JEL codes: F10, F12, F14

Transcription

1 Teoretically-Consistent Parameterization of a Multi-sector Global Model wit Heterogeneous Firms by Zeynep Akgul 1, Nelson Villoria, Tomas Hertel April 2015 Abstract Parameter selection in Computable General Equilibrium (CGE) models of international trade is important for trade policy analysis as parameter values affect trade and welfare responses to canges in trade barriers. Tis is particularly important if te CGE model incorporates firm eterogeneity because it introduces a new margin of adjustment and canges te interpretation of parameter estimates. A remaining obstacle to fully understanding te insigts of trade in CGE models wit firm eterogeneity is te lack of an appropriate set of parameter estimates consistent wit te underlying teory. Our objective in tis paper is to solve for structural parameters tat are teoretically consistent wit firm eterogeneity models. Specifically, we focus on te elasticity of substitution across varieties. We distinguis between te extensive and intensive margins of trade flows and estimate two gravity equations by using country-level data for te motor veicles and parts industry. Our results sow tat te elasticity values tat are consistent wit te firm eterogeneity teory are considerably lower tan Armington (1969) elasticities used in te GTAP model. Tis implies tat current implementations of Melitz-type models wic use elasticities of substitution estimated in te absence of firm eterogeneity will give overly large trade volume responses to policy reforms. Keywords: Firm Heterogeneity, Melitz, Armington, Pareto Distribution, Elasticity of Substitution, Sape Parameter, Extensive Margin, Intensive Margin, Gravity Equation JEL codes: F10, F12, F14 1 Akgul is a P.D. candidate wit te Department of Agricultural Economics, Villoria is a Researc Assistant Professor of Agricultural Economics wit te Center for Global Trade Analysis, Hertel is a Professor of Agricultural Economics and te Executive Director of te Center for Global Trade Analysis, Purdue University, West Lafayette, IN 47907, USA. 1

2 1. Introduction Teoretical and empirical developments in te trade literature sow tat accounting for firm eterogeneity witin an industry improves our understanding of ow trade barriers affect trade flows and economic welfare by providing a new margin of adjustment troug self-selection of firms into and out of markets. Due to tis added explanatory power, firm eterogeneity teory as begun to be incorporated into computable general equilibrium models (CGE) (Akgul, et al. 2014, Balistreri, et al. 2011, Balistreri and Ruterford 2012, Dixon, et al. 2015, Zai 2008). However, a remaining obstacle to fully arvesting te insigts of trade in CGE models wit firm eterogeneity is te lack of an appropriate set of estimates of te elasticities of substitution and productivity distribution parameters consistent wit te underlying teory. Pinning down te structural parameters is paramount for policy analysis, as quantitative results eavily depend on parameter values. Our objective in tis paper is to estimate elasticity of substitution tat is consistent wit existing sape parameters of Pareto distribution at te GTAP level of industry definition. Caney (2008) extends te seminal work of Melitz (2003) and demonstrates tat in models wit eterogeneous firms, canges in trade barriers affect bot te volume of sales by existing exporters (i.e., te intensive margin of trade) as well as te number of firms in te export market (i.e., te extensive margin of trade) due to productivity differences across firms. An important finding in te literature is tat te extensive margin is quantitatively very important in governing growt in international trade flows (Hummels and Klenow 2005, Yi 2003). As a result, estimates of te elasticity of substitution by models tat ignore canges in te extensive margin are biased (Caney 2008, Helpman, et al. 2008). Tis finding contrasts wit te traditional Armington (1969) view of te world, wereby canges in trade barriers only affect te intensive margin of trade, wic is governed by te elasticity of substitution across varieties, σ (Hillberry and Hummels 2013). However, in firm eterogeneity models tere is an additional parameter of interest, namely te sape parameter of Pareto distribution, γ. Te sape parameter is an inverse measure of eterogeneity in productivity across firms witin an industry and it governs te supply-side effects of trade policies. In fact, te distribution of firm productivity significantly affects aggregate trade response to reduced trade costs as demonstrated in Caney (2008), Bernard, et al. (2003) and di Giovanni and Levcenko (2013). Terefore, to work wit a firm 2

3 eterogeneity model, we need to ave estimates of te sape parameter as well as te elasticity of substitution amongst varieties. Empirical studies of international trade flows rely on gravity equations in order to estimate te structural parameters of trade models. Gravity models relate te volume of bilateral trade to distance and oter determinants of trade. In a gravity model, te marginal effect of distance on trade volumes is given by 1, were is te distance elasticity of trade. Identification of 1 requires knowledge on eiter or. However, bringing in an additional parameter to reflect firm eterogeneity, i.e., introduces furter complexities in identifying te elasticity of substitution. Crozet and Koenig (2010) sow tat, in te firm-eterogeneity setting of Caney (2008), te marginal effect of distance on te probability of a bilateral trade flow taking place is given by. Terefore, tere are tree parameters to estimate, i.e.,, and, wic implies tat an exogenous source of information is needed to identify all of tem. di Giovanni and Levcenko (2013) and Eaton, et al. (2011) circumvent tis difficulty by imposing te prior values of on te model in order to calibrate te values of. Tis metod as two drawbacks: (i) Often, estimates for are obtained from Armington-type models wic are fundamentally inconsistent wit firm eterogeneity teory. (ii) Te resulting values for typically are not sector and region-specific and terefore do not capture te significant variation of eterogeneity along tese dimensions. For example, te sape parameter estimates in Spearot (2015) sow tat electrical macinery is a more eterogeneous industry were productivity differences across firms is more pronounced, wile petroleum refining is a muc more omogeneous industry. Moreover, according to is estimates, even toug electrical macinery is eterogeneous in te US, it is muc more omogeneous in Cile. Not accounting for tese drawbacks is likely to lead to biased estimates of parameters in te calibrated model. A teory-consistent approac to estimating te sape parameter is offered by Crozet and Koenig (2010) and Spearot (2015). Bot studies present estimates of at te product level in a firm eterogeneity model. Te model in Crozet and Koenig (2010) is based on Caney (2008), wile te model in Spearot (2015) is based on Melitz and Ottaviano (2008). Even toug Spearot 3

4 (2015) provides values for by industry and by region, e does not estimate elasticities tat are consistent wit. Only Crozet and Koenig (2010) ave a ric enoug dataset to identify bot parameters. Interestingly, teir estimates of te elasticity of substitution are lower wen compared to te traditional Armington elasticity estimates in te GTAP model (Hertel, et al. 2003). Unfortunately, teir estimates are of limited use for a global general equilibrium model because tey are based only on Frenc firms and cover a limited number of industries. Against tis backdrop, our objective in tis paper is to estimate a set of elasticities of substitution tat are teoretically consistent wit trade models considering firm eterogeneity. To accomplis tis, we extend te seminal work of Melitz (2003) to a multi-sector, multi-country model and build on Caney (2008) to distinguis te intensive and extensive margins of trade. For our gravity estimations, we use bilateral trade data at te country level from GTAP Version 8.1 (Narayanan, et al. 2012) wic covers te years Tis makes sense, since our ultimate goal is to incorporate tese parameters in a model based on te GTAP data set. In addition, we use te GeoDist and Gravity databases of CEPII (Mayer and Zignago 2011) wic include bilateral data on several relevant variables suc as distance, language, colonial link among oters determinant of bilateral trade. Te resulting dataset covers 113 countries over In tis paper, we focus on te motor veicles and parts industry (MVH) of GTAP wic, according to Spearot (2015) s parameters, as one of te igest productivity dispersions across firms among manufacturing industries. Future researc will extend tis work to all of te GTAP sectors and regions. Our estimation strategy merges te approac adopted by Helpman, et al. (2008) wit te extensive margin specification used in Crozet and Koenig (2010). We distinguis between te intensive and extensive margins of trade wic results in two estimating equations. Te first equation estimates te probability of a bilateral trade taking place, wile te second equation estimates te value of bilateral trade conditional on te coice to export. We refer to te first equation as te export participation equation and refer to te second equation as te gravity equation 2. Following Crozet and Koenig (2010) in bot equations we focus on te coefficient of 2 In principle, bot equations are gravity equations. However, we adopt tis convention to distinguis te new margin of adjustment due to firm entry/exit from te traditional gravity equation tat determines trade flows. 4

5 distance. In te export participation equation te distance coefficient is a combination of te distance and substitution elasticities. On te oter and, in te gravity equation, te distance coefficient is a combination of te sape parameter and substitution elasticity. Tis gives us two equations in tree unknowns, wereupon we use te sape parameter estimates provided in Spearot (2015) to infer te teoretically consistent estimates of substitution elasticities. Our estimation results sow tat te elasticity estimate consistent wit firm eterogeneity for te motor veicles and parts industry is considerably lower tan te GTAP Armington elasticity (Hertel, et al. 2003). Tis implies tat elasticities estimated in tat traditional way were in fact picking up additional effects accruing from te supply-side eterogeneity in tis framework. In summary, Armington elasticities are ig wen employed in te context of a firm eterogeneity model because tey confound demand-side effects wit te supply-side effects. Tis finding underlines te argument in Dixon, et al. (2015) about te observational equivalence between Armington and Melitz models. In particular, tey argue tat welfare implications of trade policies are similar in magnitude between tese models if te Armington and Melitz elasticities are cosen suc tat trade responses are equal across model specifications. In suc a scenario, Armington-based elasticities are iger tan Melitz elasticities. Tis implies tat using Armington elasticities in a firm eterogeneity model migt lead to overestimated trade volumes and welfare effects. By combining te teory-consistent econometric estimates wit te firm eterogeneity model in a CGE setting, we believe tat tis work will pave te way for mainstream application of firm eterogeneity models in policy analysis witin te global trade analysis community. 2. Background on Structural Parameters of te Firm Heterogeneity Model Altoug Melitz (2003) does not impose any restrictions on productivity, te common approac in te firm eterogeneity literature is to assume tat firms draw teir productivity levels from a Pareto distribution 3. Tere are two main reasons for coosing te Pareto distribution. First, te 3 Well-known examples are Arkolakis (2010), Caney (2008), Helpman, et al. (2008), Melitz and Ottaviano (2008), Eaton, et al. (2011) and Balistreri, et al. (2011) among many oters. Tere are some alternative productivity distribution assumptions in te literature. Examples include lognormal distribution (Head, et al. 2014) and Frécet 5

6 Pareto distribution is analytically tractable. As Caney (2008) argues, an important property of Pareto distribution is its stability to truncation from below. As a result of tis property, exporters, wic are more productive and terefore at te upper tail of te distribution, are also Pareto distributed. Moreover, te same sape parameter tat governs te distribution of domestic firms also governs tat of exporters 4. Te second reason for favoring te Pareto distribution over alternatives is empirical. Te Pareto distribution is a power law and provides a good fit for te observed size distribution of firms. Empirical support for tis distribution is found for US firms (Axtell, 2011) and Frenc firms (Eaton et al., 2011) among many oters 5. Te Pareto assumption for firm sales is equivalent to assume tat firm productivity is Pareto, toug wit a different sape parameter. Furtermore, te Pareto distribution predicts a linear relationsip between te log of rank and te log of firm size (Crozet and Koenig, 2010). An ever-expanding body of empirical studies uses tis property to consistently estimate sape parameters based on firm sales data. In particular, tey estimate te Power Law exponent of firm sales given by 1 to pin down and. However, since tis expression is a combination of and, it is not possible to estimate te individual structural parameters in tese studies. A key restriction on tese parameter values in tis context is te condition 1. Tis is described in Melitz (2003) and Caney (2008) as te condition tat ensures te firm size distribution as a finite mean. Tis is equivalent to saying 1. Terefore, te relative 1 values of and become critical for quantitative outcomes suc as export sales. Table 2 presents a summary of te structural parameters in te firm eterogeneity model. distribution (Bernard, et al. 2003, Eaton and Kortum 2002). It is argued in Luttmer (2007) tat a power law relationsip is a better fit for firm size distribution compared to te lognormal distribution. 4 Tere are new empirical findings tat migt callenge tis proposition. di Giovanni, et al. (2011) argue tat te sape parameter of firm size distribution is systematically different between exporters and non-exporters. Firm size distribution of exporters is more fat-tailed and as a lower sape parameter tan non-exporters because tey are more productive. Tis in turn implies tat te Pareto sape parameter of productivity distribution is different between exporters and non-exporters given a constant elasticity of substitution for firm varieties. 5 Size distribution of firms also follows a power law in te case of Japan (Fujiwara 2004, Okuyama, et al. 1999). See Gabaix (2008) for a full survey on power laws. 6

7 Te value of te sape parameter determines price differences across firms in te industry. A small sape parameter implies a large dispersion of productivity among firms wit lowproductivity firms capturing a small sare of te market. In tis case new entrants carge iger prices compared to te existing exporters. On te oter and, in an industry wit a large sape parameter, tere is a big mass of low-productivity firms tat represent a larger sare of industry output. In tis case, prices carged by new entrants are similar to te existing exporters. Tis supply-side eterogeneity is translated into export sales based on demand-side eterogeneity. A small elasticity of substitution means tat consumers are willing to pay a premium for differentiated varieties wic makes low productivity less of a disadvantage. Terefore, new entrants can capture a larger sare of te market. However, a large elasticity of substitution increases te competition in te market and makes low productivity a bigger disadvantage. As a result, marginal firms capture a small sare in te market. Tis discussion suggests tat export sales by new entrants are largest wen tere is supply-side omogeneity (ig ) and demandside eterogeneity (low ) (Hillberry and Hummels 2013). An opposite case is were 1 wic is known as te Zipf s Law. Tis yields a fat-tailed 1 distribution of firm size were te infra-marginal firms in te industry are large and ave a disproportionate sare of overall sales compared to te small marginal firms. In tat case, te welfare impact of trade is driven by infra-marginal firms rater tan te marginal ones. Terefore, te contribution of te extensive margin to trade is found to be negligible (di Giovanni and Levcenko 2013) 6. An implication of tis finding is tat quantitative results of trade cost reductions on trade flows and welfare are very sensitive to te firm size distribution and, by extension, very sensitive to te structural parameters of firm eterogeneity. Tis raises te stakes wen it comes to obtaining reliable estimates of te Pareto parameters. Even toug tere is a growing body of empirical work aimed at estimating structural parameters, tere is still substantial uncertainty about te appropriate parameter values to use in te firm eterogeneity model. Tis is particularly true because of te callenges associated wit 6 Tis can be linked back to te discussion in Dixon, et al. (2015) about te offsetting effects of extensive margin and productivity on welfare in a tariff increase scenario. 7

8 te identification of two parameters using only one estimating equation, as mentioned above. A brief overview of parameter values used in te firm eterogeneity literature is provided in Table 3 7. Tere are tree key points tat we can draw from tis table. First, empirical studies confirm tat te Power Law exponent of firm size distribution is around 1 (Axtell 2001, di Giovanni, et al. 2011) and it is used in various studies to infer sape parameter values by relying on external sources for elasticities (di Giovanni and Levcenko 2013, Melitz and Redding 2013). Second, te sape parameter values tat are calibrated using te Power Law exponent (di Giovanni and Levcenko 2013, Eaton, et al. 2011, Melitz and Redding 2013) or by oter metods (Arkolakis, et al. 2008, Zai 2008) are iger compared to te directly estimated values (Crozet and Koenig 2010, Spearot 2015). Using calibrated values of sape parameters would attribute lower productivity dispersion to te industry, wile tere could, in fact, be muc iger productivity eterogeneity across firms. Terefore, we prefer to use te information contained in te sape parameter estimates instead of tose from te calibration exercises. Tird, aggregation as a significant effect on parameter values. Estimates based on iger levels of aggregation are found to be iger tan te ones based on lower levels of aggregation. Tis is because wen we work wit aggregated products, we fail to capture te variation across sectors and we settle on one parameter value to describe te entire industry. For example, in te two cases were te parameter values are estimated at a disaggregate level, for more tan 30 sectors, te sape parameter estimates are found to sow substantial variation in te range of in Crozet and Koenig (2010) and in Spearot (2015). On te oter and, estimates/calibrations tat are at an aggregate industry level provide few values tat are in te range of 3-7, on average (Arkolakis, et al. 2008, Balistreri, et al. 2011, Bernard, et al. 2003, Eaton and Kortum 2002, Eaton, et al. 2011, Zai 2008). Similarly, te difference in aggregation is important for te elasticity values, as well. Elasticity estimates in Crozet and Koenig (2010) are in te range of , reflecting a wide range of demand-side eterogeneity compared to te more aggregated studies. In order to account for te variation across sectors, we prefer to 7 Tis table is by no means a full review of te literature. Te aim of tis table is to present only a sample of te most relevant work to explore te mainstream approac in obtaining parameter estimates and to compare te values of key parameters used in tese studies. 8

9 work at a disaggregated level of te manufacturing industry, focusing initially on te motor veicles and parts. Aggregation is extremely important in analyzing te extensive and intensive margin effects of trade flows, as well. Hillberry and Hummels (2013) argue tat te extensive margin plays a larger role wen one works wit aggregated product lines. On te oter and, te impact of te intensive margin is more pronounced wen we work wit disaggregated product lines. Making tis distinction is paramount in interpreting te results of any policy experiment. 3. Teoretical Model We present a model of international trade wit eterogeneous firms building on te teoretical model in Helpman et al. (2008) and Caney (2008). We consider te world to be composed of R countries, were we index exporters by r = 1, 2,, R and importers by s = 1, 2,, R. Every country produces and consumes differentiated as well as omogenous products. For te omogenous goods industry, we retain te traditional assumption of national product differentiation (Armington 1969) and te industry is caracterized by perfect competition wit constant returns to scale tecnology. On te oter and, we follow Melitz (2003) and assume tat tere are H differentiated industries indexed by = 1, 2,, H. Eac industry is composed of a continuum of firms were eac firm produces a unique variety indexed by. Moreover, firms differ in teir productivity levels and operate under monopolistic competition. 3.1.Consumers We adopt a Dixit-Stiglitz treatment in te demand-side. In tis setting, consumers are caracterized by love-of-variety were tey perceive eac variety as a unique product and derive utility from tat uniqueness. Te utility function for te differentiated good in country s, U given by U q d 1 1, (1.1) s r r s, is 9

10 were indexes te variety of good imported by country s from te source country r, r is te set of all varieties of good available in country r, representative consumer in country s of variety 1 is te elasticity of substitution between te varieties of good. q is te quantity demanded by a of good imported from country r and Let Ps be te price index of good in country s, i.e. te dual price index of te Dixit-Stiglitz composite of demand in equation (1.1), wic is given by were P p d 1 1 1, (1.2) s r r p is te price in country s of variety of good imported from country r (gross of trade costs). Based on tese demand and price aggregates, we can find te demand for eac variety of good sipped from country r to s to be as follows: q p Y 1 s Ps, (1.3) were Y s is te total expenditure in country s on industry (equal to income in te relevant industry in country s) 8. In tis setting, tere are to tis is tat tere are N r varieties of good produced in te exporting country r. A corollary Nr active firms in industry in country r. Eac firm produces a unique variety and te varieties produced by firms in te exporting country r are distinct from te varieties produced by firms in te importing country s. Eac country exports only a subset of its unique varieties because only some firms find it profitable to export into a given market. As a result, exports from country r to s includes only N Nr varieties being sipped on te r-s trade route. Tis means tat te total number of varieties of good available to consumers in Y P U p q d. 8 Please note tat s s s s 10

11 country s is N s domestic varieties plus N r imported varieties. Te following section gives more details as to wy only some firms are able to export in tis framework. 3.2.Producers Producer beavior is based on Melitz (2003). As previously mentioned tere are N r active firms in te monopolistically competitive industry of country r eac producing a different variety,, wit different productivity,. Firms in industry incur variable and fixed costs of production and of exporting. Tere are two types of fixed costs: sunk-entry costs to produce in te domestic market and fixed export costs to enter export markets. Fixed export costs are source-destination specific and are assumed to be identical across firms on te same bilateral trade route. Tere are two types of variable costs: marginal cost of production and transportation costs for export sipments. We adopt te standard assumption of iceberg transportation costs, in wic 1 units of good must be sipped from country r in order for one unit of good to arrive in country s. Te only type of cost tat is firm-specific in tis setting is te marginal cost of production wic equals cr / r for an active firm in industry of country r. Here, cr is te cost of te input bundle tat is used for producing one unit of output in industry of country r and r is te productivity of an active firm in industry of country r wic measures te amount of output produced by one bundle of input. Given te input bundle cost, let f measure te number of bundles tat is used by firms in industry to cover te fixed costs of exporting from country r to country s. Ten, te fixed export costs on tis particular bilateral trade route equals cr f. Te profit-maximizing price in a monopolistically competitive industry is a constant markup over marginal cost. Hence te delivered price in country s of te variety produced by a firm in country r wit productivity is given by p c 1 r, (1.4) 11

12 were 1 is te markup tat decreases wit a larger elasticity of demand. If preferences are more omogeneous (large ), te industry becomes more competitive and firms ave to carge a lower markup for teir respective varieties. Using te profit maximizing prices in equation (1.4) and utility maximizing level of sales in equation (1.3), te profit from exporting q units of good into country s is found to be 1 p q c r c f Y c f 1Ps r s r. (1.5) Firm export participation is determined by te potential profit to be made in eac bilateral market based on equation (1.5). Firm profit increases wit market size in te destination country ( Y s ), lower marginal costs ( c / ), and lower barriers to trade ( and f ). Productivity level of r r te firm plays a key role in determining te potential profit to be made on a particular trade route based on fixed costs associated wit exporting. Particularly, destination-specific fixed export costs limit te number of exporters from source country r since only te firms wit ig productivity levels can cover fixed export costs and make positive profits in te export market. Te cutoff productivity level of exporting is destination-specific and is determined by te zero profit condition on eac bilateral trade route. Te revenue made by te marginal exporting firm is just enoug to cover total costs of exporting and determines te productivity tresold. Let te * productivity tresold for firms in industry to export from country r to s be, wic is governed by te following equation * c r cr f 1 Ps Ys 1 1. (1.6) * Firms tat ave a iger productivity level tan will successfully export on te r-s route, * wile te rest of te firms, wic ave lower productivity levels tan, will only supply te domestic market. Tis self-selection mecanism determines te number of firms in export markets wic can differ across destinations. As mentioned above only a subset 12 N firms out of

13 te total Nr firms are able to export into country s and te mass of firms in tis subset depends on te productivity distribution in te industry. We assume tat firm productivity follows te Pareto distribution wit support sape parameter min, and tat satisfies te condition 1. Te associated density function, g, and cumulative distribution function, g G, are ten as follows: 1, G 1, (1.7) min were min 1, is assumed in tis paper. 9 * Given te productivity distribution, 1 G measures te proportion of firms tat ave productivity levels iger tan te tresold. Terefore, te fraction of active exporters to all firms in te industry N / N equals * 1 G. 10 min r * 3.3.Aggregate Trade Flows Te value of aggregate trade flows is te product of number of firms tat sell in te destination market and te average revenue along te bilateral trade route. Let M be te total value of demand in destination country s for good sourced in country r wic is given by * M N p q d, (1.8) were is te productivity distribution of successful firms in equilibrium, i.e. conditional distribution of g on support *, as in Melitz (2003): 9 Helpman et al. (2008) uses a truncated Pareto distribution by imposing upper and lower bounds to productivity. Te reason for tese bounds is to construct a model tat can explain zero trade flows in te country level data wit firm beavior. But, using a truncated Pareto distribution brings about nonlinearities into te model wic we do not attempt to solve in tis paper. For analytical tractability purposes we coose to impose only a lower bound for productivity. An implication of tis assumption is tat because tere is a continuum of firms in te industry, tere is a positive mass of exporters for all country pairs as noted in Head and Mayer (2014). 10 Tis follows from N N g d. * r 13

14 g * if * 1 G (1.9) 0 oterwise We simplify (1.8) by using optimal demand and price for good given by equations (1.3) and (1.4). Te simplified representation of bilateral trade flows is ten given by M 1 cr * Ys NrV if 1 P 0 oterwise, s (1.10) were V is defined as in Helpman et al. (2008) 11 : * 1 V g d (1.11) Equation (1.10) can be tougt of as a measure of te intensive margin because it takes export sales of all exporters into account in determining aggregate export sales on a particular trade route. Equation (1.10) also sows tat bilateral trade flows increase wit market size of te importer s s Y, te mass of firms in te industry N r, competition in te importing market P, reductions in barriers to trade and reductions in factor costs c s r. A quick look at equation (1.10) would suggest tat te elasticity of trade wit respect to reduced trade costs is 1. Tis corresponds to te trade-cost elasticity in te Dixit-Stiglitz-Krugman monopolistic competition model. However, tis is only part of te story. In fact, 1 only represents te demand side effects of reduced trade barriers in a firm eterogeneity model. Tere are additional effects of trade cost reductions embedded in V wic work troug te supply side. In particular, V represents ow self-selection of firms into export markets stimulate average 11 V corresponds to te average productivity in te industry. In Melitz (2003), average productivity is defined as * 1 *. Based on tis definition, we avev 1 * G d note tat since we define bilateral N. 1 V as V g d, we can express * 14. Please M in terms of N r instead of te

15 productivity and tereby increase trade flows in te case of lower trade barriers. Tis mecanism introduces te supply side effects of trade cost canges into equation (1.10). Te combined effect of demand and supply side effects reveals tat te trade-cost elasticity of trade flows in a firm eterogeneity model is different from tat of a model wit omogenous firms. In fact, Caney (2008) sows analytically tat trade-cost elasticity 12 is equal to te supply side parameter in a multi-country Melitz (2003) framework. Tis finding paved te way for subsequent empirical work tat canged te interpretation of parameter estimates in gravity equations in te presence of eterogeneous firms. 3.4.Extensive, Intensive and Compositional Trade Margins Many empirical studies in te gravity literature distinguis between two margins of adjustment to trade socks: intensive and extensive margins. As trade costs fall, not only does te volume of sales from eac exporter increase, i.e. intensive margin, but te set of exporters canges as well, i.e. extensive margin. As opposed to tis two-way decomposition, Head and Mayer (2014) offer a tree-way decomposition by arguing tat an implicit margin is embedded in te conventional interpretation. Since new entrants are less productive tan te existing exporters, sales of new entrants are lower tan te average sipment prior to trade cost reductions. Te margin of adjustment as a result of tis difference in sales is referred to as te compositional margin by Head and Mayer (2014). Te compositional margin is a part of te extensive margin in Caney (2008) and Crozet and Koenig (2010), wile it is included in te intensive margin in Bernard et al. (2007) and Hilberry and Hummels (2008). Needless to say, depending on ow te compositional effects are assigned, te relative contribution of te intensive and extensive margins of trade will vary across oterwise identical studies. Terefore, it is appealing to break out tis compositional effect. Here we explicitly sow te tree-way decomposition of trade-cost elasticity. Trade flows in equation (1.8) can be written as te product of te number of exporters and average sales per 12 Elasticity is defined as M M. 15

16 exporter, were average sales is defined as M N m m m d. * Using te Leibniz rule, as in Caney (2008), we obtain a decomposition of te trade-cost elasticity similar to te one in Head and Mayer (2014) as follows: ln M 1 ln m m ln m ln * extensive margin intensive margin ln N ln 1 G ln ln ln * * m * ln 1 * m compositional margin d. (1.12) Te first component in equation (1.12) is te intensive margin wic gives te adjustment in trade-cost elasticity due to canges in sales of te existing exporters. As mentioned before, te intensive margin effect is te same as in te traditional Armington model. Te second component is te extensive margin, due to canges in te set of exporters. Te tird component is te compositional margin due to lower per firm sales of new entrants. In particular, te term m m * 1 captures te difference between lower sales of new exporters and te average sales of te incumbents in te export market. We follow Head and Mayer (2014) in simplifying equation (1.12) by applying te Pareto distribution and using te optimal demand and pricing equations. Te resulting trade-cost elasticity of trade flows is identical to Caney (2008). ln M ln 1 1. (1.13) intensive margin extensive margin compositional margin According to equation (1.13) te intensive margin depends only on te demand-side parameter and is equal to te trade-cost elasticity in a Krugman-type model wit omogenous firms. Similarly, te compositional margin also depends on te demand-side parameter as sales of new entrants are also governed by te substitution elasticity. An important discussion in Head and 16

17 Mayer (2014) is tat te intensive and compositional margins exactly offset eac oter due to te assumed Pareto distribution. Tis is in line wit te discussion in Caney (2008) even toug is definition of te extensive margin includes te compositional part as well. He states tat firmlevel trade beaves in te same way as aggregate trade beaves in traditional models. As a result, te intensive and compositional margins affect te trade elasticity wit te same magnitude, but in opposite direction. On te oter and, te extensive margin introduces supply-side effects troug te sape parameter. In te end, wat determines te final trade-cost elasticity of trade flows is te extensive margin in a firm eterogeneity model. An interesting point Caney (2008) makes is tat in firm eterogeneity models, te impact of trade barrier canges on trade flows is larger tan tat of te representative firm models. Tis due to te required condition 1 wic sows tat te quantitative importance of te extensive margin on trade flows is iger in a firm eterogeneity setting compared to te intensive margin effect. In tis paper we adopt te convention in Caney (2008) and include te compositional margin witin te extensive margin. Terefore, our definition of te extensive margin captures te combined effect of export sales per new exporter and te cange in te set of exporters. Terefore, wen we refer to te extensive margin in tis paper, we refer to Data We use two data sources in tis paper. Bilateral trade data comes from te Global Trade Analysis Project (GTAP) Version 8.1 (Narayanan, et al. 2012). Tis version includes 57 GTAP commodities and 134 GTAP regions of wic 113 country titles are available. We use te time series bilateral trade data of tis version tat covers te period 1995 to 2009 wit 2007 as te reference year. (Detailed information about data sources and variable definitions can be found in te data appendix.) In tis paper, we focus on te motor veicles and parts sector, coded as MVH in GTAP. Terefore, we only use te trade data tat is related to MVH. Tis coice is based on te information about te sape parameter estimates reported in Spearot (2015). Motor veicles and parts is one of te most eterogeneous industries wit respect to productivity in Spearot (2015) 17

18 wit a value of On te oter and, te Armington elasticity in GTAP for motor veicles and parts is 5.6 (Hertel, et al. 2003). A comparison of tese values reveals tat te condition for finite size distribution 1 is not satisfied for MVH if we stick to te Armington elasticity ( ). Trade barriers wic are modeled as iceberg trade costs are not explicitly observed in te data. Terefore, a common approac in te gravity literature is to assume tat iceberg trade cost is a function of many observable variables suc as te pysical distance between trading partners, saring a common language, aving a colonial relationsip etc. We adopt te same approac and use te distance (GeoDist) and gravity (Gravity) databases of Centre d`etudes Prospectives et d Infiormations Internationales (CEPII) to obtain te information about gravity variables. GeoDist is CEPII s distance database developed by (Mayer and Zignago 2005) and it includes country-specific data for 225 countries and bilateral data for 224 country pairs. Furter details about tis database can be found in Mayer and Zignago (2011). In our paper, data on distance, contiguity, common language, colonial links and landlocked countries are obtained from GeoDist. In addition, we use CEPII s Gravity database based on Head, et al. (2010). Tis database covers an exaustive set of variables for 224 countries for te period 1948 to In our paper, data on common legal origins, common currency, FTA and GATT/WTO membersip are obtained from Gravity. Te time period considered in tis paper is from 1995 to 2006 to matc te time series of bilateral trade from GTAP and te gravity variables from CEPII. In particular, we drop te years from te GTAP time series data and we drop te years from te CEPII Gravity data. Our final dataset is obtained by merging GTAP data wit CEPII data for motor veicles and parts industry, 113 country titles and it covers te period from 1995 to Te list of countries included in our dataset is presented in Table 1. Table 4 provides descriptive statistics for te final sample of our dataset. We also tabulate te frequency of zero trade flows in te dataset by year in Table 5. Bilateral trade datasets are known to include large numbers of zeros even at te country level (Helpman, et al. 2008). Our dataset is no exception. As reported in Table 5, zero trade flows of motor veicles and parts account for 77 18

19 per cent of te observations over te period Large fraction of zeros in te dataset is known to cause sample selection bias in coefficient estimates in gravity equations were te dependent variable is log of trade flows. Since te logaritm of zero is undefined, zero observations are dropped from te sample in traditional OLS regressions. We follow te approac adopted in Helpman, et al. (2008) to control for sample selection. Table 5 also sows tat te fraction of zero trade flows diminised across years. Wile zero trade flows account for almost 81 per cent of te observations in 1995, tis fraction reduces to 71 per cent in Tis reduction implies tat tere ave been new bilateral trade routes created over te course of 12 years in motor veicles and parts industry. We can interpret tis as te reflection of extensive margin effect in te data resulting from firm entry and exit over te years. 5. Empirical Metodology We follow te common practice of estimating te intensive and extensive margins of trade using a specification based on te gravity equation. Our empirical strategy draws on te work of Helpman et al. (2008) and Crozet and Koenig (2010). Te empirical strategy in Helpman et al. (2008) is to develop a two-stage Heckman estimation procedure were tey explicitly account for unobserved firm eterogeneity and sample selection bias to consistently estimate te gravity equation in a firm eterogeneity model. Similarly, we consider two equations. Te first one is an export participation equation in wic we estimate te effect of distance on te probability tat a firm exports on te r-s route. Te second one is a gravity equation in wic we estimate te effect of distance on aggregate trade flows. We diverge from Helpman et al. (2008) on two fronts. First, we estimate tese two equations separately, not simultaneously. Second, our latent variable definition for te first equation is different and follows Crozet and Koenig (2010). Since we focus only on te motor veicles and parts industry, we suppress te subscript for industries in te rest of te paper. Moreover, we introduce a time subscript t to te variables tat ave different values across years. 5.1.Export Participation: Probit 19

20 Te first equation we estimate is te probability of firm participation in export markets wic captures entry/exit of firms, i.e. te extensive margin effect. Firm activity is not explicit in our dataset because we only observe trade flows at te country level. Helpman et al. (2008) use a latent variable in order to capture firm beavior in country level observations. Teir latent variable is defined as te ratio of variable export profits to fixed export costs. According to tis specification, positive trade flows are observed at te country level if and only if te latent variable is greater tan one. However, tis specification does not use te information implicit in te productivity distribution. As a result, te Pareto sape parameter does not appear in te export selection equation considered in Helpman et al. (2008). In tis paper, we want to sow te interaction between te sape parameter ( ) and te substitution elasticity ( ) wic requires use of te productivity distribution. Terefore, we follow te latent variable definition in Crozet and Koenig (2010) and compare firm productivity wit te productivity tresold in te export market. We now turn to te details of tis approac. A firm wit productivity exports from country r to s if its productivity level passes te * tresold level, i.e. rs. Let T rst be an indicator variable were Trst 1 if te country r exports MVH to country s in year t, and zero oterwise. Ten, te probability tat a firm exports * from r to s in year t is given by Pr Trst 1 Pr rst distribution function of te Pareto distribution we obtain. Wen we apply te cumulative T * * rst rst rst Pr 1 Pr. (1.14) Substituting equation (1.6) into (1.14) and rearranging, we obtain te following equation for firm selection into export markets rstc r cr f rst rst f rst Pr Trst 1 1 Ps Ys 1 Ps Ys c 1 r. (1.15) We do not ave information about te value of variable trade costs and bilateral fixed export costs in our dataset. Hence we follow te convention of imposing additional structure on variable 20

21 and fixed costs. Variable trade costs are assumed to be a function of distance between countries and several oter trade barriers as follows: D expk u, (1.16) rst rs rst rst were Drs is te distance between country r and s, is te distance elasticity of trade wic is strictly positive, 2 u rst is a vector of trade impeding and trade facilitating variables and u N 0, captures unobserved trade costs tat are i.i.d. rst We follow Balistreri et al. (2011) and Helpman et al. (2008) and model fixed export costs as a combination of barriers imposed by importers only, by exporters only and by a county-pair specific bilateral cost. Let f exp v, were r are fixed export costs rst r s rs rst common across destinations incurred by exporting country r, imposed by te importing country on all exporters, 2 barriers, and rst 0, v s are te fixed trade barriers rs are country-pair specific fixed trade v N captures unmeasured trade frictions. Helpman et al. (2008) notes tat v rst is i.i.d; owever, tey may be correlated wit te unmeasured variable trade costs, u rst. Incorporating tese definitions of variable and fixed export costs into equation (1.15) and taking logaritms of bot sides we get te following probit equation: T 0 D E E 4 5 Pr 1 ln, (1.17) rst rs r s rs rst rst were 0 ln 1, 4, 5 k, E ln 1 r cr r 1 1 effect wic controls for te marginal cost ( c r is an exporter fixed ) and fixed cost ( r ) tat are associated wit te exporter, Es ln Ps lnys s is an importer fixed effect wic controls for market

22 2 2 size and fixed costs associated wit te importer and urst vrst rst N 0, u v is i.i.d 13. We also add a year dummy tat controls for te omitted variables wic vary across years but common to all trade flows. Te estimating equation, ten, becomes were T 0 D E E E 4 5 Pr 1 ln, (1.18) rst rs r s t rs rst rst E t is a year dummy. In our first step regression, we estimate te Probit equation in (1.18) for motor veicles and parts industry. Since fixed export costs, captured by te variable rs, only affect te probability of a bilateral trade taking place, we can use tem as exclusion restrictions. We will turn to tis again in te results section Trade Value: OLS Te second step in our empirical strategy is to estimate te value of export sales using te gravity equation. We use te aggregate sales of motor veicles and parts from country r to country s tat is governed by equation (1.8). Log linearizing equation (1.8) and using variable trade costs defined as (1.16), we obtain te following regression equation: ln M 1 ln D E E lnv u, (1.19) rst 0 rs r s 4 rst rst rst were, k 0 1 ln E 1 ln c ln N is an exporter fixed effect r r r wic controls for te marginal cost ( c r ) and new varieties ( N r ) tat are associated wit te exporter, E 1 lnp lny is an importer fixed effect wic controls for importer size and s s s 2 prices, and rst 0, u u N is i.i.d. Consistent estimation of Equation (1.19) requires two corrections as argued in Helpman, et al. (2008). Te first correction requires adding a control variable into (1.19) for te sample selection bias. Omitting country pairs tat ave zero trade flows from te dataset migt cause a correlation 13 Tere is an implicit assumption we impose ere. For simplicity, we assume tat Helpman, et u v al. (2008) do not impose tis restriction wic means tat all coefficient estimates in teir Probit specification is normalized by.

23 between te unobserved estimate for., 1 rst rst u rst and te explanatory variables. Terefore, we need a consistent E u T. Following Helpman, et al. (2008) we define te consistent estimate as Eu., T 1 corr u, were E., T 1 rst rst rst rst u rst. In order to be rst rst rst able use tis in te gravity equation, we also need a consistent estimate of rst. As is customary in te Heckman procedure, we obtain tis consistent estimate from te inverse Mills ratio ˆ rst ˆ rst ˆ rst, were ˆrst te estimated Probit equation in (1.18). be te predicted probability of trade between country r and s based on Te second correction requires adding a control variable into (1.19) for te entry/exit of firms into export markets wic is captured by te variable lnv rst. Since firm productivity is not observed, we need a consistent estimate for lnv., 1 E T. Here, we diverge from Helpman, et al. (2008) because our export participation is different from teirs. Instead, we use te relationsip between lnv rst and rst rst * ln rst and apply te cumulative distribution function of firm productivity. Te predicted value of our latent variable is ˆ ˆ* rst rst. In log-linear form tis is equivalent to ln ˆ ln ˆ rst. Using tis condition and te definition in (1.11), a consistent * 1 estimate for lnv rst is given by te following: ˆ 1 ln ln ln ˆ 1 V rst rst. (1.20) We use (1.20) to transform our gravity equation in (1.19) wic gives ˆ ln M 1 ln D E E E ln ˆ, (1.21) rst o rs r s t rst rst rst rst were o 0 ln 1, 4 4, 5 new error term rst 1 satisfies te condition E T and estimate te gravity equation in (1.21) for motor veicles and parts. 6 corr u rst, rst u. We note tat te., 1 0. In our second step regression, we rst rst 23

24 Equation (1.17) delivers a combination of te distance elasticity and te sape parameter,, wile equation (1.19) delivers a combination of te distance and demand elasticities, 1 However, estimates of. and 1 are not enoug to identify tree parameters separately. To circumvent tis difficulty Crozet and Koenig (2010) estimate a tird equation tat governs te relationsip between eac firm s total factor productivity and its production by using firm level data. From tis equation tey obtain an estimate of 1, wic facilitates te identification of tree parameters in tree equations. Wit country-level data we cannot determine te relationsip between firm sales and teir total factor productivity. Instead, we take te ratio of te two coefficients from te Probit and OLS equations wic gives estimates of 1. Incidentally, tis fraction is te Power Law exponent of firm size distribution. In order to solve for te elasticity of substitution in tis fraction, we use te sape parameter estimates provided in Spearot (2015). Tis metod delivers estimates of, wic are conditional on \gamma, and terefore, consistent wit te underlying firm eterogeneity teory; tis estimate of \sigma is assumed to capture canges in trade flows coming from substitutability in consumption wile \gamma captures te canges in trade flows taking into account te variation in productivity across industries and regions. 6. Results and Discussion 6.1.Estimation Results Table 6 presents our estimation results. Te first two columns give te regression results for a Probit model tat determines te probability of firm export participation. Column (1) reports marginal effects evaluated at sample means, wile estimates reported in (2) are parameter estimates. Column (3) gives our bencmark model wic is a standard gravity equation estimated using ordinary least squares Column (4) reports estimation results for equation (1.21) were we include te variables X and Y wic correct for sample selection as well as firm eterogeneity. All models in Table 6 include country-specific fixed effects as well as year dummies. Standard errors reported in all models are adjusted for clustering on country-pairs. 24