Importers, Exporters and the Division of the Gainsfrom Trade∗†

Andrew B. Bernard

Tuck School of Business at Dartmouth, CEPR & NBER
Swati Dhingra‡

LSE, CEP & CEPR
This Version: October, 2016

Abstract
This paper examines the microstructure of import markets and the division of the gains
from trade among consumers, importers and exporters. When exporters and importers transact
through anonymous markets, double marginalization and business stealing among competing
importers lead to lower prots. Trading parties can overcome these ineciencies by investingin richer arrangements such as bilateral contracts that eliminate double marginalization andjoint contracts that also internalize business stealing. Introducing the microstructure of importmarkets into a trade model, we show that trade liberalization increases the incentive to engage
in joint contracts, thus raising the prots of these exporters and importers at the expense of
consumer welfare. We examine the implications of the model for prices, quantities and exporterimporter matches in Colombian import markets before and after the US-Colombia free trade
agreement. US exporters that started to enjoy duty-free access were more likely to increase
their average price, decrease their quantity exported and reduce the number of import partners.
These exporters increased their average tari-inclusive price by as much as 25%, leading to a
low average pass-through rate of less than 4% for all imports that received duty-free access into
Colombia.

Keywords: Heterogeneous rms, exporters, importers, pass through, contracts, microstructure, consumer welfare.
JEL codes: F10, F12, F14.

∗

We are grateful to John Morrow, Emanuel Ornelas, Gianmarco Ottaviano, Chris Snyder, Catherine Thomas,

Dan Treer, Tony Venables, Alwyn Young and seminar participants at Aarhus, Berkeley-Stanford, Bologna, ERWIT,
FGV Sao Paulo, IIFT, KU Milan, Oslo, Oxford, LSE, Paris, Princeton Summer Workshop, PSU, PUC, Salento,
SED, Sussex, Toronto, Tuck (Dartmouth), World Bank and UEA for helpful comments. We thank Giovanni Maggi
and Dan Treer for detailed discussions and Angela Gu and Yan Liang for excellent research assistance. A previous
version of this paper circulated under the title Contracting and the Divisions of the Gains from Trade.
†
100 Tuck Hall, Hanover, NH 03755, USA, tel: +1 603 646 0302, email: andrew.b.bernard (at) tuck.dartmouth.edu‡
Houghton Street, London, WC2A 2AE UK; tel: +44(0)20-7955-7804, email: s.dhingra (at) lse.ac.uk

Importers, Exporters and the Division of the Gains from Trade1

Introduction

Trade liberalization can generate substantial improvements in welfare through increased productvariety, lower prices and the reallocation of resources from less to more ecient producers. Domestic
consumers gain from easier access to imports, but they rarely have direct access to foreign products.
Trade is typically between rms who exercise market power in buying and selling foreign products.
This paper examines how the behavior of importers and their relationships with exporters aect thedivision of the gains from trade. Trading partners make endogenous choices among dierent typesof contracts, which gives them dierent degrees of market power in importing. Trade liberalizationaects the incentives for dierent contracts. This leads to a change in the microstructure of importmarkets, which provides a qualitatively new channel for the division of the gains from trade. Foreignexporters and domestic importers potentially gain market power and benet at the expense ofdomestic consumers.
In line with the concerns of the European Commission and the Federal Trade Commission,
market integration can induce rms to replace trade barriers with microstructures that limit thegains from market access to consumers (Ra and Schmitt 2005).

Typically, foreign competitionis associated with lower price-cost margins (Tybout 2003; Levinsohn 1993; Harrison 1994) but agrowing literature documents that the pass-through of border prices into home market prices is low

1 In our framework, the low pass-through of tradein macro studies and in detailed micro work.

cost reductions into import prices is a result of the changes in the contracts between exporters andimporters.
Exporters and importers operate in thin markets, that do not reect anonymous transactions.
Anonymous transactions lead to two ineciencies in prot maximization. First, when exporters andimporters engage through anonymous market-clearing prices, market power of importers leads todouble marginalization and lower prots. Exporters can overcome this ineciency by moving awayfrom unit prices and oering bilateral contracts that specify total payments and quantities. Second,
importers in an anonymous market are unable to internalize the business stealing eect of their sales
on competing importers that sell varieties of the same foreign product. An exporter can mitigate
this externality by investing in joint contracts with these competing importers. This leads to higher
prots by restricting sales and driving up prices charged to consumers. We embed the microstructureof richer contracts into a standard trade model. The microstructure channel reinforces the gains

1

See for example Engel and Rogers (1996); Burstein et al. (2003); Campa and Goldberg (2005) in the macro

literature. Detailed micro studies include Ganslandt and Maskus (2004) for Swedish pharmaceuticals, De Loecker
et al. (2012) and Mallick and Marques (2008) for Indian manufacturing, Badinger (2007) for manufacturing andservices in the European Single Market, and Konings et al. (2005) for Bulgarian and Romanian manufacturingindustries.

1

Importers, Exporters and the Division of the Gains from Tradefrom trade when rms enter into bilateral contracts that mitigate double marginalization. But asrms start to invest in internalizing business stealing, trade liberalization increases their market
power and aects the division of the gains from trade.

They engage in complex relationships toovercome the ineciencies of anonymous markets.
In our model, market expansion increases the returns to joint contracts, relative to bilateralcontracts. This is because market expansion enables rms to better amortize the higher xed costsof joint contracts and because import competition does less damage to the prots of rms withgreater market power.

As rms switch to joint contracts, they internalize the business stealingeect of their sales. They raise consumer prices and get more of the surplus from consumers. We
show that the microstructure eect is a new channel for the gains from trade that goes beyond thestandard gains from variety expansion and pro-competitive eects, and that increases prots at theexpense of consumer welfare.
To test for the microstructure eect, we would ideally like to examine the impact of tradeliberalization on the actual relationships between exporters and importers. Such data is unavailable
so we examine the distinct observable implications for prices, quantities and exporter-importer
matches during a period of trade liberalization. If the microstructure matters, trade liberalization
will induce exporters to consolidate their import market. They will benet from higher prices byscaling back on the quantity they sell and the number of importing partners that they sell to in
the liberalizing country. We test these implications for Colombian imports before and after the USColombia Free Trade Agreement (FTA) using transaction-level matched importer-exporter data. In
keeping with the theory, we nd that US exporters whose products started to enjoy duty-free accessthrough the FTA were more likely to simultaneously increase their import price, lower their quantity
and reduce the number of their importer partners in Colombia. This conrms the Metzler paradoxof domestic prices rising in response to tari reductions and we nd that it persists after adjustingfor quality in prices. Among exporters with more than $10,000 of sales in the Colombian market,
rms in the rst and second terciles of initial size increased their free-on-board import prices by 8
to 30% on average. This contributed to a less than 4% average reduction in tari-inclusive prices
for all Colombian imports that received duty-free access.
The main theoretical contribution of the paper is to provide a model that embeds two-sided
market power in a general equilibrium setting.

We build on the vertical relations literature inindustrial organization to model the relationship between exporters and importers (Hart and Tirole
1990). While a large literature examines these relationships, its focus is on rm behavior, typicallyin a stylized setting of two buyers and sellers. We embed the rm behavior in a general equilibrium
setting with multiple rms, which is important for understanding the gains from trade because they
are also aected by the labor market and by rms' decisions to enter and exit product markets.This
is also useful in taking the theoretical predictions to trade data that is usually available through2

Importers, Exporters and the Division of the Gains from Traderm-level customs transactions.
Our focus on vertical relations is related to work in international trade on intermediation (Akerman 2010; Bernard et al. 2010; Blum et al. 2010; Ahn et al. 2011; Atkin and Donaldson 2012),
retailing (Eckel 2009; Ra and Schmitt 2012; Blanchard et al. 2013) and vertical integration (Feenstra et al. 2003; Antràs and Helpman 2004; Conconi et al. 2012).

As is well-known, embedding

two-sided market power in general equilibrium gives intractable models so many of these papers
focus on rm characteristics and abstract from the market power of importers. Ra and Schmitt(2005, 2009) examine importer market power in an oligopoly model of trade and retailing to show
trade liberalization can reduce welfare due to vertical restraints. We embed vertical restraints in a
general setting with many heterogeneous exporters and importers to obtain predictions that can betaken to the data. We obtain tractability by using the tools developed in the variable markups literature under monopolistic competition (Parenti et al. (2014); Neary and Mrazova (2013); Dhingra
and Morrow (2012); Mayer et al. (2014)). This enables us to generalize the results for rm behavior
to a wide class of demand functions, which is important in revealing new gains from trade that do
not arise under the knife-edge cases of standard demand systems.
The focus on consumption side gains is similar to a large literature on the impact of tradeliberalization on markups and prices. Tybout (2003) surveys the research using industry-level dataand plant-level panel data and concludes that most studies nd higher industry-level exposure
to foreign competition is associated with lower price-cost margins or markups, e.g.

Levinsohn(1993); Harrison et al. (2005). The pass-through of reductions in trade costs to domestic prices istypically low, and recent studies nd the behavior of domestic rms determines the extent to which
trade policy aects prices at home. Mallick and Marques (2008) nd low tari rate pass-throughinto import prices in Indian manufacturing during the liberalization of 1991.

De Loecker et al.

(2012) estimate that on average, factory-gate prices fell by 18 percent despite average import tari
declines of 62 percentage points, as domestic Indian rms did not pass on the reductions in trade
costs to consumers. Badinger (2007) nds the European Single Market led to an overall reduction
in markups for manufacturing products, but markups rose in several manufacturing and services
industries that also experienced an increase in industry concentration and average rm size. In early
work on Japanese imports, Lawrence and Saxonhouse (1991) document that the presence of large
conglomerates at home is associated with lower import penetration, suggesting the import-inhibitingeects of rms with high market power. Lawrence (1991) argues market power of intermediaries
can explain why Japanese consumer prices were higher than German import prices for the same
export from the US. Yeats (1978) nds iron and steel prices are higher in more concentrated importmarkets. In early theoretical work, Venables (1985) shows unilateral reductions in trade barriers
can increase consumer prices in the liberalizing country when entry and exit induce prot shifting
across countries.

3

Importers, Exporters and the Division of the Gains from Trade

Our pricing predictions are consistent with these ndings, and provide systematic evidence for
the Metzler paradox (Venables 1985; Bagwell and Staiger 2012; Bagwell and Lee 2015). A reduction
in taris induces more consolidation in the import market of medium-sized US exporters in Colombia. Previous work has suggested that trade policy is a substitute for competition policy. Small open
economies can increase competition in the domestic market by integrating with world markets andbeneting from import competition. Our results show that when exporters and importers operate
in thin markets, trade policy and competition policy are complements. Trade liberalization would
be most benecial when competition policy is used in conjunction with trade policy to encouragerms to pass on the cost savings to consumers.
We introduce contracting choices to see how market power in import markets changes the gains
from trade. This is related to several dierent strains of work in international trade. Bernard et al.
(2009), Castellani et al. (2010) and Muuls and Pisu (2009) document substantial heterogeneity acrossimporting rms for the US, Italy and Belgium respectively and also show that importers dier from
non-importers. Papers by Rauch (1999), Rauch and Watson (2004), Antràs and Costinot (2011),
Chaney (2014) and Petropoulou (2011) model the formation of matches between exporters andimporters. These papers adopt a search and matching approach to match formation. Our paper
is also closely related to the recent set of papers using matched exporter-importer data.

Blum

et al. (2010, 2012) examine characteristics of trade transactions for the exporter-importer pairs ofChile-Colombia and Argentina-Chile while Eaton et al. (2014) consider exports of Colombian rmsto specic importing rms in the United States. Carballo et al. (2013) and Bernard et al. (2014)use matched data to study the role of buyers in rm-level trade ows.

We abstract from thesemechanisms and focus on the microstructure of import markets to understand the resulting eects
on prices, quantities and the division of the gains from trade. A growing literature also shows how
imported inputs increase the productivity of importers, see Amiti and Konings (2007), Halpern
et al. (2015), Boler et al. (2015) and Fieler et al. (2014). We focus on the consumption side role ofimporters.
The rest of the paper is organized as follows: Section 2 introduces a model where exporters
and importers transact through anonymous markets, as a benchmark. We then introduce bilateralcontracts and joint contracts, and show that trade liberalization aects the division of the gains
from trade among domestic consumers, home importers, and foreign exporters. Section 3 develops
the testable predictions of the model for prices, quantities, and matches. Section 4 takes the testablepredictions to Colombian import data and Section 5 concludes.

2

Model of Exporters and Importers

This section describes the economy which consists of consumers, exporters and importers. We workwith a standard trade model akin to Krugman (1979), and introduce importers with market power.

4

Importers, Exporters and the Division of the Gains from Trade

As is well-known, two-sided market power in an industry equilibrium often leads to intractablemodels. This is why several papers in intermediation abstract from market power at least on one
side of the market. As our focus is on the division of the gains from trade, we model market power ofexporters and importers in an industry equilibrium. We achieve this by using the tools developed inDhingra and Morrow (2012) for monopolistic competition trade models. For ease of exposition, we
start with homogeneous rms in this Section. The next Section examines the testable variety-level
predictions of the theory under rm heterogeneity and xed entry.
In a standard setting, exporters sell to importers in anonymous markets which means they set
a unit price at which any importer can buy from them.

We rst model the rm problem in ananonymous market with unit prices, and show that market power results in double marginalization
and business stealing among importers of a product. When exporters are not constrained to set unit
prices, exporters and importers choose payments and quantities that maximize their joint prots
by overcoming the externalities induced by an anonymous market. We specify the simplest settingthat departs from anonymous markets to provide a richer microstructure for the import market.
There are two countries, Home and Foreign (with x indexing exports from the foreign country
to the home country). Dierentiated products are produced at home and abroad, and are further
dierentiated by domestic rms (importers) who sell to consumers. The home country has L workers,
each of whom is endowed with a unit of labor and has preferences over consumption goods. We
specify the demand and technology in the next sub-sections, and then discuss rm decisions underanonymous markets.

2.1 Preferences
Each worker has identical preferences over varieties of a dierentiated good. Preferences for dierentiated goods take the form of nested variable elasticity of substitution (VES) utility. A dierentiatedproduct in the upper nest is indexed by i, and is a composite of further dierentiated variants inthe lower nest which are indexed by ij . The utility function is as follows:ˆU≡ˆ
u(qi )di,qi =v(qij )dj,

u0 , v 0 > 0, u00 , v 00 < 0.

The VES inverse demand builds on a growing literature of variable markup frameworks like Parenti
et al. (2014); Neary and Mrazova (2013); Dhingra and Morrow (2012); Mayer et al. (2014). The subutility functions u and v are thrice continuously dierentiable, strictly increasing, strictly concaveon (0, ∞), normalized to zero at zero quantities and satisfy Inada conditions. Concavity ensuresthat consumers purchase all available varieties and the inverse demand for variety ij ispij = v 0 (qij )u0 (qj )/δ5(1)

Importers, Exporters and the Division of the Gains from Trade

where δ is the consumer's budget multiplier. For a worker with income I , the budget multiplier isˆ ˆδ=qij v 0 (qij )u0 (qj )didj/I.

A well-dened equilibrium will require conditions on the demand elasticities across the two nests

0of preferences. Following Dhingra and Morrow (2012), the elasticity of utility is εx (q) ≡ x (q)q/x(q)for x ∈ {u, v} and the elasticity of marginal utility is µx ≡ −x

00 (q)q/x0 (q). These elasticities arebounded below by b > 0 and above by 1 − b < 1, and are increasing in q . To x ideas, CES demandis x(q) = q

ρ which implies ε (q) = ρ and µ (q) = 1 − ρ are between 0 and 1, and correspond to the
x
x
0

0

special case with εx (q), µx (q) = 0. While CES demand provides simple pricing decisions, we departfrom CES demand because it gives knife-edge results that trade liberalization has no impact on the
microstructure, similar to the lack of pro-competitive eects in Krugman (1979) and Melitz (2003)
under CES demand.

2.2 Technology
Following Krugman (1980), there are Mc identical producers at home. Each producer supplies a
unique dierentiated product with a linear technology. Each producer faces a unit cost c. Producers
are monopolistically competitive and pay xed operation costs fc . Producers cannot directly accessnal consumers. They must engage distributors to deliver their products to consumers.
There are Md identical distributors at home. Producers at home and abroad must sell throughthese distributors to the consumers. Distributors are monopolistically competitive and transformthe producer's product into a dierentiated variety for nal consumption. A distributor with unit
cost d transforms producer c's product from x(c) units of production into y(c, d) = x(c)/d units ofthe nal dierentiated variety. If p
the unit cost of a distributor is p

x (c) is the unit price of variety c charged by the producer, thenx (c)d. Under this formulation, distributors perform the function oflowering the costs of delivery to consumers.
Before proceeding to the equilibrium, we need to specify where the producers and distributors
t into the nesting structure of demand. To capture rich substitutability patterns, we specify theupper nest quantity as qj = θqc + (1 − θ)qd for θ ∈ {0, 1}. When θ = 0, qj = qd and distributors
are in the upper nest. For θ = 1, qj = qc and producers are in the upper nest. We will show thatθ = 1 leads to interesting results because the lower nest distributors do not internalize the impactof their sales on other distributors. This provides a role for richer contracting arrangements andgives new results for the impact of trade liberalization on the gains from trade. As we will initially
focus on a free trade equilibrium, all rms will engage in international trade and we will use theterm exporters to denote c rms and importers to denote d rms.

6

Importers, Exporters and the Division of the Gains from Trade

2.3 Anonymous Market Equilibrium
A natural way of introducing importers into a standard trade model is through anonymous market
transactions. An exporter chooses the market price for her product and then takes her product toan import market. The importers choose how much to buy. They further dierentiate the productand supply nal varieties to consumers. Then cd indexes a nal variety exported by c and imported
by d. We start with this benchmark case of anonymous markets to illustrate the ineciencies thatlead to richer relationships between exporters and importers. To formalize the setting, the timing
is as follows.

• Firms pay their xed costs of operation (fc ,fd ).
• c chooses her market price px (c).
• d buys xcd units at price px (c).
• Quantities qcd are supplied to nal consumers at price pcd .
Markets are segmented and we solve for an equilibrium by rst determining the nal quantities soldto consumers. Then we derive the demand for the producer's product and determine the optimal
price chosen by the producer. We abstract from variety-specic search costs fcd until the Section
with heterogeneous rms where they lead to interesting selection eects.

2.3.1 Prices in Anonymous Markets
Importer d faces the inverse demand function pcd= v 0 (qcd )u0 (θqc + (1 − θ)qd ) /δ .

He cannot in-uence the aggregate market conditions δ and the producer's total sales in the home country qc .

x

At unit price pc of c's product, the importer chooses nal quantities qcd and his total quantity qd
to maximize prots. His variable prot is πd ≡ Mc






pcd qcd , qd , q̂c , δ̂ − pxc d qcd Ld where the hat

denotes that the distributor takes these components of the inverse demand as given. Summing thexdemand of all importers in the home country xc ≡ Md xcd Ld = Md dqcd (pc ) Ld , exporter c chooses

pxc to maximize variable prots πc = Md (pxc − c) dqcd (pxc ) Ld .
To ensure a well-dened rm problem, we assume that marginal revenues are decreasing and0that µv q < (1 − µv ) (1 − µv − µu εv ). We will also assume that µu εv ≤ min µv · min (1 − µv ) which
ensures that the direct impact of own quantity on price is greater than the indirect impact of othervarieties through the upper nest quantities.

This condition is equivalent to the substitutability

restriction of a nested CES demand system and later we will show that it ensures prices are higher
under anonymous markets compared to bilateral and multilateral prot maximization among rms.
Under anonymous markets, the optimal price chosen by d is

pcd = pxc d/(1 − θ)u0 (qd )1 − µv (qcd ) − 0µu (qd )εv (qcd )θu (qc ) + (1 − θ)u0 (qd )7Importers, Exporters and the Division of the Gains from Tradex = c/ (1 − γ ) where γ ≡ µ
c
c
vcd +

. Using subscripts for brevity, the exporter's optimal price is pc

µ0vcd qcd / 1 − µvcd −(1−θ)u0 (qd )θu0 (qc )+(1−θ)u0 (qd )µu (qd )εvcd .

Putting the two optimal price functions together, the nal price of variety cd under anonymous
markets is









pcd = cd/ 

1−γ| {z }c

Double Marginalization(1 − θ)u0 (qd )µu (qd )εvcd 0 .
0θu (qc )+(1 − θ)u (qd )| {z }·
1 − µvcd −(2)Business Stealing

The rst term in square brackets in Equation 2 is the markup charged by the exporter to the importer
which reects the classic double marginalization problem in anonymous markets. Exporters takex = c/ (1 − γ ) > c.
cinto account the derived demand for their product and charge pc

Importers

further mark up the price (with the term in parenthesis) and consumers end up with having to pay
double markups.

This double marginalization leads to lower bilateral prots for c and d due toreduced sales. If producers and distributors can engage outside of anonymous transactions, thenthey need not set market-clearing unit prices. They can specify payments and quantities that get
rid of double marginalization and increase the bilateral prots from their relationship.

We willconsider these bilateral contracts in the next Section and show that trade liberalization has theusual eect of increasing sales and reducing prices when exporters and importers transact underbilateral contracts.
The term in parenthesis shows the markup charged by the importer. Importers account for thecannibalization of their own varieties on each other.

This cannibalization translates into higher

nal markups through µu (qd ). But they do not account for the business stealing impact of theirsales on competing distributors of an exporter's product, which can be seen from the denominatorin parenthesis. There is no µu (qc ) in the optimal markup and competition among distributors inthe nal goods market implies that the total prot from an exporter's product is not maximized.
We will therefore consider joint contracts that maximize the total prots of an exporter and herimporters. While an importer can internalize cannibalization of her own varieties by virtue of being
second in the chain of sales, exporters and importers are unable to overcome the business stealing
externality through anonymous markets.
Anonymous markets therefore provide two reasons for switching to richer contracts. The rstreason is that unit pricing in anonymous markets leads to double marginalization which lowers thebilateral prot of an exporter and an importer. Bilaterally prot maximizing contracts that specify
payments and quantities can overcome the double marginalization problem and reduce consumer
prices.

Importers internalize the cannibalization of their own sales.

upper nest (θWhen importers are in the= 0), there is no other reason to enter into richer contracts with the exporters.

Bilateral contracts solve the double marginalization problem and the cannibalization eect is already8

Importers, Exporters and the Division of the Gains from Tradeaccounted for. The second reason for rms to move away from anonymous markets is that importers
do not account for their business stealing eects. When exporters are in the upper nest (θ = 1),
there is an incentive for an exporter and her importers to enter into joint contracts to get rid ofbusiness stealing. Consumer prices are higher compared to bilateral contracts because competition
among importers is reduced to maximize multilateral prots of the exporter and her importers.
Bilateral contracts reinforce the usual gains from trade because they reduce consumer prices
further.

Joint contracts have the opposite eects.

to increase the prices faced by consumers.

Competition in the import market is reduced

We examine how these richer arrangements between

exporters and importers determine the division of the gains from trade liberalization between exporters, importers and consumers.

To avoid a taxonomical analysis, we focus on the case where

exporters are in the upper nest and importers are in the lower nest, so that joint contracts aredesirable. We explain the contracting arrangements that mitigate the externalities of anonymous
markets and proceed to the industry equilibrium under this richer microstructure.

2.4 Microstructure of Import Markets
Exporters and importers often have long-standing and complex relationships. It is therefore likelythat they engage in contracts that overcome the ineciencies from anonymous transactions. Following the seminal work of Hart and Tirole (1990), we consider two distinct contracts that overcome
these ineciencies. The rst type of contract overcomes double marginalization by specifying quantities and payments that maximize bilateral prots of the exporter-importer pair. The second typeof contract overcomes double marginalization and business stealing by committing to all quantities
and payments that maximize the joint prot of an exporter and her importers.
The main advantage of the Hart-Tirole approach is that we do not need to specify the methods through which rms maximize bilateral prots or joint prots, and instead can focus on theobservable outcomes of quantities and payments that result from implementing prot-maximizing
contracts. For instance, an exporter can maximize bilateral prots by setting a two-part tari thatx (c) = c), and a xed fee that recoups

charges the importer a price equal to her marginal cost (ppart or all of the bilateral prots without changing sales incentives. The exporter could also havemaximized bilateral prots through resale price maintenance. The importer is then obliged to sell
at a price chosen by the exporter. As we will show later in this Section, when the exporter chooses
the nal price, the resulting quantity allocation is the same as a two-part tari and bilateral protsof the exporter-importer pair are maximized.
The industrial organization literature provides dierent methods through which rms avoid
double marginalization and business stealing, such as xed fees, quantity discounts and resale pricemaintenance.

2

2 These are rarely observable, and these methods can often take the form of informal

This is an area of ongoing research in industrial organization and Miklos-Thal et al. (2010) provide an overview

9

Importers, Exporters and the Division of the Gains from Tradepractices or implicit arrangements that are sustained through repeated interaction. Following Hart
and Tirole (1990), we therefore abstract from the methods used to implement bilateral or joint
prot maximization, and focus instead on the implications for observable outcomes, such as quantity
allocations and payments, that are the same across dierent methods.
We start with bilateral prot maximization and then discuss joint prot maximization.

Themarket does not maximize bilateral prots of an exporter-importer pair due to double marginalization.

This problem is overcome when an exporter engages in a

an importer.

bilateral private contract with

The bilateral contract species a nal quantity and a payment to be made to theexporter (qcd and Tcd ).

As the exporter no longer relies on unit prices that are marked up, thenal quantity is chosen to maximize the bilateral prot of the exporter-importer pair. Following
Horn and Wolinsky (1988), the exporter and the importer split the bilateral prots through Nashbargaining, and this determines the payments from the importer to the exporter.

The bilateralcontract overcomes double marginalization and results in higher quantities and lower prices for thenal consumers.
But bilateral contracts do not mitigate the business stealing externality imposed by importers
on each other.

The competition between dierent importers implies that prices are lower thanthe monopolistic price that the exporter would have chosen. The key insight of Hart and Tirole(1990) is that a seller cannot commit to selling lower quantities of her product because she would
prefer to bypass her existing buyers and sell more to earn higher prots. Even though the exporter
could oer contracts that account for the business stealing externality, this opportunism of theexporter prevents importers from entering into such arrangements because they know the exporter
would nd it more protable to deviate from these contracts. The exporter's opportunism prevents
maximization of multilateral joint prots.
To overcome business stealing, the exporter must commit to restricting the total sales of her
product to induce higher consumer prices by forming a

joint contract with her importers.3 Just

like bilateral contracts, joint contracts specify bilateral quantities and payments, but now the total
quantity of the exporter qc is also specied in the contract and is not simply an outcome of thedierent bilateral contracts. Joint contracts can be implemented through various methods such asvertical integration that would eliminate the exporter's opportunism by aligning the interests of allparties. The integrated parties would internalize business stealing to maximize joint prots, andconsumers would end up with lower quantities and higher prices than under bilateral contracts.
The exporter could also implement joint prot maximization through other methods that do not
involve ownership. For instance, importers would internalize business stealing if the exporter asof the ndings.

3

Joint contracts often refer to cross-ownership between the parties. We use the term joint contract to refer to acontracting choice between the exporter and importer which might, but does not necessarily, include cross-ownership.
Martin et al. (2001) and Mollers et al. (2014) use experimental data to show vertical restraints of various forms (thatdo not entail vertical integration of rms) are sucient to maximize joint prots.

10

Importers, Exporters and the Division of the Gains from Tradesigns them exclusive territories. The outcomes of the joint contract can also be replicated throughimplicit exclusive dealing when exporters have reputational concerns due to repeated interaction
with their importers (Rey and Tirole 2007). We abstract from the methods through which joint
prot maximization is implemented, and focus instead on observable outcomes such as prices andquantities.
To formally model the dierent microstructures resulting from these contracts, we specify thetiming as follows:• Exporters and importers pay their sunk costs of operation (fc , fd )• Exporters and importers meet each other.
• Exporters and importers decide whether to engage in bilateral or joint contracts and pay theircontracting costs.

• Importers order quantities xcd from the exporters and pay Tcd .
• Quantities qcd are supplied to nal consumers at price pcd .
Exporters and importers need to pay xed costs for contracting.

Both will decide whether it isworthwhile to engage in richer contracts, but only one of their conditions will be binding.

We

assume that the exporter's contracting condition is binding, because this will give new results forthe gains from trade.

In the opposite case, when importer's contracting costs are binding, thechange in the gains from trade goes in the same direction as the standard gains from trade. For
simplicity, we set the contracting costs incurred by importers to zero because this does not change4

the qualitative results from the model.

2.5 Bilateral Private Contracts
To overcome double marginalization, an exporter can make xed investments in bilateral contracts
that depart from unit pricing. After paying the xed costs, an exporter engages in private contracts
with each importer bilaterally.

Importers hold passive beliefs which means that they expect thecontracts oered to the other importers to be xed at their equilibrium values. We rst discuss thesurplus division, and then proceed to determining optimal prices and entry into bilateral contracts.

2.5.1 Importer Payments
Under bilateral contracts, the importer chooses quantities qcd to maximize his prot



B
πcd
= p(qcd , qd , q̂c , δ̂) − cd qcd − Tcd
4

No new information is revealed after the contracting costs are paid. If the contracting costs of each party are

sunk, then the opportunism problem remains and the qualitative results in the subsequent Sections are unaltered,but it would be more reasonable to think that the division of surplus is over the revenues, rather than prots.

11

Importers, Exporters and the Division of the Gains from Trade

where Tcd is the payment to exporter c for supplying xcd = dqcd units of her product sent to d.
The importer holds passive beliefs so he takes the contracts oered to his competitors as given

0 6= d). For exibility, we follow Horn and Wolinsky (1988) and assume that the((T̂cd0 , q̂cd0 ) for any dpayments are set through bilateral Nash bargaining, with β denoting the bargaining weight of theexporter and with zero disagreement payos. As d takes the contracts oered to other importers asgiven, the optimal payment from Nash bargaining is T̂cd =hiβp(qcd , qd , q̂c , δ̂) + (1 − β)cd qcd which

ensures the division of gross surplus is proportional to the bargaining weights.

5

Substituting for the optimal payments, d chooses to sell quantities that maximize

ˆ cmax (d) himax (1 − β)p(qcd , qd , q̂c , δ̂) − cd qcd dGc .

qcd ,qd

cmin (d)The prot function shows that an importer ignores how his quantity aects the prot of otherimporters of exporter c's product (through qc ) but internalizes the cannibalization eect of his own
quantities on each other (through qd ). The optimal nal price of variety cd under bilateral contracts
is








pB
cd = cd/ 1 − µvcd −
(1 − θ)u0 (qd )µu (qd )εvcd 0 ≡ cd/ (1 − µvcd − (1 − θ)µ̃d ) .
0θu (qc )+(1 − θ)u (qd )| {z }

Business Stealing(3)
This gets rid of the double marginalization problem because exporters do not charge unit pricesthat exceed their unit costs. In fact, optimal nal quantities correspond to a two-part tari wherexthe exporters do not mark up their costs (pc = c). We summarize this result in Proposition 1.

Proposition 1. Bilateral private contracts ensure lower prices than anonymous market transactions
because they eliminate double marginalization.
Bilateral contracts overcome double marginalization, but not business stealing as shown in Equation 3. The next sub-section discusses joint contracts that maximize multilateral prots from anexporter's product.

2.6 Joint Contracts
By partnering with her importers, an exporter can ensure that prots from her product are maximized by internalizing the business stealing eect imposed by importers on each other.

Joint

contracts provide higher prices, but involve xed investments in building a relationship.

This is5

Using experimental data, Martin et al. (2001) show that the ability to reject an upstream rm's oer enables

the downstream rm to get a positive share of the surplus from the relationship. In an alternative version of themodel, we show that our results hold when the exporters and importers can replicate the other party's role in therelationship to some degree. This follows from the drop in delivered costs of exports after a trade liberalization whichraise the ex-post bargaining share for exporters.

12

Importers, Exporters and the Division of the Gains from Trade

because exporters need to demonstrate that they are committed to restricting quantities to theirimporters.

We start with a discussion of the surplus division within the joint contract and thendetermine the optimal prices and the contracting decision.

2.6.1 Importer Payments
When the exporter negotiates jointly with her importers, the importer's prot function is the sameas earlier but now the exporter's total quantity is no longer taken as given. The importer observes theJexporter's quantity, and chooses qcd to maximize πd =´ cmax (d) hcmin (d)ip(qcd , qd , qc , δ̂) − cd qcd − Tcd dGc .

The split of prots and hence the payments Tcd are again determined by Nash bargaining where
the exporter's bargaining weight is β and the disagreement payos are again zero.

The optimalhipayment is once more T̂cd = βpcd (qcd , qd , qc , δ̂) + (1 − β)cd qcd .
Substituting for the optimal payments and summing over all importers, the exporter chooses
quantities to maximize maxqcd ,qc βi´ dmax (c) h
p(q
,
q
,
q
,
δ̂)
−
cd
qcd dGd . Joint contracts enable imcd d cdmin (c)porters to internalize the business stealing eect which implies the optimal price is

pJcd = cd/ (1 − µvcd − (1 − θ)µ̃d − θµ̃c )µ̃c ≡u0 (qc )µu (qc )εvcd .
θu0 (qc ) + (1 − θ)u0 (qd )(4)

Prices are set at the prot-maximizing monopoly levels. The exporter ensures prices are higher
than under bilateral contracts because importer competition is reduced.

But under the earlier

condition on elasticities µu εv < min µv · min (1 − µv ), the joint contract price is lower than the pricefrom anonymous markets because double marginalization is avoided. The optimal quantity sold toconsumers corresponds to the monopoly quantity in the nal goods market and is therefore lower
than the quantity supplied under bilateral contracts where importers compete with each other. We
summarize this result in Proposition 2.

Proposition 2. Joint contracts eliminate double marginalization and business stealing in the nalgoods market, leading to pM > pJ > pB .
We are interested in the impact of trade liberalization on rm's ability to engage in richer
contracts and will examine the qualitatively new results of the importing microstructure on thedivision of the gains from trade. The business stealing externality arises when importers' varietiesof an exporter's products are more substitutable than the exporters' products.

Then as rms

move from bilateral contracts to joint contracts, they increase the prices charged to consumers.
The opposite happens - prices fall - when rms switch from anonymous transaction to bilateralcontracts. We therefore focus on the case of exporters in the upper nest and the choice between
bilateral contracts and joint contracts because the other cases reinforce the standard gains fromtrade by reducing prices further. In the remainder of this Section, we derive the market equilibrium
and then discuss the implications of opening to free trade in the next Section.

13

Importers, Exporters and the Division of the Gains from Trade

2.7 Equilibrium
We start with specifying the equilibrium of a closed economy. As we are interested in the divisionof the gains from trade, the mass of rms is xed so that they earn positive prots. Assuming asymmetric equilibrium, we can write pcd = p and qcd = q for brevity. Let m ≡ µv (q) + 1J µu (qc )εv (q)denote the markup charged in the nal goods market, where 1J is 1 under joint contracts and 0 oth-00erwise. From optimal pricing, p = cd/ (1 − m) where the inverse demand is p = v (q)u (Md v(q)) /δ
and the budget constraint is Mc Md pq = 1 (which gives the consumer's budget multiplier δ ).
Then the optimal contracting decision is to invest in joint contracts if

Md β

h

µv
mJ
qB
q J − 1−µ
1−mJ
v

i

J − πB
Md β πcdcd=cdL ≥ fcJ , where the superscript J denotes the quantity implied underjoint contracts and B denotes the quantity implied under bilateral contracts from the optimal pricing condition. The importer always nds the joint contracting decision viable when this conditionJJ

holds as long as his relative contracting costs are low (fd /Mc (1 − β) < fc /Md β ). The four conditions - optimal pricing, the inverse demand, the budget constraint and the optimal contracting
decision - summarize the market equilibrium under xed entry.

2.8 Opening to International Trade
When the economy opens up to free trade, all producers and distributors engage in international
trade. We show that looking at the microstructure of import markets reveals new sources of gains
from trade, beyond the usual gains from variety and pro-competitive eects.

Opening to trade

makes joint contracts more protable, and exporters and importers become more likely to enter
into joint contracts. Consumers still experience the usual gains from access to foreign varieties, butthey do not get the full benet of openness on prices because rms reduce competition in the importmarket through joint contracts. Firms gain at the expense of consumers, and later we show thatthese forces are present even under free entry of rms.
Opening to free trade increases the mass of consumers available to producers from L to sL wheres is the scaling factor for the increase in consumers from trade. The equilibrium conditions for optimal pricing and inverse demand are unchanged. The budget constraint now accounts for the factthat consumers have access to sMc > Mc producers and their budget constraint is sMc Md pq = 1.
The optimal contracting decision of rms is to invest in joint contracts if sMd βJ − π B ≥ f J .6
πcd
c
cd

As long as prots are supermodular in markups and market size, international trade makes joint
contracts more likely. We specify the supermodularity condition in Assumption 2.8 below and provide the conditions on primitives in the Appendix.

Assumption 1. Prots πc (m, s) are supermodular in markups m and market size s.
6JJ
The contracting cost can also be exibly specied as fc (s) such that d ln fc (s)/d ln s < 0 so that there are some

economies of scale in contracting.

14

Importers, Exporters and the Division of the Gains from Trade

CES demand ensures prots are modular and we get the knife-edge case where prots rise at thesame rate for all prot levels. This implies that prots rise at the same rate under joint contracts
and bilateral contracts, so that opening to trade has no impact on the likelihood of entering into
joint contracts (that provide higher prots). To overcome this knife-edge result, we assume that therate of change of markups is such that prots are supermodular in markups and market size. Thenprots rise more after free trade trade for higher prot levels, as is standard in most trade models
with variable markups.
The reasoning behind Assumption 2.8 is as follows. As market size expands, the direct impact
is to increase prots which are greater under joint contracts. The indirect impact is that prots
earned from an individual consumer decline due to competition. This prot drop is smaller whenmarkups are higher and rms have a greater ability to absorb the negative prot eect of importcompetition.

But the rate of change in markups diers across contracts.

The drop in prots isbigger when the rate of change in markups is greater. The rate of change in markups under joint0

contracts includes the rate of change in own markups µ (q) and the rate of change in markups from0internalizing business stealing (µu ε) .

The supermodularity condition therefore ensures that therate of change in markups from business stealing is small enough to not completely mitigate thedirect impact of market expansion and the indirect impact of higher markups. Having specied thesupermodularity condition, we discuss the impact of trade on the division of the gains from tradeunder xed entry, and then show that these results are robust to free entry where prots are wipedaway.

2.8.1 The Division of the Gains from Trade
Opening to trade gives foreign exporters access to home consumers, so the size of the market
expands. Consumers get access to imported varieties and the change in welfare is ∆ ln U = ∆ ln Mc +∆ ln u(Md v(q)) where ∆ denotes changes. Under xed entry, the change in variety is sMc Md −Mc Md
as there is no feedback eect into entry of rms. Quantities per variety q change due to the usual
forces of import competition and the new source of changes in contracting choice. We decompose
the change in consumer welfare into the standard gains from variety and pro-competitive eects,
and the new gains from changes in the microstructure of import markets.
Let ∆s x(s) ≡ x(s) − x(1) denote the change in outcome x when the market size rises from L tosL, under a xed microstructure. Let ∆V xV (s) ≡ xJ (s) − xB (s) for V ∈ {B.J} denote the change
in outcome x when rms move from bilateral contracts to joint contracts for a xed level of market

15

Importers, Exporters and the Division of the Gains from Trade

size s. Then the change in consumer welfare can be decomposed as:∆s ln sMc u Md v(q B (s)){z}|∆ ln U =Gain from Variety & Pro-Competitive Eects>0+∆V ln u Md v(q V (s))
|
{z
}

(5)

Gain from Change in Microstructure<0The rst line of Equation 5 shows the standard gains from trade for consumers for a given contracting
form. Entry of foreign varieties provides higher welfare through Gains from Imported Variety and
Gains from Pro-Competitive Eects. Prices fall due to foreign competition because d ln p/d ln s =−1+1/ (1 + µ0v q/ (1 − µv )) < 0 and consumers get access to foreign varieties so that welfare increasesB0
by d ln sMc u Md v(q (s)) /d ln s = 1 − εu εv / (1 + µv q/ (1 − µv )) > 0.
The second line shows a new source of change in consumer welfare arising from the microstructureof the import market. Increase in the market size available to producers makes joint contracts more
likely.

This change in the microstructure of the import market increases the price of a variety.

Combining the budget constraint, the demand function and the pricing condition, optimal quantity
is determined by(1 − µv (q) − 1J µu (Md v(q)) εv (q)) /q = sMc Md cd.

The LHS is decreasing inquantity, and is smaller under joint contracts because rms account for the business stealing eect
through µu εv .

Firms reduce their quantities under joint contracts and prices rise (because p =v 0 (q)u0 (Md v(q)) /δ = 1/sMc Md q ).

The consolidation of the import market therefore lowers thegains from trade that are passed on to consumers.

V

J

Total prots for rms in a country are Π = sMc Md πcd − Md fd − Mc fc − 1J Mc fc , and the change
in prots after opening to trade can be decomposed into the standard pro-competitive eects fromforeign varieties and the new gains from the change in the microstructure of the import market.
Firms gain access to more consumers but also face competition from imports which leads to lower
prots, as shown in the rst line below. The second line is the rise in prots when rms move frombilateral contracts to joint contracts. Firms gain at the expense of consumers, as the import market
is consolidated.

B∆s sMc Md πcd(s) − Md fd − Mc fc
|
{z
}

∆Π =

Gains from Market Access and Pro-Competitive Eects<0+
V∆V sMc Md πcd(s) − 1J Mc fcJ|{z}

Gains from Change in Microstructure>0
The rst line follows from the drop in markups after opening to trade. Substituting for the inverse
demand and the budget constraint, the optimal quantity sold to each worker is(1 − µv ) /q =sMc Md cd, and foreign competition lowers the quantity by d ln q/d ln s = −1/ (1 + µ0v q/ (1 − µv )).
0Markups therefore fall by d ln µv /d ln s = (µv q/µv ) (d ln q/d ln s) and the prot from home consumers

16

Importers, Exporters and the Division of the Gains from Trade00decreases by d ln sπ/d ln s = − (µv q/µv ) (1 − µv ) / (1 − µv + µv q) < 0. The second line is the gainin prots from investing in joint contracts, which is positive for all switches because rms internalize
business stealing.
We summarize the results for the division of the gains form trade in Proposition 3, and relegate
details of the proof to the Appendix.

Proposition 3. Under Assumption 2.8, opening to trade makes joint contracts more likely. Thischange in the microstructure of import markets increases rms prots at the expense of consumer
welfare.

2.8.2 The Division of the Gains from Trade under Free Entry
We will also show that the qualitative results for consumer welfare persist under free entry of rms

ρwhen prots are wiped away. For simplicity, we specify a CES upper nest u(qc ) = qc and examine
the free entry equilibrium. When rms can enter freely, there will be two additional conditions forequilibrium in the economy. Distributors can enter freely and this will drive down their prots net ofV

entry costs to zero, sMc (1 − β) πcd = fd for the optimal contract V∈ {B, J}. Likewise, producers
VJ

enter till their prot margin net of entry costs is driven down to zero, sMd βπcd = fc + 1J fc .
Opening to trade increases the size of the market available to producers. As earlier, the change
in consumer welfare can be decomposed into the standard gains from trade and the gains arisingfrom the change in the microstructure of markets:∆s ln sMc u Md v(q B (s)){z}|∆ ln U =Gain from Variety & Pro-Competitive Eects>0+∆V ln u Md v(q V (s))
|
{z
}

(6)

Gain from Change in Microstructure<0The rst line of Equation 6 shows the standard gains from trade for consumers for a given contracting
form. Entry of foreign varieties provides higher welfare through Gains from Imported Variety and
Gains from Pro-Competitive Eects. Although the mass of importers per market falls, consumers
get access to new foreign varieties and rms charge lower markups. And the net eect is an increasein consumer welfare from the standard gains from trade. The second line, as earlier, is the impactof trade through the microstructure of the import market. Consumers lose out as rms switch frombilateral to joint contracts. Although more importers enter, there is a drop in the mass of producers
because they need higher scale to justify the bigger xed investments. The rise in markups fromthe switch to joint contracts and the fall in producer entry overwhelm the entry of importers, andconsumer welfare falls because of the change in the microstructure. Market expansion makes joint
contracts more likely, under the supermodularity condition of Assumption 2.8.

Firm prots areunchanged because of free entry. Therefore, the aggregate impact of opening to trade on welfare is

17

Importers, Exporters and the Division of the Gains from Tradepositive through the standard channels of variety and pro-competitive eects, but negative throughthe new channel of market microstructure. Details are in the Appendix.
Having discussed the division of the gains from trade through changes in the microstructureof markets, we proceed to testing the observable implications of the model. As we will work with
rm-level data during an episode of tari cuts, the next Section will introduce rm heterogeneity
and trade costs.

3

Firm-Level Predictions

Section 2 highlights how the microstructure of importing aects the division of the gains from trade.
Ideally we would test the model by examining how the microstructure changes between exporters andimporters in a period of falling trade costs. Data on contracting choices are not available in standard
datasets. Further, informal arrangements can replicate bilateral contracts and joint contracts, as
discussed earlier. We focus on the unique predictions of the model for observable outcomes - prices,quantities and importer-exporter matches.

In this section, we start by incorporating dierencesin importer cost cutos across exporters. We then provide dierence-in-dierence predictions forchanges in prices, quantities and the number of importers per exporter under dierent contracts.

3.1 Microstructure of Import Markets
Continuing with the framework of Section 2, we examine a model with heterogeneous exporters
and importers. For simplicity, we assume that there is an outside good q0 that is freely traded andproduced one for one with labor. As is well-known, the outside good mitigates income eects andwe focus on the price eects arising from changes in the microstructure of the import market forη for 0 < η < 1, where the dierentiateddierentiated varieties. The welfare function is W = q0 + Q
varieties are Q = U =´u(qj )dj and qj =´v(qij )di. For exporters in the upper nest and importers
0in the lower nest, the inverse demand is pcd ≡ ν (qcd )Q

η−1 u0 (q ) which is similar to Section 2. Wecwill look at reductions in taris and specify τ > 1 as the ad valorem trade cost incurred on payments
made to exporters. Specically, importer d pays τ Tcd to exporter c, who receives just Tcd .
Firms dier in the unit costs c and d which are drawn from cumulative densities Gc (c) and Gd (d).
As earlier, contracts specify quantities and payments and the surplus from a variety is split throughbilateral Nash bargaining.

Firms chose quantities that maximize bilateral prots under bilateralcontracts and that maximize multilateral prots under joint contracts. Then the optimal nal pricefor variety cd is pcd = cd/ (µv (qcd ) + 1J µu (qc )ε̄vc ) where ε̄vc ≡´ dm
0εv (qcd ) ´ dm v(qcd )0v(qcd )dGd

dGd .

As rms dier in costs, we introduce matching costs because this will generate dierences in therange of exporters and importers that transact with each other. Exporters and importers face a

7 So matches will need to be productive enough to justify transactions, andmatching cost fcd > 0.

7

Bernard et al. (2014) introduce importer-specic xed costs in a trade model with heterogeneity of both exporters

18

Importers, Exporters and the Division of the Gains from Trade

this leads to an endogenous cost cuto for import partners of each exporter, which we can take to theV∈ {B, J}. The bilateral prot from
qcd , q̂c , Q̂ − fcd so exporter c sells to all importers with variable prots greater thandata. Exporter c supplies to all importers with d ≤ dm (c) for V
a match is πcdthe xed cost of matching. Importers in joint contracts also account for the business stealing eectof their actions, and this is reected in the optimal importer range decision as πcdm


qcdm , qc , Q̂ +(∂πcdm /∂qc ) (∂qc /∂dm ) = fcd . Substituting for the change with respect to upper nest quantities, theoptimal importer cost cuto is given by (pcdm − cdm ) qcdm − 1J pcdm qcdm µu (qc )ε̄vc /εv (qcdm ) = fcd /L.
As rms move from bilateral contracts to joint contracts, they extract a higher markup by selling
fewer units. Consumer prices rise, total quantities of an exporter fall and the importer cost cuto
of exporters falls. Exporters switching from bilateral to joint contracts therefore consolidate theirimport market to extract more of the consumer surplus. As is well-known, lower trade costs reduce
prices directly.

The new nding is that the price response to trade liberalization diers acrossthe contractual choice of exporters and importers. Exporters and importers moving from bilateralcontracts to joint contracts increase the nal markup charged to consumers by overcoming businessstealing among importers. The import price paid by the importer to the exporter also rises. Let

pxcd denote the unit price paid to exporter c by importer d.

In anonymous markets, there is astraightforward market-clearing price per unit paid by the importer. Under bilateral contracts, theunit price is the variable component of the payments to exporters, which rises as rms extract moreof the consumer surplus.

8 Having incorporated the extensive margin of importers, we can determine

the change in the range of importers chosen across dierent contracts.

Exporters that switch tojoint contracts lower their importer range because this reduces business stealing and increases nalprices. For the same reason, these exporters also scale back on their quantities. Therefore, moving
to joint contracts results in a consolidation of the import market for the product. The import priceis increased, quantities are reduced and fewer importers carry the variety under joint contracts.
Joint contracts become more likely after trade liberalization when the prot function (πc (m, −τ ))is supermodular in markups and openness. This requires a condition similar to the one in Section
2 with modications to reect the cost distribution. We summarize this assumption and the comparison between bilateral contracts and joint contracts in Proposition 4 below and provide details
in the Appendix.

Proposition 4. When exporter prots are supermodular in markups and openness, exporters switching from bilateral contracts to joint contracts increase their prices, reduce their sales, and sell to
fewer importers.
To understand the impact of trade liberalization through the microstructure, we examine theseand importers. They focus on the implications of variation in importer heterogeneity across destination markets anddo not model contracting choice.

8

In an earlier working paper with CES demand, we show that these predictions persist when disagreement payos

are non-zero because the ex-post share of exporters under joint contracts rises after trade liberalization.

19

Importers, Exporters and the Division of the Gains from Tradeunique observable outcomes of higher import prices, lower imports and fewer import partners in
response to a reduction in taris. Import prices and quantities are routinely observed in customs
data, so we can use the above predictions to examine the main mechanism of the theory. The main
prediction is that import prices rise after trade liberalization for varieties whose exporters reduce
their importer cost cutos and import quantities. The prediction that trade liberalization induces
exporters to simultaneously increase prices, reduce quantities and reduce importers does not arise
in standard trade models. While the possibility of quality upgrading can lead to increased prices
after trade liberalization, there is no clear theoretical prediction in the quality literature on how
quantity varies with changes in quality (e.g. Eckel et al. 2015). Incorporating quality and quantity
in dierent ways, Baller (2013) shows that standard trade models would predict a rise in quantities
when there are economies of scale in quality upgrading. Going by this and ruling out other ways inwhich quality could be confounding our results, we will provide evidence for Proposition 4.
To directly test for the mechanism in the theory, the reduction in the number of import partners
in Proposition 4 will be important for the empirical application.

Recent models incorporating

importer margins of trade also predict that trade liberalization induces exporters to increase theirimporter range as a result of higher export protability. The range of import partners would riserather than fall after trade liberalization in these models. Indeed, this is important because a fallin the number of importers is a direct measure of our theoretical mechanism that competition falls
among importers of the product. We therefore test for the triple prediction of higher prices, lower
quantities

and fewer importers to isolate the quality upgrading eect from the contracting eectof trade liberalization. The subsequent section operationalizes the triple prediction by examining
prices, quantities and importer matches following a major trade liberalization episode in Colombia.

4

Empirics

The microstructure eect of trade liberalization increases the probability that an exporter switchesfrom using bilateral contracts to joint contracts. This implies an increase in the prevalence of thetriple prediction of increased price, reduced quantities and fewer importers for exporters experiencing
trade liberalization.

We examine the empirical relevance of the triple prediction using data on

Colombian imports after the implementation of the US-Colombia Free Trade Agreement (FTA).
This Section contains a discussion of the data, the baseline empirical specication, and a series ofrobustness checks.

4.1 Data
We examine the triple prediction of higher prices, lower quantities and fewer matches for imports
into Colombia before and after the implementation of the US-Colombia FTA. Transaction-level
import data for Colombia identies the exporter and the importer for each import transaction as

20

Importers, Exporters and the Division of the Gains from Trade

Figure 1: Colombian Taris on US Products in 2011 (Pre-FTA) and 2012 (Post-FTA)

Note: Size of the marker indicates the number of HS8 products.

well as the total value, quantity, date and product. Aggregating the transaction-level import data
to the exporter-product pair enables us to obtain the average import price of the product, the total
quantity of the product shipped by the exporter to Colombia, Xcsht , and the number of Colombianmaximporters per exporter-country-product dcsht .
While matched exporter-importer data is available for other countries, the Colombian importdata is unusual because it covers a major trade liberalization with the largest trading partner. The
US-Colombia FTA was implemented on May 15, 2012.

The agreement immediately eliminatedduties on 80 percent of US exports of consumer and industrial products to Colombia.

Figure 1

shows the Colombian tari rates charged to the US before and after the US-Colombia FTA. Most
US exports obtain duty-free status after the FTA. Table 1 provides summary statistics for Colombiantaris faced by US exporters and a comparable set of exporters from developed countries before
and after the FTA. The pre-FTA tari for 2011 fell from an average of 11 percentage points to an
average of 4 percentage points in our sample. The tari elimination was largely on the Colombianside because 90 percent of US imports from Colombia enjoyed duty free access before the FTA.
The US is Colombia's leading trade partner and the FTA was a substantial step towards tradeliberalization in Colombia. Between June 2012 and April 2013, US exports to Colombia increasedby 14.2 percent over the same period a year earlier while total Colombian imports were up only 4.6
percent.
The theoretical predictions of the model focus on the simultaneous rise in prices and drop in
quantities and import partners.

An exporter, c, increases the import price of its product (m̃c ),max ).

reduces its total quantity (qc ) and reduces the number of its importers (dc

We dene thetriple prediction as ∆Triplecsht = 1 if exporter c from source country s selling product h at time t

21

Importers, Exporters and the Division of the Gains from Trade

increases its average price across all its importers (4 ln Import Pricecsht > 0)
quantity sold to all its importers (∆Xcsht < 0)and reduces the total

and reduces the number of importers of its productmax(∆dcsht < 0). If any one of these events does not happen, then ∆Triplecsht = 0.
To test the theoretical results, we need measures of ∆Triplecsht and the treatment variables. We
use Colombian import transactions data recorded by its customs authority, which lists the name of

9 We clean the names by harmonizing

the importer and the exporter for each import transaction.

commonly occurring prexes and suxes and then aggregating imports to the exporter-countryproduct level in each time period (csht).

10

November for each year (2009-2012).

A time period consists of the months from June to

For each time period, import values and quantities arerecorded at the 8-digit level under the Colombian implementation of Harmonized System (HS)classication. We compute the average import price (unit value in USD), the total quantity, andthe total number of importers for each exporter-country-product-year,

csht.

We then compute∆Triplecsht = 1 for exporter-country-products that have a higher average price, lower total quantityand fewer importers compared to the previous period.
As customs data are known to be noisy, we typically separate the set of exporter-countryproducts with initial sales of less than US$10,000 and only include the set of country-product pairs
with more than one exporter in 2009. The theory applies to incumbent exporters, so we focus onexporters who sell from 2009 to 2012. Pierce and Schott (2012) show that HS codes change overtime and this can lead to estimation bias. To account for this, we work with the set of productswith HS codes that are unchanged between 2009-2012. This covers 84 percent of all products in our
sample, alleviating concerns regarding generality of the results.
To construct the treatment variables, tari data for the US-Colombia FTA is obtained from theOce of the US Trade Representative. Taris were reduced from their initial levels by one of four
FTA multipliers: 0% of the initial tari, 80% of the initial tari, 87% of the initial tari or 90% of
the initial tari. Table 2 summarizes the distribution of HS-codes by the FTA tari multiplier. We
classify Treath = 1 for product codes with a Tari multiplier equal to zero. For all other productcodes, Treath = 0.

4.2 Baseline Empirical Specication
We examine whether the US-Colombia FTA induced US exporters to increase prices, reduce quantities and reduce the number of importers in Colombia. To control for underlying trends, we examine
whether exporters from the US selling products that started to receive duty-free access into Colombia were more likely to increase their prices, reduce their quantities and reduce their number of

910

The raw data come from www.importgenius.com.
The interval starts in June since the FTA came into force in the middle of May 2012.

The period ends inNovember since data for December 2011 are missing. We also do not have data for July 2009 and quantities havebeen appropriately scaled to account for this. Results are robust to using 2010 as the initial period (available uponrequest).

22

Importers, Exporters and the Division of the Gains from Trade

importers relative to the previous period. We dene Postt = 1 for the period after the FTA and
0 for the period before the FTA. In addition, we compare the probabilities for US exporters to acontrol group of exporters that did not experience the FTA tari reduction. We focus on exportersfrom developed countries to construct a suitable control group. Accordingly, USAs = 1 for exportersfrom the United States and 0 for exporters from any other developed country.
Table 3 summarizes the triple dummy and exporter characteristics for exporters in the control
and the treatment groups separately for 2012. As expected, the triple prediction is more prevalent
for the treatment group, but this could be due to dierences in product composition or due to otherevents specic to the post-FTA time period. In order to minimize these concerns, we proceed to adierence-in-dierence estimation which accounts for product-specic and country-specic eects.
We examine the prevalence of simultaneous increases in prices, reductions in quantities andreductions in the number of importers of an exporter.

The estimating equation for the triple

prediction for exporter c from source country s selling product h at time t is a linear probability
model,∆Triplecsht =β · Postt · Treath · USAs + γXcsht + αst + αht + εcsht(7)where εcsht is a disturbance term while αst and αht are source country-year and product-year xedeects that account for changes such as exchange rate uctuations and aggregate demand shocks.

Xcsht includes all interactions between Postt , Treath , and USAs , and other controls such as pretrends and their interactions (where Pret

= 1 for observations in 2011 and 0 otherwise).

The

coecient of interest is β which we expect to be positive if the FTA led exporters to consolidate
their import market resulting in higher import prices, lower import quantities and fewer importers.
From the theoretical results in Section 3, we expect the triple prediction to vary across exportersof dierent levels of productivity. High productivity exporters are expected to have already paid
the costs of consolidating their import market, so bilateral trade liberalization would lead to consolidation in the import markets of less productive exporters from the US. To account for dierencesin responses across exporters, we allow the coecient on Postt · Treath · USAs to vary with exporter
size. For each exporter-country-product observation, exporter size is measured by the z-score of theinitial value of sales of the exporter in 2009, relative to all exporters of the product from developed
countries in 2009. Let ecsh,2009 denote the initial value of sales of exporter c from country s of product h in 2009. The z-score of initial size is Sizecsh ≡ (ecsh,2009 − µh,2009 ) /σh,2009 which measures
the initial sales of an exporter relative to exporters of that product from all developed countries.

11

Accounting for possible dierential responses across rms, the estimating equation is∆Triplecsht =β · Postt · Treath · USAs + β1 · Postt · Treath · USAs · Sizecsh + γXcsht + αst + αht + εcsht(8)11µh,2009 is the mean of ecsh,2009 across all exporters of product h from developed countries and σh,2009 is thecorresponding standard deviation.

23

Importers, Exporters and the Division of the Gains from Trade

Table 1: Colombia Taris Before and After the FTA for Exporters in 2009
Variable

Obs.

Mean

S.D.

Min

Max

Taris Charged to US Exporters
Pre-FTA Tari in 2011

1,750

11.05

5.54

0

35

Post-FTA Tari in 2012

1,750

4.27

6.37

0

31.5

Taris Charged to Non-US Developed Country Exporters
Pre-FTA Tari in 2011

1,747

6.57

3.52

0

30

Post-FTA Tari in 2012

1,747

6.82

3.56

0

30

Note: Mean refers to an average across exporters in the sample, weighted by the initialvalue of Colombian imports from developed countries for each HS code in 2009.

Table 2: US-Colombia FTA Tari Multipliers for Colombian Non-agricultural Taris
Tari Multiplier# of Products% of Products

4,560

76.18

0
0.80

317

5.30

0.86

52

0.87

0.90

1,057

17.66

Note: Tari Multiplier = Post-FTA Tari/ Pre-FTA Tari. Post-FTA Tari is the tari
on a product from the US in the year after the implementation of the FTA

Table 3: Summary Statistics for Exporter-Products in 2012
Control Group: Exporter-Products with Treath · USAs = 0
Obs (csht)

Variable

Mean

S.D.

Min

Max

∆Triplecsht = 1

17,547

0.044

0.205

0

1

Initial trade valuecsh,2009 ($mn)

17,547

0.054

1.298

<0.001

126

Initial number of importerscsh,2009

17,547

1.314

0.897

1

19

Sizecsh17,373

0.004

0.513

-1.593

6.522

Treatment Group: Exporter-Products with Treath · USAs = 1
Obs (csht)

Mean

S.D.

Min

Max

∆Triplecsht = 1

6,225

0.064

0.245

0

1

Initial trade valuecsh,2009 ($mn)

6,225

0.107

1.101

<0.001

60.1

Initial number of importerscsh,2009

6,225

1.533

1.703

1

54

Sizecsh

6,116

0.052

0.665

-1.485

5.911

Variable∆Triplecsht = 1 if 4ImportP ricecsht > 0 & 4ImportQuantity csht < 0 &4#Importerscsht < 0 from period t − 1 to t and 0 otherwise. Sizecsh is the z-score
of initial export value ecsh,2009 in 2009 relative to all exporters of the product for all

Note:developed countries in 2009.

24

Importers, Exporters and the Division of the Gains from Trade

where Xcsht includes interactions of Sizecsh with Postt , Treath , USAs and Pret as well. Coecientβ1 allows the impact of the FTA liberalization to vary by initial size of the exporter. We cluster
standard errors for each estimating equation by exporter-country pairs to account for correlation
across time and products within an exporter-country pair.

4.3 Baseline Results
Table 4 summarizes the results from estimation of the linear probability models in Equations 7 and
8.

4.3.1 Baseline Specication
Column (1) shows that exporters who experienced duty-free access from the US-Colombia FTA
are more likely to increase their average price, reduce their total quantities and sell through fewer
importers, relative to a control group of developed country exporters who did not experience dutyfree access for the product. The likelihood of a triple for the treated exporters rises 1.5 percentage
points more after the FTA relative to the change for other exporters.

4.3.2 Triple Prediction by Exporter Type
Column (2) adds the interaction with the initial size of the exporter.

From the theory, the signof the interaction term is expected to be negative as less productive exporters are more likely toconsolidate their import market after the FTA. The results in Column (2) show that exporters withsmaller initial size are indeed more likely to consolidate their import market. Figure 2 plots thehistogram of the estimated impact of the FTA across all exporters, β̂0 · Postt · Treath · USAs + β̂1 ·Postt · Treath · USAs · Sizecsh . Most of the exporters from the US have an increase in the probabilityof higher prices, lower quantities and fewer partners as a result of the liberalization.
Another way of capturing the dierences in the triple prediction is to estimate the treatmentcoecient separately for exporters of dierent sizes. Instead of using a continuous measure of initialsize, we estimate dierent coecients for exporters by their size category. We divide all exporters ofa product into dierent size bins and estimate separate coecients on Postt · Treath · USAs for eachsize bin. Among exporters that earn over USD10,000 per time period, Tercile1csh = 1 if exporterc's initial size measured by Sizecsh is below the 33rd percentile of all exporters of that product fromdeveloped countries, and 0 otherwise.

Similarly, Tercile2csh= 1 if c's initial size is between the

33rd and 66th percentile, and Tercile3csh = 1 if c's initial size is greater than the 66th percentile
for exporters of that product. We separate the Tiny exporter-country-products with initial sales
less than US$10,000 into another size bin (Tinycsh = 1ecsh,2009 ≤10000 ). Column (1) of Table 5 showsthat the triple prediction continues to hold and it is the medium-sized exporters in the rst andsecond terciles that increase prices, reduce quantities and reduce their number of importers. This is25

Importers, Exporters and the Division of the Gains from Trade

Table 4: Baseline results: Triple Prediction

Dependent Variable: ∆Triplecsht

Variable

Postt · Treath · USAs
Pret · Treath · USAs
Postt · Treath · USAs · Sizecsh

(1)
Coef.
(S.E.)

0.015**(0.007)0.004(0.008)Pret · Treath · USAs · Sizecsh
Treath · USAs
Treath · USAs · Sizecsh-0.002(0.005)

Postt · Treath · Sizecsh
Postt · USAs · Sizecsh
Postt · Sizecsh
Treath · Sizecsh
USAs · Sizecsh
Pret · Treath · Sizecsh
Pret · USAs · Sizecsh
Pret · Sizecsh
Sizecsh∆MFNht · Sizecsh

Product-Year FE αht
Country-Year FE αst
N
R2

yes
yes
71,316
0.119

(2)
Coef.
(S.E.)(3)
Coef.
(S.E.)

yes
yes
70,643
0.114

yes
yes
14,2050.254

0.015**(0.007)0.004(0.007)-0.036**(0.017)0.004(0.017)-0.002(0.004)0.005(0.010)0.029***(0.011)
0.021**(0.013)-0.007(0.007)-0.009(0.007)-0.001(0.007)-0.0003(0.001)-0.011(0.015)0.009(0.009)0.005(0.006)

0.053*(0.028)0.047(0.032)-0.092***(0.032)0.002(0.050)-0.022(0.019)0.027(0.024)0.072***(0.027)0.051**(0.020)-0.019(0.017)-0.036*(0.020)-0.019(0.014)-0.004(0.025)0.0003(0.040)0.024(0.024)0.008(0.018)(4)
Coef.
(S.E.)

0.015**(0.007)0.004(0.008)-0.036**(0.016)0.004(0.015)-0.002(0.004)0.005(0.009)0.030***(0.011)
0.021*(0.011)-0.007(0.007)-0.009(0.007)-0.001(0.008)-0.003(0.011)-0.010(0.013)0.013(0.010)0.005(0.007)0.001(0.001)yes
yes
70,5890.114∆Triplecsht = 1 if 4ImportP ricecsht > 0 & 4ImportQuantity csht < 0 &4#Importerscsht < 0 from period t − 1 to t and 0 otherwise. Treath = 1 for HS-

Note:

Codes that received duty-free access from the US-Colombia FTA and 0 otherwise. The
sample covers changes in import outcomes in 2010, 2011 and 2012. Postt = 1 for 2012 and0 otherwise while Pret = 1 for 2011 and 0 otherwise. USAs = 1 for exporters from theUnited States and 0 for exporters from other developed countries. Sizecsh is the z-score of
initial export value ecsh,2009 in 2009 relative to all exporters of the product from developed
countries in 2009. ∆MFNht is the change in MFN taris from period t−1 to t. Signicance∗∗∗ ∗∗∗,, andfor 1, 5 and 10 percent respectively.

levels are indicated by26

Importers, Exporters and the Division of the Gains from Trade0

Percentage of Treated US Exporter-Product Pairs
20
40
60

Figure 2: Distribution of Estimated Treatment Eects in 2012

-.2
-.15
-.1
-.05
0
.05
Estimated Treatment Effect by Initial Size of Treated US Exporter-Product Pairs

Note: Horizontal axis shows the magnitude of the estimated treatment eect.

consistent with the theory because the most and least productive exporters do not switch contracts
and it is the medium productivity exporters that switch from bilateral to joint contracts.

The

coecient on the second tercile is less precisely estimated, and the pre-treatment variables arealways statistically insignicant. It is also reassuring that tiny exporters show the opposite results
which suggests that it is not purely selection eects at the bottom end of the exporter distributionthat drives the results.

Theoretically, the selection eects would work to increase exports of thetiny exporters. Column (2) of Table 5 shows that the triple prediction holds when tari-inclusive
prices are used instead of free-on-board (FOB) prices. So the rise in import prices is large enoughto oset the direct impact of a reduction in taris after the FTA.
One shortcoming of measuring consolidation in the import market through the ∆Triplecsht indicator is that it will always be zero for exporters that sell to only one importer in the previous
period. This underestimates the relative prevalence of the triple prediction among the set of exporters that sell to more than one importer initially. Column (3) restricts the estimation sample toexporter-country-products with more than one import partner initially. As expected, the coecient

12 Exporters who gained duty-free

on Postt · Treath · USAs increases to over 5 percentage points.

access from the FTA are more likely to increase prices, lower quantities and sell to fewer importers.
This eect varies across exporters of dierent initial size with smaller exporters more likely to engage

12

Another concern might be that the higher prevalence of the triple prediction could be due to an increase in thevariance of price changes, quantity changes and changes in the number of importers. While increases in the variancesof these outcomes is consistent with the theory, we also re-estimate the regressions controlling for changes in thevariances. The main results are unchanged but our sample is smaller because computing changes in variances for the
US and other developed countries separately is more demanding on the data (available upon request).

27

Importers, Exporters and the Division of the Gains from Trade

Table 5: Tercile results: Triple Prediction and Unit Value Changes by Size Bins

Variable

Tercile3csh · Postt · Treath · USAs
Tercile2csh · Postt · Treath · USAs
Tercile1csh · Postt · Treath · USAs
Tinycsh · Postt · Treath · USAs
Controls (including Pre-treatment)
Product-Year FE αht
Country-Year FE αstNR2(1) fob
Coef.
(S.E.)∆Triplecsht-0.021(0.021)
0.043(0.027)0.077***(0.024)-0.067 **(0.027)yes
yes
yes
71,3160.121∆ ln Import Pricecsht(2) w/tari (3) fob
Coef.
Coef.
(S.E.)(S.E.)-0.031(0.022)0.037(0.024)0.068**(0.027)-0.064**(0.028)yes
yes
yes
71,3160.117-0.025(0.104)0.084*(0.133)0.314**(0.139)-0.353**(0.149)yes
yes
yes
71,3160.089(4) w/tari
Coef.
(S.E.)-0.069(0.104)0.040(0.133)0.257*(0.139)-0.347**(0.149)yes
yes
yes
71,2850.089∆Triplecsht = 1 if 4ImportP ricecsht > 0 & 4ImportQuantity csht < 0 &4#Importerscsht < 0 from period t − 1 to t and 0 otherwise. ∆ ln Import Pricecsht

Note:is the log change in the exporter-level average unit value. Columns (1) and (3) use FOB
prices and Columns (2) and (4) use prices inclusive of eective duty rates.

Treath = 1

for HS-Codes that received duty-free access from the US-Colombia FTA and 0 otherwise.
The sample covers changes in import outcomes in 2010, 2011 and 2012.

Postt= 1 for2012 and 0 otherwise while Pret = 1 for 2011 and 0 otherwise. USAs = 1 for exportersfrom the United States and 0 for exporters from other developed countries. Sizecsh is thez-score of initial export value ecsh,2009 in 2009 relative to all exporters of the product fromdeveloped countries in 2009. Tercile1csh = 1 for the 33rd tercile of Sizecsh , Tercile2csh = 1
for the 66th tercile and Tercile3csh = 1 for the top tercile. Tinycsh = 1 for all exportersfrom developed countries with total sales of less than USD10,000 in 2009. Controls include all interactions between Postt , Treath , USAs , Pret and indicators for initial size bins.
∗∗∗ ∗∗∗
Signicance levels are indicated by,, andfor 1, 5 and 10 percent respectively.

28

Importers, Exporters and the Division of the Gains from Tradein consolidation of their import markets.

4.3.3 Quantitative Interpretation
An advantage of testing the model with the triple prediction is that it lets us examine a unique
prediction which does not arise in standard models. A limitation of the triple prediction however isthat it does not let us put a number on the price increases faced by the importers. To get a senseof the magnitude of the changes, we examine how unit values respond to duty-free access to the
Colombian market.
Using a specication similar to the baseline, we regress changes in unit values to determine
the coecient on Postt · Treath · USAs for each tercile of US exporters.

The dependent variablein Column (3) of Table 5 reports the change in the average FOB price charged by exporter c for
product h and Column (4) reports the change in the tari-inclusive price where the tari is theMFN or preferential average applied duty rate. As earlier, tiny exporters and large exporters (inthe third tercile) reduce their prices.

From the theory, these are the rms that will not switch

contracts after trade liberalization and their decisions will reinforce the standard gains from trade.
Medium-size importers (in the rst and second terciles of initial size greater than $10,000) show
the opposite eect. These are the rms that are expected to consolidate their import market byswitching to joint contracts. And we nd that they indeed increase their prices between 8 to 30%.
To interpret the price changes, we regress the log change in tari-inclusive unit values of each
exporter on the indicator for Postt · Treath · USAs for all exporters, without any size conditioning.
The coecient is -0.0425 which is estimated imprecisely. This implies that duty-free access to the
Colombian import market induced exporters to reduce their tari-inclusive prices by 4.25%. This
low pass-through reects the fact that the medium-size exporters increase their prices.
Having discussed the baseline results, we examine the robustness of these predictions with aseries of checks on our results.

4.4 Robustness Checks
The robustness checks in this sub-section can be broadly divided into three types. First, we control
for other explanations such as contemporaneous tari cuts for trade partners to other developed
countries to minimize bias in the baseline estimates from omitted variables. Second, we look at aquality-based explanations for the triple prediction. Finally, we examine whether the triple prediction continues to hold when we look within exporter-importer pairs.

4.4.1 Multilateral tari cuts
The time period that we study also includes a unilateral tari reform in Colombia that reduced
the average tari from 12.2 percent to 8.2 percent on November 5 2010 (WTO 2012). The stated29Importers, Exporters and the Division of the Gains from Trade

aim of this tari reform was to reduce the dispersion in taris and eliminate the negative eective
protection that existed in some industries. The reform reduced most-favored-nation (MFN) taris
on a subset of products. For products in our sample, the average MFN duty was 10.3 percentage
points before the reform and the duty fell by 1.3 percentage points as a result of the reform.
To account for unilateral changes in Colombia's MFN taris, Column (4) of Table 4 includes aninteraction between the change in MFN taris and initial size of the exporter. As the MFN tari
change applies to all trade partners with MFN status, the eect of ∆MFNht is subsumed in the
product-time xed eects αht . Across dierent specications, we nd that our main ndings areunaected, and the interaction between MFN tari changes and initial size is small and statisticallyinsignicant for the triple prediction.

4.4.2 Revenue Predictions
Increases in unit values following a trade liberalization are often interpreted as quality upgradingby exporters (Verhoogen 2008; Khandelwal 2010).

Colombia is a small country relative to otherdestinations of US exporters, making it less likely that the unit values pick up investments in quality
upgrading of US exporters following duty-free access to the Colombian market. In fact, lower trade
costs would make it more likely for lower quality US exporters to be able to sell to the Colombian
market, because the exporting cost cuto typically rises after trade liberalization in heterogenous
rm trade models. Empirically, higher quality products are more likely to be shipped out when tradebarriers are higher (Hummels and Skiba 2004). To ensure however that our results are not driven
by quality increases, we examine another triple prediction which looks at a decline in total revenue
rather than total quantity of the exporter. If the observed price rise is accompanied by a reduction
in revenues and fewer importers, then it is more straightforward to explain it with a reduction in

13competition rather than an improvement in quality which would be expected to increase revenues.

The variety-level model of Section 3 predicts that exporters who switch from bilateral contracts
to joint contracts increase their prots but sell lower quantities to fewer importers.

An extreme

prediction of the model is that these exporters might also lower their sales values to earn higher
prot margins per unit. The main intuition here is that under joint contracts, the rm need notsell many units of the product if the markup is large and the xed costs of joint versus bilateralcontracts are relatively low. So if we nd that US exporters are more likely to reduce revenues when
they increase prices and sell to fewer importers, it would be another piece of evidence that duty-freeaccess induced exporters to increase markups rather than quality.
We examine the revenue-based triple prediction of higher prices, lower revenues and fewer im-

Revenue

porters in a way similar to the baseline analysis. Specically, ∆Triplecsht= 1 if exporter c fromsource country s selling product h at time t increases its average price across all its importers

13

We are grateful to Penny Goldberg and Marc Melitz for pointing us in this direction.

30

and

Importers, Exporters and the Division of the Gains from Trade

reduces the total revenue received from all its importers

and reduces the number of importers of

Revenuemax= 0. As
its product (dcsht < 0). If any one of these events does not happen, then ∆Triplecsht
in the baseline results, Table 6 shows US exporters who receive duty-free access are more likely tohave higher prices, lower revenues and fewer importers, and these exporters tend to be the smaller
exporters. As expected, the revenue-based triple prediction becomes more likely after the FTA and
its increased likelihood is slightly smaller than that of the quantity-based triple prediction in the14baseline analysis.

Table 6: Estimation results: Revenue-Based Triple Prediction
Revenue∆csht

Dependent Variable:

Variable

Postt · Treath · USAs
Postt · Treath · USAs · Sizecsh
Controls (including Pre-treatment)
Product-Year FE αht
Country-Year FE αst
N
R2

Triple(1) fob
Coef.
(S.E.)

0.016 **
(0.006)-0.038***(0.014)yes
yes
yes
71,3160.125(2) w/tari
Coef.
(S.E.)

0.012*(0.007)-0.041***(0.014)yes
yes
yes
70,612
0.113∆TripleRevenue= 1 if 4ImportP ricecsht > 0 & 4ImportRevenuecsht < 0 &csht
4#Importerscsht < 0 from period t − 1 to t and 0 otherwise. Column (1) uses FOB
Note:prices and revenues, and Column (2) uses prices and revenues, inclusive of eective duty
rates. Treath = 1 for HS-Codes that received duty-free access from the US-Colombia FTA
and 0 otherwise. The sample covers changes in import outcomes in 2010, 2011 and 2012.
Postt = 1 for 2012 and 0 otherwise while Pret = 1 for 2011 and 0 otherwise. USAs = 1
for exporters from the United States and 0 for exporters from other developed countries.
Sizecsh is the z-score of initial export value ecsh,2009 in 2009 relative to all exporters of
the product from developed countries in 2009. Controls include all interactions between∗∗∗ ∗∗∗
Postt , Treath , USAs , Sizecsh and Pret . Signicance levels are indicated by,, andfor 1, 5 and 10 percent respectively.

4.4.3 Quality Estimation
To look further into the quality explanation, we estimate quality based on standard methods anda exible approach that is consistent with our theory.

We show that the triple prediction using

quality-adjusted prices (instead of simple unit values) continues to hold.

Exporters who gained

duty-free access became more likely to increase prices, reduce quantities and reduce the number of
their importers, even after adjusting for estimated quality.

14

The main results are similar when we only use a double prediction of lower revenue and fewer importers on the

HS (available upon request).

31

Importers, Exporters and the Division of the Gains from Trade

Let λc denote the quality of exporter c's variety. Then welfare from the dierentiated goods isQ=´

λc u(qc )dGc . We are interested in quality-adjusted prices which net out changes in exporter-

level quality λc before and after the trade liberalization.

v 0 (q

The quality adjusted price is pcd /λc =0
η−1 and we will infer it in two ways. First, we follow Khandelwal et al. (2013) andcd )u (qc )Q

use the elasticities of substitution from the literature to recover quality-adjusted prices, based on
the markup assumptions in the theory of Section 2. Then we will discuss a more exible approachthat enables us to directly approximate the lower nest marginal utility.
For an exporter c that sells to more than one importer d, the inverse demand for the variety isln pcd = ln v 0 (qcd ) + (ln λc + ln u0 (qc ) − (1 − η) ln Q) ≡ ln v 0 (qcd ) + αc where αc is an exporter-specicterm. We typically have estimates for the elasticity in the upper nest of u(qc ) but do not have readily
available measures of the elasticity in the lower nest v(qcd ).

To make progress, we augment theapproach of Khandelwal et al. (2013) to recover quality using demand elasticities from Broda and1−µv

Weinstein (2006) and Soderbery (2015). Assuming v(qcd ) ≡ qcd

0, ln v (qcd ) = ln (1 − µv )−µv ln qcd .

A key assumption in our theory is that the elasticity of demand in the upper nest is smaller than theelasticity in the lower nest (µu εv < min µv min (1 − µv )), so we get a lower bound for the elasticity inthe lower nest. Let the upper nest utility function be CES with a dierentiation parameter denotedby 1 − µu .

Then we know that the elasticity for the lower nest is bounded below by the upper

nest elasticity so that µv = κµu for 0 < κ < 1, and we will use the upper nest elasticities from theliterature to estimate quality. We estimate the unit value of the variety of exporter-importer cd foreach HS code h from source country s in each time period t asln pcdsht = −κ · µuh ln qcdsht + αcsht + cdsht
where µuh is obtained from Broda-Weinstein-Soderbery elasticities (σh ≡ 1/µuh ). The key identifying assumptions are that κ does not vary across products and that quality varies at the exporterproduct-time level.

Having estimatedκ̂ and α̂csht , we recover quality ln λ̂csht as a residual byregressing α̂csht + µuh ln qchst − ln (1 − µuh ) on product-time xed eects and using µuh from the
Broda-Weinstein-Soderbery estimates of elasticities of substitution across product groups.

Thenthe quality-adjusted prices are ln pcdsht − ln λcsht which we use to determine the changes in qualityadjusted price in the triple prediction.
Under the exible approach, we move away from the lower bound method and approximate the0lower nest marginal utility as a function of quantities. The rst step is to estimate v (qcd ) which
we take to be a cubic function of ln qcd . The unit value of exporter-importer cd for each HS code hfrom source country s in each time period t isln pcdsht = β1 ln qcdsht + β2 (ln qcdsht )2 + β3 (ln qcdsht )3 + αcsht + cdsht .
2

0

Having approximated v̂ (qcd ) = β̂1 ln qcd + β̂2 (ln qcd )suming+ β̂3 (ln qcd )3 , we proceed to recover λc . As-

u0 (qc ) = qc1−µu , our estimated exporter-specic quality is ln λcsht + ln αht = ln pcdsht −32

Importers, Exporters and the Division of the Gains from Tradeln v̂ 0 (qcdsht ) + µuh ln qcsht − ln (1 − µuh ) which is identied up to a constant and where µuh is basedon Broda-Weinstein-Soderbery estimates of elasticities of substitution for the product group h. Details of the quality estimation are provided in the Appendix and here we discuss the triple prediction
using quality-adjusted prices.
The triple prediction continues to show similar results when quality-adjusted prices are usedinstead of unit prices. Column (1) of Table 7 is based on the quality-adjusted prices from the rstmethod and Column (2) is based on the exible method.

We nd once again that exporters in

terciles 1 and 2 are more likely to consolidate their import market.

Table 7: Tercile results: Quality-adjusted Triple Prediction by Size Bins

Dependent Variable: ∆Triplecsht

Variable

Tercile3csh · Postt · Treath · USAs

Tercile2csh · Postt · Treath · USAs
Tercile1csh · Postt · Treath · USAs
Tinycsh · Postt · Treath · USAs
Controls (including Pre-treatment)
Product-Year FE αht
Country-Year FE αst
N
R2

(1)
Coef.
(S.E.)

0.001(0.023)0.026(0.021)0.071**(0.032)-0.063**(0.031)yes
yes
yes
57,480
0.112

(2)
Coef.
(S.E.)-0.006(0.023)0.019(0.023)0.061**(0.030)-0.056*(0.030)yes
yes
yes
57,4800.124

Note: ∆Triplecsht = 1 if 4QualityAdjImportP ricecsht > 0 & 4ImportQuantity csht < 0& 4#Importerscsht < 0 from period t − 1 to t and 0 otherwise. Treath = 1 for HS-Codes
that received duty-free access from the US-Colombia FTA and 0 otherwise. The sample
covers changes in import outcomes in 2010, 2011 and 2012.
otherwise while Pret

= 1 for 2011 and 0 otherwise.

USAs

Postt = 1 for 2012 and 0= 1 for exporters from theUnited States and 0 for exporters from other developed countries. Sizecsh is the z-score of
initial export value ecsh,2009 in 2009 relative to all exporters of the product from developed
countries in 2009. Tercile1csh = 1 for the 33rd tercile of Sizecsh , Tercile2csh = 1 for the 66th
tercile and Tercile3csh = 1 for the top tercile. Tinycsh = 1 for all exporters from developed
countries with total sales of less than USD10,000 in 2009. Controls include all interactions
between Postt , Treath , USAs , Pret and indicators for initial size bins. Standard errors are∗∗∗ ∗∗
bootstrapped and clustered by exporter. Signicance levels are indicated by
,
, and
∗
for 1, 5 and 10 percent respectively.

4.4.4 Within-Exporter-Importer Pairs
While the baseline results examine the triple prediction at the level of the exporter, the model
predicts that the results should also hold for some exporter-importer pairs so we estimate the triple

33

Importers, Exporters and the Division of the Gains from Trade

prediction at the exporter-importer pair level.

Let d denote a Colombian importer that imports

from exporter c. The triple variable is now dened as ∆Triplecdsht = 1 for exporter-importer pairs

cd that experience an increase in their bilateral price, a fall in their bilateral quantity (∆qcdsht < 0)max

and a decrease in the importers that buy from c (∆dcsht < 0). If any one of these events does not
happen, then ∆Triplecdsht = 0. Columns (1) and (2) of Table 8 show that the likelihood of increasing
import prices, reducing quantities and reducing the number of importers goes up after the tradeliberalization. As earlier, exporter-importer pairs in the middle of the exporter size distribution are
more likely to see the triple prediction hold. The exporter-importer pairs of tiny and large exporters
who are not expected to switch contracts show small eects or a reduction in the likelihood of thetriple prediction.

Table 8: Exporter-Importer results: Triple Prediction Within Exporter-Importer Pairs

Dependent Variable: ∆Triplecdsht

Variable

Tercile3csh · Postt · Treath · USAs
Tercile2csh · Postt · Treath · USAs
Tercile1csh · Postt · Treath · USAs
Tinycsh · Postt · Treath · USAs
Controls (inc. Pre-treatment)
Product-Year FE αht
Country-Year FE αstNR2(1) fob
Coef.
(S.E.)-0.005(0.025)0.046*(0.028)0.053**(0.026)-0.0414(0.028)yes
yes
yes
82,1300.110(2) w/tari
Coef.
(S.E.)-0.017(0.025)0.028(0.027)0.051**(0.026)-0.049*(0.027)yes
yes
yes
82,1300.106∆Triplecdsht = 1 if 4ImportP ricecdsht > 0 & 4ImportQuantity cdsht < 0 &4#Importerscsht < 0 from period t − 1 to t and 0 otherwise. Column (1) uses FOB
prices and Column (2) uses prices inclusive of eective duty rates. Treath = 1 for HSNote:

Codes that received duty-free access from the US-Colombia FTA and 0 otherwise. The
sample covers changes in import outcomes in 2010, 2011 and 2012. Postt = 1 for 2012 and0 otherwise while Pret = 1 for 2011 and 0 otherwise. USAs = 1 for exporters from theUnited States and 0 for exporters from other developed countries. Sizecsh is the z-score of
initial export value ecsh,2009 in 2009 relative to all exporters of the product from developed
countries in 2009. Tercile1csh = 1 for the 33rd tercile of Sizecsh , Tercile2csh = 1 for the= 1 for the top tercile. Tinycsh = 1 for all exporters fromdeveloped countries with total sales of less than USD10,000 in 2009. Controls include
66th tercile and Tercile3csh

all interactions between Postt , Treath , USAs , Pret and indicators for initial size bins.
∗∗∗ ∗∗∗
Signicance levels are indicated by,, andfor 1, 5 and 10 percent respectively.

34

Importers, Exporters and the Division of the Gains from Trade

5

Conclusion

This paper examines how the microstructure of import markets aects the division of the gains fromtrade among consumers, importers and exporters. When an exporter sells a product to importers
through anonymous markets, double marginalization and business stealing among competing importers lead to lower prots.

Exporters and importers can invest in relationships that overcome

these sources of lower prots.
We embed the choice of contracts between exporters and importers into a trade model withheterogeneous exporters and importers. Exporters can oer bilateral contracts that eliminate double marginalization, leading to higher prots and lower prices. Exporters can internalize businessstealing across importers by investing in joint contracts.

This enables an exporter to commit tomitigating competition among its importers to maximize nultilateral prots. When investments injoint contracts embody economies of scale and markups rise with quantities, trade liberalization
changes the relative incentives to engage in bilateral contracts and joint contracts.

Lower trade

costs increase the surplus from joint contracts, and this change in the microstructure of the importmarket increases rm prots at the expense of consumer welfare.
The model enables us to derive unique predictions for changes in import prices, quantities
and the number of importers per exporter.

Testing these implications empirically, we show thatbilateral trade liberalization between Colombia and the US induced US exporters to consolidate theirimport market, increasing the probability of higher prices, reduced quantity and fewer Colombian
importers per exporter.

These observable predictions suggest that the actions of exporters andimporters aect the ability of consumers to gain from trade.

The estimated elasticity of importprices with respect to trade costs shows substantial increases in prices for certain products from tradeliberalization. Future work can shed more light on how this translates into consumer price changes
and its contribution to the aggregate pass-through of reduction in trade barriers into consumer
prices.

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For Online Publication: Appendix

Fixed Entry
We will show that the prots of the exporters are supermodular in market size and contracting
choice under conditions on the rate at which markups change with quantities.
The exporter's optimal prot is πc = s (m(q)q/(1 − m(q))) Md βcdL where the markup is m(q) ≡µv (q) + zµu (Md v(q)) εv (q) for z ∈ {0, 1} at the optimally chosen quantity q . This formulation lets
us specify the dierent contracting choices through z . Prots under bilateral contracts correspondtoz = 0 and prots under joint contracts correspond to z = 1.
00termined by u (Md v(q)) v (q) (1 − m)= δcd.

The optimal quantity is de-

The consumer budget multiplier is taken as xed

0
0by the rm and is given by δ = sMc Md u (Md v(q)) v (q) in equilibrium. As z rises, the protmq qd ln qzµu εvd ln πfunction changes byd ln z = 1 + m(1−m) d ln z + m(1−m) . From the optimal pricing condition,mq qzµu εvd ln qln δ + ln u0 (Md v(q)) v 0 (q) (1 − µv − zµu εv ) = cd so that − µ + µu ε + 1−m
d ln z = 1−m and quan(1−z)q sMd (µu εv )2tities fall under joint contracts. Substituting in the prot derivative, πz = βLτ cd
mq q(1−m)2 µv +µu εv + 1−m
d ln qso sπzs /πz = 1 +d ln smq qd ln(µv +µu εv + 1−m)2mq qd ln µu εv
q
1 + 2 d ln q + 1−m −≡ 1 + (1 + Aq ) dd ln
d ln qln s .

From optimal contracting, πz = βLτ cd(1−z)q xMd (µu εv )2J
mq q = fc so that dierentiating with re(1−m)2 µv +µu εv + 1−mmq qd ln( 1−m )2zµu εd ln qd ln z.
d ln s + (Az − z/(1 − z)) ds = 0 for Az ≡1−m − d ln zmq qd ln qFrom optimal pricing and the budget multiplier, 1 − m = sqMc Md cd implying − 1 +1−m d ln s −zµu εvzµu εv(1+Aq )mq q
zµu εv d ln z
1−m
1−m
=
1
. Putting the two together, − 1 +
+
(d
ln
q/d
ln
s)
=
1+
z
1−m d ln s
1−m−Azz/(1−z)−Az .
1−z


 
zµu εv(1+Aq )
mq q
mq q
1−m
Substituting for this, d ln πz /d ln s =. So as long as Aq , Az ≤z
1−m − Aq / 1 + 1−m +−Azspect to market size gives 1 + (1 + Aq )1−z0, d2 πc /dzds > 0 and market expansion makes higher values of z more desirable.

Free Entry
To examine the robustness of the qualitative predictions, we specify the upper nest as CES (u(qc ) =qcρ ).

Under free entry, the additional conditions arehsMc (1 − β)him
1−m τ cdqL − fcd

i= fd andmJ
1−m τ cdqL − fcd = fc + zfc . Dierentiating πz with respect to market size, d ln πz /d ln s =qd ln Mc
1 + ddlnlnMsd + (1 + Aq ) dd ln
imply=
ln s . As z is chosen optimally, the free entry conditions

d ln smq q
mq q
d ln qd ln qd ln Md−1 − 1 + 1−m
d ln s = d ln s . From optimal pricing and optimal contracting, − 1 + 1−m d ln s −zµu ε d ln zqd ln Mdd ln Mdd ln Mcd ln zAq ) dd lnz − z/(1 − z)) d ln s = 0. Solv1−m d ln s − d ln s − d ln s = 1 and 1 + (1 + 
ln s + d ln s + (Azµu εvzµu εv
Aq d ln q
mq q
1−m
1−m
ing for quantity changes using free entry, − 1 +zz
1−m 1 + 1−z−Az − 1−z−Az
d ln s = 1. Then

sMd β

q
d ln πz /d ln s = 1 + ddlnlnMsd + (1 + Aq ) dd ln
ln s = −mq q
1−m − Aq41

d ln qd ln s > 0.

Importers, Exporters and the Division of the Gains from Trade

WelfareWelfare is U

d ln qd ln Mdd ln McU= sMc u (Md v (q)) so that ddln
ln z = d ln z + εu d ln z + εu εv d ln z . Under xed entry,

d ln U/d ln z = εu ε (d ln q/d ln z) which is negative because rms scale back quantities under joint
contracts as shown above. We have also shown above that πz > 0 so prots rise under joint contracts.
Under free entry with a CES upper nest, optimal pricing implies −



m q

q
1 + 1−mmq q

d ln qzµu εd ln Mcd ln z = 1−m + d ln z +mq q

d ln 1−m2zµu εd ln qd ln Mdd ln Mdz1−md ln z and optimal contracting implies 0 = − 1−z + 1−m − µ+µu ε+ mq q d ln z + d ln z + d ln z Aq .
1−m

mq q d ln Md
From free entry,−m d ln z



m

1−m

mq q
1 + m(1−m)



ln Md
d ln Mcd ln McJJ=
d ln z and d ln z = d ln z + zfc / fc + zfc . Entrymq q
1+ m(1−m)mq q/mzfcJ
zfcJ
d ln Mdd ln Mcchanges byd ln z = − 1+ 2−m mq q fc +zfcJ and d ln z = 1+ 2−m mq q fc +zfcJ . So the change in quantities

is −



mq q
1 + 1−m





m

m q

m

1−m

m q

−

1−m

q
1+ 1−mzfcJ
d ln qzµu ε. Substituting in the welfare derivative,
=
+
mq q
2−m
d ln z1−m
fc +zfcJ
1+

m q

q
εu
εu ε + mq − εu − 1−mεu εd ln U zµu ε(1 − z)mµu ε
m
/
=
+
mq q
mq q
mq q
d ln z 1 − m 1 + 1−mµ+ µu ε + 1−m
1 + 2−m
m 1−m

m q

m q

q
q
1
m + m 1−m
1−ε+ m
εu ε
1−m
≥
1
−
mq q
mq q
mq q (1 − z)µu
1 + 1−mµ + µu ε + 1−m
1 + 2−m
m 1−m
εu ε
≥
mq q (1 − (1 − z)µu ) ≥ 0
1 + 1−m!

A switch to joint contracts lowers consumer welfare.
Under free entry, the change in welfare for bilateral contracts is d ln U/d ln s = 1+d ln Mc /d ln s+



mq q
d ln qd ln Mdd ln Mcεu d ln Md /d ln s + εu εv d ln q B /d ln s. From optimal pricing, − 1 + 1−m
d ln s = 1 + d ln s + d ln s
mq qd ln qd ln Mdd ln Mcand free entry implies
d ln s = d ln s = −1− 1 + m(1−m) d ln s . Putting these conditions together,
mq q
quantities and entry fall because d ln q/d ln s = −1/ 1 +
(2/m
−
1)
and d ln Mc /d ln s =
1−m
mq q


1+
mq q 2−m d ln Ud ln Md /d ln s = −1 + 1+ mm(1−m)
1 + 1−mq q 2−m . Substituting in the welfare derivative,md ln s =
m q

1−m

m

q
1 − εu ε + m(1−m)(1 − εu (1 − m)) > 0.

Variety-Level Model
This section explains the variety-level predictions in a model with relationship-specic cost fcd > 0,ad valorem trade costs τ > 1 and xed potential entry. The optimal price is pcd (1 − mcd ) = cd form = µ + z and the optimal importer cost cuto is (mcdm − z/εm ) cdm qcdm / (1 − mcdm ) = fcd /L.

mq (qcd )qcd d ln qcd
d ln qcz
From optimal pricing, − µcd +1−mcd
d ln z = 1−mcd +µu (qc ) d ln z and from the optimal cuto,
1−z/εcdm
mq (qcdm )qcdm d ln qcdm
z−z/εcdm
d ln dm
z
µ
+
cd
m
1−mcd
d ln z + d ln z + mcd −z/εcd + 1−mcd = 0. Substituting formcd −z/εcd
m

m

m

m

m

m

the change in quantities and re-writing, the change in the importer cost cuto is−d ln qc
d ln dmz/εcdm1 − z/εcdm=+µuc
d ln z
1 − mcdm
1 − mcdm
d ln z42

Importers, Exporters and the Division of the Gains from Trade´ v0 (qcd )qcd dGd
vcdm dm (1−z/εcdm )qc++
m (q )qµuc
mcdm −z/εcdmµ + q cd cd

´ dm

!

µu ddlnlnqzc =v(q)dG, total quantity changes by
cd
1−mcd
!
´ v0 (qcd )qcd dGdz/εz. So d ln qc /d ln z < 0 and total quantities always fall
− vcdm dm 1−mcdcdm +mq (qcd )qcd 1−mcd

As qc =

0

µcd +

m

1−mcd

after joint contracts. Substituting for the change
in the importer cost in total quantity, the change´cuto is (1 − mcdm )d ln dm
d ln z= −ε−1cdm

1−µcd −εcd
z
m dG
d
mq (qcd )qcd
1−µcd −zµcd + 1−mcd.
´ v0 (qcd )qcd dGd1−z/εqc /µuc +vcdm dm 1−m cdm +
m
(q
)q
q
cd cd
cdm
µcd + 1−m
cd

v 0 (qcd )qcd 1+

We will show that

(1 − µcd − µuc ε̄vc ) µcd + (1 − µcd − εcdm ) µuc ε̄vc + mq (qcd )qcd > 0 so that the importer cost cuto
falls under joint contracts.

0First note that the LHS of the inequality is decreasing in µuc ε̄vc under (1 − ε)

> 0.

And

(1−µcd )µcd
we will need to show that µuc ε̄vc <2µcd +εcdm −1 . The RHS of this inequality is decreasing in µcd
εm +1
εm +1
m )(1−µ)∂ ln RHS
because= − (1−µ)(2µ+ε+ µ1 = −(1−ε+ µ1 < − 2µ+ε∂µµ(2µ+εm −1) < 0. So the most binding
m −1
m −1)
b(1−b)
inequality is at the highest µcd and εcdm . At these values, the RHS is2−3b . By assumption,µuc ε̄v < min µv min (1 − µv ) ≤ b2 which is less than the RHS because 3b2 − 3b + 1 > 0 for b ∈ (0, 1).
So d ln dm /d ln z < 0 and the importer cuto is lower for joint contracts. Finally, the price changeln qd ln pcd /d ln z = −d ln(1 − mcd )/d ln z which gives (1 − mcd ) d ln pcd /d ln z = mq q dd lnz + z =
mq qd ln qcµz− µ+ mq q µu d ln z + µ+ mq q > 0.

is

1−m

1−m

Having discussed the changes in observable outcomes across contracts, we will provide conditions
for an increase in the cost cuto for joint contracts after a reduction in import taris.
at a reduction in ad valorem taris.
just T .

We lookIf τ T is the amount paid to exporters, then they receive

The exporter's problem can be written as Πc´d= τ −1 β 0 m [(pcd − cd) qcd Ld − fcd ] dGd +´dτ −1 βλc Ld zqc − 0 m ν(qcd )dGd − z 2 fcJ for a continuous choice of contracting denoted by z . Thenhthe nal markup is mi

≡ µvcd + µuc ε̄´vc /z ≡ µv + y/z .

−1 d2 Πcinto joint contracts if βdτ −1 dz=

Firms will become more likely to enter´ dm
d 0dm [(pcd −cd)qcd Ld −fcd ]d ln Q d 0 pq
−
(1
−
η)
dz
dz
d ln τ −1> 0. We knowthat the rst terms is positive for joint contracts that are viable. When revenues fall under joint
contracts, as happens in our empirical work, we need to show that aggregate quantities rise withtrade liberalization. Whenever aggregate trade volumes rise with trade liberalization, prots will
be supermodular in contracting choice and the exporter cost cuto will rise. We therefore provide
conditions on primitives that ensure aggregate trade volumes rise after trade liberalization.

´ v0 q(1−µ−ε̄) d ln q
µ0u qc d ln qc
d ln ym dm d ln dm´
dGd + (εm´ −ε̄)vd ln τ = µu d ln τ +d ln τ . From optimal pricv 0 qdGd d ln τv 0 qdGdy/z d ln z
y/z d ln y
µ0 qd ln qd ln Qd ln qc
ing, − µ +1−m d ln τ = (1 − η) d ln τ − 1−m d ln τ + 1−m d ln τ + µu d ln τ . From optimal contracting,d ln yd ln Qln z
ln y + (η − 1) ln Q + ln u0 + ln qc − 2 ln z = ln τ + ln 2fcJ /βL so that 2 dd ln
τ = d ln τ − (1 − η) d ln τ +qc
d ln dm1(1 − µu ) ddln
ln τ − 1. From the optimal cuto and substituting for optimal prices, d ln τ = − 1−mm (1 −´ dmy/zεm d ln yy/zεm −1Qd ln qcη) dd lnln τ − 1−mm d ln τ + 1−mm µu d ln τ . From ln qc = ln 0 v(q)dGd , the change in total quantities´ v0 q d ln qd ln qc´vm dm d ln dm +´is. Substituting for the changes in optimal contracts, cutosd ln τ =vdGd d ln τ
vdGd d ln τ
By denition,and markups, we obtain the change in qc in terms of changes in the aggregate quantity Q which can

43Importers, Exporters and the Division of the Gains from Trade-4-5

Quality Adjusted Unit Prices
1005

Changes of Quality Adjusted Unit Prices
-2
0
2

4

15

Figure 3: Distribution of Unit Values and Quality-adjusted Unit Values

-5

0

5
Original Unit Prices

10

15

-10

-5

0
Changes of Original Unit Prices

510

Note: Estimates based on the method of Khandelwal et al. (2013).

then be solved using the denition of Q ≡´u(qc )dGc . The change in the production cost cuto is´ dm
d ln Q ´ dm
0 cdqcd dGd = − 0  [(pcd − cd) qcd − fcd /L] dGd − (1 − η) d ln τ  0 pcd qcd dGd . The change´ v0 qy/z
dGdvm dm 1−y/zεm1
d ln qc
´
´
1
+
µ
1
+
+
µ
(1/µ
−
1)
+
A
0
u
u
u
c
in exporter-level quantity is
=
µ q
2
1−m
vdG 1−mmvdG
d ln cm
d ln τ

´ dm

d µ+

d

Q
−A/2 − AQ (1 − η) dd lnln τ where´ v0 qdm y/zεmAy ≡ ´vm+ 21 ´ vdG
vdG 1−mm

´

dG

0
d
d µ+ µ q 1−m1−m
v 0 q(1−µ−ε̄)

d

A≡

y/z

1


/ 1+

´

´
0
y/z
y/z
1
´ vq

´
dGd ,
0 q 1−m dGd + Ay
0µvdGd µ+µ+ µ q
v 0 q 1−m
1−m

Ac ≡ Ayµ0u qcµu −´d ln τ

1−m!

v 0 q(1−µ−ε̄)y/z
m dm y/zεm´dGd + (εm´ −ε̄)vµ0 q
v 0 qdGd 1−mmµ+ 1−mv 0 qdGd 1−m

,

1−m

0
 v q(1−µ−ε̄)´µ0 qµ+ 1−mv 0 qdGd´ v0 qdm
1
AQ ≡ ´vm+ ´ vdG
vdG 1−mmd10d µ+ µ q
1−m



y/z
µu − 12 1−m(1 − µu )







y/z
1 + 12 1−m
dGd +Ay!
m dm 1−y/zεm´dGd − (εm −ε̄)v
1−mm µu
v0 q

v 0 q(1−µ−ε̄)

´

µ0 q
v 0 qdGdµ+ 1−mandy/z(εm −ε̄)v´ m dm
1 + 21 1−m
dGd + (1−m0m ) v qdG

Then aggregate quantity rises after a reduction in taris as long as A > 0 and Ac > −1 for z ∈ [0, 1].

Estimating quality
Table 9 shows the quality estimation procedure. Column (1) contains the Broda-Weinstein-Soderbery
estimates and Column (2) contains the exible method estimates. The elasticities of substitution
are available at the HS 8-digit, and we take the mean for each HS 6-digit category in our data. We
report estimates for the elasticities from the hybrid method of Soderbery. Results are similar withother elasticity estimates.
The correlation between the unit prices and the quality-adjusted units prices is about 0.8. Thisis shown in Figures 3 and 4 which show graph the scatter plots for the prices and the qualityadjusted prices for each method, and the changes in these variable which are used in the subsequentestimation.

44

!



d

.

Importers, Exporters and the Division of the Gains from Trade

Table 9: Demand results: Quality Estimation

Dependent Variable: ∆ ln Import Pricecdsht

Variableln Import Quantitycdsht /Elasticityh

(1)
Coef.
(S.E.)(2)
Coef.
(S.E.)

yes
yes
1,272,789
0.988-0.297***(0.003)0.009***(0.001)-0.0003***(0.00003)
yes
yes
1,701,645
0.988-0.377***(0.002)ln Import Quantitycdsht(ln Import Quantitycdsht )2(ln Import Quantitycdsht )2

Exporter-Product-Year FE αcsht
Country-Year FE αstN
R2

Note: Note: ∆ ln Import Pricecdsht is the change in import prices in logs from period t − 1
to t and ln Import Quantitycdsht is the change in import quantities.

Elasticityh is the
Broda-Weinstein-Soderbery elasticity of substitution for product h. Signicance levels are∗∗∗ ∗∗∗
indicated by,, andfor 1, 5 and 10 percent respectively.

-5

-10

-5

Quality Adjusted Unit Prices
50
10Changes of Quality Adjusted Unit Prices
0
5

15

Figure 4: Distribution of Unit Values and Quality-adjusted Unit Values: Flexible Approach

-5

0

5
Original Unit Prices

10

15

-10

Note: Estimates based on the exible method of Section 4.

45

-5

0
Changes of Original Unit Prices

510