Latent Exports: Almost Ideal Gravity and Zeros∗

James E. Anderson† Penglong Zhang‡

November 2019

Abstract

The Almost Ideal gravity model generates zero trade flows from variable and fixed

trade cost variations within a flexible demand structure. Latent predicted trade shares

between non-partners are based on the Tobit estimator of the model applied to bilat-

eral trade among 75 countries and 25 sectors in 2006. Latent Trade Bias (LTB) is the

difference between the latent trade share and the as-if-frictionless trade share. The ex-

plained LTB variance is decomposed into 48% from variable trade cost combined with

heterogeneous price elasticities, 26% from non-homothetic income effects, and 26%

from fixed trade cost. Export promotion effects on zeros are quantified with counter-

factual variable (fixed) cost cuts. Elimination reduces zeros by 88% (33%). Cuts of

10% suggest successful export promotion for targeted cases.

Keywords: Zero flows, variable cost, fixed cost, latent trade.

JEL Codes: F10, F14.

∗We thank Pol Antras, Andrew Bernard, Arnaud Constinot, Thibault Fally, Marc Muendler, DennisNovy, Theodore Papageorgiou, Steve Redding, Anthony Venables and seminar participants at the Aus-tralasian Trade Workshop, Boston College, the Empirical Investigations in Trade and Investment Workshop,and the Tsinghua Workshop on International Trade for their helpful comments.†Boston College, Department of Economics, Chestnut Hill, MA 02467, email: james.anderson@bc.edu.‡Tsinghua University, School of Public Policy and Management, Beijing, 100084, email: zhangpeng-

long@tsinghua.edu.cn.

1 Introduction

Zeros dominate bilateral product-level trade flows, and changes on the extensive margin

(entry or exit) of trade account for a significant portion in trade volume.1 The standard

Constant Elasticity of Substitution (CES) gravity model loads all of the explanation of ze-

ros onto fixed export costs – per-unit trade costs have no role. In contrast, economic intu-

ition suggests that choke price exceeded by high per-unit trade cost may be an important

alternative explanation for zeros. Choke price variation is intuitively likely to be large –

demand elasticities with respect to price vary across source countries and bilateral trade

costs vary across destinations. Income effects may differ across destination countries, as

variations in income per capita interact with income elasticities that differ from one. An

Almost Ideal (Demand System) gravity model is developed in this paper to explain zeros

by a combination of choke price variation and fixed export costs. Variable costs and their

interaction with varying demand elasticities account in the estimated model for a much

higher proportion of zeros than do fixed costs or varying income elasticities.

The estimated model is used to evaluate the potential for export promotion on the ex-

tensive margin. Export promotion motivates national policy, both unilateral and in trade

negotiations, while firms seek potentially profitable destination markets that are not cur-

rently being served. Measures of the extent of the various causes of zeros are needed

to guide extensive margin export promotion. Some types of export promotion policies

are permissible under WTO rules, basically affecting fixed costs via providing informa-

tion, facilitating links, helping with licensing and regulation requirements, and negoti-

ating bilateral fair treatment in the application of regulations. Exporter countries could

target export promotion more effectively if they knew which cost was more important.

1A report on the incidence of zeros in U.S. trade in 2005 by Baldwin and Harrigan (2011) shows thatthe U.S. imports nearly 17,000 different HS10 categories from 228 countries, but over 90 percent of thesepotential trade flows are zeros. Besedes and Prusa (2006) examine time-series variation in product-levelzeros. They find that there is a remarkable amount of entry and exit in the U.S. import market, and thatthe period of time a country is ‘in’ the market is often fleeting. About 30% of trade relationships experience‘flipping’ on and off.

1

Commercial attaches to embassies and consulates in each destination could allocate time

between intensive and extensive margin export trade accordingly. Exporting firms could

target entry markets more effectively with a sense of which of the zeros were viable for

given cost advantages.

A gravity model based on Almost Ideal Demand System (AIDS) preferences and het-

erogeneous firms has a closed form suitable for estimation. The version developed in this

paper is flexible enough to allow heterogeneous price and income elasticities to interact

with a combination of fixed costs and iceberg costs in determining trade flows both posi-

tive and latent. Trade Bias is the difference between predicted trade and as-if-frictionless

trade, the absolute value of a negative number for cross-border trade. Latent Trade Bias

(LTB), as used in this paper, is the difference between the latent trade share and the as-if-

frictionless trade share – a Trade Bias concept applicable to both latent and positive trade.

The Tobit estimator of AI gravity predicts the latent value of bilateral trade shares for non-

partners, given the inferred bilateral iceberg costs and entry costs as well as the demand

parameters. The estimated sectoral AI gravity model implies that, on average, variable

cost explains 48% of the variation in LTBs, while fixed cost explains 26%. The remaining

26% is explained by income effects on demand due to the variations in per capita income

interacting with variation in origin-specific income elasticities. Variable cost dominates

fixed cost and income effects for all sectors. The variation in the causes of zeros implies

differences in the efficacy of export promotion policies on the extensive margin.

AI gravity is estimated using the bilateral manufacturing trade data among 75 coun-

tries and 25 sectors in 2006. In order to reduce the parameter dimension, we project the

price elasticity as a linear function of exporter income. Intuitively, goods produced by rich

countries are less likely to be substituted for, and thus are price-inelastic. The estimation

results show that bilateral distance reduces trade by less for richer exporters. This sug-

gests that there is a significant distance (price) elasticity heterogeneity across exporters.

In addition, the price elasticity heterogeneity varies significantly across sectors.

2

Counterfactual experiments in export promotion assess the relative importance of

variable and fixed costs in preventing trade from occurring. Cost reductions can shift

the delivered price below the price associated with the break-even quantity. An extreme

counterfactual eliminates either variable or fixed cost. On average, the elimination of bi-

lateral variable cost decreases the number of current sectoral zero flows much more than

does the elimination of bilateral fixed cost. These are the upper bounds for what the hypo-

thetical export promotion policy could do. More relevant to export promotion targeting,

a 10% cut in variable cost induces trade in a much larger number of potential bilateral

pairs than does a 10% cut in fixed cost. Here, the two-digit level of the data presumably

hides a much larger number of potential targets in more disaggregated sectors.

An alternative clue to export promotion from our application is that reducing vari-

able cost improves the probability of a new trading partner more if the source country is

poorer. The results are consistent with the intuition that products from poor countries are

more price-elastic and thus are more likely to induce trade to occur when variable trade

costs decrease. In contrast, reducing export fixed cost (e.g., regulation cost) improves the

probability symmetrically across exporters. The marginal effect of reducing fixed cost on

switching zero trade to positive is smaller than reducing variable cost.

A headline example is Ethiopia’s export trade in leather goods in 2006. The application

suggests that a 10% cut in pair-specific fixed entry cost would open 16 export markets. A

10% cut in pair-specific variable cost would open 38 export markets. In both cases, the

new destination markets of Ethiopia’s leather goods are mainly in countries with middle

to high income per capita (e.g., Norway and Poland in Europe, and Canada and Mexico

in North America).

Our methods to conduct counterfactual export promotion experiments should be re-

garded as a “proof of concept”. Our estimation strategy is based on choosing variable

and fixed cost proxies that plausibly do not affect both.2 Variable cost is proxied by bi-

2Variables such as Free Trade Agreement membership, common language, common legal traditions etc.affect both fixed and variable cost. Tariffs are directly a variable cost but may be systematically related to

3

lateral distance. The fixed cost proxy is the regulation cost of firm entry. Future work

on export promotion targeting should add to our inferred measures of variable and fixed

costs any available direct trade cost measures. Variable and fixed cost counterfactuals can

combine variation in such costs with the structural gravity parameters estimated with our

methods.

Our treatment of zero trade flows contrasts with preceding literature. One treatment

in the literature assumes away an extensive margin by modeling trade as a Poisson arrival

process with zeros accounted for as events with no observed shipments in the observation

window. Allowing for an extensive margin implies that standard CES gravity estimators

that exclude zero flows are potentially biased due to selection effects. Helpman, Melitz,

and Rubinstein (2008) adopt the Heckman two-stage estimation procedure that uses an

equation for selection of trade partners in the first stage and a trade flow equation in the

second.3 Baldwin and Harrigan (2011) add quality-selection to the Melitz (2003) model

and, together with productivity-selection, show that only firms with the lowest quality-

adjusted price export. Choke prices without fixed costs can be generated in quadratic

demand systems, e.g., in Melitz and Ottaviano (2008), but this structure does not generate

a tractable model suitable for estimation. Also, Pollak and Wales (1992) offer evidence

that the translog somewhat outperforms the quadratic expenditure system in household

budget studies. Novy (2013) uses the one-parameter translog demand system by Feenstra

(2003) to derive a micro-founded gravity equation that features an endogenous trade cost

elasticity and potential choke prices, but does not explore zeros since there are very few

zeros in his sample.4 This demand structure is the special case in which all goods enter

“symmetrically”.

fixed costs (i.e., interest group pressures for tariffs are low in sectors where fixed costs already limit trade.)3Fixed costs of bilateral exporting combined with heterogeneously productive firms and CES demand

are the explanation for zeros in influential literature based on Melitz (2003). Firms draw productivities froma bounded Pareto distribution. The value of the bound is essential to the model because there would beno zeros with a sufficiently high bound. In this sense, fixed cost alone explains zeros – sufficiently highvariable cost cannot generate zeros in the CES structure with the elasticity of substitution greater than one.

4Novy (2013) uses aggregate exports among 28 OECD countries for the year 2000. Only seven of thebilateral observations are zeros.

4

Our alternative AI gravity model implies that latent trade is associated with observed

zeros while the same model applies to positive trade flows. A Tobit estimator of AI grav-

ity is thus appropriate, treating the zero flows as left-censored observations at zero. In

contrast to homothetic demand systems, choke prices can be due to the combined effect of

high income-elasticity and low per capita income. Applying this insight, Fajgelbaum and

Khandelwal (2016) extend Feenstra’s one-parameter translog to a nonhomothetic AIDS

gravity structure with income elasticities that can vary by source country. We extend their

model to allow price (variable cost) elasticity heterogeneity across all N source countries.5

Our version of AIDS allows variable cost to affect trade (including latent trade) flows dif-

ferently across exporters. It is a reasonable compromise between parsimony and a realistic

approximation of origin-specific variations in demand elasticity reflecting quality varia-

tions inter alia. Relative to Fajgelbaum and Khandelwal (2016) we find that allowing for

price elasticity variation greatly reduces the role of income elasticity variation.

Our paper is also related to a wider literature on zeros in international trade. Armenter

and Koren (2014) propose a statistical model using balls and bins to account for the large

number of zeros in firm- and product-level international shipments. Our economic struc-

tural model accounts for the same pattern in a setting from which policy implications are

drawn. Eaton et al. (2012) show that the standard heterogeneous firm model can be mod-

ified to generate an integer number of firms that account for the zeros in bilateral trade

data. Our model nests heterogeneous firms within a more general demand structure.

The remainder of the paper is organized as follows. The next section presents the zero

flows in data. Section 3 derives the Almost Ideal gravity model. The model estimation

is discussed in Section 4, and applied to quantify causes of the zero flows in Section 5.

Section 6 conducts counterfactuals on export promotion policies. Section 7 concludes. An

online appendix contains additional details on derivation of the model, descriptions of

the data and estimation, robustness checks and added counterfactual details.5The general bilateral price elasticity matrix of AIDS has N × (N − 1)/2 parameters in Deaton and

Muellbauer (1980). AI gravity as applied here reduces the number of parameters to N × 1.

5

2 Zeros in the Data

We use trade and production data for the world’s 75 largest economies in the year of

2006 sourced from CEPII.6 The data record bilateral trade flows and production across 25

industrial sectors in the International Standard Industrial Classification (ISIC) Revision 2.

Thus, there are 75*75 = 5625 country pairs (including domestic trade observations). On

average, the frequency of zeros across all sectors and pairs is 28%. Figure 2 shows the zero

flow frequency in each sector. The blue bars represent the fraction of zero flows, while

the yellow bars are the fraction of positive flows. The zero flow frequency in the leather

sector is closest to the average level. 15% of the country pairs do not trade machines. 65%

of the trade flows in the tobacco sector among the country pairs are zero. Zero trade flows

are more likely to occur in tobacco, petroleum, and furniture sectors, while less likely to

occur in machinery, electrics, and textiles sectors.

Zeros could be simply a result of a group of countries not trading with one another.

To dismiss this possibility, we take the ”average” sector, leather, as an example.7 Figure 3

plots the trade matrix among all importers (rows) and exporters (columns) in descending

order ranked by GDP. So the first row (column) displays the U.S. import from (export to)

each country (including itself). The second row (column) follows Japan and succeeding

columns follow Germany, China, etc.8 Again, the blue dots represent zero flows, and

the yellow dots represent positive observations. The diagonal elements are the domestic

trade of each country and are all positive. Note first the general sparseness of the trade

matrix – the fraction of zero observations is around 30%, and almost all countries are

associated with zero flows. More specifically, there are zero flows in every row (column),

meaning that no one imports (exports) leather products from (to) everywhere. The two

exceptions appear in the third and fourth columns – Germany and China export their

6See Appendix Table B.1 for the country list.7The zero frequency of international trade in the leather sector is 30%, close to the average zero frequency

of 28%.8Notice the year is 2006 in our sample.

6

leather products everywhere. Second, note that zero relationships are concentrated in

the lower-right corner, implying smaller countries are less likely to trade with each other.

Third, note the many zeros in the lower-left (upper-right) corner, which suggests that

even large importers (exporters) are associated with many zeros. For example, the U.S.

neither exports leather products to nor imports them from Tajikistan. The trade flow is

also zero from the U.S. to Yemen. Furthermore, even some of the large economies do

not trade with each other to some extent. For example, the observations from Russia

to Ireland, from Chile to Russia, and from Norway to Indonesia are all zeros. Fourth,

more zero relationships are distributed in the upper triangular matrix than in the lower.

This implies that small exporters generate more zero flows than small importers do in the

leather sector trade.

Although the zero frequency is different across sectors, the distribution pattern is very

similar to that in the leather sector. The prevalence of zeros in sectoral trade does not just

come about because of a certain group of countries, but every country is involved to some

extent. (See Appendix Figures B.1-B.4 for the trade matrix of each sector).

3 Model

This section outlines a general equilibrium model and derives a gravity equation that can

reconcile both positive and zero international trade flows.

3.1 Preferences

We consider a world economy with N countries, a continuum of goods ω ∈ Ω, and labor

as the only factor of production. Denote the exporter as i and the importer as j. Con-

sumers have the Almost Ideal Demand System (AIDS) preference introduced by Deaton

and Muellbauer (1980), which can be rationalized as a non-homothetic second-order ap-

proximation to an arbitrary expenditure system. Specifically, in any country j, there is a

7

representative consumer with an expenditure function given in logarithmic form as

ln ej = ln Qj + uj ∏ω∈Ωj

pj(ω)φ(ω), (1)

where ej is the minimum expenditure at which the consumer can obtain utility uj given

prices pj(ω). The Ωj denotes the set of goods available in country j. The price index ln Qj

is given in logarithmic form as

ln Qj =∫

ω∈Ωj

α(ω) ln pj(ω)dω +12

∫∫ω,ω′∈Ωj

γ(ω, ω′) ln pj(ω′) ln pj(ω)dω′dω. (2)

To satisfy homogeneity of degree one, the parameters are constrained by α(ω) ∈ (0, 1),∫α(ω)dω = 1 and

∫γ(ω, ω′)dω = 0 for any ω′. Symmetry is imposed to satisfy Young’s

Theorem, γ(ω, ω′) = γ(ω′, ω). Concavity is imposed by the requirement that γ(ω′, ω)

is negative semi-definite.

We let

γ(ω, ω′) =

γβ(ω)β(ω′), if ω 6= ω′

−γβ(ω), otherwise,(3)

where β(ω) ∈ (0, 1) and∫

β(ω)dω = 1. Specialization (3) satisfies the general restric-

tions of the AIDS but imposes a tight restriction on the cross-effects. In particular, com-

plementarity is ruled out – all off-diagonal terms of the substitution effects matrix are

non-negative.9

Applying Shephard’s lemma and differentiating the expenditure function with respect

to log price pj(ω) generates the expenditure share in good ω for consumers at country j

equal to

sj(ω) = α(ω)− γβ(ω) ln

(pj(ω)

pj

)+ φ(ω) ln rj, (4)

9β(ω) = β(ω′), α(ω) = α(ω′) for all ω and ω′, is the special case proposed by Feenstra (2003) followedby Arkolakis, Costinot, and Rodriguez-Clare (2010), Novy (2013), and Fajgelbaum and Khandelwal (2016).

8

where

ln pj =∫

ω∈Ωj

β(ω) ln pj(ω)dω. (5)

These expenditure shares have some nice features. First, α(ω) is a taste parameter

for the good ω, which shifts the expenditure share independently from the prices and

income. Second, γβ(ω) is the price elasticity for good ω. The variation of β(ω) allows

for asymmetric demand responses to price changes. This gives AIDS preference CES-like

components because the price terms −γβ(ω) ln(pj(ω)/ pj) captures cross-effects in sub-

stitution with the log of a ratio of own price to an average price pj. Third, φ(ω) is the

income elasticity which captures the non-homothetic component of the preference. Posi-

tive φ(ω) implies luxury goods (with high quality) while negative φ(ω) implies necessary

goods (with low quality).10 We refer to rj = ej/Qj as adjusted real income (expenditure)

by individual price index. When φ(ω) = 0 for all ω, AIDS becomes the homothetic

translog preference. When β(ω) = 0 and φ(ω) = 0 for all ω, AIDS becomes the Cobb-

Douglas preference. AIDS allows for choke prices beyond which demand is zero, defined

by: ln pmaxj = [α(ω) + γβ(ω) ln pj + φ(ω) ln rj]/γβ(ω).

3.2 Firms

In any country i, there is a pool of monopolistically competitive firms. With the demand

function (4), firm ω maximizes its profit pj(ω)qj(ω)− witijz(ω)

qj(ω) where qj(ω) is the quan-

tity, tij > 1 reflects bilateral iceberg trade cost between country i and country j, and

wi is the wage rate. Assume symmetry across the varieties ω from country i such that

α(ω) = αi, β(ω) = βi, and φ(ω) = φi.

Assume firms cannot observe their productivities until they set their markups. The

firms in each country i draw productivities from the same distribution, so they set a

10Note that γβ(ω) and φ(ω) are semi-elasticities since they relate expenditure shares to logs of prices andincome, but we refer to them as elasticities to save notation.

9

common markup, but markups can vary by country of origin.11 The profit-maximizing

markup is 1 + (γβi)−1sij if markets are segmented. For simplicity, we assume that mar-

kets are not segmented,12 hence arbitrage forces markups by firms of country i to be the

same across destinations. Firm ω from country i thus sets its markup based on the ex-

pected firm share in the world market which is denoted as si. The common markup is

denoted as µi. Thus

µi = 1 + (γβi)−1si. (6)

Then a firm receives a productivity in log-level ln z randomly from a distribution F(.).

The equilibrium price in log is

ln pij(z) = ln µiwitij − ln z. (7)

From equation (4), firm z’s market share in country j is

sij(z) = αi − γβi ln(µiwitij/ pj) + φi ln rj + γβi ln z, (8)

and its profit

πij(z) = (1− µ−1i )sij(z)Ej − Fij, (9)

where Ej is the total expenditure of country j, Fij denotes the fixed cost for firms from

country i export to country j. Then from zero profit condition πij(z∗ij) = 0, we can get the

cutoff productivity in log is

ln z∗ij = (γβi)−1[

µi

µi − 1fij − αi + γβi ln(µiwitij/ pj)− φi ln rj], (10)

11In contrast, models of monopolistic competition with CES preferences require uniform mark-ups bycountry of origin.

12The assumption avoids having to deal with a complex endogeneity problem in firm-destinationmarkups, but is also plausible for many sectors. Segmented markets require firm-destination-specific bar-riers that prevent spatial arbitrage. For many products, these seem unlikely. Nevertheless, the no segmen-tation assumption rules out pricing-to-market behavior observable in some well-known sectors.

10

where

fij = Fij/Ej (11)

denotes the adjusted fixed cost by the total market expenditure. For simplicity, let’s de-

note a = ln z and assume a follows a special bounded Pareto distribution with accumula-

tive density function as

G(a) =ln aln H

, 1 < a < H, (12)

where 1 and H are the lower and upper bounds of the distribution, respectively. Parame-

ter H also reflects the dispersion of the productivity.

3.3 Aggregates

Let Sij denote the total market share of country j imports from all firms of country i. By

definition, the bilateral import share is

Sij = Ni

∫ H

ln z∗ijsij(a)dG(a), (13)

where Ni is the measure of firms in country i. Then equation (8) and (10) give,13

Sij/Ni = α′i − γβ′i ln(µiwitij/ pj)− λ′i fij + φ′i ln rj, (14)

where

α′i = (1/ ln H)αi + (H/ ln H)γβi (15)

β′i = (1/ ln H)βi (16)

λ′i = (1/ ln H)µi/(µi − 1) (17)

φ′i = (1/ ln H)φi. (18)

13Proof in Appendix A.1.

11

Note that α′i, γβ′i, and φ′i are productivity-adjusted tastes, productivity-adjusted price

elasticities, and productivity-adjusted income elasticities. Thus, α′i > 0, γβ′i > 0, φ′i

and φi have the same sign. Relative to αi, γβi, and φi, they include dependence on the

supply side productivity distribution parameter H. Finally λ′i is the marginal effect of

fixed cost on trade shares. The coefficients satisfy ∑i Niα′i = (1/ ln H) + (H/ ln H)γ,

∑i Niβ′i = (1/ ln H), and ∑i Niφ

′i = 0. And thus βi = β′i/ ∑i Niβ

′i. Note that the total

number of firms Ni is exogeneously given, but the fraction of firms that export is endoge-

nously determined.14

Aggregate share per firm in (14) is decomposed into four parts. The first term α′i in-

cludes all origin-specific factors and the last term φ′i ln rj includes all destination-specific

factors multiplied by an origin-specific coefficient. The two terms in the middle are the

effects of bilateral variable costs and fixed costs.

3.4 Gravity

Market clearance for each origin i is given by

Yi = ∑j

SijEj, (19)

where Yi is the total income of country i. Using market clearance in the AIDS share equa-

tion yields the AI gravity equation.15 Thus:

Sij/Ni −Yi

Y/Ni = −γβ′i ln(

tij

ΠiPj)− λ′i( fij −Ψi) + φ′i ln(rj/R), (20)

14The endogenous fraction of exporting firms is also in the firm heterogeneity models of Chaney (2008)and Novy (2013).

15Proof in Appendix A.2.

12

where Y is world total income, and

ln Πi ≡∑j(Ej/Y) ln tij, (21)

ln Pj ≡∑i

Niβi ln(tij/Πi), (22)

Ψi ≡∑j(Ej/Y) fij, (23)

ln R ≡∑j(Ej/Y) ln rj. (24)

On the left hand side, Sij/Ni − YiY /Ni is the deviation of bilateral trade per firm from

its frictionless level YiY /Ni. There are three terms on the right hand side, which cap-

ture the variable cost effect, fixed cost effect, and income effect, respectively. The first term,

−γβi ln(

tijΠiPj

), is the effect of relative bilateral trade resistance from origin i to destina-

tion j where ln Πi and ln Pj are the outward and inward multilateral resistances in logs,

respectively. The relative resistance term is very similar to the CES structural gravity

of Anderson and van Wincoop (2003). The last term, φi ln(rj/R), is the non-homothetic

component of the gravity equation and captures the effect of relative income per capita of

market j where ln R is the average world income per capita in log.

The middle term,−λ′i( fij−Ψi) exploits the AI structure to capture the effect of relative

trade “fixed cost” that reduces bilateral trade via the firm-level extensive margin from

origin i to destination j. The intuition is that fixed cost raises the market entry barrier

and fewer firms export. We refer to Ψi as the outward “multilateral fixed resistance” that

summarizes the average trade fixed cost between a country and its trading partners.

We dub equation (20) the Almost Ideal (AI) gravity model. A simple justification is

that this gravity representation of equilibrium trade is derived from the Almost Ideal

Demand System. A deeper justification is that (20) is the most flexible and complete

gravity model in the international trade literature thus far: (i) AI gravity includes both

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variable and fixed trade costs; (ii) AI gravity incorporates both the intensive margin and

the extensive margin of trade; (iii) AI gravity has non-homothetic components; (iv) AI

gravity allows for asymmetric price elasticities across exporters; and (v) AI gravity can

generate latent trade flows analytically.

4 Estimation

The estimation of AI gravity derived in Section 3 is described in this section. Section 4.1

describes the data and specifications. Estimation results using aggregate trade data are

presented in Section 4.2 and results using sectoral trade data are presented in Section 4.3.

4.1 Data and Specifications

Trade and production data for 75 countries in the year 2006 comprise the sample.16 We

follow Novy (2013) to measure the number of goods that originate from each country, Ni,

with the extensive margin data constructed by Hummels and Klenow (2005). The exten-

sive margin is measured by weighting categories of goods by their overall importance in

exports.17

Bilateral variable cost is projected by

ln tij = ρ ln distij + εtij, (25)

where dij is bilateral distance as calculated by CEPII. We follow Helpman, Melitz, and

Rubinstein (2008) to proxy fixed trade cost by the regulation costs of firm entry, collected

and analyzed by Djankov, La Porta, Lopez-de Silanes, and Shleifer (2002). These entry

costs are measured via their effects on the number of days, the number of legal proce-

dures, and the relative cost (as a percentage of GDP per capita) for an entrepreneur to

16Details are discussed in Section 2.17We also use other measures for the number of goods as robustness checks in Section C.1.

14

legally start operating a business. We use the monetary cost in our baseline estimation

and non-monetary costs in the robustness check.18 Moreover, we construct the bilateral

fixed cost as the average cost for an entrepreneur to start a business in the exporter and

the importer country. Thus it is country-pair specific. Then we divide this cost by the im-

porter’s total expenditure, according to equation (11), to compute the adjusted bilateral

entry cost fij.

A key estimation problem faced by all attempts using gravity to separate inferred fixed

from variable costs is the need to find proxies that arguably do not affect both. Our proxy

for variable cost is bilateral distance.19 We augment the variable and fixed cost proxies

with a uniform cross-border friction that in principle combines both variable and fixed

cost components. We check for omitted variable bias due to our sparse specification of

trade frictions by adding standard trade frictions (contiguity, common language, colonial

relationship, and common colonizer) to the gravity equation. Our estimates turn out to

be essentially invariant to these added frictions.

Recall that real expenditure per capita is defined as ln rj = ln(ej/Qj) where ej, nominal

expenditures per capita, are observable. Aggregate price index ln Qj can be proxied by a

Stone index following the literature,20 that is

ln Qj =N

∑i=1

Sij ln(piidistρ0ij ), (26)

where pii are the quality-adjusted prices estimated by Feenstra and Romalis (2014). We

pick ρ0 = 0.177 following Fajgelbaum and Khandelwal (2016).

18See Appendix Section C.3.19Many of the standard proxy variables in the gravity literature reflect both. For example, trade partner-

ships and common language very likely affect both fixed and variable trade costs. Even tariffs could reflectboth if high fixed cost in protectionist countries is associated with low tariffs.

20Deaton and Muellbauer (1980) were first to use a Stone index to proxy the AIDS price index. The tradeliterature, like Atkin (2013) and Fajgelbaum and Khandelwal (2016), uses this approximation.

15

The AI gravity equation derived above is

Sij/Ni −Yi

Y/Ni = −γβ′i ln(

tij

ΠiPj)− λ′i( fij −Ψi) + φ′i ln(rj/R),

where there are a large number of parameters to be estimated. There is a set of productivity-

adjusted variable cost (price) elasticities γβ′i, a set of fixed cost elasticity parameters

λ′i, and a set of productivity-adjusted income elasticities φ′i. In order to reduce the

number of estimated parameters, we impose some restrictions. First, we impose the con-

straint φ′i = c0 + c ln ri where c > 0 and ri is the exporter income, similar to Fajgelbaum

and Khandelwal (2016). This is because rich countries are more likely to export high-

quality goods. The theoretical restriction ∑Ni=1 Niφi = 0 implies c0 = −c ∑N

i=1 Ni ln ri,

transforming this linear relationship to

φ′i = c(ln ri − ln r), (27)

where ln r = ∑Nk=1 Nk ln rk, and reducing the number of productivity-adjusted income

elasticities to be estimated from N to one, i.e., coefficient c.

Second, we assume productivity-adjusted price elasticities are also correlated to ex-

porter income. Specifically

γβ′i = b0 − b1 ln ri, (28)

where ri is the GDP per capita of the exporting country i and b1 > 0.21 Poor countries are

more likely to export price-elastic goods. Then we reduce the number of productivity-

adjusted price elasticities to be estimated from N to 2, i.e., coefficients b0 and b1.22

Third, we impose a symmetric fixed cost effect, i.e.

λ′i = λ, (29)

21Novy (2013) and Fajgelbaum and Khandelwal (2016) assume symmetric price elasticities, i.e., b1 = 0.22We also use exporter-specific fixed effects to estimate γβ′i as robustness checks in Appendix Section C.2.

16

and λ > 0. This is reasonable because we focus on aggregate and sectoral trade instead

of firm-level trade, and thus the markup differences implicitly in λi are not the interests

of the paper.23 Then the specification of the AI gravity equation becomes

Sij/Ni = −b0ρ ln distij + b1ρ ln ri × ln distij − λ entrycostij + c ln ri × ln rj

+ δ Internalij + b1 ln Pj × ln ri + f ei + f ej + εij, (30)

where f ei =YiY /Ni + (b0 − b1 ln ri) ln Πi + λΨi − φ′i ln R, and f ej = b0ρ ln Pj − c ln rj × ln r

are exporter- and importer-specific fixed effects. The multilateral resistance terms ln Pj are

not observable since they have inside parameters βiNi=1. But b1 ln Pj can be controlled by

exporter-specific coefficients on ln ri. We also add a dummy variable Internalij, which is

0 for import and 1 for internal trade, to capture all the other unobserved trade cost across

border, similar to Ramondo et al. (2016) and Anderson and Yotov (2017). Unfortunately ρ

cannot be identified from b0 and b1. So we pick ρ = 0.117 directly following the literature,

and then b0 and b1 are identified. We expect the coefficients of ln distij and entrycostij

are both negative, while those of the interaction terms ln ri × ln distij and ln ri × ln rj are

both positive. In other word, all parameter estimates b0, b1, λ, c should be positive. The

productivity-adjusted elasticity parameters are identified by

γβ′i = b0 − b1 ln ri

λ′i = λ

φ′i = c ln(ri/r).

Unfortunately, γ and β′i cannot be identified form each other. The original demand pa-

rameters φi cannot be identified from the productivity distribution parameter H. But the

23See equation (17). We also estimate the asymmetric case as a robustness check in Appendix Section C.4.

17

original βi are identified by

βi = (b0 − b1 ln ri)/ ∑k

Nk(b0 − b1 ln rk). (31)

To investigate more extreme variation of zero trade flows, we estimate sectoral AI

gravity equations using disaggregated data. Specifically, we estimate

Skij/Ni = −bk

0ρ ln distij + bk1ρ ln rk

i × ln distij − λkentrycostij + ck ln rki × ln rk

j

+ δk Internalij + bk1 ln Pk

j × ln rki + f ek

i + f ekj + εk

ij, (32)

where all variables with a superscript k are defined in the same way to those without any

superscript but in sector k. Distance is constant across sectors. Since the sectoral data on

entry cost and extensive margin are not available, we use the same measure as those in

the aggregate estimation. We run the regression separately with corresponding data and

obtain the estimates sector by sector.

The AI gravity model incorporates zeros and action on the extensive margin because

it theoretically generates both positive and non-positive trade flows to match non-zeros

and zeros in data. The Tobit method is thus appropriate to estimate AI gravity. A poten-

tial import share could be negative when the associated bilateral trade barriers are large

enough. Since the negative share is censored at zero in the data, Sij in the AI gravity equa-

tion is the latent value of the systematic (observed) trade share. If we denote the observed

import share in data as Sij, then

Sij/Ni =

Sij/Ni, if Sij ≥ 0

0, if Sij < 0.(33)

Note that (33) can be estimated using the Tobit model given the censoring mechanism.24

24Helpman, Melitz, and Rubinstein (2008) also pointed out the potential use of the Tobit model. If such

18

4.2 Aggregate Results

We begin by estimating the AI gravity model in equation (30) with aggregate manufactur-

ing trade data. The results are reported in column (1) in Table 1. The estimated exporter-

and importer-specific fixed effects are dropped since they are not the parameters of inter-

est. As always in gravity estimation, the coefficient of distance is significantly negative –

distance reduces the bilateral trade share. A more novel result is that the coefficient of the

interaction term of distance and exporter income is significantly positive, implying that

the distance reduces trade by less for rich exporters than for poor exporters. This sug-

gests that there is a significant distance (price) elasticity heterogeneity across exporters,

and the magnitude of the coefficient reflects the size of the distance elasticity dispersion.

Since we assume that ρ = 0.177, the estimates imply that b0 = 1.190/0.177 = 6.723 and

b1 = 0.131/0.177 = 6.390. Thus the productivity-adjusted variable cost (price) elasticity

is γβ′i = b0 − b1 ln ri, where ri is exporter GDP per capita. And βiNi=1 can be calcu-

lated from equation (31). As discussed earlier, γ and H cannot be identified from their

estimated product.

The coefficient of entry cost is significantly negative, which implies that the entry cost

also reduces the bilateral trade share. The fixed cost elasticity parameter λ = 0.265.

The coefficient of the income interaction term is not significantly different from zero.

This suggests that there is little income elasticity heterogeneity across exporters – non-

homotheticity is not statistically significant in aggregate trade. The income elasticity pa-

rameter c = 0.006. This positive coefficient implies that richer importers (higher ln rj) are

more likely to spend larger shares on products from richer exporters (higher ln ri), condi-

tional on trade costs. The productivity-adjusted income elasticity is φ′i = c ln(ri/r).25 The

coefficient of the internal trade dummy is also significant, implying internal trade share

zero trade values were just the outcome of censoring, then a Tobit specification would provide the best fitto the data.

25Note that the φis are semi income elasticities, which measure the deviations from the unitary elasticity.We call them income elasticities to save notation, as discussed earlier in the model. Actually, the incomeelasticities are 1 + φi/(Sij/Ni).

19

is larger given all else equal. This home-bias term picks up all the relevant forces that

discriminate between internal and international trade.

The interpretation of the Tobit estimates for latent trade is not straightforward. The

Tobit coefficient estimates the linear increase of the latent variable for each unit increase

of the predictor. As the latent variable is identical to the observed variable for all obser-

vations that are above the threshold, it also measures the linear increase of the predictor

on the response for all observations above that threshold.26 For example, the estimated

coefficient of entry cost, -0.265, is the marginal effect of the entry cost on the latent share

Sij/Ni, as well as its the marginal effect on the observed trade share Sij/Ni above zeros.

The slope for zero observations is different from this number. The Tobit model suggests

that the average marginal effect of the predictor on the response for all observations is

equal to its marginal effect on the latent variable multiplied by an adjustment factor. With

the estimated standard deviation of the error term, σ, we can compute the adjustment

factor. Its value is about 0.504, evaluated at the estimates and the mean values of inde-

pendent variables.27 Thus the average marginal effect of entry cost on the observed trade

share Sij/Ni is -0.265×0.504 = -0.134. Similarly, taking the interaction term into account,

a one percent increase in distance leads to an increase of (1.190-0.131 ln ri) in the latent

trade share, in contrast to an increase of 0.504×(1.190-0.131 ln ri) in observed trade share

Sij/Ni. For example, China’s GDP per capita in log is 7.62 and thus the average marginal

effect of log distance on the observed import share from China is -0.089.

The Tobit estimates are related to but differ from the OLS results reported in column

(2). The Tobit coefficient estimates have the same sign as the corresponding OLS esti-

mates, and the statistical significance of the estimates is similar. But directly comparing

the coefficients with the Tobit estimates is not informative. Note that the entry cost co-

efficient -0.265 is the marginal effect on latent trade share Sij/Ni. Its average marginal

26See Wooldridge (2010) for detailed explanations of the Tobit model and how to calculate the conditionalexpectation for the variable of interest.

27In the Tobit model, the adjustment factor of the coefficient is Φ(xb/σ).

20

effect on observed trade share Sij/Ni is -0.134 which is smaller than the OLS estimate -

0.219 in magnitude. The distance semi elasticity of China estimated by the OLS model is

-1.154+0.128×7.62 = -0.178.

As a robustness check, we compare the Tobit estimates with the Heckman two-stage

method (Heckit) which regards the zero flows as missing values. Similar to Helpman,

Melitz, and Rubinstein (2008), the first stage estimates the inverse Mills ratio using a

probit model. The second stage runs an OLS estimation by adding the inverse Mills ratio

into the regressors and the results are reported in column (3).28 All coefficients have the

intuitive signs. The coefficient of the inverse Mills ratio is significant, which implies there

is a sample selection bias when dropping the zero flows in the gravity estimation. This

result confirms the systematic nature of the extensive margin, and suggests applying the

richer structure of AI gravity using the Tobit estimator. Although there are very few zeros

in the aggregate trade flows, there are sizable differences in results between OLS, Heckit

and Tobit estimators. The differences are even more significant in sectoral estimation,

where zero frequencies are higher.

We also report the estimates of AI gravity with different elasticity specifications in Ta-

ble 2. Column (1) is our baseline result for equation (30). In column (2) we drop the elas-

ticity heterogeneity term measured by the interaction of distance and exporter income,

yielding a distance elasticity equal to -0.038.29 The coefficients on distance and its interac-

tion with exporter income are robust for the translog model in which the non-homothetic

term is dropped as shown in column (3). When we further shut down the distance elastic-

ity heterogeneity as shown in column (4), all coefficients remain significant with intuitive

signs. We check our results with Fajgelbaum and Khandelwal (2016) by keeping the dis-

tance and non-homothetic term as shown in column (5), and with Novy (2013) by keeping

only distance as shown in the last column. All results are similar.

28See Heckman (1979) for detailed explanations of the inverse Mills ratio.29The estimate of the distance elasticity is -0.025 in Novy (2013) and -0.043 in Fajgelbaum and Khandelwal

(2016). Our result is in between.

21

To check on sensitivity to omitted variable bias in our base specification of trade fric-

tions, we add standard iceberg trade frictions to the gravity equation. Table 3 reports

the results. In addition to distance and entry cost, the coefficients of contiguity are also

significant, implying that common border raises bilateral import shares. The other three

friction variables, common language, colonial relationship, and common colonizer, are

not significant. In contrast to the (log) level of import which is very sensitive to those

trade frictions above in the CES gravity equation, the share of import in AI gravity is not

sensitive because the frictional (promotion) effect on level is offset by that of the total.

More importantly, columns (2) and (3) show that the coefficient of the interaction of dis-

tance and exporter’s income remains the same, 0.131. The coefficients of distance are both

-0.18, very close to that in the baseline estimation, as shown in column (1). The difference

is only 0.01, within one standard deviation.

4.3 Sectoral Results

We report AI gravity estimates by sectors in row (2)-(26) of Appendix Table B.2. For ref-

erence, the aggregate estimation results are reported again in row (1), equal to column (1)

in Table 1. The sectors are sorted in descending order by the coefficient of the interaction

term of distance and exporter income. Overall, the disaggregated AI gravity model works

well. The coefficients of the variables are, in most cases, significant and the estimates vary

across sectors in a sensible way.

First, distance is a large impediment to sectoral trade: all estimated distance coeffi-

cients are negative and statistically significant. Distance elasticities vary greatly across

sectors, consistently with variation in value to weight and the physical requirements of

transportation. All the coefficients of the interaction term of distance and exporter income

are significantly positive, implying that the distance elasticity heterogeneity is common

across all sectors. Products produced by richer exporters are less distance elastic. The

coefficients of this interaction term are different in magnitude, which suggests different

22

sizes of the distance elasticity dispersion. The largest value of this coefficient is 0.291 and

is almost five times as large as the smallest value, 0.062, which implies a big difference in

the price elasticity dispersion among sectors. Furniture, beverages, and tobaccos are the

three sectors with the biggest distance elasticity heterogeneity, while metals, chemicals,

and machines are among the sectors with the smallest distance elasticity dispersion. This

is intuitive because products in the former sectors are more differentiated than those in

the latter sectors.

Second, all estimated entry cost coefficients are negative and very few of them are

insignificant – entry costs impede bilateral trade significantly for most sectors in our sam-

ple. Insignificant entry cost effects are found in sectors like furniture, leather, footwear,

apparel, and paper products. At the other extreme, food and transport are the sectors

most sensitive to entry cost in international trade. The reason might be that food and

vehicles are more restricted to safety regulations.

Third, most estimated coefficients of the income interaction term are positive, but only

four of them are significantly positive. This suggests that the non-homothetic effect is

weak in most sectors. Significant non-homothetic income effects are found in sectors like

machines and non-ferrous Metals. In these sectors, richer countries are more likely to

export high-quality goods and also more likely to import high-quality goods.

Last, international borders reduce trade, all else equal. All the estimates of the coef-

ficients on internal (the dummy variable capturing border effect) are positive, large, and

significant at any level. Furniture, food, and beverages are the sectors with the highest

internal estimate, while machines and tobacco are the ones with the lowest estimate. This

is intuitive because the other unobserved trade barriers, like consumer tastes, play an

important role in the former sectors while are weak in the latter.

23

5 Zeros and the Roles of Variable and Fixed Costs

In this section, we use the estimation results from Section 4 to quantify the roles of vari-

able and fixed costs in causing international zero trade flows. Section 5.1 constructs a

hypothetical negative trade variable that measures how far from trade a non-partner rela-

tionship is. In Section 5.2, we decompose the variation in the hypothetical trade measure

into a variable cost component, a fixed cost component and an income effect component.

5.1 Latent Trade

How can we understand the latent value of bilateral trade censored at zero in the setting

of our model? A diagram illustrates the micro-structure of this unobservable negative

value.

pij

qij

D(pij)

S(pij)

qij

pij

pvij

q*ij

pcij

virtu

al s

ubsi

dy

virtual quantity

D(pij)

0 qij

pgij

latent resistance

LTBijEj /pij

Figure 1: Latent Trade

24

Recall that demand qij(z) for good z from i sold in j is implied as a decreasing function

D(pij) of pij by equation (8), i.e.,30

pij(z)qij(z)/ej = αi − γβi ln(µiwitij/ pj) + φi ln rj + γβi ln z. (34)

The break-even-condition for good z is determined by the quantity qij(z) at which average

cost equals price:

pij(z) = witij/z + Fij/qij(z). (35)

Denote the break-even quantity as S(pij). Figure 1 plots D(pij) against S(pij). pcij is the

choke price. Since D(pij) for the firm with the highest productivity draw z is everywhere

below the break-even condition supply S(pij), no trade occurs. A hypothetical larger mar-

ket D(pij) for the highest productivity firm is tangent to the break-even-condition supply

curve and generates the minimal level of quantity demanded qij that initiates trade.

One way to induce the buyer to consume the break-even quantity qij is to offer a

buyer’s price pvij, the virtual price.31 Trade occurs with a subsidy to the buyer equal to

pij − pvij, the virtual subsidy. An alternative hypothetical way to induce trade is central to

this paper. Endow the buyer with the hypothetical quantity equal to qij − q∗ij (also equal

to qij + |q∗ij|). We use this distance from the negative value to the break-even demand to

measure how far from break-even is the implied demand, i.e., how far from occurring is

the trade. We term this distance latent resistance. In the negative region, the consumer

would hypothetically sell the product if she or he has inventory. If the consumer owned

the full amount qij − q∗ij to enable consumption qij, the amount |q∗ij| is sold in the world

market at price pij and the remainder is consumed in the amount qij. The latent resistance

qij− q∗ij is welfare equivalent to the virtual subsidy pij− pvij .32 One plausible way to make

30Note z is the productivity of firm z. Firms from the same origins charge the same markup beforedrawing productivities.

31The virtual price developed by Neary and Roberts (1980) is the price that would induce an initiallyunconstrained consumer to demand the level of a good when under quantity control (rationing).

32Virtual quantity in the literature, e.g., Neary (1985) and Squires (2016), is the quantity of a good that the

25

the virtual variables actual is as follows. The government buys the amount qij − q∗ij from

the world market at the break-even price. It resells the amount |q∗ij| on the world market

at that price, while sells the amount qij on the domestic market at the virtual price pvij.

The net loss is ( pij − pvij)qij, just as in the virtual subsidy case where the virtual subsidy is

implemented.

The final step to our application is based on hypothetical frictionless trade. pgij is the

factory gate price and qij is the frictionless level quantity when all trade costs are zero.

The distance from the (negative) quantity q∗ij associated with the break-even-price to the

quantity qij for the frictionless price is the latent quantity bias. Since the trade share is

our econometric variable of interest, we further define Latent Trade Bias in terms of the

expenditure share of the latent quantity bias of the product. Specifically,

LTBij(z) = pij(z)(qij(z)− q∗ij(z))/Ej, (36)

where q∗ij(z), the latent value of quantity demand, is negative. We use this full distance to

measure how far from frictionless is the implied demand, i.e., how far from the maximum

is the trade of product z. This trade bias definition has the advantage of applying equally

to positive trade flows, for which predicted latent trade qij(z)∗ in equation (36) is replaced

by the predicted positive value of trade. LTB captures the effects of trade costs, as well as

the effects of price elasticity γβi and income elasticity φi.

5.2 Latent Trade Bias Decomposition

This section quantitatively projects the latent trade bias associated with zeros and per-

forms a variance decomposition to measure the extent to which zero trade flows are ex-

plained by variable cost, fixed cost, and income effect respectively.33

initially quantity-constrained consumer would demand once unconstrained, given that quantity control’smarket or accounting price. It is qij on the diagram. Latent resistance in our paper is distinct.

33We also add a complementary analysis of how decreases in trade costs raise the chance of trade rela-tionships with the Tobit estimates (see Appendix Section D).

26

Equation (36) implies that the latent trade bias of a product could be expressed as

the difference between the frictionless (pij(z)qij(z)/Ej) and the latent expenditure shares

(pij(z)q∗ij(z)/Ej). Using the estimated model we measure the aggregate latent trade bias

(LTB) as

LTBij ≡Yi

Y/Ni − Sij/Ni, (37)

where Sij is the latent trade share when the actual trade share is zero, i.e., the latent value

of trade share in the Tobit regression. The LTB can be predicted by the AI gravity equation

(20) with all the gravity parameters estimated by the Tobit regression in equation (30), i.e.

LTBij =Yi

Y/Ni − Sij/Ni. (38)

An advantage of the AI gravity equation (20) is that the LTB can be decomposed into three

effects

LTBij = γβ′i ln(

tij

ΠiPj)︸ ︷︷ ︸

Xtij

+ λ( fij − Ψi)︸ ︷︷ ︸X f

ij

−φ′i ln(rj/R)︸ ︷︷ ︸Xr

ij

, (39)

where components Xtij, X f

ij, and Xrij are the effects of variable cost, fixed cost, and income.

All of them can be computed with the parameters estimated. Then we can decompose the

LTB variation across country pairs into three margins by the regression method following

the literature.34 Specifically, we regress each component in equation (39) on the LTB and

estimate the simultaneous equations

Xtij = ηt LTBij + εt

ij, (40)

X fij = η f LTBij + ε

fij, (41)

Xrij = ηr LTBij + εr

ij, (42)

34See Eaton, Kortum, and Kramarz (2004), Hottman, Redding, and Weinstein (2016), and Bernard, Dhyne,Magerman, Manova, and Moxnes (2019).

27

with the constraint

ηt + η f + ηr = 1. (43)

By the properties of OLS, the coefficients ηt, η f , and ηr provide us with a measure of

how much of the variation in the LTB for zero flows can be attributed to the effect of

variable cost, fixed cost, and income, respectively. This helps us to identify which of the

components is the more important one to cause non-partner relationships. Replacing the

aggregate LTB and its three components with the corresponding sectoral variables, we

can determine the variance decomposition for each sector.

The results are reported in Table 4. Row (1) shows the LTB decomposition for the ag-

gregate trade zeros. Variable cost (distance) explains 70%, fixed cost (entry cost) explains

16%, and income effect explains 14% of the zero flows. Since there are many fewer zeros

in aggregate trade, we report the results by sectors in row (2)-(26). The coefficients in all

sectors are significantly positive and between zero and one. On average, variable cost

explains 48%, Fixed cost explains 26%, and income effect explains 26% of the zero flows.

The entry cost effect is usually less important for aggregate trade (16%) than in sectoral

trade (26%), which is consistent with our intuition. This also holds for the income effect.

To visualize the results, Figure 4 plots the decomposition. We find that the variable cost

effect is larger than both fixed cost effect and income effect for all sectors. Variable cost

effect is strongest in shaping zeros in apparel and transport sectors, while is weakest in

rubber, wood, and machines sectors. Fixed cost impedes the trade to occur most likely in

rubber and wood sectors, while least likely in apparel and transport sectors. The income

effect is the strongest in shaping zeros in wood and machines sectors, while is weakest in

apparel and transport sectors. We also report the decomposition results for positive trade

flows, as shown in Table B.3. The pattern is very similar.

Variable cost explains a higher proportion of zero flows more than fixed cost both

within sectors across partners and across sectors for given partners. For each sector, Fig-

ure 5 plots the zero trade frequency across country pairs and the average price elasticity

28

across exporters. We find a significant positive correlation between the two, which im-

plies that the price elasticity accounts for the cross-sector variation of the zero frequency

well. This is quite different from the effect of fixed cost elasticity that is not correlated

with zero frequency across sectors at all, as shown in Figure 6. Thus cross-sector zeros are

more attributed to variable cost than fixed cost.

6 Counterfactuals

In this section, we conduct counterfactuals to analyze whether a zero flow turns positive

(i.e., a zero-to-one transition) or not as export promotion policies reduce trade costs.35

There are two sets of promotion policies. One is proportional to the export volume and

acts as a negative variable cost, e.g., subsidy, tax and financial benefits, duty drawback,

export insurance, and exchange rate management.36 The other set works as a negative

fixed cost, e.g., providing information, facilitating links, helping with licensing and reg-

ulation requirements, and negotiating bilateral fair treatment in the application of reg-

ulations. The estimated model permits measurement of the effects of the two types of

promotion policies on zero trade flows.

First of all, we calculate the latent values of the trade shares with zero flows by the AI

gravity equation (20), i.e.,

Sij/Ni =Yi

Y/Ni − γβ

′i ln(

tij

ΠiPj)− λ( fij − Ψi) + φ′i ln(rj/R), (44)

and then check the signs of those values. If a latent value is negative, the corresponding

country pair is predicted as a zero relationship. The majority of the zero relationships are

successfully predicted by our model (See Appendix Figure B.5).

35We focus on the extensive margin change with the AIDS structure. See Novy (2013) for discussion onthe intensive margin changes with the translog gravity.

36Most of this set of policies are not permissible under WTO rules with some exceptions, e.g., improvingthe transportation infrastructure to reduce freight costs or managing exchange rates.

29

In addition, the latent trade measured by the predicted latent value of trade share

implies how far the current relationship is from trade. For example, The U.K. does not

export tobacco to Lithuania, but the absolute value of the latent trade is much smaller

than to other markets, suggesting that the U.K.’s potential tobacco export to Lithuania is

closer becoming actual than with other potential partners (See Appendix Figure B.6 for

more examples).

Now we turn to our first question, namely, what proportion of zeros turn positive if

we reduce the bilateral cost by 10%, 50%, and 100%, respectively? The answer to this

question is important because it tells us the effectiveness of the promotion policy, i.e.,

the probability of building a new relationship given a country pair not trading with each

other yet. Specifically, for any zero flow, we calculate the bilateral cost direct effect as well

as its indirect effect(s) through the multilateral resistance(s).37 Then we predict the new

latent value of the trade share of that country pair using the AI gravity equation (20). If

the predicted latent share becomes positive, the country pair switch to trade (zero-to-one

transition). If the predicted latent share remains negative, the flow remains zero.

We first take the leather sector as an example. Appendix Figure B.7 plots the zero-to-

one transitions if we reduce bilateral variable cost by 100% for each country pair. Most of

the relationships turn positive as a result, represented by the yellow dots, while very few

non-partners remain..38 In contrast, a reduction of bilateral fixed cost by 100% for each

country pair leaves most of the zeros unaltered as shown in Appendix Figure B.8. Also,

we find that zero flows of smaller exporters are more likely to switch on in response to

the export promotion policy than those of larger exporters.

Then we investigate all sectoral zero flows, and the results are reported in Table 5. All

numbers are positive which implies cutting trade cost decreases the number of zeros in

sectoral trade. On average, zeros in sectoral trade decrease by 88% due to VC elimination,

37The indirect effects are usually limited because the weights on the bilateral costs, the importer’s GDPshares, are usually very small. See equations (21) and (23).

38Not every zero flow transits to positive when all variable trade costs are eliminated. This is because theamount demanded may remain below the break-even level.

30

while by 33% only due to FC elimination. Similar patterns are found for 10% and 50%

trade cost cut. The greater the trade cost cut is, the more zero-to-one transitions we get.

Furthermore, the return in terms of building new trading partners is increasing faster for

VC cut than FC cut. Comparison of the results for 10%, 50%, and 100% shows that the

marginal return of VC cut is decreasing. Lastly, eliminating VC reduces the trade zeros

most in footwear and non-ferrous metal sectors, while least in leather and apparel sectors.

Eliminating FC reduces the trade zeros most in machines and textile sectors, while least

in transport and paper sectors. But the effects of FC cut are less dispersed than those of

VC cut. More importantly, the decreases in zero trade frequency due to VC cut are larger

than due to FC cut for all sectors, implying that variable cost is more important than fixed

cost in trade policy adjustments aiming to encourage the occurrence of trade.

There are different effects across exporters with different trade (price) elasticities. Intu-

itively, rich exporters export more inelastic products and thus are less affected by VC cut,

while poor exporters increase their (latent) trade shares a lot.39 Specifically, we divide all

exporters into two groups in terms of their GDP per capita and check the difference across

groups. Table 6 reports the zero-to-one transitions resulting from reducing bilateral vari-

able costs by 10%. The first three columns outline the average number of non-partners for

exporters in different groups. On average, a poor exporter has 33 non-partners out of 74.

A rich exporter has 11 non-partners out of 74.40 The last three columns report the effect

of a VC cut, revealing it is much larger for poor exporters than for rich exporters. The

reason is that the demand is more sensitive to the price change of price-elastic products

produced by poor exporters and thus the effect of VC cut for poor exporters is stronger.

Individual cases of export promotion on the extensive margin are exemplified by our

headline case of Ethiopia’s potential export of leather goods.41 The 10% cut in variable

39See more discussion on the relationship between exporter income and price elasticity in Section C.2.40There are 75 countries in our sample and thus each exporter has 74 trading partners at most.41Ethiopia in 2006 enjoyed robust GDP and trade growth in excess of 10%. Its external trade goes through

the important port of neighbor Djibouti. Ethiopia was at peace with neighboring Eritrea but in conflictwith neighboring Somalia and also suffered from civil conflict internally. Its robust trade and GDP growthsuggests no effect of conflict on the extensive margin of trade.

31

(fixed) cost produces 38 (16) new markets. The new partners are countries with middle to

high per capita incomes, e.g., Norway and Poland in Europe, and Canada and Mexico in

North America (See Table 7).

Now we turn to our second question, which is: what proportion of zeros turn positive

if exporters unilaterally reduce trade cost by 10%, 50%, and 100%, respectively? The an-

swer to this question is important because it indicates the effectiveness of the unilateral

promotion policy, i.e., the probability of building new relationships given an exporter.

Appendix Table B.4 reports the number of non-partners for each exporter in each sector.

Specifically, for any zero flow, we calculate the bilateral cost direct effect as well as its indi-

rect effect(s) through the multilateral resistance(s). The indirect effects are also important

because multilateral resistances change at the same speed as trade costs do (See equations

(21) and (23)). We predict the new latent value of any trade share of that exporter using

the AI gravity equation (20). If the predicted latent share becomes positive, the destina-

tion country becomes a trading partner (a zero-to-one transition). If the predicted latent

share remains negative, the flow remains zero.

The results are reported in Table 8. On average, zeros in sectoral trade decrease by

46% due to VC elimination, and 33% due to FC elimination. No differences between vari-

able and fixed cost reductions are found in the case of a 10% cut, and little difference is

found for a 50% cut. Furthermore, the return in terms of building new trading partners is

increasing slowly in the case of both VC cut and FC cut. Lastly, cutting VC unilaterally re-

duces the trade zeros most in footwear and petroleum sectors, while least in professional

and scientific equipment, and plastic sectors. Cutting FC unilaterally reduces the trade

zeros most in wood, professional and scientific equipment, and chemicals sectors, while

least in beverage, machines and textiles sectors. The dispersion of the effects of VC cut is

larger than that of FC cut. Again, the decreases in zero trade frequency due to VC cuts are

larger than due to FC cuts for most sectors, implying that variable cost is more important

than fixed cost in trade policy adjustment to make trade to occur.

32

7 Conclusion

This paper applies Almost Ideal Demand System (AIDS) preferences to the firm hetero-

geneity framework and derives an AI gravity equation that explains zero trade flows

theoretically in a tractable form used for estimation. We use latent trade to theoretically

measure the distance from trade for any non-partner relationship. AI gravity features

price (variable cost) elasticity heterogeneity across exporters. This is important because

countries considering export facilitation policies would be differentially affected accord-

ing to their demand characteristics. AI gravity also features income elasticity heterogene-

ity across importers, again conditioning the effects of export promotion. Variable and

fixed export cost variation across bilateral partners further condition the effects of export

promotion. These features in combination promise to shed more light on trade promotion

policies for non-partners, especially developing countries with higher zero trade frequen-

cies.

Latent trade measured by the predicted latent value has potentially important policy

implications. Trade promotion policies could be targeted toward potential markets on the

margin that are much closer to zero. We quantitatively assess the roles played by variable

and fixed costs in forming zero international trade flows. The results show that variable

cost explains zero trade flows more than fixed cost does for all sectors. The marginal effect

of a fixed cost reduction in turning zero trade to positive is smaller than that of a variable

cost reduction.

The empirical results presented in this paper are based on country-level trade flows.

A natural extension would be an application using firm-level data. Implications of the

estimated model could suggest that some firms could profitably enter currently unserved

markets. On the importer side, the estimated model could suggest potential sources of

inputs. Disaggregation to more finely delimited sectors will come closer to firm-level

activity and present some of the same opportunities.

33

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Tables and Figures

0 20 40 60 80 100Percent of country pairs

TobaccoPetroleum refineries

Furniture except metalFootwear

Wood products except furnitureBeverages

Non−ferrous metalsOther non−metal min. prod.

Iron and steelGlass and products

Leather productsRubber products

Paper and productsIndustrial chemicals

Printing and publishingPlastic products

Transport equipmentProf. and sci. equipment

Wearing apparelOther chemicals

Fabricated metal productsFood products

TextilesMachinery electric

Machinery except electrical

Aggregate manufacturing

No trade Trade

Figure 2: Zero Trade Frequency across Sectors

37

10 20 30 40 50 60 70

Exporter ranked by GDP

10

20

30

40

50

60

70

Imp

ort

er

ran

ked

by

GD

P

Leather

IDN_NOR TJK_USARUS_CHLYEM_USA

IRL_RUS

USA_TJK

Figure 3: Zero Trade Flows by Country Pairs: Leather Sector

38

Table 1: AI Gravity Estimation: Baseline

(1) (2) (3)Tobit OLS Heckit

Distance -1.190∗∗∗ -1.154∗∗∗ -1.147∗∗∗

(0.025) (0.025) (0.026)

Distance × Income ex 0.131∗∗∗ 0.128∗∗∗ 0.127∗∗∗

(0.003) (0.003) (0.003)

Entry cost -0.265∗∗∗ -0.219∗∗ -0.215∗∗

(0.088) (0.087) (0.089)

Income im × Income ex 0.006 0.008 0.035(0.021) (0.021) (0.022)

Internal 2.859∗∗∗ 2.916∗∗∗ 2.902∗∗∗

(0.080) (0.080) (0.081)σ 0.121∗∗∗

(0.002)

Mills -0.126∗∗∗

(0.047)Observations 5625 5625 5625R-squared 0.572 0.640Log-likelihood value -2098.992 -1951.326

Notes: Table reports the estimates of the AI gravity in equation (30). Esti-mated exporter- and importer-specific fixed effects are dropped. Robuststandard errors in parentheses. Significance * .10, ** .05, *** .01.

39

Table 2: AI Gravity Estimation: Specifications

(1) (2) (3) (4) (5) (6)Import share per firm

Distance -1.190∗∗∗ -0.038∗∗∗ -1.190∗∗∗ -0.041∗∗∗ -0.037∗∗∗ -0.043∗∗∗

(0.025) (0.010) (0.025) (0.009) (0.010) (0.009)

Distance × Income ex 0.131∗∗∗ 0.131∗∗∗

(0.003) (0.003)

Entry cost -0.265∗∗∗ -0.316∗∗∗ -0.265∗∗∗ -0.353∗∗∗

(0.088) (0.098) (0.088) (0.096)

Income im × Income ex 0.006 0.004∗ 0.006∗∗

(0.021) (0.002) (0.002)

Internal 2.859∗∗∗ 3.024∗∗∗ 2.859∗∗∗ 3.000∗∗∗ 3.038∗∗∗ 3.003∗∗∗

(0.080) (0.095) (0.080) (0.094) (0.095) (0.094)Observations 5625 5625 5625 5625 5625 5625R-squared 0.572 0.352 0.572 0.352 0.351 0.350

Notes: Table reports the estimates of the AI gravity in equation (30) with different specifications. Estimatedexporter- and importer-specific fixed effects are dropped. Robust standard errors in parentheses. Significance* .10, ** .05, *** .01.

40

Table 3: AI Gravity Estimation: Additional Trade Frictions

(1) (2) (3)Import share per firm

Distance -1.190∗∗∗ -1.180∗∗∗ -1.180∗∗∗

(0.025) (0.025) (0.025)

Distance × Income ex 0.131∗∗∗ 0.131∗∗∗ 0.131∗∗∗

(0.003) (0.003) (0.003)

Entry cost -0.265∗∗∗ -0.261∗∗∗ -0.262∗∗∗

(0.088) (0.088) (0.088)

Income im × Income ex -0.006 -0.006 -0.005(0.021) (0.021) (0.021)

Internal 2.859∗∗∗ 2.942∗∗∗ 2.936∗∗∗

(0.080) (0.089) (0.089)

Contiguity 0.081∗∗∗ 0.076∗∗

(0.031) (0.031)

Common language -0.009 -0.011(0.021) (0.023)

Colonial relationship ever 0.025(0.035)

Common colonizer post 1945 -0.010(0.027)

Observations 5625 5625 5625R2 0.572 0.573 0.573

Notes: Table reports the estimates of the AI gravity in equation (30) withadditional trade frictions. Estimated exporter- and importer-specific fixedeffects are dropped. Robust standard errors in parentheses. Significance *.10, ** .05, *** .01.

41

Table 4: Latent Trade Bias Decomposition for Zero Flows

Distance Entry cost Income Observations(1) Aggregate 0.697*** 0.166*** 0.137*** 201

(0.02) (0.01) (0.01)

(2) Apparel 0.632*** 0.213*** 0.155*** 1156(0.01) (0.01) (0.01)

(3) Transport 0.618*** 0.191*** 0.191*** 1191(0.01) (0.01) (0.01)

(4) OthChem 0.555*** 0.222*** 0.222*** 1089(0.01) (0.00) (0.00)

(5) Food 0.531*** 0.230*** 0.239*** 958(0.01) (0.00) (0.00)

(6) Textiles 0.527*** 0.238*** 0.235*** 925(0.01) (0.01) (0.01)

(7) Furniture 0.526*** 0.246*** 0.228*** 2072(0.01) (0.00) (0.00)

(8) NfMetals 0.516*** 0.242*** 0.242*** 1959(0.01) (0.00) (0.00)

(9) Plastic 0.506*** 0.245*** 0.248*** 1224(0.01) (0.00) (0.00)

(10) Leather 0.493*** 0.285*** 0.222*** 1655(0.01) (0.00) (0.01)

(11) MetalProd 0.490*** 0.301*** 0.209*** 967(0.01) (0.01) (0.02)

(12) Tobacco 0.478*** 0.270*** 0.252*** 3676(0.00) (0.00) (0.00)

(13) Beverages 0.475*** 0.262*** 0.263*** 1960(0.01) (0.00) (0.00)

(14) IronSteel 0.473*** 0.264*** 0.263*** 1858(0.01) (0.00) (0.00)

(15) Printing 0.473*** 0.262*** 0.264*** 1233(0.01) (0.00) (0.00)

(16) NonMetal 0.464*** 0.267*** 0.269*** 1927(0.01) (0.00) (0.00)

(17) Petroleum 0.449*** 0.275*** 0.276*** 2530(0.00) (0.00) (0.00)

(18) Footwear 0.446*** 0.277*** 0.277*** 2016(0.01) (0.00) (0.00)

(19) ProfSci 0.445*** 0.279*** 0.276*** 1183(0.01) (0.00) (0.00)

(20) Glass 0.437*** 0.292*** 0.272*** 1786(0.01) (0.00) (0.01)

(21) Electrics 0.435*** 0.302*** 0.263*** 828(0.01) (0.00) (0.01)

(22) IndChem 0.435*** 0.291*** 0.275*** 1283(0.01) (0.00) (0.01)

(23) Paper 0.422*** 0.305*** 0.272*** 1547(0.01) (0.00) (0.00)

(24) Rubber 0.407*** 0.320*** 0.274*** 1581(0.01) (0.01) (0.01)

(25) Machines 0.384*** 0.243*** 0.373*** 808(0.01) (0.01) (0.02)

(26) Wood 0.378*** 0.310*** 0.312*** 1989(0.00) (0.00) (0.00)

Mean .48 .265 .255St. d. .063 .033 .041

Notes: Table reports the latent trade bias decomposition for zeroflows by estimating equation system (40)-(42) with constraint (43).Robust standard errors in parentheses. Significance * .10, ** .05, ***.01.

42

0 20 40 60 80 100Percent

WoodMachines

RubberPaper

IndChemElectrics

GlassProfSci

FootwearPetroleumNonMetal

PrintingIronSteel

BeveragesTobacco

MetalProdLeatherPlastic

NfMetalsFurnitureTextiles

FoodOthChemTransport

Apparel

Aggregate

VC IM

FC

Figure 4: Latent Trade Bias Decomposition for Zero Flows

43

Food

Beverages

Tobacco

Textiles

Apparel

Leather

FootwearWoodFurniture

Paper

PrintingIndChem

OthChem

Petroleum

Rubber

Plastic

GlassNonMetal

IronSteelNfMetals

MetalProd

MachinesElectrics

TransportProfSci

0.2

.4.6

Ze

ro f

req

ue

ncy

.1 .2 .3 .4 .5 .6Average price elasticity

Figure 5: Zero Frequency and Average Price Elasticity

Food

Beverages

Tobacco

Textiles

Apparel

Leather

Footwear WoodFurniture

Paper

PrintingIndChem

OthChem

Petroleum

Rubber

Plastic

GlassNonMetal

IronSteelNfMetals

MetalProd

MachinesElectrics

TransportProfSci

0.2

.4.6

Ze

ro f

req

ue

ncy

0 .2 .4 .6 .8Fixed cost elasticity

Figure 6: Zero Frequency and Fixed Cost Elasticity

44

Table 5: Zero-to-One Transitions from Reducing Bilateral Costs

reducing VC by reducing FC by

10% 50% 100% 10% 50% 100%

(1) Machines 0.70 0.79 0.85 0.42 0.46 0.47

(2) Electrics 0.71 0.86 0.89 0.25 0.25 0.27

(3) Textiles 0.58 0.82 0.87 0.16 0.24 0.45

(4) Food 0.59 0.92 0.96 0.15 0.20 0.31

(5) MetalProd 0.63 0.78 0.80 0.37 0.38 0.39

(6) OthChem 0.82 0.96 0.99 0.26 0.30 0.35

(7) Apparel 0.57 0.68 0.71 0.25 0.26 0.26

(8) ProfSci 0.59 0.89 0.94 0.19 0.23 0.38

(9) Transport 0.58 0.82 0.89 0.14 0.14 0.21

(10) Plastic 0.58 0.83 0.90 0.15 0.18 0.34

(11) Printing 0.59 0.83 0.88 0.15 0.17 0.35

(12) IndChem 0.58 0.72 0.74 0.23 0.25 0.31

(13) Paper 0.61 0.74 0.76 0.21 0.23 0.23

(14) Rubber 0.63 0.75 0.76 0.36 0.36 0.38

(15) Leather 0.58 0.67 0.68 0.26 0.26 0.27

(16) Glass 0.56 0.69 0.71 0.26 0.26 0.27

(17) IronSteel 0.67 0.88 0.93 0.21 0.23 0.37

(18) NonMetal 0.74 0.93 0.97 0.22 0.26 0.34

(19) NfMetals 0.72 0.95 1.00 0.23 0.25 0.35

(20) Beverages 0.67 0.86 0.91 0.23 0.25 0.42

(21) Wood 0.75 0.93 0.96 0.27 0.29 0.38

(22) Footwear 0.87 1.00 1.00 0.32 0.34 0.37

(23) Furniture 0.53 0.76 0.88 0.16 0.18 0.23

(24) Petroleum 0.78 0.94 0.95 0.26 0.29 0.40

(25) Tobacco 0.72 0.91 0.94 0.25 0.26 0.28

Mean 0.65 0.84 0.88 0.24 0.26 0.33

St. d. 0.09 0.10 0.10 0.07 0.07 0.07

Notes: Table reports the decrease (%) in number of zeros ifbilateral trade costs are reduced.

45

Table 6: Zero-to-One Transitions from Reducing Bilateral Costs: by Exporter Groups

# of zeros reducing VC

poor exporter rich exporter poor exporter rich exporter

(1) Machines 21 3 0.99 0.06

(2) Electrics 21 3 0.99 0.09

(3) Textiles 21 6 0.91 0.25

(4) Food 22 6 0.84 0.30

(5) MetalProd 23 5 0.99 0.10

(6) Apparel 24 9 1.00 0.13

(7) OthChem 27 5 0.94 0.65

(8) Transport 28 6 0.85 0.18

(9) ProfSci 29 5 0.82 0.24

(10) Plastic 29 6 0.89 0.20

(11) Printing 29 6 0.84 0.23

(12) IndChem 30 7 0.97 0.15

(13) Leather 34 13 0.99 0.15

(14) Paper 35 8 0.99 0.20

(15) Rubber 37 8 0.97 0.17

(16) Footwear 38 18 0.95 0.79

(17) Glass 39 11 0.99 0.12

(18) Furniture 39 19 0.87 0.20

(19) IronSteel 39 13 0.93 0.41

(20) NfMetals 40 14 0.95 0.49

(21) NonMetal 40 13 0.96 0.52

(22) Wood 40 15 0.93 0.58

(23) Beverages 41 14 0.89 0.44

(24) Petroleum 49 21 0.96 0.61

(25) Tobacco 60 40 0.95 0.49

Mean 33 11 0.93 0.31

St. d. 10 8 0.06 0.21

Notes: Table reports the decrease (%) in number of zeros of different types ofexporters if bilateral trade costs are reduced by 10%.

46

Table 7: Ethiopia’s New Markets of Leather Export with Trade Cost Reductions

new markets with 10% cut invariable cost fixed costAlbania AustriaArmenia BrazilAustria BulgariaAzerbaijan CanadaBrazil ChileBulgaria JordanCanada KazakstanChile MexicoColombia New ZealandEcuador NigerEstonia NorwayIceland PolandIreland PortugalJordan TanzaniaKazakstan TunisiaKyrgyzstan YemenLatviaLithuaniaMacedoniaMadagascarMexicoMoldovaMongoliaMoroccoNew ZealandNigerNigeriaNorwayPeruPolandPortugalSloveniaSri LankaTanzaniaTunisiaUruguayViet NamYemen

Notes: Table reports Ethiopia’s new marketsof leather export with trade cost reductions.

47

Table 8: Zero-to-One Transitions from Reducing Unilateral Costs

reducing VC by reducing FC by

10% 50% 100% 10% 50% 100%

(1) Machines 0.43 0.48 0.56 0.42 0.46 0.47

(2) Electrics 0.25 0.35 0.56 0.25 0.25 0.27

(3) Textiles 0.16 0.16 0.32 0.16 0.22 0.42

(4) Food 0.14 0.17 0.41 0.15 0.20 0.30

(5) MetalProd 0.39 0.46 0.53 0.37 0.38 0.39

(6) OthChem 0.25 0.29 0.59 0.26 0.29 0.34

(7) Apparel 0.26 0.33 0.50 0.25 0.26 0.26

(8) ProfSci 0.19 0.18 0.23 0.19 0.23 0.36

(9) Transport 0.14 0.16 0.34 0.14 0.14 0.21

(10) Plastic 0.15 0.15 0.19 0.15 0.18 0.34

(11) Printing 0.13 0.15 0.30 0.15 0.17 0.35

(12) IndChem 0.23 0.27 0.36 0.23 0.25 0.30

(13) Paper 0.23 0.29 0.47 0.21 0.23 0.23

(14) Rubber 0.36 0.40 0.47 0.36 0.36 0.38

(15) Leather 0.28 0.35 0.48 0.26 0.26 0.27

(16) Glass 0.26 0.32 0.41 0.25 0.26 0.26

(17) IronSteel 0.20 0.20 0.38 0.21 0.23 0.36

(18) NonMetal 0.22 0.25 0.55 0.22 0.26 0.34

(19) NfMetals 0.24 0.26 0.48 0.23 0.25 0.34

(20) Beverages 0.23 0.25 0.49 0.23 0.25 0.42

(21) Wood 0.27 0.29 0.51 0.27 0.29 0.37

(22) Footwear 0.34 0.42 0.86 0.32 0.34 0.37

(23) Furniture 0.16 0.17 0.41 0.16 0.18 0.22

(24) Petroleum 0.25 0.28 0.62 0.26 0.29 0.39

(25) Tobacco 0.25 0.26 0.47 0.25 0.26 0.27

Mean 0.24 0.28 0.46 0.24 0.26 0.33

St. d. 0.08 0.10 0.14 0.07 0.07 0.07

Notes: Table reports the decrease (%) in number of zeros ifunilateral trade costs are reduced.

48

Online appendix for:“Latent Exports: Almost Ideal Gravity and Zeros”

A Appendix to Model

A.1 Firm Aggregation

Equation (8) and (10) imply

Sij = Ni

∫ H

ln z∗ijsij(a)dG(a)

Sij/Ni = [αi − γβi ln(µiwitij/ pj) + φi ln rj]∫ H

ln z∗ijdG(a) + γβi

∫ H

ln z∗ijadG(a)

≈ γβi

∫ H

ln z∗ijadG(a)

= γβi(H − ln z∗ij)/ ln H

= (1/ ln H)[αi − γβi ln(µiwitij/ pj) + φi ln rj]

+(H/ ln H)γβi − (1/ ln H)µi/(µi − 1) fij

= (1/ ln H)αi + (H/ ln H)γβi

−(1/ ln H)γβi ln(µiwitij/ pj)

−(1/ ln H)µi/(µi − 1) fij

+(1/ ln H)φi ln rj

where∫ H

ln z∗ijdG(a) ≈ 0 given only a very small fraction of firms export in every country.

1

A.2 Gravity

Plug equation (14) into equation (19),

(Yi/Y)/Ni = ∑j(Ej/Y)[α′i − γβ′i ln(µiwitij/ pj)− λ′i fij + φ′i ln rj]

= [α′i − γβ′i ln(µiwi) + γβ′i ∑k

Nkβk ln µkwk]

−∑j(Ej/Y)[γβ′i(ln tij −∑

kNkβk ln tkj) + λ′i fij − φ′i ln rj]

Then

Sij/Ni = [α′i − γβ′i ln(µiwi) + γβ′i ∑k

Nkβk ln µkwk]

−[γβ′i(ln tij −∑k

Nk ln tkj) + λ′i fij − φ′i ln rj]

= (Yi/Y)/Ni + ∑j(Ej/Y)[γβ′i(ln tij −∑

kNkβk ln tkj) + λ′i fij − φ′i ln rj]

−[γβ′i(ln tij −∑k

Nkβk ln tkj) + λ′i fij − φ′i ln rj]

= (Yi/Y)/Ni

−γβ′i[ln tij −∑j(Ej/Y) ln tij −∑

kNkβk ln tkj + ∑

j(Ej/Y)∑

kNkβk ln tkj]

−λ′i[ fij −∑j(Ej/Y) fij]

−φ′i [ln rj −∑j(Ej/Y)rj]

B Appendix to Tables and Figures

2

10 20 30 40 50 60 70

Exporter ranked by GDP

10

20

30

40

50

60

70

Imp

ort

er

ran

ked

by

GD

P

Machines

CHN_ETHJPN_AZERUS_NGA

BRA_TJK

Figure B.1: Zero Trade Flows by Country Pairs: Machines Sector

10 20 30 40 50 60 70

Exporter ranked by GDP

10

20

30

40

50

60

70

Imp

ort

er

ran

ked

by

GD

P

Tobacco

FRA_JPNUSA_RUS

SPA_CHN

Figure B.2: Zero Trade Flows by Country Pairs: Tobacco Sector

3

Machines Electrics Textiles

Food MetalProd OthChem

Apparel ProfSci Transport

Plastic Printing IndChem

Figure B.3: Zero Trade Flows by Country Pairs: All Other Sectors I

4

Paper Rubber Glass

IronSteel NonMetal NfMetals

Beverages Wood Footwear

Furniture Petroleum Tobacco

Figure B.4: Zero Trade Flows by Country Pairs: All Other Sectors II

5

10 20 30 40 50 60 70

Exporter ranked by GDP

10

20

30

40

50

60

70

Import

er

ranked b

y G

DP

Figure B.5: Zero Flow Prediction: Leather Sector

−.6 −.4 −.2 0Latent trade share

Ecuador

Tajikistan

Ghana

Uruguay

Macedonia

Viet Nam

Peru

Georgia

Lithuania

GBR, Tobacco

−.3 −.2 −.1 0Latent trade share

Tajikistan

Niger

Sri Lanka

Uruguay

Azerbaijan

Albania

Moldova

CAN, Footwear

−.4 −.3 −.2 −.1 0Latent trade share

Tajikistan

Nigeria

Albania

Niger

Kyrgyzstan

Morocco

Tunisia

Yemen

AUS, Leather

−.3 −.2 −.1 0Latent trade share

Tajikistan

Ethiopia

Niger

Albania

Armenia

Moldova

Macedonia

Madagascar

MEX, IronSteel

−.15 −.1 −.05 0Latent trade share

Kyrgyzstan

Yemen

Albania

Nigeria

Mongolia

Tajikistan

COL, Textile

−.15 −.1 −.05 0Latent trade share

GhanaMadagascarEcuadorMoroccoNigeriaTunisiaAlbaniaYemenKenyaNigerMacedoniaSloveniaTanzaniaSri LankaJordanGreeceGeorgiaArmeniaLatviaMoldova

MNG, Food

Figure B.6: Latent Trade Examples

6

10 20 30 40 50 60 70

Exporter ranked by GDP

10

20

30

40

50

60

70

Import

er

ranked b

y G

DP

Leather

Figure B.7: Zero-to-One Transitions from Removing Bilateral Variable Costs: Leather Sec-tor

10 20 30 40 50 60 70

Exporter ranked by GDP

10

20

30

40

50

60

70

Import

er

ranked b

y G

DP

Leather

Figure B.8: Zero-to-One Transitions from Removing Bilateral Fixed Costs: Leather Sector

7

Table B.1: Country List by GDP

ISO country ISO country1 USA United States 39 PHL Philippines2 JPN Japan 40 NGA Nigeria3 DEU Germany 41 HUN Hungary4 CHN China 42 UKR Ukraine5 GBR United Kingdom 43 NZL New Zealand6 FRA France 44 PER Peru7 ITA Italy 45 KAZ Kazakstan8 CAN Canada 46 VNM Viet Nam9 ESP Spain 47 MAR Morocco

10 BRA Brazil 48 SVK Slovakia11 RUS Russia 49 ECU Ecuador12 IND India 50 SVN Slovenia13 KOR Korea 51 BGR Bulgaria14 MEX Mexico 52 TUN Tunisia15 AUS Australia 53 LTU Lithuania16 NLD Netherlands 54 LKA Sri Lanka17 TUR Turkey 55 KEN Kenya18 SWE Sweden 56 AZE Azerbaijan19 CHE Switzerland 57 LVA Latvia20 IDN Indonesia 58 URY Uruguay21 POL Poland 59 YEM Yemen22 AUT Austria 60 EST Estonia23 NOR Norway 61 ISL Iceland24 DNK Denmark 62 JOR Jordan25 ZAF South Africa 63 ETH Ethiopia26 GRC Greece 64 GHA Ghana27 IRL Ireland 65 TZA Tanzania28 FIN Finland 66 ALB Albania29 THA Thailand 67 GEO Georgia30 PRT Portugal 68 ARM Armenia31 HKG Hong Kong 69 MKD Macedonia32 MYS Malaysia 70 MDG Madagascar33 CHL Chile 71 NER Niger34 CZE Czech 72 MDA Moldova35 COL Colombia 73 TJK Tajikistan36 SGP Singapore 74 KGZ Kyrgyzstan37 PAK Pakistan 75 MNG Mongolia38 ROM Romania

Notes: Table lists the sample of countries in our paper. Thecountries are sorted by GDP in descending order.

8

Table B.2: AI Gravity Estimation by Sector

Distance Dist.×Inc ex Entry cost Inc im×Inc ex Internal Obs. R-sq.(1) Aggregate -1.190*** 0.131*** -0.265*** 0.006 2.859*** 5625 0.572

(0.03) (0.00) (0.09) (0.02) (0.08)

(2) Furniture -2.754*** 0.291*** -0.405 0.009 4.597*** 5625 0.329(0.06) (0.01) (0.25) (0.06) (0.20)

(3) Beverages -2.571*** 0.272*** -0.412** -0.017 3.746*** 5625 0.333(0.06) (0.01) (0.21) (0.05) (0.18)

(4) Tobacco -2.820*** 0.263*** -0.600* 0.022 1.066*** 5625 0.348(0.08) (0.01) (0.34) (0.07) (0.25)

(5) Petroleum -2.331*** 0.227*** -0.231 -0.059 1.375*** 5625 0.290(0.06) (0.01) (0.23) (0.06) (0.20)

(6) NonMetal -2.157*** 0.224*** -0.195 -0.025 3.407*** 5625 0.319(0.06) (0.01) (0.20) (0.05) (0.17)

(7) Leather -1.809*** 0.190*** -0.145 0.055 1.695*** 5625 0.261(0.05) (0.01) (0.19) (0.04) (0.16)

(8) Food -1.717*** 0.186*** -0.416*** -0.022 3.782*** 5625 0.356(0.04) (0.00) (0.15) (0.04) (0.13)

(9) NfMetals -1.759*** 0.180*** -0.272* -0.028 1.463*** 5625 0.331(0.04) (0.00) (0.16) (0.04) (0.13)

(10) Plastic -1.660*** 0.176*** -0.291** -0.009 2.405*** 5625 0.338(0.04) (0.00) (0.14) (0.03) (0.13)

(11) Glass -1.509*** 0.156*** -0.325** 0.064* 2.274*** 5625 0.358(0.04) (0.00) (0.15) (0.04) (0.13)

(12) Printing -1.381*** 0.149*** -0.309** -0.076** 3.806*** 5625 0.373(0.04) (0.00) (0.14) (0.04) (0.13)

(13) Wood -1.420*** 0.143*** -0.207* -0.002 2.001*** 5625 0.488(0.03) (0.00) (0.13) (0.03) (0.10)

(14) Apparel -1.185*** 0.126*** -0.073 0.021 1.929*** 5625 0.587(0.02) (0.00) (0.09) (0.02) (0.08)

(15) Transport -1.165*** 0.125*** -0.308*** 0.003 1.718*** 5625 0.603(0.02) (0.00) (0.08) (0.02) (0.07)

(16) Footwear -1.169*** 0.118*** -0.039 -0.018 1.116*** 5625 0.396(0.03) (0.00) (0.12) (0.03) (0.10)

(17) IronSteel -1.104*** 0.111*** -0.318** -0.040 1.811*** 5625 0.405(0.03) (0.00) (0.12) (0.03) (0.11)

(18) Paper -1.068*** 0.108*** -0.064 0.024 1.476*** 5625 0.500(0.03) (0.00) (0.10) (0.02) (0.09)

(19) Textiles -0.970*** 0.103*** -0.223** -0.045** 1.757*** 5625 0.549(0.02) (0.00) (0.09) (0.02) (0.08)

(20) OthChem -0.974*** 0.102*** -0.074 -0.010 1.454*** 5625 0.693(0.02) (0.00) (0.07) (0.02) (0.07)

(21) ProfSci -0.834*** 0.089*** -0.171 -0.031 1.247*** 5625 0.316(0.03) (0.00) (0.11) (0.03) (0.10)

(22) Electrics -0.682*** 0.072*** -0.152 0.013 1.327*** 5625 0.279(0.03) (0.00) (0.11) (0.03) (0.10)

(23) Rubber -0.680*** 0.067*** -0.223** 0.068*** 1.257*** 5625 0.388(0.03) (0.00) (0.10) (0.02) (0.09)

(24) Machines -0.627*** 0.066*** -0.213*** 0.037** 0.998*** 5625 0.538(0.02) (0.00) (0.07) (0.02) (0.07)

(25) IndChem -0.626*** 0.064*** -0.239*** 0.015 1.637*** 5625 0.554(0.02) (0.00) (0.08) (0.02) (0.07)

(26) MetalProd -0.618*** 0.062*** -0.150* 0.039** 1.784*** 5625 0.550(0.02) (0.00) (0.08) (0.02) (0.07)

Notes: Table reports the estimates of the sectoral AI gravity in equation (32). Estimated exporter- andimporter-specific fixed effects are dropped. Robust standard errors in parentheses. Significance * .10, **.05, *** .01.

9

Table B.3: Latent Trade Bias Decomposition for Non-zero Flows

Distance Entry cost Inc im×Inc ex Observations(1) Aggregate 0.550*** 0.227*** 0.223*** 5424

(0.00) (0.00) (0.00)

(2) Tobacco 0.899*** 0.045*** 0.056*** 1949(0.00) (0.00) (0.00)

(3) Petroleum 0.770*** 0.116*** 0.115*** 3095(0.00) (0.00) (0.00)

(4) NfMetals 0.733*** 0.134*** 0.132*** 3666(0.00) (0.00) (0.00)

(5) Wood 0.702*** 0.150*** 0.148*** 3636(0.00) (0.00) (0.00)

(6) Footwear 0.677*** 0.162*** 0.161*** 3609(0.00) (0.00) (0.00)

(7) Beverages 0.667*** 0.168*** 0.165*** 3665(0.00) (0.00) (0.00)

(8) OthChem 0.655*** 0.173*** 0.172*** 4536(0.00) (0.00) (0.00)

(9) Paper 0.652*** 0.153*** 0.196*** 4078(0.00) (0.00) (0.00)

(10) Transport 0.647*** 0.178*** 0.176*** 4434(0.00) (0.00) (0.00)

(11) NonMetal 0.646*** 0.177*** 0.176*** 3698(0.00) (0.00) (0.00)

(12) Furniture 0.646*** 0.175*** 0.179*** 3553(0.00) (0.00) (0.00)

(13) IronSteel 0.640*** 0.182*** 0.178*** 3767(0.00) (0.00) (0.00)

(14) Apparel 0.633*** 0.165*** 0.202*** 4469(0.00) (0.00) (0.00)

(15) Plastic 0.620*** 0.192*** 0.189*** 4401(0.00) (0.00) (0.00)

(16) Leather 0.612*** 0.162*** 0.226*** 3970(0.00) (0.00) (0.00)

(17) Glass 0.603*** 0.151*** 0.247*** 3839(0.00) (0.00) (0.00)

(18) Textiles 0.603*** 0.200*** 0.197*** 4700(0.00) (0.00) (0.00)

(19) Food 0.563*** 0.220*** 0.216*** 4667(0.00) (0.00) (0.00)

(20) IndChem 0.524*** 0.227*** 0.248*** 4342(0.00) (0.00) (0.00)

(21) Printing 0.523*** 0.240*** 0.237*** 4392(0.00) (0.00) (0.00)

(22) ProfSci 0.516*** 0.243*** 0.241*** 4442(0.00) (0.00) (0.00)

(23) Machines 0.488*** 0.191*** 0.321*** 4817(0.00) (0.00) (0.00)

(24) MetalProd 0.478*** 0.204*** 0.319*** 4658(0.00) (0.00) (0.00)

(25) Electrics 0.470*** 0.257*** 0.272*** 4797(0.00) (0.00) (0.00)

(26) Rubber 0.468*** 0.172*** 0.360*** 4044(0.00) (0.00) (0.00)

Mean .617 .177 .205St. d. .101 .044 .067

Notes: Table reports the latent trade bias decomposition for non-zeroflows by estimating equation system (40)-(42) with constraint (43). Ro-bust standard errors in parentheses. Significance * .10, ** .05, *** .01.

10

Tabl

eB.

4:N

umbe

rof

Zer

oFl

ows

byEx

port

eran

dSe

ctor

(75

coun

trie

s)

Expo

rter

Toba

cco

Petr

oleu

mFu

rnit

ure

Woo

dFo

otw

ear

Beve

rage

sN

onM

etal

NfM

etal

sIr

onSt

eel

Gla

ssLe

athe

rR

ubbe

rPa

per

IndC

hem

Plas

tic

Prof

Sci

Prin

ting

Tran

spor

tO

thC

hem

App

arel

Met

alPr

odFo

odTe

xtile

sM

achi

nes

Elec

tric

sM

ean

TJK

7273

7173

6773

7048

6872

7068

7262

6563

6562

6652

5562

4241

4663

YEM

7061

7271

7269

6157

6470

6165

6155

5446

5041

5357

4031

5639

3757

NER

7056

6569

6467

6165

6264

6258

5449

5247

5445

5250

4948

5039

3155

KG

Z65

4965

6756

6160

5856

6958

6657

4657

5258

4349

4942

4940

4439

54ET

H74

7158

7158

6060

5765

5739

6262

6452

5248

5444

4045

2931

5045

54M

NG

6762

6056

5357

6366

6363

4857

6162

5349

4843

5431

4355

2741

4153

AR

M50

7060

6263

4550

5448

5559

6453

3350

4351

5446

5045

4747

3742

51A

LB71

6458

6041

6262

5357

6059

5652

5351

4445

4442

3037

5240

3036

50A

ZE

6648

5758

6360

6654

5444

4957

5544

4537

3641

4654

3041

3324

2347

MD

G69

5438

5358

6347

6354

5943

5946

5547

5155

5037

1837

3415

4034

47TZ

A65

6034

4762

3259

5154

6046

6558

4947

4747

4245

4534

2023

4131

47N

GA

7053

5539

5356

6151

5061

4838

5546

4939

3741

4342

4234

4226

3146

GH

A71

6428

2059

5359

4559

5350

4957

5347

5046

4035

4829

2243

3732

46M

DA

5567

6048

3732

6559

5455

5562

4656

3940

4144

4125

4429

2727

3246

MK

D70

5359

4741

3750

5444

5948

5251

4541

4039

3444

2638

3826

2226

43U

RY

6570

6347

4936

5356

5154

2249

4437

3631

3539

3027

3510

1233

2941

KA

Z62

3955

5457

5159

3314

4540

4753

2342

2931

3236

3927

3627

1826

39JO

R49

7258

6660

6147

4354

4452

4737

1225

2728

299

1316

3118

1221

37G

EO65

5563

4450

3352

4538

4353

4439

2734

2728

2417

4120

3228

1215

37K

EN68

5928

4440

4033

4950

4632

5442

3734

4029

2631

2528

1120

2324

37EC

U66

5535

2552

5048

4637

4838

4239

3126

2938

3327

3427

830

2226

36IS

L73

3161

5356

5252

4541

3936

3441

3220

2120

2817

3120

1225

916

35PE

R67

5535

3845

3938

2246

3827

4536

1533

3424

3626

1420

811

2027

32C

OL

5555

4246

3842

4548

4633

2137

1919

1926

2025

1817

184

1518

1530

TUN

6442

4849

2445

3746

4248

1930

2917

2021

3019

228

1621

1111

829

LKA

7068

2239

3548

4647

5432

199

1830

824

1021

176

96

613

1627

CH

L62

5638

1646

938

2832

3932

3022

1417

2726

3014

2415

523

1218

27M

AR

7258

2934

1739

2541

3818

2024

3526

1925

2724

198

145

416

1026

EST

5930

3222

3738

3431

3229

3023

1512

1617

2113

1322

1517

1512

824

LVA

5137

2619

3818

4434

3432

4025

2020

1415

1514

1217

1320

153

323

LTU

4333

3223

3937

3633

3027

3215

177

158

1213

915

1217

95

621

NZ

L64

5234

3329

1530

1831

2717

1517

187

35

79

184

011

12

19PA

K65

5821

3710

3414

3230

186

613

115

211

128

13

40

106

17SV

K56

4035

1817

3024

2415

1024

88

69

510

33

102

139

11

15PH

L42

4311

2714

2618

3424

1513

1616

208

97

85

64

26

41

15SV

N66

3822

2323

3311

1613

1615

82

26

33

55

133

127

02

14V

NM

5747

818

327

1433

2113

79

149

216

1310

72

00

13

414

RO

M54

1726

1312

2229

229

820

513

46

48

58

123

156

31

13M

EX37

2921

2824

819

2619

719

99

75

34

63

103

128

11

13BG

R49

1922

2319

1321

1819

1517

1012

16

45

60

83

52

12

12U

KR

5222

3319

3014

1217

28

176

91

25

92

49

36

60

412

NO

R51

2124

1624

2114

1510

1617

66

65

22

11

112

24

10

11IR

L39

2624

2329

413

1817

1113

49

42

12

41

93

25

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11H

UN

5418

2421

2114

1213

1411

135

56

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08

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PRT

4938

610

87

523

207

157

68

35

82

26

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31

210

GR

C26

2225

2423

83

913

1314

811

65

61

42

63

22

22

10SG

P45

2123

1716

1714

1312

115

34

52

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23

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9A

US

5626

1812

144

78

74

103

45

10

00

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21

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IDN

3533

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423

916

164

51

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32

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5914

127

1814

59

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91

11

21

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09

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HK

G24

324

103

307

1311

32

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61

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60

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7R

US

3812

1310

1711

85

15

142

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F31

1213

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105

108

45

21

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51

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2119

225

1011

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127

121

43

31

03

12

11

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BRA

4126

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54

48

53

81

85

21

53

16

10

31

16

CZ

E45

1812

1014

74

63

19

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61

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A56

233

72

125

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33

11

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6PO

L29

1813

616

102

63

37

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60

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5JP

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179

152

14

11

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11

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21

21

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4K

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385

915

613

34

12

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10

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02

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SWE

374

106

113

34

04

60

01

10

00

14

02

20

04

CA

N55

46

37

52

32

11

02

11

00

00

20

02

00

4D

NK

2210

910

76

47

41

60

20

00

00

02

00

10

04

TUR

426

77

514

11

00

10

30

00

10

00

00

00

04

AU

T39

77

48

23

45

31

00

20

00

00

00

10

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3IN

D24

152

42

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41

01

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2IT

A44

22

10

10

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01

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2ES

P22

42

21

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10

11

11

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2N

LD8

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63

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22

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01

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20

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2C

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81

23

15

12

11

01

10

10

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01

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CH

N29

00

00

10

00

00

00

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00

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1G

BR10

12

60

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1FR

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12

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1D

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0

11

C Robustness

In this section, we demonstrate the robustness of our baseline estimates in Section 4 to

alternative measures of the number of goods in Section C.1, to an alternative specification

without a projection in Section C.2, to an alternative measure of fixed costs in Section C.3,

and to an alternative specification with heterogeneous fixed cost effects in Section C.4.

C.1 Alternative Measure of the Number of Goods

Our baseline estimation results are reasonably robust with changes in the particular mea-

sure of the number of goods Ni. We replace the extensive margin in the baseline estima-

tion with two alternative variables. The first one is the total number of firms for each

country sourced from CEPII, and the second one is the log GDP for each country. We nor-

malize each variable by dividing the sum across all countries to obtain a share measure.

The results, together with our baseline estimates, are reported in Table C.5. In column

(2), we use the number of firms to replace the extensive margin. The coefficient of distance

is significantly negative. The coefficient of the interaction term of distance and exporter

income is significantly positive, implying that the distance reduces trade by less for richer

exporters. This suggests that there is a significant price elasticity heterogeneity across

exporters. Both coefficients are smaller than the baseline results in column (1) due to less

variation in the number of firms compared to the extensive margin measure. But the price

elasticity heterogeneity pattern is consistent. Similar results are obtained when we use log

GDP in column (3). The coefficients of entry cost are all significantly negative, which is

very close to the results in column (1). The coefficient of the income interaction term is

insignificantly different from zero in the last two regressions. This suggests that there is

little income elasticity heterogeneity across exporters for aggregate manufacturing trade.

The coefficient of the internal trade dummy is also significant, implying the internal trade

share is larger than foreign trade, given all else equal.

12

C.2 Heterogeneous Distance Elasticity without Constraint

In this part, we remove the constraint equation (28) on price elasticities. Exporter-specific

coefficients are estimated instead. Then the specification for AI gravity trade share is

Sij/Ni = −γβ′iρ ln distij − λentrycostij + c ln ri × ln rj

+ γβ′iρ ln Pj + f ei + f ej + εij, (45)

where f ei =YiY /Ni + γβ′i ln Πi + λΨi − φ′i ln R, and f ej = −c ln rj × ln r are exporter- and

importer-specific fixed effects, respectively. We expect the coefficients of ln distij will be

exporter-specific and all negative.

Unfortunately, both γβ′iρ and ln Pj are unobserved. If we take both unobservables

as parameters to be estimated, their interaction term will cause nonlinearity in the re-

gression. Bai (2009) extends the argument in Mundlak (1978) and Chamberlain (1984) to

models with interactive effects, and shows that more consistent estimates are obtained

with a projection of the interactive term onto an average of regressors when interest is

centered on the coefficients of non-interactive terms. We follow his idea to project the

unobservables such that ln Pj = η ln Pj + εj where

ln Pj = (1/N)N

∑i=1

ln distij. (46)

Then the econometric specification of the AI gravity equation becomes

Sij/Ni = −biρ ln distij − λentrycostij + c ln ri × ln rj

+ biρη ln Pj + f ei + f ej + vij, (47)

where vij = εij + γβ′iρεj. There are N + 2 parameters of interest in total, b1, ..., bN, λ, c.

And biρ can be estimated as exporter-specific coefficients on ln distij. We again pick

13

ρ = 0.117 and then bi are identified. We expect the coefficients of ln distij and entrycostij

are all negative, while the coefficient of the interaction term ln ri × ln rj is positive. In

other word, all parameters b1, ..., bN, λ, c should be positive. The productivity-adjusted

elasticity parameters are identified by

γβ′iρ = bi. (48)

The demand structural parameters are identified by

βi = bi/ ∑k

Nkbk. (49)

The results are reported in Table C.6. The entry cost reduces bilateral trade share sig-

nificantly. The estimate of the income elasticity parameter is marginally significant from

zero. The table also reports the estimates of the 75 distance elasticities bi, one correspond-

ing to each exporter, in the subsequent rows. The estimates are significantly negative for

most exporters. The three exporters with the biggest distance elasticity, i.e., with export

products that are very distance elastic, are Ethiopia, Yemen, and Moldova. In contrast,

Hong Kong, Switzerland, and the Netherlands have the smallest distance elasticity, i.e.,

the products that they export are distance inelastic. Figure C.9 shows that the correlation

assumption on the price elasticities and the exporter income in equation (28) in our base-

line estimation is very consistent with data. Products from rich exporters are less price

elastic. The R-squared is 0.34. Figure C.10 displays both the price and income elasticities

for each exporter’s products.

C.3 Alternative Measure of Fixed Cost

In this part, we examine another measure for the fixed cost to ensure that the coefficient

patterns in our baseline regression do not hinge on a particular measure.

14

In Table C.7, we replace entry cost with entry days & proc which is the sum of the num-

ber of days and the number of legal procedures necessary for an entrepreneur to legally

start operating a business.42 It is a nonmonetary measure of fixed cost to supplement

the entry cost, which is a monetary measure. We take an average of these nonmonetary

costs from the exporter and importer sides as the bilateral measure. By construction, en-

try days & proc. reflects regulation costs that should not depend on a firm’s volume of

exports to a particular country. The purpose of using the alternative fixed cost variable

is to check whether the distance coefficient patterns in Table B.2 are driven by the mea-

surement of fixed costs. We find that the coefficients on distance and its interaction with

exporter income are very similar to the baseline table. This implies that the result regard-

ing the heterogeneity of the distance elasticity is robust. And the order of the sectoral

results is close to the baseline results also, suggesting that the relative degree of the elas-

ticity dispersion among sectors is also robust. The coefficients of entry days & proc. are

significantly negative for most sectors. The results are robust.

C.4 Heterogeneous Fixed Cost Effects

In this part, we remove the symmetry constraint equation (29) on fixed cost elasticities.

The purpose is to check whether the price elasticity heterogeneity is robust when we

allow asymmetry in fixed cost effects. The structural model suggests that the coefficient

on fixed cost is a function of the markup in equation (17), and thus a function of the price

elasticity parameters implied in equation (6). Then we have

λ′i = (1/ ln H)(1 + γβi/si). (50)

42Helpman, Melitz, and Rubinstein (2008) also use the sum of these two measures of fixed costs to obtainsufficient variations.

15

Since the fixed cost coefficient is linear in the price elasticity, we can estimate λ′i in a similar

way to distance elasticities. Specifically, similar to (28), we assume

λi = b f0 − b f

1 ln ri, (51)

where ri is the exporter income of exporter i and b f1 > 0. The rich country’s goods are

more likely to have a smaller price elasticity, a higher markup, and thus a smaller fixed

cost effect on trade compared with those of the poor country’s goods. Then the specifica-

tion for AI gravity becomes

Sij/Ni = −b0ρ ln distij + b1ρ ln ri × ln distij − b f0 entrycostij + b f

1 ln ri × entrycostij

+ c ln ri × ln rj + δInternalij + b1 ln Pj × ln ri + f ei + f ej + εij, (52)

where f ei and f ej are exporter- and importer-specific fixed effects, respectively. We expect

the coefficients of ln distij and entrycostij are both negative, while the coefficients of the

three interaction terms are all positive. In other words, parameters b0, b1, b f0 , b f

1 , c are

the parameters of interest and should be all positive.

The results are reported in Table C.8. Row (1) shows the estimates for the aggregate

trade. The coefficients of distance and its interaction term with exporter income are very

close to the results in our baseline regression. The coefficient of entry cost is significantly

negative, which implies that the entry cost reduces the bilateral trade share. The coeffi-

cient of the interaction term of entry cost and exporter income is significantly positive,

implying that the entry cost reduces trade by less for richer exporters. Row (2)-(26) re-

port the sectoral results. The coefficients of the entry cost interaction term are, in most

cases, significant and the estimates vary across sectors in a sensible way. Importantly, we

find that the coefficients on distance and its interaction with exporter income are very

similar to those in Table B.2 – distance elasticity heterogeneity is robust to allowance for

16

Table C.5: Robustness: Alternative Measures of Number of Goods

(1) (2) (3)Extensive Margin No. of Firms ln GDP

mainDistance -1.1896∗∗∗ -0.6585∗∗∗ -0.5845∗∗∗

(0.0251) (0.0266) (0.0231)

Distance × Income ex 0.1314∗∗∗ 0.0483∗∗∗ 0.0419∗∗∗

(0.0027) (0.0029) (0.0025)

Entry cost -0.2649∗∗∗ -0.2117∗∗ -0.2361∗∗∗

(0.0880) (0.0932) (0.0810)

Income im × Income ex 0.0059 -0.0331 -0.0092(0.0211) (0.0227) (0.0196)

Internal 2.8591∗∗∗ 7.9369∗∗∗ 7.9551∗∗∗

(0.0804) (0.0850) (0.0739)Observations 5625 5625 5625r2 p 0.5721 0.7353 0.8166

Notes: Table reports the estimates of the AI gravity in equation (30) with alter-native measures of number of goods. Estimated exporter- and importer-specificfixed effects are dropped. Robust standard errors in parentheses. Significance *.10, ** .05, *** .01.

asymmetric fixed export cost. Moreover, the order of the sectoral distance elasticities is

close to those of the baseline regressions. Thus the ranking of sectors in terms of distance

elasticities is robust to allowance for asymmetric fixed cost effect.

17

Table C.6: AI gravity Estimation without Constraint

Variables (1A) (1B)Entry cost -0.2158*** (0.0731)Income im × Income ex 0.0009* (0.0005)

Ethiopia × Distance -0.3279*** (0.0088) Portugal × Distance -0.0284*** (0.0092)Yemen × Distance -0.2012*** (0.0091) Brazil × Distance -0.0279** (0.0109)Moldova × Distance -0.1690*** (0.0124) Tunisia × Distance -0.0278** (0.0114)Jordan × Distance -0.1506*** (0.0090) Romania × Distance -0.0268* (0.0147)Iceland × Distance -0.1323*** (0.0087) Australia × Distance -0.0264* (0.0141)Tanzania × Distance -0.1314*** (0.0089) Czech × Distance -0.0243** (0.0122)Niger × Distance -0.1217*** (0.0098) Ireland × Distance -0.0215** (0.0088)Madagascar × Distance -0.0998*** (0.0095) Viet Nam × Distance -0.0214*** (0.0071)Kenya × Distance -0.0916*** (0.0082) Bulgaria × Distance -0.0206 (0.0126)Greece × Distance -0.0897*** (0.0117) Spain × Distance -0.0205* (0.0106)Mongolia × Distance -0.0851*** (0.0090) India × Distance -0.0193** (0.0093)Tajikistan × Distance -0.0849*** (0.0079) United States × Distance -0.0170 (0.0123)Peru × Distance -0.0819*** (0.0086) Japan × Distance -0.0153* (0.0083)Ghana × Distance -0.0779*** (0.0083) China × Distance -0.0140* (0.0084)Georgia × Distance -0.0770*** (0.0092) Denmark × Distance -0.0140 (0.0104)Armenia × Distance -0.0754*** (0.0080) Sweden × Distance -0.0140 (0.0112)Nigeria × Distance -0.0743*** (0.0092) Korea × Distance -0.0131* (0.0071)Kyrgyzstan × Distance -0.0731*** (0.0081) Poland × Distance -0.0130 (0.0144)Uruguay × Distance -0.0703*** (0.0082) Indonesia × Distance -0.0128 (0.0081)Sri Lanka × Distance -0.0689*** (0.0076) Italy × Distance -0.0127 (0.0142)New Zealand × Distance -0.0661*** (0.0129) Slovenia × Distance -0.0119 (0.0108)Albania × Distance -0.0647*** (0.0103) Philippines × Distance -0.0111 (0.0074)Chile × Distance -0.0637*** (0.0097) Thailand × Distance -0.0104 (0.0066)Lithuania × Distance -0.0595*** (0.0113) France × Distance -0.0095 (0.0115)Ukraine × Distance -0.0579*** (0.0177) Slovakia × Distance -0.0094 (0.0126)Russia × Distance -0.0551*** (0.0198) Norway × Distance -0.0094 (0.0113)Pakistan × Distance -0.0546*** (0.0092) Hungary × Distance -0.0093 (0.0126)Ecuador × Distance -0.0539*** (0.0075) Mexico × Distance -0.0090 (0.0107)Macedonia × Distance -0.0490*** (0.0101) Germany × Distance -0.0088 (0.0121)Estonia × Distance -0.0481*** (0.0096) United Kingdom × Distance -0.0087 (0.0097)Azerbaijan × Distance -0.0465*** (0.0092) Malaysia × Distance -0.0082 (0.0070)Latvia × Distance -0.0404*** (0.0100) Singapore × Distance -0.0077 (0.0050)Turkey × Distance -0.0372** (0.0150) Austria × Distance -0.0071 (0.0118)South Africa × Distance -0.0369*** (0.0111) Canada × Distance -0.0064 (0.0125)Colombia × Distance -0.0342*** (0.0083) Hong Kong × Distance -0.0061 (0.0054)Kazakstan × Distance -0.0301*** (0.0110) Switzerland × Distance -0.0060 (0.0105)Finland × Distance -0.0296*** (0.0105) Netherlands × Distance -0.0050 (0.0093)Morocco × Distance -0.0292*** (0.0094)

Observations 5625

Notes: Table reports the estimates of the AI gravity without constraint (28) in (45). Estimatedexporter- and importer-specific fixed effects are dropped. Robust standard errors in parentheses.Significance * .10, ** .05, *** .01.

18

ALB

ARM

AUS

AUT

AZE

BGRBRA

CANCHE

CHL

CHN

COL

CZE

DEUDNK

ECU

ESP

EST

FIN

FRAGBR

GEOGHA

GRC

HKGHUNIDN

IND IRL

ISL

ITA

JOR

JPN

KAZ

KEN

KGZ

KOR

LKA

LTU

LVA

MAR

MDA

MDG

MEX

MKD

MNG

MYS

NER

NGA

NLDNOR

NZL

PAK

PER

PHL POL

PRTROM

RUS

SGPSVK SVN SWETHA

TJK

TUN

TUR

TZA

UKR

URY

USAVNM

YEM

ZAF

0.5

1P

rice

ela

sticity (

γβ’ i)

6 8 10 12Exporter GDP per capita in log

Figure C.9: Price Elasticity and Exporter Income (R2 = 0.34)

ALB

ARM

AUS

AUT

AZE

BGRBRA

CANCHE

CHL

CHN

COL

CZE

DEUDNK

ECU

ESP

EST

FIN

FRAGBR

GEOGHA

GRC

HKGHUNIDN

IND IRL

ISL

ITA

JOR

JPN

KAZ

KEN

KGZ

KOR

LKA

LTU

LVA

MAR

MDA

MDG

MEX

MKD

MNG

MYS

NER

NGA

NLDNOR

NZL

PAK

PER

PHL POL

PRTROM

RUS

SGPSVK SVN SWETHA

TJK

TUN

TUR

TZA

UKR

URY

USAVNM

YEM

ZAF

0.5

1P

rice

ela

sticity (

γβ’ i)

−.003 −.002 −.001 0 .001 .002Income elasticity (φ’i)

Figure C.10: Price Elasticity and Income Elasticity

19

Table C.7: Robustness: Alternative Fixed Cost

Distance Dist.×Inc ex Entry days & proc. Inc im×Inc ex Internal Observations(1) Aggregate -1.166*** 0.129*** -0.017*** -0.002 2.833*** 5625

(0.03) (0.00) (0.00) (0.02) (0.08)

(2) Furniture -2.608*** 0.275*** -0.098*** 0.029 4.428*** 5625(0.06) (0.01) (0.01) (0.06) (0.20)

(3) Beverages -2.494*** 0.263*** -0.055*** -0.006 3.659*** 5625(0.06) (0.01) (0.01) (0.05) (0.18)

(4) Tobacco -2.754*** 0.256*** -0.044*** 0.034 1.004*** 5625(0.08) (0.01) (0.02) (0.07) (0.25)

(5) Petroleum -2.314*** 0.225*** -0.012 -0.056 1.358*** 5625(0.07) (0.01) (0.01) (0.06) (0.20)

(6) NonMetal -2.113*** 0.219*** -0.029*** -0.019 3.360*** 5625(0.06) (0.01) (0.01) (0.05) (0.18)

(7) Leather -1.762*** 0.184*** -0.032*** 0.061 1.639*** 5625(0.05) (0.01) (0.01) (0.04) (0.16)

(8) Food -1.682*** 0.182*** -0.025*** -0.015 3.745*** 5625(0.04) (0.00) (0.01) (0.04) (0.13)

(9) Plastic -1.653*** 0.175*** -0.006 -0.007 2.402*** 5625(0.04) (0.00) (0.01) (0.03) (0.13)

(10) NfMetals -1.681*** 0.172*** -0.053*** -0.017 1.368*** 5625(0.04) (0.00) (0.01) (0.04) (0.13)

(11) Glass -1.457*** 0.150*** -0.037*** 0.072** 2.216*** 5625(0.04) (0.00) (0.01) (0.03) (0.13)

(12) Printing -1.352*** 0.145*** -0.020*** -0.071** 3.775*** 5625(0.04) (0.00) (0.01) (0.04) (0.13)

(13) Wood -1.406*** 0.141*** -0.010* 0.001 1.989*** 5625(0.03) (0.00) (0.01) (0.03) (0.10)

(14) Apparel -1.134*** 0.120*** -0.035*** 0.028 1.868*** 5625(0.02) (0.00) (0.00) (0.02) (0.08)

(15) Footwear -1.171*** 0.118*** 0.002 -0.018 1.120*** 5625(0.03) (0.00) (0.01) (0.03) (0.11)

(16) Transport -1.083*** 0.116*** -0.057*** 0.015 1.618*** 5625(0.02) (0.00) (0.00) (0.02) (0.07)

(17) Paper -1.085*** 0.110*** 0.011** 0.023 1.496*** 5625(0.03) (0.00) (0.00) (0.02) (0.09)

(18) OthChem -0.975*** 0.102*** 0.000 -0.009 1.456*** 5625(0.02) (0.00) (0.00) (0.02) (0.07)

(19) IronSteel -1.023*** 0.102*** -0.056*** -0.027 1.715*** 5625(0.03) (0.00) (0.01) (0.03) (0.11)

(20) Textiles -0.894*** 0.094*** -0.051*** -0.034 1.665*** 5625(0.02) (0.00) (0.00) (0.02) (0.07)

(21) ProfSci -0.832*** 0.089*** -0.002 -0.030 1.249*** 5625(0.03) (0.00) (0.00) (0.03) (0.10)

(22) Electrics -0.677*** 0.071*** -0.004 0.014 1.323*** 5625(0.03) (0.00) (0.00) (0.03) (0.10)

(23) Rubber -0.664*** 0.065*** -0.011** 0.071*** 1.245*** 5625(0.03) (0.00) (0.00) (0.02) (0.09)

(24) MetalProd -0.627*** 0.063*** 0.005 0.039** 1.797*** 5625(0.02) (0.00) (0.00) (0.02) (0.07)

(25) Machines -0.587*** 0.061*** -0.028*** 0.043** 0.950*** 5625(0.02) (0.00) (0.00) (0.02) (0.07)

(26) IndChem -0.584*** 0.059*** -0.028*** 0.021 1.592*** 5625(0.02) (0.00) (0.00) (0.02) (0.07)

Notes: Table reports the estimates of the sectoral AI gravity in equation (32) with alternative fixed cost.Estimated exporter- and importer-specific fixed effects are dropped. Robust standard errors in paren-theses. Significance * .10, ** .05, *** .01.

20

Table C.8: Robustness: Asymmetric Fixed Cost Effects

Distance Dist.×Inc ex Entry cost Entry×Inc ex Inc im×Inc ex Internal Observations(1) Aggregate -1.158*** 0.128*** -5.805*** 0.550*** 0.017 2.829*** 5625

(0.03) (0.00) (0.89) (0.09) (0.02) (0.08)

(2) Furniture -2.590*** 0.273*** -31.600*** 3.042*** 0.131** 4.438*** 5625(0.06) (0.01) (3.28) (0.32) (0.06) (0.20)

(3) Beverages -2.481*** 0.262*** -18.458*** 1.766*** 0.053 3.651*** 5625(0.06) (0.01) (2.77) (0.27) (0.05) (0.18)

(4) Tobacco -2.729*** 0.253*** -17.598*** 1.655*** 0.088 0.982*** 5625(0.08) (0.01) (4.44) (0.43) (0.08) (0.25)

(5) Petroleum -2.259*** 0.219*** -13.764*** 1.319*** -0.007 1.303*** 5625(0.07) (0.01) (3.31) (0.32) (0.06) (0.20)

(6) NonMetal -2.102*** 0.218*** -10.446*** 1.005*** 0.015 3.353*** 5625(0.06) (0.01) (2.57) (0.25) (0.05) (0.18)

(7) Food -1.668*** 0.181*** -9.341*** 0.882*** 0.014 3.735*** 5625(0.04) (0.00) (1.61) (0.16) (0.04) (0.13)

(8) Leather -1.722*** 0.180*** -16.545*** 1.605*** 0.120*** 1.606*** 5625(0.05) (0.01) (2.35) (0.23) (0.05) (0.16)

(9) Plastic -1.595*** 0.168*** -12.297*** 1.179*** 0.039 2.339*** 5625(0.04) (0.00) (1.76) (0.17) (0.04) (0.13)

(10) NfMetals -1.588*** 0.161*** -33.161*** 3.202*** 0.100*** 1.282*** 5625(0.04) (0.00) (2.34) (0.23) (0.04) (0.13)

(11) Printing -1.346*** 0.145*** -6.614*** 0.620*** -0.051 3.772*** 5625(0.04) (0.00) (1.65) (0.16) (0.04) (0.13)

(12) Glass -1.401*** 0.144*** -20.687*** 1.991*** 0.145*** 2.171*** 5625(0.04) (0.00) (2.01) (0.19) (0.04) (0.13)

(13) Wood -1.361*** 0.136*** -11.530*** 1.107*** 0.042 1.944*** 5625(0.03) (0.00) (1.65) (0.16) (0.03) (0.10)

(14) Apparel -1.127*** 0.119*** -10.551*** 1.033*** 0.064*** 1.875*** 5625(0.02) (0.00) (1.03) (0.10) (0.02) (0.08)

(15) Transport -1.079*** 0.116*** -16.138*** 1.552*** 0.067*** 1.634*** 5625(0.02) (0.00) (1.06) (0.10) (0.02) (0.07)

(16) Footwear -1.146*** 0.115*** -4.491*** 0.435*** -0.001 1.091*** 5625(0.03) (0.00) (1.60) (0.16) (0.03) (0.11)

(17) Paper -1.043*** 0.105*** -4.738*** 0.459*** 0.043* 1.452*** 5625(0.03) (0.00) (1.17) (0.11) (0.02) (0.09)

(18) IronSteel -1.013*** 0.101*** -17.747*** 1.700*** 0.028 1.718*** 5625(0.03) (0.00) (1.77) (0.17) (0.03) (0.10)

(19) OthChem -0.968*** 0.101*** -1.073 0.099 -0.006 1.449*** 5625(0.02) (0.00) (0.80) (0.08) (0.02) (0.07)

(20) Textiles -0.899*** 0.095*** -12.911*** 1.250*** 0.006 1.691*** 5625(0.02) (0.00) (1.02) (0.10) (0.02) (0.07)

(21) ProfSci -0.819*** 0.087*** -2.783** 0.257** -0.020 1.234*** 5625(0.03) (0.00) (1.25) (0.12) (0.03) (0.10)

(22) Electrics -0.672*** 0.071*** -1.889* 0.172 0.020 1.317*** 5625(0.03) (0.00) (1.13) (0.11) (0.03) (0.10)

(23) Rubber -0.659*** 0.065*** -3.861*** 0.358*** 0.083*** 1.239*** 5625(0.03) (0.00) (1.23) (0.12) (0.02) (0.09)

(24) MetalProd -0.607*** 0.061*** -2.020** 0.185** 0.046** 1.774*** 5625(0.02) (0.00) (0.90) (0.09) (0.02) (0.07)

(25) Machines -0.572*** 0.060*** -9.887*** 0.956*** 0.077*** 0.945*** 5625(0.02) (0.00) (0.83) (0.08) (0.02) (0.07)

(26) IndChem -0.576*** 0.058*** -9.312*** 0.891*** 0.052*** 1.588*** 5625(0.02) (0.00) (1.02) (0.10) (0.02) (0.07)

Notes: Table reports the estimates of the AI gravity with asymmetric fixed cost effects in equation (52). Esti-mated exporter- and importer-specific fixed effects are dropped. Robust standard errors in parentheses. Signif-icance * .10, ** .05, *** .01.

21

D Trade Probability

It is also useful to analyze the marginal effect of a change in trade costs on the probability

that a given country pair trade with each other. In order to compare the marginal effect

of variable cost and fixed cost on trade probability, we standardize both trade costs, and

then investigate the change in trade probability due to a one-standard-deviation decrease

in variable and fixed cost, respectively. First we construct VC = ρ ln distij and FC =

fij where ρ = 0.117, and VC and FC denote the variable and fixed costs, respectively.

Then we standardize them by subtracting their means and divided by their standard

deviations, resulting in variables of zero sample mean and unit sample variance. In order

to get an average marginal effect of variable cost across exporters with heterogeneous

price elasticities, we shut down the interaction terms ln ri × ln distij and ln Pj × ln ri in

equation (30). Then the specification of the symmetric AI gravity equation becomes

Sij/Ni = −bvVCij − b f FCij + c ln ri × ln rj + δ Internalij + f ei + f ej + εij, (53)

and the observed trade share

Sij/Ni =

Sij/Ni, if Sij ≥ 0,

0, if Sij < 0,

where Sij is the latent value of the systematic trade share. f ei and f ej are exporter- and

importer-specific fixed effects, respectively. The dummy variable Internalij is zero for

import and one for the internal trade, capturing all the other unobserved trade cost across

borders. We assume the error term ε ∼ Normal (0, σ2). Then the probability that a given

country pair trade with each other is

Prob(S > 0) = Prob(ε > −Xb) = Φ(Xb/σ), (54)

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where matrix X is the vector of all independent variables, b is the vector of all their coeffi-

cients in equation (53) and Φ(.) is the standard normal cumulative distribution function.

Thus the marginal changes in trade probability due to trade costs are computed by

∂Prob(S > 0)∂VC

= bvφ(Xb/σ)/σ, (55)

and∂Prob(S > 0)

∂FC= b f φ(Xb/σ)/σ, (56)

where φ(.) is the standard normal probability density function, and X denotes the vector

of mean values.

The results are reported in Table D.9. Row (1) shows the marginal changes in trade

probability for the aggregate trade. One standard deviation decrease in VC improves the

trade probability by 5 percentage points, while one standard deviation decrease in FC

improves the trade probability by 3 percentage points. Since there are many fewer zeros

in aggregate trade, we further report the results by sectors in row (2)-(26). All numbers

are positive which implies lowering trade cost increases the trade probability. On average,

one standard deviation decrease in VC improves the trade probability by 10 percentage

points, while one standard deviation decrease in FC improves the trade probability by

2 percentage points. To visualize the results, Figure D.11 plots the results of marginal

effects of VC and FC on trade probability respectively, as well as their 95% confidence

intervals. VC raises the trade probability most in petroleum, wood, and tobacco sectors,

while least in professional and scientific equipment, electrics, and printing sectors. FC

raises the trade probability most in transport, textiles, and machines sectors, while least

in electrics, paper, and professional and scientific equipment sectors. More importantly,

marginal changes in trade probability due to VC are larger than to FC for all sectors,

implying that variable cost is more important than fixed cost in trade policy adjustment

to make trade to occur.

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Table D.9: Marginal Effect on Trade Probability

Variable cost Fixed cost

(1) Aggregate .046 (.0119) .0282 (.0088)

(2) Petroleum .149 (.0116) .0143 (.0089)

(3) Wood .1471 (.012) .03 (.0101)

(4) Tobacco .145 (.0097) .0224 (.0084)

(5) Paper .1327 (.0121) .0049 (.0093)

(6) NfMetals .1238 (.012) .0339 (.0095)

(7) IronSteel .1208 (.0121) .0352 (.0095)

(8) OthChem .1201 (.0122) .0053 (.009)

(9) Footwear .1179 (.0119) .0072 (.0094)

(10) MetalProd .1044 (.0122) .0073 (.0091)

(11) Apparel .1038 (.0122) .0267 (.0094)

(12) Rubber .1016 (.0121) .0141 (.0092)

(13) IndChem .1004 (.0122) .032 (.0094)

(14) NonMetal .0979 (.012) .0166 (.0092)

(15) Glass .0971 (.0121) .0307 (.0094)

(16) Beverages .0884 (.012) .0275 (.0094)

(17) Textiles .0879 (.0121) .0407 (.0092)

(18) Plastic .0853 (.0121) .0184 (.0092)

(19) Transport .0848 (.0122) .0507 (.0092)

(20) Leather .0829 (.012) .0146 (.0096)

(21) Machines .0826 (.0121) .0346 (.009)

(22) Furniture .0811 (.012) .0325 (.0099)

(23) Food .0605 (.0121) .0294 (.009)

(24) Printing .0579 (.0122) .0226 (.0091)

(25) Electrics .057 (.0121) .0049 (.009)

(26) ProfSci .0563 (.0121) .0062 (.0092)

Mean .0995 .0225

St. d. .0276 .0127

Notes: Table reports the marginal effect of one-standard-deviation decrease in trade costs on tradeprobability by estimating equation (53). Robuststandard errors in parentheses.

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Figure D.11: Marginal Effect on Trade Probability

25