Firm-level Distortions and Aggregate Productivity: The Trade Channel

Transcription

1 Firm-level Distortions and Aggregate Productivity: The Trade Channel By Lucas Scottini PRELIMINARY AND INCOMPLETE Abstract This paper proposes a novel mechanism by which firm-level distortions affect aggregate TFP. I study a multi-country general equilibrium model of international trade featuring rich cross-country heterogeneity, in which heterogeneous firms are subject to idiosyncratic distortions and to costly access to export markets. Because more-productive firms engage more intensely in international trade than lessproductive ones, firm-level distortions - beyond their traditional closed-economy consequences - reduce aggregate productivity by depressing the economy s trade openness. I explore the quantitative properties of the model by calibrating it to firm-level and aggregate data for a set of 81 countries. I find that international trade amplifies the average impact of micro distortions on aggregate TFP by a factor of two. Selection and reallocation channels play a prominent role in accounting for this magnification effect. Moreover, reducing distortions to the US level increases average trade openness in the manufacturing sector by 50% and halves the elasticity of trade flows with respect to trade costs, boosting the welfare gains from trade. JEL classification: F12, F63, L25, O11, O47 Keywords: Misallocation, Firm-Level Distortions, Gravity Equation, International Trade Ph.D. Candidate, Department of Economics, Brown University. lucas scottini@brown.edu. I am extremely grateful to Jonathan Eaton and Joaquin Blaum for invaluable guidance and encouragement. I thank Jesse Shapiro, Oded Galor, David Weil, Arnaud Costinot, Sharon Traiberman, Heitor Pellegrina, Michael Peters and seminar participants at Brown University, Penn State University and EconCon Conference at University of Pennsylvania for helpful comments. I also thank Bruce Boucek for helping with the UNIDO industrial dataset and Ana Margarida Fernandes for providing access to non-public moments of the World Bank s Exporters Dynamic Survey. All remaining errors are my own. 1

2 1 Introduction Recent theoretical and empirical research has shed light on how cross-country differences in aggregate productivity relate to differences in within-industry allocative efficiency. The main hypothesis of this emerging literature is that firm-level distortions, stemming from market failures or policy-related elements, prevent productive factors from flowing to the most efficient entrepreneurs of the economy. One branch of this research agenda consists of closed-economy models tailored to study the aggregate impact of purely domestic micro frictions. Examples include imperfect output markets (Peters [2013]), size-dependent policies (Guner et al. [2008] and Garicano et al. [2016]), contractual frictions (Akcigit et al. [2016]) and financial frictions (Buera et al. [2011] and Moll [2014]). Another strain of work, based on the seminal contributions of Melitz [2003] and Bernard et al. [2003], has investigated how barriers to international trade influence industry performance by shifting resources among firms of heterogeneous efficiencies. As successful as these two literatures have been, little quantitative work has attempted to provide a bridge between them. In particular, the interaction between domestic firm-level frictions and trade frictions in the determination of aggregate outcomes has remained relatively unexplored. 1 This paper investigates the role of micro distortions in explaining aggregate TFP when there is endogenous selection of firms into export markets. My analysis builds on two empirical regularities: (i) factors that distort firm size, particularly in developing countries, tend to harm larger firms disproportionately and (ii) large firms tend to engage in export and import activities, whereas small firms do not. Under these circumstances, I show that distortions to the size distribution of firms have amplified impacts on aggregate productivity because they also affect the economy s trade openness. I argue that this mechanism helps to tie together three apparently unrelated stylized facts from the macro development and international trade literatures: (i) distortions to firm size tend to be more severe in developing countries, 2 (ii) developing economies are relatively more unproductive in tradable sectors, 3 and (iii) trade openness increases with development. 4 1 A notable exception is Manova [2013], who studies the relationship between misallocation of capital among heterogeneous producers and export performance. However, her exercise does not solve and estimate an equilibrium model, which prevents it from assessing the effects of financial frictions on aggregate productivity and international trade in general equilibrium. Ho& [2010] also studies the relationship between trade and firm-level distortions in the context of India s 1991 trade liberalization. However, her methodology is limited to a stylized two-country model and does not take into account the effects of firm-level distortions on trade elasticities when there is endogenous selection of producers into exporting. Finally, Tombe [2015] and Swikecki [2017] introduce inter-sectoral frictions in quantitative trade models. 2 For empirical evidence, see Hsieh and Klenow [2009] and Hsieh and Klenow [2014], Aterido et al. [2007] and Bartelsman et al. [2013]. 3 For empirical evidence, see Hsieh and Klenow [2007]. Buera et al. [2011] and Blaum et al. [2012] show that imperfections in credit markets are particularly harmful to aggregate productivity in sectors with large scales of operation, which are more likely to be tradable. 4 See Helpman et al. [2008], Fieler [2011], Manova [2013] and Tombe [2015]. 2

3 My starting point is a multi-country general equilibrium model of international trade with heterogeneous firms, in the spirit of Chaney [2008] and Eaton et al. [2011], extended to incorporate key ingredients from the development literature. Countries are characterized by a Pareto distribution of firm-level technologies, a set of bilateral trade costs and domestic institutions that shape the environment for firm entry, exit and growth. Each economy has two sectors: a perfectly competitive final-good sector, which combines labor with domestic and imported inputs to produce a homogeneous nontradable good; and a manufacturing sector, with monopolistic competition and free-entry of heterogeneous firms that produce intermediate varieties for domestic and foreign markets. As in Melitz [2003], firms in the manufacturing sector endogenously select into production and exporting. The central feature of the model is that manufacturing firms are subject to idiosyncratic tax-like wedges, as in Restuccia and Rogerson [2008], Bartelsman et al. [2013] and Hsieh and Klenow [2014]. These wedges capture market failures and policy-related obstacles, such as regulations, licenses and taxes, that apply with varying degrees of intensity according to firm size. Importantly, I assume that such distortions are driven by exclusively domestic factors and, therefore, are unaffected by trade liberalization. The elasticity of wedge to firm efficiency, which I refer to as the schedule of distortions, controls the quality of the business environment. This elasticity maps to the withinsector dispersion of measured productivity across firms, a common metric of allocative efficiency. For instance, a perfectly flat schedule results in the equalization of marginal products across manufacturing firms, whereas a steep schedule implies that more efficient firms run into stronger constraints to achieve their optimal sizes. I use this theoretical framework firstly to provide two analytic results on how domestic distortions affect the economic impacts of trade barriers. First, according to the gravity equation emerging from the model, a steeper schedule of distortions in the origin country makes its aggregate export sales more sensitive to trade barriers. In other words, the same trade barrier represents a larger impediment to exports for more distorted economies. The reason is that, with firm heterogeneity and selection into export markets, the trade elasticity captures the size of marginal exporters relative to the size of inframarginal exporters. Correlated distortions, by reducing the relative size of the most efficient firms, compresses the distribution of firm size, which ultimately increases the trade elasticity in the origin country. From an aggregate perspective, a distorted economy looks as if it faces higher costs to export its goods. This result implies that cross-country differences in allocative efficiency endogenously generate the within-sector asymmetric trade patterns between rich and poor countries found in the gravity literature. 5 Second and related, a sufficient-statistic equation akin to the one in Arkolakis 5 As emphasized by Waugh [2010], export costs need to be systematically higher in poor countries in order to reconcile a standard gravity model with aggregate price data. Helpman et al. [2008] find robust evidence of asymmetric trade relationships between advanced and developed economies. 3

4 et al. [2012] describes the gains from trade in the model. This equation demonstrates that, for any given dispersion of firm-level technologies, a steeper schedule of distortions obstructs the reallocation of productive factors to the most efficient firms of the economy, thereby reducing the welfare gains from trade liberalization. 6 The connection between domestic frictions and trade elasticity amplifies the impact of firm-level distortions on aggregate TFP in the following way. In a closed economy, a less steep schedule of distortions boosts aggregate productivity through three channels: (i) increased entry in the manufacturing sector, (ii) exit of less productive entrepreneurs and (iii) reallocation of labor to surviving entrepreneurs with high marginal productivity. In an open economy with costly trade, a flatter schedule has the additional effect of reducing trade barriers relative to the distribution of firm size, thereby increasing trade openness and ultimately reinforcing the initial impact of the selection and reallocation mechanisms on aggregate TFP. One can interpret this trade channel as an example of a recent result in Hopenhayn [2014], according to which distortions are more harmful to aggregate TFP when they concentrate at a larger mass of employment. Intuitively, by making the relative size of the most productive firms even larger, international trade concentrates more resources in plants with high marginal products, thus worsening the productivity losses from micro frictions. The empirical implementation of the model consists of three steps. The first step estimates each economy s schedule of distortions with firm-level data on revenues and input use from domestic firms. The data come from the latest version of the World Bank Enterprise Survey (2016), which covers more than 100 countries. Earlier versions of this dataset have been used by other studies in the misallocation literature (see Asker et al. [2014] and Bento and Restuccia [2016]). I follow the standard procedure in Hsieh and Klenow [2009] of calculating for each firm two measures of productivity: a revenue-based measure (T F P R) and a quantity-based measure (T F P Q). According to the theory, in the absence of distortions and overhead costs, all the firm-level heterogeneity in physical productivity (T F P Q) is compensated for with variation in revenues and input use, thereby eliminating the within-sector dispersion of T F P R across firms. In a distorted economy, however, the dispersion in T F P R becomes a measure of the idiosyncratic distortions faced by firms. I then estimate the schedule of distortions as the within-sector elasticity between T F P R and T F P Q. The results reveal that schedules tend to become smoother with development. Developed countries like Spain, Sweden, Israel and Ireland have elasticities approximately 50% lower than emerging economies like China and India. Furthermore, the slope is highest in Sub-Saharan African countries and Eastern European economies, and lowest in the US. The second step recovers the shape parameters of the Pareto distributions of micro technologies. These parameters determine the amount of technological heterogeneity in the tradable sector and, therefore, delimit the scope of potential gains from reallocation. 6 For more on this topic, see Melitz and Redding [2015]. 4

5 I exploit the model s prediction that the elasticity of aggregate exports with respect to variable trade costs informs us on the dispersion of firm size, which is a convolution of the shape parameter and the schedule of distortions. Using bilateral data on manufacturing trade and tariffs for the year 2007, I estimate a structural non-linear gravity equation to recover exporter-specific trade elasticities. Contrary to the standard assumption in the gravity literature, I find considerable within-sector dispersion of trade elasticities across exporting countries. Whereas OECD economies present trade elasticities between 4 and 5, developing countries display much larger elasticities, ranging from 10 to 15. These findings have important implications for the analysis of commercial policy, particularly when it involves countries at different stages of development. I validate my estimates by showing that they strongly correlate to measures of dispersion and skewness of firmlevel exports for a sub-sample of countries with available microdata. Armed with these elasticities and the schedules from the first step, I am able to identify the dispersion of micro technologies. The third step consists of choosing the remaining parameters of the model. I pin down the mass of entrants in each country using cross-country data on the costs of starting a business provided by the World Bank s Doing Business Survey. I also take advantage of information on tariffs, geographic distance and freight costs to define variable trade costs. Finally, I calibrate technological parameters and fixed trade costs such that the model matches the empirical bilateral trade shares. With a fully parameterized version of the model in hand, I first quantify the TFP losses from firm-level distortions in a trading economy - i.e, an economy with the calibrated trade costs. This counterfactual exercise consists of endowing each country in the sample - one at a time - with the US efficiency and then computing the new world trade equilibrium. The US schedule of distortions is a crucial benchmark in this case because even an economy at its first-best equilibrium can look distorted because of overhead costs, adjustment costs, or model misspecification. I find an average gain in aggregate TFP of 23%. The majority of this effect comes from the selection and reallocation channels - approximately 20 percentage points - whereas the entry channel plays a minor role. These gains are very unevenly distributed across economies. At the low end of the gain spectrum are OECD economies, which are undistorted relatively to the US to begin with, and poor and closed countries, that are very distorted but lack high diversity of manufacturing micro-technologies. The benefits are largest among emerging economies that combine very steep schedules of distortions with large technological heterogeneity. This group includes big emerging economies like Brazil, Russia, India and China, whose aggregate TFP increase, respectively, by 52%, 100%, 31% and 53%. I then repeat this same counterfactual exercise in the closed-economy case. In this context, the world economy becomes just a sequence of isolated domestic economies. The cross-country average productivity gain from converging to the US efficiency significantly drops to 11%. Selection and reallocation channels totally account for this 5

6 reduction, with their contribution to average TFP gain dropping from 20 percentage points to 7.7 percentage points. These results indicate that international trade potentially plays a crucial role in magnifying the aggregate productivity effects of distortions to firm size. In other words, the payoff of domestic reforms aimed at improving the business environment is even larger when the economy is integrated to the global trade network. I further study this reinforcing mechanism by investigating the effect of firm-level distortions on trade openness, as measured by the import penetration ratio (IPR) in the manufacturing sector. 7 Moving to the US efficiency increases the average manufacturing IP R from 50% to 77%. This helps to narrow the gap in trade openness between developed and developing economies observed in the data. Furthermore, it suggests that purely domestic policies have great potential to affect trade performance even when they don t target trade costs directly. I also show that by increasing IP R and by reducing the aggregate trade elasticity, the alleviation of micro distortions enhances the gains from trade considerably. The average productivity gains of moving from a closed economy to an equilibrium with the calibrated trade costs increases from 3% to 14%. My last counterfactual exercise addresses the following question: in a world economy integrated by trade, what would the cross-country distribution of aggregate output per worker look like if all countries had access to the US schedule of distortions? In this scenario, any given country is affected by two forces: (i) the direct impact examined earlier; and (ii) the indirect impact, which stems from the increased access to imported goods due to the improvement in the size distribution of the sourcing countries. I find that the cross-country variance of log of output per worker would reduce by 38% and the 90 th to 10 th percentile ratio would decrease by 41%. These effects become negligible when international trade is shut down. Therefore, institutions that distort the size distribution of firms potentially explain a non-negligible share of cross-country differences in standards of living, and international trade is instrumental for this contribution. Related Literature This paper mainly contributes to the macro-development literature about the effects of micro frictions on aggregate TFP. Restuccia and Rogerson [2008], Alfaro et al. [2008] and Bartelsman et al. [2013] introduce firm-level policy distortions in closed-economy growth models. Hsieh and Klenow [2009] use micro data to quantify the amount of resource misallocation in the manufacturing sector in China and India relative to the US. Hsieh and Klenow [2014] demonstrate that misallocation that harms large establishments disproportionately can account for slower growth of plant-level productivity in Mexico and India. My results stress that international trade, by increasing the importance of large firms in the economy, amplifies considerably the aggregate losses stemming from 7 This measure differs from the usual trade-to-gdp ratio because it uses the value of intermediate goods, as opposed to the value of final goods, in the denominator. 6

7 size distortions. Moreover, my work highlights the importance of cross-country differences in allocative efficiency to understanding international trade patterns, in particular the asymmetric trade between developed and developing economies identified by the gravity literature. This work also speaks to the literature on trade and firm heterogeneity. Arkolakis et al. [2012] - ACR, henceforth - show that the new gravity models with micro-level heterogeneity have aggregate behavior similar to the traditional models with representative firms. Since then, some papers have proposed alternative approaches to demonstrate that firm heterogeneity matters for the aggregate effects of trade. Simonovska and Waugh [2014] show that models with micro-level heterogeneity entail lower trade elasticities to fit price data and, therefore, display higher gains from trade than models without the firm-selection margin. Melitz and Redding [2015] prove that even small departures from the ACR s assumptions lead to increased gains from trade in heterogeneous-firms models relative to representative-firm theories. My paper borrows the insight from the development literature that the degree of firm heterogeneity varies across countries. In this sense, the extensive margin effects highlighted by the new trade theory matter in the aggregate exactly because they interact with the distribution of firm size, which is a country-specific object. Relatedly, my work extends the workhorse multi-country trade model to allow for countryspecific distributions of firm size. I develop a novel numerical strategy to compute the general equilibrium in this highly non-linear environment. I also prove that, under mild assumptions, the general equilibrium exists and is unique. Spearot [2016] is one pioneering work that introduces this rich kind of cross-country heterogeneity in a multi-country gravity model. The crucial difference between my framework and his is that I solve and estimate the model in levels instead of differences. This strategy is more costly because it requires the calibration of all structural parameters of the model, but it allows me to perform a broader set of counterfactual exercises in general equilibrium, beyond those based on changes of import tariffs. Finally, my paper offers a rationale for the results in Waugh [2010], according to which eliminating the asymmetry in trade costs between advanced and developing economies considerably reduces the cross-country inequality in aggregate productivity. I show that this asymmetry in trade costs in part captures differences in domestic distortions, and its elimination is equivalent to an institutional improvement as well as a reduction of international trade costs. Therefore, the impact of trade barriers on the international income distribution is potentially lower than previously estimated. Separating differences in trade costs from differences in trade elasticities does not affect the fit of the trade model in hand, but is crucial from a policy perspective. On the one hand, if trade costs are the main bottleneck of exports, policies targeted at improving transportation infrastructure and promoting trade agreements are a more fruitful path. On the other hand, if exports suffer because firms are too small to overcome trade costs, domestic 7

8 policies eliminating obstructions to firm growth are a better alternative. Road Map The paper is organized as follows. Section 2 presents the quantitative model and theoretical results. Section 3 describes the empirical implementation of the model and the main empirical results. I present the counterfactual exercises in Section 4. Section 5 presents robustness checks and Section 6 concludes. The appendix contains proofs, auxiliary simulations and details of data construction. 2 Theoretical Framework 2.1 The Environment This section describes the quantitative model used in the paper. The minimalist framework to study the effects of correlated distortions on international trade and on aggregate TFP must include: (i) distributions of micro-level technologies that vary across trade partners and can easily be matched to data; (ii) a distortion function to capture domestic institutions that affect firm size and entry; (iii) endogenous entry of firms; and (iv) selection of firms into production and exporting. It is fundamental that the inclusion of these features do not compromise the amenability of the model to quantitative analysis. Therefore, in my choices of functional forms for firm-level variables I try to be as flexible as possible given tractability constraints. Final-good Sector Consider a world economy comprised of N countries indexed by i. There are L i agents in country i. There is free mobility of labor across sectors and firms within a country but no mobility between countries. The representative consumer s utility is linear in the consumption good C i and her budget constraint is Y i = w i L i + Π i + R i. The consumer spends her entire income, which is the sum of total wages (w i L i ), distributed profits (Π i ), and net government transfers (R i ). I do away with the outside-good assumption and determine wages in general equilibrium. The final-good sector, or service sector, in country i is perfectly competitive and produces a homogeneous good according to the following Cobb-Douglas production function: C i = (L f i )α (I i ) 1 α where L f i represents labor employed in the final sector and I i is a bundle of intermediate inputs. Note that countries work with the same technology in the service sector. The 8

9 input bundle is a CES aggregator of intermediate varieties as follows: ( ) σ I i = q(ω) σ 1 σ 1 σ dω Ω i where q(ω) is the quantity of variety ω and σ > 1. The set Ω i is determined endogenously and includes both imported and domestic varieties of intermediate inputs. The expenditure in variety ω is: ( ) pi (ω) 1 σ x i (ω) = Z i where Z i is the total amount spent on inputs by the final sector and P i is the ideal price index defined as: ( ) 1 P i p i (ω) 1 σ 1 σ dω Ω i The perfect competition assumption implies that Z i = (1 α)y i. Manufacturing sector P i The manufacturing sector is characterized by a steady state equilibrium of monopolisticallycompetitive firms. In country i, a mass κ i of ex-ante identical entrepreneurs pays an exploration cost of w i fi e. This cost represents the formal and informal expenses with taxes, regulations and permits necessary to start a business. After this payment, the producers access a productivity draw ω from the following unbounded Pareto distribution: G i (ω) = 1 A θ i i ω θ i (1) The Pareto distribution is a common choice in the literature mainly for three reasons: (i) it provides analytical tractability for the computation and calibration of the multicountry general equilibrium; (ii) standard processes of technological innovation give rise to Pareto distributions (see Arkolakis [2016]); (iii) there is abundant empirical evidence that the upper tails of the firm size distribution are Pareto (see Axtell [2001] and Di Giovanni et al. [2011]). The parameter A i captures cross-country productivity differences stemming from factors that uniformly affect firms performance independently of their size. For instance, an improvement in A i, which I refer to as scale parameter, increases the average manufacturing productivity without changing the relative productivity between any pair of firms. In Ricardian trade models, this parameter regulates a country s technological level (or absolute advantage). The novelty in equation (1) is the fact that the tail parameter (θ i ) is country-specific. This assumption in fundamental in my analysis for two reasons. First, the aggregate losses from micro distortions and trade barriers largely depend on the initial degree of productivity heterogeneity. If firms are less heterogeneous to start with (higher θ i ), the gains from selection and reallocation are smaller. Second, new micro evidence has shown that firm size distributions in advanced countries tend to present fatter upper tails (see Fernandes et al. [2016] and Poschke [2014]). Developed countries are not only more productive on average but are also more 9

10 likely to host superstar firms with extremely high productivities. As documented in many empirical trade studies, these firms play a pivotal role in shaping international trade. 8 Manufacturing firms use labor as the sole input of a linear production function. The total cost of selling q units of product ω from origin i to destination j is : c ji (ω, q) = qw id ji ω + w i f ji The term d ji 1 represents iceberg trade costs and f ji is the fixed cost in terms of the origin country s labor. For every country i, d ii and f ii are normalized to one. Thus, the domestic fixed cost measures the entrepreneur s opportunity cost of running a business. 9 For every pair of countries, both fixed and iceberg costs can be asymmetric. Firms in country i are subject to an idiosyncratic distortion τ i (ω) that works as a revenue tax/subsidy. The after-tax revenue is defined as: r ji (ω) = τ i (ω)x ji (ω) where x ji (ω) is country j s spending on country i s variety ω as defined earlier. If τ i (ω) > 1 the distortion works as a subsidy; if τ i (ω) < 1, as a tax. These wedges distort firm s decision both at the intensive margin - how much to sell - and at the extensive margin - which markets to enter. It is important to emphasize that introducing idiosyncratic distortions in the model as taxes and subsidies is simply an analytical convenience. These wedges can also be taxes and subsidies, but in this context they are meant to be a parsimonious representation of the whole set of policies and institutions that distort firm size. The literature on misallocation usually assumes that τ i (ω) depends stochastically on ω, with the correlation between these variables controlling the severity of the micro distortions. In my baseline model, I work with the following deterministic relationship between τ i (ω) and ω: 10 τ i (ω) = b i ω γ i I demonstrate in the robustness section that the introduction of a stochastic component in the distortion function, as long as it is independent and separable from the systematic component, does not affect the results (the random component is integrated out of the relevant functions and becomes isomorphic to A i ). Despite its simplicity, this distortion function is flexible enough to perform the typical exercises of the misallocation literature. More precisely, the presence of two parameters, level (b i ) and elasticity (γ i ), allows for variation in the dispersion of distortions while keeping the average distortion level constant. This permits me to isolate the effects of micro distortions from the more 8 See Bernard et al. [2003], Eaton et al. [2011] and Gaubert and Itskhoki [2015]. 9 Kehoe et al. [2016] validates this interpretation of fixed costs by showing that the aggregate outcomes of a model with fixed costs are the same as in a model with occupational choice a la Lucas (1978). 10 See Jaef and Roberto [2011] and Buera and Fattal-Jaef [2014] for recent examples (2) 10

11 conventional effects associated with changes in macro prices, which in this context are two: the relative price between labor and the manufacturing input bundle and the economy s terms of trade. For the rest of the paper, I adjust b i such that E(τ i (ω)) = 1, γ i. 11 Using this adjustment, it is easy to show that: V ar(τ i ) = (θ i + γ i ) 2 (θ i + γ i ) 2 γ 2 i 1 = (3) 1 ( ) θi 2 +1 γ i Therefore, for γ i > 0, which is the relevant empirical case, increases in γ i leads to more dispersed distortions but does not affect the average distortion. In principle, γ i could be so high that more productive firms end up performing worse than less productive ones. To avoid this extreme case, I assume that i the following inequality, which I refer to as the non-ranking reversal condition, is true: ɛ i σ 1 γ i σ > 0 (4) Intuitively, condition (4) assures that, despite heavier distortions, more productive firms still make higher after-tax profits and, therefore, sell more and access more markets than less productive firms. I show in the next section that the empirical estimates of {γ i } N i=1 comfortably satisfy this condition for the values of σ usually used in the trade and macro literatures. The first part of the firm s problem is to determine the optimal price and quantity in each potential destination. This decision consists of maximizing after-tax profits: max τ i (ω)p ji (ω)q ji (ω) c ji (ω, q ji (ω)) q ji,p ji Defining m σ σ 1 s.t. the optimal price is: q ji (ω) = Z j p ji (ω) σ P σ 1 j p ji (ω) = mw id ji b i ω 1 γ i (5) The equation above shows that firm-level distortions introduce markup dispersion across active producers. This intensive-margin distortion or allocation effect represents the first mechanism by which micro distortions affect aggregate productivity in the model. Figure 1 shows how increases in γ worsen allocation efficiency by increasing markup dispersion across a given set of heterogeneous producers. Notably, small changes in the schedule of distortions result in large changes in markup dispersion. 11 More specifically: b i = (θ i+γ i ) θ i A γ i i 11

12 Figure 1: Markups and Schedule of Distortions The second part of the firm s problem is choosing which destinations (domestic market included) to serve. Firm ω activates market j if and only if π ji (ω) 0. For each pair (j, i) there is a threshold productivity ωji such that π ji(ω) = 0. This marginal productivity is given by: ( w σ i σf ji d σ 1 ji ω ji = b σ i Z jp σ 1 j m 1 σ ) 1 ɛ i (6) Abstracting from general equilibrium effects, the impact on selection of an increase in the slope of distortions is ambiguous. On the one hand, given a constant b i, a steeper schedule increases the productivity threshold, pushing out of domestic and foreign markets firms that would otherwise be able to serve these destinations. In other words, selection become fiercer. On the other hand, a larger γ i increases b i, which reduces the productivity threshold and contributes to the survival of low-productive entrepreneurs. My quantitative results suggest that when the general equilibrium effect of distortions on wages is strong enough, the former force prevails. Gravity Equation The goal of this subsection is to examine the consequences for aggregate trade patterns of the micro structure laid out above. I start by studying the conditions under which the aggregate objects are well-defined. A well-known property of gravity models is that trade flows from country i to country j reflect the contribution of i to j s price index. Country j s manufacturing price is given by the following equation: P 1 σ j = N ( ) mwi d 1 σ ji κ i b i ω 1 γ dg i i (ω) i=1 ω ji The integrals on the right-hand side of the equation above converge if, and only if, the 12

13 following regularity condition is satisfied i: χ i θ i + (σ 1)(γ i 1) > 0 (7) Condition (7) subsumes the standard regularity condition of gravity models with Pareto or Frechet distributions of micro technologies (θ > σ 1). This condition rules out the case in which consumers can achieve an arbitrarily low price index by concentrating demand on a few extremely productive varieties. Analogously, it says that countries cannot have productivity distributions with excessive fat upper tails. In particular, it rules out the Zipf s law case (θ = σ 1). If the non-ranking reversal condition holds and the empirical elasticity of exports with respect to variable trade costs is negative, then the regularity condition is automatically satisfied. I show in the empirical section that that is the case in my sample. Combining the optimality condition of country j s final-good sector with the price equation and the expression for the threshold productivity, the following equation describes aggregate exports from country i to j: ( ) βi X ji = T i (Z j Pj σ 1 σ 1 ) d β i ji ( ) σ 1 βi σ 1 fji (8) where T i is a convolution of factors that affect country i s competitiveness 12 and β i captures how sensitive i s aggregate exports are to trade barriers and to others importer s demand shifters. The unconventional aspect of this gravity equation is that the trade elasticity varies across exporting countries according to their firm size distribution. 13 Crucially, the trade elasticity β i is defined as: β i (σ 1) ( 1 + χ ) i ɛ i = (σ 1) ( 1 + θ ) i + (σ 1)(γ i 1) σ 1 σγ i If conditions (4) and (7) hold, then β i > 0. This new trade elasticity is a function of three parameters: the elasticity of demand, the dispersion of technology and the schedule of distortions. Differently from the gravity models in Eaton and Kortum [2002] and Chaney [2008], the intensive margin effect does not vanish from the trade elasticity. In fact, their gravity equations become a special case of the formulation above when γ i = 0 i and θ i = θ i. 14 I highlight these results in the next proposition. Proposition 1. Assuming that conditions (4) and (7) hold and keeping the price index constant, the elasticity of aggregate exports with respect to fixed trade costs is ln(x ji) ( ) ln(f ji ) = σ 1 βi σ 1 < 0. This effect captures the changes in trade flows stemming from changes in the number of exporting firms - the extensive margin. The elasticity of exports with respect to variable trade cost is ln(x ji) ln(d ji ) = β i = (1 σ) + (1 σ) χ i ɛ i < 0. The first term of this equation captures the effect of iceberg costs on the value exported per firm 12 T i κ i ( mwi b i ) 1 σ θi A θi i χ i ( ) χ σ i ( bi ɛ i m 1 σ w i σ ) χ i ɛ i 13 Spearot [2016] also works with a gravity equation with non-constant trade elasticities. 14 For more on this point, see Amand and Pelgrin [2016]. (9) 13

14 - the intensive margin - whereas the second term measures their effect on the extensive margin. Finally, the( elasticity ) of trade flows with respect to importer s demand shifters is ln(x ji) ln(z j ) = β i σ 1 = 1 + χ i ɛ i > 0. As before, the first term reflects the impact of market size on the sales per exporting firm, whereas the second term captures the effect on the number of exporting firms. The critical ingredient of the model is the relationship between domestic distortions and trade elasticity. In the next proposition, I show that a higher degree of domestic misallocation leads to larger trade elasticity and, consequentially, less trade: Proposition 2. If conditions (4) and (7) hold, the effect of distortions on exporter s trade elasticities is β i γ i > 0. Therefore, considering the empirically relevant case of γ i > 0, increases in the dispersion of idiosyncratic distortions in the exporting country result in higher trade elasticities in absolute terms. Proof. β i γ i ( χi ɛ i ) γ i > 0. ( ) = (σ 1) χi ( ɛ i γ i = (σ 1) σ 1 ɛ i ) + σχ i. If σ > 1, and (4) and (7) hold, then ɛ 2 i To clarify the mechanisms involved in the result above, consider two economies (a and b) that only differ in their schedule of distortions. For instance, let s assume that γ a = 0 and γ b > 0. Despite the fact that the two countries have the same distribution of firm-level technologies, the steeper schedule of distortions in country b results in an equilibrium firm size distribution that is more compressed than a s undistorted distribution. This distortion increases the export sales of marginal exporters relatively to the sales of inframarginal exporters. As a result, total exports from b become more sensitive to trade costs or, equivalently, economy b behaves in the aggregate as if it faces higher costs to export its goods. 2.2 Equilibrium To compute the general equilibrium, I follow the strategy in Allen et al. [2015] and break up the system into three more manageable blocks. The first block consists of solving for the mass of entry and the aggregate net revenues in each country given vectors of prices and wages. The second block takes the vector of wages and the solution from the first block as given and calculates prices. Due to the high non-linearity of the price system, the usual iterative fixed-point procedure is unable to find the solution. I overcome this problem by applying a bisection algorithm to this system. The third block finds the set of wages that equalizes exports and imports in every country. I show in the appendix that the general equilibrium exists and is unique (up-to-scale). The framework developed here can be easily adapted to analyze other trade questions in which cross-country 14

15 heterogeneity is salient. A few examples are (i) the role of multinational or superstar firms in shaping aggregate trade flows and (ii) the impact on trade flows of non-neutral technological change. Free-Entry and Aggregate Tax Revenues The free-entry condition establishes that expected profits in the manufacturing sector must equal the entry cost. It follows then that aggregate profits must be equal to total startup costs: N κ i j=1 ωji π ji (ω)dg i (ω) = κ i w i f e i (10) The net tax revenue distributed to the representative consumer is given by the difference between aggregate before-tax revenues and aggregate after-tax revenues. Intuitively, the revenue created by taxes on larger firms returns to the system as subsidies to smaller establishments and a lump-sum payment (or charge) to consumers. The expression for R i is N N R i = x ji (ω)dg i (ω) r ji (ω)dg i (ω) (11) j=1 ω ji j=1 The next proposition establishes values for κ i and R i. Proposition 3. Assuming free-entry, balanced trade and labor market equilibrium we have: κ i = (σ 1 σγ i) σθ i fi e (1 α)l i and R i = 0 ω ji Proof. See Appendix. Therefore, a steeper schedule of distortions discourage entry in the tradable sector by reducing after-tax profits. This entry effect is isomorphic to a higher startup cost. Price Index Given the values of {κ i, R i } N i=1 from the first step, the next step finds N prices that solve the following system of N independent equations for any strictly positive vector of nominal wages: ( ) N χ i Pj 1 σ ɛ = T i Z i j P (σ 1) χ i ɛ i j d (1 σ) 1+ χ i ɛ i ji f χ i ɛ i ji (12) i=1 15

16 Naturally, the price level in one country depends on the number of firms that enter the market, which itself is a function of prices. However, this latter relationship is controlled by the shape of the exporter s firm size distribution. Since there are differences in the distribution of firm size among exporters, the price equation becomes highly non-linear. It turns out that the following proof of existence and uniqueness of the price vector embeds a computational strategy to solve the problem. Proposition 4. If conditions (4) and (7) hold, the price equation has a unique solution for any strictly positive vector of nominal wages which can be computed by a bisection algorithm. χ i i=1 T ɛ iz i P (σ 1) χ i ɛ i j ( ) d (1 σ) χi +1 ɛ i ji f χ i ɛ i ji Proof. Define the function Φ(P j ) Pj 1 σ N j. Φ(.) is defined over the domain (0, ). Since: (i) Φ (P j ) < 0; (ii) lim Φ(P j) = ; and (iii) P j 0 lim Φ(P j) < 0, there exists a unique P such that Φ(P ) = 0. P j Balanced Trade and Wages Finally, defining s ji = X ji Z j as the share of country j s expenditures on tradable goods that is devoted to i s goods, the following balanced trade condition pins down wages: Definition w i L i = N s ji w j L j (13) j=1 Given parameters {σ, α}, {A i, L i, γ i, θ i, fi e}n i=1 and trade costs (f j,i, d j,i ) N i,j=1, an equilibrium is a vector {w i, P i, κ i, R i } N i=1 such that: i trade is balanced Goods and labor markets clear Free-entry condition holds Prices satisfy equation (12) Selection satisfies equation (6) If conditions (4) and (7) are satisfied, the general equilibrium exists and is unique (see Appendix). 16

17 2.3 Gains from Trade Despite not satisfying one of the three ACR macro restrictions on gravity models (constant trade elasticities across exporting countries), my model still delivers a sufficientstatistic equation to compute the welfare gains from trade. The sufficient statistics are the same as in ACR s analysis: (i) the change in the share of spending devoted to domestic goods and (ii) the trade elasticity with respect to variable trade costs. At the heart of this result are the free-entry and balanced trade assumptions, which guarantee that aggregate spending is a function of total wages only, and the Pareto assumption, which assures that the trade system is almost CES. Defining ŝ ii as the change in country i s home share, the impact of any change in trade costs on country i s welfare can be computed as: 15 (1 α) β Ûi = ŝ i ii (14) A corollary of the result above is that country i s welfare change caused by a move from autarky to the observed trade equilibrium is: (1 α) β Û i = s i ii (15) Therefore, for a given domestic trade share, the fact that β i γ i > 0 implies that more distorted economies present smaller gains from trade. Intuitively, domestic misallocation obstructs the reallocation of labor to the most productive firms triggered by trade liberalization. This result suggests that estimates of gains from trade based on a constant-elasticity approach might be problematic. For instance, if the elasticities computed through a standard gravity equation are a convex combination of the real, exporter-specific, elasticities, then the conventional ACR approach might understate the gains from trade for developed economies and overstate the gains for developing countries. The result above also sheds lights on the causes behind the positive relationship between development and trade openness observed both in cross-sectional and time-series data. By gaining less from trade, distorted economies have lower incentives to adopt pro-trade policies as well. This supply-side mechanism complements the traditional demand-based theories of trade and development summarized in Caron et al. [2014]. 2.4 Output per Worker Finally, we can summarize all the effects above with the following equation for aggregate output per worker: 15 See appendix for derivation (1 α) β i u i U i = K sii L i }{{} Trade M(γ i, θ i, f e i ) }{{} Domestic Distortion 1 (σ 1) (Li A i ) 1 α }{{} Endowment (16) 17

18 K is a constant that does not affect relative productivity. 16 The second term reflects the contribution of international trade to productivity. A more open economy (lower s ii ) is able to scale up its most productive firms, thereby increasing its aggregate TFP. This effect is stronger the less steep is the schedule of domestic distortions, i.e, the better are domestic institutions. The third term represents domestic distortions and it s a function of: 17 (i) the amount of productivity heterogeneity in manufacturing (θ i ); (ii) the schedule of distortions (γ i ), which affect allocative efficiency through the allocation, selection and entry channels; (iii) startup costs (fi e ), which controls the mass of domestic varieties. Finally, the last term captures the impact of endowments on aggregate output per worker. A i captures the level of technology in manufacturing and L i affects the mass of domestic varieties. In a closed economy (s ii = 1), micro distortions affect aggregate TFP only through M(γ i, θ i, fi e ). This term represents the traditional static effects of misallocation on aggregate productivity. The inclusion of international trade introduces an extra channel: a lower γ i also improves aggregate productivity by fostering trade, i.e, lowering s ii. The goal of the rest of the paper is to measure how strong this last effect is and how it depends on the economy s primitives. 3 Taking the Model to the Data The empirical implementation of the model is organized in three parts. In the first part, I estimate the schedule of distortions ({γ i } N i=1 ) for a large cross-section of countries using establishment-level data. The next step consists of recovering the heterogeneity parameters ({θ i } N i=1 ) from estimates of exporter-specific trade elasticities with respect to observed variable trade costs ({β i } N i=1 ). Finally, the third part combines data on freight costs, population and entry costs with the structure of the model to estimate the structural trade costs ({d ji, f ji } N i,j=1 ) and technology levels ({A i} N i=1 ). The model perfectly replicates the world matrix of manufacturing trade ({s ji } N i,j=1 ) and successfully predicts a number of non-targeted moments as: (i) the world distribution of output per worker; (ii) the cross-country distribution of average firm size; and (iii) moments from the firm-level distribution of export sales. ( 16 K α α (1 α) (1 α) (1 α) 1 α σ 1 ( ) 1 α 17 M(γ i, θ i, fi e ) ɛi β i χ i f i e ( θi +γ i θ i ) (1 α) 1 σ 1 σm ) (σ 1) (1 α)(σ(θi 1)+1) (σ 1)(θ i γ i ) 18

19 3.1 Schedule of Distortions Data The establishment-level data come from the World Bank s Enterprise Survey (WBES) version The WBES is an ongoing research project to collect establishment-level data from a broad cross-section of countries. The information is collected through faceto-face surveys in the most important economic areas of each country. The sample used in this paper was collected during the period and contains over 37,000 establishments from 84 countries in all 2-digit ISIC revision 3 sectors. I focus on the digits corresponding to the manufacturing sector. The dataset spans the whole spectrum of the world income distribution, including OECD countries (Spain, Israel, Sweden and Ireland), big emerging economies (Brazil, Russia, India, China and Indonesia) and developing countries (Nigeria, Cambodia and Bolivia). A well-known feature of this dataset is that it tends to oversample larger firms. Despite being a disadvantage in other contexts, this characteristic is actually a strength in the context of this study. Crucially, the dataset contains standardized establishment-level information on: total sales, spending on raw materials and intermediate goods, net book value of assets and total cost of labor (including wages, salaries, bonuses and social security payments). 18 To focus on domestic distortions, I only include firms whose domestic sales comprise at least 95% of total sales. The appendix contains a detailed description of the data and the construction of the final sample. Analysis The first step to estimate the schedule of distortions is to calculate establishment-level measures of productivity and idiosyncratic distortions. I follow the procedure in Hsieh and Klenow [2009] and define physical productivity of firm i in sector s as: T F P Q si ω si = Y si K αs si L1 αs si Despite the fact that labor is the sole factor of production in the theoretical model, I include physical capital in the empirical analysis in order to get more precise estimates of firm-level productivity. Introducing capital into the model does not affect the analysis because cross-country differences in capital per worker are isomorphic to differences in A i. 19 Combining the production function above with the optimality condition of a purely domestic firm, we have: (P si Y si ) σ σ 1 K αs si L1 αs si = κ s ω si 18 Recent papers have used WBES to infer measures of productivity dispersion and distortions. A few examples include: Asker et al. [2014] and Bento and Restuccia [2016]. 19 This would not be the case in a multi-sector model in which the production of different types of good differ in capital intensity. 19

20 Given values of σ and α s, we can recover the left-hand side of the equation above with firm-level data. P si Y si is measured as value added (sales minus spending with intermediate inputs and raw materials); L si is total wage bill (using wages instead of number of workers has the advantage of providing an implicit control for human capital difference across workers); and K si is the net book value of capital. With these information, firm i s TFPQ is identified up to a sectoral constant. 20 In a similar vein, firm i s distortion (τ si ) is recovered from the revenue-based productivity measure (T F P R si ): T F P R si P siy si K αs si L1 αs si = λ s τ si In the baseline estimation, I assume that (1 α s ) is the cross-country average share of labor income in value added in sector s. I also assume σ = For each country j, the schedule of distortions is estimated as the OLS slope coefficient of the following regression: 22 ( ) ( ) T F P R j si log T F P R j = β j 0 + γ T F P Q j si jlog s T F P Q j + ɛ j i s I show the estimates in the figure below. Rich countries present the smallest coefficients. For instance, the US slope is.09 and slopes of the other OECD countries in the sample are all below.29. Namibia, Angola and Czech Republic are on the other end of the distribution, with elasticities above.6. Middle income countries in Latin America like Brazil, Mexico, Argentina, Chile and Uruguay present slopes between.3 and.4. The numbers for China and India (.47 and.45) compare to Hsieh and Klenow [2009] estimates. In general, the correlation between T F P Q and T F P R significantly decreases with aggregate output per worker with a semi-elasticity of.03. Finally, for σ = 3 all but two countries (Angola and Czech Republic) satisfy the non-ranking reversal condition. 20 The advantage of this procedure is that it allows me to recover firm-level physical productivity without data on firm-level prices. However, since it relies on the structure of demand and on the monopolistically competitive market structure, it is less robust to model misspecification. 21 This is the same value used in Hsieh and Klenow [2009] and it is close to the 2.98 estimated in Eaton et al. [2011]. ( ) 1 22 Where I define T F P Q s i T F P Q(σ 1) σ 1 si and T F P R s is the weighted average of T F P R si with weights given by firm i s share of industry s value added. 20

21 Figure 2: Schedule of Distortions Note Estimates are the inter-sectoral elasticity between firms T F P R and T F P Q. The estimate for the US economy comes from Hsieh and Klenow [2014]. I only include countries with at least 100 observations. The median number of firms per country is 265 and the average is 456. All regressions include time fixed effects. The dispersion of measured productivity - a conventional measure of misallocation - closely relates to the elasticities estimated above. In general, a steeper schedule of distortions is associated with worse allocative efficiency across firms. The next graph shows this relationship using the standard deviation of the logarithm of within-sector T F P R as a measure of productivity dispersion. Figure 3: Distortions and TFPR dispersion 21

22 3.2 Trade Elasticities Data In this section, I estimate the structural gravity equation in order to recover the trade elasticity parameters ({β i }). The trade data consists of bilateral manufacturing trade flows in the year 2007 from COMTRADE. Manufactures correspond to digits 5 through 8 of SITC Revision 4. There are 11,448 observations, featuring 160 origin countries and 72 destination countries. As cost shifters, I use aggregate import tariff data from UNC- TAD s Trade Analysis Information System (TRAINS). For every pair of importer a and exporter b, TRAINS calculates the Effectively Applied Tariff (AHS) charged by country a on country b s exports in each manufacturing sector c. The aggregate import tariff is computed as the weighted average of those tariffs, with weights given by the share of sector c in total sales from b to a. If AHS tariffs are not available, I use Most-Favored Nation (MFN) tariffs. Finally, I use Mayer and Zignago [2006] data on bilateral geographic variables - geographic distance, shared borders and common official language - as controls. Armed with the macro elasticities, I test their ability to predict moments from the firm-level distribution of export sales. The micro-data come from the World Bank s Exporter Dynamics Database (EDD). This dataset is based on more than 23 million unique observations at the country-firm-product-destination-year level collected from customs datasets. 23 The version used in this paper contains moments from the distribution of export sales for a large set of developing and developed exporting countries in the period between 1997 and The information is disaggregated at the origin level, origindestination level and origin-destination-sector level. My choice measure of dispersion is the coefficient of variation of export sales, and skewness is captured by the share of foreign sales controlled by the 1% and 5% largest exporting firms. Structural Gravity It is well known that the trade elasticity in gravity models with extensive-margin adjustments, like Eaton and Kortum [2002] and Chaney [2008], identifies the dispersion of micro-technologies across firms. This correspondence makes it possible to employ aggregate and widely-available datasets to recover moments of the productivity distribution that would otherwise require detailed micro data. This handy property of the new trade models has been extensively exploited by the quantitative trade literature. 24 However, the gravity models usually estimated implicitly assume that the distribution of micro productivities is invariant across countries. While this invariance is a comfortable 23 See Fernandes et al. [2016] for a detailed description of the data. For an application of the EDD, see Fernandes et al. [2015]. 24 A great example of quantitative work that uses the gravity structure to pin down sectoral micro-level technologies is Caliendo and Parro [2014]. 22

23 assumption in the context of Anderson [1979] or Krugman [1980] models, in which the trade elasticity is the degree of substitutability among varieties in a sector, the same is not true in the case of the new trade theory. Some recent papers like Bas et al. [2015], Yang [2017] and Adao et al. [2015] have addressed this issue by proposing more flexible forms for the productivity distribution. In the context of this paper, non-constant trade elasticities arise both because of variation in productivity distributions and because of variation in schedules of distortions. I start by rewriting the gravity equation (8) in a more convenient form: X ji = T i (Z 1 σ 1 j P j f 1 σ 1 ji ) β i d β i ji f ji In order to estimate the equation above, I need to assume functional forms for d ji and f ji. The equation for iceberg trade costs is: d ji = (1 + t ji )exp(a d j + b d i + z jiδ d ) (17) where t ji is the ad-valorem import tariff, a d j is the importer s fixed effect, bd i is the exporter s fixed effect, and z ji is a set of geographic controls. Tariffs are assumed to apply only to the cost of imported goods (as opposed to sales revenue) and do not generate tariff revenues. 25 A similar specification applies for fixed trade costs: f ji = exp(a f j + bf i + z jiδ f ) (18) The two specifications above are extremely flexible. In particular, the presence of both importers fixed effects and exporters fixed effects allows for a rich pattern of asymmetric bilateral trade costs. Plugging the trade cost equations into the structural gravity and taking logs, the estimating version of the gravity equation becomes: X ji = Π i + ξ j + β i ζ j β i log(1 + t ji ) + z jiδ i + ɛ ji (19) where {Π i, β i, δ i } N i=1 and {ξ j, ζ j } N j=1 are parameters to be estimated, { X ji, z ji, t ji } N i,j=1 are data, and ɛ ji is an i.i.d error term. The novel feature of the equation above is the non-linear term β i ζ j. It reflects the fact that the structural terms contained in the importer fixed effect ζ j, like market size and importer-specific trade costs, affect aggregate imports according to the firm size distribution of the exporter. This term, combined with variation in tariffs, will help to identify {β i } N i=1. I estimate the gravity equation by Non-linear Least Squares, using the iterative fixed-point algorithm proposed by De la Roca and Puga [2017]. To grasp the intuition behind the identification of {β i } N i=1, it is useful to understand the iterative structure of the estimator. The algorithm consists of two steps. The first step estimates a vector β given a vector ζ. Therefore, this steps just features an OLS regression because ζ is treated as data. The second step updates the value of ζ according to the results from the first step. Starting with a first guess ζ (0) = 0, the bilateral 25 When tariffs generate revenues, the gravity equation assumes a different form. For more on this topic, see Caliendo et al. [2015]. 23

24 variation in tariffs identifies β (1). This step also produces residuals ˆɛ (1) j,i. The second step calculates ζ (1) based on importer-specific covariances between ˆɛ (1) j,i and β (1). If this covariance is large (small), then the algorithm increases (decreases) ζ (2) relatively to ζ (1). Intuitively, if country j imports relatively more from high-elasticity exporters (or, equivalently, if j imports relatively more despite the exporters high trade elasticities) then j must have larger market size, lower trade costs or both. The procedure then returns to the first step, which combines variation in the updated ζ (2) with variation in tariffs to identify β (2) and so on and so forth. The estimator stops when a fixed point is achieved. I present the estimation results below. Table 1 displays the estimates of the unconstrained model (heterogeneous) and of the traditional model (homogeneous). First, the heterogeneous estimator fits the data better than the homogeneous model, as evidenced by the F-test. The gain in goodness-of-fit is of approximately 4 percentage points. This is a non-trivial improvement if we take into account that the constrained model is already saturated with fixed effects. Second, the new model delivers large cross-country heterogeneity in trade elasticities. These elasticities are in the interval [2.5,19.3], with mean 9.85 and standard deviation The average elasticity is close to Eaton and Kortum [2002] preferred estimate but way above the ballpark of estimates for manufacturing trade among developed countries found in recent research. For example, Eaton et al. [2011] and Caliendo and Parro [2014] find numbers between 4 and 5. Table 1: Estimates of Trade Elasticities Homogeneous Heterogeneous Min Max Mean S.E Adj R N.obs 11,448 11,448 F-stat 5.73 Note The column on the left-hand side presents the estimate of the constrained model, which assumes that trade elasticities are constant across exporters. On the right-hand side are the estimates of the unconstrained model. Standard errors are robust to heteroskedaticity. The F-test rejects the hypothesis of equivalence between the two models at 1% significance level. Only 17% of the sample reports zero trade flows. The transformation log(1 + X ji) is applied in those cases. Results are unchanged if zeros are replaced with inputed trade flows from a traditional gravity equation instead. Figure (4) starts to unveil the cause of that apparent discrepancy. The distribution of trade elasticities is bi-modal with one peak around (4, 6) and another peak around (12, 15). According to these estimates, the export side of manufacturing trade is basi- 24

25 cally characterized by two sets of countries: (i) low-elastic exporters; (ii) high-elastic exporters. This bi-modality resembles the results in Fieler [2011] and Lashkaripour [2015]. However, there are two central differences between my methodology and theirs. First, those studies assume the existence of two broad class of goods whose trade elasticities differ because of technology or markup differences. In this environment, cross-country variation in elasticities emerge because countries select into production of different types of goods. Second, the identification of elasticities in their gravity models depends fundamentally on the assumption of symmetric trade costs. Under symmetry, a low volume of exports is automatically attributed to higher trade elasticity instead of larger export costs. Figure 4: Distribution of Trade Elasticities Note Blue bars represent the density on unit intervals of elasticities. The red line is the kernel density estimate. Sample size=145 countries Figure (5) shows that elasticities covary systematically with output per worker. Lowelasticity exporters tend to be advanced countries, whereas high-elasticity exporters tend to be developing economies. In particular, OECD countries are overrepresented in the cluster of points with elasticities between 4 and 6. This result reconciles my estimates with the recent estimates in the gravity literature. Most importantly, this finding is consistent with the main prediction of the theoretical model: firm-level distortions simultaneously depress aggregate TFP and amplify the impacts of trade barriers on aggregate exports. One natural concern is that the relationship between development and trade elasticity is being driven by differences in industry composition within the manufacturing sector. I address this issue in the robustness section and I find little evidence supporting this alternative explanation. 25

26 Figure 5: Trade Elasticity and Aggregate Productivity Note Ouput per worker is measure in PPP exchange rates from PWT 8.0. Sample size=142 countries. Macro Elasticities and Micro Moments According to the theoretical model, the trade elasticities identified from aggregate data should reflect characteristics of the underlying distribution of firm-level exports. I test this prediction by matching my macro measures of dispersion to moments of the observed distribution of firm-level exports from EDD. In general, macro elasticities are strongly correlated with micro measures of dispersion and skewness of export sales. Consistent with the theory, low-elastic origin countries tend to present sales distributions that are both more dispersed and more skewed towards superstar exporters. In addition, low-elastic countries systematically have larger number of exporters and higher average export sales. Table (2) shows that a two-fold increase in the macro elasticity is associated with a 53% lower dispersion in export sales and a 7.4 percentage points smaller participation of top 1% exporters in total exports. Results in table (3) reveals that these correlations persist at the origin-destination level. For instance, if country a s elasticity decreases by 50%, the sales share of its top 1% firms in every destination is expected to increase by 5 percentage points. Finally, Table (3) presents regressions with sector fixed effects. Even within sectors, higher macro elasticities are associated with lower dispersion of export sales. 26

27 Table 2: Origin Level (1) (2) (3) (4) (5) VARIABLES Number of Exporters Mean Sales Sales Dispersion Share of Top 1% Share of Top 5% Trade Elasticity *** *** *** *** ** (0.107) (0.0782) (0.0425) (0.0130) ( ) Observations R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Note Coefficients from regressions of moments of export-sales distribution on the log of macro elasticities. Moments are computed with data at the origin-year level. The sample includes only observations from distributions calculated with at least 100 firms. Year fixed effects are included. Number of exporters is log of exporting firms minus log of population. Mean sales is also in logs. Sales dispersion is calculated as the log of the coefficient of variation of sales. Share of top x% is the share of total export sales controlled by the x% largest exporting firms. Table 3: Origin-Destination Level (1) (2) (3) (4) (5) VARIABLES Number of Exporters Mean Sales Sales Dispersion Share of Top 1% Share of Top 5% Trade Elasticity *** 0.116*** *** *** *** (0.0407) (0.0303) (0.0163) ( ) ( ) Observations 10,201 10,201 10,201 10,201 10,201 R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Note Coefficients from regressions of moments of export-sales distribution on the log of macro elasticities. Moments are computed with data at the origin-destination-year level. The sample includes only observations from distributions calculated with at least 100 firms. Year and importer fixed effects are included. Additional controls include: log of geographic distance, indicator of shared border and indicator of common official language. Number of exporters is log of exporting firms minus log of population. Mean sales is also in logs. Sales dispersion is calculated as the log of the coefficient of variation of sales. Share of top x% is the share of total export sales controlled by the x% largest exporting firms. 27

28 Table 4: Origin-Destination-Sector Level (1) (2) (3) (4) (5) VARIABLES Number of Exporters Mean Sales Sales Dispersion Share of Top 1% Share of Top 5% Trade Elasticity *** *** *** *** (0.0246) (0.0287) (0.0104) ( ) ( ) Observations 26,779 26,779 26,779 26,779 26,779 R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Note Coefficients from regressions of moments of export-sales distribution on the log of macro elasticities. Moments are computed with data at the origin-destination-sector-year level. The sample includes only observations from distributions calculated with at least 100 firms. Year, importer and sector fixed effects are included. Additional controls include: log of geographic distance, indicator of shared border and indicator of common official language. Number of exporters is log of exporting firms minus log of population. Mean sales is also in logs. Sales dispersion is calculated as the log of the coefficient of variation of sales. Share of top x% is the share of total export sales controlled by the x% largest exporting firms. Sectors are defined as 97 2-digit sections of the Harmonized System (HS) With values of {γ i, β i } in hand, I use equation (9) to recover the Pareto shape parameter θ i. In other words, I choose the dispersion of micro technologies to match the elasticities in the model with the empirical elasticities. 3.3 Technology and Trade Costs Data The goal of this section is to complete the calibration of the model. In order to maximize the number of country pairs in the structural model, I choose to work with data from year Bilateral trade and tariff data corresponds to the manufacturing section of ISIC Revision 3 (digits 151 to 369) and comes from COMTRADE and TRAINS, respectively. Data on gross manufacturing production is from UNIDO Industrial Statistics Database. Finally, data on entry costs and labor force come from World Bank s Development Indicators (WBDI) and World Bank s Doing Business Survey. The final sample contains 81 countries, which correspond to more than 95% of the world trade and income. 26 Calibration 26 Distortions are not available for 18 countries. All of them are advanced and members of the OECD. I input their γ i using the average distortion across the OECD countries for which I have estimates. The fact that their trade elasticities are very similar reassures that this procedure is a good approximation. Also, trade elasticities are not available for 5 countries (Gabon, Georgia, Guatemala, Moldova and Panama). In these cases, I use the projected elasticities in the space of output per worker as proxies of the real elasticities and calculate shape parameters based on them. 28

29 The basic idea of the calibration it to match the model s trade shares with the empirical shares {ŝ ji } N i,j=1.27 The first step is to find nominal wages {w i } N i=1 that makes the empirical trade matrix a world equilibrium. The solution is found by solving equation (13) for wages at the observed trade shares and labor forces. With nominal wages in hand, I only need a value of α to calculate spending of the tradable sector and modelconsistent trade flows ({X ji } N i,j=1 ). The parameter α is the share of the labor force employed in the non-tradable sector and a common choice in the literature is α =.7. It is convenient to rewrite the gravity equation in the following form: 1 X ji = T i (V j ) β i D ji ( ) 1 β i σ 1 σ 1 where I have defined V j Zj P j and D ji d β i ji fji. The balanced trade condition implies that i s total exports equals i s imports: Z i = N X ji = T i j=1 N j=1 (V j ) β i D ji Solving the equation above for T i and plugging the solution into the gravity equation we have: Z i X ji = N j=1 (V (V β i j) β j D ji ) (20) i Dji Defining ˆD ji = V β i j D ji, I rewrite the equations above to form the following system of equations to solve for ˆD i ( ˆD 11,..., ˆD N1 ): ˆD i = E i ˆDi where I have defined the matrix E i as: X 1i Z i X 2i E i = Z i..... X Ni Z i Note that we have all the elements to calculate {E i } N i=1. Thus, ˆD i is just the eigenvector associated with eigenvalue one of matrix E i s and T i is calculated using equation (20). Finally, given (L i, f e i, γ i, θ i ), A i is recovered by inverting the expression of T i. X 1i Z i X 2i Z i X Ni Z i Using the assumption that D jj = 1, one can show that: D ji = ( Xji T i ) ( Tj X jj ) β i β j 27 See the appendix for details about the construction of the empirical trade shares. 29

30 Note that all the elements on right-hand side are known, so we can compute D ji. However, D ji is a composite of the structural variable trade costs and fixed trade costs. Without additional data on firms average sales there is no theory-based way to separately identify those two types of costs. I follow the strategy of Di Giovanni and Levchenko [2012] and assume a functional form for variable trade costs. I then recover fixed trade costs as residuals. Consider the following specification for variable trade costs: d ji = 1 + t ji + φdist ι ji where t ji is the ad-valorem import tariff, and φdist ι ji is the ad-valorem equivalent of transportation costs. For the sake of parsimony, I model freight costs as a function of geographic distance only. I use Hummels [1999] estimates for the elasticity between freight costs and distance (ι=.3). Anderson and Van Wincoop [2004] report that transportation costs are equivalent to a 21% ad-valorem tax on US exports. I calibrate φ to match that estimate. With this information I am able to recover fixed trade costs from the expression for D ji. 3.4 Model s Fit Having calibrated the model to match perfectly the empirical bilateral trade shares, I next study the model s ability to predict untargeted moments. The model successfully replicates the distribution of PPP aggregate output per worker, with a correlation in logs of This goodness of fit is achieved despite the assumption of no international differences of technologies in the nontradable sector. Therefore, productivity differences in the tradable sector go a long way in explaining international differences in aggregate output per worker. Figure (6) gives a visual representation of the model s performance along the productivity dimension. In general, the dots tend to cluster around the 45- degree line. However, the model tends to overpredict aggregate productivity in very poor countries. Since the parameters were chosen to match trade performance in manufactures, this discrepancy might be due to the fact that a great share of labor in those countries is allocated to primary sectors like mining and agriculture, which tend to have lower labor productivity. 28 This force contributes for the model to underpredict slightly the international dispersion of productivity, as evidenced in Table (5). 28 See Lagakos and Waugh [2013]. 30

31 Figure 6: Predicted VS Empirical Output per Worker Note Output per worker is measure in PPP exchange rates from PWT 8.0. Year Sample size=81 countries. Table 5: Predicted VS Empirical Output per Worker Moments Data Model Mean Coef.of Variation Var(log) p90/p Note Output per worker is measured relative to US. Sample size=81 countries The model can also be tested along micro dimensions. I compare the model s predicted average size of manufacturing firms to data on actual size from Bento and Restuccia [2016]. Firm size is measured as the number of employees. The model performs reasonably well at forecasting cross-country differences in average firm size. The correlation between average size in the model and in the data is 0.3 (in logs) and the elasticity of the latter with respect to the former is.74. In other words, a 2-fold increase of average size in the model is associated with a 74% increase in the data. This inelastic coefficient means that there is more cross-country variation in size in the real world than in the model. Comparing the empirical and theoretical cross-country distributions reveals that the model s predictions are more accurate for countries above the median. For instance, the 25 th percentile is 7 employees in the data and 12 employees in the model, whereas for the 75 th percentile the respective numbers are 13 and 16. The cross-country average is 11.5 in the data and 14.7 in the model. Finally, the model successfully reproduces the positive relationship between development and average size found in the data, albeit in a weaker degree. Whereas the elasticity of size and output per worker is.29 in the data, it is only.1 in the model. 29 Table (6) summarizes these results. 29 Poschke [2014] finds an elasticity of

32 Table 6: Model and Empirical Average Firm Size Moment Data Model Elasticity Development Mean Standard Deviation p p p p p Note Firm Size is measures as the number of employees. The moments come from the empirical and predicted cross-country distribution of average firm size in the manufacturing sector. The elasticity with respect to development refers to the slope coefficient of a regression of log of average firm size on aggregate output per worker. 4 Counterfactuals The first goal of this section is to quantify the trade channel of domestic distortions, i.e, by how much international trade affects the aggregate TFP losses stemming from distortions to firm size. I perform this measurement by switching countries schedules to the US level (γ US =.09) and computing the new general equilibrium in two scenarios: autarky and costly international trade. The US efficiency is an important benchmark because part of the observed dispersion of measured productivity might be due to overhead or adjustment costs and not to policy or market failures. 30 Therefore, this experiment consists of reducing an economy s dispersion of T F P R to the point that is justified by its dispersion of T F P Q and natural adjustment frictions. 31 The second goal is to measure the impact of firm-level distortions on trade openness and gains from trade. Finally, I evaluate the role of domestic misallocation in the determination of international productivity differences. Firm-level Distortions and Aggregate TFP In the first set of counterfactual exercise, I eliminate distortions in one country at a time and compute the new general equilibrium. The equilibrium is separately calculated for each country in order to avoid the case in which institutional improvements in one country affect, through trade, welfare in another country. I perform this exercise in two different scenarios: in a closed economy with arbitrarily large trade costs, and in an 30 This point has been emphasized in Bartelsman et al. [2013] and Asker et al. [2014]. 31 For domestic firms in country i, Sd(log(T F P R)) i = γ isd(log(t F P Q)) i. Therefore, I interpret the difference (γ i γ US)Sd(log(T F P Q)) i as the amount of dispersion in measured productivity due to firm-level policy distortions. 32

33 open economy with the calibrated trade costs that reproduce the empirical trade shares. The countries included in this exercise must respect the following conditions: (i) have observed - as opposed to inferred - schedules of distortions and (ii) respect the stability condition at the new schedule. Out of 81 countries, 53 countries satisfy these two conditions. 32 Table (7) and Figure (7) present the results. Table 7: Average aggregate TFP gain Total Entry Selection + Reallocation Autarky (%) Trade (%) Note Cross-country average TFP gain of converging to US schedule of distortions. Sample size=53 countries. Figure 7: Aggregate TFP gain Note Cross-country TFP gain of converging to US schedule of distortions. Sample size=53 countries. International trade amplifies the gains from converging to the US efficiency considerably. The average gain in aggregate TFP is 23% in the trade equilibrium but just 11% in autarky, which corresponds to a two-fold magnification effect. This result contrasts to the standard case in which productivity increments deliver smaller impacts on welfare 32 Countries that fail to satisfy condition (i) are: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Japan, Korea, New Zealand, Norway, Portugal, Switzerland and United Kingdom. Countries that do not respect condition (ii) are: Bulgaria, Croatia, Gabon, Namibia, Pakistan, Romania, Turkey and Ukraine. 33