. Now consider subjecting te economy to a permanent decrease in tariffs of te same magnitude as te productivity sock. Te permanent cange sifts te expected future value of exporting up by muc more tan te persistent, but not permanent, sock. Te cutoff firm is now ˆtar φ, and te firms between ˆtar φ and ˆ φ begin exporting. Te larger sift in expected future profits from exporting from te tariff cange leads to a greater number of firms beginning to export. In Figure 7 we can see ow te large sift in te cutoff productivity leads to a greater number of new entrants tan in te case of te temporary sock. It is te difference in te number of new exporters under te two scenarios tat canges te implied Armington elasticity. If no new firms enter te export market in response to te productivity sock, ouseolds only substitute between te goods already being imported and domestically produced goods at te rate σ. Tis is trade growt on te intensive margin. In tis case, te measured Armington elasticity is exactly 1 ( 1 ρ ). If firms enter te export market in response to a cange in future profits, trade flows increase from te trade of te new exporters as well as te increase in trade of te continuing exporters. If newly traded goods are not accounted for, tis extensive margin growt sows up in te trade aggregates as intensive margin growt, and te response of imports appears very large. Te large response in trade to te cange in tariffs results in a large estimate of te Armington elasticity. 24