Tariffs, Competition, and the Long of Firm Heterogeneity Modes Aan Spearot University of Caifornia - Santa Cruz February 204 Abstract I derive a nove soution for the ong run, competitive effects of tariffs that is genera for many countries, robust to rich cross-country heterogeneity, and a function of ony aggregate trade data and country-by-industry Pareto shape parameters. Using this soution, I estimate a structura trade growth equation that is a function of shape parameters, trade fows and tariff cuts. The shape estimates indicate that arger and more deveoped exporters have, on average, bigger surviving firms, and when evauated on a common import market, exporters with a better shape earn arger trade revenues. Using the shape estimates, I return to the mode to back-out measures of reative competition across countries, where within-industries, smaer countries with a reativey poor shape of firms tend to have ess competitive markets. However, I find that countries with ess competitive markets experience a greater increase in competition over the sampe period, suggesting that firms enter where competition is ess fierce. Finay, counterfactuas indicate that tariff cuts over 994-2000 increased competition in 85% of markets. Key Words: Firm-heterogeneity, Free Entry, Productivity Estimation, Tariffs, Trade agreements acspearot@gmai.com. This paper has benefited from presentations at UC Santa Cruz, the Austraasian Trade Workshop, Stanford, and the Western Economics Association Annua Meetings, the Midwest Internationa Meetings Ann Arbor), and the University of Kentucky. Hepfu discussions with Zhanar Akhmetova, Eric Adrich, Joshua Aizenman, Andrew Bernard, Bruce Bonigen, Dan Friedman, Pineopi Godberg, Ryan Oprea, Jennifer Pooe, Jonathan Robinson, Katheryn Russ, Nirvikar Singh, and Robert Staiger are gratefuy acknowedged.
Introduction Tariff iberaization is often cited as a way to discipine domestic firms to the benefit of consumers, either by owering the price of imported goods or making feasibe the import of new varieties. However, the utimate effects of trade iberaization depend on the presence of firms, and their entry and exit choices. For exampe, cassica wisdom suggests that ower tariffs within an import-competing sector wi reduce the domestic reative price of that good as ong as preiminaries of the mode precude the presence of a Metzer paradox Metzer 949)). In new trade modes, whie cassica wisdom is vaid in the short-run, firms may adjust entry choices in the ong-run. Initiay discussed in Venabes 985), a common prediction in many new trade modes is one in which uniatera tariff iberaization decreases competition in the iberaizing market due to a particuary strong exit of firms. Indeed, the discipining effect of tariff cuts may go too far, and utimatey hurt consumers in the ong-run. How genera are these ong-run resuts? As much of the received iterature is based on quasi-symmetric modes with reativey few trading partners, the impications of a arge tariff shock for the word economy are not yet cear. This is especiay the case if variation in country-eve characteristics, such as productivity distributions, ead certain countries to be ess responsive to shocks and the actions of other firms. 2 Beyond the theoretica resuts, how do we characterize the effects of entry empiricay? If we are to evauate the effects of entry on the wefare of consumers, we need an empiricay feasibe mode that accounts for the ong-run decisions of firms across countries and industries. In this paper, I examine the ong-run effects of tariffs within a common firm-heterogeneity mode, but in the presence of rich cross-country heterogeneity. The primary theoretica contribution is showing that whie the ink between tariffs and free entry depends on how countries vary in their underying characteristics such as productivity distributions and tastes, there exists a simpe structura reationship between tariffs and competition that is a function of ony a biatera trade matrix and a vector of country-by-industry Pareto distribution shape parameters. Accounting for this reationship aongside a standard trade growth equation, I structuray estimate these shape parameters using trade fows and tariff cuts subsequent to the Uruguay Round. Armed with the shape estimates, I use trade data to back-out estimates of within-industry See Meitz and Ottaviano 2008). 2 Any adjustment in the abor market Demidova and Rodriguez-Care 20)) or the nature of competition de Bas and Russ 202)) can produce additiona mechanisms that change the ong-run effects of iberaization.
reative competition across countries, and counterfactuas reated to tariff shocks. The atter suggest that mutiatera iberaization subsequent to the Uruguay Round increased competition in 85% of markets, but uniatera iberaization woud amost surey decrease competition in iberaizing markets. I introduce these issues by empoying an extended version of Meitz and Ottaviano 2008), which produces variabe demand easticities simiar to those empiricay supported in Foster, Hatiwanger, and Syverson 2008). 3 The main innovation in my framework is aowing for variation in the shape of the Pareto distribution that governs productivity draws by country and industry. 4 Indeed, shape heterogeneity in the presence of easticity variation is important on three eves. First, the setup can match the empirica reationship between arger export fows and arger surviving exporting firms. 5 Second, shape variation yieds tariff easticity differences across exporting countries that match the empirica resuts presented in Spearot 203). Finay, shape variation affects average profit margins of surviving firms, the probabiity of surviva itsef, and the easticity of surviva to shocks, a of which critica for entry decisions. However, shape heterogeneity compicates the assessment of free entry conditions in that the easticity of the extensive margin to shocks now varies by ocation. As a resut, the system of free entry conditions that pins down ong-run demand within each market is highy non-inear, and may be satisfied by mutipe candidate soutions on the interior. 6 To work around this issue, I expoit a simpe ink between expected profits and expected trade vaues. Specificay, when using the Pareto distribution, expected profits and expected trade vaues are proportiona to each other, and this proportion is a simpe function of the Pareto shape parameter. Subsequenty, a percent shock to a tariff or demand parameter within expected profits is aso proportiona to trade vaue to that market. Using this ink, I show that despite the highy noninear system of free entry conditions, the ong-run response of demand in each market to trade shocks is a simpe function of the matrix of trade fows and a vector of productivity shape parameters. For any 3 I aso discuss how the resuts reate to CES modes simiar to Meitz 2003), Hepman, Meitz, and Yeape 2004), Chaney 2008), Arkoakis, Costinot, and Rodriguez-Care 20), and Meitz and Redding 203). Atkeson and Burstein 2008) aso produces variabe demand easticities, but the cournot competition assumption is intractabe in my setting. 4 This is consistent with the cass of productivity variation modeed in Demidova 2008), but different from variation in the upper bound of the cost distribution as in Meitz and Ottaviano 2008), Hsieh and Ossa 20), and Bombardini, Kurz, and Morrow 202). 5 Using Coumbian transaction eve import data for 2003, I reject the assumption that average exporter-size is constant within import categories to Coombia. See section two. 6 Simiar compications woud arise in other modes with adjustments that are not easticity neutra - for exampe, Hepman, Meitz, and Rubinstein 2008). However, in these papers free entry is not modeed. Other muti-region modes, such as Combes, Duranton, Gobion, Puga, and Roux 202), do not aow for such productivity shape heterogeneity. 2
non-degenerate matrix of trade fows, the ong-run demand response to tariffs is unique. To evauate the mode empiricay, I outine a two-step procedure to estimate a og-differentiated trade fow equation, and utiize the demand response to tariffs via free entry conditions to pin down fixed effects consistent with ong-run free entry. To structuray estimate the shape parameters, I use sectora trade fow and tariff cut data that occurred subsequent to the period of Uruguay Round tariff negotiations. To my knowedge these are the first estimates of country-by-industry Pareto shape parameters using a common dataset, and despite using aggregate data, the estimates are within sensibe bounds and in the vicinity of parameters estimated using firm-eve data eg. Eaton, Kortum, and Kramarz 20) and Di Giovanni, Levchenko, and Ranciere 20)). 7 In terms of the reationship to country and industry observabes, I find that arger, more deveoped markets are associated with a better shape of firms in terms of productivity. However surprisingy), I do not find a reationship between estimated shape parameters and countryindustry measures of capita and input intensity, suggesting that production technoogy is not driving the variation in shape. Finay, I find that mode s structura predictions regarding entry growth match observed estabishment growth, but ony when aowing for shape heterogeneity. Armed with the shape estimates, I return to the mode to back-out measures of reative competition across markets, and the response of competition to tariff shocks. In terms of the former, I show that using the shape estimates as data within a traditiona gravity context, an importer-specific coefficient on the shape estimates is precisey equa to the eve of competition within that market. Inputing the shape estimates, trade data, observed tariff cuts, and traditiona gravity factors, I empoy a Poisson esitmator to measure competition within industries reative to the US the benchmark). The resuts indicate that countries with a better shape of domestic firms, as we as countries that are arger, have a more competitive market reative to the US. Further, I find that countries with ess competitive markets experience a greater increase in competition over the sampe period, suggesting that firms enter where competition is ess fierce. To cose the paper, I use the estimates to evauate two counterfactua predictions reated to tariffs and competition. First, focusing on mutiatera iberaization, I cacuate the roe of changing competitiveness during the course of Uruguay Round tariff cuts. I find that the Uruguay Round increased competition 7 Okubo and Tomiura 203) do provide regiona estimates of productivity distributions in Japan using firm-eve data, and find that productivity is more eft-skewed in aggomerated regions. Newer work is moving toward using the og-norma distribution to better match the the moments of the data. See Head, Mayer, and Thoenig 203). 3
across 85% of country-industry pairs, with this effect most ikey in deveoped markets such as the US, UK, and Germany. 8 Finay, I use the structura mode and estimates to evauate the extent to which uniatera iberaization increases competition, where I find the striking resut that in neary every country-industry pair, uniatera tariff cuts decrease ong-run competition. In the few instances that it does not, this occurs in very sma and under-deveoped countries. Overa, this paper adds a new too in the evauation of tariffs and other trade shocks. The structura estimation is reated to Eaton and Kortum 2002), Eaton, Kortum, and Kramarz 20), Caron, Fay, and Markusen 202), Edmond, Midrigan, and Xu 202), and Breinich and Cuñat 203), though it is most ike Deke, Eaton, and Kortum 2008) and Caiendo and Parro 202) in that changes to aggregate terms are a simpe function of observabe data. However, the simpe reationship I uncover works through the proportionaity of average profits and average revenues, which is distinct from Deke, Eaton, and Kortum 2008) and Caiendo and Parro 202), and may vary country-by-industry with the shape of the Pareto distribution. Hsieh and Ossa 20) aso aow for country-by-industry heterogeneity, though focus on the support of the distribution rather than the shape. The paper is aso reated to Arkoakis, Costinot, and Rodriguez-Care 20), Arkoakis, Costinot, Donadson, and Rodríguez-Care 202), Costinot and Rodríguez-Care 202) and Burstein and Cravino 202), which prove, quantify, and/or evauate the wefare gains from trade for a wide cass of modes. My approach is distinct in that it focuses on ony entry as the conduit for aggregate effects, and outines an empirica approach that is robust to heterogeneity in productivity distributions and other exporter and importer shocks not reated to tariffs. However, my paper heaviy) expoits proportionaity in average profits and average revenues at the biatera eve, which is simiar to the aggregate restrictions in Arkoakis, Costinot, and Rodriguez-Care 20). More importanty, I do not evauate aggregate gains or osses from trade but rather on how firms-respond to a give tariff shock in terms of entry decisions. Indeed, combining a approaches may yied future gains in terms of unpacking the components of firm-heterogeneity modes and their impact on economic aggregates. Finay, my paper provides two ways to view seection and the response of seection to shocks, compementing the theoretica treatment in Mrázová and Neary 203). 8 This is consistent with the empirica work in Feenstra and Weinstein 200), which estimates that mark-ups in the US have faen over this period. 4
2 Genera Setup and Motivation In terms of the genera setup, I wi utiize the framework in Meitz and Ottaviano 2008) as the base mode. However, I wi adjust this particuar firm-heterogeneity mode to account for differences in productivity distributions across suppying countries, in tastes across consuming countries, and for differences in the eve of interna mark-up within each market. Further, I wi discuss how other modes eg. constant easticity demand) reate to the structura reationships presented in the manuscript. Consumers Consumer preferences in each country are specified according to the foowing form U = x c 0, + θ qi, c di ) 2 i Ω 2 η qi, c di i Ω 2 γ ) q c 2 i, di, ) i Ω where Ω represents the measure of varieties avaiabe in country, q c i, is the consumption of variety i by the representative consumer in, and the parameters θ > 0) and η > 0) determine the substitution pattern between the differentiated industry and the outside good, x c 0,. Note that I aow θ to differ across countries, which impies that countries may differ fundamentay in their vauation for the differentiated good reative to the numeraire. Finay, γ > 0) represents the degree to which varieties are substitutabe. If γ were zero, a firms woud price at the same eve, since products woud be homogeneous in the eyes of the consumer. The budget constraint faced by consumers in country is written as: x c 0, + i Ω j p c i, qc i, di I 2) where p c i, is the deivered consumer price of variety i to. Note that impicit in this budget constraint is the assumption that the numeraire is freey traded. As in the existing iterature, I wi assume that income I is such that consumers have positive consumption in both the outside good and differentiated industries. 5
Hence, the inverse demand function for a given variety i in country is derived as: p c i, = θ ηq c }{{} A γ L }{{} b q i, = A b q i, 3) In 3), q i, is tota quantity sod of i to a consumers in, Q c is the tota quantity sod by a firms to the representative consumer in, and A contains a aggregate terms within the demand curve for each variety in. The focus of the paper wi be how competition changes with tariffs as refected in A. Finay, b wi measure the sope of the aggregate demand curve for each variety in, which is γ scaed inversey by the number of consumers in. Firms The characterization of firms in each country j is reativey simpe. Firms enter under uncertainty, paying a fixed entry cost F j. Upon entry, firms from country j draw a margina cost c from a country-specific Pareto distribution with the foowing pdf: gc) = k j c k j c m j )k j, c [0, c m j ] 4) In 4), there are two-ayers of productivity heterogeneity across countries. First, sighty more standard in the iterature is variation in the upper-bound of the distribution c m j, which we henceforth assume to be non-binding for any country seing to any market. 9 The second-ayer, which is non-standard other than a simiar cass of heterogeneity in Demidova 2008) and Demidova and Rodriguez-Care 20)), is variation in the Pareto parameter, k j. Variation in this parameter across countries wi be crucia for the resuts, and we wi discuss the empirica impications of this parameter shorty. Each firm from a given country j may se one variety to each market, paying an ad-vaorem tariff τ j on the vaue of each unit sod from j to. Note that we aow this tariff to be negative, in that case impying an import subsidy, and that τ j = 0 when j =. In addition to the tariff, a firms seing to market wi be subject to an ad-vaorem saes tax s. Though we refer to it as a saes tax for exposition, I wi ater 9 For exampe, see Meitz and Ottaviano 2008), Hsieh and Ossa 20) and Bombardini, Kurz, and Morrow 202). 6
discuss how other domestic characteristics have a simiar effect on demand. 0 The reationship between the consumer price for variety i detaied in 3) and the price that the foreign producer of i receives is p c i,j = + τ j) + s )p s i,j. This yieds the foowing inverse demand function that suppier i from country j uses to optimay set production for market. p s i,j = t j s A b q i,j ) where, t j = + τ j ) and s = + s ). Firms choose quantities to maximize profits, where the maximization probem for firm i from j exporting to is written as: { } π i,j c i ) = max A b q i,j ) q i,j c i q i,j. q i,j t j s Suppressing i s for the remainder of the paper, the optima quantity in seing to from j is written as, q j c) = A ct j s 2b, producer revenues are written as v j c) = A2 ct js ) 2 4b t j s, and profits are written as π j c) = A ct j s ) 2 4b t j s. Pareto Shape and Average Firm-size To motivate the more nuanced differences in productivity distributions that I expoit throughout the paper, I now sove for the average surviving) firm-eve export vaue from country j to import market. Precisey, 0 And though it may seem superfuous for a majority of the theory, s wi be crucia in terms of deriving an empirica specification that is robust to unobserved market-specific shocks. 7
A I integrate the firm-eve revenues over [0, t j s ], subject to the truncated productivity distribution, g j c) : G j A ) t j s v j = 0 A t j s A 2 ct js ) 2 4b t j s g j c) G j A t j s ) dc = A2 2b s t j k j + 2) 5) In 5), the average surviving firm-eve export vaue does not depend on the upper bound of the Pareto parameter. This is due to average export vaue being a truncated average conditiona on export status). Thus, when imposing the Pareto distribution, and after controing for tariffs, average exporter size within an industry does not vary across exporters uness the Pareto parameter k j differs across j. Further, given the monotone reationship between revenues and easticities, average easticities do not vary when k j is homogenous since average firm-eve revenues do not vary. In Figure, I present evidence using transaction-eve import data from Coombia that is not consistent with the assumption of constant k j across exporters. Specificay, I show that within HS6 products, there is a strong and positive reationship between tota export vaue to Coombia by Exporter-HS6 group V j ), and the average revenues earned by the successfu exporting firms v j ) within the same Exporter-HS6 group. Whie this reationship is intuitive, with no variation in k j, there shoud be no such reationship in the data. Further, in Spearot 203), I provide evidence the rejects the assumption of constant tariff easticities when evauating MFN tariff cuts and imports to the US. On both eves, aowing for k j s to differ by country and industry is important to capture the composition of exporting firms across countries, and the response of these firms to shocks. Pareto Shape and Trade Fows Another impication of variation in the Pareto shape parameter is present when estimating a trade fow equation. To see this, tota trade vaue from exporter j to market is written as foows: ) A V j = N j G v j = t j s 2b s k j+ t k j+ j N j A k j+2 k j + 2)c m j )k j 6) See Spearot 203). 8
Figure : Tota Exports and Average Firm-eve Exports to Coombia - Within HS6 Drop Exporter-HS6 with fewer than 2 firms Drop Exporter-HS6 with fewer than 0 firms Within-HS6 Log Avg Firm Exports to Coombia -0-5 0 5 Within-HS6 Log Avg Firm Exports to Coombia -4-2 0 2 4 6-0 -5 0 5 Within-HS6 Log Tota Exports to Coombia -6-4 -2 0 2 4 6 Within-HS6 Log Tota Exports to Coombia Notes: This figure pots the og of average firm-eve exports to Coombia by Exporter-HS6 group against the og of tota exports to Coombia by Exporter-HS6 group. A data de-meaned by HS6 product. Left-pane requires two or more firms to construct Exporter-HS6 average, and right-pane requires 0 or more firms. A data from 2003. Taking ogs and fuy differentiating with respect to endogenous variabes and tariffs, we get: dv j V j = dn j N j + k j + 2) da A k j + ) dt j t j 7) The typica approach in the iterature is to use importer and exporter fixed effects when estimating a trade fow equation in eves or changes. However, when there is variation in the Pareto parameter, the effects of aggregate changes to the import market, da A, are not absorbed by the importer fixed effect. Hence, uness one can provide a soution for da A as a function of observabe trade data, it wi be in the error term, and cruciay, a function of the observabe trade shock. Further, as the trade shocks and Pareto parameters wi have a structura effect on da A, an interaction of exporter and importer dummy variabes with crossequation restrictions) to proxy for k j + 2) da A wi be missing key structura reationships between trading partners. Hence, the remainder of the paper is focused on evauating da A within a genera set of trading reationships, and providing a way to estimate da A using observabe trade and tariff data. 9
Long Free Entry With the basics of the mode and the motivation for varying Pareto shape parameters in-hand, I now turn to the ong-run equiibrium conditions. The first invoves ong run free-entry, in which firms enter unti the expected profits are equa to a fixed cost of entry, F j. By imposing the Pareto assumption in 4), the expected profits of seing from j to are written as: π j = A k j+2 2b k j + 2)k j + )c m j )k jt k j+ j s k. j+ Aggregating over a avaiabe markets, the free entry condition for country j is written as: A k j+2 2b k j + 2)k j + )c m j )k jt k j+ j s k j+ = F j. 8) In 8), the key issue is that if k j s are identica across countries and equa to k, then the ong-run equiibrium consists of a system of equations which are inear in A k+2 for a. However, when k j s vary, the system of free entry conditions wi exhibit a different degree of non-inearity for each country. Indeed, this can ead to mutipe soutions to the system of free entry conditions such that A > 0 for a. 2 Though ony used in the Appendix for extended intuition within a two-country mode, the fina component of the equiibrium is the number of firms that enter each country, which given the soutions) to the system of free entry conditions, are pinned down using the definition of A. To back-out the number of entering firms, note that q c j, the expected quantity sod to the representative consumer in by a given entrant in j, is written as: q c j = A k j+ γk j + )c m j )k jt k j j sk j Using A = θ η j N jq c j, where N j is the number of firms that have entered j, N j s are inked to A via A = θ η j A k j+ N j γk j + )c m j )k jt k. 9) j j sk j 2 An earier working paper detais these issues using a two-country mode in which two soutions are possibe, and numericay soves a three-country mode in which 6 candidate soutions exist on the interior. 0
In equiibrium, this inear system of equations in N j given A s) wi determine when a candidate soution to free entry conditions in 8) is consistent with N j > 0 for a j. 2. Tariffs and Free Entry conditions. I now examine how the system of free entry conditions in 8) responds to an arbitrary group of tariff shocks. Specificay, I wi focus on how the A s respond to tariffs, within an industry and subject to an arbitrary number of trading partners. Indeed, the A s are an important measure in some cases a sufficient statistic) to evauate wefare within firm heterogeneity modes Meitz and Ottaviano, 2008; Meitz and Redding, 203). Hence, I wi begin by providing a genera soution to how the A s change with tariffs, and aso provide a simpe formua that maps a matrix of trade fows within an industry to a unique set of changes to A s after a trade shock. In doing so, I highight a new and simpe structura impication of firm-heterogeneity modes in the ong run. 3 To begin, reca from above the free entry condition for each country j: A k j+2 2b k j + 2)k j + )c m j )k jt k j+ j s k j+ = F j. Again, these conditions pin down the A s, and hence, the eve of competition in each industry or aternativey the highest cost domestic firm that can operate after accounting for the interna tax). Fuy differentiating the free entry condition for j with respect to a A s and t j s, we get: A k j+2 da 2b k j + )c m j )k jt k j+ j s k j+ A = A k j+2 dt j 2b k j + 2)c m j )k jt k j+ j s k j+ t j k Mutipying both sides by N j +) j k j +2), and imposing trade vaue from 6), 0) can be written as: =..M da V j = k j + ) A k j + 2) V j dt j t j. 0) Note that the direct impact of t j is a function of the vaue of trade, V j, and a function of the Pareto shape parameter, k j+) k j +2). The former governs the size of shocks reative to other markets that j serves. 3 For those readers interested in extended intuition from a two-country framework, see Appendix C.
In terms of the atter, the shape correction k j+) k j +2) governs the average easticity of producers in j on any market, and hence, the responsiveness of producers from j to demand shocks within each market. 4 This differentia impact wi be crucia for the theoretica resuts discussed beow. Stacking a differentiated free entry conditions in matrix form, and soving for da A s, we have: da A. da A. da m A m V... V... V m...... = V... V... V...... V m... V m... V mm k + k +2 r=..m V r dt r t r k m+ k m+2. r=..m V mr dtmr t mr. k + k +2 r=..m V r dt r t r ) The power of this transformation is that the movement of the demand curve in each country subsequent to an arbitrary group of trade shocks is a simpe structura function of in theory) observabe trade and productivity data. With regard the former, one needs domestic saes by domestic firms aong with trade data to fi the square matrix of trade fows. There are additiona terms reated to the shape of the productivity distribution, but these can be estimated using firm-eve data, and ater, I detai a strategy to estimate these shape parameters structuray using aggregate data. Using both trade data and the structura estimates, I can then predict in which countries and industries a trade shock increases competition. Comparison to Constant-easticity Demand As ) is derived using a fairy specific preference structure, a natura question is to what degree the reationship between competition and tariffs is genera for other demand systems, and other assumptions over trade costs. In Appendix A, I derive a simiar resut for CES demand system of the form, q i, = I p σ i i Ω p σ s ds where σ is the easticity of substitution within the differentiated sector in country, I is income in country spent on the differentiated industry, i Ω p σ s ds is a transformation of the CES-type price index for 4 This is simiar to the type of demand shock that is identified in Foster, Hatiwanger, and Syverson 2008). 2
country, and p i is the price of each variety. I aow for arbitrary biatera ad-vaorem tariffs t j ) and fixed costs F j ) in serving each market. Further, I make no assumptions over the cost distribution other σ than that it is we-behaved. Defining B = σ σ ) as the anaogous demand eve within I i Ω p σ s ds σ the CES setup, we can write profits of j seing to as π ces j as v ces j = σ B t σ j = B t σ j c σ i F j, and firm-eve trade vaue c σ i. Given these assumptions, the ink between an arbitrary set of trade shocks and demand eve changes in each country is written as: σ db B. σ r db r B r. σ m db m B m = V... V r... V m...... V r... V rr... V r...... V m... V rm... V mm dt =..M t V. dt r =..M t r V r. =..M dt m t m V m Hence, the effect of tariffs for CES has the same basic form as the quasi-inear quadratic preferences used in this paper, and in some cases is more genera since no distributiona assumptions have been used. However, since demand easticities in CES are constant across markets, there are no differentia effects of demand shocks on average profits across exporters within markets, and hence, no Pareto or other distributiona correction is needed. Indeed, this is what distinguishes the variabe-easticity demand system from others, and the remainder of the paper wi be focused on anaytica resuts and empirica impementation of this demand system to evauate the ong-run effects of tariffs. 3 Theory to Empirics Moving back to the quasi-inear quadratic mode, the key to using ) in an empirica context is the proxy for, or the estimation of, the unobserved Pareto shape parameters. Unfortunatey, existing firm-eve studies such as Di Giovanni, Levchenko, and Ranciere 20) and Eaton, Kortum, and Kramarz 20) do not provide Pareto shape estimates that vary by both industry and country, and thus I must find another way to account for the shape parameters. 5 Beow, I outine an approach that treats the shape parameters 5 Further, their estimates are scaed by the easticity of substitution, and hence, additiona estimates of demand easticities are required to recover the fundamenta productivity parameters. 3
as the primary object of estimation. Indeed, this is sensibe given that the shape parameters are the ony free parameters other than trade data and trade shocks in ). To begin, defining Λ V, and Λ s representing the th row and s th coumn of Λ, one can expand the soution for da A from ) as foows: da A = s=..m Λ s k s + k s + 2 r=..m V sr dt sr t sr Substituting da A into the og trade fow equation in 7), we get: dv j = k j + 2) V j s=..m Λ s k s + k s + 2 r=..m V sr dt sr t sr ) k j + ) dt j t j + dn j N j 2) In 2) there are M Pareto parameters to estimate. Further, we can aso empoy M exporter fixed effects to absorb the changes to the number of entering firms, dn j N j. However, as ong as there are more than 2M trading reationships there is a maximum of MxM), one can estimate these parameters and fixed effects by using variation across trading partners within each exporter. Other Importer and Exporter Shocks We have yet to account for other shocks, such as changes in market size L, the interna tax s, or shifts in the upper-bound of the cost distribution, c m j. Further, though not modeed due to the presence of the outside good, there may aso be changes in wages in suppying markets or the margina utiity of income in consuming markets. A of these shocks affect trade growth as we as the structura reationship within the free entry conditions, and hence, compicate the estimation of shape parameters required for counterfactua anaysis. 6 By adopting a simiar approach as in 2) - that is, expanding the soution to da A to incude a other shocks - we can estimate shape parameters and other shocks using the foowing rather compicated) 6 See Simonovska 200) for an anaysis of income effects within trade modes, and Cosar and Fajgebaum 202) and Atkin and Donadson 202) for the effects of interna frictions. 4
equation. dv j = k j + 2) V j s=..m k s + dtsr Λ s V sr k s + 2 t r=..m sr k s + dm r + ) )) k s + dx s k j + ) dt j t j + d m d x j + n x j 3) In 3), given data to construct dv j V j, Λ, V sr, and dtsr t sr, we are eft to estimate M separate d x j s, dm s, n x j s and finay, k j s. Here, d m = s b, d x j = k dc m j j c m j + df j F j and n x j = dn j N j + df j F j. However, to avoid such a compicated estimating equation, there exists a simpe transformation on the mode that consistenty estimates shape parameters and satisfies the ong-run aspects of the mode. To begin, define define dz Z = da A ds s, which is precisey the change in the east productive firm that operates in country. Importanty, if s is changing, we can ony identify changes to A s. However, this is not so bad since Z = A s is the east productive domestic firm in, and is sti a vaid measure of competition on market via seection. Log-differentiating trade vaues, and adding error in the measurement of trade growth, we get: dv j = k j + 2) dz k j + ) dt j + ds db dc m j k j V j Z t j s b c m j + dn j N j + ε j By og-differentiating the free entry condition for country j, we get: M V j k j + 2) dz Z = k j + ) dt j t j + ds s db b k j dc m j c m j df j F j ) = 0 Note that og-differentiated trade vaue and the og differentiated free-entry condition share many of the same common terms. This motivates a simpe two-step procedure to estimate shape parameters but aso quantify some of the fixed effects that satisfy the ong-run structure of the mode. For the first step, using a non-inear estimator, and data for dv j V j equation as a function of k j s, dz Z s, d s and d j s. and dt j t j, we estimate a trade growth dv j = k j + 2) dz k j + ) dt j + d + d j + ε j 4) V j Z t j 5
Since there wi be biatera variation in tariffs, t j, the trade growth equation can identify vaues of k j + ) as an exporter-specific coefficient on dt j t j. However, to successfuy identify dz Z = da A ds s s, we must excude at east one group in the importer and exporter fixed effects d and d j ). To satisfy the ong-run structure of the mode, step two simpy requires rearranging 4) after coecting residuas, ε j, and soving for impied changes to entry conditions: M = V j dvj V j ε j dn j N j n j = dn j N j df ) j F j = 0 + df j F j = dv j V j M s j ε j 5) = where s j = V j M = V j is the share of j s saes that go to. Interestingy, this technique is equivaent to expanding the soution for da A ds s to account for a shocks this is made cear in appendix C). However, the presented two-step procedure is much more reveaing in that a exporter and importer shocks are the same in both trade vaues and free entry conditions with the exception of N j and F j. Hence, we can using the residuas from the trade growth equation aong with the structure of the free entry conditions to sove for the impied changes to entry conditions that satisfy the ong-run structure of the mode. Later, we wi compare dn j N j approach. + df j F j to observed changes in the number of estabishments to the test the vaidity of this I now outine the data to be used in estimation, and present the resuts from estimation using a case study of tariff cuts subsequent to the Uruguay round. 4 The Long of Manufacturing in the 90 s In this section, I structuray estimate trade fows, and the Pareto parameters that govern them, using sectora data during the impementation period of Uruguay Round WTO tariff cuts. The primary data I use is sourced from the Trade, Production, and Protection database from the Word Bank, as described in Nicita and Oarreaga 2007). The dataset itsef consists of two fies, both reported at the 3-digit ISIC cassification revision 2). The first is a biatera trade dataset that incudes importer and exporter-reported trade vaues. The second is a country-eve dataset that reports output by industry, aong with aggregate 6
exports and imports, and trade protection measures. 7 Tariff data at the ISIC eve is obtained from the Wordbank TRAINS dataset, where for each exporter-importer-isic group, I use the average appied tariff across corresponding HS6 products. If the appied tariff is not reported, I use the importer-isic most-favored nation tariff as a substitute. I now describe the construction of the sampe, by industry. The primary requirements for the empirica strategy outined in the previous section are a matrix of trade vaues prior to iberaization, tariff growth rates, and the subsequent growth rates in trade. A growth rates are measured in og changes. To define the set of countries active in a given industry i in a given year, I first restrict the sampe to those countries that report output in that industry in that year ie. countries within which firms have entered). Then, subject to this restricted set of countries, compare exporter-reported exports and importer-reported imports for each country pair. I keep biatera trade data in the sampe if both the importer and exporter report that trade occurred. I assign domestic saes from j to j as tota output in that industry i in that year minus tota exports. For exports from j to in industry i, I use the exporter reported FOB trade vaues. The two years I use to construct growth rates in trade are 994 and 2000. The motivation for these two years is that Uruguay Round tariff cuts were impemented in arge part over this period, and hence, this is a period of arge and quasi-exogenous changes to tariffs that provide usefu variation for estimating the parameters in 4). A initia conditions are measured in 994. When trade data is missing for 994 or 2000, I use averages from 993 and 995 for the former, and 999 and 200 for the atter. Whie not idea, this choice is made on the side of caution so as to incude as many trading reationships as possibe, independent of whether a country reports trade vaues in 994 or 2000. When tariff data is missing for 994, I take the maximum appied tariff over the period 990-994 Uruguay Round negotiation period). When tariff data is missing in 2000, I use the minimum tariff over the period 2000-2004. The fina sampe incudes 58 countries, which is sighty arger than the sampe in Deke, Eaton, and Kortum 2008). However, not a countries wi be avaiabe for every industry. 7 Since New Zeaand and China do not report the required data within the Word Bank dataset, I obtain suppementa information from the CEPII TradeProd dataset as described in De Sousa, Mayer, and Zignago 202). 7
Estimation To estimate M Pareto shape parameters, M exporter shocks, M importer shocks, and M changes in competition for each industry, I estimate 4) via non-inear east squares NLS). Given the arge number of parameters to estimate, I use a simuated anneaing agorithm to ensure that the estimates do not converge at a oca minimum rather than goba). 8 Since Pareto shape parameters shoud be positive for a propery defined PDF, I use constrained NLS to ensure that the estimates are consistent with a propery defined productivity distribution. I wi report the degree to which the estimates are at the bounds. Indeed, this is the working assumption in trade theory. I aso bound the exporter and importer shocks to ie between -5 and 5 og growth) to reduce the size of the parameter space. Finay, since the trade equation outined in 4) is primariy driven by an interaction of variabes that vary individuay) in j and, I cannot identify a exporter and importer shocks whie sti being abe to recover da A Hence, for one country within each industry, I normaize the d j and d shocks to zero. ds s. Once a k j s have been estimated, I associate the estimated k j s with outside measures, such as deveopment, country size, and production technoogy by country-industry. 9 Then, I derive a technique to use the shape estimates to measure reative competition across markets. Finay, using the soution in ), I cacuate the contribution of tariff cuts over the period 994 to changes in A s, and aso use the mode to generate the predicted effects of uniatera iberaization. 4. Resuts To begin, Tabe reports the average and median k j estimates by industry, the share of those estimates that hit the ower bound zero), and the number of countries used within each industry for estimation. In the ast row of the tabe, which tabuates the average and median shape estimates across a manufacturing industries, we find that the median shape estimate of.47 is in the vicinity of estimates of the firm-size distribution for France, as discussed in Eaton, Kortum, and Kramarz 20) and Di Giovanni, Levchenko, 8 Simuated anneaing is essentiay a smart grid search that randomy chooses points within a pre-defined space and buids up picture of the estimating surface. The agorithm sowy reduces the search space as good candidate soutions arise. The procedure I use is described by the coding authors in Xiang, Gubian, Suomea, and Hoeng 203). 9 The Pareto shape estimates are avaiabe at the author s website. 8
and Ranciere 20). 20 However, it is notabe that approximatey 0% of estimates are predicted to be at the ower bound of the constrained NLS procedure zero). In terms of goodness of fit, I present two diagnostic measures reated to the improvement in the sum of squared residuas SSR) when aowing for shape heterogeneity. First, I report the simpe improvement reduction) in SSR when aowing for shape variation, which wi obviousy be positive since we are aowing for a more fexibe mode with such variation. However, the improvement in SSR is substantia, where in the coumn abeed % Improve, the sum of squared error fas by around 22% on average, with some industries exhibiting massive reductions in SSR Manufacture of misceaneous products of petroeum and coa fas 66%, for exampe). More rigorousy, I run a F-test after every regression, with the unrestricted mode being that with shape variation, and the restricted mode requiring that shape parameters are homogeneous across countries within an industry. For a industries, I can reject the restricted mode with shape-homogeneity, and amost aways with a high eve of significance. Overa, I find that the shape estimates are sensibe on average, but differ in a way meaningfu for capturing trade fows. Next, I present the tabuated resuts by country in Tabe 2. Again, there is wide variation across countries in the shape estimates, and these differences are economicay meaningfu. For exampe, whie Chie has a mean shape estimate of 3.09, Canada has a mean shape estimate of.67. It terms of average exporter size as derived in 5), this difference impies that observed exporters from Canada are 38.6% arger than observed exporters from Chie when measured on a common market. This heterogeneity more coherent in Figure 2, where in the eft-hand pane there is a noticeabe and statisticay significant) downward reationship between GDP per capita and average shape estimates by country. 2 In the right-hand pane of Figure 2, we find another negative and significant) reationship between the og of popuation and average shape estimates. Hence, the resuts in Figure 2 suggest that deveoped and arge countries tend to have a better shape of firms. An interesting impication of the resuts for ess-deveoped countries is that higher shape parameters may yied an additiona component of voatiity aong with institutions or the natura impications of differences in country size as discussed in di Giovanni and Levchenko 202). Indeed, within industries, countries with higher k estimates wi 20 For exampe, in Eaton, Kortum, and Kramarz 20), the shape estimate for export vaues is.25, and is an estimate of k, where σ is the easticity of substitution. Adjusting using the median easticity of substitution estimate of 2.2 from Broda σ and Weinstein 2006), the impied Pareto parameter of the productivity distribution is.04. 2 GDP per capita and popuation data are sourced from the Penn Word Tabes. 9
Tabe : Pareto Shape Estimates and Estimation Diagnostics - by Manufacturing Industry # Shape Estimates NLS SSR ISIC Manufacturing Industry Ctry Avg. Med. at ower at upper % Imp F stat 3 Food 53 0.93 0.47 0.9 0.02 0.4 5.329*** 33 Beverage industries 48.55 0.59 0.7 0.04 0.26 6.455*** 34 Tobacco 39 2.3.52 0.23 0.03 0.37 3.632*** 32 Texties 48 2.77 2.63 0.08 0.04 0.22 7.876*** 322 Wearing appare, except footwear 28 2.45 2.09 0. 0.00 0.34 8.564*** 323 Leather, products of eather, eather substitutes 25 3.85 3.85 0.08 0.08 0.34 6.964*** and fur, except footwear and wearing appare 324 Footwear, except vucanized or mouded rubber 37 2.37.20 0. 0.08 0.30 5.79*** or pastic footwear 33 Wood and cork products, except furniture 45.82 0.74 0.3 0.09 0.22 6.603*** 332 Furniture and fixtures, except primariy of 44.26 0.90 0.07 0.02 0.20 5.94*** meta 34 Paper and paper products 5 2.24.57 0.6 0.06 0.22 6.990*** 342 Printing, pubishing and aied industries 5.65 0.88 0.6 0.06 0.23 7.630*** 35 Industria chemicas 35.7.0 0.4 0.00 0.25 7.546*** 352 Other chemica products 44 2.30.90 0.07 0.04 0.2 6.996*** 353 Petroeum refineries 32 3.93 3.87 0.2 0.06 0.34 5.302*** 354 Misc. products of petroeum and coa 0 4.7 3.7 0.0 0.0 0.67 2.223* 355 Rubber products 36 2.39.85 0.03 0.03 0.23 6.350*** 356 Pastic products not esewhere cassified 49 2.20.59 0.08 0.04 0.22 7.720*** 36 Pottery, china and earthenware 32 3.26 2.05 0.6 0.09 0.27 5.699*** 362 Gass and gass products 43 2.24.66 0.07 0.02 0.22 6.24*** 369 Other non-metaic minera products 47 2.37.86 0.3 0.06 0.24 6.588*** 37 Iron and stee basic industries 36 2.67 2.3 0.06 0.03 0.26 6.83*** 372 Non-ferrous meta basic industries 26 2.70 2.08 0.5 0.04 0.28 6.292*** 38 Fabricated meta products no machinery/equip.) 45.09 0.54 0.3 0.02 0.2 7.82*** 382 Machinery except eectrica 30 0.69 0.30 0.3 0.00 0.25 7.05*** 383 Eectrica machinery, appiances and suppies 4.95.39 0.0 0.05 0.22 7.992*** 384 Transport equipment 38 2.3.29 0.3 0.05 0.8 5.485*** 385 Scientific/measuring/controing/photographic 29.62.4 0.7 0.03 0.27 7.796*** equip. 390 Other Manufacturing Industries 22.8.05 0.4 0.04 0.29 4.844*** Notes: The coumn ower reports the share of estimates that are at the NLS estimation bound of k=0, and upper reports those at the upper bound of k=0. # Cntry reports the number of countries in the sampe for each industry. Improve reports the percent improvement in SSR when aowing for shape heterogeneity. F stat reports the F statistic from treating the heterogeneous shape mode as the unrestricted mode, and the common shape mode as the restricted mode. *** p<0.0, ** p<0.05, * p<0. 20
Tabe 2: Average and Median Pareto Shape - by Country Country #ISIC Avg. Med. at ower at upper Country #ISIC Avg. Med. at ower at upper Argentina 20 2.94 2.9 0.0 0.05 Latvia 3 4.05.93 0.00 0.23 Austraia 20.87.3 0.05 0.05 Lithuania 4 2.86.6 0.4 0.07 Austria 9.20.34 0.0 0.00 Macedonia 4.60.90 0.25 0.00 Begium-Lux. 4.07 0.9 0.00 0.00 Maaysia 2 2.4.66 0.05 0.00 Benin 4.75.0 0.25 0.00 Mata 4 4.07 2.4 0.29 0.29 Boivia 8 3.08.83 0. 0.7 Mexico 7.57.64 0.2 0.00 Canada 26.67.40 0.04 0.00 Modova 2.05 0.63 0.36 0.09 Chie 27 3.09.95 0.5 0.07 Morocco 20 2.57.86 0.0 0.05 China 24.62.52 0.00 0.00 Netherands 5.28.2 0.00 0.00 Coombia 27 2.07.5 0.26 0.00 New Zeaand 4 0.54 0.29 0.25 0.00 Costa Rica 8 3.94 3.78 0.22 0. Norway 22.66.4 0.04 0.00 Cyprus 2 2.45.42 0.24 0.4 Oman 5 2.39 0.8 0.27 0.07 Ecuador 26 2.24.92 0.9 0.08 Panama 9 2.96.63 0.32 0.6 Finand 26.62.63 0.2 0.00 Poand 0.02 0.70 0.00 0.00 France 22.47.50 0.00 0.00 Portuga 27.40.34 0.8 0.00 Germany 24.42.45 0.00 0.00 Qatar 3.69.94 0.27 0.27 Great Britain 26.50.58 0.04 0.00 Romania 22.95.39 0.4 0.00 Hungary 8.76.42 0.06 0.00 Senega 5 3.30 2.8 0.40 0.3 India 25.57.56 0.04 0.00 Sovakia 2 0.8 0.66 0.42 0.00 Indonesia 7 2.30.58 0.00 0.06 Sovenia 3.86 0.9 0.00 0.00 Ireand 8.84.22 0. 0.06 Spain 27.67.62 0.04 0.00 Israe 5.26 0.90 0.07 0.00 Sri Lanka 2.92.33 0.4 0.00 Itay 25.35.24 0.00 0.00 Sweden 22.56.49 0.04 0.00 Japan 28.6.27 0.00 0.00 Trinidad and Tob. 6 2.56.84 0.2 0.06 Jordan 2 2.54.96 0.9 0.05 Tunisia 7 2.38.57 0.2 0.00 Kenya 22 2.43.5 0.27 0.09 Turkey 26 2.04.79 0.5 0.00 Korea 27 2.0.6 0.07 0.00 United States 26.49.46 0.00 0.00 Kuwait 9 3.02 0.35 0.32 0.6 Uruguay 22 3.57 2.33 0.23 0.8 Tota 28 2.09.47 0.2 0.04 Notes: This tabe presents mean and median shape estimates by country. at ower reports the share of estimates that are at the NLS estimation bound of k=0. at upper reports those estimates that are at the upper bound k=0. # ISIC reports the number of ISIC industries for each country. 2
Figure 2: Estimate Pareto Shape Parameters, Deveopment, and Country Size Avg. k vs. GDP per Capita Avg. k vs. ogpopuation) k-avg 2 3 4 R^2 = 0.9 k-avg 2 3 4 R^2 = 0.4 0 5000 0000 5000 20000 25000 30000 6 8 0 2 4 GDP per Capita ogpopuation) Notes: The eft-hand figure is average k by country and GDP per capita, and the right-hand figure is average k by country and og of Popuation. Bubbe size is proportiona to number of observations per country. be more responsive to shocks at the intensive and extensive margin, the former being reated to higher absoute demand easticities, and the atter due to the higher easticity of surviva to shocks. To dig deeper into the associations between country and industry characteristics, I regress the shape estimates for industry i in country j against the og of country j GDP per capita and popuation, incuding industry fixed effects. kij = α oggdp P C j ) + α 2 ogp opuation j ) + α i + ε ij The resuts from estimating 6) are presented in the first two coumns of Tabe 3. Again, the resuts indicate that there is a negative and statisticay significant reationship between Pareto shape parameters and both deveopment and popuation. However, since we are using industry-fixed effects, we are absorbing a variation reated to productivity distributions that may be specific to each industry. To evauate the robustness of these reationships, I now add measures of capita and input intensity, which are country-by-industry characteristics that may correate with popuation and deveopment, but aso 22
infuence how cost draws govern profitabiity. For exampe, perhaps the cost-variation that is heterogeneous across firms is skewed toward capita within a Cobb-Dougas aggregator), and hence, variation in cost draws may be ampified or mitigated via capita intensity. In terms of recovering shape parameters and associating them with deveopment, if deveoped countries are more capita intensive, we may be erroneousy associating higher deveopment and ower k when in fact capita intensity is paying a roe. Simiary, if arger, more deveoped countries have a arger cost share in outsourcing, but cost-variation is ony appied to the cost share of fina assemby, then again it is possibe that we are erroneousy associating shape estimates with these country-by-industry technoogy parameters. To test for these possibiities, I acquire country-industry specific capita-abor and input-output ratios for 994, and add them to the estimating equation. These ratios are obtained from the Trade, Production, and Protection dataset. To cacuate the capita-abor ratio, I use the ratio of gross fixed capita formation to wages. To cacuate the input-output ratio, I take the difference between Output and Vaue-Added of industry i in country j and divide this measure by the output of industry i in country j. Adding these measures to the estimating equation, the resuts are presented in coumn 3) of Tabe 3. Here, we find no appreciabe reationship between capita intensity or input intensity and estimated shape parameters. However, despite the much smaer sampe due to the avaiabiity of capita and abor data), the reationships of shape estimates to deveopment and country size sti remain. Finay, I test the reationships when incuding industry and country fixed effects, thereby eaving ony variation in capita and input intensity. The coefficients are again insignificant. Hence, the resuts do not indicate that the variation in k ij across countries within industries is associated with factor intensities. Pareto Shape and Trade Fows In Spearot 203), I derive how countries are ess responsive to trade shocks when their exporting firms are reativey arge. To test the mode, I use 0-digit data on imports to the US. Absent data on exporterproduct Pareto shape parameters or average exporter size at that eve of disaggregation, I discuss some conditions under which tota export vaue from each exporter-product group is positivey correated with average exporting-firm size. In the current exercise, I evauate whether within the market for industry i in country, higher Pareto shape parameters of export suppiers correate negativey with the vaue of 23