Within-Industry Specializationand Global Market Power

Ahmad Lashkaripour

Indiana University

March 28, 2019

Abstract

Export price levels exhibit tremendous cross-national and spatial varia-

tion, even within narrowly-defined industries. Standard theories attribute

this variation to within-industry quality specialization. This paper argues

that a significant portion of the export price variation is driven by rich and

remote economies specializing in high-market power, high-returns-to-scale

segments of industries. I also argue that this particular pattern of specializa-

tion (i) accounts for 30% of the overall gains from trade, and (ii) explains

more than 37% of the observed cross-national income inequality.

1 Introduction

For some time now, there has been a consensus among trade economists thatinternational specialization occurs predominantly within rather than across in-dustries (Schott (2004)). Accordingly, there has been a surge in new theoriesof within-industry specialization, many of which are motivated by two obser-vations. First, there is tremendous variation in export price levels even withinnarrowly-defined industries. Second, these variations are systematic:1

1. Export price levels increase with the exporter’s income per capita; and

2. Export price levels increase with geo-distance to global markets.

The dominant thesis in explaining the above facts is that high-income and geo-graphically distant economies specialize in high-quality varieties within indus-

1See Schott (2004), Hummels and Skiba (2004), and Hummels and Klenow (2005).

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tries. Quality specialization, in these instances, is fueled by either factor-drivencomparative cost advantage (Schott (2004)), geography-driven comparative costadvantage (Hummels and Skiba (2004)), or the home-market effect (Fajgelbaumet al. (2011)).2 The quality specialization thesis has proven to be quite influential,motivating a vibrant strand of macro-economic growth theories (Grossman andHelpman (1991)), as well as enhancing our understanding of trade-inducedinequality (see Verhoogen (2008) and Fajgelbaum et al. (2011)).

This paper, however, argues that this dominant thesis goes too far in attributingFacts (i) and (ii) to exclusively quality specialization. As a matter of arithmetic,price depends on (a) the marginal cost that varies with output quality, and (b)the markup that varies with the degree of market power. An accumulating bodyof evidence indicate that the markup component is non-trivial.3 Even morerevealing, I present new evidence that aggregate measures of export markupcovary with income per capita and geo-distance in a fashion that exactly mirrorthe variation in export price levels.

Motivated by such evidence, I propose an alternative view of within-industryspecialization that emphasizes the market power channel. That is, industriesare comprised of multiple segments with differential degrees of market power.4

Firms in each country sort into high- and low-market power segments of in-dustries, taking into account aggregate cost measures such as the wage rateor distance to global markets. Collectively, these firm-level decisions lead tointernational specialization across low- and high-market power segments ofindustries. This pattern of specialization, in turn, provides an alternative expla-nation for Facts (i) and (ii). More importantly, it delivers a set of macro-levelimplications that are starkly different from the quality specialization thesis.

I establish my theory using a general framework that nests an extensive classof trade models featuring firm heterogeneity, quality-sorting, and variablemarkups, as a special case. Extending the result in Arkolakis et al. (2018), Ishow that in this general framework, variable markups alone cannot explain the

2See also, among others, Sutton (2007); Hallak (2006); Choi et al. (2009); Khandelwal (2010);Baldwin and Harrigan (2011); Crozet et al. (2012); Johnson (2012); Lugovskyy and Skiba (2014);Feenstra and Romalis (2014); Sutton and Trefler (2014); and Dingel (2016), who emphasize thequality specialization channel.

3For instance, according to Berry et al. (1995), more than 30% of the price variation in theauto industry is due to markup differences.

4The view that industries consist of segments with differential degrees of market power, hasdeep roots in the literature. See, for example, the case of specialty versus popular-market beer inHausman et al. (1994) or luxury versus economy cars in Berry et al. (1995) and Goldberg (1995).

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cross-national heterogeneity in export price levels to a given market. However,under a set of testable assumptions, such heterogeneity can arise from withinindustry specialization across low- and high-markup segments of industries.

The intuition behind my theory is the following. Goods manufactured withhigh-wage labor or transported over long distance exhibit a cost disadvantage.To circumvent such a disadvantage, high-wage and remote economies specializein industry segments where aggregate demand is relatively less sensitive to costand relatively more sensitive to output quality. I label such segments of anindustry as “quality-intensive.” From the perspective of a standard trade model,“quality-intensive” segments are those that are subject to a lower trade elasticity.

My testable claim is that quality-intensive segments are also those where in-dividual firms enjoy more market power. Hence, international specializationacross low- and high-quality intensive segments can be always interpreted asspecialization across low- and high-markup segments. Under this interpretation,international specialization creates a positive link between an economy’s wagerate or distance to global markets and its average export markup levels. Thispositive link, in turn, provides an alternative markup-based explanation forFacts (i) and (ii) presented earlier.

Employing rich micro-level trade data, I present support for the main assump-tion underlying my theory. That is, I estimate that the degree of firm-level marketpower is significantly greater in high quality-intensive segments of industries.Furthermore, I find that the composition of country-level exports aligns with theprediction that high-wage and distant economies export relatively more in highmarket power segments of each industry.

Beyond this evidence, the present theory fits well with the observation thatmarkup levels have diverged between rich and poor economies in the pastfew decades (De Loecker and Eeckhout (2018); Diez et al. (2018)). Relatedly, itcan explain why local prices and markups have risen in Europe (De Loeckeret al. (2014)), but have fallen in China following trade liberalization (Brandtet al. (2017)). From the standpoint of standard variable markup theories, theasymmetric effects of import competition on high- versus low-wage economiesare difficult to explain. The present theory, however, predicts that import com-petition will induce European firms to sort into high market power segmentsof industries, and Chinese firms to sort into the low market power segments.These asymmetric effects will raise the average market power and markup ofEuropean firms, while reducing them for firms in China.

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At the macro-level, my view of within-industry specialization produces distinctimplications relative to the quality specialization thesis. The reason being thatspecialization, here, occurs across industry segments that differ in their (1)degree of market power, (2) degree of returns to scale, and (3) trade elasticity.Considering that the latter two characteristics regulate aggregate productivityand the gains from trade, within-industry specialization along these marginscan profoundly influence macroeconomic outcomes.

To quantify macro-level implications, I estimate my model using industry-leveltrade and production data from the World Input-Output Database, covering 35industries and 32 major economies. Using the estimated model, I find that thegains from trade are (on average) 20% in terms of real GDP. Of the total gains,6% is driven by within-industry specialization across low- and high-marketpower segments, while the remaining 14% is driven by traditional forces in theArkolakis et al. (2012) framework.

There is, however, tremendous cross-national heterogeneity in the gains fromwithin-industry specialization. Advanced or remote economies like Australia,France, and Germany gain significantly more as they specialize in high mar-ket power segments where the degree of scale economies and returns to spe-cialization are higher. In comparison, the pure gains from specialization aremuch smaller (and even negative) for developing economies like Mexico andIndonesia, as they specialize in low-returns-to-scale segments where returns tospecialization are relatively low.

At a broader level, the present model sheds new light on cross-country incomedifferences that are believed to be puzzlingly large, and have attracted consid-erable attention in the literature.5 From the perspective of the present theory,high-TFP economies tend to specialize in high market power segments where re-turns to scale and specialization are higher. This pattern of specialization, in turn,multiplies the fundamental TFP differences between rich and poor economies.Based on my estimated model, within-industry specialization across high- andlow-returns-to-scale segments can explain up to 37.3% of the cross-national realincome inequality.

Aside for the vast literature on quality specialization, this paper is closely relatedto a growing literature on variable markups and pricing-to market in interna-

5See, for example, Klenow and Rodriguez-Clare (1997); Prescott (1998); Hall and Jones (1999);Parente and Prescott (1999); Acemoglu et al. (2000); Parente and Prescott (2000); Caselli (2005);Jones (2011).

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tional settings. Generally speaking, this literature is either focused on (i) thepro-competitive effects of trade (Melitz and Ottaviano (2008); Spearot (2013);Holmes et al. (2014); De Blas and Russ (2015); Edmond et al. (2015); De Loeckeret al. (2016)), or (ii) export price discrimination across markets (e.g., Hummelsand Lugovskyy (2009); Alessandria and Kaboski (2011); Simonovska (2015);Bertoletti and Etro (2017)). In comparison, this paper concerns (i) the hetero-geneity in export price levels within markets, as well as (ii) the asymmetriceffects of trade liberalization on markups in low versus high-income economies.

My theory also shares common elements with Fieler (2011).6 In both models,rich economies specialize in low trade elasticity product categories. The presenttheory, however, exhibits two key differences. First, it identifies a new source ofheterogeneity in the trade elasticities, whereby differences in the segment-leveltrade elasticities are driven by difference in the degree of quality-intensity. Sec-ond, my theory establishes a systematic link between patterns of specialization,degree of global market power, and export price levels, which are absent in Fieler(2011). That being the case, my model delivers strictly different macro-levelpredictions relative to the perfectly competitive model in Fieler (2011).

Finally, the present paper is related to a growing literature concerning aggrega-tion bias in the estimated gains from trade (e.g., Costinot and Rodríguez-Clare(2014); Levchenko and Zhang (2014); Ossa (2015); Brooks and Pujolas (2016)). Mypaper contributes to this literature by identifying a systematic source of aggrega-tion bias that is triggered by specialization across low- and high-returns-to-scalesegments of industries.

2 Suggestive Evidence

As noted in the Introduction, many theories of within-industry specializationare motivated by the fact that export price levels increase systematically withthe exporting economy’s (i) income per capita and (ii) geo-distance to globalmarkets. Moreover, the thesis underlying these theories is that these two factsare driven by quality specialization within industries—see Schott (2004) andHummels and Skiba (2004), among others.

6Relatedly, see Kraay and Ventura (2007); Coibion et al. (2007); McCalman and Spearot (2013);Holmes and Stevens (2014) for other papers that emphasize specialization across more- andless-differentiated goods.

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In this section, I present suggestive evidence that Facts (i) and (ii) can bepartially attributed to cross-national differences in export markup levels. Thatis, they arise due to high-income and remote exporters either charging highermarkups for the same good or specializing in the production of high-markupvarieties within industries

As a useful benchmark, I first present the evidence corresponding to Facts(i) and (ii). I then proceed to presenting additional evidence that highlightthe importance of the previously-overlooked markup channel. My analysishere employs two different datasets. To analyze export price levels, I use thethe COMTRADE-BACI database. To study aggregate markup levels, I use thethe CEPII TRADEPROD database (De Sousa et al. (2012)). TO make the twodatasets compatible, I restrict my analysis to 149 economies and 27 three-digitISIC industries that are represented in both datasets. Even after making thetwo datasets compatible, the COMTRADE-BACI database remains considerablymore granular as it reports bilateral trade statistics at the 6-digit HarmonizedSystem (HS) level of aggregation. By comparison, the TRADEPROD databaseonly reports production statistics at the 3-digit ISIC level of aggregation—a morecomprehensive description of both datasets in provided in Appendix A.7

The effect of income per capita and geographical remoteness on export pricelevels can be estimated using the following equation,

ln pjkt = β1 ln Distj + β2 ln GDPcapjt + β3 ln GDPjt + δkt + ε jkt, (1)

where pjkt denotes the (quantity-weighted) unit price of country j’s exports inindustry k in year t. On the right-hand side, Distj is country j’s population-weighted distance to global markets; GDPcapjt and GDPjt control for country j’sGDP per capita and market size in year t; and, finally, δkt controls for industry-year fixed effects.

Since the BACI data reports trade statistics at HS6 level of aggregation, I conductthe above estimation independently with both HS6-year and ISIC-year fixedeffects. Estimation results are reported in Table 1, re-establishing the widely-held belief that export price levels increase systematically with the exportingeconomies GDP per capita and remoteness.

7The TRADEPROD database has a more comprehensive longitudinal coverage. It spans 26years from 1980 to 2006. The COMTRADE-BACI database, by comparison, covers the years 2003to 2015.

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Noting that export price levels, P = mC(ϕ), are composed of a markup compo-nent, m, and a marginal cost components, C(ϕ), there are two ways to interpretthe cross-national export price variation. The standard “quality specialization”thesis attributes the variation to cross-national quality differences. That is,the patterns documented in Table 1 are attributed to high-income and remoteeconomies specializing in high-ϕ (high-quality) varieties within industries.8

Below, I present evidence in favor of the alternative view that the observed exportprice variation is partly driven by markup differences. To present my claim, Ifirst calculate aggregate markup levels by closely following the methodology inDe Loecker and Eeckhout (2018). That is, I assume a conventional productionfunction for country j in industry k in year t. Namely, Qjkt = TjktV

αktjkt Kβkt

jkt , whereQjkt denotes the units of output produced, Vjkt denotes the variable input (e.g.,labor, intermediate inputs, etc.), Kjkt denotes capital, and Tjkt denotes Total FactorProductivity. As in De Loecker and Eeckhout (2018), this production structureimplicitly assumes that countries vary in their TFP and the chosen inputs, butnot in the technology Q.

The Lagrangian of the cost minimization problem is thus given by PVjktVjkt +

PKjktKjkt − νjkt

(TjktV

αktjkt Kβkt

jkt − Qjkt

), where PV

jkt and PKjkt denote input prices, νjkt

is the Lagrangian multiplier, and Qjkt is a constant. The first order condition ofthis problem with respect to Vjkt implies that νjkt = PV

jktVjkt/αktQjkt. Given thatthe shadow price of the Lagrangian is, by construction, equal to the marginalcost, the markup mji,k = Pjkt/νjkt can, therefore, be expressed as

mjkt = αktPjktQjkt

PVjktVjkt

.

Given the above expression, I can calculate mjkt up to an industry×year-specificoutput elasticity, using data on total output, PjktQjkt, and variable input cost,PV

jktVjkt, from the CEPII TRADEPROD database. Doing so, I can run the followingregression that is analogous to 1, but includes m as the dependent variable:

ln mjkt = β1 ln Distj + β2 ln GDPcapjt + β3 ln GDPjt + δkt + ε jkt, (2)

As before δkt, in the above equation, controls for industry-year fixed effects and

8To be more specific, existing theories attribute the effect of GDP per capita to factor-driven ordemand-driven quality specialization, and attribute the effect of remoteness to the “WashingtonApples” effect or quality-sorting.

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absorbs all the variation in the output elasticity, αkt.9

The last column in Table 1 reports the estimation results corresponding to themarkup regression. Evidently, the output sold by high-income and remoteeconomies exhibits a systematically higher markup level. Moreover, the elas-ticity at which markups increase with GDP per capita and remoteness closelyresembles the corresponding elasticity for export prices. The higher number ofobservations in the first two columns is simply reflective of the COMTRADE-BACI

data reporting export price levels a much finer level of aggregation.

Table 1: Cross-National Variation in Export Price and Markup Levels

Dependent (log)

Unit Price Markup

Remoteness (log) 0.145∗∗∗ 0.242∗∗∗ 0.290∗∗∗

(0.002) (0.029) (0.016)

GDP p/c (log) 0.141∗∗∗ 0.162∗∗∗ 0.026∗∗∗

(0.002) (0.014) (0.003)

GDP (log) −0.058∗∗∗ −0.062∗∗∗ 0.001(0.001) (0.008) (0.003)

Observations 4,345,390 50,851Fixed Effects HS6×year ISIC×year ISIC×yearR-squared 0.64 0.37 0.53

Note: The estimating equation are 1 and 2. In the markup regression, each observations isweighted by the number of represneted firms, which is proportional to the number of workersbased on the forthcoming model. Robust standard errors are reported in parentheses. *** denotessignificance at the 1% level.

While revealing, the evidence presented in Table 1 is subject to an importantcaveat. I use country-level production data to identify the aggregate markuplevel in each economy. So, if firm-level markup distribution is highly dispersedwithin each economy, the results presented in Table 1 may be be subject toaggregation bias; the extent of which depends on how the firm-level markupdispersion covaries with GDP per capita and remoteness.10

9It should be re-emphasized that the assumption that αkt is industry×year-specific has prece-dent in the literature. De Loecker and Eeckhout (2018) and Diez et al. (2018), for instance, adopta similar assumption when analyzing global market power using firm-level data.

10Importantly, running Regression 2 using the markups estimated by De Loecker and Eeckhout(2018) with firm-level data for a sample of 40 countries, produces qualitatively similar results.

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3 A Model of Within-Industry Specialization

Consider a world economy consisting of i = 1, ...,N countries. Country i ispopulated by Li individuals, each endowed with one unit of labor, which isthe sole factor of production. All individuals are perfectly mobile across theproduction of different goods but are immobile across countries; and are paid awage, wi, in country i. There are K industries indexed by k, each comprised ofmultiple segments that differ in characteristics such as degree of market powerand quality intensity. Segments are indexed by z, with Zk denoting the set ofall segments pertaining to industry k—for example, k can be the auto industrywhich is composed of luxury, economy, and cross-over vehicle segments.

Consumers. All individuals have similar preferences that are characterized by ageneral utility function, U (U1, ...,UK), where Uk is the sub-utility correspondingto industry k. The industry-level sub-utility is a function of the compositeconsumption bundle, which combines goods from various segments in thatindustry. In particular,

Uk = Uk (C1, ..., CZ ) ; 1, ..,Z ∈ Zk

where the segment-level sub-utility, Cz, is a function of the quantity q ≡ [qω]ω∈Ωz

and quality ϕ≡ [ϕω]ω∈Ωzof firm-level varieties (indexed by ω) available to the

consumer in segment z. Contrary to the dominant approach in the literature, Iimpose only weak isomorphism between quality and quantity, which is outlinedby the following assumption.

A1. Quality and quantity are only weakly isomorphic. In particular, Cz is a function ofthe quantity and quality of the goods in one’s consumption basket:

Cz

(ϕρz q1−ρz

).

Correspondingly, ρz ∈ [0, 1] denotes the relative importance of product quality insegment z, which I hereafter refer to as the degree of quality intensity.11

Note that A1 imposes weaker conditions on preferences than conventional theo-ries, which typically assume exact isomorphism between quality and quantity

11In the CES case, A1 can be states as Cz(ϕρz q1−ρz

)=[∫

ω∈Ωz

(ϕ

ρzω q1−ρz

ω

)ηzdω]1/ηz(1−ρz)

.

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(see Melitz and Redding (2014)).12 To elaborate, exact isomorphism correspondsto a special case of A1 where ρz is uniform across all segments. In such a case,there is no real distinction between quality and quantity, and productivity differ-ences across producers can be interpreted as quality differences and vice versa.13

There is, however, exhaustive evidence from consumer surveys that individ-uals care relatively more about quality (and relatively less about price) whenpurchasing certain product categories (see Fornell et al. (1996)). By relaxingthe uniformity restriction on ρz, Assumption A1 accommodates this featureof the data. Accordingly, I will hereafter refer to high-ρ segments as “highquality-intensive” segments of the industry.

According to A1 consumers maximize their utility along both the quality andquantity dimensions. To streamline the presentation, however, I can convertthe consumer problem into a one-dimensional one that is expressed in terms ofeffective (or quality-adjusted) quantities and prices. To this end, I use the tilde nota-tion to denote effective values, with q =

(ϕ1−ρz qρz

)1/ρz and p ≡(

pρz /ϕ1−ρz)1/ρz

respectively denoting effective quantity and price. Considering this choice of no-tation, I assume that Ui (.) and Ui,k (.) are additively separable and Cz (.) exhibitsa parameterization that delivers the following class of demand functions.

A2. [Generalized Gorman-Pollak Demand] For a consumer with income y, facinga schedule of effective prices p ≡ [ pω]ω∈Ω, the Marshallian demand for variety ω ∈ Ωassumes the following formulation

qω = Dz (Fz (Λz) pω/y) Qz(Λz)

where Dz (.) is a strictly decreasing function; Fz (.) and Qz (.) are differentiable func-tions; and Λz ≡ Λz (p, y) is a scalar demand shifter that firms take as given and whichimplicitly solves by the budget constraint.14

The above demand system nests (i) the directly separable preferences in Arko-lakis et al. (2018) as a case where Qz(Λz) is constant and Fz (Λz) = Λz; (ii) theindirectly additive preferences in Bertoletti et al. (2018) as a case where Fz(Λz) is

12Hallak and Sivadasan (2013) and Sutton (2007) have challenged the exact quality-quantityisomorphism from a theoretical perspective, while Bils and Klenow (2001), Baldwin and Ito(2008), Fan et al. (2015), and Flach (2017) have challenged it based on empirical evidence.

13As we will see shortly, the multi-industry Melitz-Pareto model in Chaney (2008) correspondsto a special case of the present model where ρz is uniform and equal to 1/2 in all industries.

14Specifically, Λz is an implicit solution to∫

ω∈ΩzpωDz (Fz (Λz) pω/y) Qz(Λz)dω = ezαky,

where αk and ez respectively denote the share of expenditure on industry k and segment z ∈ Zk.

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constant and Qz (Λz) = Λz; and (iii) the homothetic single aggregator in Mat-suyama and Ushchev (2017), as a case where Fz(Λz) = Qz (Λz) = Λz. Anotherwell-know special case of A2 is the CES demand system, which arises whenFz(Λz) is constant, Qz (Λz) = Λz, and Dz (x) = x−εz .15

It is important to note that the theoretical propositions that follow apply toseveral demand systems that are not readily nested by A2. For instance, thetheory presented here applies equally to (iv) the quadratic but non-separabledemand system (Ottaviano et al. (2002); Melitz and Ottaviano (2008)); (v) theQMOR expenditure function; as well as (vi) Kimball preferences (e.g., Kimball(1995); Klenow and Willis (2016)).

To simplify the notation, and given that the schedule of prices, p, and income,y, vary across markets, I henceforth use Λi,z ≡ Λz (pi, yi); Qi,z ≡ Qz(Λi,z) andFi,z ≡ Fz (Λi,z) to denote demand shifters associated with country i’s market insegments z.

Firms. Every industry k is populated with Nj,k firms from country j, whichcompete under monopolistic competition. There is free entry, whereby a largepool of ex-ante identical firms in country j can pay an entry cost, wj f e

k , to enterthe industry. The free entry assumption introduces scale effects that magnifythe extent of international specialization, but is not consequential to the mainpredictions of the model.

Firms operating in segment z of industry k are heterogeneous in their outputquality, ϕ, which is the realization of a random variable drawn independentlyacross firms from a distribution Gj,z. As a key assumption, I impose that Gj,z isPareto with the same shape parameter γk > 0 in all countries and in all segmentspertaining to industry k.

A3. For all ϕ and all z ∈ Zk, Gj,z(ϕ) = 1−Aj,z ϕ−γk , with γk > 0 .16

The Pareto parametrization specified by A3 is by far the most common distri-butional assumption in heterogeneous firm models (e.g., Chaney (2008); Melitzand Ottaviano (2008); Simonovska (2015); Arkolakis et al. (2018)). As we will seeshortly, the main advantage of Assumption A3 is delivering the gravity equationfor aggregate trade flows. The more specific assumption that γk is uniformwithin industries is not consequential for the results that follow. Instead, it will

15See Fally (2019) and Fally (2018) for a more thorough discussion regarding the generalizedGorman-Pollak demand system.

16The support of distribution Gj,z(ϕ) is ϕ ≥ A1/γkj,z .

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allow me to highlight a previously-unknown source of variation in the tradeelasticities. Moreover, if ρz is also uniform across industries (i.e., quality andquantity are exactly isomorphic), the quality heterogeneity specified by A3 canbe trivially reinterpreted as productivity heterogeneity (see Melitz and Redding(2014)). In that regards, the present framework also nests an extensive class ofmodels featuring heterogeneous productivity firms.

Considering A1-A3, firm ω is uniquely characterized by its output quality, ϕ.So, to simplify the notation without risk of confusion, I henceforth drop firmindices and use lower case letters to denote firm-level variables as a function offirm-level quality and aggregate variables.

Upon entry, a firm can supply a differentiated good in each segment of industryk.17 The production of differentiated goods is governed by constant returns toscale technologies, whereby firms from country j face the following linear costfunction when serving segment z ∈ Zk in market i:

C(q; τji,k, fi,z, wj, wi) = τji,kazwjq + wi fi,z.

In the above expression q is the quantity supplied, with cz(τji,k, wj

)≡ τji,kazwj

denoting for the marginal cost of production and transportation that is paidin terms of the domestic labor wage, wj. The marginal cost is governed by asegment-specific cost shifter, az, and an exporter-importer specific term, τji,k, thataccounts for international differences in production and transportation costs—asshown in Appendix B, the above cost function and the corresponding analysiscan be easily generalized to allow for the dependence of C(.) on output quality.Finally, wi fi,k accounts for the fixed cost of serving market i which is paid interms of labor in the destination market. Accordingly, the cost function can bere-formulated in terms of effective output, q, as follows:

C(q, ϕ; τji,k, fi,z, wj, wi) = τji,kazwjqϕρz

ρz−1 + wi fi,z.

Under monopolistic competition, a firm operating with an effective variable cost,cz(ϕ; τji,k, wj) ≡ τji,kazwj ϕ

ρzρz−1 , chooses a market and segment-specific effective

17By allowing firms to serve multiple segments, the present model accommodates firm het-erogeneity in product scope. According to Hottman et al. (2016), product quality and productscope, together, explain more than four fifths of the variation in firm sales.

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price pz (cz, Pi,z,Qi,z) in order to maximize profits:

π(cz, Pi,z,Qi,z, Li) = maxpz

( pz − cz) q ( pz, Pi,z,Qi,z) Li.

where q (.)× Li is the total demand facing the firm in market i. Given that thereis zero cross-cost passthrough between different varieties of a given firm, thefirst-order condition for the above problem entails that firms charge a monopolymarkup that is inversely related to the underlying demand elasticity (Laffontand Tirole (1993)). Considering the optimal markup, a firm will serve segment zof market i, if and only if π(cz, Pi,z,Qi,z, Li) ≥ wi fi,z.

3.1 Trade Equilibrium

Below, I characterize equilibrium outcomes at the firm and at the aggregatelevels—in doing so, I borrow heavily from the analysis in Arkolakis et al.(2018).18 Subsequently, I present a formal summary of the trade equilibrium.

Firm-Level Outcomes. To outline the firm-level outcomes, consider a firm serv-ing segment z in market i, with effective cost ci,z and effective price pi,z—keep inmind that ci,z ≡ cz(ϕ; τji,k, wj) is a function of country of origin characteristicsand firm-level quality. Following Assumption A2, the Marshallian demandelasticity facing such a firm can be expressed as a function of its effective price,pi,z, relative to a market-level index, Pi,z ≡ wi/Fi,z, as follows:

εz ( pi,z/Pi,z) ≡ −∂ lnD ( pi,z/Pi,z) /∂ ln pi,z.

Hence, defining νi,z ≡ Pi,z/ci,z, the optimal markup, mi,z ≡ pi,z/ci,z = pi,z/ci,z

on any variety sold in segment z can be calculated as

mi,z =εz ( pi,z/Pi,z)

εz ( pi,z/Pi,z)− 1=

εz (mi,z/νi,z)

εz (mi,z/νi,z)− 1,

It is straightforward to verify that if ε′z(x) > 0, there exists a unique markupfunction, mi,z ≡ µi,z(νi,z), that implicitly solves the above equation. More im-portantly, µi,z(.) does not depend on the firm’s country of origin. Altogether,

18While I closely follow Arkolakis et al. (2018) in deriving the gravity equation, the presentmodel exhibits key differences with Arkolakis et al. (2018). Most importantly, aside fromconsidering a more general demand system, Arkolakis et al. (2018) is a special case of thepresent model where ρz is uniform across segments and equal to 1/2. As a result, the pattern ofspecialization highlighted in Section 3.3 is absent in the Arkolakis et al. (2018) framework.

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given the demand function specified by A2, and noting that pi,z = mi,z ci,z withci,z = Pi,z/νi,z, the total sales of a firm serving segment z ∈ Zk of market i can becalculated as

x(νi,z, Pi,z,Qi,z, Li) =µi,z(νi,z)

νi,zPi,z Dz

(µi,z(νi,z)

νi,z

)Qi,zLi.

The above expression then implies the following segment-specific profit function:

π(νi,z, Pi,z,Qi,z, Li) = [(µi,z(νi,z)− 1) /µi,z(νi,z)] x(νi,z, Pi,z,Qi,z, Li).

The zero-profit cutoff condition for segment z in market i can, therefore, beexpressed as follows

π(ν∗i,z, Pi,z,Qi,z, Li) = wi fi,z.

The implicit solution to the above equation, ν∗i,z, implies a cut-off that dependssolely on the characteristics of market i and is independent of the origin coun-try.19 Alternatively, the demand structure specified by A2, is general enough toadmit a choke price, bi,z, such that πi,z = 0 if ci,z ≥ bi,z. So even in the case wherefi,z = 0, there exists a cut-off ν∗i,z = Pi,z/bi,z that is invariant to the characteristicsof the origin country.

Aggregate Outcomes. Total sales of country j to market i in segment z ∈ Zk

can be calculated as the sum of all firm-level sales as follows:

Xji,z = Nj,k

∫ϕ

x(Pi,z/τji,kazwj ϕρz

ρz−1 , Pi,z,Qi,z, Li) dGj,z(ϕ).

Noting that (i) dGj,z = γkAj,z ϕ−γk−1, by A3, and (ii) νi,z =(

Pi,z/τji,kazwj)

ϕρz

1−ρz ,the above equation can be re-formulated as:

Xji,z = χi,zAj,zNj,k(τji,kwj

)−γk

(1

ρz−1)

, (3)

19The quality cut-off, ϕ∗ji,z, implied by ν∗i,z is, however, origin country specific.

14

where χi,z ≡ γka−θzz Qi,zPi,z

∫ ∞ν∗i,z

µi,z(ν)ν Dz

(µi,z(ν)

ν

)ν−γk

1−ρzρz dν

ν .20 Correspondingly,the aggregate segment-level profits collected from sales to market i is given by

Πji,z = Nj,k

∫ϕ

π(Pi,z/τji,kazwj ϕρz

ρz−1 , Pi,z,Qi,z, Li) dGi,z(ϕ)

= ζi,zχi,zAj,zNj,k(τji,kwj

)−γk

(1

ρz−1)

,

where

ζi,z ≡

∫ ∞ν∗i,z

µi,z(ν)−1µi,z(ν)

(µi,z(ν)

ν

)Dz

(µi,z(ν)

ν

)ν−γk

1−ρzρz dν

ν∫ ∞ν∗i,z

(µi,z(ν)

ν

)Dz

(µi,z(ν)

ν

)ν−γk

1−ρzρz dν

ν

.

The above equations imply that the share of country j’s profits, Πj,k, from totalsales,Rj,k, in industry k is equal to ζ j,k ≡ Πj,k/Rj,k =

(∑i,z∈Zk

ζi,zXji,z)

/(∑i,z∈Zk

Xji,z).

Note that if we were also to assume that ν∗i,z is uniform across markets à la Arko-lakis et al. (2018), then ζi,z will be constant and uniform within segment z andprofits will be a constant share of total revenue.

Summary of Equilibrium. A trade equilibrium is a N ×K vector of entrantsN ≡ [Ni,k], a N × 1 vector of national wage rates, w ≡ [wi], a N ×K vector ofindustry-level employment, L ≡ [Li,k], a N × 1 vector of income levels, y ≡ [yi],and a N × K×Z vector of market-specific cut–offs, ν∗ ≡

[ν∗i,z

], that satisfy (i)

the free entry condition (FE), (ii) the industry and aggregate-level labor marketclearing conditions (LMC), (iii) the representative consumers budget constraint,and (vi) the zero-profit cutoff condition (ZPC):21

Nj,k = ζ j,kLj,k/ f ek , (FE)

wjLj,k = ∑Ni=1 ∑z∈ZkXji,z + Nji,zwj f j,z − Nij,zwi fi,z, (industry LMC)

∑Kk=1 Lj,k = Lj, (aggregate LMC)

yiLi = wiLi = ∑Nn=1 ∑Kk=1 ∑z∈ZkXin,z, (BC)

π(ν∗i,z, Pi,z,Qi,z, Li) = wi fi,z (ZPC)

20The term θz ≡ γk (1/ρz − 1) denotes the trade elasticity, which I will elaborate on later. Also,in the integrals, the subscript for ν is dropped in the interest of brevity.

21The existence and uniqueness of equilibrium in the present setup is non- trivial. But, for agiven vector ν∗, the present model falls under the class of multi-industry gravity models studiedin Kucheryavyy et al. (2016); and satisfies the necessary condition for uniqueness and existenceof equilibrium in these models—see Propositions 2-6 in Kucheryavyy et al. (2016).

15

where Nji,z ≡ Nj,k

(1− Gji,z(ν

∗i,z))

denotes the mass of country j firms that can

profitably serve market i in segment z ∈ Zk.22 In constructing the equilibrium,note that given the markup equation, the vector of wages, w = y, fully deter-mines the income levels, the entire schedule of prices in each market, as well asPz (p, y) and Qz (p, y). Also, given that the Marshallian demand must satisfythe budget constraint (BC) of the representative consumer, trade is necessarilybalanced, i.e., ∑n ∑k ∑z∈Zk

Xin,z = ∑j ∑k ∑z∈ZkXji,z for every country i.

Gravity Equation. An attractive feature of the present framework is that country-level export flows within each segment are characterized by a gravity equation.Specifically, let αi,k denote country i’s expenditure share on industry k, and ei,z

denote country i’s (within-industry) expenditure share on segment z. Equation3 then implies that total export flows from country j to i within segment z ofindustry k are given by

Xji,z =Aj,zNj,k

(τji,kwj

)γk

(1− 1

ρz

)

∑Nn=1An,zNn,k (τni,kwn)γk

(1− 1

ρz

) ei,zαi,kYi, (4)

where Yi ≡ wiLi denotes total income in country i. The trade elasticity underlyingthe above gravity equation, θz ≡ γk (1− 1/ρz), depends on both (i) the industry-level degree of firm heterogeneity, γk, and (ii) the segment-level degree of qualityintensity, ρz. Only in the case of exact isomorphism between quality and quantity(which amounts to setting ρz = 1/2, ∀z ), the trade elasticity becomes identicalto the Pareto shape parameter, γk, as in Chaney (2008).

3.2 A Special Case: CES without q-ϕ Isomorphism

To put the above model in perspective, it can be useful to outline a special caseof the model with familiar CES preferences. This special case is essentially avariation of Chaney (2008) that relaxes the exact isomorphism between qualityand quantity. In this special case, the utility of the representative consumer hasthe following parametric structure,

Wi =K

∏k=1

∏z∈Zk

(∫ω∈Ωi,z

ϕ1εzω q

1− 1εz

ω dω

) εzεz−1 ei,zαi,k

,

22dGji,z(ν) ≡ dGj,z

(τji,kazwjν

1/ρz−1/Pi,z

)denotes the PDF of ν for country j firms selling to

market i in segment z.

16

where αi,k denotes the share of market i’s expenditure on industry k while ei,z

denotes the (within-industry) share of expenditure on segment z, with ∑k αi,k = 1and ∑z∈Zk

ei,z = 1. Based on the above utility, ρz = 1/εz and the demand

function facing firm ω is qω =(

p−εzω / ∑k

∫ω′ p1−εz

ω′ dω)

ei,zyi, with the effective

quantities and prices defined as qω ≡ qω ϕ1/(εz−1)ω and pω ≡ pω/ϕ

1/(εz−1)ω . One

can verify, either directly or by using Equation 4, that the gravity equation inthis special case adopts the following formulation,

Xji,z =Aj,zNj,k

(τji,kwj

)γk(1−εz)

∑Nn=1An,zNn,k (τni,kwn)γk(1−εz)

ei,zαi,kYi.

Based on the above gravity equation, the trade elasticity, θz = γk (1− εz), de-pends on both the firm-level demand elasticity, εz, which governs the degree ofquality intensity, and the Pareto shape parameter, γk. In other words, the modelpredicts a strong link between the degree of firm-level and country-level marketpowers, which as I will argue later has sharp macro-level implications.

3.3 The Structure of Within-Industry Specialization

The present framework offers a new perspective on the structure of within-industry specialization. As a first step in demonstrating this, I use the gravityequation to determine the composition of country-level exports across segmentsof an industry. Following Equation 4, the relative exports of countries j and n tomarket i across segments z and z′ ∈ Zk is given by:

Xji,z/Xji,z′

Xni,z/Xni,z′=

( Aj,z/Aj,z′

An,z/An,z′

) (τji,kwj

τni,kwn

)γk

(1

ρz′− 1

ρz

). (5)

Based on Equation 5, revealed comparative advantage across segments of an in-dustry is governed by (i) technical comparative advantage throughAj,zAn,z′/Aj,z′An,z,as well as (ii) differences in trade costs, τ, and labor cost, w. The latter marginyields a clear pattern of specialization, which is outlined below.

Lemma 1. [ρ-Driven Specialization] Absent technical comparative advantage (i.e.,Aj,z = Aj,kAz), high-w and high-τ economies have a revealed comparative advantagein high-ρ (quality-intensive) segments of industries.

Lemma 1 is a reduced-form result that follows directly from Equation 5, relatinga country’s export composition to its wage level and geo-location, which are

17

both observable. While Lemma 1 is agnostic to the source of cross-national wagedifferences, it requires the segment-neutrality of A’s a sufficient condition torule out cases where low-w or low-τ economies have a technical comparativeadvantage (i.e., a higher relative A) in high-ρ segments. To the extent thatLemma 1 outlines a pattern of specialization across industry segments withdifferent trade elasticities, θz ≡ γk (1− 1/ρz), it resembles the theory in Fieler(2011). The present model, however, identifies a novel source of variation inthe trade elasticities that operates through ρz, and that is absent in Fieler (2011)or prior gravity models. Accordingly, specialization across low- and high-tradeelasticity segments, in the present model, assumes a different interpretationcompared to Fieler (2011).

The next step is to determine how the pattern of specialization outlined byLemma 1, dictates the structure of export market power and markups. Thistransition is guided by an important feature of the model, where even thoughmarkups are variable, the distribution of firm-level markups is invariant to thecharacteristics of the exporting country. To demonstrate this, letMji,z(m; wj, τji,k) =

Pr

µz(ν) ≤ m | ν ≥ ν∗i,z

denote the distribution of firm-level export markups

from country j to i in segment z. Appendix C demonstrates thatMji,z is invariantto the exporting country’s characteristics, τji,k and wj, and is given by

Mji,z(m; wj, τji,k) =Mi,z(m) = 1−(

ν∗i,zµ−1i,z (m)

)−γk

(1

ρz−1)

.

The distribution of export markups, however, varies systematically across seg-ments and also with the characteristics of the importing country i. The across-market variation in markups is a reflection of pricing-to-market as in Simonovska(2015). The following lemma summarizes the result concerning the invariance ofmarkup distribution across exporters.

Lemma 2. [Invariance of markup distribution within-z] The distribution of exportmarkups (within segment z) is invariant to the exporting country’s characteristics.

The intuition behind Lemma 2 is similar to that provided by Arkolakis et al.(2018), which is based on the countervailing effects of higher costs on markups.While lower transport costs, τji,k, or labor costs, wj, induce firms from countryj to charge higher markups in market i, they also induce lower quality firmsfrom country j to export, and such firms charge lower markups. These twoeffects exactly offset one-another in the Pareto case, leading to the invariance of

18

the markup distribution. Importantly, Lemma 2 indicates that in the extensiveclass of models covered here (e.g., Melitz and Ottaviano (2008) and Simonovska(2015)), variable markups do not create a systematic link between country-levelcharacteristics and the average export markup or price level, within segments.Instead, the industry-level heterogeneity in export markup levels is drivenexclusively by the composition of exports across segments.

Lemma 2 points to two important corollaries. First, it entails that the distributionof demand elasticities facing firms exporting from country j to market i, is alsoinvariant to country j’s characteristics: Eji,z(m; wj, τji,k) = Ei,z(ε). Given theinvariance of the markup and demand elasticity distributions, I henceforth use εi,z

and mi,z to denote the average demand elasticity and markup level associatedwith segment z in market i:εi,z ≡

∫ε ε dEi,z(ε)

mi,z ≡∫

m m dMi,z(m)

Correspondingly, in each market, we can uniquely rank segments within indus-try k by their average firm-level markup or elasticity level. Such a ranking isalso significant from a macro-level perspective given that, under free entry, mi,z

represents the degree of scale economies in segment z. To elaborate, consider thestandard definition of the scale elasticity, which is the elasticity at which total costincreases with firm-level output: ψ ≡ ∂ ln C/∂ ln q. It is a well-known that if (i)firms are profit-maximizing (MC = MR) and (ii) there is free entry (AC = p),this elasticity equals the firm-level markup (see Hanoch (1975) and Helpman(1984)). In particular,

scale elasticity : ψ ≡ MCAC

=MR

p=

ε

ε− 1= m,

where MC, AC, and MR respectively denote the firm-level marginal cost, av-erage cost, and marginal revenue. Considering the above equation, high-m orlow-ε segments can be viewed as high-scale intensive. As one may expect, thisconnection has basic implications for the gains from trade and cross-countryincome differences—a point I will return to in Section 5.

The final step in establishing my theoretical proposition is to relate ρ-drivenspecialization (Lemma 1) to the markup and scale-intensity of a nation’s exports.To this end, I impose the following testable assumption that links the segment-

19

level quality intensity, ρz, to its average demand elasticity, εi,z.

A4. [Link between ε and ρ] Firms on average face a lower demand elasticity, εi,z, inhigh quality-intensive (high-ρz) segments of an industry.

The above assumption is already implicit in the CES case outlined in Section3.2, where ρz = 1/εz. Beyond CES, the prior literature has occasionally invokedA4, with Rodrik (1994), for instance, arguing that quality-intensive segments areless standardized and, therefore, less price sensitive. But more importantly, A4is an empirically testable assumption. In Section 4, I employ rich micro-leveldata to establish that the empirical relationship between quality intensity andthe demand elasticity aligns with A4.

Assumption A4 paired with Lemmas 1 and 2 imply my main proposition thathigh-income and geographically remote economies specialize in high-markup,high-scale intensive segments of industries. Appendix C provides a formal proofof this claim, and the following provides a formal statement.

Proposition 1. Absent technical comparative advantage, high-wage and geographicallyremote economies specialize in high-scale intensive, high-markup segments of industries.

The intuition behind proposition 1 is straightforward. National industries thatface high labor or transportation costs tend to export relatively more in quality-intensive (low trade elasticity) segments were aggregate sales are less sensitiveto aggregate cost measures. Per A4, high quality-intensive segments are alsothose in which firms, as an individual unit, enjoy greater market power andset higher markups. Altogether, these two patterns yield the proposition statedabove. To better understand Proposition 1, bear in mind that higher wage levelsin the present model are a reflection of the economy being agglomerated withhigh-quality firms (which will be reflected in a higher A). Proposition 1, merelystates that an agglomeration of high-quality firms in an economy puts upwardpressure on the local wages, inducing firms to specialize in high-market power,high scale-intensive segments of industries.

Discussion Assumptions A1-A4 outline a set of sufficient conditions that de-liver Proposition 1. Of these assumptions, A1 is less consequential. It relaxesthe quality-quantity isomorphism in favor of a less-restrictive assumption toidentify a new source of variation in the trade elasticities. A2 and A3 are con-ventional assumptions that deliver the gravity equation—as noted earlier, bothassumptions underlie an important class of constant and variable markup trade

20

models. A4, however, is a major assumption that can be tested with micro-leveldata, and the following section is dedicated to this task.

Note, however, that even a weaker version of A4 will still yield Proposition1. Specifically, as long as the segment-wide trade elasticity θz ≡ γk (1− 1/ρz)

is positively correlated with the average firm-level demand elasticity, εi,z, thepattern of revealed comparative advantage outlined by Lemma 1, will yieldProposition 1. Accordingly, the present version of A4, which concerns thecase were the across segment heterogeneity in trade elasticities is driven solelyby differences in quality intensities, can be easily amended to also allow forheterogeneity in γk, without undermining the main thesis of the model.

Finally, the specialization pattern outlined by Proposition 1 can concurrentlyoccur at various levels of aggregation. In the interest of consistency, the theorywas cast here as one of within industry specialization. But one can alternativelyassume that A1-A4 hold across (rather than within) industries to arrive at a simi-lar proposition regarding across-industry specialization. In that case, high-wageand remote economies specialize in high market power, high scale-intensiveindustries.

3.4 An Alternative View on Export Price Levels

Proposition 1 offers a new perspective on Facts (i) and (ii) (from the Introduc-tion) that export price levels, to a given market, increase with bilateral distance andthe income per capita of the exporting country. As noted before, the dominantview in the literature is that these patterns reflect quality specialization drivenby differences in factor proportions (Schott (2004)) or additive trade costs (Hum-mels and Skiba (2004)). Against the backdrop of this dominant view, Proposition1 highlights the markup channel as an alternative driver of the aforementionedFacts, while Lemma 1 provides an alternative view on the origins of qualityspecialization.

To elaborate, note that the average f.o.b. price of exports from country j tomarket i in industry k can be decomposed as follows:

pji,k = µ(τji,k, wj

)︸ ︷︷ ︸markup-driven

× a(τji,k, wj

)wj︸ ︷︷ ︸

cost-driven

,

where a(τji,k, wj

)≡ ∑z∈Zk

azrji,z(τji,k, wj

)and µ(τji,k,wj) ≡ ∑z∈Zk

mi,zrji,z(τji,k, wj

)respectively denote the average markup and unit labor cost embedded in coun-

21

try j’s industry-level exports to markets i, with rji,z ≡ Xji,z/ ∑z∈ZkXji,z being

the share of segment z from total industry-level export sales. In the above ex-pression, the markup-driven competent, µ (τ, w), has a clear connotation. Thecost-driven term, a (τ, w)w, meanwhile, primarily accounts for quality differ-ences. In particular, a(τ, w)w may be higher due to (i) a higher wage, whichreflects an agglomeration of high-quality firms in the economy, or (ii) a highera (.), which reflects a higher share of exports in high-quality intensive segments,provided that az is increasing in the degree of quality-intensity, ρz.

From the lens of the present model, the markup-driven term, alone, can explainwhy exports from rich and distant suppliers exhibit higher price levels. In par-ticular, Proposition 1 asserts that ∂2rji,z/∂τji,k∂mi,z > 0 and ∂2rji,z/∂wj∂mi,z> 0,which along with the fact that ∑z∈Zk

rji,z = 1, imply the following:∂µ(τji,k,wj)

∂τji,k= ∑z∈Zk

mi,z∂rji,z∂τji,k

> 0∂µ(τji,k,wj)

∂wj= ∑z∈Zk

mi,z∂rji,z∂wj

> 0. (6)

Based on the above, the “Washington apples” effect, ∂pji,k/∂τji,k > 0, is partlydriven by distant exporters sorting into high-markup segments; or the obser-vation that ∂pji,k/∂wj > 0 is reflective of high-income economies exportingrelatively more goods pertaining to high-markup segments of industries. Eventhough this mechanism concerns export markups, it operates orthogonal to thewell-known variable markup mechanism. As implied by Lemma 2, markupscan be variable across firms, but the distribution of markups, within segments, isthe same for all exporting countries. That being the case, variable markups canexplain why Australian firms set higher prices in the US market than in China,but not why the US imports higher price goods from Australia than from sayCanada. The above mechanism, by contrast, explains this exact type of variation.

Finally, in the present model, the quality margin also contributes to the posi-tive relationship between τji,k, wj, and pji,k, but through a mechanism that isdistinct from those specified in the prior literature. Specifically, provided thathigh quality-intensive (high-ρ) segments involve a higher productions cost, az,Lemma 1 implies that ∂a(τ, w)/∂τ > 0 and ∂a(τ, w)/∂w > 0. That is, absentmarkup heterogeneity, a higher τji,k or wj increases the aggregate export pricelevel, pji,k, by inducing specialization in quality-intensive segments.

22

4 Micro-Level Evidence

Even if the full schedule of export markups were observable, testing Proposition1 directly would remain challenging as it requires information on the full vectorof deep technology parameters, A ≡ [Ai,z]. To elaborate, suppose the datasuggests that high-wage and remote economies export relatively more in high-markup segments. It may very well be the case that they have a factor-drivenor a historical scale-driven comparative advantage in these segments—whichwill be reflected in a higher A. Alternatively, high-wage and remote economiesmay have a fundamental comparative disadvantage in high-markup segments,which will negate the mechanism highlighted in this paper.

Despite such complications, one can still indirectly test Proposition1 by evaluatingthe sufficient conditions that lead to it. As noted earlier, of the assumptionsleading to Proposition 1, A1 is not consequential; A2 and A3 are standardassumptions that deliver the gravity equation (see Arkolakis et al. (2018)); butA4 is a unique assumption that is empirically testable. Considering this, I firstconduct a formal test of assumption A4 in this section. I then present directevidence that factual export patterns do in fact comply with Proposition 1.Finally, I discuss the limitations of my analysis and provide auxiliary evidenceon across-segment specialization.

Data Description. The empirical analysis that follows uses import transactionsdata from the Colombian Customs Office for the 2007–2013 period.23 The datacovers the universe of all import transactions in Colombia, reporting the fol-lowing information per transaction: date of transaction, Harmonized System10-digit product category (HS10), importing and exporting firm’s ids,24 f.o.b.values of shipments in US dollars, quantity and the unit its measured in, freightin US dollars, insurance in US dollars, import tariff and value-added tax rates,and country of origin. Table 10 in the appendix reports a summary of basic tradestatistics for this data set. A possible challenge when working with this data set

23The data is obtained from Datamyne, a company that specializes in documenting importand export transactions in Americas. For more detail, please see www.datamyne.com.

24The identification of the Colombian importing firms is standardized by the national taxID number. For the foreign exporting firms, the data provide the name of the firm, phonenumber, and address. The names of the firms are not standardized, and thus there are instancesin which the name of a firm and its address are recorded differently (e.g., using abbreviations,capital and lower-case letters, dashes, etc.). To deal with this problem, I follow the guidelines inLashkaripour and Lugovskyy (2018), which involves standardizing the spelling and the lengthof the names along with utilizing the data on firms’ phone numbers.

23

is that Colombia has been changing the HS10 classification for some productsbetween 2007 and 2013. Fortunately, the Colombian Statistical Agency, DANE,has kept track of these changes, permitting the concordance of Colombian HS10codes over time—the concordance procedure closely follows the guidelines inLashkaripour and Lugovskyy (2018), with changes in HS10 codes affecting lessthan 0.1% of the observations between 2007 and 2013. My analysis also requires(i) data on monthly average exchange rates, which are taken from the Bank ofCanada, (ii) data on national accounts that are taken from the PENN WORLD

TABLE version 9, and (iii) data on geo-distance, which are taken from the CEPII

database (Mayer and Zignago (2011)).25

To map theory to data, I take a similar approach to Holmes and Stevens (2014),using the 4-digit Standard Industrial Classification (SIC) to define industriesand the 10-digit HS10 product classification to specify segments within anindustry. To fix minds, consider the following group of HS10 product segments:“PASSENGER CARS WITH 1000-1500CC ENGINES,” “PASSENGER CARS WITH

LARGER THAN 3000CC ENGINES,” “LIMOUSINES,” “TRACTORS,” “GOLF CARTS,”and so on. Based on the Standard Industrial Classification, these segmentsare grouped together into SIC 3711, which corresponds to “MOTOR VEHICLES

AND PASSENGER CAR BODIES.” The analysis that follows concerns specializationacross these narrowly-defined HS10 segments that are grouped into broadly-defined SIC industries.

4.1 Estimating the Segment-Level Demand Elasticity: εz

For every variety ω, zt exported to Colombia by firm ω, in HS10 segment z, in yeart, I observe export quantity, qω,zt, as well as the f.o.b. value plus transportationcosts and tariff/tax charges, which can be used to construct the consumer price,pω,zt, associated with that variety. Given data on firm-level quantities and prices,I estimate the average demand elasticity facing firms in segment z using thefollowing estimating equation:

ln qω,zt = −εz ln pω,zt + δωz + δzt + ξω,zt, (7)

where δωz and δzt control for firm-product and product-year fixed effects, andξω,zt represent non-price demand shifters such a measurement errors or time-varying components of quality, ϕω,zt.

25See http://www.bankofcanada.ca/rates/exchange/monthly-average-lookup/.

24

Table 2: Summary of the estimated segment-level elasticities:

mean median 1st quartile 3rd quartileNumber of

sig. estimates

segment-level demand elasticity: εz

OLS 1.13 0.90 0.61 1.23 4,391(0.11) (0.25) (0.16)

2SLS 2.74 1.88 1.20 3.03 1,283(1.22) (0.68) (2.61)

LIML 2.78 1.93 1.21 3.26 1,627(1.26) (0.17) (1.89)

segment-level trade elasticity: θz ≡ (1/ρz − 1) γk

OLS 1.05 0.76 0.42 1.28 2,706(0.14) (0.28) (0.36)

2SLS 2.24 1.69 1.05 2.75 1,827(0.77) (0.11) (1.88)

LIML 2.58 1.89 1.16 3.21 1,701(0.50) (0.69) (1.48)

To eliminate the firm-product fixed effects, I take first-differences from Equation7 to arrive at the following estimating equation:

∆ ln qω,zt = −εz∆ ln pω,zt + ∆δzt + ∆ξω,zt (8)

The first-difference estimator exhibits a couple of attractive features for thepurpose of my analysis: (i) it eliminates observations pertaining to one-timeexporters, (ii) it is more efficient than the fixed effect estimator when ξω,kt’s aresequentially correlated, and (iii) it requires a weaker orthogonality condition,E [∆ ln pω,zt | ∆ξω,zt] = 0, than the fixed effect estimator.

As a first step, I separately estimate Equation 8 for 5,669 HS10 segments using thefirst-difference OLS estimator. For 4,391 of these HS10 segments the estimationproduces a positive elasticity, εz, (i.e., a negative coefficient on unit price) witha robust t-statistic that is greater than one.26 A basic summary of the OLS-estimated demand elasticities is reported in the first row of Table 2.

26Throughout this section I drop elasticity estimates that exhibit a robust t-statistic belowor equal to one. My analysis, however, produces qualitatively similar results when I dropelasticities that exhibit a robust t-statistic below or equal to two.

25

IV Estimation. A general concern when estimating Equation 8 is that de-mand shocks, ∆ξω,zt, may be correlated with longitudinal changes in price,∆ ln pω,zt. Such a correlation, which may be driven by measurement errorsor by quality upgrading, leads to a violation of the orthogonality condition,E [∆ ln pω,zt | ∆ξω,zt] 6= 0. The standard approach to handing such a concernis to instrument for ∆ ln pω,zt with a plausibly exogenous cost shifter that isorthogonal to ∆ξω,zt. Changes in import tariff rates are often considered to bean appropriate instrument in these circumstances. But since Equation 8 is beingestimated at the firm level, import tariffs do not qualify as a strong instrument,as they exhibit little-to-no variation across firms from the same country.

To overcome the identification challenge, I use the methodology in Lashkaripourand Lugovskyy (2018), which is to instrument for ∆ ln pω,zt using a plausiblyexogenous measure of exposure to aggregate exchange rate shocks.27 This pro-cedure involves compiling an external database on aggregate monthly exchangerates, and interacting the monthly variation in aggregate exchange rates withthe monthly composition of firm-level exports in the prior two years. Doing so,delivers the following shift-share instrument:

Zω,zt = ∑`=1,2

12

∑m=1

∆Ejt (m)× rω,zt−` (m) ,

with ∆Ejt (m) denoting the change in country j’s exchange rate with Colombia inmonth m of year t; and rω,zt−` (m) and denotes the prior share of firm ω’s monthm sales in year t− `. To elaborate, Zω,zt measures the variety-specific exposure toexchange rate shocks. It builds on the fact that aggregate exchange rate movementsmay have differential effects on firms, depending on the monthly compositiontheir export sales. In that regard, Zω,zt resembles the widely-used Bartik instru-ment. Perhaps most importantly, Zω,zt captures a plausibly exogenous sourceof variation in firm-level costs, provided that aggregate exchange rates andhistorical export patterns are independent of concurrent demand shocks.

27The estimation conducted here differs from Lashkaripour and Lugovskyy (2018) in twobasic aspects. First, Lashkaripour and Lugovskyy (2018) jointly estimate the country-level andfirm-level demand elasticities, by assuming a nested-CES demand system. Second, given thefocus of that paper, the elasticities are estimated at WIOD industry level of aggregation. Here,I neither impose that the underlying demand is CES nor do I assume that the elasticities areuniform within industries. As a result, I can estimate reduced-form demand elasticities at theHS10 level of aggregation, in order to test Assumption A4. However, unlike Lashkaripour andLugovskyy (2018), the estimated elasticities no longer assume a structural interpretation andthe country-level trade elasticities have to be estimated separately from the firm-level demandelasticities.

26

Table 3: First-Stage Diagnostics: pooled sampleEstimating Parameter

Demand Elasticity εz Trade Elasticity θz

Kleibergen-Paap LM statistic (under-identification) 373.58 1589.54Kleibergen-Paap LM p-value 0.000 0.000

Kleibergen-Paap Wald rk F-stat (weak instruments) 121.54 494.14

Anderson-Rubin Wald test F-stat 235.72 2223.92Anderson-Rubin Wald test p-value 0.000 0.000

Observations 1,341,480 500,064

I conduct a battery of tests to diagnose the strength of my price instruments inTable 3. Given that errors may be heteroskedastic, I use the heteroskedasticity-robust Kleibergen and Paap (2006) test statistics to diagnose under-identificationand weak instruments. Based on the Kleibergen-Paap LM statistic, I can rejectthe null hypothesis that the model is un-identified. To test if the instrumentsare only weakly correlated with unit price, I also report heteroskedasticity-robust Kleibergen and Paap (2006) Wald rk F-statistic. While critical valuesfor the Cragg and Donald (1993) F-statistic have been provided by Stock andYogo (2002) in the homoskedastic case, there is no tabulation of such valuesfor the heteroskedastic case. So, as is common in the literature, I compare theheteroskedasticity-robust statistic to the Stock and Yogo (2002) critical values,which allows me to reject the null of weak instruments. Finally, Table 3 alsoreports the Anderson et al. (1949) Wald test, which strictly rejects the null that thecoefficients on the excluded instruments are jointly zero when they are includedin place of unit price, ∆ ln pω,zt, in the estimating Equation 8.

The results attained under the 2SLS estimator are reported in the second row ofTable 2. Encouragingly, the 2SLS estimates are lower than the OLS estimates,which suggest that the instruments are operating in the right direction. However,as expected, the standard errors corresponding to the 2SLS estimation are higher;so, that for only 1,283 HS10 segments the estimated elasticity is positive andexhibits a robust t-statistic greater than one. Given that that HS10 segmentsmay feature a small sample of firm-level observations, I also estimate Equation8 using the Limited Information Maximum Likelihood (LIML) estimator, whichis more robust than 2SLS in the presence of weak instruments and small samplebias (Stock and Yogo (2002)). The results corresponding to the LIML estimationare summarized in the third row of Table 2, and are qualitatively similar to the

27

2SLS estimates.

4.2 Estimating the Segment-Level Quality Intensity: ρz

Using the gravity equation one can estimate a segment-specific trade elasticity,θz = γk (1/ρz − 1) , which determines ρz up to an industry-wide Pareto shapeparameter, γk. There is an extensive literature on estimating the trade elasticity,and what follows builds heavily on this literature. To express the estimatingequation, I take logs from Equation 3; drop the importer subscript i as I amdealing with data from a unique market; and write the equation in stochasticform. Altogether, country j’s sales-per-firm to the Colombian market, in HS10segment z, in year t can be stated as,

ln Xj,zt/Nj,kt = −γk

(1ρz− 1)

ln τj,ztwj,t + δzt + ξ j,zt , z ∈ Zk (9)

where δzt = ln χzt can be treated as an HS10–year fixed effect and ξ j,zt is anunobserved error term that, among other things, encompasses measurementerrors or longitudinal variations in national product quality, Aj,zt. Based onHead and Mayer’s (2014) survey of the literature, there are multiple approachesto estimating the above equation. The first approach, which is more suited tocross-sectional data, is to control for wj using exporter fixed effects and identifythe trade elasticity using the variation in transport costs (e.g., Hummels (2001);Hertel et al. (2007)) or tariff rates (e.g., Romalis (2007); Caliendo and Parro (2014)).An alternative approach for panel data is to control for τj,ztwj,t, using the averageunit price of country-level exports, pj,zt = mztaztτj,ztwj,t (e.g., Erkel-Rousse andMirza (2002); Broda and Weinstein (2006)); and to instrument for pj,zt in order toaddress the possible endogeneity concern. Given the panel structure of my data,I adopt the latter approach.

To estimate Equation 9, all firm-level variables are aggregated up to constructcountry-level variables. This procedure leaves me with 500,064 observationswith the unit of observation being exporting country–HS10 segment–year. For eachobservation, I have the average sales per firm Xj,zt/Nj,kt and the average price,pj,zt = mztaztτj,ztwj,t, associated with these sales. Using these variables, I firstestimate Equation 9 using an OLS estimator, with a summary of the estimationresults reported in the fourth row of Table 2.28 The results indicate that for 2,706

28Stated formally, the estimating equation is ln Xj,zt/Nj,kt = −γk

(1ρz− 1)

ln pj,zt + δzt + ξ j,zt.

28

HS10 segments, the estimated trade elasticity is positive and exhibits a robustt-statistic greater than one. Perhaps expectedly, the median trade elasticity isalso lower than the median demand elasticity facing individual firms.

As with the firm-level estimation, one may be concerned that the orthogonalitycondition, E

[pj,zt | ξ j,zt

]= 0, is violated due to measurement error or longitudi-

nal changes in the national quality distribution, Aj,zt. To address these concerns,I also estimate Equation 9 using a 2SLS estimator, where I instrument for pj,zt

with the exporter-specific tariff and value added tax rates. Here, the identifyingassumption, as in Caliendo and Parro (2014), is that import tax rates are plausiblyexogenous to ξ j,zt. Correspondingly, the second column in Table 3 reports a set offirst-stage diagnosis tests, which reject the null hypothesis of weak instrumentsor the model being un-identified.

The 2SLS estimates of θz = γk (1/ρz − 1) are summarized in the fifth row ofTable 2. The 2SLS estimates are encouragingly lower than the OLS estimates,but exhibit higher standard errors. Overall, the 2SLS-estimated trade elasticitiesare positive and exhibit a robust t-statistic greater than one for only 1,827 HS10segments. As before, I also estimate Equation 8 using the LIML estimator, whichis more robust than the 2SLS estimator in the presence of weak instruments andsmall sample bias. The results, which are summarized in the last row of Table 2,are qualitatively similar to the 2SLS case. Generally speaking, my trade elasticityestimates are slightly lower than those produced by Caliendo and Parro (2014)and Simonovska and Waugh (2011). These differences may stem from the factthat (i) I explicitly control for the number of firms, Nj,kt, instead of treatingcountries as one integrated entity, and (ii) I estimate the trade elasticity at amore refined level of aggregation, which circumvents some of the aggregationbiases highlighted in Imbs and Mejean (2015).

Before employing the estimated elasticities to test my theory, let me brieflydiscuss the plausibility of my estimates. In Table 11 in the appendix, I reportthe average estimated demand elasticity and quality-intensity for a range ofbroadly defined industries. The quality intensity is simply measured as ρz =

1/ (1 + θz/γk), where γk is assigned a value of 2.46 based on the estimates ofEaton et al. (2010). Based on my estimates, the ’Machinery’ and ’Electrical &Optical Equipment’ sectors are comprised of the most quality-intensive HS10segments, while the ’Food’ and ’Paper’ sectors are comprised of the least quality-intensive HS10 segments. These results sit well with evidence from consumersurveys that durables are more quality-intensive than non-durables (Fornell

29

et al. (1996)). Similarly, the ’Machinery’ and ’Electrical & Optical Equipment’sectors are comprised of the least price-elastic segments, while the ’Food’ and’Agriculture & Mining’ include the most price-elastic HS10 segments. Theserankings align well with the classification in Campa and Goldberg (1995)

4.3 Testing A4: The Link between ρz and εz

The segment-level trade elasticity, θz = (1/ρz − 1) γk, identifies the segment-level quality-intensity up to an industry-wide Pareto shape parameter, γk. Hence,to test assumption A4, I can use the estimated HS10-level trade and demandelasticities (θz and εz), to run the following regression:29

ln (1/ρz − 1) γk = β · ln εz + δk + ξz; z ∈ Zk (10)

where δk controls for SIC industry fixed effects. I estimate the above relationshipusing the elasticities attained under all estimators–namely, OLS, 2SLS, and LIML.As reported in Table 4, in all incidences the segment-level trade elasticity ispositively correlated with the average demand elasticity, εz, facing individualfirms in that segment, with the relationship being statistically significant atthe 99% confidence level. This positive relationship assures that high-qualityintensive (high-ρz) segments of the industry exhibit a lower demand elasticity,which is the assertion of A4.

When running Regression 10, the value of γk is irrelevant as it is absorbed bythe industry fixed effect. However, I can alternatively test A4 by calculatingρz = 1/ (1 + θz/γk) based on γk = 2.46 from Eaton et al. (2011), and runningthe following regression instead:

ln ρz = β · ln εz + δk + ξz; z ∈ Zk,

The estimation results corresponding to the above regression are reported inthe right panel of Table 4. Expectedly, this approach delivers a similar set ofresults, pointing to a strong, negative relationship between quality-intensity anddemand elasticity across segments, which again corroborates A4.

As a clarifying point, note that the number of observations in Table 4 variesacross columns because each of the OLS, 2SLS, and LIML estimators produces a

29Assumption A4 only requires that ρz and εz be positively related. The parametric formof the relationship is inconsequential. Nonetheless, Table 13 in the appendix also reports therelationship between ρz and εz in levels (rather than in logs), which yields similar outcomes.

30

Table 4: The relationship between quality-intensity and demand elasticity (A4)

Dependent: trade elasticity Dependent: quality intensity

Regressor OLS 2SLS LIML OLS 2SLS LIML

demand elasticity, log εz 0.346*** 0.250*** 0.177*** -0.102*** -0.115*** -0.084***(0.029) (0.051) (0.046) (0.007) (0.023) (0.021)

Observations 1,851 435 516 1,851 435 516No. of SIC Industry FE 95 52 63 95 52 63R-Squared 0.45 0.28 0.20 0.39 0.27 0.20

different set of plausible, and statistically significant trade and demand elasticityestimates. For 1,851 HS10 segments (spanning 95 SIC industries) The OLSestimation delivers a statistically significant estimate of both εz and θz, whichcan be used to estimate Equation 10. The 2SLS and LIML estimators, whileconceivably more reliable, produce statistically significant trade and demandelasticities for a fewer number of SIC industries and HS10 segments.30

4.4 The Composition of Industry-Level Exports

The previous section presented empirical support for A4, as the key conditionthat prompts across-segment specialization in Proposition 1. Now, I turn todirectly testing the outcomes predicted by Proposition 1 and by Lemma 1. To testLemma 1, I use my trade elasticity estimates to calculate the degree of qualityintensity, ρz, per HS10 segment in order to construct the following measure:

ρj,kt =∑z∈Zk

ρzXi,zt

∑z∈ZkXi,zt

.

To be more specific, ρj,kt measures the average quality intensity of country j’sexports to Colombia in SIC industry k. Lemma 1 predicts that ρj,kt is increasingin country j’s income per worker, wj,t, and its distance to Colombia, Distj; whichI can test by running the following regression:

ln ρj,kt = β1 ln wj,t + β2 ln Distj + β3 ln Yj,t + δkt + ξ j,kt.

30Industries that produce significant 2SLS and LIML estimates are typically those with signifi-cantly more observations. This, is important to note as one may be concerned with the issue ofendogenous selection.

31

Table 5: The composition of country-level exports to ColombiaAvg. Quality Intensity Avg. Market Power

Regressor OLS 2SLS LIML OLS 2SLS LIML

ln wj 0.005*** 0.001 0.004** 0.013*** 0.021*** 0.031***(0.001) (0.002) (0.002) (0.002) (0.004) (0.004)

ln Distj 0.014*** 0.023*** 0.027*** 0.017*** 0.029*** 0.028***(0.001) (0.002) (0.002) (0.003) (0.004) (0.005)

ln Yj -0.005*** -0.005*** -0.006*** -0.010*** -0.019*** -0.028***(0.001) (0.001) (0.001) (0.001) (0.002) (0.003)

Observations 16,207 15,582 15,353 23,095 14,896 16,555R-squared 0.59 0.59 0.56 0.61 0.55 0.50

In the above regression, δkt accounts for industry-year fixed effects, and Yj,t

controls for country j’s total GDP. The results corresponding to this regressionare reported in the left panel of Table 5, and confirm the prediction that high-wage and distant economies export relatively more in high-quality intensivesegments of each industry.

Similarly, to test Proposition 1, I use my estimated HS10-level demand elasticitiesto construct the following measure

MP j,kt =∑z∈Zk

Xi,zt/εz

∑z∈ZkXi,zt

,

which reflects the average market power of firms’ exporting from country j toColombia in SIC industry k. Proposition 1 predicts thatMP j,kt is increasing incountry j’s income per worker, wj,t, and its distance to Colombia, Distj, which Ican test by running the following regression:

lnMP j,kt = β1 ln wj,t + β2 ln Distj + β3 ln Yj,t + δkt + ξ j,kt,

As before, δkt accounts for industry-year fixed effects and Yj,t controls for countyj’s total GDP. The results corresponding to this regression are reported in theright panel of Table 5, and again decisively confirm the prediction that high-wageand distant economies export relatively more in high market power segments of

32

each industry. While these results are encouraging, one should exercise cautionwhen interpreting them. Specifically, as noted earlier, the findings presentedin Table 5 may be an artifact of factor-driven specialization. That is, it can bethe case that distant and high-wage economies have a factor-driven compara-tive advantage in low-θ and low-ε segments, which reinforces the mechanismhighlighted in this paper.

4.5 Discussion and Auxiliary Evidence

Here, I will briefly discuss the extensions and limitations of my analysis. Beforedoing so, let me take stock. This section estimated two key elasticities for a rangeof HS10 segments: (i) the trade elasticity θz, which reflects the collective marketpower of a country in segment z, and (ii) the firm-level demand elasticity, εz,which reflects the average market power of individual firms in that segment.Following Chaney (2008), it has been widely-believed that the link between θz

and εz is theoretically unclear. The results in this section, however, establisheda positive empirical link between θz and εz. This relationship plus trade flowsbeing governed by a gravity equation, suffice to prompt specialization based onthe mechanism introduced in this paper.

The assumption that γk does not vary across segments is not consequential tothe conclusions in this section. More specifically, the across segment variation inthe trade elasticity, θz, may very well reflect across-segment heterogeneity in γ.But this does not cast a problem for my analysis, as Proposition 1 holds so longas θz is positively correlated with εz across segments and irrespective of whattriggers the variation in θz.

Looking closer at the evidence, the theory developed here can also explainacross-industry and within-segment specialization. Specifically, as shown in Table12 of the appendix, the negative relationship between ρz and εz prevails notonly within industries but also across industries. Per Proposition 1, such arelationship will prompt specialization across low- and high-markup (or low-and high-scale intensive) industries. Moreover, a similar pattern of specializationmay occur within HS10 segments. In fact, I find basic evidence that high-wageand distant economies specialize in high-markup niches of HS10 segments. Theevidence is based on the following demand estimation, which admits elasticityheterogeneity across suppliers within an HS10 segment:

∆ ln qω,zt = −(εc + ετ · ln Distj + εw · ln wj

)∆ ln pω,zt +∆δzt +∆ξω,zt ; ω ∈ Ωj,zt

33

Table 6: Evidence on within-segment specialization

Estimator

Regressor LIML 2SLS OLS

∆ ln pω,zt (−εc) -5.509*** -3.787*** -0.702***(0.733) (0.355) (0.005)

∆ ln pω,zt × ln Distj (−ετ) 4.456*** 3.001*** -0.109***(1.246) (0.591) (0.009)

∆ ln pω,zt × ln wj (−εw) 16.586*** 9.804*** 0.562***(2.018) (0.834) (0.012)

Kleibergen-Paap LM statistic 235.4 ...Kleibergen-Paap LM p-value 0.000 ...Kleibergen Paap Wald rk F-stat 25.32 ...Anderson-Rubin Wald F-stat 82.22 ...Anderson-Rubin Wald p-value 0.000 ...Observations 1,279,875

In the above equation ∆δzt , as before, controls for HS10-year fixed effects, whileDistj and wj denote the normalized distance and income per worker of countryj, which applies to each firm ω exporting from that country. I use the samemethodology, explained earlier, to estimate the above equation. The estimationresults presented in Table 6 indicate that firm-level exports from high-wageand distant economies face significantly lower demand elasticities, which isindicative of specialization in high-market power niches within HS10 segments.

The obvious limitation of the present analysis is its reliance on the monopolisticcompetition assumption. This assumption is widely-used, but difficult to test.Importantly, the link between the average firm-level demand elasticity and theaverage markup should be amended if the monopolistic competition assumptionis violated. That being said, in line with Hottman et al. (2016), I find that inmost product categories in my sample, the number of exporting firms is largeenough to render the monopolistic competition assumption plausible. The othershortcoming, which is due to a lack of better data, is the inability to test Lemma 1and Proposition 1, while conditioning on the effect of factor-driven specializationat the firm level.

34

5 Macro-level Implications

Within-industry specialization based on Proposition 1 determines the distribu-tion of economic activity across industry segments that differ in their (i) degreeof market power, (ii) degree of returns to scale, and (iii) trade elasticity. Thelatter two characteristics determine the extent to which countries can gain frominternational specialization or trade. So, how national resources are dividedalong these margins can profoundly influence macroeconomic outcomes. Below,I fit my theoretical model to aggregate trade data to quantify these macro-levelimplications.

5.1 Quantitative Strategy

To set the stage for a transparent presentation of macro-level implications, Ifirst describe the quantitative strategy by which the model is fitted to data. Thestrategy is closely related to a structural gravity estimation à la Anderson andVan Wincoop (2003).31 That is, I identify the structural parameters of the modelby fitting it to the matrix of aggregate bilateral trade values. However, unlikethe standard structural gravity estimation, I allow for industries to be comprisedof multiple segments with different trade elasticities.

I estimate the model using two distinct datasets. First, the 2008 version of theWorld Input Output Database (WIOD), which reports industry-level trade andproduction data for 32 major economies across 34 industries (15 of which aretradable). Estimating the model with this dataset will allow me to quantify thegains from within-industry specialization. Second, I also estimate the modelusing country-level trade and production data, which covers 100 economiesin the year 2000. Estimating the model with this second data set allows me tostudy cross-country TFP differences for a wider range of economies. AppendixD provides a more detailed description of both datasets.

5.1.1 Parametric Restrictions

The theoretical model presented in Section 3 only required preferences to beadditively separable across industries. But to map the model to data, I need toimpose more specific structure on the cross-industry utility aggregator. Consid-

31See Head and Mayer (2014) for a review of the literature on structural gravity estimation

35

ering this, I impose the following restriction, which allows me to estimate themodel separately for each industry.

R1. The cross-industry utility aggregator is Cobb-Douglas. That is, Wi = ∏Kk=1 Uαi,ki,k ,

where ∑k αi,k = 1.

The above restriction is a standard staple in the quantitative trade literature(see Costinot and Rodríguez-Clare (2014)). Since the industry-level expenditureshares, α ≡ [αi,k], are observable, Restriction R1 reduces the estimation problemto that of matching aN × (N − 1) matrix of trade values, Xk ≡

[Xji,k

], separately

for each industry k.

To characterize the industry-level trade values, I further impose the followingrestriction on the demand structure across segments within an industry.

R2. Each industry k is comprised of two segments, Zk = H,L; with ei,z denotingthe constant share of expenditure on segment z in country i.

Unlike αk, the segment-level expenditure shares, ek ≡ [ei,z], are not observable.So, I treat them as free-moving parameters that are estimated. Given R1 and R2,the industry-level bilateral trade values, Xji,k, can be calculated as

Xji,k = ∑z∈Zk

λji,kei,zαi,kwiLi

where λji,z denotes the share of country i’s expenditure on country j varieties insegment z of industry k. Following the gravity Equation 4, derived in Section 3,λji,z can be expressed as follows,

λji,z =Tj,k

(wjτji,k

)−θz

∑Nn=1 Tn,k (wnτni,k)−θz

, z ∈ Zk. (11)

where θz = γk (εz − 1) denotes the segment-level trade elasticity, and Tj,k ≡Aj,k Mj,k. The implicit assumption underlying the above equation is that tech-nology parameters are segment-neutral, i.e., Aj,z = Aj,kAz. Correspondingly,Az drops out of the gravity equation and Tj,k ≡ Aj,k Mj,k can be treated asan industry×exporter fixed effect that is estimated. Considering the above,λz ≡

[λji,z

]is fully determined as a function of the segment-level trade elas-

ticity, θz, country-level wages, w ≡[wj], the vector of exporter fixed effects,

T k ≡[Tj,k], and the industry-wide matrix of variable trade costs τk ≡

[τji,k].

36

If one were to treat the elements of τk as free-moving parameters, the estimationwill be over-identified, as the matrix of trade flows, Xk =

[Xji,k

], can be perfectly

matched by freely choosing the elements of τk. So, in line with the literature, Ihandle the over-identification problem by imposing the following parametricrestriction on the bilateral trade costs.

R3. The iceberg trade costs assume the following parametrization:

τji,k = βk · βborder,k · βlang,k · βagreement,k(Distji

)βdist,k ,

where Distji denotes the distance (in thousands of kilometers) between countries j and i.βborder, βlang, βagreement are respectively “one” if countries j and i do not have a commonborder, common language, and trade agreement and an estimated parameter otherwise.

An analogue of the above parameterization, which imposes symmetry in tradecosts, underlies many applications including Anderson and Van Wincoop (2003),Fieler (2011), and Caliendo and Parro (2014).32 Based on R3, the matrix oftrade costs in industry k is fully characterized by a vector of parameters, βk ≡

βk, βborder,k, βlang,k, βagreement,k, βdist,k

, plus data on distance, trade agreements,common-language and borders, which I henceforth refer to as, D. Correspond-ingly, given Equation 11, the matrix of trade shares in segment z ∈ Zk can befully calculated as function of w and D, and estimated parameters T k, βk, andθz; namely, λz = λ (θz, βk,T k; w, D).

Subsequently, the entire matrix of industry-level trade flows can be computed asa function of free-moving parameters θH, θL, T k, βk, and ek, plus data on wage,population size, geo-political characteristics, and industry-level expenditureshares (namely, w, L, D, αk) as follows:

Xji,k = Xji,k (θH, θL, ek,T k, βk; αk, w, L, D)

= ∑z=Zk

Tj,k(wjτji,k (βk; D)

)−θz

∑Nn=1 Tn,k (wnτni,k (βk; D))−θzei,zαi,kwiLi (12)

The above estimation is subject to a basic identification challenge, which iswell known in the structural gravity literature. That is, the effect of both θH

32An alternative approach is to allow for reduced-form asymmetries in trade costs as inWaugh (2010). However, as noted by Waugh (2010), such asymmetries “may be reduced-formrepresentations of equilibrium responses to the fundamentals faced by agents.” As I willargue shortly, and in-line with the quoted remark, even under R2 the present model featuresasymmetries in real trade costs that arise due to equilibrium responses.

37

and θL on trade values cannot be separately identified from that of βk. Thestandard solution to this problem is to set the trade elasticity to a value, whichis externally estimated with auxiliary data. This solution is, however, not fullyapplicable here, given that the trade elasticity is estimable only up to the samelevel of aggregation at which multilateral trade flows are reported. To handlethis issue, I impose the following restriction that trade elasticities estimated withindustry-level data are a trade-weighted average of the segment-level elasticities.

R4. If θk is a trade elasticity estimated using industry-level trade data, then

θk =∑j,i ∑z∈Zk

θzXji,z

∑j,i ∑z∈ZkXji,z

,

where θz is the unobservable segment-level trade elasticity.

To elaborate on Restriction R4, consider my main dataset that reports tradeflows at the level of WIOD industries. Caliendo and Parro (2014) merge theWIOD data with industry-level tariff data to estimate the trade elasticity, θk, foreach WIOD industry. R4 allows me to relate their estimated elasticity, θk, tosegment-level elasticities, θH and θL, for each industry. In other words, per R4,I can take the externally-estimated θk and estimate a spread, ρk ≡ θL/θH, touniquely determine both θH and θL as follows:

θH(ρk, XH, XL; θk

)=

(∑j,i ∑z=H,L Xji,z

∑j,i Xji,H+ρ−1 ∑j,i Xji,L

)θk

θL(ρk, XH, XL; θk

)=(

∑j,i ∑z=H,L Xji,zρ ∑j,i Xji,H+∑j,i Xji,L

)θk

. (13)

Importantly, unlike the trade elasticity levels, the spread ρk ≡ θL/θH can beseparately identified from βk.33

5.1.2 The Estimation Problem

Given parametric restrictions R1-R4; data on wage and population size, wand L, geo-political variables, D, industry-level expenditure shares, αk, andrevenue shares, rk =

[rj,k]; we can estimate the vector of parameters, Θk =

ρk, ek,T k, βk, separately for each industry to match the factual matrix ofindustry-level trade values, XDk =

[XDji,k

]. The estimation problem can be

33See Fieler (2011) for a thorough discussion on the how the trade elasticity spread, ρk, isseparately identified from the trade cost parameters, βk.

38

formally stated as follows:

minΘk

N∑j=1

∑i 6=j

(ln XDji,k − ln Xji,k (Θk; αk, w, L, D)

)2

s.t.

Xji,k = ∑z=H,L λji,zei,zαi,kwiLi ∀i, j

λji,z = Tj,k(wjτji,k

)−θz /(

∑Nn=1 Tn,k (wnτni,k)−θz)

∀i, j; z = H,L

τji,k = βk · βborder,k · βlang,k · βagreement,k(Distji

)βdist,k ∀i, j

θz = θz(ρk, XH, XL; θk

)z = H,L

∑Ni=1 Xji,k = rj,kwjLj (LMC); ∀j

,

where the last constraint corresponds to the equilibrium labor market clearingcondition (LMC), and θk (.) is described by 13. The above estimator is a basicextension of the structural gravity estimation in Anderson and Van Wincoop(2003). More specifically, the structural gravity estimation in Anderson andVan Wincoop (2003) corresponds to a restricted version of the above estimatorthat imposes ρk ≡ θL/θH = 1. Following Anderson and Van Wincoop (2003),the non-linear least square (NLLS) estimator, specified above, is unbiased ifε ≡ XD − X is uncorrelated with the derivative of Xji,k (Θk; αk, w, L, D) withrespect to αk, w, L, and D, which is the case if ε represents measurement errors.

As noted earlier, I run the above estimation using two different data-sets. First, Iestimate the model with country-level trade data for a sample of 100 countries.The country-level estimation treats each economy as one integrated industry.Second, I estimate the model separately for 15 traded WIOD industries usingindustry-level bilateral trade and production data for 32 major economies. Theformer estimation is used to study the implications of the model for interna-tional TFP differences. The latter estimation is used to quantify the gains fromwithin-industry specialization—Appendix D provides further details about eachestimation.

Finally, to conduct the above estimation, I borrow trade elasticity estimates(namely, θk) from the literature. For the industry-level estimation conductedon the WIOD sample, I take the elasticities from Caliendo and Parro (2014),with details provided in Table 9. For the country-level estimation, where eachcountry is treated as one integrated industry, I set θ = 4 as in Anderson andVan Wincoop (2003). This choice according the meta-analysis in Head and Mayer(2014), approximates the median elasticity estimated in the existing literature.

39

In-Sample Fit. Before moving forward, a brief discussion regarding the in-sample fit of the model is in order (a more thorough discussion is also providedin Appendix D). I center the discussion here around the model estimated usingcountry-level data, noting that similar arguments apply to the industry-levelestimation. The country-level estimation (where N = 100) fits the model to100× (100− 1) = 9, 900 data points on bilateral trade values.34 Figure 1 displaysthe in-sample fit of the estimated model. Table 8 (in the appendix) also reports asummary of the main estimated parameters and compares them those attainedunder the standard structural gravity estimation à la Anderson and Van Wincoop(2003). A notable contrast between the two estimations is that the main modelexhibits an R2 = 0.65, which is significantly higher than that of the standardstructural gravity estimation.35

As discussed in Appendix D, the superior in-sample fit of the main model isdue to its ability to match (i) the low volume of trade between similar tradingpartners (South-South and North-North trade) as well as (ii) the high-volumeof trade between dissimilar partners (North-South trade). The standard gravityestimation, by comparison, has difficulty matching the differential levels ofsimilar-similar and dissimilar-dissimilar trade (see Figure 2 in the appendix).This feature of the present model is comparable to that of Fieler (2011).

Out-of-Sample Prediction with respect to Markups. The initial motivationbehind my theory where two facts: that export price and markup levels increasewith the exporting economy’s (i) income per capita, and (ii) distance to globalmarkets. Encouragingly, the estimated model reproduces theses out-of-samplefacts relatively well. To demonstrate this, I suppose the underlying demandsystem is CES, so that markups are constant within each segment. Based on thisassumption, I can easily compute the model-implied average export markup foreach country j in the sample, labeling it mj. After calculating the export markuplevels, I run the following regression,

ln mj = 0.07(0.005)

ln GDP p/cj + 0.32(0.006)

ln Distji + εj,

34The number of estimated parameters in the country-level case is 206, which includes 100exporter fixed effects (labeled T ), 100 country-level expenditure shares on segmentH (labeled,e), 6 trade cost parameters (labeled β), plus an across-segment trade elasticity spread (labeled ρ).

35Another way of enhancing the in-sample fit of the structural gravity model is to relax thesymmetric trade cost assumption. In that case, trade is no longer bilaterally balanced andthe exporter and importer fixed effects need not to be equal. In fact, with asymmetric tradecosts, a reduced-form gravity estimation that uses a PPML estimator becomes isomorphic to thestructural gravity estimation (see Head and Mayer (2014)).

40

Figure 1: Fit of the Model Estimated with Country-Level Data

5

10

15

20

25

log T

rade

Val

ue

(Mod

el)

0 5 10 15 20 25

log Trade Value (Data)

which implies that predicted export markup level increases significantly withboth income per capita, GDP p/cj, and remoteness, Distji. In comparison, thestandard gravity model that does not admit low- and high-markup segmentswithin industries, predicts a uniform markup across all exporters.

5.2 The Gains from Within-Industry Specialization

In this section, I use the model estimated with industry-level data to compute thegains from within-industry specialization. As shown in Appendix C, the overallgains from trade for country i can be calculated using the following formula:36

GTi = 1−K∏k=1

∏z∈Zk

(Si,kλii,z)ei,zαi,k/θz , (14)

where λii,z denotes the share of country i’s expenditure on domestic varieties insegment z, and Si,k ≡ αi,k/ri,k

[(∑z∈Zk

ei,z/εz)

/(∑z∈Zk

ri,z/εz)]

is a term that

36The above formula implicitly assumes that the within-segment demand is CES and markupsare constant. Nonetheless, as it will become clear, variable markups are inconsequential to theinsights presented hereafter.

41

accounts for the scale-driven gains—as before, ri,k is used to denote the share ofcountry i’s output generated in industry k and, correspondingly, ri,z denotes the(within-industry) fraction of output generated in segment z ∈ Zk. The aboveequation is a simple extension of the celebrated Arkolakis et al. (2012) (ACR,hereafter) formula. The challenge in evaluating Equation 14 is that it requiresdata on segment-level variables, λii,z, ri,z, and θz. The estimation outlined inthe previous section, identifies these exact variables from industry-level tradeand production data as well as industry-level trade elasticity estimates (fromCaliendo and Parro (2014)). Since among the estimated parameter values, thesegment-level elasticities, θH and θL, are especially key to Equation 14, Table 9explicitly reports them for each of the WIOD industries.

Equation 14 determines the overall gains from trade, which include the tradi-tional ACR-type gains plus the gains from within-industry specialization. Hence,to determine the pure gains from within-industry specialization, I need to purgeGTi from the ACR-driven gains. To pin down the ACR-driven gains, one canshut down heterogeneity within industries to eliminate within-industry special-ization across low- and high-θ segments. Doing so, the gains from trade will bedriven solely by traditional forces, and following Costinot and Rodríguez-Clare(2014) will be given by

GTACRi = 1−

K∏k=1

(SACR

i,k λii,k

)αi,k/θk,

with SACRi,k ≡ αi,k/ri,k accounting for scale effects in the traditional ACR class of

models. To evaluate the above equation, I take an identical approach to that ofCostinot and Rodríguez-Clare (2014), which is to use industry-level data on λii,k,ri,k, and αi,k from the WIOD, plus trade elasticity estimates, θk, from Caliendoand Parro (2014). After computing GTi and GTACR

i , I calculate the pure gainsfrom within-industry specialization for every country i as follows:

Gains from specialization = GTi − GTACRi .

Table 7 reports the gains from specialization, along with the overall and ACR-driven gains from trade. In summary, the main model featuring within-industryspecialization predicts gains from trade that are, on average, 46% larger thanthose implied by the ACR formula (20.4% versus 14% increase in real GDP).Based on these number, one can deduce that within-industry specialization,

42

alone, increases the real GDP by around 6.4% for the average economy.

The gains from specialization are, however, quite heterogeneous across countries.High-wage or remote economies like Germany, France, and Australia gain signif-icantly more as they specialize in high scale-intensive segments, where returns tospecialization are higher. In comparison, the pure gains from specialization areconsiderably smaller (an even negative) for developing economies like Mexicoand Indonesia, as they specialize in low-scale intensive segments where returnsto specialization are relatively low.

5.3 International Specialization and TFP Differences

Beyond the gains from trade, the present model sheds new light on the profoundgap in the standard of living across rich and poor countries. As noted by Jones(2011), “by the end of the 20th century, per capita income in the United States wasmore than 50 times higher than per capita income in Ethiopia and Tanzania. Dispersionacross the 95th-5th percentiles of countries was more than a factor of 32.” There is anabundance of theories that seek to explain these persistent gaps.37 The generaltheme of such theories is to identify multiplier effects that amplify cross-countryincome/TFP differences.

The theory of international specialization presented here identifies a possiblynew multiplier effect. To demonstrate this, consider the special case of con-stant markups presented in Section 3.2. Let Li,k denote the number of work-ers engaged in industry k; free entry entails that country i will host a mass`i,k ≡

(∑z∈Zk

ri,z/εz)

Li,k/ f ke of local firms in that industry. Consequently, the

real income per worker in country i will be given by (see Appendix C),38

Wi = Ai

(K∏k=1

∏z∈Zk

`αi,kei,z/θzi,k

)︸ ︷︷ ︸

scale effects

(K∏k=1

∏z∈Zk

λ−αi,kei,z/θzii,z

)︸ ︷︷ ︸

trade openness

, (15)

where Ai, the fundamental TFP of country i, reflects its absolute advantage inproducing high-quality output; `i,k reflects the effective scale of country i inindustry k; and θz = γk/ (ψz − 1) is the segment-level trade elasticity, which

37See Klenow and Rodriguez-Clare (1997); Prescott (1998); Hall and Jones (1999); Parente andPrescott (1999); Acemoglu et al. (2000); Parente and Prescott (2000); Caselli (2005); Jones (2011).

38In the above expression Ai ≡ ς ∏Kk=1 ∏z∈ZkAei,z/γk(1−σz)

i,z , where ς encapsulates a combina-tion of constant parameters. Also, the equation assumes firms are symmetric, but can be triviallyextended to account for firm heterogeneity and selection effects—see Kucheryavyy et al. (2016).

43

44

Table 7: The gains from within-industry specialization

Gains from trade

CountryGDP

(US=1)Population

(US=1)Remoteness

(US=1)ACR Main Model

Gains fromSpecialization

AUS 0.07 0.07 1.47 3.7% 16.7% 12.9%AUT 0.03 0.03 0.41 30.5% 33.7% 3.1%BEL 0.04 0.04 0.57 32.4% 57.6% 25.3%BRA 0.11 0.63 0.74 4.3% 9.5% 5.2%CAN 0.10 0.11 0.98 15.3% 25.2% 9.9%CHN 0.31 4.36 0.59 4.0% 8.3% 4.3%CZE 0.02 0.03 0.40 21.2% 19.0% -2.2%DEU 0.26 0.27 0.53 17.6% 32.7% 15.1%DNK 0.02 0.02 0.52 24.8% 25.1% 0.3%ESP 0.11 0.15 0.54 9.5% 24.3% 14.8%FIN 0.02 0.02 0.47 10.5% 10.3% -0.3%FRA 0.20 0.21 0.49 11.1% 23.4% 12.3%GBR 0.19 0.20 0.62 11.7% 21.3% 9.6%GRC 0.02 0.04 0.53 4.7% 9.1% 4.4%HUN 0.01 0.03 0.46 31.2% 23.9% -7.3%IDN 0.03 0.77 0.72 4.0% 6.4% 2.4%IND 0.08 3.86 0.64 4.3% 16.7% 12.4%IRL 0.02 0.01 0.53 14.2% 14.7% 0.5%ITA 0.16 0.19 0.45 9.2% 21.6% 12.4%JPN 0.33 0.42 0.53 3.7% 11.4% 7.7%KOR 0.07 0.16 0.63 8.6% 14.3% 5.7%MEX 0.07 0.38 0.80 12.1% 15.6% 3.5%NLD 0.06 0.05 0.73 23.1% 43.4% 20.3%POL 0.04 0.13 0.40 19.7% 28.0% 8.3%PRT 0.02 0.03 0.48 20.6% 15.6% -5.0%ROM 0.01 0.07 0.36 12.7% 12.5% -0.2%RUS 0.11 0.47 0.65 0.9% 19.4% 18.5%SVK 0.01 0.02 0.52 23.6% 16.2% -7.4%SVN 0.00 0.01 0.55 39.3% 24.5% -14.8%SWE 0.03 0.03 0.47 14.5% 19.4% 4.9%TUR 0.05 0.23 0.51 13.3% 23.8% 10.6%TWN 0.03 0.08 0.98 9.9% 14.6% 4.7%USA 1.00 1.00 1.00 3.8% 8.6% 4.8%RoW 0.61 8.00 2.49 7.3% 14.8% 7.5%

is inversely related to the segment-level scale elasticity ψz = εz/ (εz − 1) (asdefined in Section 3). Aside from the fundamental TFP, Ai, the above equationstates that real income depends on the scale-driven gains from specialization(first parenthesis) and trade openness (second parenthesis).

Given Proposition 1, the scale-driven term operates as a TFP multiplier. Toelaborate, note that all else equal, high-A countries pay higher equilibriumwages, which is easily verifiable using the balanced trade condition. GivenProposition 1, the higher wage induces high-A countries to specialize in low-εz segments, which leads to a higher `i,k. Relatedly, high-A economies alsospecialize in industries that exhibit on average a higher scale elasticity. To-gether, these effects multiply the TFP differences, whereby the scale-driven term,

∏Kk=1 ∏z∈Zk`

αi,kei,z/θzi,k , is systematically larger for high-Ai economies.

To calculate the contribution of specialization-driven scale effects to income differ-ences, note that the scale-driven component in Equation 15 can be decomposedinto (i) a standard size-driven component, and (ii) a specialization-driven com-ponent as follows

K∏k=1

∏z∈Zk

`αi,kei,z/θzi,k =

(K∏k=1

Lαi,k/θki,k

)︸ ︷︷ ︸

size-driven

[(K∏k=1

∏z∈Zk

`αi,kei,z/θzi,k

)/

(K∏k=1

Lαi,k/θki,k

)]︸ ︷︷ ︸

specialization-driven

,

where θk is the industry-level trade elasticity that is itself a weighted average ofthe segment-level trade elasticities per R4. Note that the size-driven componentis relatively well-known, as it is also present in the standard ACR class of models.But the specialization-driven component is unique to the present model, andabsent (or equal to one for all countries) in the ACR class of models.

Considering the above decomposition, we can appeal to the estimated model tocalculate the counterfactual real income of each country i, net of specialization-driven scale effects. Doing so using the model fitted to country-level tradedata for 100 economies, implies that specialization across low- and high-scaleintensive segments explains around 37.3% of the cross-national heterogeneity inreal income levels, as measured by var (log Wi).39

39These results are related to Bento (2014), who shows that accounting for heterogeneity withinindustries increases the elasticity of welfare with respect to entry costs.

45

6 Concluding Remarks

This paper presented an alternative view of within-industry specialization; thethesis of which is that, even in the absence of Ricardian or factor-driven compar-ative advantage, high-wage and remote economies have a tendency to specializein high market power segments of industries. I argued that this patterns ofspecialization (i) explains the cross-national and spatial variation in export pricelevels, and (ii) delivers macro-level implications that are distinct from traditionaltheories of within-industry quality specialization. Some of these macro-levelimplications were discussed thoroughly in this paper, but several others meritfurther attention.

First, the present theory can shed light on a recently-circulating thesis thatmarket power has been rising in the US economy (De Loecker and Eeckhout(2017)). Many factors can be responsible for this rise. From the perspective ofthe present theory, this rise can reflect a trade-induced hyper-specialization ofUS-based firms in high-market power segments of industries. An empiricalassessment of this hypothesis presents a promising avenue for future research.

Second, the present paper raises some old questions about industrial policyin an open economy. First, in the present framework, the labor allocation inhigh market power segments is inefficiently low. This creates a scope for policyintervention, which is absent in the standard heterogeneous firm models of tradeand geography. Additionally, the differential degrees of scale economies acrosssegments creates a scope for industrial targeting, whereby countries can improvetheir terms-of-trade by heavily protecting the high-returns to scale segments ofeach industry.

References

Acemoglu, D., S. Johnson, and J. A. Robinson (2000). The colonial originsof comparative development: An empirical investigation. Technical report,National bureau of economic research.

Alessandria, G. and J. P. Kaboski (2011). Pricing-to-market and the failure ofabsolute ppp. American Economic Journal: Macroeconomics 3(1), 91–127.

46

Anderson, J. E. and E. Van Wincoop (2003). Gravity with gravitas: A solution tothe border puzzle. The American Economic Review 93(1), 170–192.

Anderson, T. W., H. Rubin, et al. (1949). Estimation of the parameters of asingle equation in a complete system of stochastic equations. The Annals ofMathematical Statistics 20(1), 46–63.

Arkolakis, C., A. Costinot, D. Donaldson, and A. Rodríguez-Clare (2018). Theelusive pro-competitive effects of trade. The Review of Economic Studies.

Arkolakis, C., A. Costinot, and A. Rodriguez (2012). Clare, 2012, new trademodels, same old gains. American Economic Review 102(1), 94.

Baldwin, R. and J. Harrigan (2011). Zeros, quality, and space: Trade theory andtrade evidence. American Economic Journal: Microeconomics 3(2), 60–88.

Baldwin, R. E. and T. Ito (2008). Quality competition versus price competitiongoods: An empirical classification. Technical report, National Bureau ofEconomic Research.

Bento, P. (2014). Niche firms, mass markets, and income across countries: Ac-counting for the impact of entry costs. Journal of Economic Dynamics andControl 48, 147–158.

Berry, S., J. Levinsohn, and A. Pakes (1995). Automobile prices in marketequilibrium. Econometrica: Journal of the Econometric Society, 841–890.

Bertoletti, P. and F. Etro (2017). Monopolistic competition when income matters.The Economic Journal 127(603), 1217–1243.

Bertoletti, P., F. Etro, and I. Simonovska (2018). International trade with indirectadditivity. American Economic Journal: Microeconomics 10(2), 1–57.

Bils, M. J. and P. Klenow (2001). Quantifying quality growth. American EconomicReview 91(4), 1006–1030.

Brandt, L., J. Van Biesebroeck, L. Wang, and Y. Zhang (2017, September). Wtoaccession and performance of chinese manufacturing firms. American EconomicReview 107(9), 2784–2820.

Broda, C. and D. E. Weinstein (2006). Globalization and the gains from variety.The Quarterly Journal of Economics 121(2), 541–585.

47

Brooks, W. and P. Pujolas (2016). Nonlinear gravity.

Caliendo, L. and F. Parro (2014). Estimates of the trade and welfare effects ofnafta. The Review of Economic Studies, rdu035.

Campa, J. and L. S. Goldberg (1995). Investment in manufacturing, exchangerates and external exposure. Journal of International Economics 38(3-4), 297–320.

Caselli, F. (2005). Accounting for cross-country income differences. Handbook ofeconomic growth 1, 679–741.

Chaney, T. (2008). Distorted gravity: the intensive and extensive margins ofinternational trade. The American Economic Review 98(4), 1707–1721.

Choi, Y. C., D. Hummels, and C. Xiang (2009). Explaining import quality: Therole of the income distribution. Journal of International Economics 78(2), 293–303.

Coibion, O., L. Einav, and J. C. Hallak (2007). Equilibrium demand elasticitiesacross quality segments. International Journal of Industrial Organization 25(1),13–30.

Comtrade, U. (2010). United nations commodity trade statistics database. URL:http://comtrade. un. org.

Costinot, A. and A. Rodríguez-Clare (2014). Trade theory with numbers: Quanti-fying the consequences of globalization. Handbook of International Economics 4,197.

Cragg, J. G. and S. G. Donald (1993). Testing identifiability and specification ininstrumental variable models. Econometric Theory 9(2), 222–240.

Crozet, M., K. Head, and T. Mayer (2012). Quality sorting and trade: Firm-levelevidence for french wine. The Review of Economic Studies 79(2), 609–644.

De Blas, B. and K. N. Russ (2015). Understanding markups in the open economy.American Economic Journal: Macroeconomics 7(2), 157–180.

De Loecker, J. and J. Eeckhout (2017). The rise of market power and the macroeco-nomic implications. Technical report, National Bureau of Economic Research.

De Loecker, J. and J. Eeckhout (2018). Global market power. Technical report,National Bureau of Economic Research.

48

De Loecker, J., C. Fuss, and J. Van Biesebroeck (2014). International competitionand firm performance: Evidence from belgium. Technical report, WorkingPaper Research.

De Loecker, J., P. K. Goldberg, A. K. Khandelwal, and N. Pavcnik (2016). Prices,markups, and trade reform. Econometrica 84(2), 445–510.

De Sousa, J., T. Mayer, and S. Zignago (2012). Market access in global andregional trade. Regional Science and Urban Economics 42(6), 1037–1052.

Diez, F., D. Leigh, S. Tambunlertchai, et al. (2018). Global market power and itsmacroeconomic implications. Technical report, International Monetary Fund.

Dingel, J. I. (2016). The determinants of quality specialization. The Review ofEconomic Studies 84(4), 1551–1582.

Eaton, J., M. Eslava, M. Kugler, and J. Tybout (2010). A search and learningmodel of export dynamics.(penn state university, unpublished).

Eaton, J., S. Kortum, and F. Kramarz (2011). An anatomy of international trade:Evidence from french firms. Econometrica 79(5), 1453–1498.

Edmond, C., V. Midrigan, and D. Y. Xu (2015). Competition, markups, andthe gains from international trade. The American Economic Review 105(10),3183–3221.

Erkel-Rousse, H. and D. Mirza (2002). Import price elasticities: reconsideringthe evidence. Canadian Journal of Economics 35(2), 282–306.

Fajgelbaum, P., G. M. Grossman, and E. Helpman (2011). kincome distribution.Product Quality, and International Trade, lJournal of Political Economy 118(4), 721.

Fally, T. (2018). Integrability and generalized separability. Technical report,National Bureau of Economic Research.

Fally, T. (2019). Generalized separability and the gains from trade. EconomicsLetters 178, 8–12.

Fan, H., Y. A. Li, and S. R. Yeaple (2015). Trade liberalization, quality, and exportprices. Review of Economics and Statistics (0).

Feenstra, R. C. and J. Romalis (2014). International prices and endogenousquality. The Quarterly Journal of Economics 129(2), 477–527.

49

Fieler, A. C. (2011). Nonhomotheticity and bilateral trade: evidence and aquantitative explanation. Econometrica 79(4), 1069–1101.

Flach, L. (2017). A note on the isomorphism of heterogeneous firms models.Economics Letters 155, 24–27.

Fornell, C., M. D. Johnson, E. W. Anderson, J. Cha, and B. E. Bryant (1996).The american customer satisfaction index: nature, purpose, and findings. theJournal of Marketing, 7–18.

Gaulier, G. and S. Zignago (2010). Baci: international trade database at theproduct-level (the 1994-2007 version).

Goldberg, P. K. (1995). Product differentiation and oligopoly in internationalmarkets: The case of the us automobile industry. Econometrica: Journal of theEconometric Society, 891–951.

Grossman, G. M. and E. Helpman (1991). Quality ladders in the theory of growth.The Review of Economic Studies 58(1), 43–61.

Hall, R. E. and C. I. Jones (1999). Why do some countries produce so muchmore output per worker than others? The quarterly journal of economics 114(1),83–116.

Hallak, J. C. (2006). Product quality and the direction of trade. Journal ofInternational Economics 68(1), 238–265.

Hallak, J. C. and J. Sivadasan (2013). Product and process productivity: Implica-tions for quality choice and conditional exporter premia. Journal of InternationalEconomics 91(1), 53–67.

Hanoch, G. (1975). The elasticity of scale and the shape of average costs. TheAmerican Economic Review 65(3), 492–497.

Hausman, J., G. Leonard, and J. D. Zona (1994). Competitive analysis withdifferenciated products. Annales d’Economie et de Statistique, 159–180.

Head, K. and T. Mayer (2014). Gravity equations: Workhorse, toolkit, andcookbook. Handbook of International Economics 4, 131.

Head, K., T. Mayer, and J. Ries (2010). The erosion of colonial trade linkagesafter independence. Journal of International Economics 81(1), 1–14.

50

Helpman, E. (1984). Increasing returns, imperfect markets, and trade theory.Handbook of international economics 1, 325–365.

Hertel, T., D. Hummels, M. Ivanic, and R. Keeney (2007). How confident canwe be of cge-based assessments of free trade agreements? Economic Mod-elling 24(4), 611–635.

Holmes, T. J., W.-T. Hsu, and S. Lee (2014). Allocative efficiency, mark-ups, andthe welfare gains from trade. Journal of International Economics 94(2), 195–206.

Holmes, T. J. and J. J. Stevens (2014). An alternative theory of the plant sizedistribution, with geography and intra-and international trade. Journal ofPolitical Economy 122(2), 369–421.

Hottman, C. J., S. J. Redding, and D. E. Weinstein (2016). Quantifying the sourcesof firm heterogeneity. The Quarterly Journal of Economics 131(3), 1291–1364.

Hummels, D. (2001). Toward a geography of trade costs.

Hummels, D. and P. J. Klenow (2005). 9the variety and quality of a nation sexports9. The American Economic Review 95(3).

Hummels, D. and V. Lugovskyy (2009). International pricing in a generalizedmodel of ideal variety. Journal of Money, Credit and Banking 41(s1), 3–33.

Hummels, D. and A. Skiba (2004). Shipping the good apples out? an empiricalconfirmation of the alchian-allen conjecture. Journal of Political Economy 112(6).

Imbs, J. and I. Mejean (2015). Elasticity optimism. American Economic Journal:Macroeconomics 7(3), 43–83.

Johnson, R. C. (2012). Trade and prices with heterogeneous firms. Journal ofInternational Economics 86(1), 43–56.

Jones, C. I. (2011). Intermediate goods and weak links in the theory of economicdevelopment. American Economic Journal: Macroeconomics 3(2), 1–28.

Khandelwal, A. (2010). The long and short (of) quality ladders. The Review ofEconomic Studies 77(4), 1450–1476.

Kimball, M. S. (1995). The quantitative analytics of the basic neomonetaristmodel. Technical report, National Bureau of Economic Research.

51

Kleibergen, F. and R. Paap (2006). Generalized reduced rank tests using thesingular value decomposition. Journal of econometrics 133(1), 97–126.

Klenow, P. J. and A. Rodriguez-Clare (1997). The neoclassical revival in growtheconomics: Has it gone too far? NBER macroeconomics annual 12, 73–103.

Klenow, P. J. and J. L. Willis (2016). Real rigidities and nominal price changes.Economica 83(331), 443–472.

Kraay, A. and J. Ventura (2007). Comparative advantage and the cross-section ofbusiness cycles. Journal of the European Economic Association 5(6), 1300–1333.

Kucheryavyy, K., G. Lyn, and A. Rodríguez-Clare (2016). Grounded by gravity:A well-behaved trade model with industry-level economies of scale. Technicalreport, National Bureau of Economic Research.

Laffont, J.-J. and J. Tirole (1993). A theory of incentives in procurement and regulation.MIT press.

Lashkaripour, A. and V. Lugovskyy (2018). Scale economies and the structure oftrade and industrial policy.

Levchenko, A. A. and J. Zhang (2014). Ricardian productivity differences andthe gains from trade. European Economic Review 65, 45–65.

Lugovskyy, V. and A. Skiba (2014). How geography affects quality. Journal ofDevelopment Economics (Forthcoming).

Matsuyama, K. and P. Ushchev (2017). Beyond ces: Three alternative cases offlexible homothetic demand systems.

Mayer, T. and S. Zignago (2011). Notes on cepii’s distances measures: Thegeodist database.

McCalman, P. and A. Spearot (2013). Why trucks jump: Offshoring and productcharacteristics. Journal of International Economics 91(1), 82–95.

Melitz, M. J. and G. I. Ottaviano (2008). Market size, trade, and productivity. Thereview of economic studies 75(1), 295–316.

Melitz, M. J. and S. J. Redding (2014). Heterogeneous firms and trade. InHandbook of international economics, Volume 4, pp. 1–54. Elsevier.

52

Nicita, A. and M. Olarreaga (2007). Trade, production, and protection database,1976–2004. The World Bank Economic Review 21(1), 165–171.

Ossa, R. (2015). Why trade matters after all. Journal of International Economics 97(2),266–277.

Ottaviano, G., T. Tabuchi, and J.-F. Thisse (2002). Agglomeration and traderevisited. International Economic Review 43(2), 409–435.

Parente, S. L. and E. C. Prescott (1999). Monopoly rights: A barrier to riches.American Economic Review, 1216–1233.

Parente, S. L. and E. C. Prescott (2000). Barriers to riches. MIT press.

Prescott, E. C. (1998). Lawrence r. klein lecture 1997: Needed: A theory of totalfactor productivity. International economic review, 525–551.

Rodrik, D. (1994). Industrial organization and product quality: Evidence fromsouth korean and taiwanese exports. In Empirical studies of strategic trade policy,pp. 195–210. University of Chicago Press.

Romalis, J. (2007). Nafta’s and cusfta’s impact on international trade. The Reviewof Economics and Statistics 89(3), 416–435.

Schott, P. K. (2004). Across-product versus within-product specialization ininternational trade. The Quarterly Journal of Economics 119(2), 647–678.

Simonovska, I. (2015). Income differences and prices of tradables: Insights froman online retailer. The Review of Economic Studies 82(4), 1612–1656.

Simonovska, I. and M. E. Waugh (2011). The elasticity of trade: Estimates andevidence. Technical report, National Bureau of Economic Research.

Spearot, A. C. (2013). Variable demand elasticities and tariff liberalization. Journalof International Economics 89(1), 26–41.

Stock, J. H. and M. Yogo (2002). Testing for weak instruments in linear ivregression.

Sutton, J. (2007). Quality, trade and the moving window: The globalisationprocess. The Economic Journal 117(524).

Sutton, J. and D. Trefler (2014). Capabilities, wealth and trade. Journal of PoliticalEconomy Forthcoming.

53

Timmer, M., A. A. Erumban, R. Gouma, B. Los, U. Temurshoev, G. J. de Vries, I.-a.Arto, V. A. A. Genty, F. Neuwahl, J. Francois, et al. (2012). The world input-output database (wiod): contents, sources and methods. Technical report,Institue for International and Development Economics.

Verhoogen, E. A. (2008). Trade, quality upgrading, and wage inequality inthe mexican manufacturing sector. The Quarterly Journal of Economics 123(2),489–530.

Waugh, M. (2010). International trade and income differences. The AmericanEconomic Review 100(5), 2093–2124.

World-Bank (2012). World Development Indicators 2012. World Bank-free PDF.

A Description of Data Used in Section 2

The data used to calculate export unit prices is from the COMTRADE-BACI

database compiled by the CEPII. This is the most comprehensive publicly-available data that permits the construction of export unit prices. The dataoriginates from the United Nations COMTRADE database. The BACI variationof the data uses a harmonization methodology to reconcile mirror flows, whichprovides more complete geographical coverage than if only a single direction ofCOMTRADE statistics were to be used—see Gaulier and Zignago (2010) for a de-scription the BACI approach to harmonization. The COMTRADE-BACI databaseprovides physical quantities (only in units of weight) and values of annual bi-lateral trade flows by 6-digit HS product categories from 2003 to 2015. For 224countries Head et al. (2010) report matching data for GDP, distance, and popu-lation size. The country-level production data is taken from the TRADEPROD

database compiled by the CEPII. This dataset is built on the Trade, Productionand Protection database made available by the World Bank (Nicita and Olar-reaga (2007)). It covers 26 industrial sectors in the ISIC Revision 2 from 1980 to2006—see De Sousa et al. (2012) for more details.

B General Cost Function

In the interest of exposition, the main model abstracted from intra-national costheterogeneity across firms within a segment. However, given the weak isomor-

54

phism between quality and productivity, the model can be trivially amended toalso accommodate cost heterogeneity across firms. To this end, suppose firmsare heterogeneous in their unit labor cost, az(ϕ), which increases with outputquality at elasticity, κ—i.e., ∂ ln az(ϕ)/∂ ln ϕ = κ. Considering this specification,the effective marginal cost facing a firm becomes

cz(

ϕ; τji,k, wj)= τji,kazwj ϕ

κ+ρz

ρz−1 .

Expectedly, under κ = 0, the above expression reduces to the one presented inSection 3. The above marginal cost function can be reformulated in terms of anaugmented degree of quality intensity, ρz ≡ 1− 1−ρz

1−κ(1−ρz), as follows

cz(

ϕ; τji,k, wj)= τji,kwj ϕ

ρzρz−1 .

If 1 + κ < 1/ (1− ρz), then (i) ρz < 1, and (ii) ρz is strictly increasing in ρz. Thatbeing the case, all the results presented in the paper follow qualitatively in thismore general setup, but have to be re-formulated in terms of ρz instead of ρz.For example, the gravity equation 4 will assume the following formulation,

Xji,z =Aj,zNj,k

(τji,kwj

)γk

(1− 1

ρz

)

∑Nn=1An,zNn,k (τni,kwn)γk

(1− 1

ρz

) ei,zαi,kYi,

which immediately implies Lemma 1. That is, high-w and high-τ economies havea revealed comparative advantage in high-ρ segments, which are also the high-ρsegments, by construction. The assumption that 1 + κ < 1/ (1− ρz) ensuresthat a higher output quality does not increase the production cost so much thatit puts the high-quality firms at a disadvantage—a very similar assumptionunderlies Baldwin and Harrigan’s (2011) quality-sorting model.

C Proofs and Derivations

Proof of Lemma 2. The distribution of export markups from country j to marketi cane be defined as a function of the bilateral trade costs, τji,k, and country j’swage rate, wj, as follows:

Mi,z(m; wj, τji,k) = Pr

µ(ν) ≤ m | ν ≥ ν∗i,z

55

Note that given the definition of ν ≡ P/c, the market specific cut-off ν∗i,zcan beexpressed as (

Pi,z/τji,kwj) (

ϕ∗ji,z

) ρz1−ρz = ν∗i,z,

where recall that ϕ∗ji,z denotes the lowest quality under which a firm can prof-itably export from country j to i. Considering (i) the above equation for ν∗i,z.

and (ii) that for each firm exporting from country j, ν = ν∗i,z

[ϕ/ϕ∗ji,z

]ρz/1−ρz, the

markup distribution can be stated as

Mi,z(m; wj, τji,k) =

Pr(

µi,z

(ν∗i,z

[ϕ/ϕ∗ji,z

] ρz1−ρz)< m , ϕ < ϕ∗ji,z

)Pr(

ϕ < ϕ∗ji,z

) .

Given A3, dGj,z(ϕ) = γkAj,z ϕ−γk−1, which simplifies the above expression asfollows,

Mji,z(m; wj, τji,k) =

∫ (ν∗i,zµ−1i,z (m))

1−ρzρz ϕ∗ji,z

ϕ∗ji,zdGj,z(ϕ)∫ ∞

ϕ∗ji,zdGj,z(ϕ)

= 1−(

ν∗i,zµ−1i,z (m)

)− 1−ρzρz γk

,

which clearly does not depend on the characteristics of the exporting country, j.

Proof of Proposition 1. To prove Proposition 1, it suffices to show that high-wand high-τ economies specialize in high-trade elasticity segments, where thetrade elasticity is θz = γk (1− 1/ρz). Once this claim is established, Proposition1 follows immediately from A4. First, note that the segment-neutrality of tech-nology parameters entails thatAi,z = Ai,kAz for z ∈ Zk. Plugging this conditioninto Equation 3, the total output of country j in segment z ∈ Zk can be expressedas follows:

Rz(Aj, wj, τ j,k

)= Aj,kNj,kw

γk

(1

ρz−1)

j

N

∑i=1

τγk

(1

ρz−1)

ji,k Yi,z

where the term Yi,z ≡ Azχi,zQi,zYi is introduced to simplify the notation, andτ j,k =

τji,k

. Note that, based on the above equation, national output persegment z ∈ Zk, is uniquely determined by Aj,k, wj, τ j,k, where wj itself is animplicit function of Aj,k and τ j,k. Correspondingly, the share of segment z ∈ Zk

56

in total industry-level output can be expressed solely as a function of wj and τ j,k:

rz(wj, τ j,k

)≡ Rz

∑z′∈ZkRz′

=w−θz

j ∑Ni=1 τ−θzji,k Yi,z

∑z′∈Zkw−θz′

j ∑Ni=1 τ−θz′ji,k Yi,z′

.

That is, the effect ofAj,k on rz is entirely passed through the economy-wide wagerate. Now, consider segmentsH and L ∈ Zk that differ in their trade elasticityθH < θL. An α-fold increase in country j’s wage (holding τ j,k fixed) leads to anαθB−θA-fold increase in rH/rL, where αθL−θH > 1⇐⇒ α > 1. In particular,

rH(αwj, τ j,k

)rL(αwj, τ j,k

) = αθL−θHrH(wj, τ j,k

)rL(wj, τ j,k

) >rH(wj, ατ j,k

)rL(wj, ατ j,k

) (16)

Similarly, an α-fold increase in country j’s remoteness (holding wj fixed40) leadsto an αθL−θH-fold increase in in rH/rL, where αθL−θH > 1 ⇐⇒ α > 1. Inparticular

rH(wj, ατ j,k

)rL(wj, ατ j,k

) = αθL−θHrH(wj, ατ j,k

)rL(wj, ατ j,k

) >rH(wj, ατ j,k

)rL(wj, ατ j,k

) (17)

Together, Inequalities 16 and 17 imply that high-wage and remote economiesspecialize in low-θ segments, which per A4 are also the high market powersegments of the industry.

Welfare Formulas. Here, I derive formulas that characterize the gains fromtrade in the estimated model. To derive the formula for GTi, I follow the samesteps as in Costinot and Rodríguez-Clare (2014). From the gravity Equation 4, Ican deduce the following two expressions for λii,z and Pi,z,λii,z = Ai,zNi,k

(τii,kwj

)−θz / ∑jAj,zNj,k(τji,kwj

)−θz

Pi,z = ςi,z

(∑jAj,zNj,k

(τji,kwj

)θz)1/θz ,

where ςi,z is composed of market-specific constants that are invariant to tradecosts. Combining the above two equations implies that Ci,z = wi/Pi = ςi,z (λii,z/Ai,zNi,k)

−1/θz ;which combined with R1 and R2 yields the following formula for aggregate

40Holding wj fixed entails an increase in Aj to counter the increase in trade costs.

57

welfare

Wi = ∏k

∏z∈Zk

Cαi,kei,zi,z = ∏

k∏

z∈Zk

ςi,z (λii,z/Ai,zNi,k)−αi,kei,z/θz , (18)

Using the familiar hat notation to denote the change in variables when movingfrom the factual to the counter-factual equilibrium, I can arrive at the followingexpression for changes in welfare:

Wi = ∏k

∏z∈Zk

(λii,z/Ni,k

)−αi,kei,z/θz .

To characterize Ni,k in the above equation, I can appeal to the free entry condition(FE), which can be stated as follows in the constant markup case:

wiNi,k f ek = ∑

z∈Zk

Ri,z

εz,

with Ri,z = ∑Nn=1 Xin,z denoting the total revenue generated by economy i insegment z ∈ Zk. Rearranging the above equation and noting thatRi = wiLi, wecan arrive at the following equation describing the mass of firms,

Ni,k =1f ek

(∑Ri,z/Ri,k

εz

) Ri,k

Ri

Ri

wi=

(∑

z∈Zk

ri,z

εz

)ri,kLi,

where, by definition, ri,z ≡ Ri,z/Ri,k and ri,k ≡ Ri,k/Ri. The above equation

immediately implies that Ni,k =

(∑z∈Zk

ri,zεz

)ri,k, which when plugged back into

the formula for Wi, delivers the following:

Wi =K∏k=1

∏z∈Zk

(λii,z/

[∑

z∈Zk

ri,z

εz

]ri,k

)−αi,kei,z/θz

.

Noting that in autarky (i) λii,z = 1; (ii) ri,k = αi,k, and (iii) ∑z∈Zk

ri,zεz

= ∑z∈Zk

ei,zεz

,the above equation implies the following formula for the gains from trade,

GTi = 1− 1/Wi =K∏k=1

∏z∈Zk

(Si,kλii,z)αi,kei,z/θz ,

where Si,k ≡ αi,k/ri,k[(

∑z∈Zkei,z/εz

)/(∑z∈Zk

ri,z/εz)]

. Similarly, the expres-sion for aggregate welfare (Equation 15) can be derived by appealing to Equation

58

18, as follows,

Wi =K∏k=1

∏z∈Zk

ςi,z (λii,z/Ai,zNi,k)−αi,kei,z/θz

=

(ςi

K∏k=1

∏z∈Zk

Aαi,kei,z/θzi,z

)(K∏k=1

∏z∈Zk

`αi,kei,z/θzi,k

)(K∏k=1

∏z∈Zk

λ−αi,kei,z/θzii,z

),

where ςi ≡ ∏k ∏z∈Zkςi,z and `i,k ≡

(∑z∈Zk

ri,z/εz)

Li,k. Replacing θz = γk (εz − 1)and noting (from Section 3) that ψz = εz/ (εz − 1), we will arrive at the welfareformula specified by Equation 15.

D Gravity Estimation Details

This appendix provides details regarding the data employed and parametervalues attained under the country- and industry-level estimations in Section 5.

D.1 Country-Level Estimation

The economy-wide estimation treats each economy as one integrated industry,i.e., K = 1.41 So I present the results here without the industry subscript, k. Toconduct the estimation, I take country-level trade data from the U.N. COMTRADE

database (Comtrade (2010)) for a sample of the 100 largest economies (in termsof real GDP) in year 2000—this sample accounts for more than 95% of worldtrade in that year. I merge this data with (i) data on population size and GDPfrom the World Bank (World-Bank (2012)), and data on geo-distance, commonlanguage, borders, and trade agreements from Mayer and Zignago (2011).

In the country-level implementation, I am estimating 206 structural parametersby fitting the model to (100− 1)× 100 = 9, 900 data points on bilateral tradevalues, namely X =

[Xji]. The estimated parameters are the following:

1. One hundred exporter fixed effects, T =[Tj];

2. One hundred imported fixed effects, e = [ei,H], that characterize the expen-diture shares on segmentH;42

3. Five parameters, vector β, that characterize the iceberg trade costs; and

41This treatment of the economy resembles the approach taken by Fieler (2011).42Once e is known, the expenditure share on segmentL is automatically given by [ei,L] = 1− e.

59

4. One parameter, ρ = θH/θL, describing the spread between the tradeelasticity in segmentsH and L.

Table 8 presents the estimation results. In the interest of space, I only report themain parameters, β and ρ. The same table also compares the results to thoseattained under the standard structural gravity estimation with no heterogeneityin trade elasticities à la Anderson and Van Wincoop (2003). Evidently, themain model exhibits a significantly higher predictive power than the standard,uniform elasticity model—the main model exhibits an R2 = 0.65, whereas thestandard model exhibits an R2 = 0.46.

Table 8: Estimation results with country-level data

ParametersStandard Gravity Model

θH = θL

Main ModelθH < θL

ρ ≡ θHθL

... 0.54(0.004)

βconst2.83

(0.020)4.73

(0.065)

βdist0.43

(0.003)0.36

(0.006)

βborder0.53

(0.006)0.87

(0.015)

βlang0.52

(0.005)0.84

(0.011)

βagreement0.98

(0.010)0.93

(0.020)

R-Squared 0.46 0.65Observations 9,900

Notes: standard errors are reported in parenthesis.

The present model’s superior fit stems from its ability to match the followingfeature of bilateral trade data: rich-poor trading partners engage in significantlymore two-way trade (i.e., have a higher Xji) than rich-rich or poor-poor tradingpartners. To illustrate this point formally, let North denote the richest 20 coun-tries in my sample and South denote the other 80 countries. Figure 2 illustrates

60

that in year 2000 North-South trade was conducted more intensively than bothNorth-North trade. As illustrated in Figure 2, the standard model estimatedsubject to θH/θL = 1 has difficulty matching this pattern. The reason beingthat, under θH/θL = 1, the model admits no systematic pattern of intra-industryspecialization that makes North-South trade relatively more attractive thanNorth-North trade. The estimated model that treats θH/θL < 1 as free-movingparameter, however, admits North-South specialization across low- and high-θsegments. This feature of the model renders North-South trade relatively moreattractive. Importantly, the extent of North-South specialization depends onθH/θL and e = [ei,H], which in turn guides the identification of these parameters.

Figure 2: The composition of aggregate trade flows: Model vs Data

Note: The North corresponds to the 20 richest countries in the sample.

D.2 Industry-Level Estimation

The industry-level estimation uses data from the World Input-Output Database(WIOD, Timmer et al. (2012)) in 2008. The original WIOD database covers 35industries and 40 countries, which account for more than 85% of world GDP,plus an aggregate of the rest of the world. The countries in the sample includeall 27 members of the European Union plus 13 other major economies, namely,Australia, Brazil, Canada, China, India, Indonesia, Japan, Mexico, Russia, SouthKorea, Taiwan, Turkey, and the United States. The 35 industries in WIODdatabase are listed in Table 9, which include 15 tradable industries plus 20

61

service-related industries. Following Costinot and Rodríguez-Clare (2014), Icontract the WIOD database into a sample of 32 major economies (listed inTable 7) plus an aggregate of the rest of the world. For each industry k, thetrimmed WIOD data reports the industry-level vector of expenditure shares,αk ≡ [αi,k], revenue shares, rk ≡ [ri,k], the full matrix of industry-level tradeflows, Xk ≡

[Xji,k

], as well as country-level data on income, Yi = wiLi, and

population size Li. As with the country-level data, I complement the WIOD withdata on geo-distance, common language, borders, and trade agreements fromMayer and Zignago (2011). Following Costinot and Rodríguez-Clare (2014), theindustry-level trade elasticity estimates are taken from Caliendo and Parro (2014)and are reported in Table 9.

Here, for each of the 15 (non-service) industries in the sample, I am separatelyestimating 70 structural parameters by fitting the model to (32− 1)× 32 = 992data points on industry-level bilateral trade values, namely Xk =

[Xji,k

].43 The

estimated parameters are

1. Thirty-two exporter×industry fixed effects, T k =[Tj,k];

2. Thirty-two importer×industry fixed effects, ek = [ei,H], that characterizethe expenditure shares on segmentH in industry k;44

3. Five parameters, vector βk, that characterize the iceberg trade costs inindustry k; and

4. One parameter, ρk = θH/θL, describing the spread between the segment-level trade elasticities in industry k.

In all incidences, the industry-level estimation exhibits an R-squared of 0.50 orgreater. The last two columns in Table 9 report the segment-level trade elasticitiesestimated for each of the 15 non-service industries in the WIOD sample. Forsome industries, such as ’Petroleum’ or ’Fabricated Metals,’ θH and θL are notsignificantly different, whereas in the ’Machinery’ and ’Food’ industries theestimation identifies a significant degree of within-industry θ heterogeneity.

43So, in total, I am estimating 15× 70 = 1050 parameters across all industries in the sample.44Once ek is known, the expenditure share on segment L is automatically given by [ei,L] =

1− ek.

62

63

Table 9: List of WIOD industries in the industry-level estimation.

WIOD Sector Sector’s DescriptionIndustry-Level θ

(Caliendo-Parro)θH θL

1 Agriculture, Hunting, Forestry and Fishing 8.11 6.28 9.43

2 Mining and Quarrying 15.72 11.53 17.12

3 Food, Beverages and Tobacco 2.55 0.89 3.71

4Textiles and Textile Products

5.56 3.93 7.06Leather and Footwear

5 Wood and Products of Wood and Cork 10.83 9.10 12.00

6 Pulp, Paper, Paper, Printing and Publishing 9.07 6.03 9.92

7 Coke, Refined Petroleum and Nuclear Fuel 51.08 49.38 55.10

8 Chemicals and Chemical Products 4.75 3.80 5.82

9 Rubber and Plastics 1.66 0.62 3.35

10 Other Non-Metallic Mineral 2.76 0.91 3.57

11 Basic Metals and Fabricated Metal 7.99 6.55 9.03

12 Machinery, Nec 1.52 0.56 4.90

13 Electrical and Optical Equipment 10.60 8.78 12.48

14 Transport Equipment 0.37 0.16 0.75

15 Manufacturing, Nec; Recycling 5.00 3.29 6.76

16

Electricity, Gas and Water Supply

5 ... ...

ConstructionSale, Maintenance and Repair of Motor Vehicles and Motorcycles;Retail Sale of FuelWholesale Trade and Commission Trade, Except of MotorVehicles and MotorcyclesRetail Trade, Except of Motor Vehicles and Motorcycles; Repair ofHousehold Goods

Hotels and Restaurants

Inland Transport

Water Transport

Air TransportOther Supporting and Auxiliary Transport Activities; Activitiesof Travel Agencies

Post and Telecommunications

Financial Intermediation

Real Estate Activities

Renting of M&Eq and Other Business Activities

Education

Health and Social Work

Public Admin and Defence; Compulsory Social Security

Other Community, Social and Personal Services

Private Households with Employed Persons

E Additional Tables

Table 10: Summary Statistics of the Colombian Import Data.

Year

Statistic 2007 2008 2009 2010 2011 2012 2013

F.O.B. value (billion dollars) 30.77 37.26 31.39 38.41 52.00 55.79 56.92

C.I.F. valueF.O.B. value 1.08 1.07 1.05 1.06 1.05 1.05 1.05

C.I.F. + tax valueF.O.B. value 1.28 1.21 1.14 1.19 1.15 1.18 1.15

No. of exporting countries 210 219 213 216 213 221 224

No. of imported varieties 483,286 480,363 457,000 509,524 594,918 633,008 649,561

Notes. Tax value includes tariff and value-added tax. The number of varieties indexes the number ofcountry-firm-product combination in a given year.

Table 11: Average demand elasticity and quality intensity across traded sectors.

LIML 2SLS OLS

Sector ISIC4 codes εz ρz εz ρz εz ρz

Agriculture & Mining 100-1499 3.94 0.57 3.55 0.58 1.90 0.69

Food 1500-1699 5.17 0.49 5.51 0.52 1.86 0.65

Textiles, Leather & Footwear 1700-1999 2.93 0.58 3.32 0.62 1.16 0.80

Wood 2000-2099 1.78 0.59 1.69 0.61 1.04 0.80

Paper 2100-2099 2.39 0.49 2.48 0.51 1.36 0.69

Petroleum 2300-2399 1.61 0.51 1.74 0.55 1.19 0.71

Chemicals 2400-2499 2.67 0.55 2.62 0.58 1.33 0.72

Rubber & Plastic 2500-2599 2.47 0.57 2.57 0.60 0.98 0.82

Minerals 2600-2699 2.59 0.59 2.10 0.62 1.03 0.82

Basic & Fabricated Metals 2700-2899 2.92 0.53 2.89 0.56 1.20 0.74

Machinery 2900-3099 1.73 0.62 1.54 0.67 0.73 0.84

Electrical & Optical Equipment 3100-3399 1.91 0.66 1.80 0.69 0.58 0.88

Transport Equipment 3400-3599 2.60 0.49 2.96 0.52 0.60 0.85

N.E.C. & Recycling 3600-3799 1.93 0.60 2.15 0.64 0.82 0.87

Notes. This table presents the average estimated HS10-level demand elasticity and quality intensity withinvarious WIOD sectors, under the OLS, 2SLS, and LIML estimators.

64

65

Table 12: The across-industry relationship between ρz and εz

Dependent: trade elasticity Dependent: quality intensity

Regressor OLS 2SLS LIML OLS 2SLS LIML

demand elasticity, log εz 0.619*** 0.323*** 0.208*** -0.152*** -0.146*** -0.097***(0.042) (0.046) (0.046) (0.020) (0.021) (0.020)

Observations 1,851 435 516 1,851 435 516R-Squared 0.18 0.10 0.05 0.05 0.10 0.19

Table 13: The relationship between ρz and εz in levels

Dependent: trade elasticity Dependent: quality intensity

Regressor OLS 2SLS LIML OLS 2SLS LIML

demand elasticity, εz 0.297*** 0.290*** 0.151*** -0.025*** -0.015*** -0.009***(0.013) (0.043) (0.039) (0.002) (0.003) (0.003)

Observations 1,851 435 516 1,851 435 516No. of SIC Industry FE 95 52 63 95 52 63R-Squared 0.40 0.28 0.18 0.42 0.27 0.19