Trade, Productivity and (Mis)allocation1
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 2 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 3 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 4 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

We examine the gains from globalization in the presence of firm heterogeneity and potential resource misallocation. We show theoretically that without distortions, bilateral and export liberalizations increase aggregate welfare and productivity, while import liberalization has ambiguous effects. Resource misallocation can either amplify, dampen or reverse the gains from trade. Using model-consistent measures and unique new data on 14 European countries and 20 industries in 1998-2011, we empirically establish that exogenous shocks to export demand and import competition both generate large aggregate productivity gains. Guided by theory, we provide evidence consistent with these effects operating through reallocations across firms in the presence of distortions: (i) Both export and import expansion increase average firm productivity, but the former also shifts activity towards more productive firms, while the latter acts in reverse; (ii) Both export and import exposure raise the productivity threshold for survival, but this cut-off is not a sufficient statistic for aggregate productivity; (iii) Efficient institutions, factor and product markets amplify the gains from import competition but dampen those from export access.

Abstract

We examine the gains from globalization in the presence of firm heterogeneity and potential resource misallocation. We show theoretically that without distortions, bilateral and export liberalizations increase aggregate welfare and productivity, while import liberalization has ambiguous effects. Resource misallocation can either amplify, dampen or reverse the gains from trade. Using model-consistent measures and unique new data on 14 European countries and 20 industries in 1998-2011, we empirically establish that exogenous shocks to export demand and import competition both generate large aggregate productivity gains. Guided by theory, we provide evidence consistent with these effects operating through reallocations across firms in the presence of distortions: (i) Both export and import expansion increase average firm productivity, but the former also shifts activity towards more productive firms, while the latter acts in reverse; (ii) Both export and import exposure raise the productivity threshold for survival, but this cut-off is not a sufficient statistic for aggregate productivity; (iii) Efficient institutions, factor and product markets amplify the gains from import competition but dampen those from export access.

1 Introduction

World trade has grown faster than world GDP since the early 1970s, and it expanded twice as quickly between 1985 and 2007.1 Of great policy interest is how globalization affects aggregate productivity and welfare, and how its impact differs across countries at different levels of economic development. In advanced economies, increased competition from low-wage countries has exacerbated public debates about the gains from trade, amidst rising concerns about employment, inequality and China’s dramatic expansion. In developing countries, trade reforms have not always yielded all or only desired benefits, leading policymakers to question the merits of trade openness in the face of weak macroeconomic fundamentals and slow structural transformation.

Trade theory provides a clear rationale for trade liberalization: it enables a more efficient organization of production across countries, sectors and firms, which generates aggregate productivity and welfare gains. In particular, heterogeneous-firm models emphasize the importance of firm selection and reallocation across firms in mediating these gains (e.g. Melitz 2003, Lileeva and Trefler 2010). At the same time, macroeconomics and growth research highlights that institutional and market frictions distort the allocation of productive resources across firms and thereby reduce aggregate productivity (e.g. Hsieh and Klenow 2009). However, how such frictions modify the gains from trade remains poorly understood.

This paper investigates the gains from globalization in the presence of firm heterogeneity and potential resource misallocation. We first show theoretically that without distortions, bilateral and export liberalizations increase aggregate welfare and productivity, while import liberalization has ambiguous effects. Resource misallocation can either amplify, dampen or reverse the gains from trade. Using model-consistent measures and unique new data on 14 European countries and 20 industries in 1998–2011, we then empirically establish that exogenous shocks to export demand and import competition both generate large aggregate productivity gains. Guided by theory, we provide evidence consistent with these effects operating through reallocations across firms in the presence of distortions. First, we decompose the aggregate productivity gains. Both export and import expansion increase average firm productivity, but the former also shifts activity towards more productive firms, while the latter acts in reverse. Second, both export and import exposure raise the productivity threshold for survival, but this cut-off is not a sufficient statistic for aggregate productivity. Finally, efficient institutions, factor and product markets amplify the gains from import competition but dampen those from export access.

Our first contribution is theoretical. We examine the impact of trade liberalization and resource misallocation in a standard heterogeneous-firm trade model, and numerically evaluate its predictions. In the absence of misallocation, reductions in bilateral trade costs or unilateral export costs unambiguously raise aggregate productivity and welfare, as in Melitz (2003) and Melitz and Redding (2014). On the extensive margin, such reforms raise the productivity cut-off above which domestic firms can operate. On the intensive margin, they shift activity from less towards more productive firms. By contrast, unilateral import reforms have ambiguous consequences because they increase market competitiveness both in the liberalizing country and in its trade partner, with opposing effects on the productivity cut-off at home. This results in welfare and productivity gains when wages are flexible and Metzler-paradox losses when wages are fixed, as in Demidova and Rodriguez-Clare (2013) and Bagwell and Lee (2018).

Under resource misallocation, the impact of both bilateral and unilateral trade liberalization on aggregate productivity and welfare becomes ambiguous. Moreover, it is not monotonic in the degree of misallocation, such that distortions may amplify, dampen or reverse the gains from trade. In the model, firms receive two exogenous draws, productivity φ and distortion δ. Distortions create a wedge between social and private marginal costs of production, and generate an inefficient allocation of productive resources and market shares across firms that is based on distorted productivity φ = φδ rather than true productivity φ. This misallocation arises only due to institutional imperfections that cause frictions in the market for input factors (or equivalently, for output products). Globalization has ambiguous effects because distorted economies operate in a second-best world and trade reforms can worsen or improve allocative efficiency. This occurs even though the underlying institutional frictions and distortion draws remain unaffected, unlike environments with endogenous heterogeneous mark-ups where gains from trade depend on the change in the joint distribution of firms’ mark-up and productivity as in Dhingra and Morrow (2019).

Our second contribution is methodological. We demonstrate how key theoretical concepts map to empirically observable variables and how theoretical mechanisms can be assessed with available data. In terms of measurement, we establish that firm-level real value added per worker is monotonic in theoretical firm productivity inclusive of any distortions, conditional on export status. However, while welfare is proportional to a productivity aggregate across all domestic and foreign firms whose goods enter the domestic consumption basket, welfare is generally not monotonic in measured aggregate productivity, which is the employment-weighted average real value added per worker of domestic firms.2 The latter two are proportional under flexible wages, Pareto-distributed productivity, and no misallocation. They also co-move in a wide segment of the parameter space away from this special case, but only when there are no distortions.

We then show how the role of misallocation in the adjustment to trade reforms can be inferred in the absence of direct measures of misallocation. We decompose measured aggregate productivity into unweighted average firm productivity and the covariance of firm productivity and employment share, as in Olley and Pakes (1996). The OP covariance is not a sufficient statistic for either the distribution of distortions δ or realized allocative efficiency. However, numerical simulations indicate that trade liberalization can move the two OP productivity components in opposite directions only under misallocation. In the model, reductions in variable export and import costs exert qualitatively isomorphic effects as positive foreign demand and supply shocks, respectively. These results together motivate and discipline our empirical design.

Our third contribution is empirical. We assess the effect of international trade on aggregate productivity and the mechanisms through which it operates, using unique new data assembled by the Competitive Research Network of the ECB (CompNet) for 14 European countries and 20 manufacturing industries in 1998–2011. These data are unprecedented in capturing not only aggregate outcomes, but also multiple moments of the underlying distribution across firms. They also provide precise empirical counterparts to theoretical productivity objects of interest, as they rely on real value added per worker deflated by value-added producer price indices by country-industry-year. This enables us to both implement the OP decomposition of aggregate productivity and exploit variation in institutional and trade conditions for a large panel of countries and sectors. We can thus for the first time overcome the trade-off in the prior literature between using micro-level data for one country (to estimate model-based misallocation or firm reallocation after a single trade reform) and using aggregate data for multiple countries (to harness differences in institutional frictions and trade shocks).

Our baseline measures of export access and import competition are gross exports and gross imports (less own-sector imported inputs) by country and sector, from the World Input-Output Database. We establish causality with an IV strategy that exploits variation in the initial composition of countries’ trade baskets and contemporaneous value-added trade flows by sector of final use. We instrument for export demand with the weighted average absorption across a country’s export destinations, by sector. We instrument for import supply with import tariffs and the weighted average of value-added exports for final consumption across a country’s import origins, by sector. These instruments improve on standard practice in the literature by proxying demand with absorption instead of imports (to account for domestic production and exports) and by using value-added instead of gross trade flows (to account for global value chains).3

We find that export access and import penetration both significantly increase measured aggregate productivity. The estimates imply that a 20% rise in export demand and import competition would generate productivity gains of 7.6%-8.2% and 1%-10% respectively. We perform three exercises to uncover the mechanisms driving these effects. The results indicate that firm heterogeneity and resource misallocation jointly determine the gains from trade. Moreover, distorted economies adjust asymmetrically to positive shocks to domestic firms such as stronger export demand and negative shocks such as tougher import competition.

First, the OP decomposition reveals that export growth both raises average firm productivity (61–77%) and reallocates activity towards more productive firms (23–39%). By contrast, the gains from import competition stem entirely from higher average firm productivity (117–136%) and are partly offset by a shift in activity towards less productive firms (- 17–36%). Through the lens of the model, these patterns can only be rationalized with trade inducing reallocations across firms in the presence of distortions.

Second, both export and import exposure increase the minimum productivity among active firms, consistent with trade improving firm selection by triggering exit from the left tail of the distribution. However, the productivity threshold is not a sufficient statistic for the effect of trade on aggregate productivity, counter to model predictions for the case of no misallocation.

Finally, efficient institutions, factor and product markets amplify the productivity gains from import competition and dampen those from export expansion. We measure broad institutional quality with rule of law and corruption, and proxy institutional frictions in specific input and output markets with indices of labor market flexibility, creditor rights’protection and product market regulation. This direct, assumption-free evidence suggests that misallocation does moderate the impact of globalization, and informs the theoretically ambiguous sign of this moderating force.

We contribute to several strands of literature. We advance research on the role of firm heterogeneity for the gains from trade. Work-horse trade models emphasize the importance of reallocations across heterogeneous firms for the realization of welfare and productivity gains from globalization (e.g. Arkolakis et al. 2012, Melitz and Redding 2014). Prior empirical work has studied episodes of unilateral trade reforms with micro-level data for a single country. For example, Bernard et al. (2006) show that following a decline in trade barriers in the U.S., productivity grew in liberalized sectors both because the least productive firms exited and because more productive firms expanded more. Pavcnik (2002) estimates that about 2/3 of the aggregate productivity gains from trade reforms in Chile in the late 1970s can be attributed to the OP covariance, while Harrison et al. (2013) conclude that trade liberalization in India during 1990–2010 mostly improved the average productivity of surviving firms.4 To the best of our knowledge, we provide the first causal cross-country evidence for high- and middle-income countries that nevertheless informs the firm dimension and we compare export and import access.

We also add to a large literature on the implications of resource misallocation for aggregate growth and productivity. A key finding is that frictions in input and output markets distort the allocation of production resources across firms, lower aggregate productivity, and contribute to its large variation across countries (e.g. Restuccia and Rogerson 2008, Hsieh and Klenow 2009, Bartelsman et al. 2013, Hopenhayn 2014, Gopinath et al. 2017, Foster et al. 2008, Foster et al. 2016, Baqaee and Farhi 2019b). Since different micro-foundations for misallocation have different implications for measured cross-firm dispersion in productivity and marginal products of capital and labor, quantifying misallocation in the data poses challenges. We extend these insights to and generate rich additional effects in an open economy, general-equilibrium trade model. We do not aim to develop new misallocation measures, but instead study observed aggregate productivity inclusive of any distortions as the policy-relevant concept of effective productivity. We characterize the disconnect between welfare and measured aggregate productivity, theoretically analyze the gains from trade with and without misallocation, and provide empirical evidence consistent with model predictions for the case of misallocation.5

Most directly, we contribute to vibrant research on the impact of institutional and market frictions on international trade. This body of work departs from the traditional assumption in the trade literature that resources are efficiently and instantaneously reallocated across firms. Credit constraints have been shown to disrupt export entry, various dimensions of import and export activity at the firm level, and aggregate trade flows (e.g. Chor and Manova 2012, Manova 2013, Foley and Manova 2015), and labor market frictions shape the allocation of workers across firms and the adjustment to trade reforms (e.g. Helpman et al. 2010, Ruggieri 2018, Dix-Careino et al. 2019, Kim and Vogel 2020).

We extend this research by turning to the fundamental question of how resource misallocation affects the gains from trade. Our analysis implies that welfare results from workhorse quantifiable gravity trade models (Costinot and Rodriguez-Clare 2014, Donaldson 2015) no longer hold in the presence of distortions due to weak institutions. This is consistent with the literature on trade reforms in developing countries (Atkin and Khandelwal 2019) and work on the role of intersectoral and interregional misallocation for the gains from trade (Swiecki 2017, Caliendo et al. 2017, Hornbeck and Rotemberg 2019).

Our work is most closely related to concurrent studies on the role of firm-level distortions in a trade context. Bai et al. (2019) consider the effects of bilateral liberalization from autarky to free trade in the presence of distortionary sales taxes and subsidies on heterogeneous producers. They decompose the welfare gains from trade into adjustment channels, and their numerical exercises and model calibrated to Chinese firm data show that misallocation can generate welfare losses from trade. Sandoz (2018) establishes that access to cheaper imported inputs fosters aggregate productivity growth by improving resource allocative efficiency, and offers quantitative evidence for France. Bajgar (2016) finds that the gains from trade tend to increase with distortions to domestic sales only, to fall with distortions to exports only, and to become ambiguous with both distortions. Chung (2018) demonstrates how (potentially different) subsidies and taxes on domestic and export sales influence the observed dispersion in firm productivity and the gains from trade, and provides empirical evidence for China.

In comparison, we fully characterize the impact of bilateral and unilateral gradual trade reforms on both welfare and aggregate productivity, map theoretical objects to observed data, and decompose measured aggregate productivity. We formally consider the impact of misallocation both when trade brings welfare gains and when trade begets welfare losses (Metzler paradox) in the first best. We then theoretically and numerically establish that misallocation can generate gains or losses from trade and that it can amplify, dampen or reverse trade gains/losses compared to the first best. We also use reduced-form estimation to establish causal effects of import and export expansion on measured aggregate productivity and to thereby empirically inform the role of misallocation.

Also related if less directly are studies of other sources of misallocation in trade, Khandelwal et al. (2013) find that the inefficient allocation of quota rights across producers affected Chinese export activity under the Multi-Fiber Agreement, while Ben Yahmed and Dougherty (2017) show that the impact of import competition on firm productivity depends on the degree of product market regulation.6 Separately, variable mark-ups also entail market share misallocation across firms and limit the welfare gains from increased trade or market size (Epifani and Gancia 2011, Edmond et al. 2015, Feenstra and Weinstein 2017, Dhingra and Morrow 2019, Arkolakis et al. 2019, Baqaee and Farhi 2020).

The rest of the paper is organized as follows. Section 2 theoretically and numerically examines the impact of globalization on welfare and aggregate productivity. Section 3 introduces the CompNet and WIOD data, and Section 4 presents baseline OLS estimates. Section 5 develops the IV estimation strategy, reports the main IV results, and performs extensive sensitivity analysis. Section 6 explores the mechanisms that mediate the productivity effects of trade. The last section concludes.

2 Theoretical Framework

We examine the impact of international trade on aggregate welfare and productivity in a general-equilibrium model with firm heterogeneity in productivity as in Melitz (2003) and Chaney (2008) and potential resource misallocation as in Hsieh and Klenow (2009) and Bartelsman et al (2013). Our goal is threefold. First, we highlight that in the absence of misallocation, bilateral and unilateral export liberalizations always raise aggregate welfare and productivity, while unilateral import liberalization can have ambiguous effects. Second, we show that all three types of globalization have ambiguous consequences in the presence of misallocation. Third, we characterize the relationship between welfare and aggregate productivity in the model and aggregate productivity measures in the data to provide a bridge between theory and empirics. We relegate detailed proofs to Appendix A.

2.1 Set Up

Economic environment: Consider a world with two potentially asymmetric countries i = 1, 2 and

free firm entry into production.7 In each country, a measure Li of consumers inelastically supply a unit of labor, and aggregate expenditure is Ei. A representative consumer derives utility Ui from consuming a homogenous good Hi and differentiated varieties zΩi:

Ui=Hi1βQiβ,Qi=[zΩiqi(z)αdz]1/α.(2.1)

Demand qi(z) for variety z with price Pi(z) in country i is thus qi(z)=βEiPiQσ1pi(z)σ, where βEi is total expenditure on differentiated goods, PiQ=[zΩipi(z)αdz]1/(1α) is the ideal price index in the differentiated sector, and α = 1/(1 α) > 1 is the elasticity of substitution across varieties.

The homogeneous good is freely tradeable and produced under CRS technology that converts one unit of labor into one unit of output. When β is sufficiently low, both countries produce the homogeneous good, such that it serves as the numeraire, PiH = 1, and fixes wages to unity, wi = 1. We will refer to this case simply as β< 1. When β = 1 by contrast, only differentiated goods are consumed, and wages are endogenously determined in equilibrium. The aggregate consumer price index is thus Pi=PiQβ.

In each country, a continuum of monopolistically competitive firms produce horizontally differentiated varieties that they can sell at home and potentially export. Firms pay a sunk entry cost wifiE and, should they commence production, fixed operation costs wifii and constant marginal costs. Exporting from i to j requires fixed overhead costs wifij and iceberg trade costs such that τij units of a good need to be shipped for 1 unit to arrive, where τii = 1 and τij 1 if ij. We allow for τijτij, and analyze symmetric and asymmetric reductions in τij to assess the impact of different trade reforms.

Firm productivity and resource misallocation: In the absence of misallocation, firms in country i draw productivity φ upon entry from a known Pareto distribution Gi(φ)=1(φim/φ)θ, where θ>σ1andφim>0.8 This fixes firms’ constant marginal cost to wi. Under resource misallocation on the other hand, firms draw both productivity φ and distortion δ from a known joint distribution Hi(φ,τ). Firms’ marginal cost is now determined by their distorted productivity φ = φδ and equals wi/φ = wi/(φδ).9 For comparability with the case of no misallocation, we assume that φ is Pareto distributed with scale parameter φ¯im and shape parameter θ.

Conceptually, τ captures any distortion that creates a wedge between the social marginal cost of an input bundle and the private marginal cost to the firm. Formally, this implies a firm-specific wedge in the first-order condition for profit maximization. Such a wedge may result from frictions in capital or labor markets or from generally weak contractual institutions that support inefficient practices like corruption and nepotism.10 Distortions τ will lead to deviations from the first-best allocation of productive resources across firms: If a firm can access “too much” labor “too cheaply”, this would be equivalent to a subsidy of τ > 1. Conversely, capacity constraints, hiring and firing costs would correspond to a tax of τ < 1.

Modeling misallocation in this way has several appealing features. First, it permits a transparent comparison of firm and economy-wide outcomes with and without misallocation. Under misallocation, firm selection, production and export activity depend on φ and τ only through distorted productivity φ = φτ, while optimal resource allocation in the first best depends on φ alone. Thus two parameters regulate the degree of misallocation: the dispersion of the distortion draw, στ, and the correlation between the distortion and productivity draws, ρ(φ,τ).11 Misallocation occurs if and only if ρτ > 0, but its severity need not vary monotonically in the ρτ ρ(φ,τ) space.12

Second, introducing distortions on the input side is qualitatively isomorphic to allowing for distortions in output markets, such as firm-specific sales taxes.13 Our theoretical formulation thus ensures tractability without loss of generality. In the empirical analysis, we correspondingly exploit different measures of broad institutional quality, capital and labor market frictions, and product market regulations.

Within the differentiated sector, misallocation stems from the inefficient allocation of production resources and consequently market shares across firms. Since CES preferences and monopolistic competition will imply a constant mark-up μ = 1/α > 1, there is no additional misallocation due to variable mark-ups across firms as in Dhingra and Morrow (2016). When β < 1, however, there will also be markup driven misallocation across sectors: Because perfectly competitive producers of the CRS homogeneous good do not charge a mark-up, the differentiated sector will be “too small”.

2.2 Economy Equilibrium

Firm behavior: Producers choose their price Pij(φ) and quantity qij(φ) to maximize profits πij(φ) separately in each market j. With no distortions, the optimal behavior of a firm with productivity φ is:

maxp,qπij(φ)=pij(φ)qij(φ)wiτijqij(φ)/φwifijs.t.qij(φ)=βEjPjQσ1pij(φ)σ(2.2)
pij(φ)=wiτijαφ,qij(φ)=βEjPjQσ1(αφwiτij)σ,(2.3)
lij(φ)=fij+τijqij(φ)φ,cij(φ)=wi(fij+τijqij(φ)φ),(2.4)
rij(φ)=βEj(αPjQφwiτij)σ1,πij(φ)=rij(φ)σwifij.(2.5)

where lij(φ), cij(φ) and rij (φ) are the employment, costs and revenues associated with sales in j.

Since profits are monotonically increasing in productivity, firms in country i sell in market j only if their productivity exceeds threshold φij*. The domestic and export cut-offs are implicitly defined by:

rii(φii*)=σwifii,rij(φij*)=σwifij.(2.6)

Upon entry, firms commence production if their productivity is above φii*, and exit otherwise. We assume as standard that the parameter space guarantees selection into exporting, φii*>φii*, for any τij > 1. In the case of misallocation, the profit-maximization problem of a firm with distorted productivity φ = φτ generates the following second-best outcomes:

maxp,qπij(φ,η)=pij(φ,η)qij(φ,η)wiτijqij(φ,η)/φηwifijs.t.qij(φ,η)=βEjPjQσ1pij(φ,η)σ(2.7)
pij(φ,η)=wiτijαφη,qij(φ,η)=βEjPjQσ1(αφηwiτij)σ,(2.8)
lij(φ,η)=fij+τijqij(φ,η)φ,cij(φ,η)=wi(fij+τijqij(φ,η)φη),(2.9)
rij(φ,η)=βEj(αPjQφηwiτij)σ1,πij(φ,η)=rij(φ,η)σwifij.(2.10)

While it would be socially optimal to allocate input factors and output sales based on true firm productivity φ, in the market equilibrium this allocation is instead pinned down by distorted productivity φ. Along the intensive margin, firms with low (high) distortions φ produce and earn less (more) than in the first best, and set higher (lower) prices than efficient. Along the extensive margin, a highly productive firm might be forced to exit if it faces prohibitively high taxes, while a less productive firm might be able to operate or export if it benefits from especially high subsidies. Firms thus sell in the domestic and foreign market if their distorted productivity exceeds cut-offs φ¯ii*andφ¯ij*, respectively:

rii(φ¯ii*)=σwifii,rij(φ¯ij*)=σwifij.(2.11)

General equilibrium: The general equilibrium is characterized by conditions that ensure free entry, labor market clearing, income-expenditure balance, and trade balance in each country.

Consider first the case of no misallocation. With free entry, ex-ante expected profits must be zero:

jEi[πij(φ)I(φφij*)]=wifiE,(2.12)

where Ei[·] is the expectation operator and I(·) is the indicator function.14

A key implication of the free-entry condition is that the productivity cut-offs in country i for production and exporting must always move in opposite directions following trade reforms that affect τij or τij. Intuitively, any force that lowers φij* tends to increase expected export profits conditional on production. For free entry to continue to hold, φii* must therefore rise, such that the probability of survival conditional on entry falls and overall expected profits from entry remain unchanged.

Let LiH and LiQ denote respectively total labor employed in the homogeneous and differentiated sectors. Labor market clearing in country i requires:

Li=LiH+LiQ=LiH+MifiE+jMiEi[lij(φ)I(φφij*)],(2.13)

where Mi is the mass of entering firms in the differentiated sector. When β < 1, we restrict the parameter space to ensure LIH > 0, such that the wage is determined by productivity in the homogenous-good sector. When β = 1 and LiH = 0, by contrast, wages are flexible and determined by LiH = LiQ.

In equilibrium, aggregate income must equal aggregate expenditure. With free entry, aggregate corporate profits net of entry costs are 0, such that total income corresponds to the total wage bill. Consumers’utility maximization implies the following income-expenditure balance:15

βwjLj=βEj=iMiEi[rij(φ)I(φφij*)].(2.14)

Consider next the case of misallocation. The free entry and labor market clearing conditions are analogous to those above after replacing productivity φ with distorted productivity φ = φτ. The income-expenditure balance, however, has to be amended. While firm (φ, τ]) incurs production costs cij(φ,η)=wi(fij+τijqij(φ,η)φη), the payment received by workers is ciji(φ,η)=wi(fij+τijqij(φ,η)φ). The gap cij'(φ,η)cij(φ,η) is the social cost of distortionary firm-specific taxes or subsidies, which we assume are covered through lump-sum taxation Ti of consumers in i. When a firm is subsidized and cij(φ,η)<cij'(φ,η) for example, it pays its employees less than what it would have without the subsidy, and consumers pay the difference. The new equilibrium conditions become:

jEi[πij(φ,η)I(φηφ¯ij*)]=wifiE,(2.15)
Li=LiH+LiQ=LiH+MifiE+jMiEi[lij(φ,η)I(φηφ¯ij*)],(2.16)
β(wjLjTj)=βEj=iMiEi[rij(φ,η)I(φηφ¯ij*)],(2.17)
Ti=jMiEi[[cij'(φ,η)cij(φ,η)]I(φηφ¯ij*)].(2.18)

Welfare: Welfare in country i is given by real consumption per capita and can be expressed as:

Wi={(1β)1βββwiPiχiifβ<1wiPiχiifβ=1}whereχi=EiwiLi=wiLiTiwiLi.(2.19)

Welfare is thus proportional to the real wage, wi/Pi, and the ratio of disposable income to gross income, χi. In the absence of misallocation, all income accrues to worker-consumers, such that Ei = wiLi and χi = 1. In the presence of misallocation, by contrast, some income is not available to consumers due to the tax burden of distortions, such that Ei = wiLi Ti and χi < 1; albeit less realistic, it is in principle possible that χi > 1. Misallocation also affects the price index Pi through distortions to firm selection on the extensive margin and to firm prices and market shares on the intensive margin.

One can show that the real wage, and therefore also welfare, is a function of two equilibrium outcomes: the (distorted) productivity cut-off for production, φii*orφ¯ii*, and the share of disposable income, χi:16

Wi{(Liσfii)βσ1(φii**)βwithoutmisallocation(Liσfii)βσ1(χi)β+σ1σ1(φ¯ii**)βwithmisallocation}.(2.20)

Lemma 1 Without misallocation, welfare increases with the domestic productivity cut-off, dWidφii*>0. With misallocation, welfare increases with the distorted domestic productivity cut-off (holding x% fixed), Wiφ¯ii*>0, and with the share of disposable income in gross income (holding φ¯ii* fixed), Wiχi>0.

With efficient resource allocation, a higher productivity cut-off φii* implies a shift in economic activity towards more productive firms, which tends to lower the aggregate price index and increase consumers’ real income. With misallocation, distortions affect welfare through the reduction in disposable income χi and through the sub-optimal selection and size of active firms based on distorted productivity φ rather than true productivity φ. One direct implication of Lemma 1 is that welfare is proportional to the domestic productivity cut-off if and only if there are no allocative frictions. Another implication is that the welfare impact of trade liberalization depends on how a reduction in τij affects φii*,φ¯ii*, and χi.

Note that in the two-sector general equilibrium, welfare reflects both distortion-driven misallocation across firms within the differentiated sector and markup-driven misallocation across sectors, both of which are reflected in the economy-wide price index Pi. One cannot analytically decompose these two sources of misallocation, and their relative contribution is state-dependent.17

2.3 From Theory to Empirics

A key challenge in evaluating the gains from trade is that productivity and welfare are not directly observable. Here we characterize the mapping between these theoretical objects and their empirical counterparts. We focus on firm and aggregate productivity in the differentiated sector, which are the objects of interest in both the single- and two-sector models.

Theoretical vs. measured firm productivity: The theoretical concept of firm productivity is quantity-based, while empirical measures are generally revenue-based. For our purposes, real value added per worker is a valid proxy for effective firm productivity inclusive of any distortions.

Without misallocation, observed value added and employment correspond respectively to total firm revenues, ri(φ)=jrij(φ)I(φφij*), and total labor hired, li(φ)=jlij(φ)I(φφij*). Denoting labor used towards fixed costs as fi(φ)=jfij(φ)I(φφij*) and normalizing by the price index in the dierentiated industry PiQ=Pi1/β, real value added per worker Φi(φ) is:

Φi(φ)=ri(φ)PiQli(φ)=wiαPi1/β[1fi(φ)li(φ)].(2.21)

One can show that without distortions, real value added per worker increases monotonically with theoretical firm productivity conditional on export status, Φi'(φ|φ<φij*)>0andΦi'(φ|φφij*)>0.18

In the case of misallocation, real value added per worker reflects firms’ effective productive capacity given distortions, and can thus be labeled Φi(φ,τ]). It is now monotonic in theoretical distorted productivity conditional on export status, Φ¯i'(φη|φη<Φ¯ij*)>0andΦ¯i'(φη|φηΦ¯ij*)>0:19

Φ¯i(φ,η)=ri(φ,η)PiQli(φ,η)=wiαPi1/βη[1fi(φ,η)li(φ,η)].(2.22)

Measured aggregate productivity and OP decomposition: Let measured aggregate productivity, Φ˜i, be the weighted average of measured firm productivity. Without distortions, Φ˜i is:

Φ˜iφi*θi(φ)Φi(φ)dGi(φ)1Gi(φii*),(2.23)

where θi(φ)li(φ)/[φii*li(φ)dGi(φ)1Gi(φii*)], is firm φ's share of aggregate employment.20 This will correspond exactly to employment-weighted average real value added per worker across firms in our CompNet data. Of note, the choice of employment shares as firm weights ensures that Φ˜i equal the ratio of aggregate revenue to aggregate employment in the differentiated sector adjusted by the sectoral price index; this in turn parallels how statistical agencies measure aggregate labor productivity with real GDP per worker deflated by sector price indices.

As an accounting identity, measured aggregate productivity, Φ˜i, can be decomposed into the measured unweighted average productivity across firms, Φ¯i, and the measured covariance of firms’ productivity and share of economic activity, Φ˜i, known as the OP gap (Olley and Pakes, 1996):

Φ˜i=Φ¯i+Φ¨i=φii*Φi(φ)dGi(φ)1Gi(φii*)+φii*[Φi(φ)Φ¯i][θi(φ)θ¯i]dGi(φ)1Gi(φii*).(2.24)

The OP decomposition reveals how adjustments across and within firms shape aggregate measured productivity. Changes in Φ¯i reflect two effects of firm selection: exit/entry into production modifies the set of active firms, and exit/entry into production or exporting impacts measured firm productivity. Changes in Φ¨i indicate reallocation of activity across firms with different productivity levels through changes in their share of production resources and implicitly sales. The OP decomposition remains valid in the case of misallocation, when φ¯,φii*,Φ¯i(φ,η),andHi(φ,η)replaceφ,φii*,Φi(φ), and Gi(φ) in (2.24).

Welfare vs. measured aggregate productivity: From a policy perspective, welfare and domestic aggregate productivity matter for different objectives: The former captures consumer utility at a point in time, while the latter indicates a country’s productive capacity, improvements in which drive growth over time. However, these two objects can differ, even under allocative efficiency: Welfare in country i depends on the price index Pi faced by consumers in i, which reflects the prices of all varieties sold in i. Intuitively, Wi is related to the weighted average productivity of all domestic and foreign firms supplying i, using their activity in i as weights. By contrast, Φ˜i is the weighted average productivity of domestic firms, using their total employment as weights. This distinction is irrelevant in special cases, such as symmetric countries and bilateral trade costs, when the measure, productivity, prices and market shares of firms exporting from i to j are identical to those of firms exporting from j to i.21

One can express measured aggregate productivity as a function of the real wage, wi/Pi, and the size-weighted average distortion across firms, η˜i, where δ = 1 and η˜i=1 without misallocation:

Φ˜i={σθσθ(σ1)wiPi1/βwithoutmisallocationσθ(σ1)θη¯i+θ(σ1)wiPi1/βwithmisallocation,(2.25)whereη˜i=jEi[ηrij(φ,η)I(φηφ¯ij*)]jEi[rij(φ,η)I(φηφ¯ij*)].

Together, equations (2.19), (2.20) and (2.25) imply that shocks that move the (distorted) productivity cut-offs for production and exporting will shift Φ˜i through their effect on the equilibrium wage wi (if β = 1), the aggregate price index Pi, and the average distortion η˜i. In particular:

Lemma 2 Without misallocation, measured aggregate productivity increases with the domestic productivity cut-off, dΦ˜idφii*>0. With misallocation, this relationship becomes ambiguous, dΦ˜idφ¯ii*0.

Lemmas 1 and 2 imply that measured aggregate productivity can be a sufficient statistic for welfare only without misallocation.22 With misallocation, Wi and Φ˜i are not closed-form functions of the misallocation parameters, and we therefore simulate the model using standard parameters from the literature (see Section 2.5) to numerically explore their relationship. We assume productivity and distortions are joint log-normal with μφ = μσ = 1, σφ = 1, and vary the levels of distortion dispersion ση ∈ [0,0.5] and productivity-distortion correlation ρ(φ,η) ∈ [0.4,0.4].

Figure 1A shows that welfare peaks at ση = ρ(φ,η) = 0 and falls as the distortion dispersion widens for the given ρ(φ,η). At low levels of ση, Wi rises as the distortion and productivity draws become more positively correlated, but the opposite holds at sufficiently high levels of ση. While measured aggregate productivity behaves similarly under this parametrization in Figure 1B, Wi and Φ˜i need not co-move under alternative assumptions (unreported). For completeness, Figure 1C plots measured average productivity Φ¯i against the misallocation parameters.

Figure 1.
Figure 1.

Numerical Simulation: Welfare and Measured Aggregate Productivity

Citation: IMF Working Papers 2020, 163; 10.5089/9781513554440.001.A001

OP covariance vs. misallocation: The OP covariance is related to allocative efficiency in that Φ¨i>0 in a frictionless economy (when both Φi(φ) and θi(φ) conditionally increase in φ) but Φ¨i0 in the presence of distortions.23 However, one cannot interpret a rise in Φ¨i as an improvement in allocative efficiency, because the optimal allocation of resources across firms is generally state-dependent and reliant on the economic environment (i.e. demand structure, cost structure, market structure, productivity distribution). Even if the optimal covariance Φ¨i* were known, both values below and above it would indicate deviations from the first best. Moreover, the absolute difference |Φ¨i*Φ¨i| need not be proportional to or even monotonic in the degree of misallocation and the welfare loss associated with it.

Figure 1D illustrates that the OP covariance can indeed be negative, zero or positive at different points in the ση ρ(φ,η) space. Given ρ(φ,η), higher distortion dispersion is associated with lower Φ¨i, consistent with more productive firms becoming sub-optimally smaller. Given ση, higher ρ(φ,η) tends to imply lower Φ¨i; although productive firms get inefficiently large, this counterintuitive pattern reflects distortion-induced measurement error in Φi(φ,η). This measurement error also explains why Φ¨i does not peak at ρ(φ,η) = 0 if ση > 0, when misallocation would intuitively be lowest. Alternative parameterizations can also produce non-monotonic patterns for Φ¨i in ση and ρ(φ,η).

Inspecting Figures 1A and 1D, the comparative statics for Wi and Φ¨i are not perfectly aligned, reinforcing the conclusion that Φ¨i does not fully capture the welfare cost of misallocation.24 One can therefore not unambiguously interpret a rise (fall) in Φ¨i in response to an exogenous shock as an improvement (deterioration) in allocative efficiency.

In sum, we are not able to develop a model-based index of misallocation that would be observable in the data and that would allow one to decompose measured aggregate productivity into potential productivity and distortions. However, this is also not the goal of our exercise: We are interested in the impact of globalization on effective aggregate productivity inclusive of any distortions. As we show below, our theoretical framework allows to predict and contrast this impact in environments with and without misallocation. Indeed, the combined effect of trade shocks on the three OP productivity terms can reveal the presence of misallocation.

2.4 Trade Liberalization

We can now examine the impact of trade liberalization on welfare Wi and measured aggregate productivity Φ˜i, average productivity Φ¯i, and productivity covariance Φ¨i. We consider three forms of trade liberalization: symmetric bilateral reduction in variable trade costs τij and τij, unilateral reduction in export costs τij, and unilateral reduction in import costs τij.

2.4.1 Efficient allocation

In the case of efficient resource allocation, firms respond to trade reforms based on their productivity.

Consider first export liberalization. A fall in τij creates more export opportunities for firms in i, as they can charge lower prices in j and benefit from higher export demand. This decreases the productivity cut-off for exporting φij*, more firms commence exporting, and continuing exporters expand sales abroad. For free entry in i to continue to hold, expected profits from domestic sales must fall, and the productivity threshold for survival, φii*, rises. This effect is amplified when wages can flexibly adjust, as export expansion bids up labor demand and wages in i, such that even more low-productivity firms are no longer profitable.

Consider next import liberalization. A decline in τji enables foreign firms to sell more cheaply to i. This lowers the productivity cut-off for exporting from j to i, φji*, and induces continuing j exporters to ship more to i. The direct effect is tougher import competition in i, reducing the aggregate price index and demand for locally produced varieties. This lessens domestic firms’ home sales and pushes up i’s domestic productivity cut-off, φii*. The indirect effect is a higher productivity threshold for survival in j, φjj* so that free entry still holds now that j firms expect higher export profits. This makes j a more competitive market, raises the cut-off for exporting from i to j, φij*, and with free entry in i, acts to depress the survival threshold, φii*. When wages are flexible, their fall dampens the indirect effect and the direct effect dominates. Conversely, when wages are fixed, the indirect effect prevails.

A symmetric bilateral liberalization combines the impacts of unilateral export and import reforms. One can show that this raises the domestic productivity cut-off, φii*, regardless of wage flexibility. This is associated with the reallocation of activity across firms via the exit of low-productivity firms on the extensive margin and the shift in market share towards more productive firms on the intensive margin.

From Lemmas 1 and 2, changes in the productivity threshold φii* signal changes in aggregate outcomes. Thus bilateral and unilateral export liberalizations unambiguously increase welfare Wj, as in Melitz (2003), Melitz and Redding (2014), Arkolakis et al. (2012), and Demidova and Rodriguez-Clare (2013). Unilateral import liberalizations raise welfare under flexible wages, but generate welfare losses with fixed wages, as in Demidova (2008) and Bagwell and Lee (2018).25 We further establish that in the absence of distortions, measured aggregate productivity Φ˜i moves in the same direction as Wi.

Turning to the OP decomposition, it is clear that if globalization raises (lowers) Φ˜i, then either average productivity Φ¯i, or the productivity covariance Φ¨i, or both must rise (fall) as well. However, one cannot analytically sign the response of these OP terms without further parameter restrictions. This ambiguity arises due to the counteracting effects of the shift in activity towards more productive firms and the differential change in measured productivity Φ(φ) along the productivity distribution.

Proposition 1 Under no misallocation and flexible wages (β = 1), bilateral and unilateral trade liberalizations (i.e. reductions in τij, τji, or both τij and τji) increase welfare Wi and measured aggregate productivity Φ˜i, but have ambiguous effects on average productivity Φ¯i and covariance Φ¨i.

Proposition 2 Under no misallocation and fixed wages (β < 1), bilateral and unilateral export liberalizations (i.e. reductions in τij or both τij and τji) increase welfare Wi and measured aggregate productivity Φ˜i, but have ambiguous effects on average productivity Φ¯i and covarianceΦ¨i. Unilateral import liberalization (i.e. reduction in τji) reduces Wi and Φ˜i but has ambiguous effects on Φ¯iandΦ¨i.

2.4.2 Resource misallocation

In the presence of misallocation, economies operate in a sub-optimal equilibrium both before and after any trade reforms. Trade liberalization now triggers reallocation across firms based on distorted productivity φ rather than true productivity φ. While trade does not affect the underlying institutions that generate distortions (i.e. ση and ρ(φ,η), it can in principle improve or worsen allocative efficiency. From the theory of the second best, it is therefore not possible to unambiguously determine the impact of trade reforms on aggregate welfare and productivity: It hinges on initial state variables and model parameters, in particular, the joint distribution Hi(φ,η).

The effects of trade also need not be monotonic in the distortion parameters ση and ρ(φ,η) or the initial degree of misallocation. In other words, more severe market frictions may amplify, dampen or reverse the gains from globalization. On the one hand, countries with more efficient resource allocation may more effectively adjust to trade reforms and reap greater productivity returns. On the other hand, such countries are closer to the first best to begin with, and may benefit less from further trade liberalization.

Intuitively, misallocation acts by distorting firm selection on the extensive margin and firm market shares on the intensive margin. Misallocation would reduce the gains from trade if more productive firms cannot fully respond to growth opportunities, while less productive firms are not forced to exit. For example, trade liberalization could magnify existing distortions if firms with inefficiently abundant access to inputs can expand their activity relatively more than firms with inefficiently constrained resources (e.g. if new loans are extended based on collateralizable tangible assets accumulated with past loans). Conversely, misallocation may increase the gains from trade if trade has a cleansing effect on the economy and serves to reallocate activity towards truly more productive firms (e.g. new loans are granted based on future profitable opportunities).

Note that models with endogenous heterogeneous mark-ups across firms also feature static misallocation of market shares (c.f. Edmond et al. 2015, Arkolakis et al. 2019, Dhingra and Morrow 2019). However, what determines the welfare impact of trade liberalization in that environment is the change in the joint distribution of firms’ mark-up and productivity. We show instead that even holding the firm-specific wedge η and thus the distortion-productivity distribution fixed, trade liberalization can shift the ex-post productivity-size distribution that regulates the extent of misallocation.

Proposition 3 Under resource misallocation, bilateral and unilateral trade liberalizations (i.e. reductions in τij, τji, or both τij and τji) have ambiguous effects on welfare Wi, measured aggregate productivity Φ˜i, average productivity Φ¯i, and covariance Φ¨i.

2.5 Numerical Simulation

We explore the impact of counterfactual trade reforms through numerical simulations, to inform both its sign and magnitude. We consider 20% reductions in trade costs from initial values of τij = τji = 1.81 in three scenarios: bilateral liberalization (shocks to both τij and τji), export liberalization (shock to τij), and import liberalization (shock to τji).

We use model parameters from the literature (e.g. Burstein and Cravino 2015), and set the elasticity of substitution to σ = 3. We assume that both countries have a unit measure of consumers, Li = Lj = 1, and symmetric fixed costs of entry, production and exporting, fiE=fjE=0.1, fii = fjj = 1.2, and fij = fji = 1.75. In the case of no misallocation, we let productivity in both countries be distributed Pareto ~ G(φ) = 1 m/φ)θ, φm = 1, θ = 2.567) or log-normal (In φ ~ N(μφ, σφ), μφ = 0, σφ = 1).26 In the case of misallocation, we assume the productivity and distortion draws are bivariate log-normal distributed, [lnφlnη]N(μ,Σ),μ=[μφφη],Σ=[σφ2ρσφσηρσφσηση2]. We set μφ = μη = 0 and σφ = 1 in both countries. We fix ση = 0.05 and ρ = 0 in Foreign, and consider varying degrees of misallocation in Home in the range ση ∈ {0, 0.05, 0.15} and ρ ∈ [0.5, 0.5].27

Figure 2 visualizes the full set of results for fixed wages; without loss of generality, we set the expenditure share of differentiated goods to β = 0.7. Table 1 presents snapshots for both fixed and flexible wages for the cases of no misallocation and misallocation with high distortion dispersion η = 0.15) and different productivity-distortion correlations ∈ {0.4, 0, 0.4}).

Figure 2.
Figure 2.
Figure 2.

Numerical Simulation: Trade Liberalization

Citation: IMF Working Papers 2020, 163; 10.5089/9781513554440.001.A001

Table 1.

Numerical Simulation: Gains from Trade

This table reports numerical and estimation results for the impact of reducing bilateral trade costs, unilateral export costs or unilateral import costs by 20%. Panels A-C show the change in welfare, aggregate productivity, average firm productivity and the covariance of firms’ productivity and employment share in different economic environments. In Panels A and B, there is no resource misallocation, and productivity is Pareto or Log-Normal distributed. In Panel C, there is misallocation, and productivity and distortions are joint Log-Normal with ση=0.15 and ρ(φ,η)={-0.4,0,0.4}. All other parameter values are as discussed in the text. Panel D reports the estimated effect of increasing export demand or import competition by 20% based on the baseline IV results in Table 5.

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Three patterns stand out in Table 1. First, in the absence of misallocation, bilateral and unilateral export liberalization increase welfare and measured aggregate productivity whether wages are flexible or not (Panels A and B). By contrast, unilateral import liberalization increases Wi and Φ˜i when wages are flexible, but reduces both when wages are fixed. This is consistent with Propositions 1 and 2.

Second, resource misallocation can amplify, dampen or reverse the welfare and productivity gains from trade, and this effect is not monotonic in the degree of misallocation, consistent with Proposition 3 (Panel C). With flexible wages, the welfare and productivity gains from trade are either smaller or only marginally higher with misallocation than without, and decrease smoothly with the correlation parameter ρ. The effects of globalization become more nuanced with fixed wages. Bilateral and unilateral export liberalizations now increase welfare strictly less with than without misallocation, but the gains are non-monotonic in ρ: they peak when distortions are close to orthogonal to productivity, but decline significantly and can turn negative away from ρ ≈ 0. At the same time, unilateral import liberalization can reduce welfare more severely with misallocation than without when ρ << 0, but may conversely increase welfare when ρ is sufficiently positive. As for productivity, trade liberalization generates less negative or higher productivity gains at higher levels of ρ. Once again, misallocation can enlarge, moderate or overturn the productivity gains that obtain in the first best.

Finally, the two components of aggregate productivity Φ˜i – average productivity Φ¯i and covariance Φ¨i – move in different directions only under misallocation. With no distortions, changes in Φ¯i account for 75% of the change in Φ˜i on average, while Φ¨i contributes 25%. With frictions, by contrast, it is possible for Φ˜iandΦ¯i to both rise even while Φ¨i falls. Extensive numerical exercises indicate that this result cannot obtain in the absence of misallocation under reasonable parameter assumptions. Overall, the behavior of Φ¯iandΦ¨i signals that reallocations across firms along both the extensive and the intensive margins of activity are important in the adjustment to trade shocks.

To anticipate our empirical results, we use baseline IV estimates to compute the implied productivity effects of a 20% rise in export demand and import competition in Panel D. The empirical findings are qualitatively consistent with the last row of Panel C, i.e. misallocation with fixed wages and ρ = 0.4. The magnitudes are in line with the numerical calculations for exports and higher for imports.

2.6 Discussion

Two model features that allow us to transition to the empirical analysis. First, for expositional simplicity, we have studied an economy with a single differentiated-good sector. Intuitively, our main conclusions would extend to a world with multiple symmetric differentiated-good sectors k, where consumer utility is a Cobb-Douglas aggregate across sector-specific CES consumption indices. The effect of any shock on aggregate productivity Φ˜i now depends on the weighted average response of sector-level productivities Φ˜ik. A uniform trade cost reduction would affect Φ˜ik equally across sectors, while a disproportionately bigger shock to sector k! would change Φ˜ik disproportionately more. This justifies our estimation strategy which exploits variation across countries, sectors and time for identification purposes.

Second, we have considered reductions to trade costs, τij and τji. The effect of exogenous shocks to foreign demand – such as a rise in foreign market size Lj or aggregate expenditure Ej - would be qualitatively the same as the effect of a fall in export costs, τij. Likewise, the effect of exogenous shocks to foreign supply – such as a rise in the measure of foreign firms Mj or a shift in the foreign productivity distribution Gj(φ) - would be similar to the effect of a fall in import costs, τji. This holds because all of these shocks operate through and only through movements in home’s (distorted) productivity cut-offs for production and exporting. This justifies our choice of instruments in the IV analysis.

3 Data

We empirically evaluate the impact of international trade on aggregate productivity using rich crosscountry, cross-sector panel data from two primary sources, CompNet and WIOD. This section describes the key variables of interest and presents stylized facts about productivity and trade activity in the panel.

3.1 CompNet Productivity Data

We exploit unique new data on macroeconomic indicators for 20 NACE 2-digit manufacturing sectors in 14 European countries over the 1998–2011 period from the CompNet Micro-Based Dataset.28 Two features of the data make it unprecedented in detail and ideally suited to our analysis. First, it contains not only aggregate measures at the country-sector-year level, but also multiple moments of the underlying firm distribution in each country-sector-year cell. This includes for example means, standard deviations and skewness of various firm characteristics, as well as moments of the joint distribution of several such characteristics. The dataset is built from raw firm-level data that are independently collected in each country and maintained by national statistical agencies and central banks. These raw data have been standardized and consistently aggregated to the country-sector-year level as part of the Competitiveness Research Network initiative of the European Central Bank and the European System of Central Banks.29

Second, CompNet includes productivity measures that map exactly to the Olley-Pakes (1996) decomposition in Section 2.3 of aggregate productivity in country i, sector k and year t (Φ˜iAggProdikt) into unweighted average firm productivity (Φ¯iAvgProdikt) and the covariance of firm productivity and share of economic activity (Φ¨iCovProdikt). In particular, we examine firms’ labor productivity defined as log real value added per worker i(φ) or Φi(φ,η])), and weight firms by their employment share i(φ)) at the country-sector-year level.30In addition to being model-consistent, labor productivity has the added advantage that it is based on directly observable data, rather than on a TFPR residual from production function that is subject to estimation bias.

In Section 2.3, we defined firm productivity as value added deflated by the consumer price index (CPI) in the differentiated sector PiQ, which is equivalent to the aggregate CPI Pi adjusted for the differentiated sector s expenditure share β, PiQ=Pi1/β. With multiple years and differentiated sectors, this would correspond to Pikt=Pit1/βk, which is not observed. As standard with productivity and GDP data, CompNet deflates firm value added by the Eurostat value-added producer price index by country-sector-year, VAPPIikt. Compared to Pikt, an advantage of VAPPIikt is that it is consistent with measured value added being net of producers’ input purchases that are absent from our model. On the other hand, the CPI aggregates the prices of both local and imported varieties, while the VAPPI aggregates only domestic producers’ prices. In our empirical analysis, we therefore control for country-year fixed effects that absorb Pit and sector-year fixed effects that absorb βk.

Table 2 documents the variation in aggregate productivity across countries, sectors and years in the panel. Additional statistics for the variation across sectors and years within countries appear in Appendix Table 1. The sample contains 2,811 observations and is unbalanced because of different time coverage across countries. Aggregate productivity averages 3.21 in the panel (standard deviation 1.13), with the covariance term contributing 0.23 (7.2%) on average (standard deviation 0.22). There are sizable differences in the level and composition of AggProdikt across economies, with CovProdikt capturing only 1.4% in Austria and 2.5% in Germany but up to 25.9% in Lithuania and 33.3% in Hungary. Moreover, the standard deviations of AggProdikt and CovProdikt across sectors and years within a country reach 0.56 and 0.17 on average, respectively. Thus economy-wide productivity could be significantly lower if labor were randomly re-assigned across firms.

Table 2.

Summary Statistics

This table summarizes the variation in aggregate economic activity, aggregate productivity, international trade activity, and institutional and market frictions across countries, sectors and years in the 1998–2011 panel. All variables are defined in the text. The unit of observation is indicated in the panel heading.

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Table 2 also provides summary statistics for aggregate productivity growth at 1-, 3- and 5-year horizons. Figure 3 shows that reallocations across firms can account for a substantial share of aggregate growth, as was the case for Austria, Italy, Hungary and Lithuania before the 2008–2009 global crisis.

Figure 3.
Figure 3.

Sources of Productivity Growth

Citation: IMF Working Papers 2020, 163; 10.5089/9781513554440.001.A001

3.2 WIOD Trade Data

We use data on international trade activity from the World Input-Output Database (WIOD). While standard trade statistics report gross flows by exporter, importer and traded sector, WIOD exploits country-specific input-output tables which makes it possible to estimate bilateral value-added flows by both traded sector and sector of final use. In particular, we use the gross sales from input sector k in origin country i to output sector s in destination country j in year t, Xijkst, as well as the value added by i that is embedded in these sales, VAXijkst.31 Input sectors are in the NACE 2-digit classification, while output sectors comprise all NACE 2-digit sectors plus several components of final consumption. Trade flows are recorded in US dollars, which we convert to euros using annual exchange rates. Although WIOD relies on proportionality assumptions to allocate input use across countries and sectors, it is the first data of its kind and has been used in path-breaking studies of global value chains (e.g. Bems and Johnson 2017).

Our baseline measure of export demand for exporting country i in sector k and year t, ExpDemandikt, is the log value of i’s gross exports in sector k. We do not distinguish between exports used for final consumption and downstream production since both represent foreign demand from the perspective of i. Our baseline measure of import competition in importing country i, sector k and year t, ImpCompikt, is the log of the value of i’s imports in sector k, less the value of sector k imports used by i in the production of sector k goods. We do not remove sector k imports used in i by producers in other sectors since such imports also compete with locally produced k goods.

ExpDemandikt=ln[Σji,sXijkst],ImpCompikt=ln[Σji,skXjikst].(3.2)

Table 2 presents summary statistics for ExpDemandikt and ImpCompikt in the matched sample with WIOD and CompNet data. ExpDemandikt averages 7.65 in the panel, with a standard deviation of 1.74. The corresponding mean and dispersion for ImpCompikt are 6.41 and 1.97, respectively. We summarize individual countries’trade exposure in Appendix Table 1, and plot its evolution over time in Figure 4. While all countries experienced steady import and export expansion before the 2008–2009 financial crisis, they saw a sharp contraction in 2009 before regaining some ground by 2011 (Figure 4A). Although EU-15 and new EU members display broadly comparable import trends, the latter saw dramatically faster export growth during the sample period (Figures 4B and 4C).

Figure 4.
Figure 4.

Trade Exposure Over Time

Citation: IMF Working Papers 2020, 163; 10.5089/9781513554440.001.A001

4 Trade and Aggregate Productivity: OLS Correlation

We empirically assess the aggregate productivity effects of international trade in three steps. In this section, we first provide OLS evidence that countries’observed export and import activity, ExpDemandikt and ImpCompikt, is systematically correlated with their aggregate productivity. Since observed trade flows capture aggregate supply and demand conditions in general equilibrium, however, ExpDemandikt confounds exogenous foreign demand for the products of country i with i’s endogenous export supply. Analogously, ImpCompikt reflects both the exogenous supply of foreign products to country i and i’s endogenous import demand. In order to identify the causal effects of globalization, in Section 5 we pursue an IV-2SLS estimation strategy to isolate the exogenous components of export demand and import competition. Finally, in Section 6 we perform additional analyses to inform the mechanisms through which export demand and import competition operate.

4.1 OLS Specification

We explore the link between trade and aggregate productivity with the following OLS specification:

Yikt=α+βEXExpDemandikt+βIMImpCompikt+ΓZikt+φit+εikt.(4.1)

Here Yikt refers to aggregate productivity in country i, sector k and year t, AggProdikt, or its OP components, the unweighted average firm productivity, AvgProdikt, and the covariance between firm productivity and employment share, CovProdikt. By the properties of OLS, the coefficient estimates from the regressions for AvgProdikt and CovProdikt will sum to the coefficient estimates from the regression for AggProdikt, but we estimate all three regressions in order to determine the sign, magnitude and significance of each effect. There are no efficiency gains from using a simultaneous system of equations because the regressions feature the same right-hand side variables.

Specification (4.1) includes country-year pair fixed effects, ψit, such that βEX and βIM are identified from the variation across sectors within countries at a given point in time. The ψit account for macroeconomic supply and demand shocks at the country-year level that affect trade and productivity symmetrically in all sectors, such as movements in aggregate income, labor supply, or exchange rates. Implicitly, the fixed effects also capture non-transient country characteristics such as geographic remoteness and global shocks such as the 2008–2009 financial crisis. We cluster standard errors, εikt, by sector-year to accommodate cross-country correlation in sector-specific shocks. The baseline results are robust to alternatively clustering by both sector-year and country-year.

We add several controls Zikt to alleviate concerns with omitted variable bias and sample selection. First, there may be worldwide sector trends in supply and demand conditions. To capture these, we condition on the average log number of firms, lnN¯kt, and the average log employment, lnN¯kt, by sector-year across countries. Second, the firm-level data that underlie CompNet are subject to minimum firm size thresholds. These thresholds vary across countries, and are subsumed by the country-year fixed effects. As extra precaution, we also include the log number of firms by country-sector-year, ln Nikt, but the results are not sensitive to this. Finally, we implement two sample corrections to guard against outliers. We exclude country-sector-year observations that are based on data for fewer than 20 firms. We also drop observations with extreme annual growth rates in the top or bottom percentile of the distribution for any of the key variables (AggProdikt, AvgProdikt, CovProdikt, ExpDemandikt, ImpCompikt, InNikt). While these two corrections filter out 11% of all observations, we nevertheless retain 96–97% of all firms, employment and real value added in the raw panel, and later confirm that the baseline results are strenghtened when we winsorize instead of drop outliers.

4.2 OLS Results

We first assess the correlation between trade and aggregate economic activity using specification (4.1). In Columns 1–3 of Table 3, we find that export expansion is associated with higher log manufacturing output, log value added and log employment. Conversely, more intense import penetration is correlated with lower domestic output and employment, but nevertheless higher value added.

Table 3.

Trade and Aggregate Performance: OLS Correlation

This table examines the relationship between aggregate economic activity, aggregate productivity and trade exposure at the country-sector-year level. The outcome variable is indicated in the column heading and described in the text. All columns include country-year pair fixed effects, and control for the log number of firms by country-sector-year, the average log number of firms across countries by sector-year, and the average log employment across countries by sector-year. Standard errors clustered by sector-year in parentheses. ***, **, * significant at 1%, 5%, 10%.

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Turning to the trade-productivity nexus in Columns 4–6, aggregate exports and imports are both positively correlated with aggregate productivity. These correlations are economically large and highly statistically significant at 1%: A 20% rise in ExpDemandikt and ImpCompikt is associated with 2.5% and 2.1% higher AggProdikt, respectively. While comparable, these magnitudes mask important differences between export and import activity. Export expansion is accompanied by both stronger average firm productivity and increased concentration of activity in more productive firms, with the former channel roughly twice the magnitude of the latter. By contrast, deeper import penetration entails higher firm productivity on average, but a shift in activity towards less productive firms.

The bin scatters in Figure 5 provide a non-parametric illustration of the conditional correlation between aggregate productivity and trade exposure. A point represents average values across country-sector-year triplets within each of 100 percentile bins, after demeaning by country-year fixed effects. The plots indicate that AggProdikt is strongly positively correlated with both ExpDemandikt and ImpCompikt across the distribution.

Figure 5.
Figure 5.

Trade Exposure and Aggregate Productivity

Citation: IMF Working Papers 2020, 163; 10.5089/9781513554440.001.A001

Although not causal, this evidence is consistent with increased foreign demand boosting aggregate productivity and production activity, and with stiffer import competition stimulating productivity growth while depressing overall production. The OLS results also suggest that different aspects of globalization may influence aggregate productivity through different channels.

Equation (4.1) identifies the long-run correlation between productivity and trade activity. We consider the short to medium term in Appendix Table 2, where we study how changes in productivity co-move with concurrent changes in imports and exports over 1-, 3- and 5-year overlapping periods.32 By first-differencing all left- and right-hand side variables and including year fixed effects, we subsume country-sector fixed effects and global growth shocks. The productivity-trade relationship is stronger at medium horizons of 3 to 5 years, but nevertheless sizeable even in the very short run of 1 year.

5 Impact of Trade on Aggregate Productivity: IV Causation

5.1 The Endogeneity Problem

The baseline OLS correlations may not identify the causal effect of globalization on aggregate productivity because of two potential sources of endogeneity. One concern is that trade and productivity performance are jointly determined by some omitted variable. Given the country-year fixed effects in the OLS specification, such omitted variable bias would have to vary systematically across sectors within country-years to explain our findings.

Reverse causality poses an arguably more important concern: Aggregate productivity can drive trade activity. In general equilibrium, export flows reflect both endogenous supply conditions in the exporting country and exogenous demand conditions in the importing country. Trade theory implies that firms in a more productive country-sector would be more competitive on world markets and therefore realize higher exports, biasing OLS estimates of βEX positively. Analogously, import flows reflect both endogenous demand conditions in the importing country and exogenous supply conditions in the exporting country. Given local demand, a less productive country-sector would be less competitive from the perspective of foreign firms and induce more entry by foreign suppliers, biasing OLS estimates of βIM negatively. Other mechanisms may generate reverse causality that biases βEX and βIM either upwards or downwards.

5.2 IV Strategy

In order to identify the causal effects of trade, we adopt a two-stage least squares (2SLS) estimation strategy. In the first stage, we use instrumental variables IVikt to isolate arguably exogenous movements in export demand and import supply, ExpDemand^iktandImpDemand^ikt, from observed exports and imports, ExpDemandikt and ImpCompikt. In the second stage, we regress aggregate productivity on these predicted exogenous trade values in place of their endogenous counterparts:

Yikt=α+βEXExpDemand^ikt+βIMImpComp^ikt+ΓZikt+ψit(+ψkt)+εikt(secondstage)(5.1)
{ExpDemandikt,ImpCompikt}=αIV+ΓIVZikt+ΘIVIVikt+ϕit(+ϕkt)+εikt(firststage)(5.2)

We condition on controls Zikt and country-year fixed effects, ψit and ψit, as in the OLS baseline. In robustness checks, we further add sector fixed effects, ψk and ψk, or sector-year fixed effects, ψkt and ψkt. These account respectively for permanent and time-variant differences in supply and demand conditions across sectors that affect all countries, such as factor intensities, technological growth and consumer preferences. We continue to cluster standard errors, εikt and εikt, by sector-year.

The ideal instruments for trade exposure would be relevant by having predictive power in explaining trade flows, and would meet the exclusion restriction by affecting productivity only through the trade channel. In the case of ExpDemandikt, we would therefore like to isolate exogenous foreign demand for ik products in year t from country i’s endogenous export supply of sector k goods in year t. In the case of ImpCompikt, we would like to separate exogenous foreign supply of k products to i in year t from i’s endogenous import demand for k goods in year t.

We use Bartik instruments, which we construct by combining information on countries’ initial trade structure at the start of the panel with their trade partners’ contemporaneous trade flows with the rest of the world.33 This IV strategy capitalizes on two ideas: First, the share of country i’s exports in sector k going to destination d at time t = 0, Xidk,t=0Xik,t=0, and the share of i’s imports coming from origin o at time t = 0, Moik,t=0Mik,t=0, are not influenced by subsequent exogenous shocks respectively to aggregate demand in d and to aggregate supply in o. Second, aggregate demand for sector k goods in destination d at time t can be proxied with d’s total absorption of k products, defined as domestic production plus imports minus exports, Ydkt + M-i,dkt – X-i,dkt. This corresponds to total expenditure in d on k, or market size in the model. Aggregate supply of sector k goods from origin o at time t can be estimated with o’s export value added for final consumption of k products, XVAi,oktfinal. This accounts for the fact that countries use imported inputs in production, and aims to isolate supply shocks specific to o. We conservatively focus on exports for final consumption to shut down any global input-output linkages and capture pure import competition induced by o. Note that we exclude bilateral trade between country i and destination d (origin o) when constructing foreign demand (supply) shocks pertinent to i.

For each country-sector-year triplet ikt, we instrument export demand with foreign demand conditions, FDemandikt, computed as the weighted average absorption across i’s export destinations using i’s initial export shares as weights. We instrument import competition with foreign supply capacity, FSupplyikt, calculated as the weighted average export value added for final consumption across i’s import origins, using i’s initial import shares as weights. To guard against measurement error or business cycle fluctuations, we take average trade shares over the first three years in the panel, 1998–2000.

In addition to the Bartik instruments, we also exploit the variation in import tariffs across countries, sectors and years, MTariffikt. We take the simple average applied tariff τipt across the NPk products p within sector k at time t, using data from WITS. MTariffikt captures trade policy shocks that affect import competition by influencing foreign producers’ incentives to enter the domestic market.

FDemandikt=ln[ΣdiXidk,t=0Xik,t=0(Ydkt+Mi,dktXi,dkt)],(5.3)
FSupplyikt=ln[ΣoiXoik,t=0Xik,t=0XVAi,oktfinal],(5.4)
MTariffikt=1NPkΣpΩkτipt.(5.5)

Conceptually, we think of FDemandikt as an instrument for ExpDemandikt, and view FSupplyikt and MTariffikt as instruments for ImpCompikt. In practice of course, all three instruments enter the IV first stage for both endogenous variables.

5.3 Baseline IV Results

Table 4 indicates that the three instruments perform well in the first stage. The measure of exogenous foreign demand has a positive effect on observed exports, the measure of exogenous foreign supply has a positive effect on observed import penetration, and import tariffs strongly deter imports. These patterns are highly statistically and economically significant and robust to adding sector or sector-year fixed effects to the baseline country-year fixed effects. The most conservative estimates in Columns 3 and 6 imply that a one-standard-deviation improvement in FDemandikt leads to 34% higher ExpDemandikt, while a one-standard-deviation rise in FSupplyikt increases ImpCompikt by 49%. Reducing import barriers by 10% translates into 13% higher imports. The R-squared in these regressions reaches 89%-99%.

Table 4.

Instrumenting Export Demand and Import Competition: IV First Stage

This table presents the baseline IV first stage. It examines the impact of foreign supply, foreign demand and import tariffs on export and import activity at the country-sector-year level. The outcome variable is indicated in the column heading and described in the text. All columns include country-year pair fixed effects and the full set of controls in Table 3. Columns 2 and 5 (3 and 6) also include sector (sector-year pair) fixed effects. Standard errors clustered by sector-year in parentheses. ***, **, * significant at 1%, 5%, 10%.

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Table 5 presents the second-stage estimates for the causal effects of globalization. Two findings stand out. First, export demand and import competition both significantly increase aggregate productivity, AggProdikt. In the baseline with only country-year fixed effects in Column 1, 20% growth in export demand boosts overall productivity by 8%, while 20% rise in import competition leads to 1.4% higher productivity. In the most restrictive specification that adds sector-year fixed effects in Column 7, these productivity gains amount to 7.3% and 10%, respectively.

Table 5.

Impact of Trade on Aggregate Productivity: IV Second Stage

This table presents the baseline IV second stage. It examines the impact of instrumented export demand and import competition on aggregate productivity at the country-sector-year level. The outcome variable is indicated in the column heading and described in the text. All columns include country-year pair fixed effects and the full set of controls in Table 3. Columns 4–6 (7–9) also include sector (sector-year pair) fixed effects. Standard errors clustered by sector-year in parentheses. ***, **, * significant at 1%, 5%, 10%.

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The asymmetric effects of export demand and import competition on allocative efficiency signal that the “right” firms may be able to access relatively more resources than the “wrong” firms during boom times, compared to bust times. This suggests that the root causes of misallocation matter. In the case of financial market frictions, for example, imperfect information may play out in different ways during peaks and troughs. Financiers may have incomplete knowledge of firm fundamentals, and make financing decisions based on expected future profits (which depend on fundamentals) and on past performance and collateralizable assets (which depend on previous distortions in capital allocation). Since expansions in export demand and import competition have opposite effects on firm profits, the results are consistent with lenders being more willing to extend capital based on the net present value of future profits during boom times, and conversely tying funding more closely to collateral during bust times.

5.4 Sensitivity Analysis

We perform extensive sensitivity analysis in Appendix Table 3 to validate the robustness of the baseline results. We record consistently large and significant effects of international trade on all three productivity outcomes, safe for imprecisely estimated effects of ImpCompikt on CovProdikt in specifications with country-year and sector-year fixed effects.

Alternative specification We first consider each dimension of trade exposure one at a time, to ensure that the estimated effects of export and import activity are not driven by multicolinearity. When we focus on export access, we include only ExpDemandikt in the second stage and use FDemandikt as the single instrument in the first stage. When we examine import penetration, we introduce only ImpCompikt in the second stage and exploit only FSupplyikt and MTariffikt as instruments in the first stage. Panel A shows that this delivers qualitatively similar results and quantitatively bigger magnitudes for each dimension of globalization.

Panel B confirms that the baseline results barely change when we lag ExpDemandikt and ImpCompikt by one year. This speaks to possible delayed effects of international trade on aggregate productivity that can arise through gradual adjustment within and across firms.

Alternative measures and controls The findings are also robust to using a relative instead of an absolute indicator of import competition. The baseline measure ImpCompikt reflects the scale of foreign suppliers’activity in the home market, where the country-year fixed effects implicitly control for home market size. Through the lens of the model, an equally valid measure of import competition is the ratio of imports to domestic production. We therefore construct ImpCompRatioikt=Σj,skXjikst/Output¯ik, averaging the denominator across years within country-industry pairs to mitigate concerns with domestic production endogenously responding to import penetration. Panel C corroborates the main results when we estimate specification (5.1) using ImpCompRatioikt in place of ImpCompikt and an analogously constructed instrument FSupplyRatioikt in place of FSupplyikt.34

Our analysis focuses on the productivity gains from export access and import competition, and abstracts away from the role of imported inputs in reducing firms’production costs. While the theoretical predictions for the first two trade channels would continue to hold should the latter also be active, we want to ensure that the empirical results for export demand and import penetration are not driven by trade-induced changes in input prices. Recall that our productivity and trade measures are based on value-added data and thus already account for the use of inputs, including potentially imported inputs. In Panel D, we nevertheless confirm that the baseline results hold when we additionally control for country-sector-year specific input price indices from OECD-STAN.35

Alternative outlier treatment We conduct additional tests to ensure that outliers are not driving the results. The baseline sample already excludes country-sector-year observations that aggregate fewer than 20 firms or exhibit annual growth in the top or bottom percentile for key variables (i.e. AggProdikt, AvgProdikt, CovProdikt, ExpDemandikt, ImpCompikt, FDemandikt, FSupplyikt).

In Panel E, we show that the main findings survive when we further winsorize these variables at the 1st and 99th percentiles. Of note, winsorizing produces a significant negative effect of ImpCompikt on CovProdikt even when the regression includes both country-year and sector-year fixed effects.

5.5 Additional Results

We next present a series of additional results that both inform economic questions of interest and help alleviate outstanding econometric concerns.

5.5.1 Sector composition

Recall from Section 2.6 that with multiple differentiated sectors, the effect of globalization on economy-wide aggregate productivity is a weighted average of the effects on sector-level productivity. The baseline specification treats sectors symmetrically, such that βEX and βIM quantify the impact of trade on the average sector. Our findings remain unchanged or stronger when we instead weight observations by the initial country-specific employment share of each industry in Panel A of Table 6. This is a model-consistent measure of an industry’s contribution to economy-wide productivity.

Table 6.

Additional Results

This table provides additional evidence on the impact of export demand and import competition on aggregate productivity at the country-sector-year level, based on Columns 1–3 and 7–9 in Table 5. Panel A weights observations at the country-sector level by the initial share of a sector in manufacturing employment. Panel B weights observations at the country-year level by the share of manufacturing in total employment. Panel C distinguishes between import competition from China vs. Rest Of the World. Panels D-E control for skill and mark-up dispersion across firms with the 90th-10th inter-percentile ratio in firm-level wages and price-to-cost margins. Standard errors clustered by sector-year in parentheses. ***, **, * significant at 1%, 5%, 10%.

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In Europe as in other advanced countries, the services sector has grown to capture a majority of aggregate employment and production. Since aggregate productivity and trade data are available only for manufacturing industries, the baseline analysis evaluates the impact of globalization in manufacturing. We can nevertheless account for the variation in the size of the services sector across country-years by weighting observations by the share of manufacturing in total employment by country-year. The weighted regressions in Panel B of Table 6 reveal quantitatively and qualitatively similar patterns as the baseline. These estimates would reflect the impact of globalization on the average sector across both manufacturing and services, under the assumption that productivity in the average manufacturing sector exhibits the same trade elasticity as the average services sector, even if these elasticities vary across individual sectors.

5.5.2 Chinese import competition

A major shock to the global economy in the 21st century has been the dramatic rise of China. China’s exports grew rapidly after it joined the WTO in 2001 and MFA binding quotas on its textiles and apparel were lifted in 2005. This shock has contributed significantly to the deepening of import competition in many developed economies not only because of its scale, but also because it has increased competition specifically from producers in a large country with lower (although growing) wages and productivity.

We compare the impact of import competition from China, ChinalmpCompikt, and import competition from the rest of the world, ROWImpCompikt, on aggregate productivity in Europe. We measure ChinalmpCompikt with country i’s imports of sector k goods from China in year t, net of sector k imports used by i in the production of k products. We calculate ROWImpCompikt as in the baseline, excluding China from the calculation. We correspondingly construct two new instruments for ChinaImpCompikt and ROW ImpCompikt, ChinaSupplyikt and ROW Supplyikt, which replace F Supplyikt in the IV first stage. For example, ChinaSupplyikt captures China’s global export supply in sector k and year t with Chinese total export value added for final consumption, XVAChina,ktfinal, and recognizes that the impact of this supply shock will vary across importing countries i based on China’s initial share in i’s imports of k goods at time t = 0, MChinaik,t=0Mik,t=0.

ChinaImpCompikt=ln[ΣskXChinai,kst],ChinaSupplyikt=ln[MChinaik,t=0Mik,t=0XVAChina,ktfinal](5.6)

We present the results in Panel C of Table 6. The findings for the productivity impact of export demand remain qualitatively and quantitatively similar. Conditioning on both country-year and sector-year fixed effects, Chinese and ROW import competition induce similar adjustments: They both stimulate aggregate productivity by raising average firm productivity while lowering the productivity covariance term. At the same time, the gains triggered by Chinese competition are about a third of the gains caused by competition from other countries of origin. Omitting the sector-year fixed effects leaves the results for ROWImpCompikt unchanged, but ChinaImpCompikt now exerts significant effects only on the covariance term.

5.5.3 Skill and mark-up dispersion

While we have emphasized the role of heterogeneity in firm productivity, in practice firms may also differ in the skill of their labor force. This may arise because firms make endogenous hiring decisions, or because exogenous variation in worker skill or firm-worker match quality is unobserved at the hiring stage. This raises the possibility that measured real value added per worker may confound firm productivity with employee skill, but the two causes for skill dispersion across firms would have different implications for the interpretation of the results: In the latter case it would pose the threat of omitted variable bias, while in the former case it would be merely a manifestation of the underlying productivity heterogeneity.

To be conservative, in Panel D of Table 6 we explicitly control for skill dispersion across firms. In particular, we condition on the 90th-10th interpercentile ratio of average wage across firms within country-sector-years, available from CompNet. The baseline results remain unchanged.

A separate concern is the potential mark-up heterogeneity across firms. The model in Section 2 shuts down variable mark-ups in the differentiated sector by assuming CES consumption and monopolistic competition, in order to focus on misallocation due to distortions to input costs. In a richer framework, endogenous mark-ups would become a separate source of misallocation if firms charge heterogeneous mark-ups and adjust them differentially in response to trade reforms. We would conceptually like to separate the two. In practice, mark-up heterogeneity can also introduce measurement error in real value-added per worker at the firm level, which can, in turn, lead to measurement error in aggregate productivity, average productivity and productivity-size covariance at the sector level.

Panel E of Table 6 provides suggestive evidence that mark-up heterogeneity does not contribute to the estimated effects of globalization on aggregate productivity. These regressions control for the 90th-10th interpercentile ratio of the price-to-cost margin across firms within country-sector-years; this is the best available proxy for mark-up dispersion and comes from CompNet.

6 How Trade Affects Productivity: Mechanisms

Our estimation approach identifies the independent effects of export demand and import competition, which we interpret as the effects of unilateral export and import liberalization through the lens of theory. We now argue that the empirical results are consistent with globalization shaping aggregate productivity by triggering reallocations across heterogeneous firms in the presence of resource misallocation.

We base this conclusion on three pieces of evidence. First, the empirical findings can be rationalized only with numerical simulations for the case of misallocation. Second, the effect of trade on firm selection is not a sufficient statistic for its effect on aggregate productivity, counter to model predictions without distortions. Finally, the impact of trade on aggregate productivity depends on countries’ measured institutional and market efficiency. Although the consequences of misallocation for the gains from trade are in principle ambiguous, finding that institutional frictions do moderate these gains implies that misallocation plays a role. While the first two arguments for misallocation rely on model-dependent inference, the last one constitutes direct, model-independent evidence.

6.1 Pattern of Trade Effects

The sign pattern for the estimated effects of ExpDemandikt on {AggProdikt, AvgProdikt, CovProdikt} is {+, +, +}, while that for ImpCompikt is {+, +,}. This suggests that export access generates aggregate productivity gains through the exit of relatively less productive firms and the reallocation of market share towards more productive firms. By contrast, import competition induces cleansing along the extensive margin and worsens allocative efficiency along the intensive margin, for a net positive effect on aggregate productivity. Our extensive numerical exercises indicate that the model in Section 2 can only generate this pattern when there is resource misallocation across firms (see Table 1 and Figure 2).

Consider first the case of no resource misallocation. Increased export demand lowers the productivity cut-off for exporting, such that the productivity cut-off for domestic production rises due to free entry, and aggregate productivity, AggProdikt, increases. By contrast, higher import competition has theoretically ambiguous effects because it intensifies competition both at home and abroad, with opposite effects on the domestic productivity cut-off. When home wages can adjust down, this cut-off rises and AggProdikt goes up, while the converse occurs when wages are fixed. Importantly, the numerical exercises indicate that AggProdikt, AvgProdikt and CovProdikt always move in the same direction.

Consider next the case of resource misallocation. Now both export and import liberalization can have ambiguous effects on aggregate productivity, because the economy transitions from one distorted steady state to another. Numerical exercises show that export liberalization increases all three productivity terms, {AggProdikt, AvgProdikt, CovProdikt}, over a wide range of the parameter space, regardless of whether wages are fixed or flexible. On the other hand, import liberalization can move these outcomes in different directions in different segments of the parameter space. In particular, with fixed wages, it is possible that AggProdikt and AvgProdikt both rise while CovProdikt declines.

Based on our benchmark IV estimates, the direction and magnitude of the productivity effects of a 20% increase in ExpDemandikt and ImpCompikt are thus in line with the numerical simulation for the case of misallocation under fixed wages, intermediate distortion dispersion, and positive productivity-dispersion correlation (see Panel D and the last line of Panel C in Table 1).

6.2 Firm Selection

We next evaluate the impact of trade exposure on firm selection at the bottom end of the productivity distribution. In the absence of misallocation, globalization can affect aggregate productivity AggProdikt by (i) raising the first-best productivity cut-off φii* and by (ii) reallocating resources across inframarginal firms. Moreover, the change in φii* is a sufficient statistic for the change in AvgProdikt and AggProdikt, but generally not for the change in CovProdikt without additional functional form assumptions. The empirical counterpart to φii* is the minimum productivity across firms in a given country-sector-year, min Prodikt. Therefore, controlling for minProduct in regression (5.1), any residual impact of international trade on {AggProdikt, AvgProdikt} would be inconsistent with efficient allocation.

In the presence of misallocation, globalization still affects aggregate productivity via (i) and (ii), but also by (iii) changing the degree of misallocation by shifting resources across firms along the extensive and intensive margins. The observed minimum productivity would now be the empirical counterpart to the distorted productivity threshold φ¯ii*, which is no longer a sufficient statistic for AvqProdikt or AggProdikt. Controlling for minProdikt, any residual impact of trade on {AggProdikt, AvgProdikt} would now be consistent with mechanism (iii) and the presence of misallocation.

We find in Panel A of Table 7 that export demand and import competition both raise min Prodikt (Columns 1 and 5). We measure min Prodikt with the first percentile of log value added per worker across firms, in order to guard against outliers due to measurement error or idiosyncratic firm shocks. The estimates imply that the productivity threshold rises by 4%-6.3% and 1.5%-5% following a 20% expansion in foreign market access and import penetration, respectively.

Table 7.

Mechanisms: Selection and Innovation

This table examines the contribution of firm selection to the effects of export demand and import competition on aggregate productivity at the country-sector-year level. The outcome variable is indicated in the column heading and described in the text. All columns include country-year pair fixed effects and the full set of controls in Table 3. Columns 5–8 also include sector-year pair fixed effects. Standard errors clustered by sector-year in parentheses. ***, **, * significant at 1%, 5%, 10%.

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We then expand IV specification (5.1) to include min Prodikt in the second stage.36 Higher min Prodikt is associated with higher aggregate and average productivity, but lower productivity-size covariance. However, controlling for min Prodikt leaves large residual effects of export demand and import competition on AggProdikt, as much as 69% and 38% of the baseline estimates (Column 2). These numbers stand at 52% and 46% when we further condition on sector-year fixed (Column 6). The point estimates for βEX and βIM are also reduced by only 48% and 57% in the regression for AvgProdikt (Column 3). In the specification for CovProdikt, β EX increases by 20%, while βIM falls by 38% (Column 4).

Through the lens of the model, these results suggest that the observed productivity effects of globalization cannot be fully attributed to the reallocation of activity across firms in a frictionless economy via channels (i) and (ii). Instead, the patterns are consistent with the presence of distortions, whereby international trade influences aggregate productivity in part by changing the efficiency with which resources are allocated across firms.37

6.3 Imperfect Institutions and Market Frictions

In order to provide model-free evidence for the role of misallocation, we finally exploit the cross-country variation in the strength of institutions that govern the efficiency of factor and product markets. This approach rests on two premises. First, institutional imperfections constitute structural problems that generate an inefficient allocation of production inputs and market shares across firms. Institutional indicators thus identify primitives that microfound resource misallocation in theoretical frameworks. Of note, the model in Section 2 considers distortions to input costs that map to measures of labor and capital market frictions, but its predictions would be qualitatively similar with revenue or profit distortions via sales or corporate taxes that map to measures of product market regulation.

Our second premise is that countries at different levels of institutional efficiency will respond differently to trade shocks if and only if misallocation is present and influences the trade-productivity nexus. Recall from Section 2 that trade expansion has theoretically ambiguous effects on aggregate productivity under misallocation, and these effects need not vary smoothly with the degree of misallocation. Showing that institutional frictions moderate the impact of trade is thus sufficient to establish a role for misallocation, while estimating the direction and magnitude of this moderating force is of independent policy relevance.

We therefore expand IV specification (5.1) to include interactions of export demand and import competition with country measures of institutional quality, Institutionit, whose level effect is subsumed by the country-year fixed effects. We instrument the main and interaction trade terms using the same instruments as before and their interactions with Institutionit.

We exploit five indicators, defined such that higher values signify more efficient and effective institutions. The first two are rule of law and corruption, from the World Bank Governance Indicators (Kaufmann et al. 2010). These are comprehensive indices respectively of general institutional capacity and scope for rent extraction for private gains, which arguably affect economic efficiency in both input and output markets. Rule of law has a mean of 1.11 and a standard deviation of 0.49 in the panel; the corresponding statistics for (inverse) corruption are 1.07 and 0.69.

The other three measures characterize institutional efficiency in specific markets. We quantify labor market flexibility with a 0–6 index that averages 21 indicators for firing and hiring costs, from the OECD Employment Database (mean 3.28, standard deviation 0.37). We proxy financial market development with a 0–12 index that captures the strength of creditor rights’protection necessary to support financial contracts, from the World Bank Doing Business Report (mean 5.86, standard deviation 1.79). Finally, we assess the (inverse) tightness of product market regulation with a 0–3 index that aggregates 18 measures for state control, barriers to entrepreneurship, and barriers to trade and investment, from the OECD Market Regulation Database (mean 1.17, standard deviation 0.25).

Table 8 reveals consistent patterns across all five institutional measures: Strong rule of law, low corruption, efficient factor and product markets amplify the productivity gains from import competition and dampen the productivity gains from export expansion. This is true for aggregate productivity, average firm productivity and allocative efficiency. The interaction terms are highly statistically and economically significant for all but 2 out of 30 coefficient estimates.38

Appendix Table 2.

Trade and Aggregate Productivity: OLS First Differences

This table examines the relationship between aggregate productivity and trade exposure at the country-sector-year level. The outcome variable is indicated in the column heading and described in the text. All left- and right-hand side variables are first differences over rolling 1-year, 3-year or 5-year overlapping periods. All columns include year fixed effects and the full set of controls in Table 3. Standard errors clustered by sector-year in parentheses. ***, **, * significant at 1%, 5%, 10%.

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These results indicate the complex interactions between international trade and market frictions in shaping aggregate productivity. They also point to an asymmetry between positive and negative shocks to domestic firms. The evidence suggests that growth opportunities, such as greater export demand, can partly correct accumulated misallocation and boost productivity more when markets and institutions are less efficient. This may occur if the “right” productive firms that start out with sub-optimal resources can more effectively scale up production than the “wrong” less productive firms. By contrast, contractionary shocks, such as stiffer import competition, can engender more cleansing reallocation under more efficient markets and institutions, such that less productive firms downsize disproportionately more.39 There may also be less scope for distortionary policy interventions such as heterogeneous subsidies across firms in response to import-induced contraction than in response to export-induced expansion.

6.4 Misallocation Measures in the Literature

We conclude by examining the impact of international trade on several measures of resource misallocation that have been proposed in the literature. While micro-founded, these measures are valid under modeling assumptions that are likely to fail in realistic economic environments. Under certain assumptions, Hsieh-Klenow (2009) and Gopinath et al. (2017) show that the observed dispersion across firms in revenue-based total factor productivity (TFPR), marginal revenue product of capital (MRPK), and marginal revenue product of labor (MRPL) monotonically increases with misallocation in input and output markets. Under certain assumptions, Edmond et al. (2015) likewise find that the observed dispersion across firms in price-cost mark-ups (PCM) signals output-market distortions.

There are several difficulties in interpreting these indicators in terms of allocative efficiency. First, measurement error in firm TFPR, MRPK, MRPL and PCM can inflate their observed dispersion. Second, TFPR, MRPK and MRPL are inferred from production function estimates, such that treating them as regression outcomes can complicate econometric inference. Third, the nature of production technology and market competition can affect these dispersion metrics even in the absence of resource misallocation. Foster et al. (2008) show that TFPR, MRPK and MRPL dispersion implies misallocation of production inputs under constant mark-ups, but not under variable mark-ups. Dhingra-Morrow (2014) further demonstrate that market-share misallocation arises in product markets with variable mark-ups even when there are no distortions in factor markets. Bartelsman et al. (2013) and Foster et al. (2015, 2016 establish that TFPR, MRPK and MRPL dispersion signals resource misallocation under constant returns to scale and no shocks to firm demand or productivity. However, this is no longer the case if firms face increasing returns to scale or adjustment costs.

Given prior empirical evidence of variable mark-ups, increasing returns to scale, and adjustment costs, it can thus be difficult to interpret the four dispersion measures. We nevertheless explore the effect of international trade on these dispersion outcomes in our data in Appendix Table 5. For each country, sector and year, CompNet reports the standard deviations of TFPR, MRPK and MRPL, as well as the 90th-10th interpercentile range for PCM. We generally find positive significant effects of import competition across the four Dispersionikt metrics, but mixed results for export demand (see also DeLoecker and Warczinsky 2012 on PCM). Were Dispersionikt and CovProdikt indicative of misallocation, our conclusion that export access (import penetration) enhances (reduces) allocative efficiency would have been consistent with Dispersionikt falling (rising) with ExpDemandikt (ImpCompikt).

7 Conclusion

We examine the impact of international trade on aggregate productivity. Theoretically, we show that bilateral and unilateral export liberalizations increase aggregate productivity, while unilateral import liberalization can either raise or reduce it. However, all three trade reforms have ambiguous effects in the presence of resource misallocation. Using unique new data on 14 European countries and 20 manufacturing industries during 1998–2011, we empirically establish that exogenous shocks to export demand and import competition generate large aggregate productivity gains. Although both trade activities increase average firm productivity, however, export expansion reallocates activity towards more productive firms, while import penetration acts in reverse. Unpacking the mechanisms of transmission, we show that improved firm selection can account for only half of the productivity gains from trade, suggesting a potential role for resource misallocation. Indeed, efficient institutions, factor and product markets amplify the productivity gains from import competition, but dampen those from export expansion.

Our findings have important implications for policy design in developing countries that aspire to promote growth through greater economic integration but suffer from weak institutions and frictions in capital, labor and product markets. The analysis suggests that reallocation across firms is a key margin of adjustment, while alleviating market distortions can be important for realizing the full welfare gains from globalization. Our results also indicate that developed economies stand to gain from import and export liberalization, despite concerns about the impact of import competition from low-wage countries.

There remains much scope for further research. Richer data would make it possible to examine how international trade affects the incentives for technological upgrading across the firm productivity distribution. It would also be valuable to assess the impact of specific frictions in capital, labor and product markets on firm selection, firm innovation, and reallocations across firms. These constitute some steps towards understanding how to design trade policy and coordinate it with structural reforms that remove institutional and market imperfections in order to improve welfare.

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