is the iceberg melting less quickly? international trade

Is the Iceberg Melting Less Quickly?

International Trade Costs after World War II�

Dennis Novyy

University of Warwick

17 May 2007

Abstract

International trade costs determine trade patterns and therefore economic per-formance. This paper develops a micro-founded measure of these internationaltrade costs. It is derived by incorporating bilateral �iceberg�trade costs intoa multi-country general equilibrium model of trade and solving for the impliedgravity equation. The innovation of this micro-founded gravity equation is toexpress multilateral resistance in the form of observable variables. As a result,it becomes possible to compute trade costs directly from this gravity equationand also to track the changes in trade costs over time. It is found that sinceWorld War II trade costs amongst OECD countries have declined markedly.The decline in trade costs has been particularly dramatic for nearby trad-ing partners, consistent with the promotion of regional economic integrationthrough NAFTA and the European Common Market.

JEL classi�cation: F1, F4Keywords: Trade Costs, Gravity, Distance, Economic Integration

�I am grateful to Petra Geraats, David Jacks, Chris Meissner, Francesco Caselli, Jakob de Haan andStephen Redding for valuable comments. I would also like to thank conference/seminar participantsat the Annual Congress of the European Economic Association (EEA) in Amsterdam, the Universityof Groningen, the University of Cambridge, the Federal Reserve Bank of St. Louis, the University ofBirmingham, the University of Oxford and the University of Warwick. Any remaining errors are mine.

yDepartment of Economics, University of Warwick, Coventry CV4 7AL, United [email protected] and http://www2.warwick.ac.uk/fac/soc/economics/sta¤/faculty/novy/

1 Introduction

Barriers to international trade are large and since they impede trade �ows, they have a

strong impact on countries�overall economic performance. Some barriers, like tari¤s and

transportation costs, are directly observable but numerous other barriers are notoriously

di¢ cult to measure, for example administrative and communication costs. The aim of this

paper is to derive a comprehensive measure of trade costs that can capture all barriers to

international trade.

This comprehensive measure of trade barriers is derived by incorporating bilateral

�iceberg� trade costs into a multi-country general equilibrium model of trade. Iceberg

trade costs mean that for each good that is exported a certain fraction melts away during

the trading process as if an iceberg were shipped across the ocean. The model yields a

micro-founded gravity equation that relates trade �ows to iceberg trade costs and output

in a simple and intuitive way. It is therefore possible to compute trade costs directly from

this micro-founded gravity equation.

The recent literature, most notably the important contribution by James Anderson and

Eric van Wincoop (2003), has given considerable attention to the measurement of trade

costs. The contribution of the current paper is to greatly simplify the measurement of trade

costs. This is achieved by �nding a convenient solution to the problem of capturing the

unobservable multilateral resistance variables highlighted by Anderson and van Wincoop

(2003). In particular, the micro-founded gravity equation includes terms for countries�

total exports and these total export terms indirectly incorporate countries�trade barriers

with the rest of the world. Intuitively, the bigger a country�s total exports are, the lower

are its trade barriers with other countries. This convenient form of expressing multilateral

resistance implies that it is easy to measure changes in trade costs over time because they

explicitly depend on observable variables.

Empirical bilateral trade costs are thus obtained for OECD countries during the post-

World War II period. For the G7 subsample trade costs fell by 26:5 percent between 1960

and 2002. Similarly, for European Union countries trade costs fell by 17:7 percent between

1977 and 2002. For both subsamples the 2002 tari¤ equivalent of trade costs stands at

about 40 percent. In general, trade costs have fallen most dramatically for nearby trading

partners, implying an increase in regional economic integration that is consistent with the

emergence of regional free trade agreements such as NAFTA and the European Common

Market.

As opposed to a comprehensive measure of trade barriers, the literature has produced

many estimates of certain trade cost components. Two well-known examples are John Mc-

Callum�s (1995) and Andrew Rose�s (2000) papers. McCallum (1995) examines the e¤ect

of the U.S.-Canadian border as a very general form of trade costs, whereas Rose (2000) fo-

cuses on common currencies. David Hummels (2007) measures the costs of transportation

1

with a focus on ocean and air freight rates. But by their very nature, such measures focus

on single trade cost components and therefore only convey a partial picture. In contrast,

this paper presents a comprehensive measure of trade costs that captures all barriers to

trade.

In their in-depth survey of trade costs, Anderson and van Wincoop (2004) combine

various trade cost components such as transportation costs, tari¤s and language barriers.

They argue that based on data from recent years, the tari¤ equivalent of representative

international trade costs is around 74 percent, a number that is consistent with the range

found in this paper. But the advantage of the comprehensive trade cost measure in this

paper is to produce trade costs that vary over time and that are country-pair speci�c.

Trade costs in fact exhibit a high degree of heterogeneity across country pairs, a �nding

which is masked by any �one-�ts-all�measure.

Apart from providing snapshots of trade costs over time, the paper also seeks to explain

the dispersion of trade costs across country pairs. The trade cost regressions reveal how

trade cost components have changed over time. For example, they show that language

barriers have declined substantially. In 1970 using the same o¢ cial language was associated

with a tari¤ equivalent of trade costs that was lower by 15 percentage points on average,

but in 2000 the language barrier is no longer signi�cantly di¤erent from zero. Likewise, the

advantage of sharing a common colonial history was substantial in 1970 but has washed

out over time and can no longer be associated with lower trade costs in 2000.

Head and Ries (2001) derive a measure for the U.S.-Canadian border e¤ect. But

since their two-country framework does not consider trade with other countries, by con-

struction it cannot account for multilateral resistance. The gravity equations developed

by Je¤rey Bergstrand (1985), Scott Baier and Je¤rey Bergstrand (2001) and Anderson

and van Wincoop (2003) include multilateral resistance terms, but they are unobservable

because they are highly non-linear theoretical constructs.1 The micro-founded gravity

equation derived in this paper is more practical since it captures multilateral resistance

with observable variables and therefore provides an easy and intuitive way of computing

trade costs. Another advantage of this gravity equation is that in order to compute trade

costs, there is no need to impose any structure on the underlying trade cost components.

In particular, no assumptions are needed as to which variables are actually important as

trade cost determinants and what functional form they take. Baier and Bergstrand (2001)

only consider transportation costs and tari¤s, whereas Anderson and van Wincoop (2003)

focus on distance and border barriers.

The paper is organized as follows. Section 2 develops the general equilibrium model

with iceberg trade costs, resulting in the essential gravity equation and the micro-founded

1Novy (2007) derives explicit solutions for the multilateral resistance variables on the basis of Andersonand van Wincoop (2003)�s model and subsequently uses them to derive a measure of international tradecosts.

2

trade cost measure. Section 3 illustrates how trade costs have changed over the past

few decades with special emphasis on the G7 and European Union countries, showing

that economic integration has progressed fastest on a regional level. Section 4 explains

the variation of trade costs across country pairs and provides a discussion of the results.

Section 5 concludes.

2 A Model with Iceberg Trade Costs

This section develops a micro-founded general equilibrium model that is similar to the

framework typically encountered in the New Open Economy Macroeconomics literature,

as for example in Obstfeld and Rogo¤ (1995), with the exception that the model abstracts

from price stickiness as it does not focus on the short run. The model augments the

standard framework in three distinct ways. First, it extends to multiple countries. Second,

it adds nontradable goods and third, as its central building block the model incorporates

iceberg trade costs of the kind introduced by Samuelson (1954) and �rst included in a

monopolistic competition model by Krugman (1980).

Optimizing consumers and �rms inhabit J countries with j = 1; 2;:::; J and J � 2.

The range of all consumers and of all goods produced in the world is the continuum [0; 1].

Country j comprises the consumer range [nj�1; nj ], and country-j monopolistic �rms each

produce one di¤erentiated good on the same range, where n0 = 0 and nJ = 1. It is assumed

that the fraction sj of goods is tradable so that [nj�1; nj�1 + sj(nj � nj�1)] is the rangeof all tradable goods produced by country j (0 < sj � 1).2 These can be purchased by allconsumers in the world. The remaining range [nj�1+sj(nj�nj�1); nj ] represents countryj�s nontradable goods. The latter are available for purchase to country-j consumers only.

Exogenous bilateral �iceberg� trade costs � j;k are incurred when goods are shipped

from country j to country k where

� j;k

(� 0 for j 6= k= 0 for j = k

Iceberg trade costs mean that for each unit of goods that is shipped from j to k the fraction

� j;k melts away as if an iceberg were shipped across the ocean (� j;k < 1 for j 6= k). It

is assumed that bilateral trade costs are symmetric (� j;k = �k;j). The assumption of

zero intranational trade costs is a normalization which can also be found in Baier and

Bergstrand (2001).3

2For an empirical motivation of this assumption see Section 3.1.3Suppose that trade costs of shipping from j to k can be decomposed into the costs up to the border of

k times the costs of intranational shipping within k (the latter the same for all origins of shipment). Thenormalization of intranational trade costs to zero then implies that � j;k should be interpreted exclusivelyas the costs of shipping up to the border of k.

3

2.1 Consumers

All consumers within one country are identical. They like consumption and dislike work

such that their utility can be described as

Uj = lnCj + � ln (1� Lj) (1)

where Cj and Lj denote per-capita consumption and labor supply of the representative

country-j consumer. The parameter � is assumed to be identical across countries. Cj is a

CES Dixit-Stiglitz composite consumption index de�ned as

Cj �"JXk=1

Z nk�1+sk(nk�nk�1)

nk�1

(cji)��1� d i+

Z nj

nj�1+sj(nj�nj�1)(cji)

��1� d i

# ��1

(2)

where cji denotes the per-capita consumption of good i in country j. The country-j

consumption index (2) is de�ned over all tradable goods produced in the world, which is

the �rst term within the brackets of (2), plus all nontradable goods produced by country

j, which are given by the second term within the brackets. � > 1 is the elasticity of

substitution and it is assumed to be identical across countries.

The consumption-based price index, de�ned as the minimum expenditure for one unit

of Cj , can be derived from (2) as

Pj =

"JXk=1

Z nk�1+sk(nk�nk�1)

nk�1

(�ji)1��

d i+

Z nj

nj�1+sj(nj�nj�1)(�ji)

1��d i

# 11��

(3)

where �ji denotes the prices of the individual goods as follows

�ji =

(1

1��k;j pTki for nk�1 � i � nk�1 + sk(nk � nk�1) 8 j; k

pNTji for nj�1 + sj(nj � nj�1) � i � nj(4)

pTki denotes the f.o.b. (free on board) price of the tradable good produced by country-k

�rm i and pTki=(1� �k;j) is the c.i.f. (cost, insurance, freight) price of the same good whentraded with country j. pNTji is the price of the nontradable good produced by country-j

�rm i. All prices are denominated in one world currency.

The c.i.f. price is 1=(1��k;j) times the f.o.b. price because when one unit of a tradablegood produced by a country-k �rm is shipped to country j, only the fraction (1 � �k;j)arrives at the destination. The tari¤ equivalent �k;j of iceberg trade costs can therefore

be expressed as

�k;j =1

1� �k;j� 1 = �k;j

1� �k;j(5)

Maximizing consumption (2) subject to the minimum expenditure (3) yields the stan-

4

dard individual demand function

cji =

��jiPj

��Cj (6)

The per-capita budget constraint in country j is given by

PjCj =WjLj + �j (7)

whereWj is the nominal wage and �j denotes per-capita nominal pro�ts made by country-j

�rms, which are fully redistributed to country-j consumers.

2.2 Firms

There is monopolistic competition such that each �rm as the single producer of one dif-

ferentiated good sets the pro�t-maximizing price. Not all �rms within one country are

symmetric since in country j the fraction sj of �rms produces tradable goods, whereas

the fraction (1� sj) produces nontradable goods. Let yTji denote the output produced bycountry-j tradable �rm i and yNTji the output produced by country-j nontradable �rm i.

In addition, let yTji;k be the tradable output of �rm i produced for country k so that

yTji �JXk=1

yTji;k (8)

All �rms face a linear production function that has constant returns to scale and that

operates with labor as the only input

yTji;k = AjLTji;k (9)

yNTji = AjLNTji (10)

where Aj is an exogenous and country-speci�c technology level that is assumed to be the

same across the tradable and nontradable sectors. LTji;k and LNTji denote the amount of

labor used to produce yTji;k and yNTji with

LTji �JXk=1

LTji;k (11)

As all consumers within one country are identical, they each spread their labor over all

domestic �rms according to how much labor input each �rm needs. Since labor is assumed

to be internationally immobile, domestic consumers do not work for foreign �rms. As

in Obstfeld and Rogo¤ (1995), production does not exhibit increasing returns to scale.

Since the number of �rms in country j is given by the range [nj�1; nj ], their pro�ts are

5

determined endogenously. This framework is therefore consistent with the approach taken

by, for instance, Anderson (1979) and Anderson and van Wincoop (2003) who assume

that each region is specialized in the production of only one good.

Using demand function (6) market clearing for the tradable good produced by country-

j �rm i requires

(1� � j;k) yTji;k = 11��j;k p

Tji

Pk

!��(nk � nk�1)Ck (12)

The right-hand side of (12) represents the amount of the tradable good i that the (nk �nk�1) consumers in country k demand. The left-hand side is the amount of the good

that arrives in country k after being shipped there from country j. Accordingly, market

clearing for a country-j nontradable good requires

yNTji =

pNTjiPj

!��(nj � nj�1)Cj (13)

The pro�t function for tradable �rm i in country j is

�Tji =

JXk=1

�pTjiy

Tji;k �WjL

Tji;k

�(14)

where Wj is the nominal wage that is the same across tradable and nontradable �rms

because workers are assumed to be mobile within countries. Plugging the production

function (9) and the market-clearing condition (12) into pro�ts (14) and maximizing with

respect to pTji yields the standard markup

pTji =�

�� 1Wj

Aj(15)

For nontradable �rms the same procedure leads to

pNTji =�

�� 1Wj

Aj(16)

so that

pTji = pNTji � pj (17)

Thus, all country-j �rms set the same price pj , irrespective of whether they produce

tradable or nontradable goods.

Appendix A.1 shows that the model outlined in Sections 2.1 and 2.2 has a unique

equilibrium solution. As one might expect, in equilibrium trade costs reduce the real

wage, consumption and real pro�ts.4

4See equations (30)-(32) and (36).

6

2.3 A Gravity Equation with Trade Costs

Given the equilibrium solution to the model, one can now derive the equilibrium trade

�ows between countries j and k. Since all country-j �rms producing tradable goods are

symmetric and since sj(nj�nj�1) is the overall number of these �rms, all goods that leavecountry j for destination country k are given by

EXPj;k = sj(nj � nj�1)yTji;k (18)

where EXPj;k denotes real exports from j to k. Likewise, all goods that leave country k

for export to country j are given by

EXPk;j = sk(nk � nk�1)yTki;j (19)

As we are ultimately interested in bilateral trade costs and as these bilateral trade costs

in�uence trade �ows in both directions, we need to combine (18) and (19) in order to

take all available information on trade �ows into account. The standard way of combining

unidirectional trade �ows is to multiply them by each other.5 This yields

EXPj;kEXPk;j = sj(nj � nj�1)yTji;ksk(nk � nk�1)yTki;j (20)

Appendix A.2 shows that one can derive a micro-founded gravity equation for EXPj;kEXPk;j .

As Appendix A.2 explains in detail, this is achieved by substituting the market-clearing

conditions for yTji;k and yTki;j and their equilibrium solutions. After various steps of algebra

one obtains a micro-founded gravity equation that explicitly includes trade costs

EXPj;kEXPk;j = sj (GDPj � EXPj) sk (GDPk � EXPk) (1� � j;k)2��2 (21)

where GDPj is the real output of country j and EXPj �Pk 6=j EXPj;k are real total

exports from j.

Of course, bilateral trade EXPj;kEXPk;j decreases if bilateral trade costs � j;k go up.

Conversely, bilateral trade increases if there are more �rms that produce tradable goods,

i.e. if the shares sj and sk go up, or if GDPj and GDPk go up. But a crucial feature

of gravity equation (21) is that bilateral trade is not solely determined by GDPj and

GDPk as in traditional gravity equations, but also by total exports EXPj and EXPk.

For example, if total exports EXPj increase, then bilateral trade will fall. The intuition is

as follows. For an increase in EXPj to occur, trade costs with third countries must have

dropped, for instance � j;l with l 6= k. This means that for any given level of � j;k, bilateraltrade between j and k has become more costly relative to other country pairs. It therefore

5See Baldwin and Taglioni (2006) for a discussion, in particular why it is problematic to take the sumof unidirectional trade �ows as opposed to their product.

7

falls. Gravity equation (21) thus takes into account the fact that in order to determine

bilateral trade �ows between j and k, it is not enough to solely focus on bilateral trade

costs between j and k. Instead, one also needs to consider bilateral trade costs with third

countries. These third-party trade costs indirectly enter (21) because they are embodied

in EXPj and EXPk.

Gravity equation (21) therefore captures what Anderson and van Wincoop (2003) call

�multilateral resistance,� i.e. the idea that trade between two countries is determined by

their bilateral trade barrier � j;k relative to their barriers with all other countries. The

total export terms EXPj and EXPk embody these barriers with all other countries and

therefore control for multilateral resistance. Whereas the multilateral resistance variables

in Anderson and van Wincoop (2003) are unobservable because they are highly nonlin-

ear functions of unknown bilateral barriers, gravity equation (21) solves this problem by

relating multilateral resistance to the observable total export terms.

An alternative way of thinking about multilateral resistance is along the lines of trade

destruction and trade diversion. For example, if bilateral trade barriers go up everywhere

in the world except between countries j and k (i.e. only � j;k is constant), then total trade

�ows in the world are diminished so that there is trade destruction. But j and k will

redirect some of the �destroyed�trade towards each other because their relative bilateral

trade barrier has dropped. Therefore, to a smaller extent there is also trade diversion.

Apart from conveniently controlling for multilateral resistance, a major advantage of

gravity equation (21) is that it allows for an easy computation of bilateral trade costs

� j;k. For simplicity it is assumed that the fraction of �rms producing tradable goods is

the same across countries (sj = sk = s).6 Gravity equation (21) can then be solved for

trade costs as

� j;k = 1��

EXPj;kEXPk;j(GDPj � EXPj) (GDPk � EXPk) s2

� 12��2

(22)

Intuitively, if bilateral trade �ows between j and k rise all else being equal, then trade

between these two countries must have become less di¢ cult and trade costs must have gone

down. Conversely, if output in either country increases without simultaneously leading to

an increase in bilateral trade, then the implied trade costs must have gone up.7 Expression

(22) implies that it is straightforward to measure the change in bilateral trade costs over

time because they explicitly depend on observable variables. Appendix A.3 shows that

expression (22) also holds in the more general case when countries run trade de�cits or

surpluses.

6See Section 3.1 for a discussion of s.7Head and Ries (2001) compute a U.S.-Canadian border e¤ect based on relative expenditure ratios, but

their two-country framework does not consider trade with partners outside North America and thus doesnot capture multilateral resistance. Neither does their framework allow for nontradable goods.

8

3 Trade Costs over Time

This section examines how bilateral trade costs have evolved over time. Its guiding ques-

tion is �By how much have trade costs fallen for which country pairs?�Using annual data

for 1960-2002, I compute iceberg trade costs on the basis of equation (22) and convert

them into tari¤ equivalents through the relationship given in (5).

3.1 Data and Parameter Assumptions

The export data, denominated in U.S. dollars, are taken from the IMF Direction of Trade

Statistics (DOTS), and the GDP data come from the IMF International Financial Statis-

tics (IFS). The data appendix gives the exact sources. The data are annual for a sample

of 31 countries, consisting of 26 OECD countries plus �ve important South American and

Asian countries (Argentina, Brazil, Chile, India and Indonesia).8 For most countries data

are reported from 1960 until 2002, but for some only more recent data are available.

Computing bilateral trade costs on the basis of (22) requires two parameter assump-

tions. The �rst is the elasticity of substitution. It is set to � = 11, which via the optimal

prices (15) and (16) corresponds to a markup of 10 percent. The elasticity of substitution

is often estimated to lie near 8 but many studies using aggregate data �nd higher values.9

For example, Eaton and Kortum (2002) estimate � to be 9:28, and under the assumption

of homogeneity across industries Head and Ries (2001) obtain an estimate of 11:4 for �.

In line with the gravity literature, I assume that � is constant over time. Broda and Wein-

stein (2006) estimate elasticities of substitution based on demand and supply relationships

for disaggregated U.S. imports. When comparing the period 1972-1988 with 1990-2001,

they only �nd a marginal decline in the median elasticity that is not always signi�cant

depending on the level of disaggregation.

It is well known that lower elasticities lead to higher trade cost estimates (see Anderson

and van Wincoop, 2004). Intuitively, a lower � means that consumers are less sensitive

to prices and trade costs and should therefore consume a larger amount of foreign goods.

Given the actual level of trade �ows, a lower � thus implies higher trade costs. For example,

under � = 11 the tari¤ equivalent of U.S.-Canadian trade costs in 1960 is 40:8 percent,

whereas under � = 8 it is 63:1 percent. The main focus of this paper, however, is not the

level of trade costs but rather the percentage change of trade costs over time. It turns out

that the percentage change is hardly dependent on �. For example, under � = 11 the tari¤

equivalent of U.S.-Canadian trade costs between 1960 and 2002 declined by 39:2 percent

(from 40:8 to 24:8 percent). Cutting the elasticity of substitution to � = 8 would result in

8The OECD countries include all current 30 OECD members except for Belgium/Luxembourg and theCzech Republic/Slovak Republic, who only report jointly.

9See the survey given in Anderson and van Wincoop (2004, Section 3.6).

9

a very similar decline of 40:7 percent (from 63:1 to 37:4 percent).10

The second parameter assumption that is needed to compute trade costs is the fraction

s of �rms that produce tradable goods. Stockman and Tesar (1990) say that this fraction is

�di¢ cult to estimate directly from the data�but report evidence that the expenditure on

nontradable goods as a share of private �nal consumption ranges from 18:9 to 44:3 percent

for �ve large OECD countries (France, Italy, Japan, United Kingdom and United States)

between 1960 and 1988. As my sample includes many smaller countries, the appropriate

share of nontradable goods is likely to be closer to the lower end of this range. I therefore

choose s = 0:8, implying that 20 percent of all goods are nontradable.

Given the general decrease in trade costs over the last decades, one might expect that

more goods have become tradable, as suggested in the literature on endogenous tradabil-

ity, for instance by Bergin and Glick (2006). However, in a recent empirical analysis of

globalization the IMF �nds that based on sectoral input-output tables �unlike in many

emerging market countries, the tradables sector share output in most industrial countries

has actually fallen slightly in recent years because of the rapid expansion of service sec-

tors� (IMF 2005, p. 131). Since my sample includes both industrial countries and some

emerging market economies, the overall e¤ect on s is unclear. But even if there has been a

slight downward trend in s, the resulting additional decrease in trade costs would be small.

For example, cutting s from 0:8 to 0:75 would merely reduce the 2002 tari¤ equivalent of

U.S.-Canadian trade costs from 24:8 to 24:1 percent.

3.2 Bilateral Trade Costs in the U.S. and UK

I now report bilateral trade costs for the United States and for the United Kingdom as

two eminent examples. The UK is picked as the second biggest European economy after

Germany whose data show a structural break in the wake of reuni�cation.

Table 1 gives a snapshot of U.S. bilateral trade costs for the years 1960 and 2002. U.S.

bilateral trade costs have fallen with almost all trading partners in the sample except for

slight increases with Chile and Iceland. The decline in trade costs has been particularly

dramatic for the two neighbors Canada and Mexico, but also for Ireland and Korea which

both experienced strong economic growth relative to other countries in the sample. The

tari¤ equivalents vary substantially across countries, with levels ranging from 24:8 percent

for Canada up to 171 percent for Greece in 2002. The average magnitude is consistent

with values typically put forward in the literature. For example, Anderson and van Win-

coop (2004) �nd that the representative tari¤ equivalent of international trade costs is 74

percent.

Table 2 is the UK counterpart to Table 1. Unlike the United States, the UK exhibits

10The regression results in Section 4 are not qualitatively a¤ected when trade costs are computed with� = 8 instead of � = 11 (see the discussion in Section 4.3 and Table A1 in the appendix).

10

Table 1: U.S. Bilateral Trade CostsTari¤ equivalent �

Partner country 1960 2002 Percentage changeArgentina 77:9Australia 77:0 66:1 �14:2Austria 76:7Brazil 59:7Canada 40:8 24:8 �39:2Chile 67:8 68:4 +0:9Denmark 80:5Finland 92:3 76:7 �16:9France 73:6 61:0 �17:1Germany 62:9 53:4 �15:1Greece 171:0Hungary 85:9Iceland 92:3 96:5 +4:6India 75:4 73:6 �2:4Indonesia 69:2Ireland 88:7 46:8 �47:2Italy 69:8 65:6 �6:0Japan 57:7 50:6 �12:3Korea 103:3 49:9 �51:7Mexico 58:5 30:9 �47:2Netherlands 61:3 53:6 �12:6New Zealand 78:9 74:8 �5:2Norway 78:9Poland 101:6Portugal 92:3Spain 83:8 79:5 �5:1Sweden 75:1 68:6 �8:7Switzerland 70:9 61:0 �14:0Turkey 79:9UK 60:3 54:1 �10:3All numbers are percentage values.Blank cells: Data not available.Computations based on (22) and (5).

11

Table 2: UK Bilateral Trade CostsTari¤ equivalent �

Partner country 1960 2002 Percentage changeArgentina 98:0Australia 44:5 66:9 +50:3Austria 61:8Brazil 79:9Canada 47:5 67:8 +42:7Chile 70:4 87:6 +24:4Denmark 52:4Finland 52:9 56:7 +7:2France 64:7 41:6 �35:7Germany 57:7 38:9 �32:6Greece 79:9 137:5 +72:1Hungary 61:3Iceland 75:1 73:6 �2:0India 57:0 72:7 +27:5Indonesia 81:8Ireland 36:4 23:0 �36:8Italy 64:2 50:8 �20:9Japan 81:8 70:9 �13:3Korea 124:2 68:4 �44:9Mexico 95:3 94:6 �0:7Netherlands 45:3 32:6 �28:0New Zealand 39:3 79:2 +101:5Norway 50:2Poland 67:2Portugal 61:0Spain 68:9 49:4 �28:3Sweden 49:0 51:1 +4:2Switzerland 62:3 55:3 �11:2Turkey 66:7United States 60:3 54:1 �10:3All numbers are percentage values.Blank cells: Data not available.Computations based on (22) and (5).

12

a number of remarkable increases in trade costs between 1960 and 2002, mostly with

former colonies that are far away such as Australia, Canada, India and New Zealand.

The increases seem less staggering if one takes into account that the initial 1960 tari¤

equivalents for these countries are comparatively low. What the U.S. and the UK have

in common is that with the exception of Korea, the most dramatic declines in trade costs

have occurred with nearby countries. In the case of the UK these are France, Germany,

Ireland, the Netherlands and Spain. These countries also exhibit the lowest levels of trade

costs in 2002.

3.3 The G7 and European Union Countries

I now compute bilateral trade costs amongst the G7 countries between 1960 and 2002.11

Figure 1 plots each country�s average bilateral tari¤ equivalent with the other G7 countries,

weighted by each trading partner�s share of combined G7 exports. All seven countries have

experienced a steady decline in their average tari¤ equivalents. The decline is strongest

for Canada, resulting in the lowest 2002 tari¤ equivalent (26:6 percent), and the decline is

weakest for Japan, resulting in the highest 2002 tari¤ equivalent (55:3 percent). It is not

surprising that Japan has the highest trade costs, given that it is far away from the other

G7 countries. In addition, Japan does not have a free trade agreement with any other G7

country.

The top graph in Figure 2 depicts the average of the graphs in Figure 1, weighted by

each country�s share of total exports amongst G7 countries. The values of the top graph

can be interpreted as the representative intra-G7 tari¤ equivalent. Between 1960 and

2002 it fell by 26:5 percent from 55 to 40:5 percent, consistent with the 74 percent tari¤

equivalent of international trade costs that Anderson and van Wincoop (2004) suggest

for a broader sample of countries. As a comparison, the bottom graph plots the tari¤

equivalent based on the world c.i.f./f.o.b. ratio that is reported by the IMF as a measure

of transportation costs. It dropped from 7:6 percent in 1960 to 3:3 percent in 2002.

Anderson and van Wincoop suggest a higher value for transportation costs (10:7 percent)

but in either case, transportation costs constitute only a fraction of overall trade costs.12

Section 4 discusses other factors such as language barriers that can be identi�ed as major

trade cost components.

As for the G7 subsample, I compute trade-weighted averages of trade costs for a

subsample of 13 European Union (EU) countries between 1977 and 2002.13 The 2002

11The G7 countries are Canada, France, Germany, Italy, Japan, the UK and the U.S.12See Anderson and van Wincoop (2004, Section 2.2) for a discussion of transportation costs. The

c.i.f./f.o.b. tari¤ equivalent is computed from the world import and export series reported in the IMFDirection of Trade Statistics. These data should be treated with caution though since their quality isquestionable, see Hummels and Lugovskyy (2006) for a discussion.13The 13 EU countries are the 15 EU member countries prior to the 2004 Eastern enlargement exclusive

of Belgium/Luxembourg who only report jointly. Some data prior to 1977 are missing.

13

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ Canada

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ France

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ Germany

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ Italy

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ Japan

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ UK

1960 1980 20000.2

0.3

0.4

0.5

0.6

Tarif

f equ

ival

ent

θ U.S.

Figure 1: Trade-weighted averages of bilateral trade costs amongst G7 countries (measuredas tari¤ equivalents).

14

1960 1970 1980 1990 20000

0.1

0.2

0.3

0.4

0.5

0.6

G7 tariff equivalent θ implied by trade costs τ

World tariff equivalent based on IMF c.i.f./f.o.b. ratio

Figure 2: G7 trade costs and the IMF world c.i.f./f.o.b. ratio (both measured as tari¤equivalents).

tari¤ equivalent is highest for Greece with 122 percent and lowest for the Netherlands

with 33 percent. Between 1977 and 2002 the trade-weighted intra-EU tari¤ equivalent fell

by 17:7 percent from 47:5 to 39:1 percent. The corresponding representative G7 values

are 45:1 and 40:5 percent so that in comparison, EU trade costs were higher in 1977 but

slightly lower in 2002. Over the past 30 years trade costs have therefore fallen more rapidly

within the European Union than amongst G7 countries. This �nding is consistent with

the previous observation that the most dramatic declines in trade costs have occurred

amongst nearby countries.

3.4 An Increase in Regional Economic Integration

Tables 1 and 2 exhibit the pattern that U.S. and UK bilateral trade costs have fallen

most dramatically for nearby trading partners. In fact, this pattern applies more gen-

erally, suggesting that over the past few decades there has been an increase in regional

economic integration. Table 3 formally demonstrates for a panel of 273 country pairs that

between 1970 and 2000 trade costs have dropped most rapidly for nearby countries.14 In

a regression of the percentage decline in tari¤ equivalents, the coe¢ cient of the logarithm

14The panel includes these countries: Australia, Austria, Brazil, Canada, Chile, Denmark, Finland,France, Germany, Greece, Hong Kong, Iceland, Indonesia, Ireland, Italy, Japan, Korea, Mexico, the Nether-lands, New Zealand, Norway, Spain, Sweden, Switzerland, the UK and the U.S.

15

Table 3: Distance and the Decline in Tari¤ Equivalents �

Percentage decline in �jk, 1970-2000

ln(Distance) �0:048��(�3:98)

�0:062�(�2:00)

Constant 0:381��(2:67)

1:228��(4:18)

Country �xed e¤ects yes yesIntra-European pairs included yes noNumber of observations 273 169R2 0.566 0.513The dependent variable is the percentage decline in �jk,de�ned as (�jk;1970 � �jk;2000)=�jk;1970.Robust OLS estimation, t-statistics given in parentheses.** and * indicate signi�cance at the 1 and 5 percent levels.

of distance is negative and signi�cant. This result holds up even if intra-European trade

relations are not included in the sample.

In essence, absolute trade �ows have increased for virtually all country pairs but they

have increased more quickly amongst nearby countries. Relative trade has therefore in-

creased with nearby trading partners and decreased with distant ones. Coughlin (2004)

comes to the same conclusion from the perspective of individual U.S. states in an analysis

of merchandise exports. Frankel, Stein and Wei (1997) identify the Americas, Europe and

Paci�c Asia as continental trading blocs that have a high degree of internal integration.

Bayoumi and Eichengreen (1997) �nd evidence of relative trade diversion in that the for-

mation of the European Community lowered the growth rate of trade with other industrial

countries by 1:7 percentage points. But the results in Table 3 suggest that the relative

increase in trade with nearby countries did not only take place amongst European nations.

As free trade agreements have typically been concluded with nearby countries, they have

certainly contributed to the increase in regional economic integration, see Venables (2001)

for a discussion. Another reason could be evidence reported by Hummels (2007) that over

recent years the cost of overland transport has declined relative to ocean transport, which

might have disproportionately favored shorter distances.

4 The Determinants of Trade Costs

Trade costs vary substantially across country pairs. For instance, why is the G7 average

tari¤ equivalent so much lower for Canada (26:6 percent) than for Japan (55:3 percent)?

In order to explain this variation across country pairs, I regress bilateral trade costs on

a number of potential trade cost determinants such as distance and common language

use that are typically found in the gravity literature, for example in Rose (2000) and

16

Fitzgerald (2007). These regressions are run for a balanced panel of 273 country pairs for

the years 1970, 1980, 1990 and 2000.14

4.1 Methodology

In the gravity literature, variables such as distance and a common language dummy are

ex ante regarded as trade cost components. But as Anderson and van Wincoop (2003)

demonstrate, simply adding such trade cost proxies to a standard gravity regression with-

out controlling for multilateral resistance leads to unfounded comparative statics and

biased trade cost estimates. This problem is particularly severe if observations are pooled

across years and if multilateral resistance changes over time. In contrast, the methodol-

ogy adopted here is a two-step procedure. First, bilateral trade costs are computed on

the basis of (22) to obtain a micro-founded trade cost measure that takes time-varying

multilateral resistance into account. Second, the variation of trade costs across country

pairs is explained ex post (i.e. after accounting for multilateral resistance) by regressing

them on potential determinants. Apart from having a solid theoretical foundation, another

advantage of this procedure is that the dummy variable coe¢ cients in those regressions

(such as the coe¢ cient on the common language dummy) represent tari¤ equivalents and

can therefore be easily interpreted and compared to each other.

The regressions are set up as follows. The tari¤ equivalent �jkt is linked to potential

trade cost determinants by

�jkt = �j + �k + �t + �1 ln(Distancejk) + �2Common Borderjk

+�3 ln(Areajk) + �4Landlockedjk + �5Islandjk

+�6Common Languagejk + �7Colonialjk

+�8Tariffsjkt + �9FTAjkt + �10ERV olatilityjkt + "jkt

(23)

where �j and �k denote country �xed e¤ects that capture unobservable country-speci�c

characteristics, �t is a time dummy and "jkt is the error term. The remaining right-

hand side variables can be divided into three rough groups. The �rst group consists of

geographical factors (�1-�5), the second group is formed by historical factors (�6-�7) and

the third group consists of institutional factors (�8-�10).

ln(Distancejk) denotes the natural logarithm of distance in km between countries

j and k. Common Borderjk is a contiguity dummy which takes on the value 1 if the

two trading partners share a common border. Both regressors can be seen as proxies for

transportation and information costs, which tend to be lower for nearby trading partners.

ln(Areajk) is the logarithm of the product of the two trading partners� surface areas.

Landlockedjk and Islandjk take on the value 1 if one of the trading partners is landlocked

or an island, the value 2 if both partners are and 0 otherwise. Colonialjk is a dummy

indicating a past colonial relationship between j and k, for example between the UK and

17

Australia. The Common Languagejk dummy indicates whether the two countries have

the same o¢ cial language. None of these geographical and historical regressors change

over time.

But the institutional regressors are time-varying. Tariffsjkt is a joint measure of

tari¤s for countries j and k that is based on country ratings of tari¤ regimes published

by the Fraser Institute in the Freedom of the World Report. The joint measure is con-

structed by multiplying the two single-country ratings for each pair. FTAjkt is a dummy

variable for free trade agreements such as NAFTA and the European Common Market.

ERV olatilityjkt measures the volatility of the nominal exchange rate between j and k over

the �ve years preceding t as the standard deviation of the �rst di¤erences of the monthly

logarithmic nominal exchange rates. The data appendix explains the variables in more

detail and gives the exact data sources.

4.2 Regression Results

Table 4 reports the results of estimating (23), both for individual years and data pooled

across years. The regressions explain 85-90 percent of the trade cost variation. The year-

speci�c dummies in the pooled regression are negative and re�ect the general drop in trade

costs over time.

Greater distance between trading partners, larger surface area and being landlocked

are the geographical factors that are associated with higher trade costs at the 1 percent

con�dence level. A large surface area often indicates large internal distances that need to

be overcome to engage in international trade. But trading partners that share a common

border or that are islands do not face signi�cantly di¤erent trade costs.

The common language and colonial dummies have the expected negative coe¢ cients.

In the pooled regression, two countries with a previous colonial relationship have a bilateral

tari¤ equivalent that is 15:9 percentage points lower compared to two countries without a

common colonial past (�7 = �0:159). Similarly, using the same o¢ cial language reducesthe tari¤ equivalent by 9:2 percentage points (�6 = �0:092). This �nding is in line withHummels�(2001) language barrier estimate and Eaton and Kortum�s (2002) estimate for

2002 data. It is interesting to see from the single-year regressions that the bene�ts of a

common colonial past and using the same language have washed out over time. The �nding

that the language coe¢ cient has subsided possibly re�ects the fact that an increasing

number of people across the world have started to learn foreign languages.15

Turning to the institutional factors, a free trade agreement reduces trade costs by 5:5

percentage points (�8 = �0:055). The fact that this coe¢ cient is not negative in thesingle-year regression for 1980 can be explained by the sharp increase in the number of

15For example, see the British Council�s report on the English language made available at http://www.britishcouncil.org/english/pdf/future.pdf.

18

Table 4: The Determinants of Trade CostsRegression

Regressors Pooled 1970 1980 1990 2000Geographical factorsln(Distance) 0:162��

(24:20)0:160��(11:01)

0:191��(13:93)

0:161��(9:81)

0:143��(10:70)

Common Border 0:005(0:25)

0:039(0:88)

0:007(0:17)

0:001(0:02)

�0:024(�0:62)

ln(Area) 0:027��(12:41)

0:020��(3:55)

0:018��(4:84)

0:029��(3:47)

0:016(0:79)

Landlocked 0:273��(14:49)

0:106(2:39)

0:132��(4:06)

0:236��(6:39)

0:242��(3:16)

Island �0:008(�0:29)

0:080(0:90)

�0:001(�0:01)

�0:150(�1:24)

�0:704(�1:85)

Historical factorsCommon Language �0:092��

(�5:49)�0:148��(�4:28)

�0:106��(�2:74)

�0:068(�2:06)

�0:044(�1:52)

Colonial �0:159��(�6:21)

�0:248��(�5:59)

�0:186��(�5:39)

�0:127��(�3:66)

�0:065(�2:14)

Institutional factorsTari¤s �0:006

(�1:14)�0:018(�1:31)

�0:031(�2:25)

0:284(1:37)

0:865(0:70)

Free Trade Agreement �0:055��(�3:76)

�0:132��(�3:68)

0:036(1:15)

�0:066(�2:17)

�0:021(�0:83)

Exchange Rate Volatility 0:000(0:14)

0:017(0:86)

�0:010(�0:59)

�0:005(�0:50)

0:041(2:33)

1980 dummy �0:067��(�5:00)

1990 dummy �0:091��(�6:71)

2000 dummy �0:151��(�10:44)

Country �xed e¤ects yes yes yes yes yesNumber of observations 1092 273 273 273 273R2 0.857 0.849 0.890 0.898 0.899The dependent variable is the tari¤ equivalent �jkt.Robust OLS estimation, t-statistics given in parentheses.** indicates signi�cance at the 1 percent level.

19

free trade agreements since 1970. The number of country pairs that were part of a mutual

free trade agreement more than doubled from 26 in 1970 to 55 in 1980. In fact, using the

1970 free trade agreement dummy in the regression for 1980 yields the expected negative

and signi�cant coe¢ cient. The number of country pairs with a free trade agreement kept

rising to 83 in 1990 and 95 in 2000.

Perhaps more surprisingly, tari¤s and exchange rate volatility are not associated with

signi�cantly higher trade costs, neither in the pooled nor in the single-year regressions.

This result is consistent with the relatively small role that policy related barriers play in

determining total trade costs. Anderson and van Wincoop (2004) calculate that policy

related barriers including tari¤s and trade agreements make up only eight out of the 44

percentage points associated with border related barriers.

Overall, it therefore seems that institutional factors are less important than geograph-

ical and historical factors in explaining the variation of trade costs across country pairs.

Distance is the only explanatory variable that is signi�cant in all single years, a �nding

which highlights the importance of transportation costs. Speaking the same language and

having a common colonial past used to be associated with substantially lower trade costs

but those initial advantages have faded over time.

4.3 Discussion

In addition to the results reported in Table 4, the country �xed e¤ects included in regres-

sion (23) also carry important information.16 In the pooled regression they are positive and

signi�cant at the 1 percent level for Austria, Greece, Iceland, Ireland and Mexico. They

are negative and signi�cant for Chile, Hong Kong, France, Germany, Italy, Japan, Korea,

the Netherlands, Sweden and the U.S. There is no obvious explanation for these �xed

e¤ects because by construction they capture unobserved characteristics. But it is striking

that a number of countries with negative �xed e¤ects and thus systematically lower trade

costs have a reputation as strong exporting nations such as Hong Kong, Germany and

Korea.

A number of robustness checks have been performed for the results in Table 4. Com-

puting trade costs based on an elasticity of substitution � = 8 instead of � = 11 leaves

the signi�cance unchanged for all coe¢ cients (see Table A1 in the appendix). The results

reported in Table 4 are not sensitive to the exclusion of particular countries like the U.S.

or UK from the sample, and neither to the exclusion of all intra-European trade relations.

The results also hold up when the sample is restricted to intra-European trade relations

or to trade relations between rich countries (see Table A2 in the appendix).17 Finally,

16 It is not possible to include country random e¤ects instead of country �xed e¤ects because eachobservation is associated with two countries.17Rich countries are de�ned as those with per-capita income of over US$ 20,000 in 2002 according to UN

data. This threshold excludes the South American countries as well as Greece, Indonesia, Mexico, New

20

the residuals of the trade cost regressions might be spatially correlated. For instance, if a

certain country is hit by a shock, its neighbors are more likely a¤ected than remote coun-

tries. To check for this possibility, I regress the residuals from the single-year regressions

on continental dummies but �nd no spatial correlation at all.18 Furthermore, allowing

for cluster e¤ects associated with individual countries or continents produces results very

similar to those in Table 4.

The period after World War II is not unprecedented as a time of enormous trade

expansion. The �rst era of globalization is generally considered to be the trade boom that

started in the late 19th century and continued until the beginning of World War I. Using

the model developed in the current paper, Jacks, Meissner and Novy (2006) �nd that the

median tari¤ equivalent of trade costs stood at 90 percent in 1870 and at 76 percent in

1913, implying a drop of 16 percent over four decades. In comparison, the average G7

tari¤ equivalent declined more rapidly from 55 percent in 1960 to 40:5 percent in 2002,

a drop of 26:5 percent over four decades. Apart from distance, important determinants

of 19th century trade costs were tari¤s, railroad infrastructure, exchange rate regime

coordination through the Gold Standard and, similar to the post-World War II period, a

common colonial history as well as the use of a common language.

5 Conclusion

This paper develops a micro-founded measure of international trade costs. It is based on

a multi-country general equilibrium model of trade with bilateral iceberg trade costs as

its central ingredient. The model yields a micro-founded gravity equation that includes

trade costs and that captures multilateral resistance in the form of total export terms.

Since all variables in the gravity equation are observable, it is possible to compute trade

costs directly from the gravity equation without the need to make any assumptions about

underlying trade cost components such as distance and tari¤s or their functional form.

The empirical results obtained with the trade cost measure are economically sensible

and consistent with the literature. Since World War II trade costs have declined markedly.

For the G7 countries they fell by 26:5 percent between 1960 and 2002, and for European

Union countries trade costs decreased by 17:7 percent between 1977 and 2002. For both

subsamples the 2002 tari¤ equivalent of trade costs stands at roughly 40 percent. In

addition, the paper �nds clear evidence that over the past few decades economic integration

has progressed most on a regional level, as trade costs dropped more quickly between

nearby trading partners than between distant ones.

The dispersion of trade costs across country pairs can best be explained by geographical

Zealand, Korea and Spain.18The dummies are de�ned as intracontinental binary variables for Europe, North America and Asia,

i.e. they only take on the value 1 if both countries in a pair are on the same continent.

21

factors like distance and being landlocked. Sharing a common colonial history and sharing

the same o¢ cial language were associated with signi�cantly lower trade costs in 1970, but

in 2000 these factors are no longer important. After controlling for geographical and

historical variables, trade costs still vary considerably across countries, indicating a high

degree of heterogeneity. Trade costs tend be high for Austria, Greece, Iceland, Ireland

and Mexico. They tend to be low for Chile, Hong Kong, France, Germany, Italy, Japan,

Korea, the Netherlands, Sweden and the U.S.

22

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24

A A Model with Iceberg Trade Costs

This appendix outlines how to derive the theoretical results presented in Section 2. Ap-

pendix A.1 derives the equilibrium solution to the model. Appendix A.2 derives the

micro-founded gravity equation. Appendix A.3 shows that trade cost measure (22) also

holds in the more general case when countries run trade de�cits or surpluses. Appendix

A.4 demonstrates how to measure trade costs on the basis of bilateral import data.

Since within one country all �rms producing tradable goods are symmetric and all

�rms producing nontradable goods are also symmetric, the index i will be dropped in the

following.

A.1 Equilibrium of the Model

Each country-j consumer maximizes utility (1) subject to budget constraint (7), leading

to the optimal labor supply condition

�

1� Lj=

Wj

PjCj(24)

In order to solve the model it is useful to de�ne per-capita output, per-capita labor supply

and per-capita pro�ts as

yj � sjyTj + (1� sj)yNTj (25)

Lj � sjLTj + (1� sj)LNTj (26)

�j � sj�Tj + (1� sj)�NTj

where yTj is the same as yTji from (8), LTj is the same L

Tji as from (11) and �Tj is the same

as �Tji from (14). The remaining right-hand side variables are the corresponding variables

for nontradable �rm i. Using the production functions (9) and (10) as well as the price

markups (15)-(17) it follows

�j = pjyj �WjLj

Combined with budget constraint (7) and the optimal labor supply condition (24) this

yields the optimal per-capita labor supply

Lj =�� 1

�� 1 + �� (27)

Express nominal wages across countries as

�1W1 = �2W2 = ::: = �jWj = ::: = �JWJ

where the ��s are auxiliary parameters yet unknown. It follows from the price markups

25

(15)-(17) that

pk = pTk =

�

�� 1Wk

Ak=

�

�� 1�j�k

Wj

Ak(28)

Use (28) in price index (3) to derive

Pj = !1

1��j

�

�� 1Wj

where

!j �

JXk=1

sk(nk � nk�1)(Ak (1� �k;j)�k�j)��1

!+ (1� sj) (nj � nj�1)A��1j (29)

An expression for the real wage follows directly as

Wj

Pj=�� 1�!

1��1j (30)

Using budget constraint (7) and the optimal labor supply condition (24), expressions for

consumption and real pro�ts follow as

Cj = Lj!1

��1j (31)

�jPj

=Lj�!

1��1j (32)

as well as

Ck = Cj

�!k!j

� 1��1

(33)

To solve for the ��s in (29), start o¤ with (25) and plug in the market-clearing con-

ditions (12) and (13). Then replace the price variables and consumption using (15)-(17),

(28), (30) and (33) to yield

yjAj= Cj!

��1j

( JPk=1

sk(nk � nk�1)(Ak (1� �k;j))��1 !j!k

sjsk

�AjAk

(1��j;k)(1��k;j)

��1!��k�j

��!

+ (1� sj) (nj � nj�1)A��1j

)(34)

At the same time, from the production functions (9) and (10), de�nitions (25) and (26)

and expression (31) it follows

Lj =yjAj

= Cj!�1��1j

It must therefore be the case that the curly brackets in (34) are equal to !j as de�ned in

26

(29). Setting the curly brackets equal to !j and using (29) yields

�k�j=

!j!k

sjsk

�AjAk

(1� � j;k)(1� �k;j)

��1! 12��1

(35)

Finally, plug (35) back into (29) to obtain

!j =

0@ JPk=1

sk(nk � nk�1)(Ak (1� �k;j))��1 !j!k

sjsk

�AjAk

(1��j;k)(1��k;j)

��1! ��12��1

1A+(1� sj) (nj � nj�1)A��1j

(36)

The system of polynomial equations represented by (36) for j = 1; 2;:::; J cannot be solved

analytically. However, it can be established numerically by repeated substitution that

a unique solution exists for the !�s for all combinations of admissible parameter values.

The admissible parameter values are 0 < nk � nk�1 < 1, 0 < sk � 1, � > 1, Ak > 0

and 0 � �k;j < 1 for all j; k. The implicit function theorem can be applied to compute

the partial e¤ects of changes in these exogenous parameters on the !�s. The !�s give rise

to sensible general equilibrium e¤ects for the real wage, consumption and real pro�ts in

(30)-(32). For example, a technology improvement in Aj increases !j and therefore the

real wage, consumption and real pro�ts for country-j citizens but, to a smaller extent, it

also increases the other !�s and is thus also bene�cial to foreign citizens.

A.2 A Gravity Equation with Trade Costs

Appendix A.2 outlines the derivation of gravity equation (21). Plug market-clearing con-

dition (12) into the right-hand side of (18) and use the country-j versions of (28) and

(35) and the country-k versions of (30) and (31). Also use production function (9) and

rearrange to yield

�!j!k

� ��12��1

=

!jLTj;k

�AjAk

(1��j;k)(1��k;j)

� �(��1)2��1

Lk

�sksj

� �2��1

(nk � nk�1)(Aj (1� � j;k))��1(37)

Plug the left-hand side of (37) into the right-hand side of (36), noting that Lj = Lk from

(27) and using (11) and (26). Also note that LTj;j = LNTj as pTj = p

NTj by (17). Solve for

!j to obtain

!j =(nj � nj�1)A��1j Lj

LTj;j(38)

27

Plug the country-j and country-k versions of (38) back into the right-hand side of expres-

sion (18) and then rearrange to obtain

EXPj;k = (1� � j;k)(��1)22��1 (1� �k;j)

�(��1)2��1 (sj)

��12��1 (sk)

�2��1 ��

(nj � nj�1)yTj;j� �2��1

�(nk � nk�1)yTk;k

� ��12��1

�nk�nk�1nj�nj�1

� 12��1

(39)

Finally, note that POPj = (nj � nj�1) and POPk = (nk � nk�1), where POPj is thepopulation of country j. Also note from (25) that GDPj = (nj � nj�1)yj and

(nj � nj�1)yj = sj(nj � nj�1)yTj + (1� sj)(nj � nj�1)yNTj

and by de�nition (8)

sj(nj � nj�1)yTj;j = sj(nj � nj�1)yTj � sj(nj � nj�1)Xk 6=jyTj;k

Using yNTj = yNTj;j = yTj;j as pNTj = pTj it follows

(nj � nj�1)yTj;j = (nj � nj�1)yj � sj(nj � nj�1)Xk 6=jyTj;k = GDPj � EXPj

The same applies to GDPk�EXPk. Now plug POPj , POPk, GDPj�EXPj and GDPk�EXPk into (39) to obtain

EXPj;k = (1� � j;k)(��1)22��1 (1� �k;j)

�(��1)2��1 (sj)

��12��1 (sk)

�2��1 �

(GDPj � EXPj)�

2��1 (GDPk � EXPk)��12��1

�POPkPOPj

� 12��1

(40)

As a special feature of gravity equation (40), the relative population of country k is a

determinant of exports from j to k. Intuitively, the more people inhabit country k, the

more imports they demand from country j. If an additional country-k consumer is born,

the marginal utility she derives from her �rst unit of a country-j good will be higher than

for an existing country-j consumer, resulting in an increase in EXPj;k. Anderson (1979)

points out that although most theoretical models do not lead to gravity equations that

include population, in empirical applications population is nevertheless frequently used as

a regressor and usually found to be signi�cant. The present model provides a theoretical

foundation.

The corresponding gravity equation for EXPk;j can be derived analogously as

EXPk;j = (1� �k;j)(��1)22��1 (1� � j;k)

�(��1)2��1 (sk)

��12��1 (sj)

�2��1 �

(GDPk � EXPk)�

2��1 (GDPj � EXPj)��12��1

�POPjPOPk

� 12��1

(41)

28

As in (20), multiply (40) and (41) by each other

EXPj;kEXPk;j = sj (GDPj � EXPj) sk (GDPk � EXPk) (1� � j;k)��1 (1� �k;j)��1

Finally, impose symmetry � j;k = �k;j in order to obtain (21).

A.3 Trade Imbalances

Many countries run trade de�cits or surpluses and these are often persistent. The model is

therefore generalized to allow for trade imbalances and it is shown that trade cost measure

(22) remains una¤ected. The per-capita budget constraint (7) is generalized to

PjCj +

JXl=1

Tj;l =WjLj + �j (42)

where Tj;l are nominal per-capita transfers from country j to l. As an accounting identity

it follows

(nj � nj�1)Tj;l = �(nl � nl�1)Tl;j

For analytical convenience it is now assumed that per-capita transfers are a fraction of

per-capita consumption spending

Tj;l = �j;lPjCj

with �j;j = 0 for all j such that budget constraint (42) can be rewritten as 1 +

JXl=1

�j;l

!PjCj =WjLj + �j (43)

IfPJl=1 �j;l > 0, then j is a creditor country and runs a net trade surplus.

The generalized model can now be solved as outlined in Sections A.1 and A.2. The key

equations are given in the following. The optimal labor supply condition (24) becomes

�

1� Lj=

Wj�1 +

JPl=1

�j;l

�PjCj

(44)

The markups (15)-(17), per-capita output (27), the real wage (30) and real pro�ts (32)

are not a¤ected. But if j runs a surplus, this reduces per-capita consumption Cj

Cj = Lj!1

��1j

1 +

JXl=1

�j;l

!�1(45)

29

Intuitively, due to logarithmic utility in (1), output Lj is constant. But if country j

transfers some of its output to other countries, then its domestic consumption must fall.

Now use the notationJXl=1

�j;l =CAj

CONSj

where CAj denotes the nominal current account of country j and CONSj denotes its

nominal consumption expenditure.

The equations corresponding to (40) and (41) are

EXPj;k = (1� � j;k)(��1)22��1 (1� �k;j)

�(��1)2��1 (sj)

��12��1 (sk)

�2��1

�POPkPOPj

� 12��1 �

(GDPj � EXPj)�

2��1 (GDPk � EXPk)��12��1

1+

CAjCONSj

1+CAk

CONSk

! ��12��1 (46)

EXPk;j = (1� �k;j)(��1)22��1 (1� � j;k)

�(��1)2��1 (sk)

��12��1 (sj)

�2��1

�POPjPOPk

� 12��1 �

(GDPk � EXPk)�

2��1 (GDPj � EXPj)��12��1

1+

CAkCONSk

1+CAj

CONSj

! ��12��1 (47)

In the case of a balanced current account (CAj = CAk = 0) equations (46) and (47)

simplify to (40) and (41). If j becomes a surplus country (CAj > 0), this implies an

increase in trade �ows EXPj;k from j to k and a decrease in trade �ows EXPk;j . Multiply

(46) and (47) by each other to obtain

EXPj;kEXPk;j = sj (GDPj � EXPj) sk (GDPk � EXPk) (1� � j;k)��1 (1� �k;j)��1

Assuming symmetry � j;k = �k;j leads to (21), which in turn implies (22). Trade cost

measure (22) therefore also holds in the more general case when countries run trade de�cits

or surpluses.

A.4 Trade Costs and Imports

Gravity equation (21) is cast in exports but for completeness imports are mentioned here.

The relationship between exports and imports is particularly simple, given by

IMPj;k = (1� � j;k)EXPj;k (48)

where IMPj;k are real imports from j arriving in k. Although its simple form looks

inviting, it is not recommended to compute trade costs on the basis of (48) due to incon-

sistencies between the export data (reported by country j) and import data (reported by

country k). These inconsistencies in the IMF Direction of Trade Statistics come about

30

through di¤erences in classi�cation concepts, time of recording, valuation and coverage of

trade �ows across countries. See Hummels and Lugovskyy (2006) for a discussion. Using

relation (48) the import version of trade cost measure (22) would follow as

� j;k = 1��

IMPj;kIMPk;j(GDPj � EXPj) (GDPk � EXPk) s2

� 12�

But since both import and export variables appear in this expression and since they are

inconsistent in practice, the import version is not used to compute bilateral trade costs.

31

B Data Appendix

B.1 Exports and GDP

The export data, denominated in U.S. dollars, are taken from the IMF Direction of

Trade Statistics (DOTS), provided by the Economic and Social Data Service (ESDS)

at http://www.esds.ac.uk/. The GDP data come from the IMF International Financial

Statistics (IFS), also provided by the ESDS. The following IFS lines are used: line 99B..ZF

(GDP in national currency), line 99BI.ZF (GDP de�ator) and line ..RF.ZF (period aver-

age exchange rate in national currency per U.S. dollar). Both the GDP and the export

data are de�ated with the respective GDP de�ators. Export de�ators are only available

for a small number of countries and are therefore not used.

B.2 Explanatory Variables

The distance data represent great-circle distances between capital cities. They have been

collected from the website http://www.indo.com/distance/.

The following variables are taken from Andrew Rose�s (2000) data set (available at

http://faculty.haas.berkeley.edu/arose/): the border dummy, the colonial dummy,

the language dummy, the free trade agreement dummy, exchange rate volatility, the surface

area variable, the landlocked variable and the island variable. The landlocked and island

variables take on the value 1 if one of the trading partners is landlocked or an island and

the value 2 if both partners are landlocked or islands. The surface area variable represents

the logarithm of the product of surface areas for each country pair.

The cut-o¤ point for the colonial dummy is 1900. According to that criterion, the

U.S. and Canada are not regarded as British colonies but Australia and Ireland had to

be converted into British colonies in the original data set (India and New Zealand were

counted as British colonies already). The language dummy needed correction in that

English had to be replaced by Italian as an o¢ cial Swiss language. The coding of the

free trade agreement dummy had to be switched for the Netherlands and New Zealand.

Australia was counted as an island.

Rose�s data are updated for the year 2000. IMF IFS exchange rate data are used

to compute the exchange rate volatility in the same way as in the original data set.

Information about recent free trade agreements is available on the WTO website at

http://www.wto.org/english/tratop_e/region_e/region_e.htm under �Facts and �g-

ures.� Amongst others the updated free trade agreement variable includes the Canada-

Chile free trade agreement, the Mercosur agreement and NAFTA.

The tari¤ variable is taken from the Economic Freedom of the World 2004 Annual

Report, published by the Fraser Institute and made available at http://www.fraserinsti

tute.ca/economicfreedom/. In particular, the tari¤ variable is constructed using data

32

from component 4A, �Taxes on international trade.�This component combines the tari¤

revenue as a percentage of exports and imports, the mean tari¤ rate and the standard

deviation of tari¤ rates. The report gives a rating on a scale from 0 to 10, where 10 is

given for the combination of low tari¤ revenue, a low mean tari¤ rate and a low standard

deviation. Joint observations for countries j and k are constructed by multiplying the

single-country ratings and then taking natural logarithms. Using the logarithms of the

products instead of the logarithms of the sums leads to symmetric and constant interaction

e¤ects. In order to make the coe¢ cients in the regressions more intuitive, the logarithms

are multiplied by (�1) such that higher values indicate higher tari¤ rates.Table A1 reports the results of running regression (23) based on trade costs that are

computed with an elasticity of substitution � = 8. Table A2 reports results of regressions

run on various subsamples. Table A3 reports simple correlations between the regressors.

33

Table A1: The Determinants of Trade Costs (Based on � = 8)Regression

Regressors Pooled 1970 1980 1990 2000Geographical factorsln(Distance) 0:300��

(21:89)0:304��(9:90)

0:357��(12:65)

0:293��(8:76)

0:253��(9:47)


0:122(1:27)

0:053(0:63)

0:043(0:53)

�0:007(�0:10)

ln(Area) 0:048��(11:30)

0:036��(3:20)

0:032��(4:49)

0:049��(3:05)

0:024(0:54)


0:184(2:02)

0:224��(3:53)

0:418��(5:73)

0:429��(2:65)

Island �0:016(�0:27)

0:177(0:96)

0:001(0:00)

�0:304(�1:30)

�1:431(�1:78)


(�5:35)�0:281��(�3:96)

�0:200��(�2:66)

�0:127(�1:96)

�0:078(�1:40)

Colonial �0:289��(�5:93)

�0:449��(�5:12)

�0:336��(�4:95)

�0:232��(�3:31)

�0:114(�1:85)


(�1:03)�0:040(�1:42)

�0:062(�2:19)

0:563(1:39)

1:778(0:67)


�0:228��(�2:97)

0:092(1:42)

�0:139(�2:17)

�0:045(�0:88)


0:032(0:78)

�0:017(�0:50)

�0:009(�0:46)

0:084(2:29)

1980 dummy �0:130��(�4:70)

1990 dummy �0:172��(�6:22)

2000 dummy �0:283��(�9:59)

Country �xed e¤ects yes yes yes yes yesNumber of observations 1092 273 273 273 273R2 0.840 0.823 0.882 0.881 0.884The dependent variable is the tari¤ equivalent �jkt.Robust OLS estimation, t-statistics given in parentheses.** indicates signi�cance at the 1 percent level.

34

Table A2: The Determinants of Trade Costs (For Various Subsamples)Regressions (see description below)

Regressors (1) (2) (3) (4) (5)Geographical factorsln(Distance) 0:162��

(23:16)0:175��(24:81)

0:143��(12:02)

0:123��(6:38)

0:137��(13:73)


0:020(0:93)

�0:072(�0:95)

�0:059��(�2:89)

�0:038(�2:35)

ln(Area) 0:026��(11:63)

0:027��(12:28)

0:026��(12:62)

0:058��(6:95)

0:030��(13:31)


0:171��(8:41)

0:370��(11:99)

0:147��(8:83)

0:174��(8:57)

Island 0:083��(4:75)

0:085��(5:17)

0:652��(8:51)

0:305��(9:15)

0:041(1:74)


(�5:97)�0:087��(�4:75)

�0:090��(�4:28)

�0:047(�1:86)

�0:069��(�3:91)

Colonial �0:153��(�5:84)

�0:149��(�5:02)

�0:153��(�5:02)

�0:127��(�3:58)

�0:114��(�4:16)


(�1:27)0:002(0:22)

�0:007(�1:12)

�0:003(�0:50)

�0:007(�1:36)


�0:050��(�3:09)

�0:067(�1:70)

�0:062��(�4:71)

�0:047��(�3:27)


�0:000(�0:09)

0:001(0:41)

0:003(0:32)

0:004(0:63)

1980 dummy �0:068��(�4:69)

�0:069��(�4:99)

�0:074��(�4:61)

�0:053��(�2:85)

�0:056��(�3:33)

1990 dummy �0:095��(�6:44)

�0:092��(�6:46)

�0:107��(�6:35)

�0:061��(�3:76)

�0:080��(�5:11)

2000 dummy �0:157��(�9:95)

�0:154��(�9:96)

�0:160��(�8:98)

�0:130��(�7:43)

�0:131��(�8:61)

Country �xed e¤ects yes yes yes yes yesNumber of observations 992 992 676 416 600R2 0.857 0.857 0.852 0.919 0.789The dependent variable is the tari¤ equivalent �jkt. Pooled over 1970, 1980, 1990 and 2000.Robust OLS estimation, t-statistics given in parentheses.** indicates signi�cance at the 1 percent level.(1) U.S. observations excluded.(2) UK observations excluded.(3) Intra-European observations excluded.(4) Intra-European observations only.(5) Rich countries only (2002 per-capita income over US$ 20,000).

35

TableA3:SimpleCorrelation

Coe¢cients

Tari¤Equiv.ln(Distance)

Borderln(Area)

Landlocked

Island

Language

ColonialTari¤s

FTA

ERVol.

Tari¤Equiv.

1:00

ln(Distance)

0:36

1:00

Border

�0:30

�0:44

1:00

ln(Area)

0:14

0:34

�0:03

1:00

Landlocked

�0:05

�0:24

0:18

�0:25

1:00

Island

�0:01

0:18

�0:16

0:06

�0:18

1:00

Language

�0:22

0:01

0:30

0:06

0:04

0:15

1:00

Colonial

�0:12

0:06

0:08

�0:06

�0:06

0:25

0:30

1:00

Tari¤s

0:25

0:18

�0:10

0:28

�0:09

0:17

�0:01

0:07

1:00

FTA

�0:22

�0:61

0:25

�0:25

0:17

�0:01

�0:03

�0:03

�0:18

1:00

ERVolatility

0:17

0:40

�0:18

0:30

�0:13

0:09

�0:09

0:01

0:38

�0:25

1:00

Numberofobservations:1092foreachvariable.

36

is the iceberg melting less quickly? international trade

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