the twin peaks of the export intensity...

The Twin Peaks of the Export Intensity Distribution∗

Fabrice Defever†, Alejandro Riaño‡

December 14, 2018

Abstract

We document that, contrary to received wisdom, the distribution of export intensity varies sub-stantially across countries and in most of them displays ‘twin peaks’, with some firms exportinga lot of their output, and others a little. We show that this feature arises in a two-countrymodel of trade in which firms face firm-destination-specific revenue shifters that are distributedlognormal, gamma, or Fréchet with sufficiently high dispersion. We structurally estimate ourmodel to quantify the contribution of a wide range of firm-, industry-, and country-level char-acteristics in explaining the ubiquity of twin peaks around the world.

Keywords: Exports; Export Intensity Distribution; Bimodality; Firm Heterogeneity.JEL classification: F12, F14, C12, O50.

∗We thank Peter Egger, Julian di Giovanni, Keith Head, Chris Jones, Emanuel Ornelas, Veronica Rappoport,Dani Rodrik, and seminar participants at Universitat Barcelona, City, University of London, ETH Zurich, LSE/CEP,Universidad del Rosario, the 2015 EIIT conference at Purdue University, the 2016 Royal Economic Society Meetings,the 2016 conference in Industrial Organization and Spatial Economics, St. Petersburg and the 2017 SED AnnualMeetings for their helpful comments. We would like to thank Facundo Albornoz-Crespo, Salamat Ali, RobertoAlvarez, Paulo Bastos, Carlos Casacuberta, Banu Demir, Ha Doan, Robert Elliott, Mulalo Mamburu, SourafelGirma, Kozo Kiyota, Balász Muraközy and Steven Poelhekke for sharing their data or export intensity moments withus. All remaining errors are our own.†City, University of London; GEP; CESifo and CEP/LSE. [email protected]‡University of Nottingham; GEP; CFCM and CESifo. [email protected]

mailto:[email protected]:[email protected]

1 Introduction

Received wisdom suggests that the majority of exporters within a country sell most of their output

domestically while only a very small minority of them concentrate their sales abroad (Bernard

et al., 2003; Brooks, 2006; Arkolakis, 2010; Eaton et al., 2011). This is considered to be one of the

key empirical regularities characterizing the behavior of manufacturing exporters summarized in

the reviews by Bernard et al. (2007) and Melitz and Redding (2014).1 In this paper we challenge

this notion.

Using harmonized firm-level data for 72 (mostly developing and transition) countries drawn from

the World Bank Enterprise Surveys (WBES), we show that the distribution of export intensity—the

share of an exporting firm’s sales accounted for by exports—varies tremendously across countries.

This is vividly illustrated in Figure 1. In Argentina, for example, 62% of exporters have an export

intensity below 0.2 while only 7% of them export more than 80% of their output—the same pattern

identified in previous studies. The distribution in Bangladesh, on the other hand, resembles the

mirror image of that in Argentina: 85% of exporters have an intensity greater than 0.8 and only

7% have an intensity below 0.2. In Ireland we instead observe ‘twin peaks’, a high concentration

of firms on both ends of the distribution’s support.

Figure 1: Export Intensity Distribution Across Countries: Selected Examples

0.2

.4.6

.8Sh

are

of E

xpor

ters

1 2 3 4 5

Argentina Ireland Bangladesh

Export Intensity Bins

The figure depicts a histogram of export intensity—the share of total sales ac-counted for by exports among exporters—across 5 bins ((0,0.2], (0.2,0.4], (0.4,0.6],(0.6,0.8], and (0.8,1]). The data comes from the World Bank Enterprise Surveys.

1The other two stylized facts identified by the literature are that only a minority of firms engage in exporting,and that exporters are ‘better’ than non-exporters across a host of performance measures such as size, productivity,average wages and capital- and skill-intensity. These two results have been verified across a wide range of countries.

1

The key feature that the distributions in these examples have in common is that their mass is

concentrated near the boundaries of the support, not around the middle—i.e. exporters either sell

most of their output domestically or abroad. Quite frequently, however, large shares of these two

types of exporter coexist along each other in the same country. The first contribution of our paper

is to show that rather than an oddity, export intensity distributions displaying twin peaks are quite

common across the world. To be more precise, we find that the distribution of export intensity

in 47 out of 72 countries in our data is bimodal. As we discuss in more detail below, accurately

modelling the distribution of export intensity is critical to quantify the impact of distortions to

international trade that differ across firms, the response of firms to external shocks such as real

exchange rate depreciations and the sales diversification benefits that firms derive from exporting.

Delving deeper into the rich data available in WBES, we show that bimodality is a salient

feature of the distribution of export intensity no matter how we slice the data. Consistent with

the existing evidence, we find that the presence of large numbers of high-intensity exporters re-

flects the importance of the international fragmentation of production along global value chains

in international trade (Dı́az de Astarloa et al., 2013; Antràs and Yeaple, 2014; Manova and Yu,

2016; Dai et al., 2016; Defever and Riaño, 2017a). These firms are more likely to be affiliates of

multinational enterprises and to be engaged in assembly and processing activities. They are also

more prevalent in developing countries and where subsidies that explicitly require firms to export at

least a certain share of their output are available. High intensity exporters are also more abundant

in certain sectors (e.g. textiles and clothing), and, in the limited cases for which we observe firms’

sales to specific destinations, we find that they are also more common in South-North exports than

in South-South ones (e.g. among Indian firms selling to the U.S. rather than to China). Important

as all these factors are, they do not fully explain the prevalence of high-intensity exporters nor the

level of heterogeneity we identify in the distribution of export intensity across countries. As a case

in point, we find that one-third of the countries have bimodal export intensity distributions even

when we exclude firms that export all their output.

The workhorse models of international trade in which firms only differ in terms of their produc-

tivity, such as Melitz (2003), are at odds with the wide range of patterns presented in Figure 1. In

a two-country model with CES preferences, the share of revenues accounted for by exports is the

same for all exporters in a country—i.e. the distribution of export intensity is degenerate. With

more than two countries, more productive firms have a higher export intensity than less produc-

tive ones because the former serve more markets than the latter. Nevertheless, this model cannot

generate right-skewed nor bimodal export intensity distributions if it is to be consistent with the

main stylized fact characterizing the size distribution of firms—that is, that a small number of large

firms coexist alongside a large number of small firms (see Simon and Bonini, 1958; Axtell, 2001).2

We show that with one single modification, the standard two-country model of trade with CES

preferences can generate the wide variety of shapes depicted in Figure 1 quite successfully. Namely,

2The positive correlation between productivity and export intensity also arises in the Melitz and Ottaviano (2008)two-country model with quasi-linear utility. This again implies that the distribution of export intensity inherits theproperties of the productivity distribution.

2

it requires large idiosyncratic differences in firms’ sales that are independent across domestic and

export markets. These could be due to a wide range of supply and demand factors such as differ-

ences in tastes across countries, the extent of firms’ network of customers, participation in global

value chains, the presence of foreign-born workers that facilitate reaching customers abroad, dif-

ferential access to export promotion schemes, among others. Conditional on firms’ having chosen

to export, we generate heterogeneity in their sales across markets by assuming that they draw

destination-specific revenue shifters from a probability distribution. We then derive closed-form

expressions for the probability density function of export intensity when revenue shifters are dis-

tributed lognormal, gamma or Fréchet—three of the most frequently used distributions to model

firm heterogeneity—and show that when the dispersion of revenue shifters is sufficiently high, the

distribution of export intensity is bimodal. The modes are located near 0 and 1 and their ‘height’ is

determined by a country’s relative market size with respect to the rest of the world. Thus, most ex-

porters in relatively small countries are high-intensity ones while the opposite is true in large ones;

in countries of intermediate size, the distribution of export intensity displays twin peaks instead.

While our analytical results are derived from an admittedly stylized model, we provide evidence

suggesting that the mechanism we investigate can also generate bimodality in the distribution of

export intensity in models with more than two countries and where revenue shifters affect firms’

selection into exporting.

We estimate the structural parameters that govern the distribution of export intensity—the

shape parameter of the distribution of revenue shifters and relative market size. We tease out the

latter directly from the data—without having to solve for the full general equilibrium of the model—

by showing that there is a one-to-one relationship between relative market size and the median

export intensity which is independent of the shape parameter for all distributions we consider.

Conditional on this inferred measure of relative market size, we estimate the shape parameter by

maximum likelihood.3 The identification of this parameter is very transparent: if the conditions

for twin peaks are satisfied, greater dispersion of revenue shifters increases the distribution’s mass

in the boundaries of the support. Conversely, if dispersion is low, then the distribution of export

intensity is unimodal and its mass is tightly concentrated around the median in the interior of the

support.

Our results provide strong support for the existence of twin peaks. When we estimate country-

specific scale and shape parameters, the conditions for bimodality are satisfied in all but a handful

of cases. We then pool together our data to estimate a ‘single-shape-parameter’ model in which

firms across all countries draw their domestic and export revenue shifters from a distribution with

the same shape parameter. This implies that all differences in the distribution of export intensity

across countries are due to differences in their relative size vis-à-vis the rest of the world. Our

results are astounding. We find that our model with only one shape parameter—common to firms

in all countries and in both domestic and export markets—accounts for most of the variation

3We also use domestic and export sales data to calculate an alternative measure of relative market size whenrevenue shifters are lognormally distributed. The two measures are highly correlated and, therefore, produce verysimilar estimates of the shape parameter. These results are presented in Section 8.

3

in the distribution of export intensity we observe across the world. Relatively small and large

countries exhibit distributions that ‘look’ unimodal—in the sense that a statistical test does not

reject unimodality—while countries of intermediate size display prominent twin peaks.

We then quantify the contribution of a wide range of firm-, industry-, and country-level char-

acteristics to explain the high level of dispersion of revenue shifters that generates twin peaks. To

do so, we estimate the single-shape-parameter model excluding different subsets of observations

one at a time. Exploiting the fact that the shape parameter under lognormality is the sum of the

variances of domestic and export revenue shifters allows us to compare the estimates for different

subsamples against our benchmark results in a straightforward manner.

This exercise yields two conclusions. First, the conditions for bimodality are always satisfied

across all distributions of revenue shifters and subsamples— even when we estimate our model

using bilateral, rather than total, export intensity or within industries. Second, we find that

the composition of exporters in a country, the availability of subsidies targeted to high-intensity

exporters and a country’s level of development can explain up to 42% of the sum of the total

variance of revenue shifters. Thus, we find that different proxies reflecting the importance of global

value chains account for a substantial share of the dispersion of firms’ sales across domestic and

export markets that generates twin peaks. Crucially, our results show that the remaining dispersion

unaccounted for observable characteristics is always sufficiently high to generate bimodality in the

export intensity distribution—even when we exclude pure exporters from the estimation. Therefore,

the occurrence of twin peaks in the export intensity distribution in a country is not fully accounted

for by the prevalence of specific types of exporters, the sectoral composition of its exports nor the

foreign destinations that its exporters serve.

Related Literature

Our paper documents substantial differences in the distribution of export intensity across countries

and shows that large shares of both low- and high-intensity exporters operate alongside each other

in many countries. Previously, Lu (2010) and Defever and Riaño (2017a) had identified the marked

bimodality of the distribution of export intensity in China. We now show that this pattern is not

specific to China, and is actually quite common across the world. In so doing we contribute to the

literature pioneered by Bernard and Jensen (1995), Roberts and Tybout (1996) and Bernard and

Jensen (1999) that uncovered the key empirical regularities characterizing the behavior of exporters

and spurred the heterogeneous firm revolution in international trade.

A large body of empirical work has shown that firm-destination-specific heterogeneity is central

to explain the variation of exports at the firm-level (e.g. Kee and Krishna, 2008; Crozet et al.,

2012; Munch and Nguyen, 2014; Lawless and Whelan, 2014; Bas et al., 2017). Quantitative models

of the decision to export, such as Eaton et al. (2011) and Fernandes et al. (2018), incorporate

firm-destination-specific revenue shifters to accommodate this stylized fact and to avoid the coun-

terfactual result that exporters serve foreign markets according to a strict hierarchy—as would be

the case if they only differed in terms of their productivity. In this respect, our paper is very closely

4

related to this body of work. We differ from Eaton et al. (2011) and Fernandes et al. (2018) in two

key aspects, however: the dimensions of the data we seek to explain and the use we give to our

quantitative model. More specifically, while Eaton et al. (2011) seek to match French firms’ sales

across markets and Fernandes et al. (2018) focus on the intensive margin of exports, we are inter-

ested instead in the variation in the distribution of export intensity across countries. In a similar

vein, we utilize our model to investigate the economic factors that generate bimodality while Eaton

et al. and Fernandes et al. quantify the effect of a reduction in trade costs on welfare. Our finding

that a high dispersion of exporters’ sales across markets allows to explain why export intensity dis-

tributions differ so much around the world is similar in spirit to the results of Armenter and Koren

(2015). They show that the Melitz model necessitates a substantial amount of size-independent

heterogeneity to reproduce simultaneously the share of exporters and their size premium observed

in the data.

The rest of the paper is organized as follows. Section 2 discusses why is it important to

understand the export intensity distribution and model it accurately. Section 3 presents the data

used in the paper and documents the prevalence of bimodality of the distribution of export intensity

across countries and different subsamples. It also compares export intensity distributions calculated

with WBES data with those obtained from more representative, national firm-level surveys for a

selected group of countries. Section 4 presents our theoretical framework. In it we derive closed-form

expressions for the probability density function of export intensity and characterize the conditions

under which the distribution of export intensity is bimodal; we also discuss the main assumptions

we rely upon to obtain analytical solutions and explain why the insights derived from those carry

over to richer environments. Section 5 presents our identification strategy and the estimates from

our structural model. Section 6 shows that conditional on the dispersion of firm-destination revenue

shifters being sufficiently high, cross-country differences in relative market size account for most

of the variation in the distribution of export intensity that we observe in the data. Section 7

investigates the determinants of the dispersion in firm-destination-specific shifters that generate

twin peaks. In Section 8 we estimate the parameters governing the distribution of export intensity

under using data on domestic and export sales instead of export intensity. Section 9 concludes.

2 Why is the Export Intensity Distribution Important?

Export intensity measures the relative importance of international markets for firms’ sales. For this

reason, the mean export intensity has been used extensively to pin down the magnitude of costs

that impede the international flow of goods in models of trade with heterogeneous firms. Notable

examples include Melitz and Redding (2015) and Head et al. (2014) in models with two symmetric

countries, Eaton et al. (2011) in a multi-country environment and Atkeson and Burstein (2010)

and Alessandria and Choi (2014) in dynamic models.

A common feature of these models is that the variable cost associated with exporting is the

same for all firms selling in a given destination. Several distortions to international trade are

5

firm-specific, however. Some prominent examples include the allocation of export quota rights

(Khandelwal et al., 2014) and the provision of subsidies targeted to specific subsets of firms, e.g.

according to their location or foreign ownership status (Farole and Akinci, 2011), whether they

export the majority of their output (Defever and Riaño, 2017a; Defever et al., forthcoming), or if

they produce goods considered to be of “strategic importance” (Westphal, 1990; Kalouptsidi, 2018).

Since these policies affect the incentives to export relative to selling domestically differently across

firms, we need to infer how the distribution of export intensity would have looked in the absence

of distortions in order to gauge their impact. The idea is analogous to the approach pioneered

by Restuccia and Rogerson (2008) and Hsieh and Klenow (2009) to measure the mis-allocation

of inputs across producers and its impact on aggregate total factor productivity. To illustrate it,

consider the exercise conducted by Defever and Riaño (2017a). They study how a tax deduction

granted to firms exporting more than 70% of their output affects aggregate welfare in China. They

show that this policy distorts the export intensity distribution by inducing a subset of firms to

export a larger share of their output than they would otherwise do. Defever and Riaño construct

the undistorted counterfactual by combining the export intensity distributions of large developing

countries that do not provide subsidies subject to export share requirements. Similarly, Brooks

and Wang (2016) show that the dispersion in export intensity can be used to gauge distortions

associated with the variable cost of international trade, and assess the extent of these in China

by comparing its export intensity distribution with that of France. In this paper we show that

counterfactual export intensity distributions—which can be used to evaluate the impact of policies

like the ones discussed above and more—can be readily calculated, only requiring information on a

country’s domestic market size relative to the rest of the world. We also show that the two-country

version of the Melitz model augmented with firm-destination-specific revenue shifters can generate

a wide range of shapes of the export intensity distribution in the absence of distortions. Thus,

the use of our estimates does not presuppose that particular patterns of the distribution such as

bimodality are due to policy-related distortions.4

Recent research has shown that firms’ response to external shocks—most notably to real ex-

change rate (RER) depreciations—is substantially heterogeneous across the distribution of export

intensity. Alfaro et al. (2017) find that while firms in East Asia increase their productivity, expe-

rience faster growth in sales and invest more in R&D following a RER depreciation, firms in Latin

America respond in the diametrically opposite way, and firms in industrialized countries do not

exhibit any significant change. They show that this heterogeneous response is due to the fact that

firms in Latin America are substantially less export intensive than firms in East Asia—a pattern

that we also observe in our data and that our model can readily reproduce (see Figure 6 below).

RER depreciations increase firms’ demand the most when firms have a high export intensity, and in

so doing, also help to relax financial constraints allowing firms to overcome the fixed costs involved

in R&D investment. Closely related, Kohn et al. (2017) show that the response of aggregate exports

4See for example the recent debate about whether the lack of bimodality in the size distribution of firms indeveloping countries implies or not a rejection of the “missing middle” hypothesis (Hsieh and Olken, 2014; Tybout,2014).

6

to large RER depreciations is fundamentally shaped by the distribution of export intensity when

firms rely on foreign currency borrowing to finance their investment. Under these circumstances, a

large RER depreciation increases a firm’s demand for exports, while simultaneously raising its bor-

rowing costs and tightening financial constraints. In an economy in which the majority of exporters

have low export intensity, firms can expand their exports much faster in response to a depreciation

because they can reallocate their sales from the domestic to the export market without having to

expand their capital stock. This margin of adjustment, on the other hand, is dampened in countries

where high-intensity exporters are more prevalent.

The shape of the export intensity distribution also affects the sales diversification benefits

that firms derive from exporting. When firms are buffeted by idiosyncratic demand shocks across

markets, selling both domestically and abroad reduces the volatility of the growth rate of their sales

(Riaño, 2011; Vannoorenberghe, 2012). This matters because lower volatility makes firms more

responsive to policy stimuli, increases their ability to raise external finance and reduces risk premia

and the probability of default (Adrian and Rosenberg, 2008; Froot et al., 1993; Bloom et al., 2007).

In Appendix D we show that there is a U-shaped relationship between the volatility of a firm’s sales

growth and its export intensity. This implies that when a country’s export intensity distribution

exhibits twin peaks, the volatility-reducing benefits of exporting are significantly reduced because

most exporters have intensities either near 0 or 1.

3 Data

Our data comes from several waves of the World Bank Enterprise Surveys (WBES) spanning the

period 2002-2016. These surveys are carried out by the World Bank’s Enterprise Analysis Unit

using a uniform methodology and core questionnaire, and are designed to be representative of a

country’s non-agricultural private economy.5 The unit of observation is the establishment, i.e. a

physical location where business is carried out or industrial operations take place which should have

its own management and control over its own workforce. Since the vast majority of establishments

surveyed report to be single-establishment firms, hereafter we refer to them as ‘firms’. We use data

for the manufacturing sector only—i.e. firms that belong to ISIC Rev. 3.1 sectors 15-37.

The WBES provides information on firms’ main sector of operation, total sales, export intensity,

ownership status (whether the firm is domestic or foreign-owned), labor productivity and the share

of material inputs accounted for by imports. Export intensity—our main variable of interest—is

defined as the share of sales that a firm exported directly or indirectly through an intermediary in

a fiscal year, and therefore takes values in the interval p0, 1s.6Table 1 provides information on the number of exporters and the number of WBES survey waves

per country. Our sample consists of 72 developing and transition countries (with the exception of

5More specifically, the survey includes formal (registered) firms with more than 5 employees that are not 100%state-owned. A new survey wave is usually conducted in each country every 3-4 years.

6Since the survey asks firms directly about the percentage of their sales exported, the response is bounded at100%, and therefore does not capture ‘carry along’ trade—a situation in which firms export goods that they do notproduce, and which can generate export intensities greater than 1 (Bernard et al., forthcoming).

7

Tab

le1:

Sam

ple

Com

pos

itio

n

Cou

ntr

yC

od

eS

urv

eyW

aves

#E

SR

Cou

ntr

yC

od

eS

urv

eyW

aves

#E

SR

Exp

ort

ers

Exp

ort

ers

Alb

ania

AL

B20

02,

05,

07,

13

116

No

Lit

hu

ania

LT

U2002,

04,

05,

09,

13

258

No

Arg

enti

na

AR

G20

06,

101,1

40

No

Mad

agasc

ar

MD

G2005,

09,

13

256

Yes

Arm

enia

AR

M20

02,

05,

09,

13

170

No

Mala

ysi

aM

YS

2002,

15

735

Yes

Ban

glad

esh

BG

D20

02,

07,

131,2

55

Yes

Mau

riti

us

MU

S2005,

09

183

No

Bel

aru

sB

LR

2002

,05

,08

,13

146

Yes

Mex

ico

ME

X2006,

10

727

No

Bol

ivia

BO

L20

06,

10242

No

Mold

ova

MD

A2002,

03,

05,

09,

13

221

No

Bos

nia

&H

erze

govin

aB

IH20

02,

05,

09,

13

200

Yes

Moro

cco

MA

R2004,

13

585

Yes

Bra

zil

BR

A20

03,

09832

Yes

Nam

ibia

NA

M2006,

14

109

Yes

Bu

lgar

iaB

GR

2002

,04

,05

,07,

09,

13

538

No

Nic

ara

gu

aN

IC2003,

06,

10

283

Yes

Ch

ile

CH

L20

04,

06,

101,0

01

No

Nig

eria

NG

A2007,

14

316

Yes

Ch

ina

CH

N20

02,

03,

121,4

39

Yes

Pakis

tan

PA

K2002,

07,

13

534

Yes

Col

omb

iaC

OL

2006

,10

703

No

Pan

am

aP

AN

2006,

10

134

No

Cos

taR

ica

CR

I20

05,

10238

Yes

Para

gu

ayP

RY

2006,

10

246

Yes

Cro

atia

HR

V20

02,

05,

07,

13

335

No

Per

uP

ER

2006,

10

701

Yes

Cze

chR

ep.

CZ

E20

02,

05,

09,

13

232

No

Ph

ilip

pin

esP

HL

2003,

09,

15

914

Yes

Ecu

ador

EC

U20

03,

06,

10385

No

Pola

nd

PO

L2002,

03,

05,

09,

13

439

No

Egy

pt

EG

Y20

04,

13676

Yes

Rom

an

iaR

OU

2002,

05,

09,

13

290

No

El

Sal

vad

orS

LV

2003

,06

,10

,16

840

No

Ru

ssia

nF

ed.

RU

S2002,

05,

09,

12

468

No

Est

onia

ES

T20

02,

05,

09,

13

175

No

Sen

egal

SE

N2003,

07,

14

148

Yes

Eth

iop

hia

ET

H20

02,

11,

15118

Yes

Ser

bia

SR

B2002,

03,

05,

09,

13

330

No

FY

RM

aced

onia

MK

D20

02,

05,

09,

13

191

No

Slo

vak

Rep

.S

VK

2002,

05,

09,

13

164

No

Gh

ana

GH

A20

07,

13159

Yes

Slo

ven

iaS

VN

2002,

05,

09,

13

245

No

Gu

atem

ala

GT

M20

03,

06,

10580

Yes

Sou

thA

fric

aZ

AF

2003,

07

558

No

Hon

du

ras

HN

D20

03,

06,

10345

Yes

Sri

Lan

kaL

KA

2004,

11

403

Yes

Hu

nga

ryH

UN

2002

,05

,09

,13

300

No

Sw

eden

SW

E2014

286

No

Ind

iaIN

D20

02,

06,

142,2

12

Yes

Syri

an

Ara

bR

ep.

SY

R2003

251

No

Ind

ones

iaID

N20

03,

09,

15720

Yes

Tan

zan

iaT

ZA

2003,

06,

13

222

Yes

Irel

and

IRL

2005

97

No

Th

ailan

dT

HA

2004,

16

1,0

66

Yes

Jor

dan

JO

R20

06,

13377

No

Tu

nis

iaT

UN

2013

213

Yes

Kaz

akh

stan

KA

Z20

02,

05,

09,

13

116

No

Tu

rkey

TU

R2002,

04,

05,

08,

13

2,1

52

Yes

Ken

yaK

EN

2003

,07

,13

511

No

Ugan

da

UG

A2003,

06,

13

221

Yes

Kor

ea,

Rep

.K

OR

2005

99

No

Ukra

ine

UK

R2002,

05,

08,

13

435

No

Kyrg

yz

Rep

.K

GZ

2002

,03

,05

,09,

13

126

No

Uru

gu

ayU

RY

2006,

10

467

No

Lao

PD

RL

AO

2006

,12

,16

128

No

Uzb

ekis

tan

UZ

B2002,

03,

05,

08,

13

112

Yes

Lat

via

LV

A20

02,

05,

09,

13

161

No

Vie

tnam

VN

M2005,

09,

15

1,2

51

Yes

Leb

anon

LB

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8

Ireland and Sweden), for which we observe at least 97 exporting firms when we pool the data

across all available survey waves. The number of exporters per country ranges from 97 in Ireland

to 2,112 in India; on average, 40% of firms surveyed in a given country export some of their output.

In terms of geographic coverage, the countries in our data are evenly distributed across Eastern

Europe, Latin America and the Caribbean, Asia, and the Middle East and Africa; Ireland and

Sweden are the only two countries from Western Europe.

Table 1 also indicates whether a country provides subsidies subject to export share requirements

(ESR)—incentives directly conditioned on firms’ export intensity.7 We identify countries offering

subsidies subject to ESR by relying on information gleaned from the “Performance Requirements

and Incentives” and “Foreign Trade Zones/Free Trade Zones” sections of the Investment Climate

Statements produced by the U.S. State Department, following Defever and Riaño (2017a). Table

1 shows that half the countries in our data offer this class of subsidies.

Table 2 provides a first pass at the WBES data comparing exporters, across the distribution

of export intensity, with domestic firms. Columns (1)-(3) provide information on firm size and

productivity relative to the average value of the respective statistic in each country-survey year pair,

while columns (4) and (5) report the percentage of foreign-owned firms and the use of imported

inputs in each cell respectively. Table 2 reveals that—consistent with the evidence summarized

by Bernard et al. (2007) and Melitz and Redding (2014)—exporters are larger (both in terms of

employment and output) and more productive than domestic firms. Looking across the export

intensity distribution, we find that although there is a positive correlation between firm size and

export intensity, there is not a clear relationship between labor productivity and export intensity.8

Columns (4) and (5) show that exporters—and high-intensity ones in particular—are more likely

to be foreign-owned and to use imported intermediate inputs more intensively than domestic firms,

consistent with the evidence documented by Antràs and Yeaple (2014) and Amiti and Konings

(2007).

Figure 2 provides a bird’s eye view of the export intensity distribution across countries. In it

we calculate the share of exporters across five export intensity bins in each country and present

the distribution of these shares in each bin. Figure 2 shows that in the majority of countries,

exporters concentrate in the first and last export intensity bins—i.e. they either sell most of their

output domestically or abroad—while relatively fewer allocate similar shares of their sales across

domestic and export markets. The figure also shows that there is a high degree of heterogeneity

across countries in terms of the share of high and low-intensity exporters.

The WBES collects a wide range of information on firms’ characteristics such as foreign own-

ership status, import intensity, sector of operation, and in some cases, also provide information on

7Examples include cash transfers, tax holidays and deductions, and the provision of utilities at below-market rates.They are most frequently used in special economic zones and duty-drawback regimes.

8Dı́az de Astarloa et al. (2013) and Heid et al. (2013) find that high-intensity exporters are larger than domesticfirms and other exporters in Bangladesh and Mexico respectively. On the other hand, Defever and Riaño (2017b)document that firms that export all their output in China, although larger and more productive than domestic firms,are smaller and less productive than low-intensity exporters.

9

Table 2: Firm Characteristics by Export Status and Export Intensity

Employment Output Output % Foreign- % Importedper worker owned inputs

(1) (2) (3) (4) (5)

Non-Exporters 0.5 0.5 0.8 6.0 23.7

ExportersExport intensity:P p0.0, 0.2s 1.7 2.1 1.4 17.4 37.7P p0.2, 0.4s 1.5 1.8 1.3 18.8 35.6P p0.4, 0.6s 1.7 1.9 1.3 21.0 35.2P p0.6, 0.8s 2.3 2.3 1.4 23.0 35.4P p0.8, 1.0s 2.2 2.3 1.6 31.1 41.0

Columns (1)-(3) report the average across countries of the relative size and labor productivity of ex-porters and domestic firms relative to the mean value of each variable calculated in each country-surveyyear cell. Thus, for instance, domestic firms across all countries in our sample are 50% smaller (in termsof employment) than the average firm, while exporters with an export intensity lower than 20% are70% larger than the average firm. Column (4) reports the percentage of foreign-owned firms (firms witha share of foreign equity at least 10% or greater) and column (5) presents the percentage of importedinputs in total intermediate inputs in each export intensity bin.

Figure 2: Cross-country Distribution of the Share of Exporters Operating in Different ExportIntensity Bins—All Exporters

1 2 3 4 5

Export Intensity Bins

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sha

re o

f Exp

orte

rs

For each country in our data, we calculate the share of exporters operating across 5 exportintensity bins ((0,0.2], (0.2,0.4], (0.4,0.6], (0.6,0.8], and (0.8,1]). The figure presents the mainquantiles of the distribution of these shares across countries for each export intensity bin.The median is denoted by a circle, the top and bottom sides of each box denote respectivelythe 25th and 75th percentiles; the bottom and top of the ‘whiskers’ (represented with dashedlines) indicate the minimum and maximum respectively.

10

firms’ exports to specific destinations, which we use to calculate bilateral instead of total export

intensity. Figures A.1 and A.2 in Appendix A redo Figure 2 excluding, one at a time, different

subsets of observations based on the aforementioned characteristics. The key message delivered by

Figure 2 still holds regardless of how we slice the data: most exporters operate at either a very low

or very high export intensity. Figures A.1 and A.2 also show that high-intensity exporters are not

confined exclusively to a particular subset of firms, industries or countries.

We now shift our focus to the distribution of export intensity within countries; more specifically,

our objective is to identify which countries have bimodal distributions. To do this we use the the

dip test statistic proposed by Hartigan and Hartigan (1985). The dip statistic measures departures

from unimodality in the empirical cumulative distribution function (cdf) by relying on the fact

that a unimodal distribution has a unique inflection point.9 As Henderson et al. (2008) note,

the dip measures the amount of ‘stretching’ needed to render the empirical cdf of a multi-modal

distribution unimodal; therefore, a higher value of the dip leads to a rejection of the null hypothesis

of unimodality.10 The dip test has been widely used in economics to, among other things, identify

convergence clusters in the distribution of GDP per capita, total factor productivity and other

indicators of economic growth (Henderson et al., 2008), characterize the degree of price stickiness

(Cavallo and Rigobon, 2011) and to assess the identification of hazard function estimates (Heckman

and Singer, 1984).

It is important to note that the dip test only allows us to infer whether the null hypothesis

of unimodality is rejected or not, while kernel density based tests, such as Silverman (1981), can

identify the number of modes in the data. There are two reasons why we prefer the dip test over

the Silverman (1981) one to classify countries. First, unlike the dip test, density-based tests are

highly sensitive to the choice of the bandwidth parameter. Second, the Silverman test is not well

suited for data that, while continuous in nature like our export intensity data, exhibit clustering

at figures that are multiples of 5%. The dip test, on the other hand, can be adjusted to take into

account the discreteness of the data. Despite the advantages of the dip statistic, calculating the

Silverman test reveals that the number of modes never exceeds two in any country in our data.

Therefore, we classify a country as having a unimodal export intensity distribution if its dip test

statistic is not rejected at the 1% significance level; otherwise, we consider it to be bimodal.

Figure 3 presents the dip statistic for each country in our sample. We find that the distribution

of export intensity is bimodal in 47 out of 72 countries. This result stands in sharp contrast with

the existing literature suggesting that this distribution is generally unimodal, with a majority of

exporters selling a small share of their output abroad.

We next calculate the dip test across the different subsamples described above. We want to

make sure that the prevalence of bimodal export intensity distributions we observe is not due

to the coexistence of ‘standard’ low-intensity exporters with specific groups of firms that export

9More precisely, the cdf of a unimodal distribution is convex on the interval p�8, xmq and concave betweenpxm,�8q, where xm denotes the mode of the distribution.

10Hartigan and Hartigan (1985) choose the uniform distribution as the distribution under the null hypothesisbecause its dip is the largest among all unimodal distributions.

11

most of their output. Excluding foreign-owned and processing exporters has little effect on the

number of countries we identify as bimodal, although countries such as Costa Rica, Croatia, and

Hungary—notable for their success in attracting multinational firms—are reclassified as having

unimodal distributions. While we observe bimodality in the distributions of OECD and non-OECD

countries, we find that this feature is more prevalent among countries that incentivize high-intensity

exporters. Excluding firms that export all their output from the data altogether—a ‘brute force’

way to capture firms intertwined in global value chains—makes a significant dent on the prevalence

of bimodality, increasing the the number of countries with unimodal distributions from 25 to 46.

Thus, our results show that the existence of twin peaks is not fully accounted for by the prevalence

of a specific type of exporter operating within countries.

We also calculate the dip statistic for country-sector pairs with more than 50 exporters to allay

concerns that bimodality might be the due to a composition effect if the distribution of export

intensity differs substantially across industries. We do not find this to be the case—among the

countries that we identify as bimodal, more than half of distributions within sectors are themselves

bimodal.

Figure 3: Dip Test of Unimodality of Export Intensity

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The figure reports the value of the Hartigan and Hartigan (1985) dip test statistic of unimodality. Countries areidentified as having having a unimodal export intensity distribution if their dip statistic does not reject the nullhypothesis of unimodality at the 1% confidence level; otherwise, they are identified as bimodal. The reported value ofthe dip statistic is calculated as the mean across 1,000 bootstrapped samples of 200 exporters drawn for each country.The algorithm used to calculate the dip test statistic is adjusted to take into account the discreteness of the exportintensity data.

An important concern is that twin peaks could be an artifact of the WBES data. Asker et al.

(2014), for instance, note that the stratification procedure across sectors, size categories and ge-

12

Table 3: Comparison of Export Intensity Distributions—WBES vs Other Surveys

Country Survey # Share of Exporters with Export Intensity P:Exporters p0.0, 0.2s p0.2, 0.4s p0.4, 0.6s p0.6, 0.8s p0.8, 1.0s

Argentina ENIT 830 0.660 0.123 0.071 0.065 0.081WBES 1,140 0.535 0.225 0.102 0.067 0.071

Chile ENIA 900 0.582 0.116 0.113 0.093 0.096WBES 1,001 0.490 0.186 0.098 0.065 0.162

China NBS 50,902 0.221 0.101 0.091 0.101 0.486WBES 1,439 0.282 0.198 0.116 0.093 0.311

Colombia EAM 1,332 0.643 0.157 0.068 0.038 0.095WBES 703 0.459 0.273 0.128 0.067 0.073

Hungary APEH 7,143 0.488 0.127 0.081 0.079 0.225WBES 300 0.243 0.207 0.160 0.123 0.267

India Prowess 3,133 0.576 0.136 0.088 0.071 0.129WBES 2,212 0.260 0.214 0.116 0.072 0.338

Indonesia Census 3,949 0.124 0.097 0.089 0.127 0.563WBES 720 0.125 0.172 0.144 0.139 0.419

Ireland FAME 151 0.371 0.093 0.079 0.099 0.358WBES 173 0.330 0.155 0.113 0.082 0.320

Pakistan FRBP 6,043 0.207 0.056 0.041 0.043 0.652WBES 534 0.148 0.146 0.109 0.062 0.536

South Africa SARS-NT 7,530 0.844 0.076 0.036 0.025 0.019WBES 558 0.529 0.279 0.113 0.020 0.060

Thailand OIE 1,591 0.302 0.136 0.111 0.121 0.331WBES 1,066 0.147 0.151 0.134 0.141 0.427

Uruguay EAAE 389 0.424 0.131 0.090 0.095 0.260WBES 467 0.328 0.173 0.105 0.103 0.291

Vietnam ASE 4,946 0.292 0.108 0.094 0.115 0.391WBES 1,251 0.173 0.128 0.065 0.104 0.530

Argentina: National Survey on Innovation and Technological Behavior of Industrial Argentinean Firms (ENIT) forthe year 2001; this is a representative sample of establishments with more than 10 employees. Chile: Annual NationalIndustrial Survey (ENIA) for the year 2000, covering the universe of Chilean manufacturing plants with 10 or moreworkers. Colombia: Annual Manufacturing Survey (EIA) for they year 1991, covering the universe of Colombianmanufacturing plants with 10 or more workers. China: National Bureau of Statistics (NBS) Manufacturing Surveyfor the year 2003, which includes state-owned enterprises and private firms with sales above 5 million Chinese Yuan.Hungary: universe of manufacturing firms for the year 2014 drawn from APEH, the Hungarian tax authority. India:Prowess database collected by the Centre for Monitoring the Indian Economy (CMIE) for the year 2001. Indonesia:Indonesian Census of Manufacturing Firms for the year 2009, which surveys all registered manufacturing plants withmore than 20 employees. Ireland: FAME database collected by Bureau van Dijk for the year 2007. Pakistan: exportintensity is constructed from two administrative datasets from the Federal Board of Revenue of Pakistan (FBRP);export figures are from customs records and domestic Sales from VAT data records. The data records all firms withannual turnover above 2.5 million Pakistani rupees for the year 2013. South Africa: South African Revenue Serviceand National Treasury Firm-Level Panel (SARS-NT) for the year 2010, which covers the universe of all tax registeredfirms. Thailand: Annual Survey of Thailand’s manufacturing industries by the Office of Industrial Economics (OIE)for the year 2014. The questionnaire’s response rate is about 60% of all firms accounting for about 95% of totalmanufacturing. Uruguay: Annual Survey of Economic Activity (EAAE), which covers all manufacturing plants with10 or more employees for the year 2005. Vietnam: Annual Survey on Enterprises (ASE) for the year 2010, whichcovers all state-owned enterprises and foreign-owned firms and domestic private firms with more than 10 employees.

13

ographic locations used in the construction of the WBES leads to oversampling of larger firms.

Although it is not clear that this would necessarily increase the likelihood of observing bimodal ex-

port intensity distributions, it is crucial for our purposes to show that twin peaks also arise in more

representative datasets. To this end, we asked fellow researchers to calculate for us the share of

exporters across export intensity bins using well-known firm-level manufacturing surveys for a sub-

sample of 13 countries in our data, which we then compare with the same moments calculated from

WBES.11 The countries that we consider include 5 that we classify as unimodal (Argentina, Chile,

Colombia, Indonesia and South Africa) and 8 bimodal (China, Hungary, India, Ireland, Pakistan,

Thailand, Uruguay and Vietnam). Most surveys used in our analysis include all manufacturing

firms with more than 10 to 20 employees, although the data for China and Ireland are based on

surveys of larger firms. It is also important to note that the distribution of export intensity based

on manufacturing surveys is calculated with data for a single year, whereas our main data set pools

exporters from all survey waves available for a given country in the WBES.

Table 3 presents the results of our comparison and shows that the WBES provides an accurate

picture of the distribution export intensity. Both the WBES and the different alternative data

sources yield similar results with regards to the existence or not of twin peaks—even in the cases

in which there are sizeable differences in the share of exporters in individual bins (such as Hungary

and India). Crucially, in all countries but one, the share of exporters with export intensity in

the middle bins is higher in the WBES than in the more representative data. Thus, the results

presented in Figure 3 seem to, if anything, underestimate how common bimodal export intensity

distributions are across the world.

4 Theoretical Framework

Consider a monopolistically-competitive industry in which each firm produces a unique, differen-

tiated good indexed by ω (which will also denote a firm’s identity hereafter). Firms can sell their

output in two markets: home (indexed by d) and the rest of the world (indexed by x). Firm ω’s

sales in destination market i P td, xu, ripωq, are given by:

ripωq � Ai � zipωq � pipωq1�σ, (1)

where pipωq is the price charged by firm ω in market i, σ ¡ 1 is the elasticity of demand, Ai is ameasure of market i’s size or “attractiveness” which is common to all firms selling there, and zipωq

11The choice of countries for this exercises was driven by data availability. The manufacturing surveys that we relyupon for the comparison have been used in a large number of prominent papers in international trade, including—butnot limited to—Bustos (2011) (Argentina), Alvarez and López (2005) (Chile), Feenstra and Hanson (2005) (China),Roberts and Tybout (1997) (Colombia), Békés and Muraközy (2012) (Hungary), Goldberg et al. (2010) (India),Javorcik and Poelhekke (2017) (Indonesia), Ali et al. (2017) (Pakistan), Mamburu (2017) (South Africa), Cole et al.(2010) (Thailand), Casacuberta and Gandelman (2012) (Uruguay) and Ha and Kiyota (2014) (Vietnam).

14

is a firm-destination-specific revenue shifter.12 The latter encompasses a wide variety of demand

and supply factors that generate differences in the sales of a given firm across different markets, e.g.

cross-country differences in tastes, the extent of a firm’s network of customers, its participation in

global value chains, or the presence of workers from the foreign country that allows a home-firm to

better reach consumers abroad, among others. Empirical evidence for Bangladeshi, Danish, French

and Irish exporters has consistently found that firm-destination fixed effects account for a similar

share of the variation in export sales as firm-specific factors such as productivity (see respectively,

Kee and Krishna (2008), Munch and Nguyen (2014), Eaton et al. (2011), and Lawless and Whelan

(2014)).

As is standard in models of international trade with heterogenous firms, producers pay a sunk

cost fe to draw their idiosyncratic productivity, ϕ, from a distribution with probability density

function (pdf) gpϕq.13 Firms incur a fixed cost fd to set up a plant and produce their respective goodusing a linear technology, with labor being the only input. Thus, the marginal cost of production

for a firm of productivity ϕ is w{ϕ, where w is the wage prevailing in the firm’s domestic market.A firm that chooses to export needs to incur an additional fixed cost, fx, and an iceberg transport

cost τ ¥ 1.We assume that firms choose whether to operate or not and what markets to serve after ob-

serving their productivity, but before knowing the realization of revenue shifters. We get a lot

of mileage from this assumption.14 It allow us to derive a closed-form expression for the pdf of

export intensity and to back out the scale parameter of this distribution directly from the data

without have to solve the full general equilibrium of the model. We discuss below the implications

of allowing firms to choose in which market to sell after observing the realization of productivity

and destination-specific revenue shifters.

Having chosen in which markets to operate, firms draw their idiosyncratic revenue shifter in

market i, zipωq, from a distribution with pdf fpziq, which can be lognormal, gamma or Fréchet. Weassume that the distribution fp�q is the same in both markets, although its parameters can, in somecases, differ across destinations; furthermore, we assume that revenue shifters and productivity are

orthogonal with respect to each other. Our choice for the underlying distribution of revenue shifters

is driven both by their wide use in modelling heterogeneity in economic models and, as noted below,

the need for a closed-form expression for the pdf of the ratio of revenue shifters.15

12The revenue function (1) obtains when there is a representative consumer in each country with CES preferences of

the form: U ��°

iPtd,xu

�³ωPΩi

rzipωq1

σ�1 qipωqsσ�1σ dω

� σσ�1

, where qipωq denotes the quantity of good ω from country

i consumed, and Ωi is the set of varieties produced in market i available to consume. Under this interpretation, marketi’s size is given by Ai � RiP

σ�1i , where Ri denotes country i’s aggregate expenditure and Pi is the ideal price index.

13All fixed costs are denominated in units of labor.14This timing assumption has also been used by Cherkashin et al. (2015); it is consistent with the fact that while

firm-level productivity strongly predicts export entry, it explains much less of the variation in sales across destinationsconditional on entry (Eaton et al., 2011).

15The lognormal distribution has recently become a popular choice to model the distribution of firm-level produc-tivity in the international trade literature (see e.g. Head et al., 2014; Mrázová et al., 2015; Nigai, 2017); Hanson et al.(2016) find that the distribution of export capabilities at the industry level is also well approximated by a lognormaldistribution. Eaton et al. (2011), Fernandes et al. (2018) and Bas et al. (2017) use the lognormal distribution tomodel firm-destination-specific revenue shifters in models with more than two destination markets. Luttmer (2007)

15

A firm that is productive enough to export—i.e. one for which the expected profit of exporting

exceeds the fixed cost wfx—sets prices pdpωq � σσ�1 wϕ and pxpωq � τpdpωq at home and abroadrespectively (since revenue shifters are multiplicative, they do not affect prices). Plugging these

prices back into (1) allows us to write firm ω’s sales in market i as:

ripωq � si � Φpωq � zipωq, (2)

where sd ��σ�1σ

�σ�1w1�σAd, sx �

�σ�1σ

�σ�1w1�στ1�σAx, and Φpωq � ϕσ�1. Thus, sales in a

given destination are composed of three terms: (i) si encompasses all variables that are common

across all firms selling in i (i.e. market i’s size, home’s wage, transport costs), (ii) Φpωq (productiv-ity), which varies between firms but is the same across destinations, and (iii) zipωq which representsthe factors that determine the appeal of firm ω’s product specifically in market i.

Define an exporter’s export intensity as the share of total sales accounted for by exports. Let

Epωq denote the export intensity of firm ω, while lowercase e is a specific realization of this randomvariable. Thus,

Epωq � rxpωqrdpωq � rxpωq �

sxzxpωqsdzdpωq � sxzxpωq �

ZxpωqZdpωq � Zxpωq . (3)

Since firms can only sell their output in two destinations, and charge the same constant markup in

both, it follows that export intensity is independent of productivity. Thus, in the absence of firm-

destination-specific revenue shifters, all exporters would have the same export intensity—namely,τ1�σAx

Ad�τ1�σAx. Therefore, heterogeneity in sales at the firm-destination level is necessary for our model

to reproduce the within-country variation in export intensity that we observe in the data.

We now derive expressions for the pdf of export intensity when revenue shifters are distributed

lognormal, gamma and Fréchet by relying on the method of transformations for random vari-

ables. This approach requires two conditions: firstly, the distribution of revenue shifters has to be

closed under scalar multiplication. This implies that the scaled revenue shifters, Zdpωq � sdzdpωqand Zxpωq � sxzxpωq, follow the same distribution as the firm-destination-specific components,tzipωquiPtd,xu. Secondly, since E can be expressed as a strictly increasing function of the ratio ofexport to domestic revenue shifters, Z � Zx{Zd, we need this random variable to have a closed-formpdf. With these at hand, we can establish our first result:

Proposition 1. Assume that firm-destination-specific revenue shifters tzipωquiPtd,xu are drawn fromthe same distribution independently across destinations.

(i) When revenue shifters are distributed lognormal (LN ) with underlying mean 0 and varianceσ2zi, i.e. when zipωq � LN

�0, σ2zi

�, and therefore, Zipωq � sizipωq � LN

�lnpsiq, σ2zi

�, then

uses the gamma distribution to model the size distribution of firms, while Eaton and Kortum (2002) is the seminalreference on the use of the Fréchet distribution to model cross-country differences in productivity.

16

the probability density function of export intensity is given by:

hLN peq � 1rep1� eqs

b2πpσ2zd � σ2zxq

� exp

��

ln�

e1�e

� ln

�sxsd

22pσ2zd � σ2zxq

�� , e P p0, 1q. (4)(ii) When revenue shifters are distributed gamma (Γ) with scale parameter 1 and shape parameter

α ¡ 0, i.e. when zipωq � Γp1, αq, and therefore, Zipωq � sizipωq � Γpsi, αq, then, theprobability density function of export intensity is given by:

hΓpeq �

�sdsx

αBpα, αq �

eα�1p1� eq�p1�αq�1�

�sdsx

�e

1�e

�2α , e P p0, 1q, (5)where Bp�, �q denotes the Beta function.

(iii) When revenue shifters are distributed Fréchet with scale parameter 1 and shape parameter

α ¡ 0, i.e. when zipωq � Fréchet p1, αq, and therefore, Zipωq � sizipωq � Fréchet psi, αq, then,the probability density function of export intensity is given by:

hFréchetpeq � α�sdsx

α� e

α�1p1� eq�p1�αq�1�

�sdsx

α �e

1�e

α�2 , e P p0, 1q. (6)Proof. See Appendix B.1.

Figures B.1-B.3 in Appendix B.1 provide examples of the pdf of export intensity for each

underlying distribution of revenue shifters and different values of their shape and scale parameters.

Two remarks are in order in regards to the distributions (4)-(6). First, note that while in the

lognormal case the variance of revenue shifters can differ across markets, when revenue shifters are

distributed gamma or Fréchet, we need to assume that the shape parameter α is the same in the

domestic and export market. Doing so allows us to prove Proposition 3 for gamma-distributed

shifters, while for the case of Fréchet we require this assumption to obtain a closed-form expression

for the cdf of the ratio of revenue shifters (Nadarajah and Kotz, 2006). Second, when revenue

shifters are lognormal, export intensity follows a logit-normal distribution with scale parameter

ln psx{sdq and variance σ2zd�σ2zx; Johnson (1949) derives the main properties of this distribution.16We now move to describe the conditions under which the distribution of export intensity is

bimodal. These are spelled out in our second proposition:

Proposition 2. The distribution of export intensity is bimodal if:

16X is a logit-normal random variable if Y � logitpXq � X{p1�Xq is normally distributed. We thank Chris Jonesfor calling our attention to this fact.

17

• Revenue shifters are distributed lognormal, and the following two conditions are satisfied:

σ2zd � σ2zx ¡ 2, (7)and

|lnpsd{sxq| �σ2zd � σ2zx

�d1� 2

σ2zd � σ2zx� 2 tanh�1

�d1� 2

σ2zd � σ2zx

�. (8)

The two modes lie in the interior of the support but do not have a closed-form solution. The

major mode is located near 0 when sd{sx ¡ 1, and near 1 in the converse case; if sd{sx � 1,then the distribution is symmetric around 0.5 (see Figure B.4 in Appendix B.2.1).

• Revenue shifters are distributed gamma or Fréchet and α 1. In this case, the modes arelocated at 0 and 1. The major mode occurs at 0 when sd{sx ¡ 1, and at 1 in the conversecase; if sd{sx � 1, then the distribution is symmetric around 0.5.

Proof. See Appendix B.2.

Proposition 2 tells us that when the dispersion of revenue shifters is sufficiently high, the

distribution of export intensity exhibits twin peaks. The intuition is that since revenue shifters are

independent across destinations, the likelihood that firms face a very high demand in only one of

the two markets they serve—thereby generating export intensities close to either 0 or 1—is higher

when the dispersion of revenue shifters increases. A further increase in the variance of revenue

shifters in the lognormal case, or a reduction in the shape parameter under gamma or Fréchet,

makes the twin peaks more prominent by shifting probability mass towards the boundaries of the

support.

Although the critical value of the shape parameter necessary to produce bimodality is the same

in the gamma and Fréchet cases, there is a crucial difference between these two distributions.

Bimodality obtains with Fréchet shifters only when their dispersion is so high that their expected

value tends to infinite.17 This is problematic in models of monopolistic competition because the

integrals defining the price index and the free-entry condition would not converge. This is not

an issue for lognormal and gamma-distributed shifters because all the moments of these random

variables are finite.18

It is also important to note that the bimodality of export intensity can also arise when revenue

shifters follow distributions other than the three we consider in this paper. A notable example is

the Pareto distribution—perhaps the most frequently used distribution in the international trade

literature. Using simulations, we find that when revenue shifters are distributed Pareto with a

shape parameter below 1, the distribution of export intensity is multi-modal (it can have 2 or 3

17The central moment of order q for Fréchet-distributed random variables is finite if and only if α ¡ q.18Since the gamma random variable with shape parameter 1 follows an exponential distribution, it is the case

that twin peaks arise if gamma-distributed revenue shifters have dispersion greater than that of the exponentialdistribution.

18

modes)—however, Ali et al. (2010) show that the distribution of the ratio of two Pareto-distributed

random variables does not admit a closed-form expression.19 Other examples of distributions that

generate bimodal export intensity distributions are the beta, chi-squared and F distributions. Just

as in the case of Pareto, there is no closed-form expression for the pdf of the ratio of these random

variables, and therefore we need to use simulations to determine the number of modes.

Figure 4 shows how changes in sd{sx—caused for instance by a reduction on the iceberg tradecost faced by home exporters—affect the distribution of export intensity.20 As we move from Panel

I on the left to Panel III on the right, the relative size of the foreign market increases.21 The figure

also compares two distributions based on lognormal revenue shifters: the darker line shows the

distribution of export intensity when the sum of the variances of revenue shifters is equal to 4—

thus, producing a bimodal distribution—while the lighter line represents a unimodal distribution

(i.e. when σ2zd � σ2zx � 1).

Figure 4: Reduction in Export Costs with and without Twin Peaks

0 0.5 10

1

2

3

4

5

Pdf

Panel I

0 0.5 1Export Intensity

0

1

2

3

4

5Panel II

0 0.5 10

1

2

3

4

5Panel III

The figure plots the probability density function of export intensity when revenue shifters are lognormal with σ2zd �σ2zx � 4 (darker line) and σ

2zd � σ

2zx � 1 (lighter line) for different values of the ratio of scale parameters; namely,

sd{sx � 10 in Panel I, 2 in Panel II and 0.667 in Panel III.

In panel I of Figure 4, trade costs are so high that most exporters sell only a small share of

their output abroad regardless of the level of dispersion in revenue shifters, and therefore, the two

export intensity distributions look quite similar. As trade costs fall, the intensity of all exporters

increases and the distribution of export intensity shifts to the right. However, the difference in

the distribution with and without twin peaks also becomes starker. When the variance of revenue

19Pareto also has the same problem that we pointed out above for the Fréchet distribution—i.e. the expected valueof a Pareto-distributed random variable is infinite when the shape parameter is lower than 1.

20If both countries are symmetric in size and the reduction in trade costs is bilateral, this direct effect coincides withthe full general equilibrium change in relative market size. More generally, a lower trade cost also affects wages andprice indices in both countries. Demidova and Rodŕıguez-Clare (2013) show that it is not possible to unambiguouslysign the effect of trade liberalization on wages and price indices in the Melitz (2003) model when countries areasymmetric in terms of size, unless the model is fully parameterized and solved.

21To fix ideas, assume that the foreign country is twice as large as home, i.e. Ax{Ad � 2. Then, a sd{sx ratio of10 (Panel I) implies an iceberg cost of 4.47 (given σ � 3). Based on the same parametrization, the iceberg costs inPanels II and III are 2 and 1.15 respectively.

19

shifters is sufficiently large, greater access to foreign markets increases the prevalence of high-

intensity exporters moving mass from the left to the right tail of the distribution. In contrast,

when dispersion is lower, the increase in the intensity of exporters following liberalization is more

gradual.22

Discussion of Key Assumptions

There are two assumptions that are crucial in allowing us to prove Propositions 1 and 2: (i) firms do

not select into exporting based on the realization of revenue shifters and (ii) firms can only sell their

output in two markets. In this section we discuss the implications of relaxing these assumptions.

Selection into Exporting Based on Revenue Shifters. Suppose that firms observe the real-

ization of productivity and revenue shifters before deciding whether to export or not. In this case,

firms choose to export if the profits from selling abroad exceed the fixed cost of exporting—i.e.

when sx � Φpωq � zxpωq ¥ σwfx. This condition defines a downward-slopping mapping in tΦ, zxu-space; for a given level of productivity, only firms with sufficiently high foreign demand choose to

export, while only the most productive firms export for a given value of the export revenue shifter.

The truncation in the distribution of revenue shifters induced by the fixed cost precludes us from

using the method of transformations to characterize the pdf of export intensity because the pdf of

the ratio of truncated lognormal, gamma or Fréchet random variables do not admit a closed-form

expression.

Defever and Riaño (2017a) find that a bimodal export intensity distribution can arise when

there is selection into exporting based on productivity and lognormal revenue shifters when solving

the model numerically. In Appendix C we use simulations to show that when fixed costs increase,

the dispersion of revenue shifters among exporters is lower than the dispersion of the (ex-ante) un-

truncated distribution, and therefore the distribution of export intensity is less likely to be bimodal,

as measured by the dip statistic. For a given level of fixed costs, however, the main message of

Proposition 2 still holds true: the distribution of export intensity is bimodal when the dispersion of

revenue shifters is sufficiently high. The main difference relative to our benchmark model is that the

dispersion of revenue shifters necessary to generate bimodality increases when selection is present.23

More than Two Markets. Let us assume again that firms choose whether to export or not

based only on the realization of their productivity as in our benchmark model, but now consider

a situation in which a firm can sell its output in N � 1 markets: at home (indexed by 0) and N22Alessandria and Avila (2017) use the evolution of export intensity in Colombia between 1981 and 2013 to evaluate

the roles of trade liberalization reforms and improvements in firms’ exporting technology in accounting for theaggregate increase in the country’s openness to trade.

23Everything else equal, a greater dispersion of productivity also helps in generating twin peaks because it lessensthe truncation caused by the fixed cost.

20

foreign countries. A firm’s export intensity, conditional on exporting, is now given by:

Epωq �°Ni�1 ripωq°Ni�0 ripωq

�°Ni�1 sizipωq

s0z0pωq �°Ni�1 sizipωq

. (9)

In order to apply the method of transformations for random variables as we did in Proposition 1, we

require closed-form expressions for both the pdf of°Ni�1 sizipωq (i.e. the convolution of tsizipωqu)

and°Ni�1 sizipωq{s0z0pωq.

When revenue shifters are distributed gamma with shape parameter α and all foreign countries

are symmetric, i.e. when si � s for i � 1, . . . , N , then total export sales for a firm are distributedgamma with shape parameter Nα and scale parameter s. Since domestic sales are also distributed

gamma, we can still use the expression derived by Coelho and Mexia (2007) to derive the pdf

of export intensity, which does not require the shape parameter of the distribution of exports and

domestic sales to be the same. In this case, increasing the number of export markets that a firm can

sell to reduces the likelihood of obtaining a bimodal export intensity distribution as the dispersion

of export sales falls.

While there is no closed form expression available for the pdf of the convolution of lognormal or

Fréchet random variables, we can still make progress by noting that the sum of independent lognor-

mal random variables can be approximated by a lognormal distribution (Fenton, 1960). The Fenton-

Wilkinson approximation establishes that the distribution of X � °Ni�1 xi, where xi � LN pµx, σ2xq,can be approximated by a lognormal distribution with variance σ2X � ln

�1� exppσ2xq�1N

and mean

µX � ln pN exppµxqq � 0.5�σ2x � σ2X

�.

Using the Fenton-Wilkinson method to approximate the distribution of total export sales allows

us to use Proposition 1 to characterize the distribution of export intensity when the number of

foreign markets is greater than 1. The distribution of export intensity is bimodal when the sum of

the variance of total export sales and domestic sales is sufficiently large—just as in our two-country

benchmark.

In summary, our analysis suggests that high dispersion of firm-destination-specific revenue

shifters can also engender bimodal export intensity distributions when revenue shifters affect the

decision to export or when firms can serve multiple foreign destinations.

5 Estimation

In the previous section we showed that the distribution of export intensity is fully characterized

by the shape parameter governing the distribution of firm-destination-specific revenue shifters and

a country’s relative market size with respect to the rest of the world. We now discuss how we

estimate these parameters using the cross-country firm-level data from the WBES.

Identification Strategy. We first present a result that greatly facilitates the identification and

estimation of the parameters of interest. Namely,

21

Proposition 3. If revenue shifters are independent across firms and destinations and follow either

lognormal, gamma, or Fréchet distributions as specified in Proposition 1, then the median export

intensity, emed, is given by:

emed � sxsd � sx , (10)

which is independent of the shape parameter of revenue shifters.

Proof. See Appendix B.3.

We recover the relative market size for each country directly from the data by inverting equation

(10): �sdsx

� 1� e

med

emed. (11)

A highly convenient feature of (11) is that this measure of relative market size is invariant to the

underlying distribution of revenue shifters and the value of the shape parameter. Thus, Propo-

sition 3 allows us to estimate relative market sizes in a model-consistent way without having to

calibrate other parameters of the model such as fixed costs or the parameters governing the produc-

tivity distribution—all of which are necessary to calculate sd and sx when solving for the general

equilibrium of the model.

Conditional on relative market size, the identification of the shape parameter is quite trans-

parent. The value of this parameter is determined by whether the mass of the export intensity

distribution is concentrated in the interior or near the boundaries of the support. If the dispersion

of revenue shifters is low, then the distribution of export intensity is unimodal with most exporters

exhibiting an intensity close to sxsd�sx . On the other hand, if there are large clusters of exporters

with intensities near 0 and 1, then the shape parameter would satisfy the conditions described in

Proposition 2.

Scale Parameters. Figure 5 displays the distribution of the median export intensity in our data.

Although there is large variation across countries, the median export intensity ranges between 0.2

and 0.8 for most of them. In the lower end of the distribution, Brazil and Russia have a median

export intensity of 0.1, while at the other extreme, Bangladesh, Madagascar, Morocco, Pakistan,

Philippines and Sri Lanka all have a median export intensity greater than 0.9. Summary statistics

for the relative market size implied by countries’ median export intensity are reported in Table 4.

For the median country in our sample, the domestic market is 50% larger than the foreign one.

Country-Specific Shape Parameters. We first estimate country-specific shape parameters

for each of the three distributions of revenue shifters that we consider. These are estimated by

maximum likelihood conditional on relative market size being given by (11). Our objective is to

determine whether the conditions for bimodality of the export intensity distribution bear out in the

data. With our estimates of the shape parameter at hand, we then use the Vuong (1989) test to

22

Figure 5: Distribution of Median Export Intensity Across Countries

05

1015

20Fr

eque

ncy

(# C

ount

ries)

0 .2 .4 .6 .8 1Median Export Intensity

Source: World Bank Enterprise Surveys (WBES), 2002-2016.

Table 4: Inferred Relative Domestic Market Size

Mean Percentile5 25 50 75 95

xsdsx

1.967 0.010 0.667 1.500 2.333 5.667

compare the resulting distributions in terms of their fit to the data.24 This test has two desirable

properties for our purposes: first, it can be used to compare non-nested econometric models—in

particular those that are obtained from different families of distributions, as in our case. Second,

the test is directional—i.e. it indicates which competing model fits the data better when the null

hypothesis that the two models are indistinguishable from each other is rejected.

It is important to note that the export intensity pdfs we derive are not defined at an export

intensity of 1—i.e. they do not admit firms exporting all their output. Since ‘pure exporters’ are

ubiquitous in the data, we need to censor their export intensity, and we do so at a conservative value

of 0.99. Increasing the censoring cutoff biases the shape parameter in the direction of bimodality

(i.e. lowers the shape parameter for gamma and Fréchet and increases the sum of variances in the

lognormal case). This happens because the distribution of revenue shifters would need to generate

large shares of extremely low and high realizations to be able to produce a significant number of

exporters with intensity at or above the censoring threshold.25 To ensure that our results are not

driven by our choice of censoring threshold, in Section 7 we also re-estimate the shape parameter

dropping all pure exporters.

24Vuong’s is a likelihood-ratio (LR) test based on the Kullback-Leibler information criterion. Mrázová et al. (2015)also use the Kullback-Leibler divergence to evaluate how different combinations of demand functions and productivitydistributions fit the size distribution of French firms exporting to Germany.

25For instance, for a firm to have an export intensity of 0.99, its export revenue shifter has to be 99 times largerthan its domestic one; increasing the censoring threshold to 0.999 would shift this ratio up by an order of magnitude.

23

The country-specific shape parameter estimates are reported in Table E.1 in Appendix E. In

all but a handful of cases they imply export intensity distributions that are bimodal. The mean

estimates across countries are 6.489 for lognormal and 0.672 and 0.740 for gamma and Fréchet-

distributed revenue shifters respectively. In the lognormal case, all shape parameters satisfy con-

ditions (7) and (8) for bimodality (see Figure B.5 in Appendix B.2.1). When revenue shifters are

distributed gamma or Fréchet, we estimate shape parameters greater than 1 for 6 and 7 countries

respectively—all of which are identified as unimodal by the dip test reported in Figure 3.

Using customs-level data from France and the World Bank’s Export Dynamics Database re-

spectively, Eaton et al. (2011) and Fernandes et al. (2018) estimate structural models of trade that

incorporate lognormal firm-destination-specific revenue shifters. Although their models are richer

than ours—including, for instance, heterogeneity in fixed costs and convex marketing costs—they

both find that the variance of firm-destination-specific revenue shifters is large enough to generate

bimodality in our model.26

The results of the Vuong (1989) test reported in columns (1)-(3) and (7)-(9) of Table F.1 in

Appendix F do not indicate that one of the underlying distributions of revenue shifters clearly dom-

inates the others. Comparing the lognormal-based export intensity with the gamma and Fréchet

distributions reveals that in 20 countries we cannot discriminate between the two competing mod-

els, while the remaining ones are evenly split between lognormal and the competing distribution.

Among the set of countries for which lognormal performs worse than the alternative, gamma fits

the data better than Fréchet in all but two countries.27

6 Bimodality and Relative Market Size

The results presented above show that the conditions to generate a bimodal export intensity dis-

tribution are satisfied in most countries, regardless of the specific distribution of revenue shifters

we assume. Figure 3, however, shows that we cannot reject the null hypothesis of unimodality for

one third of the countries in our data. How does our model reconcile these seemingly contradictory

results?

In this section we show that given a sufficiently high dispersion of revenue shifters, differences

in countries’ relative market size vis-à-vis the rest of the world explain the variation in the distri-

butions of export intensity around the world extremely well and also why the dip test fails to reject

unimodality in some cases.

To focus on the role of relative market size, we assume that firms in all countries draw both

of their revenue shifters from a distribution with the same shape parameter. This means that all

the variation in the distribution of export intensity across countries is due to differences in their

26Eaton et al. estimate the variance of firm-destination specific revenue shifters to be 2.856, while Fernandes et al.find it to be 6.60. In comparison, if we assume agnostically that the variance of domestic and export shifters is thesame, the point estimate reported in column (1) of Table 5 implies a value of 3.24.

27When the Vuong test indicates that lognormal dominates gamma it also indicates that the former provides abetter fit than Fréchet. The only exception is for Uganda in which the test rejects gamma in favor of lognormal butcannot discriminate between lognormal and Fréchet.

24

market size relative to the rest of the world. We estimate this ‘restricted’ single-shape parameter

model by pooling together data across all countries, weighting each observation by the inverse of

the number of exporters in each country such that each country receives an equal weight.28

Table 5 reports our results. The point-estimates are very close to the average across the country-

specific shape parameters, and all imply bimodality. Notably, the Vuong test reveals that we cannot

discriminate between the restricted model and the one where shape parameters are country-specific

(see columns (4)-(6) and (10)-(12) of Table F.1 in Appendix F) in approximately two-thirds of the

countries in our sample—even though the latter model fits the data better by definition.

Figure 6 presents the fit of the three single-shape-parameter models to the data, with countries

sorted according to their estimated relative market

the twin peaks of the export intensity...

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