Assortative Matching of Exporters and Importers*

Yoichi Sugita†

Kensuke Teshima‡

Enrique Seira§

Julio 2021

Abstracto

This paper studies how exporting and importing ﬁrms match based on their ca-

pability by investigating the change in such exporter–importer matching during trade

liberalization. During the recent liberalization on the Mexico-US textile/apparel trade,

exporters and importers often switch their main partners as well as change trade vol-

umes. We develop a many-to-many matching model of exporters and importers where

partner switching is the principal margin of adjustment, featuring Beckerian posi-

tive assortative matching by capability. Trade liberalization achieves efﬁcient global

buyer–supplier matching and improves consumer welfare by inducing systematic part-

ner switching. The data conﬁrm the predicted partner switching patterns.

JEL Classiﬁcation: F1; Palabras clave: Firm heterogeneity, assortative matching,

two-sided heterogeneity, trade liberalization

*We are grateful to comments from three anonymous referees and the editor Amit Khandelwal, especially
their encouragement for many-to-many matching extensions. We thank Andrew Bernard, Bernardo Blum,
Kerem Cosar, Don Davis, Swati Dhingra, Lukasz Drozd, Michael Gechter, Julia Cajal Grossi, Meixin Guo,
Daniel Halvarsson, Keith Head, Wen-Tai Hsu, Mathias Iwanowsky, Hiroyuki Kasahara, Ben Li, Alberto
Ortíz, Nina Pavcnik, James Rauch, Bob Rijkers, Esteban Rossi-Hansberg, Peter Schott, Yuta Suzuki, Heiwai
Espiga, Yong Tang, Catherine Thomas, Kosuke Uetake, Yasutora Watanabe, Yuta Watabe, David Weinstein,
Shintaro Yamaguchi, Makoto Yano and participants at seminars and conferences for their comments. Nosotros
thank Secretaria de Economia of Mexico and the Banco de Mexico for help with the data. Financial supports
from the Private Enterprise Development in Low-Income Countries (PEDL), the Wallander Foundation, el
Asociacion Mexicana de Cultura, and JSPS KAKENHI (Grant Numbers 22243023, 26220503, 15H05392,
17H00986, 18K19955 and 19H01477) are gratefully acknowledged. This research beneﬁts from the IDE-
JETRO project and the RIETI project. Francisco Carrera, Diego de la Fuente, Zheng Han, Carlos Segura,
Yuri Sugiyama, Yuta Suzuki, Jumpei Takubo, Makoto Tanaka, and Stephanie Zonszein provided excellent
research assistance.

†Graduate School of Economics, Hitotsubashi University. 2-1 Naka Kunitachi, Tokio 186-8601, Japón.

(Correo electrónico: yoichi.sugita@r.hit-u.ac.jp)

‡Institute of Economic Research, Hitotsubashi University. 2-1 Naka Kunitachi, Tokio 186-8601, Japón.

(Correo electrónico: kensuke-teshima@ier.hit-u.ac.jp)

§ITAM. Av. Santa Teresa # 930, México, D. F. 10700 (Correo electrónico: enrique.seira@itam.mx)

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Review of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 Internacional (CC POR 4.0) licencia.

1 Introducción

International trade mostly takes the form of ﬁrm-to-ﬁrm transactions in which ﬁrms seek and com-

pete for capable buyers and suppliers globally. A case example is Boeing’s 787 Dreamliner team

that comprises the most capable suppliers from all over the world. Trade research in the last two

decades has revealed the huge heterogeneity in the capability of exporters and importers (p.ej., su

productivity and product quality). De este modo, the way heterogeneous exporters and importers match

along the supply chains may determine the aggregate capability of the industry and the welfare.

This paper examines how exporters and importers match based on their capability by investi-

gating the change in such exporter–importer matching during trade liberalization. From Mexico’s

customs administrative records, we construct a matched exporter–importer dataset for Mexican

textile/apparel exports to the United States from 2004 a 2007. Mexico–US textile/apparel trade

is particularly suitable for our purpose. Primero, since Mexico and the United States are large trad-

ing partners with each other, trade between them includes numerous heterogeneous exporters and

importers.1 Second, Mexico–US textile/apparel trade experienced large-scale liberalization. En

2005, the United States removed quotas on textile/apparel imports at the end of the Multi-Fibre

Arrangement (MFA). Since Mexican products already had quota-free access to the US market

under the North American Free Trade Agreement (NAFTA), the MFA’s end effectively removed

protection for Mexican products in the US market and forced them to compete with imports from

third countries, principally China. The liberalization varied across products substantially and was

arguably exogenous because the liberalization schedule was decided at the GATT Uruguay Round

(1986–94) when China’s export growth were not expected.

The MFA’s end substantially changed the partnerships between Mexican exporters and US im-

porters. Mexican exports to the United States decreased by the extensive margin (stopping exports)

1En 2004, the United States was the largest textile and apparel market for Mexico, while Mexico was the
second largest source for the United States. En efecto, 91.9% of Mexican exports are shipped to the United
States and 9.5% of US imports are from Mexico.

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and intensive margin (reducing export values). The intensive margin adjustment involved substan-

tial partner switching, often including the exporter’s largest main partners. Main partner switching

accounted for more than 50% of the intensive margin and caused a more than 230% excess re-

allocation of exports across US buyers beyond the intensive margin. As we explain in Section

2, this prevalence of main partner switching in trade liberalization was at odds with anonymous

market models (p.ej., neoclassical models, oligopoly models), love-of-variety models (the Krug-

man–Melitz model), and some recent exporter–importer matching models (p.ej., Bernard, Moxnes,

and Ulltveit-Moe, 2018) that combine the love-of-variety model and ﬁxed costs of matching.

Motivated by this new fact, we develop a many-to-many matching model of exporters and

importers in an intermediate good market in which partner switching is the principal margin of

adjustment. The model combines Sattinger’s (1979) frictionless assignment model of a contin-

uum of agents, Melitz’s (2003) standard heterogeneous ﬁrm trade model, and Bernard, Redding,

and Schott’s (2011) multi-product ﬁrm trade model. The model consists of ﬁnal producers (im-

porters) in the United States and suppliers (exporters) in Mexico and China. Final producers pro-

duce multiple products, while suppliers own multiple production lines. A ﬁnal producer’s variety-

level capability depends on its ﬁrm-level capability and idiosyncratic capability, while a supplier’s

production-line-level capability depends on its ﬁrm-level capability and idiosyncratic capability. A

ﬁnal variety matches a production line one-to-one, resulting in the many-to-many matching of ﬁnal

producers and suppliers. The Beckerian PAM of varieties and production lines arises as a stable

equilibrium when a variety’s capability and production’s capability are complements.

The model predicts that the MFA’s end induced systematic partner switching that led to efﬁ-

cient buyer–supplier matching and improved consumer welfare. As empirically documented by

Khandelwal, Schott, and Wei (2013), at the MFA’s end, Chinese suppliers at various capability

levels entered the US market. The entry of Chinese suppliers lowered the capability ranking of

each Mexican supplier in the market. Por lo tanto, to achieve PAM, Mexican exporters switched

to US importers with lower capability, while US importers switched to Mexican exporters with

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higher capability. We call these types of partner switching “partner downgrading” and “partner

upgrading,” respectively. Allowing capable Chinese suppliers to match with capable US ﬁnal pro-

ducers, this rematching achieved PAM in the global market, which improved aggregate capability

and consumer welfare. Por el contrario, in an anonymous market in which matching is independent of

capacidad, rematching should not occur in a systematic way or result in an efﬁciency gain.

We take the model’s predictions on partner switching to data. Guided by the theory, we estimate

the rankings of ﬁrm-level capability of Mexican exporters and US importers by the rankings of

su 2004 pre-liberalization product trade with their main partners. We then compare the partner

switching patterns between liberalized products (the treatment group) and other textile/apparel

products (the control group) within Harmonized System (HS) two-digit industries. We ﬁnd the

partner switching patterns to be consistent with PAM. Primero, US importers upgrade their Mexican

partners more often in the treatment group than in the control group. Al mismo tiempo, Mexican

exporters downgrade their US partners more often in the treatment group than in the control group.

Segundo, among ﬁrms that switch their main partners, the capability rankings of new partners are

positively correlated with those of old partners. Juntos, these ﬁndings provide strong support for

PAM and reject independent random matching. Además, we conﬁrm the model’s predictions

on ﬁrm exit and the number of partners. Primero, the capability cutoff for Mexican exporters increases.

Segundo, US importers and Mexican exporters decrease their number of partners.

A lo mejor de nuestro conocimiento, detecting Beckerian PAM by capability in this way is a novel

approach to addressing the endogeneity problem in the conventional approach. When matching

matters for a ﬁrm’s performance, most ﬁrm characteristics observable in typical production and

customs data (p.ej., inputs, outputs, and productivity measures) may reﬂect partners’ unobserved

capability as well as the ﬁrm’s own capability. Por lo tanto, the simple correlation of those charac-

teristics across matches may suffer from endogeneity.2 Instead, our approach utilizes the MFA’s

end as an exogenous negative shock on the capability ranking of Mexican exporters.

2Por ejemplo, Oberﬁeld (2018) showed a buyer’s employment is positively correlated with a seller’s

employment in a model in which buyers match sellers randomly and independently of capability.

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As matched exporter-importer data become available to researchers, the last decade saw the

burgeoning literature on buyer-supplier relationships in international trade.3 Our paper contributes

to a strand of this literature studying exporter-importer matching. Rauch (1996), Casella and Rauch

(2002), and Rauch and Trindade (2003) pioneered the theoretical literature by using the assignment

model of symmetric ﬁrms, while our model features ﬁrm heterogeneity in capability as in Melitz

(2003). Antras, Garicano, and Rossi-Hansberg (2006) analyzed offshoring as the PAM of man-

agers and workers across countries. The assignment model captures two distinctive features in

exporter-importer relationships. Primero, trading with high capability ﬁrms improves a ﬁrm’s perfor-

mance, but the opportunity to trade with them is scarce and something that ﬁrms compete for. Este

view echoes with recent evidence that trading with high capability foreign ﬁrms improves local

ﬁrm’s performance through various channels.4 Second, buyer–supplier matching is an allocation

of scarce trading opportunities. De este modo, trade liberalization induces partner switching to achieve a

globally efﬁcient matching. We provide the ﬁrst evidence for this matching mechanism.

Bernard et al. (2018) recently developed another approach combining match-level ﬁxed costs

and the love-of-variety (CES) production function.5 A buyer and a supplier are matched when the

match surplus exceeds the match-level ﬁxed costs. As the match surplus monotonically increases

in the buyer’s capability and the supplier’s, all the matches are realized except those between low

capability ﬁrms.6 Thus, the model can predict the negative degree assortativity reported by Blum,

Claro, and Horstmann (2010), Bernard et al. (2018), and others that a buyer’s number of partners

3Domestic buyer-supplier matched data has recently become available for research on domestic produc-

tion networks(p.ej. Bernard, Moxnes, and Saito, 2019; Dhyne, Kikkawa, Mogstad, and Tintelnot, 2021).

4See e.g., De Loecker (2007) and Atkin, Khandelwal, and Osman (2017) for learning technologies;
Macchiavello (2010) and Macchiavello and Morjaria (2015) for reputation building; Tanaka (2020) para
improving management; and Verhoogen (2008) for quality upgrading. Trading with foreign multinational
ﬁrms is also found to improve ﬁrm’s performance (p.ej., Javorcik, 2004).

5Bernard, Dhyne, Magerman, Manova, and Moxnes (2021) and Lim (2018) introduced idiosyncratic
match-level ﬁxed costs in the model of Bernard et al. (2018) and analyzed the formulation of domestic
production networks. Carballo, Ottaviano, and Volpe Martincus (2018) applied the ideal variety approach
instead of using the love-of-variety model, which incorporates the interaction between the buyer’s taste for
ideal varieties and the seller’s productivity.

6In the assignment model, por el contrario, the match surplus is a non-monotonic function. For a given ﬁrm,

the match surplus is maximized at the capability of its equilibrium partner as we show in Section 3.1 (2).

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is negatively correlated with the average number of ﬁrms to which the buyer’s partners sell.

Our ﬁnding of PAM can be compatible with negative degree assortativity both theoretically

and empirically. In Appendix D, we present a two-tier model of exporter–importer matching that

uniﬁes Bernard et al.’s (2018) model and ours to predict negative degree assortativity for the ﬁrm-

level matching and PAM for the product-level matching. In the model, a buyer (p.ej., a car maker)

has a love-of-variety production function with respect to intermediate goods and decides whether

to make or buy each intermediate good (p.ej., tires, seats), considering the match surplus and match-

level ﬁxed costs, as in Bernard et al. (2018). For each intermediate good (p.ej., a set of four tires), a

buyer matches a supplier following PAM as in our model. Our data conﬁrm the model’s prediction

by ﬁnding that negative degree assortativity holds when a match is deﬁned at the ﬁrm level, pero

becomes weaker and statistically insigniﬁcant when a match is deﬁned at the product level.

Another important strand of the literature studies the dynamics of an exporter’s and importer’s

partner choice in a steady-state environment. Macchiavello (2010) introduced reputation build-

ing in an assignment model to explain an exporter’s partner upgrading over time. Eaton, Eslava,

Jinkins, Krizan, and Tybout (2014) and Eaton, Jinkins, Tybout, and Xu (2015) developed models

incorporating search and learning frictions in partner acquisitions.7 Eaton, Kortum, and Kramartz

(2016) modeled random meeting and competition among multiple buyers and suppliers. Monarch

(2021) estimated partner switching costs in a dynamic discrete choice model. Heise (2020) docu-

mented the dependence of exchange rate pass-through on the age of trade relationships.

Benguria (2021) and Dragusanu (2014) documented positive correlations between the size and

productivity measures of exporters and importers in France–Colombia trade and India–US trade,

respectivamente. Our model featuring Beckerian PAM also predicts these ﬁndings. Benguria (2021)

and Dragusanu (2014) developed search effort models of the Stigler (1961) type to explain their

ﬁndings by a different mechanism: a high productivity exporter spends greater search efforts ﬁnd-

ing a high productivity importer. Their models, sin embargo, do not explain Mexican exporters’ partner

7Lu, Mariscal, and Mejia (2017) analyzed importer’s switching intermediates in a search/learning model.

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downgrading at the MFA’s end. In their models, search costs are sunk and importers are willing to

trade with all exporters. De este modo, Mexican exporters should continue to trade with pre-liberalization

US partners instead of downgrading partners by paying additional search costs.

Another related literature investigates non-anonymous contracts in given exporter-importer re-

lationships, using matched exporter-importer data. Macchiavello and Morjaria (2015) examined

the surplus of long-term relationships relative to anonymous spot trade. Cajal-Grossi, Macchi-

avello, and Noguera (2020) found greater markups in long-term relational trade than spot trade.

Bernard and Dhingra (2019) studied ﬁrm’s relationship investment to avoid inefﬁciency in spot

comercio. Ignatenko (2019) reports exporter’s price discriminations across importers. Our paper com-

plements this literature by showing exporters match importers in an non-anonymous way, también.

The rest of this paper is organized as follows. Sección 2 explains our data and documents new

facts on partner switching during liberalization. Sección 3 presents our model and derives predic-

ciones. Sección 4 describes our empirical strategy. Sección 5 presents the main results and robustness

checks. Sección 6 provides concluding remarks. The Online Appendix provides the calculations,

pruebas, data construction, extended models, robustness checks, and additional analyses rejecting

alternative explanations of our results.

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2 Mexico–US Textile/Apparel Trade

2.1 The End of the MFA

The MFA and its successor, the Agreement on Textiles and Clothing, are agreements about the

quotas on textile/apparel imports among GATT/WTO countries. At the GATT Uruguay Round

(1986–94), the United States (together with Canada, the European Union, and Norway) promised

to abolish the quotas in four steps (en 1995, 1998, 2002, y 2005). The MFA’s end in 2005 era

the largest liberalization in which liberalized products constituted 49% of imports in 1990.

Three facts (taken from previous studies) about the consequences resulting from the MFA’s end

motivate our analysis.

Fact 1: Surge in Chinese Exports to the United States According to Brambilla, Khandelwal,

and Schott (2010), US imports from China disproportionally increased by 271% en 2005, mientras

imports from most other countries decreased. Using Brambilla et al.’s (2010) US import quota

datos, we classify each HS six-digit textile/apparel product into two groups (see Appendix B.5 for

details): the treatment group of products in which Chinese exports subject to the binding 2004 US

import quota, and the control group of other textile/apparel products. We regress the HS six-digit

product-year-level exports of China and Mexico on the annual year dummies with product ﬁxed

effects separately for the treatment group and control group. Cifra 1 shows the coefﬁcients of

the annual year dummies with triangles for the treatment group and circles for the control group,

separately for Chinese exports and Mexican exports. The difference in the coefﬁcients between

the two groups expresses the impacts of the MFA’s end on Chinese and Mexican exports after

controlling for product-speciﬁc effects. In the left panel for Chinese exports, while the coefﬁcients

antes 2005 are stable and virtually identical between the two groups, after the 2005 quota removal,

the coefﬁcient for the treatment group increases much faster than that for the control group.8

Fact 2: Mexican Exports Faced Competition from China By 2003, Mexico already had tariff-

and quota-free access to the US market through NAFTA. With the MFA’s end, Mexico lost its

advantage over third-country exporters and faced increased competition from Chinese exporters in

the US market, as the right panel of Figure 1 shows.9 While the two groups were stable and almost

8After this substantial surge in import growth, the United States and China had agreed to impose new
quotas until 2008, but imports from China never returned to their pre-2005 levels because (1) the new quota
system covered fewer product categories than the old system (Dayaratna-Banda and Whalley, 2007) y (2)
the new quotas were substantially greater than the MFA levels (ver tabla 2 in Brambilla et al., 2010).

9In theory, Mexican ﬁrms can export products to the US that are produced from materials imported
from China; sin embargo, the number of such cases is negligible because of NAFTA’s restrictive rules of origin,
which requires “yarn forward” (US CBP, 2014). The yarn must be made in Mexico to be qualiﬁed as NAFTA

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identical before 2005, the exports in the treatment group signiﬁcantly declined thereafter.

Fact 3: Exports by New Chinese Entrants with Various Capability Levels From Chinese

customs transaction data, Khandelwal et al. (2013) decomposed the increases in Chinese exports

to the United States in liberalized products after the removal of the quota into the intensive and

extensive margins. Increases in Chinese exports were mostly driven by the entry of new exporters

that had not previously exported products. These new exporters have different capability levels to

those of incumbent exporters, with many more capable than incumbents.10

2.2 Partner Switching after the MFA’s End

Data From Mexico’s customs administrative records, we construct a matched exporter–importer

dataset from June 2004 to December 2011 for Mexican textile/apparel exports (covering HS50 to

HS63) to the United States. For each match of a Mexican exporter and a US importer, the dataset

contains the following information: exporter ID, importer ID, HS six-digit product code, annual

shipment value (USD), quantity and unit, an indicator of a duty-free processing reexport program

(Maquiladora/IMMEX), and other information.

We assign the exporter ID and importer ID throughout the dataset. The exporter ID is the

tax number unique to each ﬁrm in Mexico. Assigning importer IDs to US ﬁrms is challenging.

Although the customs records report the name, address, and employment identiﬁcation number

(EIN) of the US importer for each transaction, none of these can uniquely identify a ﬁrm because

it can use multiple names or change names, own multiple plants/establishments, or change tax

numbers. Además, a ﬁrm’s name and address may be written in multiple ways and suffer

from typographical errors. Por lo tanto, simply counting combinations of names, direcciones, y

products; por lo tanto, only ﬁbers can be imported from China. Sin embargo, Mexico’s ﬁber imports from China
es 7 million USD in 2004 and accounts for only 0.08% of Mexico’s textile/apparel exports to the US.

10Khandelwal et al. (2013) reported that incumbent exporters are mainly state-owned ﬁrms, whereas new
exporters include private and foreign ﬁrms, which are typically more productive. Además, the distribution
of unit prices set by new entrants has a lower mean but greater support than that by incumbent exporters.

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EIN would wrongly assign more than one ID to one US importer.

We therefore assign the importer ID by applying a series of record linkage techniques.11 First,

we prepare a list of name variations such as ﬁctitious names, previous names, and name abbrevia-

ciones, a list of addresses of company branches/subsidiaries, and a list of EIN from Orbis by Bureau

van Dijk, which covers 20 million company branches, subsidiaries, and headquarters in the United

Estados. Segundo, the address format is standardized using software certiﬁed by the US Postal Ofﬁce.

Tercero, we match the lists from Orbis to each of the linking variables (name, address, EIN) en el

customs data by fuzzy matching. Two types of errors can occur in fuzzy matching: “false match-

ing” (matching records that should not be matched) and “false unmatching” (not matching records

that should be matched). The criteria for fuzzy matching are chosen to minimize false unmatching

because false matching is easier to identify by manual checks. Cuatro, binary matched records

are aggregated into clusters so that each record matches another record in that cluster. Entonces, nosotros

manually check each cluster and remove falsely matched records. A resulting cluster represents a

ﬁrm and receives an importer ID. Appendix B explains the data construction process in detail.

Data cleansing drops some observations. Primero, since the dataset only covers observations from

June to December in 2004, we drop the observations from January to May in other years to make

the information in each year comparable. We obtain similar results when January–May observa-

tions are included. Segundo, while importer information is reported for most normal trade trans-

comportamiento, it is sometimes missing for processing trade transactions under the Maquiladora/IMMEX

program in which exporters do not have to report an importer for each shipment.12 We drop ex-

porters that do not report the importer information for most transactions. To address the potential

selection issues caused by this action, we distinguish normal trade and processing trade in the

analyses below and conduct weighted regressions in Appendix B.4.

11An excellent reference for record linkage is Herzog, Scheuren, and Winkler (2007). Además, nosotros

beneﬁtted from the lecture slides on “Record Linkage” by John Abowd and Lars Vilhuber.

12The Maquiladoras program started in 1986 and the IMMEX program replaced it in 2006. Under these
programas, ﬁrms in Mexico can import the materials and equipment to be used for exports duty free. Ex-
porters must register the importer’s information in advance but need not report it for each shipment.

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Mesa 1 reports the summary statistics for the product-level and ﬁrm-level matching. A product-

level match occurs if an importer and an exporter trade in a particular product, while a ﬁrm-level

match occurs if an importer and an exporter trade in at least one product. columnas (a) y (b) en

Mesa 1 report the mean and median of the product-level matching.13 The ﬁrst four rows show that

11–15 exporters and 15–20 importers exist in an average product market, but the majority of ﬁrms

trade with only one partner.14 Rows (5) y (6) show that even for ﬁrms that trade with multiple

partners, más que 70% of their trade occurs with their single main partners.15

<< Table 1 is here.>>

Excess Partner Switching after the MFA’s end Our new ﬁnding is that exporters and importers

actively switch partners during liberalization. Panel A in Table 2 reports the changes in Mexican

textile/apparel exports to the United States between 2004 y 2007 by incumbent exporters in 2004

separately for liberalized products (quota-bound) and other products (quota-free). The changes in

total exports in Column (1) are decomposed into the extensive margin in Column (2) by exiters

that stopped exporting by 2007 and intensive margin in Column (3) by continuing exporters in

2007.16 The intensive margin in Column (3) is further decomposed into three margins of partner

cambios: Partner Staying in Column (4) expresses the changes in exports to continuing buyers that

import from the exporter both in 2004 y 2007, Partner Adding in Column (5) expresses those

to new buyers in 2007 that did not import from the exporter in 2004, and Partner Dropping in

Columna (6) expresses those to dropped partners that imported from the exporter in 2004 pero no

13Mesa 1 removes products with only one exporter or one importer, which accounts for 3% of trade.
Including them decreases the numbers in Columns (1) y (2), but barely changes those in the other columns.
14Appendix E.1 presents versions of Table 1 para 2005 y 2006 and for the regression samples that exclude
new exporters and new importers after 2005 that might have started with only one partner. The statistics on
the numbers of partners in Columns (3)–(6) remain close to those in Table 1.

15The large shares of trade with main partners in Table 1 are not driven by small ﬁrms that affect total
trade to an only small extent. In an earlier version of this paper, we reported that main-to-main matches,
where the exporter is the importer’s main partner for the product and the importer is the exporter’s main
partner, account for around 80% of total trade.

16In Appendix E.2, the extensive margin is decomposed into dropping products and leaving the US.

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en 2007. The parentheses in Columns (5) y (6) report the share of export changes by Partner

Switchers that simultaneously add and drop partners. These high shares imply that most partner

changes are in fact partner switching. Columna (7) reports the excess reallocation of partners, es decir.,

|(5)| + |(6)| − |(5) + (6)|.

As Table 1 suggests, the switching of main partners plays a major role in the adjustment.

In Panel C in Table 2, the intensive margin in Column (1), which is Column (3) in Panel A, es

decomposed according to main partner’s involvement: export changes not involving main partners

in Column (2), exports to continuing main partners in 2004 y 2007 in Column (3), those to new

main buyers in 2007 that were not main buyers in 2004 in Column (4), and those to dropped main

buyers that were main buyers in 2004 but not in 2007 in Column (5). Columna (6) reports the excess

reallocation associated with main partners, es decir., |(4)| + |(5)| − |(4) + (5)|.

Mesa 2 shows that in liberalized industries, main partner switching [columnas (4)+(5)] ac-

counted for 54% of the intensive margin [Columna (1)] and caused a more than 230% excess real-

location of exports across US buyers beyond the intensive margin. This prevalence of main partner

switching is at odds with anonymous market models (perfectly competitive and oligopoly mod-

los) and love-of-variety models (the Krugman–Melitz model) including some production networks

modelos (p.ej., Bernard et al., 2018). Primero, as we show in Section 3, in anonymous markets where

ﬁrms are indifferent about partners, partner changes should be minimized to save partner switch-

ing costs. Exporters may either add or drop buyers, but should not switch among surviving buyers,

eso es, the excess reallocations in Panels A and C should be zero. Segundo, as Appendix D shows,

in models combining the love-of-variety model and match-speciﬁc ﬁxed costs, ﬁrms add and drop

marginally important partners rather than main partners. De este modo, the large main partner excess export

reallocation in Panel C is puzzling to these models.

The decompositions in Panels A and C show the overall importance of partner switching. A

examine the impact of liberalization at the disaggregated level, we regress each margin of the

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HS six-digit product-level exports on the dummy variable of quota liberalization (the Binding

ficticio) with the HS two-digit ﬁxed effects. Panel B and Panel D in Table 2 report the estimated

coeficientes. The large and statistically signiﬁcant coefﬁcients in Columns (5)–(7) in Panel B and

columnas (4)–(6) in Panel D conﬁrm the signiﬁcant roles of partner switching.

3 The Model

This section develops an exporter–importer matching model in which partner switching is the

principal margin of adjustment. Secciones 3.1 sets up the model for the case of one-to-one matching

y Sección 3.2 derives the main insights about partner switching in trade liberalization. Sección

3.3 introduces many-to-many matching and derive predictions that we take to the data.

3.1 Matching Model of Exporters and Importers

The model includes three types of a continuum of ﬁrms, a saber, US ﬁnal producers, Mexican

suppliers, and Chinese suppliers.17 US ﬁnal producers may be retailers or wholesalers. The model

has two stages. In Stage 1, a US ﬁnal producer matches with a supplier from either Mexico or China

to form a team that produces one variety of differentiated ﬁnal goods. Suppliers tailor intermediate

goods and transact them only within the team. Firms match under perfect information and each ﬁrm

joins only one team. This one-to-one frictionless matching model is the simplest model predicting

PAM. Introducing search frictions does not change the qualitative predictions that we take to the

data.18 In Stage 2, teams compete in the US ﬁnal good market under monopolistic competition.

17Our model is a partial equilibrium version of that of Sugita (2015), who presented a two-country general

equilibrium model with endogenous ﬁrm entry.

18The general conclusion of the theoretical literature on search frictions (p.ej. see Smith (2011) for an
excellent survey) is that as long as the complementarity within matches is large enough, PAM holds on
promedio, as in the frictionless matching model that we consider.

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The US representative consumer maximizes the CES utility function:

U =

δ
ρ

(cid:20)(cid:90)

ω∈Ω

i(Vaya)αq(Vaya)ρdω

(cid:21)

+ q0 s.t.

(cid:90)

ω∈Ω

pag(Vaya)q(Vaya)dω + q0 = I.

where Ω is the set of available differentiated ﬁnal goods, ω is the variety of differentiated ﬁnal

goods, pag (Vaya) is the price of ω, q(Vaya) is the consumption of ω, i(Vaya) is the capability of the team

producing ω, q0 is the consumption of the numeraire good, I is the exogenously given income.

α ≥ 0 and δ > 0 are the given parameters. Consumer demand for a variety with price p and

capability θ is derived as q(pag, i) = δθασP σ−1p−σ, where σ ≡ 1/ (1 − ρ) > 1 is the elasticity of
substitution and P ≡ (cid:2)(cid:82)

ω∈Ω p(Vaya)1−σθ (Vaya)ασ dω(cid:3)1/(1−σ)

is the ideal price index.

The team’s capability θ = θ(X, y) is increasing in the ﬁnal producer’s capability x and sup-

plier’s capability y in that team, es decir., θ1 ≡ ∂θ(X, y)/∂x > 0 and θ2 ≡ ∂θ(X, y)/∂y > 0. Allá

exists a ﬁxed mass MU of ﬁnal producers in the United States, MM of suppliers in Mexico, y

MC of suppliers in China. The cumulative distribution function (CDF) for US ﬁnal producers’ ca-

pability is F (X) with support [xmin, xmax]. Por simplicidad, a Chinese supplier is a perfect substitute

for a Mexican supplier of the same capability. The capability of Mexican and Chinese suppliers

follows an identical distribution with the CDF G(y) and support [ymin, ymax].19

Production technology is of the Leontief type. When a team with capability θ produces q units

of ﬁnal goods, the team supplier produces q units of intermediate goods at costs cyθβq + fy; entonces,

the ﬁnal producer assembles these intermediate goods into ﬁnal goods at costs cxθβq + fx, dónde

ci and fi are positive constants (i = x, y). The team’s total costs are c(i, q) = cθβq + F, dónde

c ≡ cx + cy and f ≡ fx + fy. The externalities within teams make ﬁrms’ marginal costs dependent

on both their partner’s capability and their own capability.20 For simplicity, we assume that the

19The identical distribution of Chinese and Mexican suppliers is assumed only for graphical exposition.

Appendix A.1 derives the main predictions without this assumption.

20An example of a within-team externality is quality control. Producing high-quality goods might re-
quire extra costs of quality control in each production stage because one defective component could destroy
the whole product (Kremer, 1993). Another example is knowledge spillovers. Through the teaching and
aprendiendo (p.ej., joint R&D), each member’s marginal cost may depend on the entire team’s capability.

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ﬁrm’s marginal costs depend on the team’s capability. The team’s capability θ shifts both demand

and marginal costs depending on α and β. Por lo tanto, θ may represent productivity (p.ej., Melitz,

2003) and/or quality (p.ej., Baldwin and Harrigan, 2011; Verhoogen, 2008).

Stage 2 We obtain an equilibrium by backward induction. The team’s optimal price is p(i) =

cθβ/ρ. Por eso, team revenue R(i), total costs C(i), and joint proﬁts Π (i) convertirse:

R(i) = σAθγ, C(i) = (σ − 1) Aθγ + F, and Π (i) = Aθγ − f.

(1)

where each team takes A ≡ δ
pag

(cid:1)σ−1

(cid:0) ρP
C

as given and γ ≡ ασ − β (σ − 1) > 0 is assumed so that

the team’s proﬁt increases in θ. All the calculations are in Appendix A.1. We normalize γ = 1 por

choosing the unit of θ as the comparative statics on α, β and σ is not our main interest. The price
index P = c/ (cid:0)ρΘ1/(σ−1)(cid:1) decreases in the team’s aggregate capability Θ ≡ M (cid:82) θdH(i), dónde

M and H(i) are active teams’ mass and capability distribution, respectivamente.

Stage 1 Firms choose their partners and decide how to split team proﬁts, taking A as given. Proﬁt

schedules, πx (X) and πy (y), and matching functions, mx (X) and my(y), characterize equilibrium

matching.21 A ﬁnal producer with capability x matches with a supplier having capability mx (X)

and receives the residual proﬁt πx (X) after paying proﬁts πy (mx (X)) to the partner. mi(y) es el

inverse function of mx(X), where mx(mi(y)) = y.

We focus on stable matching that satisﬁes the following two conditions: (i) individual ratio-

nality, wherein all ﬁrms earn non-negative proﬁts, πx (X) ≥ 0 and πy (y) ≥ 0 for all x and y; y

21Roth and Sotomayor (1990) and Browning, Chiappori, and Weiss (2014) provide excellent backgrounds

on matching models

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(ii) pair-wise stability, wherein each ﬁrm is the optimal partner for the other team member:

πx (X) = [Aθ(X, mx(X)) − f ] − πy(mx(X)) = max

Aθ (X, y) − πy(y) − f ;

πy (y) = [Aθ(mi(y), y) − f ] − πx(mi(y)) = max

Aθ (X, y) − πx(X) − f.

(2)

From the envelop theorem, we obtain22

X(X) = Aθ1(X, mx(X)) > 0 and π(cid:48)
Pi(cid:48)

y(y) = Aθ2(mi(X), y) > 0.

(3)

De este modo, proﬁts increase in capability. The capability cutoffs xL and yL exist such that only ﬁnal

producers with x ≥ xL and suppliers with y ≥ yL engage in trade, which satisfy

πx(xL) = πy(yL) = 0 and MU [1 − F (xL)] = (MM + MC) [1 − G(yL)] .

(4)

Eso es, the number of active ﬁnal producers equals that of active suppliers.

Differentiating (3) by x, we obtain the derivative of the matching function:

metro(cid:48)

X(X) =

Aθ12
Pi(cid:48)(cid:48)
x − Aθ11

, where θ12 ≡

∂2θ
∂x∂y

and θ11 ≡

∂2θ
∂x2 .

(5)

Since the denominator in (5) is positive from the second-order condition, the sign of θ12 is the

same as the sign of m(cid:48)

X(X), a saber, the sign of sorting in stable matching (p.ej., Becker, 1973).

Por simplicidad, we consider three cases in which the sign of θ12 is constant for all x and y: (1)

Case C (Complement) θ12 > 0, (2) Case I (Independent) θ12 = 0, y (3) Case S (Substitute)

θ12 < 0.23 In Case C, we have PAM (m(cid:48) x(x) > 0): high capability ﬁrms match with high capability

22The use of differentiation is a convenient shortcut for deriving the sorting pattern, following Sattinger

(1979). Lema 5 in Appendix D presents a general proof of sorting that can be applied to ﬁnite agents.

23In Case C and Case S, θ is also called strict supermodular and strict submodular, respectivamente. Un
example for Case C is the quality complementarity of tasks in a production process (p.ej., Kremer, 1993).
Por ejemplo, a high-quality part may be more useful when combined with other high-quality parts. Un

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0
2
3

ﬁrms, whereas low capability ﬁrms match with low capability ﬁrms. In Case S, we have negative

assortative matching (metro(cid:48)

X(X) < 0): high capability ﬁrms match with low capability ﬁrms. In Case I, we cannot determine a matching pattern (i.e., mx(x) cannot be deﬁned as a function) because each ﬁrm is indifferent about partner capability. Therefore, we assume that matching is random and independent of capability in Case I. Case I is a useful benchmark because it nests two important classes of standard models. The ﬁrst is anonymous market models in which each ﬁrm is indifferent about partner capability. The second is heterogeneous ﬁrm trade models with one-sided heterogeneity in which ﬁrm heterogene- ity exists either among exporters (θ1 = θ12 = 0) or among importers (θ2 = θ12 = 0). In the following, we focus on Case C and Case I in the main text and examine Case S in Appendix A.3. In Case C, the following “matching market-clearing” condition determines mx(x): MU [1 − F (x)] = (MM + MC) [1 − G (mx(x))] for all x ≥ xL. (6) Figure 2 (A) describes condition (6). The left rectangle has width MU and the right one has MM + MC. The left vertical axis expresses the value of F (x) and the right one the value of G(y). The left gray area equals the mass of ﬁnal producers with higher capability than x, MU [1 − F (x)], while the right gray area equals the mass of suppliers that match with them, (MM + MC) [1 − G (mx(x))]. The matching function mx(x) equalizes the size of the two gray areas. <is here.>>

Finalmente, we obtain the cutoff xL as follows. In both Case C and Case I, the team with the

capability cutoff θL comprises a ﬁnal producer with xL and a supplier with yL.

In Case C,

mx(X) determines aggregate capability Θ (xL) = MU

(cid:82) ∞
xL

i (X, mx(X)) dF (X) and the capabil-

ity cutoff θL (xL) = θ (X, mx(xL)) as functions of xL. In Case I, let θ(X, y) ≡ θx(X) + θy(y).

example of Case S is spillovers through learning and teaching. Gains from learning from highly capable
partners might be greater for low capability ﬁrms. Grossman and Maggi (2000) provided further examples.

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Condition (4) determines yL(xL) as a function of xL. Entonces, Θ (xL) = MU
(MM + MC) (cid:82) ∞

yL(xL) θy(y)dG(y) and θL(xL) = θx (xL) + θy (yL(xL)) become functions of xL.

(cid:82) ∞
xL

θx (X) dF (X) +

De (1), (4), and A = δ/σΘ, the team with the capability cutoff earns zero proﬁts:

Π (θL) =

δθ(xL)
σΘ (xL)

− f = 0.

(7)

(7) uniquely determines xL since Θ (xL) is decreasing and θL(xL) is increasing in xL.

3.2 Consequences of Chinese Firm Entry at the End of the MFA

This section analyzes the effect of the MFA’s end on matching. Motivated by Fact 3 shown in

Sección 2 that new Chinese entrants had different levels of capability, we model the event as an

increase in the mass of Chinese suppliers (dMC > 0). We assume that a ﬁrm changes its partner

only if it strictly prefers the new match over the current match. We denote the variables and

functions before the MFA’s end by “B” (antes) and variables after the MFA’s end by “A” (después).

Case C Figure 2 (B) shows how matching changes from mB

X (X) to mA

X (X) for the given capa-

bility x. Area A expresses US importers with capability higher than x. They initially match with

suppliers in areas B + C that have higher capability than mB

X (X). After the MFA’s end, el original

matches become unstable because some US importers are willing to switch to the new entrants. En

the new matching, ﬁnal producers in area A match with suppliers in areas B + D that have higher

capability than mA

X (X). A US ﬁnal producer with capability x switches its main partner from one

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with capability mB

X (X) to one with higher capability, a saber, mA

X (X). We call this change “partner

upgrading” by US ﬁnal producers. This in turn implies “partner downgrading” by Mexican sup-

pliers. Mexican suppliers with capability mA

X (X) match with ﬁnal producers with strictly higher

capability than x before the MFA’s end. Not all Mexican suppliers can match with new partners,

sin embargo, and those with low capability exit the market, as proven in Appendix A.2.

Case I Figure 2 (C) shows that the MFA’s end increases the supplier’s cutoff from yB

L to yA

l , como

proven in Appendix A.2. Since whether xL increases or decreases is generally ambiguous, el

ﬁgure depicts the case in which xL unchanged. As low capability suppliers in Area C exit, US

importers that matched with them switch to new Chinese suppliers in Area D. Other ﬁrms do not

change their partners, although they change the price and quantity of goods traded. Firms are

indifferent about their partners as long as those partners have a capability level above the cutoffs.

Rematching Gains from Trade The MFA’s end causes two adjustments. Primero, new Chinese

suppliers with high capability enter the market and Mexican suppliers with low capability exit.

This replacement effect occurs in both Cases C and I, and it corresponds to the extensive margin

adjustment in Table 2. Segundo, incumbent ﬁrms rematch. This rematching effect occurs only in

Case C and corresponds to the partner excess reallocation in Tables 2.

We show that the rematching effect in Case C is a new mechanism of gains from trade that

did not exist in standard trade models nested in Case I (perfectly competitive models and Krug-

man–Melitz models with one-sided heterogeneity). We consider a hypothetical “no-rematching”

equilibrium at which ﬁrms switch partners only if their current partners exit the market and denote

variables in this equilibrium by “NR.” The following proposition compares the price indices across

the three cases (the proof is in Appendix A.2).

Proposition 1. In Case C, P A < P N R < P B, while in Case I, P A = P N R < P B. The effect of liberalization on the price index P B − P A can be decomposed into the replace- ment effect P B − P N R and rematching effect P N R − P A. The gain from the replacement effect is well known in the heterogeneous ﬁrm trade literature. In Case C, the rematching effect creates an additional consumer gain. The proof applies a classic theorem in matching theory that stable matching maximizes the aggregate payoff, AΘ − M f , for the given A (Koopmans and Beckmann, 1957; Shapley and Shubik, 1971; Gretsky, Ostroy and Zame, 1992) and proves that aggregate ca- 18 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / . / 1 0 1 1 6 2 / r e s t _ a _ 0 1 1 1 4 2 1 4 1 9 6 5 / r e s t _ a _ 0 1 1 1 4 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Review of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. pability increases as ΘA > ΘN R > ΘB.24 In other words, trade liberalization improves consumer

welfare by improving global buyer–supplier matching and aggregate capability.

Proposition 1 also implies that a preferential trade agreement can create inefﬁcient “matching

diversion.” High capability US ﬁnal producers are diverted to match with low capability Mexican

suppliers instead of high capability Chinese suppliers.25

3.3 Many-to-Many Matching

This section introduces many-to-many matching in an intermediate good market. A ﬁnal producer

produces multiple product varieties and a supplier owns multiple production lines. Matching oc-

curs between varieties and production lines, resulting in many-to-many matching.

There exist N ﬁnal products and one intermediate good. The consumer’s utility is given by

U =

norte
(cid:88)

s=1

δ
ρ

(cid:20)(cid:90)

i(Vaya)αq(Vaya)ρdω

(cid:21)

−

norte
(cid:88)

(cid:90)

ω∈Ωs

s=1

ω∈Ωs

pag(Vaya)q(Vaya)dω + I,

where Ωs is the set of varieties of product s. A ﬁnal producer produces at most one variety of each

product, following Bernard et al. (2011). Let χis = xi + ηis be the product capability of ﬁrm i for

product s, where xi is ﬁrm capability and ηis is i.i.d. idiosyncratic capability with E (ηis) = 0 y

apoyo [ηmin, ηmax]. xi and ηis are independent and have densities fx(X) and fη(η), respectivamente.

A supplier owns multiple production lines. Each line specializes in a particular variety. A

supplier with ﬁrm capability y owns n(y) production lines and can match with at most n(y) buy-

ers. One reason for such buyer capacities is a manager’s span of control. A supplier requires a

manager’s resource to collaborate with each buyer. We assume that n(y) is weakly increasing in y.

The production line k of supplier j with ﬁrm capability yj has line capability υjk = yj + εjk,

24The intuition of the theorem follows from the deﬁnition of the supermodularity of θ such that for any
x > x(cid:48) and y > y(cid:48), i(X, y) + i(X(cid:48), y(cid:48)) > θ(X(cid:48), y) + i(X, y(cid:48)). Applying the theorem to Proposition 1 is not
trivial since A is endogenous in our setting.

25Ornelas, Tornero, and Bickwit (2019) theoretically analyzed matching diversion by a preferential trade

agreement in a model with one-sided heterogeneity.

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where εjk is i.i.d. idiosyncratic capability with E (εjk) = 0 and support [εmin, εmax]. yj and εjk

are independent. Their marginal densities are gy(y) and gε(ε), respectivamente, which are common for

both Mexican and Chinese suppliers. We assume that fη(η) and gε(ε) are log-concave.26 In other

respects, the model has the same structure as the one in Section 3.1.

Matching occurs between a ﬁnal product variety and a supplier production line. The conditions

for stable variety-to-line matching are similar to those in Section 3.1. Stable matching consists of

the matching function υ = mχ(χ) and χ = mυ(υ) between product capability χ and line capability

υ, the variety’s proﬁt schedule πχ(χ), and the line’s proﬁt schedule πυ(υ). Following (1), podemos

obtain a match’s joint proﬁt as Π (χ, υ) = Aθ (χ, υ) − f , where f is the ﬁxed cost per product.

The stability conditions continue to be (2) and the sign of θ12 determines the sign of sorting. El

matching market-clearing condition in Case C is similar to that in (6):

˜MU [1 − ˜F (χ)] =

(cid:16) ˜MM + ˜MC

(cid:17) (cid:104)

(cid:105)
1 − ˜G (mχ(χ))

(8)

where ˜MU ≡ MU N is the total mass of varieties, ˜MM ≡ MM n and ˜MC ≡ MCn are the total mass
of production lines in Mexico and China, respectivamente, and n ≡ (cid:82) ymax
ymin

norte(y)gy(y)dy is the mean

mass of production lines. The CDFs of product capability χ and line capability υ are ˜F (χ) ≡
−∞ fχ(t)dt and ˜G(υ) ≡ (cid:82) υ
(cid:82) χ
χ and υ, respectively.27 The conditions for Cases I and S can be derived analogously. The cutoff

norte(t)
n gυ(t)dt, respectivamente, where fχ(χ) and gυ(υ) are the densities of

−∞

capabilities of varieties χL and lines υL satisfy similar conditions to in (4) y (7).

While variety-to-line matching is one-to-one, ﬁrm-to-ﬁrm matching is many-to-many. We ap-

proximate the number of a ﬁnal producer’s partners by the number of production lines matching

with the ﬁnal producer, and the number of a supplier’s partners by the number of varieties matching

26The class of distributions with log-concave densities includes a wide range of unimodal parametric

distributions such as normal, uniform, logistic, Frechet and many others.

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27These densities are obtained by convolution as fχ(χ) = (cid:82) mín.{ηmin,t−xmax}

máximo{xmin,t−ηmax} fx(s)fη(t − s)dsdt and

gυ(υ) = (cid:82) mín.{εmin,t−ymax}

máximo{ymin,t−εmax} gy(s)gε(t − s)dsdt.

with the supplier.28 Note that the number of a ﬁnal producer’s active products follows a binomial

distribution with success probability [1−Fη(χL −x)] and the number of trials N , while the number

of a supplier’s active production lines follows a binomial distribution with [1 − Gε(υL − y)] y

norte(y), where Fη and Gε are the CDFs of η and ε, respectivamente. Por lo tanto, the mean number of

Mexican partners for a ﬁnal producer with capability x, N M (X), and the mean number of partners

for a Mexican supplier with ﬁrm capability y, nS(y), are given by:

N M (X) =

MM N [1 − Fη(χL − x)]
MM + MC

and nS(y) = norte(y)[1 − Gε(υL − y)].

(9)

De este modo, the mean number of partners is increasing in ﬁrm capability and decreasing in the cutoffs.

Because the equilibrium conditions remain the same as in Section 3.1 the effects of the MFA’s

end on the matching functions, capability cutoffs, and price indices are qualitatively the same as

those in Section 3.2. Let P t (t ∈ {A, B, N R}) be the product-level price indices. Entonces, el

following lemma holds with essentially the same proofs as in Section 3.2.

Lema 1. (i) In Case C after the MFA’s end: mA

χ (χ) > mB

χ (χ) for the given χ; mA

υ (υ) < mB υ (υ) for the given υ; υA L > υB

l ; and P A < P N R < P B. (ii) In Case I after the MFA’s end, υA L > υB
l

and P A = P N R < P B. Predictions of Main Partner Choices, Exit, and Number of Partners We derive the model’s predictions of ﬁrm-to-ﬁrm matching that we take to the data. Our data on Mexico–US trade only record partner switching by ﬁrms engaging in Mexico–US trade both before and after the MFA’s end. We call these ﬁrms US continuing importers and Mexican continuing exporters. We examine a ﬁrm’s main partner choice because of its importance in our dataset. First, consider Case C. Let χ∗ i ≡ xi + maxs ηis be the highest product capability of ﬁnal producer i. 28Strictly speaking, the number of a ﬁnal producer’s partners could be fewer than the number of lines matching with the ﬁnal producer. However, since production lines are heterogenous, the probability that one supplier provides multiple production lines to the same ﬁnal producer is negligible when ﬁrms are of a continuum and small when they are ﬁnite. 21 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 1 1 4 2 1 4 1 9 6 5 / r e s t _ a _ 0 1 1 1 4 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Review of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. The mean ﬁrm capability of ﬁnal producer i’s main partner is ¯yt(χ∗ i ) ≡ E (cid:2)y| y + ε = mt χ(χ∗ i )(cid:3) for t ∈ {A, B}. Similarly, the mean ﬁrm capability of supplier j’s main partner is ¯xt(υ∗ E (cid:2)x| x + η = mt j )(cid:3) for t ∈ {A, B}, where υ∗ j ≡ yj + maxk εjk. A ﬁnal producer i upgrades j ) ≡ υ(υ∗ its main partner if ¯yA(χ∗ i ) > ¯yB(χ∗

i ), and downgrades if ¯yA(χ∗

i ) < ¯yB(χ∗ i ). Similarly, a supplier j upgrades its main partner if ¯xA(υ∗ j ) > ¯xB(υ∗

j ), and downgrades if ¯xA(υ∗

j ) < ¯xB(υ∗ j ). As shown in Appendix A.2.2, the log-concavity of fη(η) and gε(ε) implies that E (cid:2)x| x + η = mυ(υ∗ j )(cid:3) increases in mυ(υ∗ j ) and that E [ y| y + ε = mχ(χ∗ i )] increases in mχ(χ∗ i ). Therefore, from Lemma 1, US continuing importers upgrade Mexican main partners, while Mexican continuing exporters downgrade US main partners. Another testable implication is that the relative ranking of main partner’s ﬁrm capability preserves. For each pair of ﬁnal producers i and j, if ¯yB(χ∗ i ) > ¯yB(χ∗

j ),

then ¯yA(χ∗

i ) > ¯yA(χ∗

j ) sostiene; similarmente, for each pair of suppliers k and h, if ¯xB(υ∗

k) > ¯xB(υ∗

h),

then ¯xA(υ∗

k) > ¯xA(υ∗

h) sostiene. Eso es, the ranking of new partners’ ﬁrm capability is positively

correlated with the ranking of that of old partners.

In Case I, no systematic partner change occurs. No US continuing importers or Mexican con-

tinuing exporters change main partners. The ﬁrm capability ranking of new partners is independent

of the ranking of old partners. En resumen, we establish the following proposition.

Proposition 2. In Case C after the MFA’s end, (C1) US continuing importers upgrade Mexican

main partners, while Mexican continuing exporters downgrade US main partners and (C2) the ﬁrm

capability ranking of new main partners is positively correlated with that of old main partners. En

Case I after the MFA’s end, (I1) No US continuing importers or Mexican continuing exporters

change main partners and (I2) the ﬁrm capability ranking of new main partners is independent of

the ranking of old main partners.

We derive the model’s predictions of ﬁrm exit and the number of partners that holds in both

Cases C and I. Primero, the ﬁrm capability cutoff for Mexican suppliers yL = υL − εmax increases.

Segundo, de (9), the number of partners N M (X) and nS(y) decrease.

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Proposition 3. In Cases C and I after the MFA’s end, (E1) the ﬁrm capability cutoff for Mexican

exporters rises and (E2) both US importers and Mexican exporters reduce their partners.

4 Empirical Strategy

4.1 Proxy for Firm Capability Rankings

To test the predictions in Propositions 2 y 3, we estimate the ranking of ﬁrm capability as follows.

Let I(X) be the mean imports of the intermediate good by US importers with ﬁrm capability x from

the main partners and let X(y) be the mean exports by Mexican exporters with ﬁrm capability y

to the main partners. The following lemma holds from the monotonic relationship between ﬁrm

capability and within-match trade (the proof is in Appendix A.2.3).

Lema 2. In Case C and Case I, I(X) and X(y) are monotonically increasing functions.

For each HS six-digit product, we rank all the US importer and all the Mexican exporters, usando

their imports and exports of the product from their main partner in 2004, respectivamente. We use these

rankings using 2004 data throughout our sample period (2004–2007) during which the ranking is

stable.29 Section 5.4 presents the results using alternative rankings.

We ﬁrst create three variables using these rankings for each product g in country c: (1) ﬁrm

i’s own ranking, OwnRankc

ig; (2) the ranking of the ﬁrm’s main partner of product g in 2004,

OldP artnerRankc

ig; y (3) the ranking of the ﬁrm’s main partner of product g in 2007, N ewP artnerRankc
ig.

We choose 2004–2007 as the sample period to avoid potential confounding from the impact of the

2008 ﬁnancial crisis on Mexican exports. These rankings are standardized using the number of

ﬁrms to fall into the range of [0,1]. Smaller rankings indicate higher capability (p.ej., ﬁrst rank-

ing means the best). OldP artnerRankc

ig differs from N ewP artnerRankc

ig if and only if the

ﬁrm switches its main partner during 2004–2007. Finalmente, the partner upgrading dummy U pc

igs

29The correlations of the rankings in 2004 y 2007 are higher than 0.85 for all the products and similar

between the treatment and control groups.

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equals one if N ewP artnerRankigs < OldP artnerRankigs and the partner downgrading dummy Downc igs equals one if N ewP artnerRankigs > OldP artnerRankigs.

4.2 Speciﬁcations

Partner Changes (C1 and I1) The following regressions test Predictions C1 and I1:

U pc

igs = βc

U Bindinggs + λs + εc

U igs

Downc

igs = βc

DBindinggs + λs + εc

Digs,

(10)

donde C, i, gramo, and s represent the country (United States and Mexico), ﬁrm, HS six-digit product,

and sector (HS two-digit level), respectivamente. The dummy variable Bindinggs equals one if Chinese

exports of product g to the United States faced a binding quota in 2004, which is constructed from

Brambilla et al. (2010). λs represents the HS two-digit-level ﬁxed effects.30 εc

U igs and εc

Dijs are the

error terms. Appendix B.5 explains the construction of the binding dummy and other variables.

The regression sample includes both continuing US importers and Mexican exporters.

The coefﬁcients of interest βc

U and βc

D in (10) are identiﬁed by comparing the treatment and

control groups within HS two-digit sectors. The treatment is the removal of binding quotas on

Chinese exports to the US. The coefﬁcients estimate its impact on the probability of partner up-

grading and downgrading, respectivamente. The HS two-digit ﬁxed effects control for basic product

characteristics such as textile/apparel and knit/woven.

Prediction C1 for PAM states that at the MFA’s end, all the continuing US importers upgrade

their main partners, whereas all the continuing Mexican exporters downgrade. Although the fric-

30We include the HS two-digit-level ﬁxed effects instead of the HS four-digit-level ﬁxed effects because
of their collinearity with the binding dummy. When the binding dummy is regressed on only the HS four-
digit-level ﬁxed effects, R2 is 0.86 in both the US and the Mexico samples, which means that only 14% de
the variation in the binding dummy can be used to estimate βC
D in (10). On the contrary, cuando el
binding dummy is regressed on only the HS two-digit-level ﬁxed effects, R2 is 0.48 for the US sample and
0.50 for the Mexico sample, which leave sufﬁcient variation. We also drop those HS two-digit sectors (HS
50, 51, 53, 56, 57, y 59) in which no variation in the binding dummy at the HS two-digit level occurs.

U and βC

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tionless matching model predicts that all the ﬁrms will change their partners, in reality, other factors

such as transaction costs are likely to prevent some from making such a change, at least in the short

run. Respectivamente, we reformulate Prediction C1 as follows: US importers’ partner upgrading and

Mexican exporters’ partner downgrading will occur more frequently in the treatment group than in

the control group, which corresponds to βU S

U > 0, βU S

D = βM ex

U = 0, and βM ex

D > 0 en (10).

Prediction I1 for independent matching states that at the MFA’s end, no continuing US importer

and Mexican exporter would change their partners. En realidad, some idiosyncratic shocks appearing

as error terms in (10) could induce partner changes. De este modo, we reformulate Prediction I1 as fol-

lows: no difference should exist in the probability of partner changes in any direction between the

treatment and control groups, which corresponds to βU S

U = βU S

D = βM ex

U = βM ex

re = 0 en (10).

Our regression (10) does not suffer from the endogeneity problem that existed in the conven-

tional correlation approach to detecting PAM that regresses an exporter’s characteristics on those of

an importer. Por ejemplo, the cross-sectional regression of an exporter’s rank on an importer’s rank

could produce a mechanical positive correlation regardless of the sign of sorting.31 We use ﬁrm

características (trade volume) only to construct the outcome variables on the left-hand side. Cualquier

discrepancy between the true capability ranking and trade ranking should appear in the error terms

U igs and εc
εc

Digs, which might reﬂect the capability of the ﬁrm and its partners, and other unobserv-

able ﬁrm and product characteristics. Sin embargo, as long as the binding dummy is uncorrelated with

these unobservables, βc

U and βc

D are consistently estimated.32

Another advantage of (10) is controlling for the various unobservable determinants of a ﬁrm’s

partner rankings. Primero, idiosyncratic shocks to demand and cost may change ﬁrm capability and

31Suppose importers are homogeneous in capability (es decir., θ1 = 0), such as homogenous warehouses.
This is a special case of Case I and there is no sorting. Entonces, the ranking of importer’s trade equals that of
unobserved exporter’s capability, which yields a positive mechanical correlation of exporters’ and importers’
rankings. Oberﬁeld (2018, Proposition 6) showed this point in a more general model.

32en nuestros datos, some ﬁrms export or import multiple products. If a pair of US and Mexican ﬁrms traded in
multiple products with each other in 2004 and if they switched to new main partners for all their products
(maybe to save transaction costs), then this might bias our estimates. Sin embargo, this is unlikely since such
pairs account for only 8% of Mexican exporters that switched partners.

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generate partner switching. As long as these shocks appearing as error terms in (10) are uncorre-

lated to the MFA liberalization, they should not bias our estimates. Segundo, the dependent variables

are constructed from time differences in partner rankings. Time differencing controls for all the

time-invariant ﬁrm-speciﬁc determinants of the level of partner rankings.

Old and New Partner Rankings (C2 and I2) To test Predictions C2 and I2, we estimate the

following regression for ﬁrms that switched partners during 2004–2007:

N ewP artnerRankc

ig = αc + γcOldP artnerRankc

ig + εc
ig

(11)

for ﬁrm iwith N ewP artnerRankc

ig (cid:54)= OldP artnerRankc
ig.

Prediction C2 predicts γc > 0, while Prediction I2 predicts γc = 0.

Two additional points need to be mentioned. Primero, if we run (11) only for ﬁrms that do not

change partners, then γc equals one by construction. To avoid this mechanical correlation, nosotros

estimate (11) only for ﬁrms that change partners. Segundo, the regression (11) combines both the

treatment and the control groups since Prediction C2 should hold for both groups in Case C.33

Capability Cutoff Changes (E1) We test Prediction E1 using two models. Primero, we esti-

mate a product-level difference-in-difference model of the export cutoffs for the pre-liberalization

(2001–2004) and post-liberalization (2004–2007) periods:34

ln ExportCutof fgsr = δ1Bindingg + δ2Bindingg × Af terr + δ3Af terr + λs + ugsr.

(12)

For surviving exporters in the ﬁnal year of period r, the minimum of their exports of product g in

the initial year of period r proxies for the capability cutoff, ExportCutof fgsr. Since importer in-

33Por ejemplo, if an industry-wide shock induces a Mexican exporter’s partner to downgrade in both the
treatment and the control groups, the model with PAM should predict γc > 0 for both groups. In Appendix
E.4, we present the regression (11) only for the treatment group.

34We thank a referee for suggesting the product-level regression of the export cutoff.

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formation is unavailable before 2004, we use Mexican exporters’ product exports as the capability

proxy, which is highly correlated with exports to the main partners in the 2004–2007 data. Af terr

is an indicator of whether period r is 2004–2007, λs represents the HS two-digit-level ﬁxed effects,

and uc

igs are the error terms.

We use the difference-in-difference speciﬁcation to test the predictions about the cutoff changes.

En (12), the cutoff increase in Prediction E1 implies δ2 > 0 as the coefﬁcient of interest. Sobre el

contrary, δ1 estimates the difference in the levels of the cutoffs between the liberalized and non-

liberalized products. We perform a placebo check of no difference in the prior trends in the cutoffs

by estimating equation (12) for the two pre-liberalization periods (1998–2001 and 2001–2004).

The product-level regression (12) raises two potential concerns. Primero, it fails to control for ﬁrm

heterogeneity within products. Segundo, a rise in the export cutoff may not imply more ﬁrm exits

from the market. Por lo tanto, we also estimate the following threshold model of a ﬁrm’s exit. En

each period r, Mexican supplier i receives a random i.i.d. shock εir to its proﬁt, which captures the

idiosyncratic factors inducing ﬁrm exit in the absence of liberalization (p.ej., Eaton et al., 2014).

The ﬁrm chooses to exit if εir is below the threshold ¯εir (y). Prediction E1 implies two predictions:

(i) the MFA’s end increases the threshold ¯εir(y) for the given capability y and (ii) the threshold

¯εir(y) is a decreasing function of the ﬁrm’s capability y. Entonces, we estimate the following ﬁrm-

level regression for Mexican ﬁrm i that exports product g to the United States in the initial year of

period r ∈ {2001 − 04, 2004 − 07}:

Exitigsr = δ1Bindingg + δ2Bindingg × Af terr + δ3Af terr + δ4 ln Exportsigr

+ δ5Af terr × ln Exportsigr + λs + uigsr.

(13)

The dummy variable Exitigsr equals one if the ﬁrm stops exporting during period r. ln Exportsigr

is the log of the ﬁrm’s total exports of product g in the initial year of period r, which proxies for

ﬁrm capability. Regression (13) uses the level of exports instead of their ranking because the level

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of capability determines the ﬁrm’s exit, while the ranking of capability determines the matching.

Predictions (i) y (ii) mentioned above are expressed as follows: (i) δ2 > 0, es decir., the end of the

MFA increased the exit probability for a given capability level, y (ii) δ4 < 0 and δ4 + δ5 < 0, i.e., small low capability ﬁrms are more likely to exit.35 Number of Partners (E2) To test Prediction E2, we regress the changes in the number of part- ners on the binding dummy for US importers and Mexican exporters: ∆#P artnersc igs = ζ c 1Bindinggs + λs + εc igs, c ∈ {M ex, U S}, (14) where ∆#P artnersc igs is the changes in the number of ﬁrm i’s partners in product g during 2004–2007, λs represents the HS two-digit-level ﬁxed effects, and εc igs are the error terms. Predic- tion E2 implies ζ M ex 1 < 0 and ζ U S 1 < 0. 5 Results 5.1 Partner Changes Panel A in Table 3 examines partner changes during 2004–2007 using linear probability models.36 The columns with odd numbers report the estimates of βc d (c = U S, M ex and d = U, D) from the baseline regressions (10). We ﬁnd that βU S U in Column (1) and βM ex D in Column (7) are positive and statistically signiﬁcant, while βU S D in Column (3) and βM ex U in Column (5) are close to and not statistically different from zero. These signs of βc d support Case C and reject Case I. The removal of 35One might think of introducing the triple interaction Bindingg × Af terr × ln Exportsigr to examine whether the treatment effect on the exit probability decreases in the ﬁrm’s initial exports. However, this alternative speciﬁcation is unsuitable for testing Prediction E1. As observed in other customs data (e.g., Eaton et al., 2014), the exit probability of small exporters is high even without liberalization. For instance, the exit rate of the smallest 20% exporters before 2004 is greater than 0.85, while that for the top 20% is around 0.55. Thus, the treatment effect on the exit probability is naturally estimated to be small for these small exporters, but this does not necessarily contradict Prediction E1. 36The probit regressions in Appendix E.3.1 provide similar results for all the regressions. 28 l D o w n o a d e d f r o m h t t p : / / d i r e c t . m i t . e d u / r e s t / l a r t i c e - p d f / d o i / / . 1 0 1 1 6 2 / r e s t _ a _ 0 1 1 1 4 2 1 4 1 9 6 5 / r e s t _ a _ 0 1 1 1 4 p d . f b y g u e s t t o n 0 8 S e p e m b e r 2 0 2 3 Review of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 International (CC BY 4.0) license. binding quotas from Chinese exports increased the probability of US importers’ partner upgrading by 5.2 percentage points and the probability of Mexican exporters’ partner downgrading by 12.7 percentage points.37 These effects are quantitatively large compared with the sample averages of U pU S igs and DownM ex igs , which are 3 and 15 percentage points, respectively.38 <is here.>>

The columns with even numbers in Panel A in Table 3 add the ﬁrm’s own ranking and its

interaction with the binding dummy. Both large and small ﬁrms switch their partners as the model

predicts. Cifra 3 illustrates these results by drawing the kernel-weighted local mean regressions of

the partner change dummies on the ﬁrm’s own ranking for apparel products.39 The dashed lines and

areas represent the regression lines with 90% conﬁdence bands for the treatment group, mientras que la

solid lines and areas represent those for the control group. A higher probability of US importers’

upgrading and Mexican exporters’ downgrading in the treatment group is found uniformly for all

the capability rankings. Por el contrario, little difference between the two groups in the probability of

US importers’ downgrading and Mexican exporters’ upgrading is found.

Panel B in Table 3 examines partner changes in the later periods of 2007–2011 and 2009–2011

to check our assumption that both the treatment and the control groups exhibit similar partner

37βM ex
D

is estimated to be larger than βU S

U because of the following partner changes within initial partners,
which is consistent with the theoretical model. Suppose that a Mexican exporter had been exporting to
two US importers in 2004 and that these two US importers buy only from that exporter. Entonces, en 2007,
the exporter stopped exporting to its 2004 main partner and exported only to the second importer. Este
is counted as partner downgrading for the exporter but not as partner upgrading for the two importers.
This causes βM ex
Ud. . Appendix E.3.5 shows the results are robust when
distinguishing a ﬁrm’s main partner change within and beyond initial partners.

to be estimated as larger than βU S

38These numbers do not mean that 97% of US importers and 85% of Mexican exporters traded with
the same main partner both in 2004 and in 2007. In the dataset, solo 12% of US importers and 12% de
Mexican exporters traded with the same main partner in both 2004 y 2007. The sample averages of U pU S
igs
and DownM ex
are likely to underestimate the probabilities of partner changes in the population. Our data
observe partner upgrading/downgrading only if the ﬁrm, new partner, and old partner are all continuing
ﬁrms. Partner switching to ﬁrms in other countries and ﬁrms not existing in 2004 are excluded.

igs

39We used the Epanechnikov kernel and chose the bandwidth to minimize the integrated mean squared

error. Appendix E.3.2 shows the plot for textile products.

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change patterns if the treatment is absent.40 For each period, we reconstruct the capability rankings

based on trade in the new initial years and recreate the upgrading/downgrading dummies. If the

transition from the old to the new equilibrium was largely completed by 2007, we should observe

no difference in partner changes between the two groups. Small and insigniﬁcant estimates for

βU S
U and βM ex

in 2007–11 and 2009–11 support our assumption.41

We conduct numerous robustness checks in Appendix E.3. Primero, we include as additional

controls several product-level and ﬁrm-product-level characteristics that statistically differ between

the treatment and control groups.42 Second, we conduct three exercises to address potential within-

ﬁrm interactions in ﬁrms trading multiple products and ﬁrms with multiple partners. We add the

number of products that a ﬁrm trades and its interaction with the binding dummy, address the

case that the main partner switching occurs within initial partners, and distinguishing ﬁrms that

had a single partner and those that had multiple partners. Finalmente, we adopt alternative variable

deﬁnitions. We deﬁne partner switching using rank bins, deﬁne quota binding under alternative

criteria, and use alternative year windows. Our results are robust to all of these alternatives.43

5.2 New and Old Partners Ranks

Cifra 4 reports regression (11), which tests Predictions C2 and I2, with the corresponding scat-

terplots. For those US importers that changed their main partners between 2004 y 2007, el

40Checking the assumption by examining partner changes before 2004 is not feasible since our data only
contain partner information from June 2004 onward. At the aggregate level, Cifra 1 demonstrates the
absence of differential time trends in aggregate exports before the removal of the MFA quota in 2005.

41The 2008–11 result differs from those in the other periods. One reason may be that the global ﬁnancial
crisis of 2008 might have introduced noise into the rankings since Mexican exports declined markedly in
the second half of 2008.

42These product-level characteristics are the number of exporters, number of importers, log product trade,
and product type dummies on whether products are for men, women, or not speciﬁc to gender and those on
whether products are made of cotton, wool, or synthetic textiles. These ﬁrm-product-level characteristics
are the log of a ﬁrm’s product trade with the main partner, share of Maquiladora/IMMEX trade in a ﬁrm’s
product trade, number of partners, and dummy of whether a US importer is an intermediary ﬁrm.

43One exception is the regression of the US importer when all the product-level and ﬁrm-product-level
characteristics are included as controls together. The coefﬁcient becomes insigniﬁcant, but remains qualita-
tively the same (βU S

U is 73% of the benchmark estimate with p-value 0.12).

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left panel displays the rankings of their old partners on the horizontal axis and those of their new

partners on the vertical axis. The right panel draws a similar plot for Mexican exporters. The lines

represent OLS regression (11). Cifra 4 and the regressions show signiﬁcant positive relation-

buques. Firms that matched with relatively high capability partners in 2004 switched to relatively

high capability partners in 2007. This result again supports Case C and rejects Case I.

5.3 Capability Cutoff Changes and Number of Partners

Mesa 4 reports the tests of Prediction E1. Columna (1) reports the baseline speciﬁcation of product-

level regression (12) and Column (2) includes as additional control variables the product character-

istics for the initial year in each period and their interactions with the after dummy. These controls,

when available, are the same as in footnote 42.44 The estimates of the positive and signiﬁcant δ2

conﬁrm the prediction that the MFA’s end increased the capability cutoff for Mexican exporters.

Columna (5) reports the baseline speciﬁcation of ﬁrm-level regression (13) and Column (6) includes

the product characteristic variables and their interactions with the after dummy. The estimates of

the positive and signiﬁcant δ2 conﬁrm that the MFA’s end increased their exit probability for a

given capability level. Además, the negative estimates of δ4 and δ4 + δ5 conﬁrm that small

exporters are more likely to exit the market.

columnas (3) y (7) show placebo checks that estimate regressions (12) y (13) using two

periods before the MFA liberalization, 1998–2001 and 2001–2004, respectively.45 Columns (4)

y (8) include the control variables. In all the placebo checks, the estimated δ2 is close to zero

44They are the number of exporters, log product trade, and product type dummies.
45For this analysis we use the customs transaction dataset for 1998-2004, which does not have US im-

porter information. See Appendix B.1 or the data construction.

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and statistically insigniﬁcant, or shows a negative sign. These results reject the concern that the

estimate of δ2 captures a prior difference in the trend between the two groups.

Panel B in Table 4 report regression (14). The negative and signiﬁcant coefﬁcients of the

binding dummy in Columns (1) y (2) conﬁrm Prediction E2 that both US importers and Mexican

exporters reduce the number of partners in liberalized industries.

5.4 Does Capability Reﬂect Quality or Productivity?

We have studied exporter-importer matching by capability without specifying whether capability

determining matching is quality or productivity. To shed a light on this question, we create rankings

based on two alternative variables: a ﬁrm’s unit price with the main partners in 2004 and a ﬁrm’s

quality estimated using the method of Khandelwal et al. (2013). If the exporter’s capability mainly

reﬂects quality rather than productivity, the two rankings may agree with the capability ranking.

On the contrary, if the exporter’s capability mainly reﬂects productivity, the unit price ranking may

become the reverse of the capability ranking.

Appendix E.5 shows that the main results are robust to the price and quality rankings.46 There-

delantero, exporter’s quality determines whether it can match with high capability importers. This result

is consistent with the literature’s ﬁnding that quality is an important determinant of a ﬁrm’s export

participación (p.ej., Kugler and Verhoogen, 2012).

5.5 Alternative Explanations

In Appendix C, we examine four alternative hypotheses for our ﬁndings. The ﬁrst hypothesis

is negative assortative matching under which trade rankings may not agree with true capability

rankings. The second hypothesis is repeated random independent matching. Suppose random

partner change occurs in every period and exhibits mean reversion. The exit of low capability

Mexican exporters may create a positive correlation between the binding dummy and downgrading

46Appendix E.5 shows our results are robust with the ranking based on a ﬁrm’s total product trade.

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by Mexican exporters. The third hypothesis is that Mexican exporters switch a product segment

from large-scale production with small markups to small-scale production with large markups. El

ﬁnal hypothesis is that a US importer’s partner switches from small to large suppliers to seek large

production capacity. For these hypotheses, we conduct additional analyses and show that none of

them fully explain our results.

6 Concluding Remarks

This study presented theory and evidence for a simple mechanism of exporter–importer matching:

Beckerian PAM by capability. Beckerian PAM offers several new insights into buyer–supplier re-

lationships in international trade. As our model showed, rematching in trade liberalization brings

about two new gain-accruing channels. Primero, at the sector or aggregate levels, trade liberaliza-

tion improves efﬁciency by rematching buyers and suppliers. Quantifying these matching-induced

gains from trade is an important topic for future research. Segundo, at the individual level, ﬁrms see

improved performance when they upgrade their partners. Regarding the second channel, Beckerian

PAM has two implications that can be brought to data in future studies. Primero, the beneﬁts to local

ﬁrms increase in the capability of foreign partners. Segundo, only ﬁrms with high capability can

maintain stable relationships with high capability foreign ﬁrms. The latter suggests the importance

of capability development policies to complement trade promotion policies.

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Cifra 1: The Effects of the MFA’s End on Chinese and Mexican Textile/Apparel Exports to the
United States

Nota: The left panel plots the coefﬁcients of the annual year dummies in the regression of the HS six-digit

product-year-level exports of China on the annual year dummies and product ﬁxed effects separately run for

the products on which the United States had imposed binding quotas against China in 2004 (the treatment

grupo, triangles) and other textile/apparel products (the control group, circles). The right panel expresses

the same information for exports from Mexico to the United States. Data source: UN Comtrade.

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Cifra 2: Matching Model’s Predictions

(A) Case C: Matching Market Clearing

(B) Case C: Rematching at the MFA’s end

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1001F(X)GRAMO(y)F(X )LG(y )LF(X)GRAMO(metro(X))xExit=MMMCSuppliersMexicoChinaExit=MUFinal ProducersThe US1001F(X)GRAMO(y)F(X)GRAMO(metro (X))xAMMMCSuppliersMexicoChinadMCMUFinal ProducersThe USG(metro (X))xBABCD1001F(X)GRAMO(y)MMMCSuppliersMexicoChinadMCMUFinal ProducersThe USABCDF(X )L G(y )LG(y )LABReview of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 Internacional (CC POR 4.0) licencia.

Cifra 3: Partner Change during 2004–2007 and Initial Capability Rankings: Apparel Products

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Nota: The dark gray lines and areas represent the kernel-weighted local mean regression lines with 90%

conﬁdence bands for the treatment group, while the light gray lines and areas represent those for the control

grupo. The conﬁdence interval for US upgrading for the control group is degenerated because no upgrading

occurred there.

-.020.02.04.060.2.4.6.81Own Relative RankBandwidth for the Control: .. Bandwidth for the Treatment: .23Upgrading Probability: US Apparel-.10.1.2.30.2.4.6.81Own Relative RankBandwidth for the Control: .14. Bandwidth for the Treatment: .21Downgrading Probability: US Apparel-.1-.050.05.10.2.4.6.81Own Relative RankBandwidth for the Control: .19. Bandwidth for the Treatment: .22Upgrading Probability: Mexico Apparel-.050.05.1.150.2.4.6.81Own Relative RankBandwidth for the Control: .22. Bandwidth for the Treatment: .62Downgrading Probability: Mexico Apparel90% CI: ControlControl90% CI: TreatmentTreatmentReview of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 Internacional (CC POR 4.0) licencia.

Cifra 4: Old and New Partner Ranks

Nota: The left panel plots the ranking of new main partners in 2007 against the ranking of old main partners

en 2004 for US importers that changed their main partners between 2004 y 2007. The right panel draws

similar partner rankings for Mexican exporters. The lines represent OLS ﬁts.

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0.2.4.6.810.2.4.6.81US importersY = 0.24 + 0.44 X, R =0.13, Obs.=88. (s.e. 0.048) (0.13) 2Old partner’s normalized rank (X) New partner’s normalized rank (Y)0.2.4.6.81 New partner’s normalized rank (Y)0.2.4.6.8Old partner’s normalized rank (X)Mexican exportersY = 0.25 + 0.74 X, R =0.24, Obs.=104 (s.e. 0.036) (0.13) 2Review of Economics and Statistics Just Accepted MS. https://doi.org/10.1162/rest_a_01114 © 2021 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology. Published under a Creative Commons Attribution 4.0 Internacional (CC POR 4.0) licencia.

Mesa 1: Summary Statistics for the HS Six-Digit Product-Level Matching and Firm-Level Match-
ing in Textile/Apparel Trade from Mexico to the United States

mean statistics (median)
(1) Number of Exporters
(2) Number of Importers
(3) Number of Exporters Selling to an Importer
(4) Number of Importers Buying from an Exporter
(5) Value Share of Main Exporter
(Number of Exporters > 1)
(6) Value Share of Main Importer
(Number of Importers > 1)

Product-Level Match

2004
(a)
15.6 (8)
20.3 (11)
1.1 (1)
1.5 (1)

0.76

0.74

2007
(b)
11.8 (6)
15.2 (8)
1.1 (1)
1.4 (1)

0.77

Firm-Level Match
2004
(C)
1,340
2,031
1.4 (1)
2.1 (1)

2007
(d)
1,036
1,541
1.3 (1)
1.9 (1)

0.75

0.78

0.73

0.76

Nota: Rows (1) y (2) are the numbers of Mexican exporters and US importers, respectivamente. Fila (3) es

the number of Mexican exporters selling to a given US importer. Fila (4) is the number of US importers

buying from a given Mexican exporter. Fila (5) is the share of imports from the main Mexican exporters

in terms of the importer’s imports. Fila (6) is the share of exports to the main US importers in terms of the

exporter’s exports. Rows (5) y (6) are calculated only for ﬁrms with multiple partners. Each row reports

the mean with the median in parentheses.

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Mesa 2: Changes in Mexican Textile/Apparel Incumbent Exports to the United States from 2004
a 2007 (Million USD)

Partner Margin Decomposition

Total

(1)

Traditional Margins
Intensive
Extensive
(3)
(2)

Partner Margins
Add
(5)

Drop
(6)

Stay
(4)

Excess
Reallocation
(7)

A. Aggregate decomposition

Quota-bound
% de (3)
Switcher share
Quota-free
% de (3)
Switcher share

-950.9

-887.4

-223.0

-179.6

-63.4
100%

-43.4
100%

-25.1
-121.9
83.5
39.5% -131.7% 192.2%
(0.82)
(0.95)
-24.0
-56.9
37.5
55.4% -86.6% 131.2%
(0.87)
(0.79)

167.1
263.4%

75.1
173.2%

B. HS six-digit product-level regression coefﬁcients

Binding
(s.e.)
HS2 FE

-4.441**
(2.046)
Sí

-4.052**
(1.883)
Sí

-0.389
(0.306)
Sí

-0.132
(0.230)
Sí

0.388**
(0.165)
Sí

-0.645**
(0.274)
Sí

0.706**
(0.296)
Sí

Main Partner Margin Decomposition

Intensive Non-Main
Margin
(1)

Partner
(2)

Main Partner Margins
Add
(4)

Drop
(5)

Stay
(3)

Main Partner
Excess Reallocation
(6)

Quota-bound
% de (1)
Quota-free
% de (1)

-63.4
100%
-43.4
100%

C. Aggregate decomposition

-15.2
24.0%
-14.2
32.8%

-13.7
-107.4
72.9
21.6% -114.9% 169.3%
-10.9
38.7
25.1% -89.2% 131.3%

-56.9

D. HS six-digit product-level regression coefﬁcients

Binding
(s.e.)
HS2 FE

-0.389
(0.306)
Sí

-0.080
(0.082)
Sí

-0.095
(0.205)
Sí

0.332**
(0.141)
Sí

-0.545**
(0.238)
Sí

145.8
229.8%
77.4
178.4%

0.602**
(0.240)
Sí

Nota: In Panel A and Panel C, each column reports the changes in Mexican textile/apparel exports to the

United States between 2004 y 2007 by incumbent exporters in 2004 for quota-bound products and other

quota-free products. In Panel A, the changes in total exports in (1) are decomposed into the extensive margin

by exiters in (2) and the intensive margin by survivors in (3). The intensive margin in (3) is decomposed into

(4) exports to continuing partners, (5) exports to new partners, y (6) exports to dropped buyers. Columna

(7) es |(5)|+|(6)|- |(5)+(6)|. In Panel C, the intensive margin changes by survivors in (1) are decomposed

en (2) exports to non-main partners, (3) exports to continuing main partners, (4) exports to new main

partners, y (5) exports to dropped main partners. Columna (6) es |(4)|+|(5)|- |(4)+(5)|. In Panel B and Panel

D, each column reports the product-level regressions of each margin on the quota-bound product dummy

(Binding) with the HS two-digit ﬁxed effects. Standard errors are clustered at the HS six-digit product level.

Signiﬁcance: * 10%, ** 5%, *** 1%.

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Mesa 3: Partner Change during 2004–07

A. Benchmark Regression

U pU S

Liner Probability Models
U pM ex

DownU S

DownM ex

Binding

OwnRank

Binding
×OwnRank
HS2 FE
Obs.

(1)
0.052**
(0.021)

Sí
718

(2)
0.041*
(0.023)
-0.001
(0.024)
0.034
(0.049)
Sí
718

(3)
-0.017
(0.027)

Sí
718

(4)
0.004
(0.042)
-0.074*
(0.042)
-0.070
(0.074)
Sí
718

(5)
-0.003
(0.020)

Sí
601

(6)
-0.000
(0.018)
0.004
(0.014)
-0.007
(0.026)
Sí
601

(7)
0.127***
(0.035)

Sí
601

(8)
0.130***
(0.049)
-0.087
(0.054)
-0.018
(0.087)
Sí
601

B. Placebo Check: Partner Change in Different Periods

Linear Probability Models

2007–11
(1)
-0.001
(0.018)
Sí
449

U pU S
2008–11
(2)
0.027**
(0.011)
Sí
575

2009–11
(3)
-0.000
(0.006)
Sí
747

DownM ex
2008–11
(5)
0.047
(0.031)
Sí
499

2007–11
(4)
-0.007
(0.036)
Sí
393

2009–11
(6)
0.005
(0.020)
Sí
655

Binding

HS2 FE
Obs.

Nota: The dependent variables U pc

igs and Downc

igs are dummy variables indicating whether during

2004–2007 ﬁrm i in country c switched its main partner of HS six-digit product g in country c(cid:48) to one

with a higher or lower capability ranking, respectivamente. Bindinggs is a dummy variable indicating whether

product g from China faced a binding US import quota in 2004. OwnRankigs is the normalized ranking

of ﬁrm i in 2004. All the regressions include the HS two-digit (sector) efectos fijos. Standard errors are in

parentheses and clustered at the HS six-digit product level. Signiﬁcance: * 10%, ** 5%, *** 1%.

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Mesa 4: Capability Cutoff Changes and Number of Partners

A. Capability Cutoff Changes

Product-Level Difference-in-Difference
ln ExportCutof f gsr

Firm-Level Difference-in-Difference
Exitigsr

Período 1
Período 2

2001–04
2004–07

1998–2001
2001–04

2001–04
2004–07

1998–2001
2001–04

Binding
(δ1)
Binding
×After (δ2)
Después
(δ3)
ln Export
(δ4)
ln Export
×After (δ5)
Control S
HS2 FE
Obs.

(1)
-1.255***
(0.281)
1.031**
(0.479)
-3.402***
(0.364)

(2)
-0.668***
(0.246)
1.188**
(0.490)
-0.863
(1.620)

(3)
-1.074***
(0.248)
0.106
(0.178)
-0.230
(0.151)

(4)
-0.786***
(0.249)
0.324
(0.244)
0.809
(0.785)

No
Sí
696

Sí
Sí
696

No
Sí
652

Sí
Sí
652

(5)
-0.040***
(0.014)
0.076***
(0.017)
-0.361***
(0.042)
-0.058***
(0.002)
0.020***
(0.003)
No
Sí
22,625

(6)
-0.028**
(0.013)
0.089***
(0.021)
-0.345***
(0.077)
-0.056***
(0.003)
0.020***
(0.003)
Sí
Sí
22,624

(7)
-0.021
(0.016)
-0.003
(0.013)
-0.119***
(0.034)
-0.069***
(0.003)
0.011***
(0.003)
No
Sí
24,043

(8)
0.009
(0.014)
-0.034**
(0.015)
-0.212***
(0.056)
-0.066***
(0.003)
0.008**
(0.003)
Sí
Sí
22,142

B. Number of Partners

Change in Number of Partners
México
(9)
-0.65**
(0.33)
Sí
601

US
(10)
-0.12*
(0.06)
Sí
718

Binding

HS2 FE
Obs.

Nota: All the regressions include the HS two-digit (sector) efectos fijos. Standard errors are shown in

parentheses and clustered at the HS six-digit product level. Signiﬁcance: * 10%, ** 5%, *** 1%.Grupo A:

ln ExportCutof f gsr is the log of the minimum of ﬁrm-product-level exports in the initial year of period

r. Exitigsr is a dummy variable indicating whether Mexican ﬁrm i stops exporting product g to the US

in period r. Bindinggs is a dummy variable indicating whether product g from China faced a binding US

import quota in 2004. Af terr is a dummy variable indicating whether period r is after 2004. lnExportigr

is the log of ﬁrm i’s exports of product g in the initial year of period r. columnas (2), (4), (6), (8) include

the product-level controls. Grupo B: the dependent variables are the change in the number of partners during

2004–2007.

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