Distorted Trade Barriers: A Dissection of Trade Costs in a Distorted Gravity Model

Transcription

1 Distorted Trade Barriers: A Dissection of Trade Costs in a Distorted Gravity Model Tibor Besedeš Georgia Institute of Tecnology Mattew T. Cole Florida International University November 18, 2014 Abstract It is quite common in te trade literature to use iceberg transport costs to represent variable trade barriers, bot tariffs and sipping costs alike. However, in models wit monopolistic competition tese are, in fact, not identical trade restrictions wic as important consequences for te teoretical model. We illustrate tese differences in a gravity model à la Caney (2008), but te implications are relevant for oter trade models including calibrated models focused on welfare analysis. We sow teoretically tat te elasticity of substitution plays a role in te elasticity of trade flows wit respect to tariffs unlike wit iceberg transport costs. Moreover, trade flows are more elastic wit respect to ad valorem tariffs tan transport costs and find a linear relationsip between te elasticities wit respect to ad valorem tariffs, iceberg transport costs, and fixed market costs. We empirically validate te latter results using data on U.S. product-level imports. JEL classification: F12; F13; F17 Keywords: Gravity; Firm eterogeneity; Monopolistic competition Cole acknowledges financial support from te Marie Curie Grant, Globalization, Investment, and Services Trade Grant Number We would like to tank Tomas Caney, Mattieu Crozet, Ronald Davies, Karl Welan, Allan Sørensen, and Ben Zissimos for elpful comments. All remaining errors are our own. Scool of Economics, Georgia Institute of Tecnology, Atlanta, GA besedes@gatec.edu Corresponding autor: Department of Economics, Florida International University, DM-316, Miami, Florida matcole@fiu.edu 1

2 1 Introduction A common approac in te trade literature is to use iceberg transport costs, sipping more tan one unit of output to ave one unit arrive as a portion melts away, to represent variable trade barriers; bot tariffs and sipping costs alike. For many models tis equivalence is a reasonable assumption. In models of perfect competition, iceberg transport costs and ad valorem tariffs are equivalent. In addition, if we are only interested in te intensive margin, ten te two trade barriers are equivalent even under monopolistic competition. However, despite te market price being identical under bot types of trade barriers in models wit monopolistic competition, te level of firm profit is not. Tis as far reacing implications as te level of profit determines firm entry and exit te extensive margin. 1 Te difference in firm profits exists because te firm is able to recoup a portion of its losses in transport via its monopolistic power, wereas tariff revenue is completely captured by te domestic government. Tis will become clearer later. Te purpose of tis paper is to make tree main points. Te first point relates to a key result of Eaton and Kortum (2002) and Caney (2008). Tese papers find tat te elasticity of trade flows wit respect to variable trade costs does not depend on te elasticity of substitution but rater it is equal to a parameter describing te dispersion of firm productivity. However, te variable trade costs in tese models are represented by iceberg transport costs and as we will sow, te elasticity of substitution does matter wit respect to tariffs. At first glance, tis may seem like a minor point. However, if te researcer is estimating a gravity model strictly based on te results of tese two models and tariffs are used as an explanatory variable, ten important cross sector variation would be ignored by not accounting for differences in sector elasticity of substitution. For instance, Yi and Van 1 Te different effect on firm profit is sown explicitly in Cole (2011), wic as fixed cost eterogeneity wit quasi-linear utility and analyzes ow iceberg transport costs and ad valorem tariffs affect te mass of varieties and welfare differently. Scröder and Sørensen (2011) additionally illustrate in a Meltiz (2003) type model ow tariffs differ from iceberg transport costs. Neiter of tese papers igligt tis difference in a gravity framework. For a welfare analysis on te differences between per-unit trade costs versus iceberg see Sørensen (2012). 2

3 Biesebroeck (2012) find tat differentiated goods ave te most sensitive tariff extensive margin elasticity by investigating Cina s induction into te WTO were Caney (2008) predicts te elasticity of te extensive margin is equal to one and does not depend on te elasticity of substitution. Moreover, if te researcer is calibrating a model of monopolistic competition to investigate te effects of a tariff reduction, teir predicted effects will be for non-value based transport costs and not value based costs like ad valorem tariffs or insurance. 2 Te second point of tis paper is to sow tat te elasticity of trade flows wit respect to ad valorem tariffs is greater tan te elasticity wit respect to iceberg transport costs. Tus, in monopolistically competitive models wit an active extensive margin, modeling iceberg costs as a generic variable trade cost may not be appropriate. For instance, Crozet and Koenig (2010) use data on Frenc firms to estimate te structural parameters of te Caney (2008) model and suggest tat te elasticity defined by iceberg transport costs can be used to infer te effects of canges in tariff policy. We sow tat suc an approac would result in downward biased conclusions since te tariff elasticity exceeds te transport cost one. Helpman, Melitz, and Rubinstein (2008) also provide a gravity model wit eterogeneous firms and estimate te structural parameters. 3 Tey igligt te importance of accounting for te extensive margin, wic is precisely te reason iceberg transport costs are different tan ad valorem tariffs. 4 Arkolakis et. al (2012) sow tat as long as te modeler assumes a CES import demand structure and a gravity equation, tere exists a common estimator of te gains from trade. Tis estimator depends only on te sare of expenditure on domestic goods and a gravity-based estimator of te elasticity of imports wit respect to variable trade costs (in wic iceberg transport costs are used to represent variable trade costs), te 2 We tank an anonymous referee for pointing out tat trade costs based on value (e.g. insurance) would ave a similar effect as to tariffs in my model. 3 MATT: HMR do not explicitly model tariffs using transport iceberg. Tey just don t model tariffs period. We need to be careful tat we don t say oters ave done someting tat tey actually didn t. Tey always talk about bilateral distance related costs. Tey only say at one point average tariffs end up in te estimated fixed effect if not controlled for directly. 4 Additionally, Lawless (2010) deconstructs te gravity equation into te extensive and intensive margins, igligting te importance of bot. 3

4 latter being te focus of tis paper. Furtermore, Giovanni and Levcenko (2013) use a model similar to Caney (2008) to investigate te welfare gains from trade liberalization, in particular, te gains from te extensive margin. Finally, Brienlic (2011) uses te Caney (2008) model (wit iceberg trade costs) to test firm level responses to te United States - Canada tariff liberalization of 1989 (CUSFTA). 5 Te second point illustrates ow te tree different elasticities are related to eac oter. Wen one correctly treats iceberg transport costs and ad valorem tariffs as different trade costs in a Caney (2008) type gravity model, an interesting (linear) relationsip arises between te elasticities wit respect to iceberg costs, ad valorem tariffs, and fixed cost of production. Specifically, we sow tat te sum of te elasticity wit respect to iceberg costs and fixed costs equals te elasticity wit respect to tariffs. Tis as empirical implications in tat a restriction on te estimated parameters is warranted. It also means tat one only needs to estimate two elasticities to infer te tird by appropriately constraining te coefficients. We apply our model to data on U.S. imports at te 10-digit HS level in te year We use tariff data from Jon Romalis s U.S. Tariff Database and calculate te iceberg transport costs from te available import data as reported by te U.S. Census. Since we are not aware of any direct measures of fixed costs of production at te product level, we examine several proxies for fixed costs. Our starting point is te inverse of te elasticity of substitution from Soderbery (2014) wic is estimated at te 10-digit HS level using U.S. data giving us product level variation as our oter variables. In order to allow for some country level variation as well (our tariffs and transport cost measures vary bot across products and countries), we interact te inverse of te elasticity of substitution wit four measures from World Bank s Ease of Doing Business Database: te ease of doing business index, cost to export, time to export, and days to export. Our results are consistent across te five proxies. We are able to empirically confirm tat tariff and transport cost elasticities are different, 5 MATT: We sould explicitly state tat tese two papers use iceberg to model tariffs as well, if tey do so. 4

5 wit te tariff one being larger, and tat te tariff elasticity is equal to te sum of te transport and fixed cost elasticities. We want to empasize tat te point of tis paper is not to claim te use of iceberg transport costs as a variable trade cost is not valid, nor is it our intention to discredit previous studies. Te purpose ere is to illustrate tat te extensive margin drives a wedge between te longstanding isomorpic relationsip of iceberg transport costs and ad valorem tariffs. Tis produces a necessary caveat wen making tariff policy recommendations based on models tat use only transport costs as trade barriers. Te rest of te paper proceeds as follows. Section 2 sets up te model, wile section 3 introduces trade into te model and finds te elasticities of trade flows wit respect to bot iceberg transport costs and ad valorem tariffs. In seciton 4 we examine our predictions empirically and section 5 concludes. 2 Setup We follow Caney (2008) very closely, maintaining te notation and setup, wit two main exceptions. First, we allow for an ad valorem tariff, s, to be carged on goods sipped from country i to country j in sector were t = 1 + s > 1. Secondly, we allow for te government to sell bonds to te general public in a very specific way. Tis is a simplifying assumption, but an important one, wic we will discuss in greater detail in subsection 2.3. Tere are N potentially asymmetric countries tat produce goods using only labor. Country n as a population of L n. Consumers in eac country maximize utility derived from te consumption of goods from H + 1 sectors. Sector 0 provides a single freely traded omogenous good tat pins down te wage in country n, w n. 6 Te oter H sectors are made of a continuum of differentiated goods. If a consumer consumes q 0 units of good 0, and q (ω) units of eac variety ω of good, for all varieties in te set Ω (determined in equilibrium), 6 We assume tat every country produces a positive amount of q 0. 5

6 se gets a utility U, U q µ 0 0 H ( ) [σ /(σ 1)]µ q (ω) (σ 1)/σ dω, (1) Ω =1 were µ 0 + H =1 µ = 1, and were σ > 1 is te elasticity of substitution between two varieties of good. 2.1 Trade Barriers and Tecnology Tere are tree types of trade barriers: two variable, tariffs, t, and iceberg transport costs, (τ, and a fixed cost, f. Eac firm in sector draws a random unit labor productivity ϕ from a Pareto distribution wit sape parameter γ. 7 Following Caney (2008), we assume te total mass of potential entrants in eac sector is proportional to w j L j. Te cost of producing q units of a good and selling tem in country j for a firm wit productivity ϕ is 8 c (p, q) = (t 1)pq + τ w i ϕ q + f (2) and te total revenue for te same firm is t pq. Terefore te profit is Π(p, q, ϕ) = t pq (t 1)pq τ w i ϕ q + f = pq τ w i ϕ q + f, (3) wic collapses to te familiar form found in te literature. Te tariff does affect profits, but only troug q, te quantity demanded. As is standard in tese models, te price a firm carges is a constant markup over marginal cost and te price a consumer pays is te price 7 Productivity is distributed over [1, + ) according to P ( ϕ < ϕ) = G (ϕ) = 1 ϕ γ, wit γ > σ 1. 8 For a cleaner equation, we abuse notation and drop te i, j subscripts on p and q. Tis is also consistent wit Caney (2008). 6

7 te firm carges plus te tariff or, p = p (ϕ) = t p = σ (σ 1) τw i ϕ σ t τw i (σ 1) ϕ Firm Price (4) Consumer Price (5) Note tat te tariff and transport cost ave te same effect on te price paid by consumers, owever te actual level of profit will be lower under an identical tariff wic will ave an effect on te extensive margin. To see tis insert te price (4) back into te profit function (3): Π(p, q, ϕ) = t [ σ (σ 1) τ w i ϕ ] q (t 1) [ σ (σ 1) τ w i ϕ ] q τ w i ϕ q + f, and as an illustrative example let w i ϕ = 100, σ = 2 and bot trade restrictions to be equal, t = τ = We decompose te firm s profit for sipping one unit in Table 1 wile only allowing for one trade barrier at a time. As can be seen, everyting is te same except te variable cost under an iceberg specification is less tan tat of a tariff. Te reason stems from wen te cost is incurred. Troug monopolistic power, te firm is able to recoup a portion of its losses in transport by carging a markup over marginal cost, wereas tariff revenue is completely captured by te domestic government. Table 1: Firm Profit Trade Barrier Revenue Variable Cost Fixed Cost Iceberg (t = 1, τ = 1.10) f Tariff (t = 1.10, τ = 1) (200)+100=120 f 7

8 2.2 Demand for Differentiated Goods Te total income spent by workers in country j, Y j, is te sum of teir labor income (w j L j ) and of te dividends tey get from teir portfolio (w j L j π), were π is te dividend per sare of te global mutual fund consisting of aggregated firm profits and government bonds. Tariff inclusive exports from country i to country j in sector, by a firm wit a labor productivity ϕ, are ( ) 1 σ p x (ϕ) = p (ϕ)q(ϕ) (ϕ) = µ Y j (6) Pj were P j is te ideal price index for good in country j. 9 If only tose firms above te productivity tresold ϕ kj in country k and sector export to country j, te ideal price index for good in country j, P j, and dividends per sare, π, are defined as N ( Pj = w k L k π = k=1 H =1 ϕ kj σ (σ 1) t kj τ w k ϕ ) 1 σ dg (ϕ) 1/(1 σ ) ( N k,l=1 w [ kl k ϕ π kl kl (ϕ) + b kl dg(ϕ)) (ϕ)] N n=1 w (8) nl n (7) were ( πkl(ϕ) = 1 (σ 1) ) τ kl w k ϕ q kl(ϕ) f kl (9) are te net profits tat a firm wit productivity ϕ in country k and sector earns from exporting to country l, and b kl = (t kl 1)p kl (ϕ)q kl (ϕ) t kl σ = ( ) (tkl 1) τ kl w k σ 1 ϕ q kl(ϕ) (10) is te return on country bond investments. Tis government bond activity plays an impor- 9 In an earlier version of tis paper, we used pre-tariff (F.O.B.) exports. Tis, owever, distracted from te main point wic is to igligt te differences in te extensive margin. Using pre-tariff exports creates an additional difference in te intensive margin, but tis is simply by construction. 8

9 tant simplifying role tat needs more explanation, but first note tat b kl is less tan te tariff revenue generated in country l for sector, wic is Tariff Revenue = (t kl 1)p kl (ϕ)q kl (ϕ) t kl = σ b kl since σ > 1. Tis means tat only a specific portion of tariff revenue is returned to consumers troug bond returns. 2.3 Home Government and Tariff Revenue It is important to note wy te particular treatment of government tariff revenue was cosen. An inerent part of te iceberg transport cost assumption is tat output is lost to te economy wereas tariffs create revenue for te government. Tis makes comparing te two trade restrictions problematic, particularly since our argument is tat tariffs affect te extensive margin differently tan typical transport costs (wic are based on quantity) regardless of any demand effects driven by tariff revenue. Terefore, we require te government to redistribute tariff revenue back to world consumers in a particular way. Tis is done for two reasons: it allows for a very reasonable point of comparison between te two trade barriers and it maintains te ig tractablility Caney s (2008) model. Toug it is not explicitly modeled wit iceberg transport costs in te literature, tere is in fact a transport sector tat receives income. It takes labor to produce te output wic is lost in transport and tis labor receives a wage. Given te assumption of te sector 0 (te numeraire), tis wage is identical across sectors wic means, from a worker s perspective, it doesn t matter wic sector (s)e is employed in, including te numeraire. Terefore, we assume tat watever government income from tariff revenue not used to pay bond olders is spent on te numeraire. It is often an assumption in te literature to simply ave te government trow tariff revenue away. For our purposes, eiter assumption yields te same result, but te latter would require an additional full-employment assumption. 9

10 In addition to teir wage, a worker receives income from a global mutual fund tat redistributes firm profits. Tis is a very nice assumption tat Caney (2008) uses to get zero profits witout aving te additional complexities of a free entry condition. Since firm profits are lower wit a tariff tan an identical iceberg transport cost, dividends from tis fund are lower and tractability is severely treatened. Terefore, we assume tat governments are active in te bond market and keep a budget tat results in a specific level of bond payments described by equation (10). Combining te firm profits, (9), wit government bond payments, (10), results in te following equation: ( ) r( ) = πkl + b 1 t kl = kl τkl w k q (σ 1) ϕ kl(ϕ) fkl, wic is identical to te dividends received in te Caney (2008) model tat only included iceberg transport costs. Tis means tat te income, associated wit eac variety in existence, consumers receive is identical regardless of ow te modeler cooses to represent trade barriers. 3 Trade wit Heterogeneous Firms In tis section, we caracterize te equilibrium wit trade. Due to te independence of sectors, we only consider sector and drop te superscript. Te profits firm ϕ earns wen exporting from country i to j are 10 π = µy [ j t σ σ (σ 1) ] 1 σ w i t τ f. ϕp j 10 Note tat in order for firm profits to be affected in te same way regardless of te trade barrier, income Y j would ave to be a multiple of t. 10

11 Define te tresold ϕ from π ( ϕ ) = 0 as te productivity of te least productive firm in country i able to export to country j: ( f t σ ) 1 (σ 1) ϕ = λ 1 Y j w i τ P j (11) were λ 1 = ( ) ( 1/(σ 1) σ σ σ 1 µ) is a constant. It is easy to see tat tariffs affect te tresold firm differently tan iceberg transport costs and tat, all else equal, a tariff would correspond to a a iger tresold (and productivity) tan an identical transport cost. Moreover, tere is empirical evidence tat supports tis; Yi and Van Biesebroeck (2012) find tat differentiated goods (goods wit a lower elasticity of substitution) ave te most sensitive tariff extensive margin elasticity by investigating Cina s induction into te WTO. 11 Recalling tat Y k = w k L k (1 + π) so w k L k = Y k, te price index can be written as (1+π) (σ 1) γ γ(σ 1) P j = λ 2 Yj θ j (12) were λ γ 2 = θ γ j = ( ) ( ) γ (σ 1) ( ) γ (σ 1) σ (σ 1) γ ( ) σ 1 + π γ µ (σ 1) Y N ( ) Yk (w k τ ) γ σγ 1+ 1 σ tkj f 1+ γ 1 σ kj. Y k=1 Te term θ j is a measure of country j s remoteness from te rest of te world suc tat τ represents te pysical distance and t represents its remoteness as a result of unilateral trade policy. Using te general equilibrium price index, (12), we can solve for firm level exports, te productivity tresolds and total world profits: 11 MATT: We can put our own evidence ere, correct? 11

12 ( ) (σ 1) Yj γ λ 3 Y x (ϕ) = 0 oterwise, ( θj w i τ t ) σ 1 ϕ σ 1, if ϕ ϕ (13) ( ) 1 ( Y γ w i τ ϕ = λ 4 Y j Y i = (1 + λ 5 )w i L i θ j ) (ft ) σ 1 (σ 1) π = λ 5 were λ 3, λ 4, and λ 5 are constants. 12 It is important to note ow tariffs and transport costs enter into te equilibrium firm level of exports and productivity tresolds. Since te price consumers pay is identical under te two trade costs, te quantity of eac variety sold is identical x (ϕ) wat canges is te number of varieties, ϕ. Tis difference translates into te following gravity equation: Total (tariff inclusive) exports, X, in sector from country i to country j are given by X = µ ( Yi Y j Y ) w iτ t σ σ 1 1 γ θ j γ f [ ] γ (σ 1) 1. (14) Exports are a function of country size (Y i and Y j ), workers productivity (w i ), te bilateral trade costs, variable (t, τ ) and fixed (f ), and te measure of j s remoteness from te rest of te world (θ j ). 13 It can easily be seen tat tariffs and trade costs enter te gravity 12 λ 3 = σλ 1 σ 4 [( ) ( ) ] 1 σ γ γ 1 λ 4 = µ γ (σ 1) (1 + λ 5 ) ( H σ 1 =1 λ 5 = 1 H =1 ) µ γ σ ( σ 1 γ ) µ σ 13 Te proof of equation (14) is available in te appendix. Furtermore, following Caney (2008), we also assume tat country i is small enoug and/or remote enoug, so tat θ j / t 0 and θ j / τ 0 12

13 function differently wic is purely driven by te extensive margin. Tis point is made more clearly by separating out te trade elasticities into te two margins. We additionally report te elasticity wit respect to fixed costs (as in Caney 2008): 14 Tariff: ϑ d ln X = (σ 1) d ln t }{{} + σγ σ 1 σ }{{} = σγ 1, (15) σ 1 Intensive Extensive Iceberg: ζ d ln X = (σ 1) + [γ (σ 1)] d ln τ }{{}}{{} = γ (16) Intensive Extensive Fixed Cost: ξ d ln X = 0 d ln f }{{} + γ σ 1 1 }{{} = γ 1. (17) σ 1 Intensive Extensive Tere are tree conclusions from tese elasticities tat warrant particular attention. Te first is tat te elasticity wit respect to tariffs is equal to te sum of te elasticity wit respect to iceberg and fixed costs: ζ + ξ = ϑ. (18) Tis means tat if te researcer believed tis model completely and took it to te data, se sould test tat te estimated coefficients satisfy tis restriction. If te restriction is not satisfied ten te parameters sould be resticted accordingly. Te second conclusion is straigtforward to see by comparing equation (15) wit (16) and also follows from point one trade flows are more elastic wit respect to canges in 14 As in Caney (2008), we report te negative of te elasticities. 13

14 tariffs tan transport costs, 15 ϑ ζ = γ (σ 1) σ 1 > 0. (19) Te difference between trade elasticities depends on two tings: te elasticity of substitution and dispersion of productivity among firms in equilibrium. Wit respect to te elasticity of substitution, te intuition is as follows: For igly competitive industries were a firm s markup is quite low, te ability of a firm to recoup some of its transport costs is also lower and tus te wedge between profit values is smaller. Additionally, te sape parameter of te firms productivity distribution plays an important role. Wen a sector as a ig γ, te smaller, less productive firms are producing relatively more of te sector s output. Since canges in tariffs ave a greater impact on weter tese firms are producing or not, it will ten also ave a greater impact on te industry s aggregate trade flow. Terefore, if one wises to use estimates of trade flow elasticities derived from data on distance, for instance, in order to assess te impact of tariff policy, te teory suggests tat tis estimate will underestimate te effect. In particular, tis is te case for industries tat are not very competitive (low σ) and are more omogeneous in productivity (ig γ). Te tird conclusion is tat te elasticity of substitution (σ) does play a role in te elasticity of trade flows wit respect to variable costs (contrary to te broad claim by Caney (2008) and Eaton and Kortum (2002)) wen te variable cost is a function of product value; e.g. ad valorem tariffs. 16 However, te claim by Caney (2008) tat te elasticity of trade flows is decreasing in te elasticity of substitution is not only maintained by using tariffs, but is strengtened by it: 17 dϑ dσ = γ < 0. (20) (σ 1) 2 15 It sould be noted tat te estimated elasticities are derived from exports tat include te tariff in te value. If a researcer was using data tat does not include tariffs, ten te difference would be even greater as ϑ = σγ σ 1, but again tis is by construction tat te intensive margin is more elastic. 16 Toug not explicitly sown in tis model, due to te specific treatment of income, it is intuitive tat oter trade costs suc as insurance would ave a similar effect. 17 Tis claim reverses te prediction of Krugman (1980). 14

15 It is crucial to point out ow important te extensive margin is for te last two results; equations (19) and (20). If, for example, tere was no entry and exit in te export sector, te tariff elasticity would be identical to te iceberg trade cost elasticity. Moreover, te magnitude would be increasing in te elasticity of substitution wic is te prediction of Krugman (1980). Terefore, as we move from te teory to te empirics, te reader sould keep in mind were a tractable (and simplified) teoretical model may fail us in te real world. In particular, te teory assumes tat te extensive margin is able to react to canges in trade costs in line wit te intensive margin. Tis can fail for various reasons; 1. Productivity is distributed by a discrete distribution instead of continuous. In tis case, te zero profit condition (equation (11)) becomes a non-negative profit condition and it is possible for te least productive exporting firm to make positive ex post profits and te next firm down in te productivity ladder would make negative profits if it exported. Terefore, a sufficiently small cange in trade costs would ave no effect on te extensive margin. 2. Eac country as free entry into te industry and no additional barriers to entry outside of te model. 3. In terms of timing, te model assumes firms can enter and exit te foreign market as quickly as an incumbent firm can adjust its production. Tis is particularly important in a time series model as te effect of te extensive margin would lag beind tat of te intensive margin oterwise. 4 Empirical Application We examine our model empirically using U.S. 10-digit HS imports data sourced from te U.S. Census Imports of Mercandize for te year To conduct an empirical investigation, in addition to trade data, we need tree more pieces of information: tariffs, transportation 15

16 costs, and fixed costs of production. We use Jon Romalis s U.S. Tariff Database (Feenstra, Romalis, and Scott 2002) as te source of tariffs rates te U.S. assessed on Wile te Census data allows one to calculate ad-valorem tariffs as it provides information on duties collected and te dutiable value (as as been done by Besedeš and Prusa 2013, among oters), we prefer to use te U.S. Tariff Database in tis application as it provides us wit actual tariffs te U.S. assesses, te rates wic firms react to. In our application we only use data on products wit positive tariffs, as our model applies to instances were trade costs are positive. 18 Te Census data allows us to calculate te ad-valorem transportation cost for every country-product pair observed in te data. We use te ratio of import carges (all freigt, insurance, and oter carges exclusive of te tariff carged) and imports as te iceberg-melt factor. Te most difficult data to obtain for our exercise are data on fixed costs of production at te country-product level. We are not familiar wit any source of data providing suc information, so we resort to several proxies for fixed costs. Assuming constant marginal costs (as is te case in our model following equation 2) and increasing returns to scale in production, te elasticity of substitution is directly related to fixed costs, wit a lower elasticity implying iger fixed costs. Our first proxy for fixed costs is te inverse of te elasticity of substitution tat we source from Soderbery (2014), wo provides estimates of te elasticity of substitution at te 10-digit HS level. We use te inverse of te elasticity of substitution so tat a iger value corresponds to iger fixed costs. One potential difficulty wit respect to using te elasticity of substitution as a proxy for fixed costs is tat it only varies across te 10-digit HS product codes, but not countries. In order to introduce variation across countries we interact te inverse of te elasticity of substitution wit data from World Bank s Ease of Doing Business Database wic ave been used to proxy for fixed costs: te ease of doing business index, cost to export, documents to export, and time to export. We 18 Te inclusion of imports of zero-tariff products wic face positive transport and fixed costs would bias te elasticity of trade wit respect to tariffs downward given tere would be a number of observations wit a zero tariff. Our results reported below are qualitatively uncanged if we include all zero-tariff observations along wit a dummy variable wic identifies tem (results available on request). 16

17 use eac measure for te earliest year available wic is 2011 for te ease of doing business index and 2005 for te remaining tree measures. As we will sow, our results are not particularly sensitive wit respect to any of tese four measures. We estimate a gravity equation using OLS wit te log of U.S. imports of product from country i (ln Xi ) as our dependent variable and regress it on te log of tariffs (ln t i ), transportation costs (ln τi ), and fixed costs (ln fi ) as te dependent variables. We include country level fixed effects as a proxy for multilateral resistance terms (r i ). We estimate ln X i = β 0 + β 1 ln t i + β 2 ln τ i + β 3 ln f i + r i + ɛ i were β 1 = ϑ, β 2 = ζ, β 3 = ξ, and ɛ i is te error term. Te results from our basic specification using all available data are sown in Table 2.Te last two rows in te table report te p-values resulting form testing weter estimated coefficients satisfy restriction 18, tat te elasticity of trade flows wit respect to tariff and transport costs add up to te elasticity wit respect to fixed costs, and and restriction 19, tat te elasticity wit respect to tariffs exceeds te elasticity wit respect to transport costs (in te case of te latter we report p-values from te one-sided test). We first note tat our estimated coefficients are largely consistent across te five difference proxies of fixed costs we use. Our estimates imply tat te elasticity of U.S. imports wit respect to tariffs is between and , wit respect to transport costs between and , and wit respect to fixed costs between and However, we are more interested in ascertaining weter te implied restrictions are satisfied tan in te size of te estimated coefficients. Let us first focus on Result 1. In every specification we cannot reject te ypotesis tat te elasticities wit respect to transport costs and fixed costs add up to te elasticity wit respect to tariffs. Since we only use a proxy for fixed costs, and not direct measures of fixed costs, our preference is tat we test weter te coefficient satisfy te predicted relationsip, rater tan appropriately constraining estimated coefficients. 17

18 Table 2: Full Sample Fixed cost proxy Elasticity of substitution interacted wit Elasticity of Ease of doing Cost Documents Time substitution business to export to export to export Tariff rate ( ϑ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Transport cost ( ζ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Fixed cost ( ξ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Constant *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Observations 72,970 69,471 69,100 69,100 69,100 Number of countries R Test p-values Result 1 ϕ = ζ + ξ Result 2 ϕ > ζ Te dependent variable is log of imports. Country fixed effects are included, robust standard errors clustered on countries are in parentesis wit *, **, *** denoting significance at 10%, 5%, and 1%. However, we note tat te trade elasticity is very close to being equal to te sum of te oter two elasticities. As far as Result 2 is concerned note tat in every specification te tariff elasticity is estimated to be larger tan te transport cost elasticity (in absolute value). Note owever, tat only wen we proxy for fixed costs using bot te elasticity of substitution and ease of doing business data do we get some evidence of te tariff elasticity being significantly iger tan te transport cost elasticity. But even in tose cases, we ave significance only at te 10% level. However, as discussed at te end of section 3 it is possible tat te extensive margin differs across products wit products were tere is a lot of entry and exit and products wit little entry and exit. For te latter group of products, we sould observe no differences in tariff and transport cost elasticities, wile te difference sould be significant for products were tere is a lot of activity along te extensive margin. In order to examine te extent to wic te extensive margin affects our results we split our sample according to te extent of activity on te extensive margin. For eac product we calculate net entry (exit-entry) 18

19 and re-estimate our model for te ig net entry sample and te low net entry sample. We define ig net entry sample as tose products wit net entry below te 10 t and above te 90 t percentile of observed net entry wic corresponds to net entry less tan -2 and more tan 5 (te former implies tat te number of exits in 2000 was by at least 3 larger tan te number of entries and te latter implies tat te number of entries exceeded exits by at least 6). Table 3 collects te results from estimating our model using te ig net entry sample. Table 3: Hig Net Entry Sample Fixed cost proxy Elasticity of substitution interacted wit Elasticity of Ease of doing Cost Documents Time substitution business to export to export to export Tariff rate ( ϑ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Transport cost ( ζ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Fixed cost ( ξ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Constant *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Observations 15,821 15,093 14,979 14,979 14,979 Number of countries R Test p-values Result 1 ϕ = ζ + ξ Result 2 ϕ > ζ Te dependent variable is log of imports. Country fixed effects are included, robust standard errors clustered on countries are in parentesis wit *, **, *** denoting significance at 10%, 5%, and 1%. Differences in te extensive margin across products play an important role. Limiting our sample to just tose products were tere is more activity along te extensive margin, improves our results. Not only does te difference between te trade and transport cost elasticities grow, it is significant at at least te 5% level in every specification. In addition, we again cannot reject te ypotesis tat te trade elasticity is equal to te sum of te transport cost and fixed cost elasticities. To fully confirm te important role played by te extensive margin, Table 4 collects te results from estimating our specifications on te remaining sample of products caracterized by low net entry. Not tat in tis sample Result 19

20 1 still olds, but not Result 2, confirming te teoretical prediction tat wen tere is not muc activity along te extensive margin te elasticity of trade flows wit respect to tariffs equals tat wit respect to transport costs. Table 4: Low Net Entry Sample Fixed cost proxy Elasticity of substitution interacted wit Elasticity of Ease of doing Cost Documents Time substitution business to export to export to export Tariff rate ( ϑ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Transport cost ( ζ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Fixed cost ( ξ) *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Constant *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) Observations 57,149 54,378 54,121 54,121 54,121 Number of countries R Test p-values Result 1 ϕ = ζ + ξ Result 2 ϕ > ζ Te dependent variable is log of imports. Country fixed effects are included, robust standard errors clustered on countries are in parentesis wit *, **, *** denoting significance at 10%, 5%, and 1%. Unfortunately, our data preclude us from examining Result 3 empirically, tat te elasticity of trade wit respect to tariffs is decreasing in te elasticity of substitution. We use te elasticity of substitution as a proxy for fixed costs giving us product level variation. For tis reason we are reluctant to also use it as elasticity of substitution given te difficulty tat would create in interpreting our results. 5 Conclusion It is common in te trade literature to simply assume iceberg transport costs as a general proxy for many types of trade restrictions (in particular ad valorem tariffs). Wen perfect competition is assumed te two trade barriers are analogous. However, in te often used 20

21 model of monopolistic competition, tis is no longer te case, particularly if tere is a lot of activity on te extensive margin. By using te Caney (2008) framework, we illustrate tat trade flows are more elastic in response to canges in tariffs tan iceberg transport costs and are a function of te elasticity of substitution. Since it is quite common to use distance to represent trade restrictions in gravity equations, it is important to understand tis difference between tariffs and transport costs wen anticipating te affects of tariff policy. Furtermore, we illustrate an interesting linear relationsip between te elasticity wit respect to all tree trade costs. We find tat te elasticity wit respect to tariffs is equal to te sum of te elasticity wit respect to iceberg and fixed costs. We validate our model empirically using data on U.S. imports sowing tat te tariff elasticity exceeds te transport cost one, especially wen tere is a lot of activity along te extensive margin, and tat te tariff elasticity is equal to te sum of te te transport cost and fixed cost elasticities. Te contribution of tis paper is not limited to strictly empirical tests of gravity models. Te researcer s decision on ow to model trade costs in a monopolistically competitive framework (wic as been te predominant workorse model for international trade for te past 30 years) as important implications for calibrated models seeking to estimate te effects of trade liberalization and empirical studies explaining te decision of firms to become exporters as well. In te end, trade costs in te real world can be diverse and difficult to encapsulate easily in a unified teoretical framework. Ultimately, it is an empirical question, but tis paper adds a more complete teoretical picture. References [1] Arkolakis, Costas, Arnaud Costinot, and Andrés Rodriguea-Clare New Trade Models, Same Old Gains? American Economic Review, 102(1), [2] Besedeš, Tibor and Tomas J. Prusa (2013), Antidumping and te Deat of Trade, NBER Working Paper No

22 [3] Breinlic, Holger Heterogeneous Firm-Level Responses to Trade Liberalisation: A Test Using Stock Price Reactions. CEP Discussion Paper No [4] Caney, Tomas Distorted Gravity: Te Intensive and Extensive Margins of International Trade. American Economic Review, 98(4), [5] Cole, Mattew T Not All Trade Restrictions are Created Equally. Review of World Economics (Weltwirtscaftlices Arciv), 147(3), [6] Crozet, Mattieu and Pamina Koenig Structural Gravity Equations wit Intensive and Extensive Margins. Canadian Journal of Economics, 43(1), [7] Eaton, Jonatan and Samuel Kortum Tecnology, Geograpy, and Trade. Eonometrica,70(5), [8] Feenstra, Robert C., Jon Romalis, and Peter K. Scott U.S. Imports, Exports and Tariff Data, NBER Working Paper No [9] Helpman, Elanan, Marc Melitz, and Yona Rubinstein Estimating Trade Flows: Trading Partners and Trading Volumes. Quarterly Journal of Economics, 123(2), [10] Giovanni, Julian di and Andrei Levcenko Firm Entry, Trade, and Welfare in Zipf s World. Journal of International Economics, 89(2), [11] Krugman, Paul Scale Economies, Product Differentiation, and te Pattern of Trade. American Economic Review, 70(5), [12] Lawless, Martina Deconstructing Gravity: Trade Costs and Extensive and Intensive Margins. Canadian Journal of Economics, 43(4), [13] Melitz, Marc Te Impact of Trade on Intraindustry Reallocations and Aggregate Industry productivity. Econometrica, 71(6), [14] Scröder, Pilipp and Allan Sørensen A welfare ranking of multilateral reductions in real and tariff trade barriers wen firms are eterogenous. Mimeo, Department of Economics and Business, Aarus University. [15] Soderbery, Anson Estimating Import Supply and Demand Elasticities: Analysis and Implications. Purdue University, mimeo. [16] Sørensen, Allan Additive versus multiplicative trade costs and te gains from trade. Working Paper. [17] Yi, Yingting and Joannes Van Biesebroeck Trade liberalization and te extensive margin of differentiated goods: Evidence from Cina. Working Paper. 22

23 A Matematical Appendix A.1 Deriving te Gravity Equation Aggregate Exports in sector from country i to country j is X = w i L i x (ϕ)dg(ϕ). Using te specific assumption about te distribution G, tis becomes X = w i L i Solving tis integral yields: ϕ λ 3 ( Yj Y ϕ ( ) (σ 1) γ θ j ) σ 1 w i t τ ϕ σ 1 ϕ γ 1 dϕ. γ ( ) ( ) (σ 1) σ 1 [ ( ) ( X Yj γ θ j w i L i λ 1 = 3γ Y λ γ wi τ Y w i t τ 4 γ (σ 1) Y j θ j ( ) ( ) γ = w i L i λ Yj 3 (t Y ) 1 σ γ θ σ 1 j γ [ λ 1 w i τ 4 (f ) γ (σ 1) ( ) ( = λ 3(λ 4) (σ 1) γ γ wi L i Y j (t γ (σ 1) Y ) 1 σ γ wi τ σ 1 θj ( ) ( = σ (λ 4) γ γ wi L i Y j (t γ (σ 1) Y ) 1 σ γ wi τ σ 1 θj ( ) ( ) = µ (1 + λ wi L i Y j 5) (t Y ) 1 σ γ wi τ γ (σ 1) γ σ 1 (σ f 1) θ j ( ) ( ) Yi Y j = µ (t Y ) 1 σ γ wi τ γ (σ 1) γ σ 1 (σ f 1) θ j ) ] (σ 1) γ (ft ) σ 1 (σ 1) ] (σ 1) γ (σ 1) ) γ (σ 1) γ (σ f 1) ) γ (σ 1) γ (σ f 1) Terefore, total X in sector from country i to country j are given by X = µ ( Yi Y j Y ) w iτ t σ σ 1 1 γ θ j γ f [ ] γ (σ 1) 1. (A-9) 23

24 A.2 Deriving Elasticities Totally differentiating (A-9) for a specific sector and assuming df = 0 yields te following elasticities: 19 ( d ln X = dx /dt = t ) x (ϕ) w i L i dg(ϕ) + t ( w i L i x( ϕ )G ( ϕ ) ϕ ) d ln t X /t X ϕ t X t }{{}}{{} Intensive margin Extensive margin ( d ln X = dx /dτ = τ ) x (ϕ) w i L i dg(ϕ) + τ ( w i L i x( ϕ )G ( ϕ ) ϕ ) d ln τ X /τ X ϕ τ X τ }{{}}{{} Intensive margin Extensive margin Using te definition of equilibrium individual exports from equation (13), and assuming tat country i is small enoug and/or remote enoug, so tat θ j / t 0 and θ j / τ 0, we get x (ϕ) t = (σ 1) x (ϕ) t Integrating over all exporters, we get and x (ϕ) τ Elasticity of te intensive margin w.r.t. tariffs = t X = (σ 1) x (ϕ) τ. ( ) x (ϕ) w i L i dg(ϕ) ϕ = (σ 1) t X w i L i = (σ 1) t X X t = (σ 1). t ϕ x (ϕ)dg(ϕ) Now, define x = λ ϕ σ 1 and note tat G (ϕ) = ϕ γ 1 /γ. Aggregate exports can be written in te following way X = w i L i λ ϕ σ 1 γϕ γ 1 = = ϕ γ γ (σ 1) w il i λ ϕ (σ 1) γ 1 γ (σ 1) w il i x ( ϕ)g ( ϕ) ϕ. 19 Te focus of tis paper is to compare te effects of iceberg transport costs wit tat of an ad valorem tariff, tus analyzing canges in fixed costs would not add anyting to te paper and would be exactly tat found in Caney (2008). t 24

25 We terefore get te simple solution for te elasticity: Elasticity of te extensive margin w.r.t. tariffs = t X Similarly for iceberg transport costs: = t X ( w i L i x ( ϕ)g ( ϕ) ϕ ) t ( ) wi L i x ( ϕ)g ( ϕ) ϕ σ t σ 1 ( ) X σ σ 1 = (γ (σ 1)) t X = σγ σ 1 σ. Elasticity of te intensive margin w.r.t. iceberg costs = τ X t ( ) x (ϕ) w i L i dg(ϕ) ϕ = (σ 1) τ X w i L i = (σ 1) τ X X τ = (σ 1). τ ϕ x (ϕ)dg(ϕ) Elasticity of te extensive margin w.r.t. tariffs = τ ( w i L i x ( ϕ)g ( ϕ) ϕ X τ = τ ( ) wi L i x ( ϕ)g ( ϕ) ϕ X τ = (γ (σ 1)) τ ( ) X = (γ (σ 1)). Te elasticity wit respect to fixed costs (as is wit iceberg transport costs) is identical to tat of Caney (2008). X τ τ ) 25