borders and growth - ucla anderson school of management...are existing national borders good or bad...

Journal of Economic Growth, 10, 331–386, 2005© 2005 Springer Science+Business Media, Inc. Manufactured in The Netherlands.

Borders and Growth

ENRICO SPOLAORE

Department of Economics, Tufts University, Medford, MA 02155

ROMAIN WACZIARG

Stanford Graduate School of Business, 518 Memorial Way, Stanford, CA 94305

This paper presents a framework to understand and measure the effects of political borders on eco-nomic growth and per capita income levels. In our model, political integration between two coun-tries results in a positive country size effect and a negative effect through reduced openness vis-a-visthe rest of the world. Additional effects stem from possible changes in other growth determinants,besides country size and openness, when countries are merged. We estimate the growth effects thatwould have resulted from the hypothetical removal of national borders between pairs of adjacentcountries under various scenarios. We identify country pairs where political integration would havebeen mutually beneficial. We find that full political integration would have slightly reduced an aver-age country’s growth rate, while most countries would benefit from a more limited form of merger,involving higher economic integration with their neighbors.

Keywords: economic integration, political unions, growth

JEL classification: F1, O5

1. Introduction

Are existing national borders good or bad for economic growth? What would thegrowth rate of per capita income in Canada have been if its border with theUnited States had not existed, that is, if they had been a single country? What ifItaly and France had merged? In brief, what is the effect of borders on economicperformance?

National borders constitute barriers to economic exchange, and may thereforereduce gains from specialization and trade. Removing national borders allows theformation of larger domestic markets, which may have a positive effect on pro-ductivity and growth if market size matters for economic activity. However, asstressed in the regional integration literature, removing borders between regionswhile maintaining barriers with the rest of the world can bring about not onlytrade creation but also trade reduction. Moreover, national borders may shieldsome countries from slow-growing neighbors, and their removal might thereforereduce productivity and economic growth.

In order to estimate the effects of borders on growth one needs to answer threedistinct but related questions:

332 SPOLAORE AND WACZIARG

(1) Is openness good for growth?

(2) Is a large market size good for growth?

(3) Does a country’s openness depend on its size?

While there exist extensive literatures addressing each of those questions sepa-rately, there are very few theoretical and empirical analyses that examine effects ofsize and openness on growth jointly, treating openness as an endogenous functionof size and other determinants. This paper argues that a simultaneous approach isessential. We will provide a unified exploration of these three important questions,and provide new quantitative answers.

We will then use our results to address whether existing national borders havebeen good or bad for growth. Specifically, we will ask a counterfactual question:

(4) Would existing countries have gained much from merging with their neigh-bors?

In a nutshell, our answers to the first three questions will be “yes”. Our answerto the last one is “it depends”.

In this paper we first present a simple theoretical framework accounting for theeffects of openness and size on income and growth.1 In our model, politicallyintegrated economies can save on trading costs, generating a market size effect ofpolitical integration. However, trade openness responds endogenously to politicalintegration. All other things being equal, in a political economy equilibrium, largercountries tend to choose higher trade barriers with respect to the rest of the world.Therefore, political integration, by increasing the size of countries and hence theirbarriers, also generates a trade reduction effect. Finally, political integration caninduce changes in the other determinants of steady-state income levels, besidescountry size, an effect we call the steady-state determination effect. Within ourstylized framework, we derive closed-form solutions for the relationship betweensteady-state income per capita, openness and country size. We also obtain a rela-tionship between openness, barriers to trade and size. We then discuss necessaryand sufficient conditions for a positive effect of political mergers on steady-stateincome per capita and on economic growth.

In the second part of this paper we provide an empirical methodology to eval-uate the effect of national borders on economic growth. We estimate the effect

1 In the empirical literature “openness” is usually measured by trade/GDP. Conceptually, we candefine a country as more “open” when it has lower barriers to trade. In our framework, a coun-try’s openness, measured by trade/GDP, is an endogenous function of trade barriers and othercharacteristics, including country size, while trade barriers also depend endogenously on countrysize. In this paper we refer to the volume of trade (trade to GDP ratio) as “openness” and topolicy determined openness as “barriers”.

BORDERS AND GROWTH 333

of market size on economic growth in a cross-country context. In our specifica-tion, derived directly from the model, market size can be increased by two means:expanding the internal market or gaining greater access to foreign markets. Con-sistent with our theoretical framework, growth is affected both by openness anddomestic size, which also interact with a negative sign (the effect of a largerdomestic size is reduced at higher levels of openness, and the effect of opennessis smaller for a larger domestic size). Openness itself is estimated—simultaneouslywith growth—as an endogenous variable which is affected by domestic size, amongother determinants. We find robust evidence of positive effects of openness and sizeon growth, and of a negative effect of size on openness.

Together, these estimates allow us to quantify the economic effect of specific bor-ders by creating hypothetical merged countries (for example the one that wouldresult from the United States merging with Canada or France merging with Italy),and estimating what their growth rate would have been over the sample period.That is, we calculate the growth rate for each “hypothetical country” resultingfrom the merger of two actual countries. For example, the hypothetical countrygiven by the merger of France and Switzerland is given by a size equal to the sumof the French and Swiss populations, an endogenously derived degree of open-ness as implied by the structural equation for a country with the size and geo-graphical characteristics of “France plus Switzerland” (e.g. the country would notbe landlocked), and other relevant steady-state determinants (e.g. human capital)as weighted averages of French and Swiss actual variables.2 This empirical exer-cise corresponds exactly to our theoretical counterfactual. We present estimates ofthe market size effect, the trade reduction effect and the steady-state determina-tion effect for all pairs of adjacent countries and proximate islands for which dataare available (123 hypothetical pairwise mergers).3 We identify cases where politi-cal integration would have been mutually beneficial to the merging countries, anddiscuss the conditions under which this occurs.

We find that the complete removal of political borders between neighbors (fullintegration) would not be growth-enhancing on average. In fact, on average itwould bring about a (slight) negative net effect on growth: −0.112 percentagepoints of annual growth. In other words, the typical country would lose from pair-wise political integration with a neighbor. Moreover, out of 123 hypothetical merg-ers, only 14 would bring about benefits for both countries involved in the merger.By contrast, integration of domestic markets in which each country remains polit-ically independent would tend, on average, to increase growth performance acrosscountries. In summary, while we find a few cases in which countries could benefiteconomically from full political integration with their neighbors, a more promisingavenue for most countries would be to extend the size of their markets by loweringbarriers to trade with their neighbors and the rest of the world, while maintainingtheir political independence.

2 Alternative scenarios to create “hypothetical countries” are discussed in Section 3.3 The methodology can be easily extended to a case in which more than two countries consider

integrating politically. We do not pursue such an extension in this paper.


This paper builds on and contributes to several related literatures. There exists avast theoretical and empirical literature on the relationship between national bor-ders and trade. Recent important contributions that directly document the effectof national borders on trade include McCallum (1995) and Helliwell (1998).4 Thisliterature suggests that removing national borders would substantially reduce bar-riers to interregional trade. A second, related body of work in the field of inter-national trade is the extensive literature on the effects of regional integration ontrade, efficiency and welfare. This literature has stressed how removing a specificpolitical border can result in trade reduction vis-a-vis third countries. In particu-lar, the classical theory of customs unions has pointed out the welfare losses fromtrade diversion.5 More generally, the literature has studied the costs and benefits ofregional integration in a second-best world in which integrated markets face barri-ers with the rest of the world.6 A third, related body of work in the field of inter-national trade, which is immediately relevant for our analysis, has focused on theendogenous formation of barriers to international trade.7

While we build on the theory and empirics of international trade, our approachin this paper is more closely linked to the growing macroeconomics literatureon the relationship between openness, market size and growth. The relationshipbetween openness and growth has been the focus of numerous studies, whichinclude Sachs and Warner (1995), Frankel and Romer (1999), Rodrıguez andRodrik (2000), Wacziarg (2001), and Alcala and Ciccone (2004) among others. Inthis literature the effect of openness on economic performance is usually stud-ied without controlling for countries’ domestic size. A second, smaller but grow-ing literature has focused on the importance of market size for productivity andgrowth. In particular, our paper is most closely related to Alesina et al. (2000,henceforth ASW), who have stressed that (a) the effects of market size and open-ness on economic performance should be studied jointly, and (b) openness shouldhave a larger effect for smaller countries, while domestic size should have a largereffect for closed countries.8

Our paper builds on the ASW framework. However, it addresses a differentset of issues and, consequently, differs from the ASW framework in several key

4 This literature is not directly concerned with the effects of national borders on economic growth.In his important book on border effects in international trade, Helliwell (1998, chapter 6,p. 112) states that “assessing the possible growth implications of home preferences is not a jobfor a one-handed economist, nor for the faint of heart”. We are not aware of research that triesto accomplish such measurement.

5 The classical reference is Viner (1950). For a textbook exposition see, for example, Vousden(1990), chapter 10.

6 For a survey of the regional-integration literature, see Baldwin and Venables (1995).7 The political economy of trade barriers and protectionism is surveyed, for instance, by Rodrik

(1995).8 The effect of the extent of the domestic market on growth has also been investigated by Ades

and Glaeser (1999). A recent confirmation of the Alesina–Spolaore–Wacziarg hypothesis on therelationship between size, openness and growth has been provided by Alcala and Ciccone (2003).


respects. A central difference with the ASW framework is that we treat opennessand barriers to trade as fully endogenous, and we consequently model and estimategrowth and openness simultaneously. The ASW analysis focused on how exoge-nous changes in the level of trade barriers affect the number and size of nations ina world of endogenous borders. By contrast, our focus is on the effects of (count-erfactual) changes in the configuration of borders on a country’s level of opennessand economic performance. Hence, in our empirical framework we jointly estimatethe effects of market size and openness on growth and income levels and the rela-tionship between openness and market size. Moreover, we use our estimates of thegrowth effects of market size and openness to construct the empirical analog toour theoretical counterfactuals, and to estimate the effects of specific borders ongrowth and income levels. Thus, we view this paper as providing a novel way toexamine the relationship among market size, openness and growth, and to providequantitative estimates of the economic effects of national borders.

This paper is structured as follows: Section 2 presents a model of economicgrowth based on scale effects, and analyzes the effect of borders on growth in thiscontext. Section 3 describes our empirical methodology for estimating the bordereffect and discusses extensions to our basic strategy. Section 4 presents our empir-ical results, and Section 5 concludes.

2. A Model of Political Integration and Growth

This section presents a stylized model that links political borders, trade opennessand productive activity. In this model, market size affects growth and income lev-els, and depends both on the degree of openness of the economy and on coun-try size. Openness, measured by the ratio of trade to output, is itself endogenous,and responds to country size via endogenous barriers to trade. In our model, theeffect of market size on productivity is not due to a technology with increasingreturns, but to the benefits of variety: lower trading costs allow easier access to aset of intermediate inputs needed for the production of a homogeneous consump-tion good, using a production function with constant returns to scale.

The basic structure of the model is as follows: Countries are sets of regions.Each region uses its own immobile capital to produce a region-specific intermedi-ate input. Intermediate inputs are traded both domestically (across regions withina country) and internationally (between regions that belong to different countries).International trade in intermediate inputs depends on the size distribution of coun-tries and their barriers to trade. Trade barriers are themselves a function of politi-cal parameters and country size. The final good is used for local consumption andthe accumulation of capital. The return to capital is also a function of the size dis-tribution of countries and their international openness.

In the context of this model, we show that income per capita in steady-stateand growth rates are increasing in country size and in international openness. Theeffect of size is larger for less open countries, while the effect of openness is largerfor smaller countries. Finally, we describe how our model can be used to predictthe effect of national borders on economic growth.


2.1. Assumptions of the Model

There is a continuum of regions, measured on the interval [0,W ]. Time is contin-uous. The intertemporal utility function in each region i is given by:

Ui =∫ ∞

0ln ci (t)e

−ρt dt, (1)

where ci (t) denotes consumption at time t by the representative household livingin region i , and ρ>0.9 At time t region i ’s capital and labor are denoted, respec-tively, by Ki (t) and Li (t). Both inputs are supplied inelastically and are not mobileacross regions. Each region i produces a specific intermediate input Xi (t) using theregion-specific capital according to the following linear production function:

Xi (t)= Ki (t). (2)

There exists a unique final good. Each region i produces yi (t) units of the finalgood, using tradeable intermediate goods from its own region and other regions,according to the production function:

yi (t)=(∫ W

0xαj i (t)d j

)L1−α

i (t) (3)

with 0<α<1. x ji (t) denotes the amount of intermediate input j used in region iat time t .

Regions are divided into N countries. Country 1 includes all regions in the inter-val [0, S1), country 2 includes all regions in the interval [S1, S1 + S2), country nincludes all regions in the interval [Sn−1, Sn−1 + Sn), and country N includes allregions in the interval [SN−1, SN−1 + SN ]. Each region inelastically supplies oneunit of labor (i.e., Li (t)= 1 for every i at every t .). Hence, the size of country n(measured by total labor) is equal to Sn , where n =1,2, . . . , N .

Intermediate inputs can be traded across regions that belong to the same coun-try at no cost (i.e., we assume no internal barriers to trade). By contrast, if oneunit of an intermediate good j that belongs to country a is shipped to a regionthat belongs to a different country (say, country b), only (1− ξa − ξb) units of theintermediate good will arrive, where 0<ξa + ξb ≤ 1. Hence, the levels of ξn ’s mea-sure barriers to trade across national borders. Let fii ′ denote the units of inter-mediate input i produced in region i of country a and shipped to region i ′ incountry b. Because of barriers to trade, the quantity of intermediate input i actu-ally used in production in region i ′ is given by xii ′ = (1− ξa − ξb) fii ′ .

9 As usual, the results generalize to any standard CRRA utility function (ci (t)1−σ − 1)/(1 − σ)

with σ >0.


2.2. Equilibrium

Intermediate inputs are sold in perfectly competitive markets. In equilibrium, eachunit of each input will be sold at a price equal to its marginal product. All regionsthat belong to the same country will use identical levels of a given input. Hence,we can let xin denote the amount of input i actually used in each region of coun-try n, while fin will denote the quantity of input i purchased by a region in coun-try n. Let Pi (t) denote the market price of intermediate input i , where region ibelongs to country a. Therefore, for every input i belonging to a country a andfor every country n �=a we must have:

Pi (t)=αxα−1ia (t)=α(1− ξa − ξn)

α f α−1in (t). (4)

By using equation (4) and the resource constraint, we can obtain the equilibriumprice of each input i produced in country a, as shown in Appendix 1:

Pi (t)=α⎡⎣Sa +

∑n �=a

Sn(1− ξa − ξn)α

1−α

⎤⎦

1−αKi (t)

α−1. (5)

Households’ net assets in region i are identical to the stock of region-specific capitalKi (t). Since each unit of capital yields one unit of intermediate input i , the net returnto capital is equal to the market price of intermediate input Pi (t) (for simplicity, weassume no depreciation). From standard intertemporal optimization we have the fol-lowing Euler equation for consumption in region i belonging to country a:

dcit

dt

1cit

= Pi (t)−ρ=α⎡⎣Sa +

∑n �=a


1−α

⎤⎦

1−αKi (t)

α−1 −ρ. (6)

As usual in a standard Ramsey model, the steady-state level of capital in eachregion i belonging to country a is obtained as the solution of the above equation

atdcit

dt

1cit

=0:10

K ssi =

(α

ρ

) 11−α

⎡⎣Sa +

∑n �=a


1−α

⎤⎦ . (7)

The steady-state level of output per capita in a region i of a country of size Sa isgiven by:11

10 For example, see Barro and Sala-i-Martin (1995), chapter 2.11 The derivation of Equation (8) is in the Appendix. A similar relationship between income per

capita, barriers to trade, and size distribution of countries would hold in a static setting inwhich there is a nonaccumulable region-specific input and all regions are equally endowed withthe same quantitities of it. The details of the derivation are available upon request. We are grate-ful to an anonymous referee for this observation.


yssi =

(α

ρ

) α1−α

⎡⎣Sa +

∑n �=a


1−α

⎤⎦ . (8)

Our model has standard neoclassical implications as far as the growth rate is con-cerned. In particular, at each point in time the growth rate of income per capitais positively related to steady-state income per capita and negatively related to thecurrent (initial) level of income:12

d ln yn(t)

dt= f (yss

n , yn,t−τ ) (9)

with∂ f

∂yssn>0,

∂ f

∂yn,t−τ<0. (10)

Therefore, the effects of size, openness or other variables on the level of incomeper capita also translate into effects on the growth rate in the transition to thesteady-state. Thus, in this theoretical section we will focus our analysis on steady-state income. Implications for growth will be studied in the empirical section.

2.3. Steady-state Income, Country Size, and International Openness

We are now ready to derive the relationships between steady-state income per cap-ita, country size, barriers to trade, and international openness. In what follows wewill consider these relationships under the simplifying assumption that barriers tointernational trade (the parameters ξ ′s in the above equations) are exogenous.13

Equation (8) implies the following:

Proposition 1 Income per capita in steady-state is increasing in country size (forgiven barriers to international trade) and decreasing in barriers to trade (for givencountry size). The positive effect of size is higher the higher are the barriers to inter-national trade (i.e., size matters more for less open countries).

Derivation of Proposition 1. Equation (8) implies that the derivative of incomeper capita in steady state for a region i in country a with respect to country a’sbarriers is:

∂yssi

∂ξa=− α

1−α(α

ρ

) α1−α ∑

n �=a


1−α−1<0. (11)

This shows that income per capita is decreasing in barriers to trade, for givencountry size. Conversely, if country size is increased by ∂Sa , while the size of

12 For a derivation of these standard results see, for example, Barro and Sala-i-Martin (1995).13 In Section 2.4 we will extend the analysis to allow for endogenous barriers to trade.


each other country is decreased by∑

n �=a ∂Sn = −∂Sa , while all barriers remainunchanged, we have:14

∂yssi

∂Sa=

(α

ρ

) α1−α

⎡⎣1− 1

N −1

∑n �=a

(1− ξa − ξn)α

1−α

⎤⎦≥0. (12)

Notice that the effect of country size is strictly positive if and only if there are bar-riers to international trade—i.e., at least some ξ ′s are positive. In the case of com-plete free trade everywhere (all ξ ′s equal to zero), the derivative in equation (12)becomes zero.15 That is, country size matters in a world of barriers to trade, whileit would not matter if there were no barriers to trade across political borders (com-plete economic integration). By the same token, an increase in the barriers to tradewould make the effect of country size on income bigger: country size matters morefor countries with higher barriers to trade (i.e., for less open countries):

∂2 yssi

∂Sa∂ξa= α

1−α(α

ρ

) α1−α 1

N −1

∑n �=a

(1− ξa − ξn)α

1−α−1 ≥0. (13)

In summary, we have shown that income per capita is increasing in country size,decreasing in barriers to trade, and that the effects of size is larger for countries withhigher barriers to trade. These relationships have been derived in terms of barriersto international trade. However, it might be empirically difficult to observe and mea-sure barriers to trade directly: in our theory these barriers include not only formaltrade barriers (tariffs, nontariff barriers) but also differences in legal systems andpolitical barriers restricting the flow of goods, which are all hard to measure.

A standard way of assessing a country’s openness to international trade is interms of its ratio of exports plus imports to output. Following standard terminol-ogy, we will refer to this ratio as “openness”. Within our theoretical framework,we can easily show that in steady-state, “openness” (which is obviously endoge-nous) bears a monotonic relationship with barriers to trade. Specifically, let Oa

denote the exports to output ratio.16 Each region in country a will use xssia units

of inputs locally, and will sell an equal amount xssia to each of the other Sa − 1

14 When studying the comparative statics of country size, it is important to make sure that anincrease in a country’s size is accompanied by a corresponding reduction in the size of oneor more of the remaining countries. An increase in the size of a given country without a cor-responding reduction in other countries’ sizes would mix two distinct effects: a “country size”effect, and an effect stemming from the overall “expansion of the world market” (i.e., from abigger parameter W ). For simplicity and without loss of generality, in our derivation we assume

that all remaining N −1 countries experience an equal reduction in size, that is, ∂Sn =− ∂Sa

N −1for all n �=a.

15 It is immediate to check that:dyss

id Sa

=(α

ρ

) α1−α [1− 1

N−1 (N −1)]=0.

16 In this model we abstract from international borrowing and lending—hence exports are alwaysequal to imports in equilibrium. Therefore, measuring openness as exports/output is identical,up to a scalar multiplication, to measuring openness as (exports + imports)/output.


regions belonging to country a. Hence, total exports of input i will be given byK ss

i − Sa xssia . Since all regions in country a export the same amount, total exports

in country a are given by (K ssi − Sa xss

ia )Sa . Country a’s total output is given byyss

i Sa . Therefore, the exports to output ratio Oa in steady-state is given as follows:

Ossa = (K ss

i − Sa xssia )Sa

yssi Sa

. (14)

By using the expression for xia derived in Appendix 1 and equations (7) and (8),we can write the equilibrium steady-state level of openness as:

Ossa =

(ρα

)α∑n �=a


1−α

Sa +∑n �=a


1−α(15)

which implies that Ossa is decreasing in ξa :

Proposition 2a Openness in steady-state is inversely related to a country’s barriers totrade.

Formally:

d Ossa

dξa=− α

1−α(ρα

)α Sa

∑n �=a


1−α−1

⎡⎣Sa +

∑n �=a


1−α

⎤⎦

2≤0 (16)

Hence, all other things being equal, higher barriers to international trade are asso-ciated with higher openness.

As we will see in the empirical section, the data are consistent with the maininsights from the above analysis, that is, (a) country size and openness are positivelyrelated to higher income per capita in steady-state (and hence higher growth in thetransition to the steady-state), and (b) other things equal, the effect of size is largerfor countries with higher barriers to trade (and, hence, lower openness), while theeffect of higher barriers and lower openness is bigger for smaller countries.

When studying these relationships both theoretically and empirically, it is impor-tant to keep in mind that openness is an endogenous variable. In particular,there are two conceptually distinct reasons why openness is endogenously relatedto country size. First, even for given barriers to international trade, openness isa function of country size, as it is immediate to verify from equation (15). Allother things equal, an increase in country size tends to be associated with loweropenness. Formally, we have:17

17 Again, we assume that the size of all other countries is equally reduced, that is, d Sn =−d Sa/(N −1)for all n �=a.


d Ossa

d Sa=−

(ρα

)αSa

N −1

∑n �=a

(1− ξa − ξn)α

1−α +∑n �=a


1−α

⎡⎣Sa +

∑n �=a


1−α

⎤⎦

2≤0, (17)

which implies:

Proposition 2b Openness in steady-state is inversely related to a country’s size, forgiven barriers to trade.

Second, as we will see below, barriers to trade can also be modeled as an endog-enous function of size. This introduces an additional channel through which sizecan affect openness negatively. These endogenous links between openness and sizewill be taken into account in our empirical analysis of the effects of countrysize and openness on income and growth—that is, openness will be explicitly mod-eled as a function of country size and other determinants.

2.4. Endogenous Barriers to Trade

So far we have considered barriers to trade as given. We will now extend theanalysis to allow for an endogenous determination of barriers. Specifically, we willassume that, for each country n barriers are given as follows:

ξn(t)= ξ

2−λn(t), (18)

where λn(t) is a variable controlled by the government of country n. A higher λn(t)means lower barriers.

It is reasonable to assume that lower trade barriers may entail political andadministrative costs. We capture the costs of lower barriers in a stylized manner,by assuming a convex cost

(φn[λn(t)]2

)/2.18 On the other hand, trade barriers may

bring about political benefits (say, rents) to a country’s policy-makers. We capturethese rents as a simple, linear function of the barriers. Specifically, we assume thatthe government of country n will choose λn(t) in order to maximize the followingobjective function:19

ψnξn(t)+ (1−ψn)cn(t)− φn

2[λn(t)]2 (19)

18 This quadratic specification is assumed for convenience in order to obtain a closed-form solu-tion below. The assumption is not necessary for an interior solution, and could be generalizedto φn [λn(t)]ζ with ζ ≥0. For example, an interior solution exists for the case of costs indepen-dent of λ (ζ =0) and for the case of costs linear in λ (ζ =1), when α<1/2.

19 For simplicity we assume that policy-makers have measure zero in the economy, and thereforetheir rents and costs do not affect per capita consumption, capital accumulation and productiondirectly, but only through policy decisions.


ψn is the weight given to the “political” benefits or rents associated with barriersto trade, while 1−ψn is the weight given to the consumption level of the represen-tative consumer at time t .20

In general, at each point in time barriers are a function of the political param-eters ψn and φn and of the determinants of the equilibrium consumption path. Inparticular, we focus on the steady-state level of barriers ξ ss

n , which is defined as thesolution of the following:

maxλn

{ψnξn + (1−ψn)

(α

ρ

) α1−α

cssn − φn

2λ2

n

}. (20)

Since steady-state consumption is equal to steady-state income in our model, wecan substitute css

n in equation (20) with yssn from equation (8). Hence the steady-

state level of λssa for a country of size Sa is given by

λssa =arg max

λa

{ψa

[ξ

2−λa

]+ (1−ψa)

(α

ρ

) α1−α

×⎡⎣Sa +

∑n �=a

Sn

(1− ξ

2+λa − ξn

) α1−α

⎤⎦− φa

2λ2

a

⎫⎬⎭ . (21)

For each country a =1,2, . . . , N , the first-order condition for λ∗a is given as fol-

lows:

−ψa + (1−ψa)α

1−α(α

ρ

) α1−α ∑

n �=a

Sn(1− ξ

2+λss

a − ξn)2α−11−α ]−φaλ

ssa =0. (22)

In general, the equilibrium level of barriers reduction in each country is a func-tion of the size distribution of all countries.21 Other things equal, smaller countriestend to have lower barriers. For example, in a world of two countries (W = Sa + Sb)with identical political parameters (ψa =ψb =ψ and φa =φb =φ) we have:22

dλssa

d Sa=−1−ψ

φ

α

1−α(α

ρ

) α1−α

(1− ξ +λssa +λss

b )2α−11−α <0. (23)

20 A specification in which policy-makers attach weight both to their rents (contributions from lob-bies) and to their citizens’ welfare is provided, for instance, in Grossman and Helpman’s (1994)classic analysis of protectionism. For a survey of this extensive literature see, for example, Ro-drik (1995). In our theory we do not model a private demand for protection explicitly, butjust assume that the government’s rents are a function of barriers. Our main results would gothrough even if ψn =0. More generally, we will assume 0≤ψn <1.

21 We assume that each country will choose its barriers taking other countries’ barriers as given.That is, in each first-order condition, other countries’ barriers will be taken as given at theirequilibrium level (i.e., ξ ss

n = ξ2 −λss

n for all n �=a). By contrast, joint maximization of world wel-fare would imply lower barriers.

22 The result can be generalized to the case of three or more countries.


A simple closed-form solution can be obtained for the case α = 1/2. Then thedegree of barrier reduction λ∗

a that maximizes output per capita minus barriersreduction costs for a country of size Sa is:

λssa = (1−ψa)(W − Sa)

2φaρ− ψa

φa(24)

which, again, implies a negative relationship between barrier reduction and size:23

dλssa

d Sa=−1−ψa

2φaρ<0. (25)

Hence, we have the following:

Proposition 3 All other things equal, larger countries will have less open trade poli-cies—that is, they will choose lower λss

a —and, consequently, higher barriers ξ ssa .

Countries with lower costs of reduction (φa), lower weight on political rents (ψa)or a lower discount rates (ρ) will be more open (that is, will have a higher λa).Why do larger countries have higher barriers, and smaller countries lower barri-ers, all other things being equal? The result stems directly from the fact that inlarger countries higher barriers are not as costly as in smaller countries in termsof income per capita and consumption per capita, because in larger countries moreintermediate inputs are purchased domestically—that is, from other regions withinthe country. In contrast, smaller countries need to purchase more intermediategoods abroad, and hence are more heavily hurt by international barriers. As aconsequence, in smaller countries politicians who attach some weight to nationalincome per capita and national consumption will choose a lower level of protec-tionism, while in larger countries they will be able to “afford” more protectionism.These results hold even though we assumed that political rents from barriers areindependent of the level of domestic production. If we were also to assume thatpolitical rents are increasing in the size of domestic production, the relationshipbetween barriers and country size would be strengthened. Finally, an interestingissue, which we do not pursue in this analysis, is the possibility that barriersbetween countries may depend on incompatibilities in administrative proceduresand legal frameworks. In this case, the costs of removing the barriers wouldinclude the costs to coordinate and harmonize procedures across countries.24

23 It is immediate to check that (23) reduces to (25) for α=1/2.24 These costs could be modeled either directly (as coordination costs), or by assuming that each

country adopts administrative and legal procedures of a given type, and that changing typeimplies political costs. This is in analogy to models in which people in different locations havedifferent preferences over the type of public services provided by the government, and mov-ing away from one’s favored type of government implies heterogeneity costs (see Alesina andSpolaore, 2003).


2.5. Political Mergers

Let us now consider a merger between country a (of size Sa) and country b (ofsize Sb). To keep things simple we will assume α=1/2 and ψa =ψb =ψ and φa =φb =φ. The steady-state levels of income per capita in country a is:

yssa =

(1

2ρ

)⎡⎣Sa +

∑n �=a

Sn(1− ξ ssa − ξ ss

n )

⎤⎦ . (26)

The steady-state income per capita in the new country of size Sm = Sa + Sb will be:

yssm =

(1

2ρ

)⎡⎣Sm +

∑n �=m

Sn(1− ξ ssm − ξ ss

n )

⎤⎦ . (27)

The net change in steady-state income for country a will be given by

yssm − yss

a =(

12ρ

)[Sb(ξ

ssa + ξ ss

b )− (W − Sa − Sb)(ξssm − ξ ss

a )]. (28)

In equation (28), the first term, (1/2ρ) Sb(ξssa + ξ ss

b ), measures the direct positivescale effect of the merger, which we call the market size effect. It is evaluated atthe level of trade barriers prevailing before the merger and corresponds to addingthe size of country b to country a.

The second term in equation (28), (1/2ρ) (W − Sa − Sb)(ξssm − ξ ss

a ), measures theindirect negative effect of the merger, via a fall in openness. We call this effectthe trade reduction effect. It corresponds to the increase in trade barriers betweenthe regions of former country a and the rest of the world (i.e., all other countriesexcept country b), brought forth by the larger size of the merged country (Sm).That is, this effect is due to the fact that the larger country will be less open withrespect to the rest of the world.

Note that there is no guarantee that the net gain in terms of steady-state income(and growth) will be positive. That is, there is no guarantee that steady-stateincome per capita in the new, larger country will be higher than in country a—i.e., that yss

m − yssa >0.

From equation (24) we have:

ξ ssa = ξ

2−λss

a = ξ

2− (1−ψ)(W − Sa)

2φρ+ ψ

φ, (29)

ξ ssb = ξ

2−λss

b = ξ

2− (1−ψ)(W − Sb)

2φρ+ ψ

φ, (30)

ξ ssm = ξ

2−λss

m = ξ

2− (1−ψ)(W − Sm)

2φρ+ ψ

φ, (31)

which, when substituted in equation (28), imply the following:


Proposition 4 A necessary and sufficient condition for yssm − yss

a >0 is:

Sm = Sa + Sb>3(1−ψ)W −2ρ(ξφ+2ψ)

2(1−ψ) . (32)

The intuition for this results is as follows. A higher Sm means a bigger positiveeffect from the merger via the market size effect, because the two merging coun-tries had larger barriers between themselves before the merger. A larger Sm (rela-tive to W ) also means that the rest of the world is relatively smaller, and thereforethe openness reduction effect (with respect to the rest of the world) has smallercosts.

It is important to note that even if a merger increases income per capita, itdoes not necessarily imply an increase in consumption per capita and welfare. Inorder to calculate changes in consumption and welfare one should subtract thecosts related to barriers reduction and any other costs associated with a merger.For example, a merger may bring about direct costs in order to eliminate inter-nal barriers to trade. A merger may also imply higher “heterogeneity” costs dueto different preferences over public goods, more costly coordination, etc.25 In ourempirical exercises we will focus on changes of income per capita.

2.6. Other Determinants of Steady-State Income Levels

In our model so far, different countries’ steady-states differ only because (1) theirsize differs and (2) as a result, their level of openness also differs. There are obvi-ously many other differences across countries, apart from size, that could yielddifferences in steady-state income levels and openness. In the context of our model,the ψ,φ and ρ parameters could differ across individual countries. Particularlypatient countries, or countries where the costs of openness reduction are lower (forexample through natural access to the sea, proximity to trading partners, and othergeographic factors) will have higher levels of steady-state income and greater levelsof openness, all else equal.

Such differences will not affect country a’s growth performance under politicalintegration with country b, unless they affect the other determinants of steady-stateincome levels and openness within country a. But it is easy to see that a mergerbetween country a and country b, when they differ along these other dimensions,will change the growth effect of the merger on country a, to the extent that themerger affects these values within country a. We should stress again that this wouldonly occur if country a’s steady-state and openness determinants (other than itssize and induced openness level) would change under political integration. This

25 On the costs of larger, more heterogeneous countries see Alesina and Spolaore (1997, 2003).


could occur as the result of factor movements such as migration or capital flows,or changes in geographic factors brought forth by the removal of borders.26

In the case where countries differ in ψ,φ and ρ, the thought experimentdescribed above to evaluate the growth incidence of political mergers can beamended to account for changes in steady-state determinants under a merger. Forexample, if countries have different costs φ’s, the analysis can be easily generalizedas follows. Let φm denote the costs of barriers reduction in the unified country ofsize Sm . Then we have the following:

Proposition 5 A political merger between a country of size Sa and a country of sizeSb will increase income in country a in steady state (that is, yss

m − yssa > 0) if and

only if the following condition holds:

Sb

[ξ + ψ

φa+ ψ

φb− (1−ψ)(W − Sa)

ρφa− (1−ψ)(W − Sb)

ρφb

]

>(W − Sa − Sb)

[ψ

φm− (1−ψ)(W − Sa − Sb)

ρφm− ψ

φa+ (1−ψ)(W − Sa)

ρφa

].

(33)

In what follows, we will label the effect of potential changes in steady-state deter-minants, besides openness and country size, as the steady-state determination effect.

3. Estimating the Growth Effect of Borders

In this section, we move from the theory to the data. That is, we describe theempirical strategy we pursue to estimate the effect of openness, country size andtheir interaction on economic growth and steady-state income levels, and thento calculate the growth effects of hypothetical mergers between pairs of coun-tries. We start with the basic methodology to compute border effects on growth.This involves constructing a hypothetical merged country with characteristics ofthe underlying pair of countries. Using our underlying model for the endogenousdetermination of growth and openness, we can then calculate the growth rate thishypothetical country would have had in the absence of borders, and compare it tothe actual growth rates of the merging countries.

We discuss various ways in which border effects can be calculated. In one sce-nario, we consider “size mergers” in which countries do not have barriers to theflow of goods but retain their own steady-state determinants (human capital, gov-ernment size, investment rates, etc.). Under such a scenario, the border effectresults only from the change in market size and the resulting endogenous response

26 For instance, a previously landlocked country can gain easier access to the sea as a result ofa political merger. This could affect the level of openness of the country, and consequently itsgrowth rate. See for instance Sachs (2001), and Gallup et al. (1999) for evidence on the impor-tance of geography for growth.


of openness levels. In another scenario, the other steady-state determinants (besidesopenness and country size) in the hypothetical merged country are populationweighted averages from the original pair. We refer to this scenario as “full integra-tion” since it amounts to assuming that under the merged state, each underlyingcountry shares exactly the same steady-state determinants. We also briefly discusshow to calculate effects on steady-state income levels rather than growth rates.

3.1. Basic Methodology

The model presented above, specifically Propositions 1 and 2a, suggests thatincome in steady-state is positively related to both country size and openness, andthat the effect of size is larger for less open countries. Hence, growth in the tran-sition to the steady-state will also be a function of such variables. A specificationconsistent with those insights is:

logyat

yat−τ=β0 +β1 log yat−τ +β2 Oat +β3 log Sat

+β4 Oat log Sat +β ′5 Zat + εat (34)

where a refers to a country, Sat denotes country size, Oat denotes trade openness,yat denotes per capita income, and Zat is a vector of control variables. We haveadded additional determinants of steady-state income levels (the Zat variables),which the model abstracts from, and an error term. The empirical predictions ofour framework are that β2>0, β3>0 and β4<0.

In our model, Propositions 2b and 3 suggests that openness is negatively relatedto country size. The second part of our econometric model reflects the negativerelationship between trade openness and country size:

Oat =α0 +α1 log Sat +α′2Wat +νat , (35)

where Wat is a vector of additional determinants of trade openness and the modelpredicts α1<0. In this econometric model, the exogenous variables are Sat , Zat andWat . We are considering the growth effect of an exogenous change in a country’ssize brought about by merging with a neighbor. Substituting equation (35) into(34), we obtain:

logyat

yat−τ=γ0 +γ1 log yat−τ +γ2 log Sat +γ3 (log Sat )

2 +γ ′4Wat log Sat

+γ5νat log Sat +γ ′6Wat +γ ′

7 Zat +µat , (36)

where the γ coefficients are functions of the parameters of the growth and tradeequations, as defined in Appendix 2.

Define �Gabt as the change in growth of country i resulting from its mergerwith country b. Since the only exogenous variable that has changed under a mergeris country size, we term this particular exercise a “size merger”.27 We focus on

27 Below we will examine how to account for changes in the Z and W variables under a merger.


the expected effect on growth, as we have little knowledge of what the randomcomponent of growth or openness (captured by εat and νat ) would have beenhad the countries been politically merged during the sample period.28 AssumingE(νat |Sat , Smt ,Wat )= 0, the expected effect on the growth rate of country a ofmerging with neighbor b, where the size of the merged country is denoted Smt

(= Sat + Sbt ), is:

�Gabt ≡ E

(� log

yat

yat−τ|Sat , Smt ,Wat

)

= log(

Smt

Sat

)[γ2 +γ3 log (Sat Smt )+γ ′

4Wat]. (37)

Thus, the effect of the merger on growth is a multiple of the percentage increase incountry size, where the multiplicative factor depends on the determinants of open-ness, the estimated parameters of the model and the sizes of countries a and b.Since our model predicts that γ3 = β4α1 is positive, Proposition 3 is also directlyapparent in equation (37).

In this basic setup, the induced effect of political integration on growth willdepend on the home country’s size, the size of the country it is considering merg-ing with, and the determinants of the home country’s trade openness volume.This combines three distinct effects of political integration on growth. Firstly, thedirect (positive) effect of an increase in country size, equal to β3 times the per-centage increase in country size resulting from the merger (log(Smt/Sat )). Sec-ondly, the indirect (negative) effect through openness reduction, which is equalto β2α1 times the percentage increase in country size. Thirdly, the effect goingthrough the interaction term, which captures the increasing impact of country sizeon growth as openness decreases. This effect, of ambiguous sign, depends on thedeterminants of a’s openness level and the sizes of both a and b, and is equalto β4

(α0 +α1 log (Smt Sat )+α′

2Wat)

times the percentage increase in country size. Itshould be noted that the determinants of openness (Wat ) and the sizes of coun-tries a and b can be such that the openness reducing effect of political integrationoutweighs the positive direct scale effect of merging. In this case, �Gabt will benegative.

Finally, an exogenous change in openness yielding an equivalent expectedchange in economic growth without a political merger can be computed usingequation (34) as:

E(�Oat |Sat , Smt ,Wat )= �Gabt

β2 +β4 log Sat. (38)

The benefits of exogenous increases in openness can thus be directly compared tothose of bilateral political mergers.

28 In Section 3.3 below, we discuss an alternative method that allows us to include the error termcomponent of the growth effect of mergers, using the estimated values of error term in the orig-inal countries.


3.2. Changes in Conditioning Variables

Equations (37) and (38) implicitly assume that a political merger does not affectthe determinants of the home country’s steady-state income level, or the determi-nants of its openness levels, other than country size. For example, if France hadbeen merged with Italy, France and Italy would each have retained their own Zat

and Wat variables. These may include the savings rate, investment in human capi-tal, characteristics of governance and government involvement in the economy, andgravity type factors such as geographic variables. As suggested in Section 2.6, thisis clearly an extreme assumption since factors other than the size of the popula-tion alone would likely be different in each merged country under political inte-gration, affecting both growth and the degree of openness. For example, increasedmigration and capital mobility across countries a and b under a merger will implythat the rates of investment in human and physical capital will differ compared towhat they would have been in the separate countries. Taking this steady-state deter-mination effect into consideration generates an additional sources of ambiguity inthe sign of the overall effect of political integration on economic growth. Clearly,this effect would tend to be negative for the home country when the hypotheti-cal merger is with a country with “worse” overall determinants of the steady-stateincome level than itself.

We can relax the assumption that political integration affects growth onlythrough country size and the induced effect of changes in country size on tradeopenness by assuming that other conditioning variables will change in both mergedunits after political integration, and in particular that they will take on the samevalue in a and b under a merger. We term this alternative scenario “full integra-tion”.29

There are obviously many ways to specify what values the other determinantsof growth (the Z variables) and openness (the W variables) will take under fullpolitical integration.30 One reasonable assumption is that each of the merged coun-tries would end up with the same population weighted average of the initial con-ditioning variables, which we can denote Zmt and Wmt , where the subscript mdenotes that a political merger has occurred and that the resulting variables are,

29 There are obviously many ways to carry out the calculation of “full integration” effects. Theproper interpretation of a hypothetical merger between two countries a and b in this paper is“what would growth have been had the border between a and b not existed”. The intepreta-tion of our counterfactual is not “what would the growth rate of the merged countries havebeen over 1960–1989 if the two countries had merged in 1960”. If that were the case, we wouldhave to consider the gradual adjustment of income (and possibly of the steady-state determinantsand openness) across the two countries, post-1960. While this would be an interesting alterna-tive assumption to explore, it is beyond the scope of this paper and we leave the correspondinganalysis for future work.

30 For example, we could assume that the merged country is assigned the best—or worst—valuesof the Z and W variables from each of country a and b. We choose an intermediate—and morereasonable—assumption by assigning to the merged country the population-weighted average ofthese variables from countries a and b.


where applicable, the population weighted averages of the regional measures.31 Theresulting effect of a political merger on growth, �Gm

abt , is then computed as:

�Gmabt ≡ E

(� log

yat

yat−τ|Sat , Smt ,Wat ,Wmt , Zat , Zmt

)

= log(

Smt

Sat

)(γ2 +γ3 log (Sat Smt )+γ ′

4Wat)

+γ1 logymt−τyat−τ

+ [γ ′

4 log Smt +γ ′6

](Wmt − Wat )+γ ′

7 (Zmt − Zat ) . (39)

This formulation includes the same size effects as equation (37), namely those thatoccur through the direct effect of market size, the indirect effect through tradereduction and the changes in the interaction term. But in addition to these effects,we now have the steady-state determination effect, equal to the terms in the sec-ond line of equation (39).32 An important consequence of this framework is that,under full political integration, expected growth will be equal for both country aand country b.33

To summarize, equations (37) and (39) result from two different assumptionsabout the effects of political integration on growth; one with complete averagingof steady-state determinants (“full integration”), the other with no changes in thesevariables (“size merger”). The effect of a hypothetical merger likely falls in betweenthese two extremes. The corresponding estimates should therefore be viewed asextreme bounds on the effects of bilateral political mergers on economic growth.

3.3. Alternative Assumptions and Extensions

So far, we have focused on estimating the expected effects of political mergerson growth, disregarding the unexplained portion of growth and openness in ourcounterfactual exercises. Whether to consider the residuals µt and νt from thegrowth and openness equations when evaluating the effects of borders on growthis largely a matter of interpretation. On the one hand, if one believes that theyreflect omitted determinants of growth and openness, then they should be treated

31 Of course, in the case of the land area, the merged variable is the sum of the correspondingareas of countries a and b. For the dummy variables in our specification, the definitions of themerged variables are as follows: the merged country is landlocked if both a and b are land-locked; the merged country is an island if both a and b are islands; the merged country is anoil exporter if either a or b is an oil exporter.

32 We can further decompose the steady-state determination effect into the term γ1 log ymt−τyat−τ

which reflects differences in initial income and the terms that are functions of (Wmt − Wat ) and(Zmt − Zat ) , which reflect differences in steady-state determinants proper. For identical values ofthe Z and W variables, if country a starts out with an initial income that is lower than countryb’s, full integration will slow a’s growth simply because it will raise its initial income—the forceof convergence implies that countries grow slower, the closer they are to their steady-states.

33 This is not the case when we do not take into account the steady-state determination effect(Section 3.1), because post-merger Z and W variables still differ across a and b.


as another steady-state determinant (analogous to the W and Z variables). As itturns out, since the explained portion of growth and openness are typically on theorder of 50 and 60% respectively, in our baseline regressions, accounting forthe unexplained components of growth and openness could alter our estimates ofthe merger effects. On the other hand, if one believes that the residuals reflect true“randomness”, then there is no good justification for including them in the analy-sis: we do not know what the random component of growth would have been, hadthe countries been merged over the sample period. Since both interpretations seemequally defensible, we also present merger effects that take into account the esti-mated residuals. Fortunately, we can easily accommodate this change in our basicempirical methodology, as we do in Appendix 3A. In Section 4, we present esti-mates both with and without the residual effects, for both size mergers and fullintegration. Our result do not depend much on alternative treatments of the errorterm.

A second extension we pursue in our empirical work is to consider the effects ofborders on steady-state income levels rather than growth rates. As explained in thetheoretical section, because our model shares the dynamic features of the neoclas-sical growth model, it is straightforward to present our results in terms of steady-state income levels rather than growth. We do not observe steady-state income,but it can be estimated readily under the assumptions of our framework, becausethe right-hand side variables of equation (34) are the determinants of steady-stateincome levels. We show how to compute border effects on steady-state incomelevels in Appendix 3B, and present the corresponding estimates in Section 4.

4. Empirical Results

4.1. Estimates of the Growth and Openness Equations

4.1.1. Data and Estimators

Equations (34) and (35) can be readily estimated using cross-country data ongrowth, country size, openness and other control variables. Our measure of open-ness consists of the ratio of imports plus exports to GDP, a commonly usedindicator of a country’s overall level of openness (this corresponds closely to themeasure derived in the theory of Section 2). The measure of country size con-sists of the log of a country’s population. The Zit variables are the commondeterminants of steady-state income levels in the cross-country literature: male andfemale human capital, the fertility rate, the ratio of government consumption toGDP and the rate of physical capital investment (see Barro and Sala-i-Martin(1995), chapter 12). Finally, the Wit variables consist of common determinants ofopenness such as geographic factors (land area, whether a country is landlockedor an island, whether it is an oil exporter) and the terms of trade shocks. In orderto capture long-term phenomena, variables are averaged, where appropriate, overthe sample period.


Our base estimates for calculating merger effects are based on PPP per capitaincome data from version 5.6 of the Penn World Tables (PWT). This 1960–1989sample consists of 92 countries. Version 6.1 of this dataset has recently been cir-culated, extending the data to 1998.34 We use these data for the purpose of reesti-mating equations (34) and (35), as a robustness check. However, because some ofthe other conditioning variables are not as readily available for recent years, theupdated sample only features 77 countries. Moreover, some “important” countriessuch as Germany are not part of this dataset for the entire sample period, pre-cluding any calculation of the effect of political mergers on growth for such a keycountry in Europe.35 Therefore, in order to maximize the number of mergers weconsider, and to base our estimates on the largest possible sample, we use estimatesfrom version 5.6 of the PWT for the purpose of calculating merger effects. Asshown below, the estimates of equations (34) and (35) do not differ much betweenversions of the PWT, so we are confident that using the more recent data wouldnot alter our results other than by limiting the country coverage.36

One issue that arises clearly from our theoretical and empirical models is theendogeneity of openness (and the interaction term between openness and coun-try size) in the growth equation. To address this, we treat equations (34) and (35)as a system of simultaneous equations to be estimated jointly. Our baseline resultstherefore consist of three-stage least squares estimates (3SLS). 3SLS treats all ofthe exogenous variables in the system (i.e. country size, initial per capita income,Zit and Wit ) as potential instruments for the endogenous variables in the system(growth, openness and the interaction term between openness and country size).Given that openness and the interaction term are the only endogenous variablesto appear on the right hand side of either equation in the system, only the Wit

variables serve as instruments for them in the growth regression. As noted above,these variables consist of plausibly exogenous geographic and terms of trade vari-ables. In addition to these instruments, we can gain precision by using additionalinstruments which do not necessarily appear as exogenous variables in either thetrade or the growth equations.37 Finally, 3SLS allows for cross-equation covariance

34 See http://pwt.econ.upenn.edu/.35 In the case of Germany, this is due to reunification in 1989. The new version of the PWT only

features data for reunified Germany since 1990. Our estimates of merger effects refer to WestGermany prior to 1990.

36 Moreover, using PWT 5.6 may actually preferable to using later PWT for the 1960–1989 periodbecause the PWT 5.6 puts much more weight on 1960–1989 benchmarks than later versions(which use benchmarks from the 1990s to adjust income estimates for the 1960–1989 period).We are grateful to an anonymous referee for pointing this out.

37 Following ASW, these are dummy variables for small countries, small islands, and the inter-action terms between population and the each of dummy variables for small countries, smallislands, islands, and landlocked countries. As long as they are jointly excludable from the growthregression, geographic variables such as these are likely to be plausibly exogenous with respectto growth, yet affect the level of openness. See Frankel and Romer (1999) for further details onemploying geographic variables to instrument for openness in growth regressions, and for argu-ments that these variables are indeed excludable from a growth specification when other deter-minants of growth are controlled for.


in the error terms εi t and νi t , generating potential efficiency gains.38 For the sakeof robustness, we also present results obtained from seemingly unrelated regression(SUR), as well as regressions excluding the Zit and Wit control variables.

4.1.2. Baseline Results

Tables 1 and 2 display results for the joint estimation of equation (34) and (35).The baseline estimates used for the merger calculations appear in column (1). Thetheoretical predictions are borne out empirically. Specifically, openness and countrysize are positively and significantly related to growth, while their interaction entersnegatively and significantly. This is consistent with the model’s insights (Proposi-tions 1 and 2a), and extends related findings in ASW, Ades and Glaeser (1999) andAlcala and Ciccone (2003). Moreover, as expected, country size affects opennessnegatively. This is consistent with our theoretical insights (Propositions 2b and 4),and extends previous findings in Alesina and Wacziarg (1998) and Wacziarg (2001).

Several additional observations are called for. First, the pattern of signs and sta-tistical significance is unchanged when the Zit and the Wit control variables areexcluded from the system, and the magnitude of the coefficients of interest is raised(column 2). While this specification is likely to be tainted by omitted variables bias,it corresponds directly to the relationships derived from theory, where countriesdiffered in no other way than size and openness. It is therefore reassuring that thepredictions of the theory hold unconditionally as well as conditionally. Second, asin Frankel and Romer (1999), instrumenting for openness using geographic vari-ables increases the magnitude of the estimated coefficient on trade openness com-pared to the specifications that do not account for the endogeneity of openness(SUR estimates are presented in column 3).

Since SUR estimates are tainted by endogeneity bias and since the uncondi-tional estimates of column 2 are tainted by omitted variables bias, we rely on the3SLS estimates of column 1 as our benchmark to compute border effects. Theseestimates are not sensitive to small changes in the list of instruments or controlvariables. In fact, as argued in ASW and further shown here, the pattern and mag-nitude of coefficients on openness, country size and their interaction are remark-ably robust, whether in cross-sectional or in panel (random effects) applications. Asa consequence, it is also the case that our estimates of the effects of borders ongrowth and income levels are quite robust to changes in the specification.

Table 3 presents various diagnostic tests for our model specifications. The firstpanel presents first stage F-tests, obtained from simple OLS regressions of open-ness and the interaction term on all of the exogenous variables in the system, andtesting the joint significance of the instruments. There are two endogenous vari-ables appearing on the right-hand side of the growth equation: openness, and itsinteraction with log population. The F-tests demonstrate that the instruments are

38 See Wacziarg (2001) for further technical details on the use of 3SLS to estimate systems ofequations in a cross-country growth context.


Tab

le1.

Syst

emes

tim

ates

ofth

egr

owth

equa

tion

.

(1)

(2)

(3)

(4)

(5)

(6)

3SL

S3S

LS

SUR

3SL

S3S

LS

SUR

PW

T5.

6,19

60–1

989

PW

T6.

1,19

60–1

998

Log

popu

lati

on0.

678

(0.1

85)*

*1.

337

(0.2

54)*

*0.

263

(0.1

34)*

0.47

2(0

.249

)*1.

387

(0.3

11)*

*0.

130

(0.1

36)

Ope

nnes

s*lo

gpo

pula

tion

−0.0

07(0

.003

)**

−0.0

07(0

.004

)*−0

.003

(0.0

02)

−0.0

05(0

.004

)−0

.009

(0.0

06)

−0.0

01(0

.002

)O

penn

ess

0.08

1(0

.023

)**

0.11

8(0

.032

)**

0.04

0(0

.017

)**

0.05

5(0

.036

)0.

124

(0.0

48)*

*0.

010

(0.0

19)

Log

1960

per

capi

tain

com

e−1

.120

(0.2

69)*

*0.

120

(0.2

05)

−1.2

62(0

.245

)**

−1.4

37(0

.321

)**

0.32

2(0

.216

)−1

.611

(0.2

63)*

*F

erti

lity

rate

−0.1

85(0

.121

)−0

.308

(0.1

14)*

*−0

.601

(0.1

52)*

*−0

.717

(0.1

36)*

*M

ale

hum

anca

pita

l1.

550

(0.4

43)*

*1.

745

(0.4

02)*

*0.

079

(0.3

17)

0.01

0(0

.295

)F

emal

ehu

man

capi

tal

−1.1

83(0

.472

)**

−1.4

15(0

.433

)**

0.16

2(0

.395

)0.

165

(0.3

73)

Gov

ernm

ent

cons

umpt

ion

rati

o−0

.053

(0.0

20)*

*−0

.061

(0.0

19)*

*−0

.024

(0.0

18)

−0.0

31(0

.017

)*In

vest

men

tra

te0.

091

(0.0

24)*

*0.

087

(0.0

22)*

*0.

073

(0.0

26)*

*0.

075

(0.0

21)*

*C

onst

ant

2.21

7(3

.327

)−1

4.44

7(2

.760

)**

8.67

6(2

.662

)**

9.78

3(4

.697

)**

−16.

243

(3.5

74)*

*15

.415

(3.1

27)*

*R

20.

680.

73

Stan

dard

erro

rsin

pare

nthe

ses;

*:si

gnifi

cant

at10

%;

**:

sign

ifica

ntat

5%.

Not

es:

(a)

Nin

ety

two

obse

rvat

ions

inco

lum

ns(1

)to

(3),

77ob

serv

atio

nsin

colu

mns

(4)

to(6

).(b

)T

heR

2is

not

wel

l-de

fined

for

3SL

Sre

gres

sion

san

dis

not

repo

rted

.(c

)In

stru

men

tsfo

rop

enne

ssan

dth

ein

tera

ctio

nof

open

ness

and

log

popu

lati

onin

the

3SL

Ssp

ecifi

cati

ons:

smal

lco

untr

ydu

mm

y,sm

all

isla

nddu

mm

y,is

land

dum

my,

land

lock

edco

untr

ydu

mm

y,th

ein

tera

ctio

nsof

thes

e4

last

vari

able

sw

ith

the

log

ofpo

pula

tion

,log

popu

lati

on,l

ogin

itia

linc

ome

1960

,log

land

area

,te

rms

oftr

ade

shoc

ks,

oil

dum

my.


Tab

le2.

Syst

emes

tim

ates

ofth

eop

enne

sseq

uati

on.

(1)

(2)

(3)

(4)

(5)

(6)

3SL

S3S

LS

SUR

3SL

S3S

LS

SUR

PW

T5.

6,19

60–1

989

PW

T6.

1,19

60–1

998

Log

popu

lati

on−6

.744

(2.6

71)*

*−1

5.00

3(2

.254

)**

−5.8

62(2

.699

)**

−7.7

23(3

.185

)**

−15.

356

(2.9

35)*

*−7

.093

(3.2

13)*

*L

og19

60pe

rca

pita

inco

me

1.33

5(3

.868

)3.

378

(4.1

39)

1.88

8(3

.902

)1.

526

(4.8

02)

0.75

3(5

.314

)1.

696

(4.8

26)

Log

land

area

−9.8

68(2

.124

)**

−10.

537

(2.1

79)*

*−1

0.51

1(2

.542

)**

−11.

271

(2.5

96)*

*T

erm

sof

trad

esh

ocks

−45.

202

(205

.930

)48

.984

(221

.254

)37

3.60

0(2

91.6

22)

377.

467

(302

.285

)O

ildu

mm

y13

.999

(21.

898)

9.77

1(2

3.59

6)−1

3.19

9(2

8.13

2)−1

5.03

1(2

9.39

3)L

andl

ock

dum

my

−2.4

72(8

.889

)1.

807

(9.6

02)

−6.3

86(1

0.28

5)−5

.702

(10.

772)

Isla

nddu

mm

y3.

186

(7.7

66)

4.33

7(8

.351

)12

.643

(9.9

34)

11.2

76(1

0.38

5)C

onst

ant

161.

089

(33.

890)

**16

9.33

7(3

4.35

4)**

152.

610

(34.

432)

**25

3.34

3(4

7.30

9)**

196.

654

(49.

215)

**25

5.88

4(4

7.73

1)**

R2

0.51

0.51

Stan

dard

erro

rsin

pare

nthe

ses;

*:si

gnifi

cant

at10

%;

**:

sign

ifica

ntat

5%.

Not

es:

(a)

Nin

ety

two

obse

rvat

ions

inco

lum

ns(1

)to

(3),

77ob

serv

atio

nsin

colu

mns

(4)

to(6

).(b

)T

heR

2is

not

wel

l-de

fined

for

3SL

Sre

gres

sion

san

dis

not

repo

rted

.

356 SPOLAORE AND WACZIARGT

able

3.D

iagn

osti

cte

sts.

Dis

trib

utio

nof

the

test

stat

isti

cV

alue

ofth

ete

stst

atis

tic

p-V

alue

Fir

stst

age

F-t

ests

Col

.(1

)-3S

LS,

Ope

nnes

sF

(11,

73)

3.11

0.00

2C

ol.

(1)-

3SL

S,O

penn

ess*

log

popu

lati

onF

(11,

73)

3.09

0.00

2C

ol.

(2)-

3SL

S,O

penn

ess

F(1

1,78

)3.

550.

0005

Col

.(2

)-3S

LS,

Ope

nnes

s*lo

gpo

pula

tion

F(1

1,78

)3.

720.

0003

Col

.(4

)-3S

LS,

Ope

nnes

sF

(11,

58)

2.40

0.01

6C

ol.

(4)-

3SL

S,O

penn

ess*

log

popu

lati

onF

(11,

58)

2.77

0.00

6C

ol.

(5)-

3SL

S,O

penn

ess

F(1

1,63

)3.

150.

002

Col

.(5

)-3S

LS,

Ope

nnes

s*lo

gpo

pula

tion

F(1

1,63

)3.

470.

0008

SU

Rdi

agno

stic

sC

ol.

(3)-

SUR

,C

ross

-equ

atio

nρ

a−0

.077

Col

.(3

)-SU

R,

Bre

usch

-Pag

anst

atis

ticb

χ2 (

1)0.

553

0.45

7C

ol.

(6)-

SUR

,C

ross

-equ

atio

nρ

a−0

.067

Col

.(6

)-SU

R,

Bre

usch

-Pag

anst

atis

ticb

χ2 (

1)0.

345

0.55

7

Ove

ride

ntifi

cati

onte

sts

Col

.(1

)-3S

LS,

Hau

sman

test

cχ

2 (8)

0.71

00.

999

Col

.(2

)-3S

LS,

Hau

sman

test

cχ

2 (6)

1.05

00.

984

Col

.(4

)-3S

LS,

Hau

sman

test

cχ

2 (7)

1.52

00.

982

Col

.(5

)-3S

LS,

Hau

sman

test

cχ

2 (6)

13.3

200.

038

Sarg

anst

atis

tic,

sing

leeq

uati

onIV

,19

60–8

9da

tad

χ2 (

9)11

.236

0.26

0Sa

rgan

stat

isti

c,si

ngle

equa

tion

IV,

1960

–98

data

dχ

2 (9)

8.45

80.

489

aT

hecr

oss-

equa

tion

ρis

the

corr

elat

ion

ofth

eer

ror

term

sof

the

grow

than

dop

enne

sseq

uati

ons

usin

gth

eSU

Res

tim

ator

.b

The

Bre

usch

–Pag

anst

atis

tic

(dis

trib

utedχ

2 (1)

)is

used

tote

stth

enu

llof

inde

pend

ence

ofth

ere

sidu

als

acro

ssth

egr

owth

and

open

ness

regr

essi

ons.

cT

heH

ausm

ante

stis

base

don

com

pari

ngth

ees

tim

ates

from

aco

nsis

tent

esti

mat

orto

thos

eof

anes

tim

ator

whi

chis

cons

iste

ntan

def

ficie

ntun

der

the

null

hypo

thes

isof

valid

over

iden

tify

ing

rest

rict

ions

.The

mai

ntai

ned

inst

rum

ents

for

the

assu

med

cons

iste

ntes

tim

ator

are

the

smal

lcou

ntry

dum

my

and

its

inte

ract

ion

wit

hlo

gpo

pula

tion

,as

inA

lesi

na,

etal

.(2

000)

;H

ausm

ante

sts

obta

ined

from

diff

eren

tas

sum

ptio

nsle

dto

sim

ilar

resu

lts

and

are

avai

labl

eup

onre

ques

t.d

Sarg

ante

sts

ofov

erid

enti

fyin

gre

stri

ctio

nsin

the

grow

theq

uati

onar

esh

own

for

the

spec

ifica

tion

sof

colu

mns

(2)

and

(5),

but

usin

gsi

ngle

equa

tion

IVin

stea

dof

3SL

S(t

here

gres

sion

outp

ut,

not

show

n,is

avai

labl

eup

onre

ques

t).


jointly related to the variables they are instrumenting for, at high levels of statisti-cal significance, no matter which specification is considered.39

In the second panel of Table 3, we present diagnostic tests pertaining to theSUR estimates of the system parameters. Simple cross-equation error correlationsand Breusch–Pagan tests suggest that the residuals across equations are largelyindependent. This is encouraging as it suggests that the possible misspecification ofone equation does not “contaminate” estimates of the other.40 On the other hand,there may not be much of a gain from using single-equation estimators rather thansystem estimators. We choose to report system estimates, but the results are robustto using single equation methods instead.

Finally, we conducted tests of overidentifying restrictions for the 3SLS esti-mates. The first set of tests are Hausman specification tests.41 Since there areonly two endogenous variables appearing on the right-hand side of each equation,an exactly identified system would require two instruments. Following ASW, wechoose the small country dummy and its interaction with log population as the“maintained” instruments when computing Hausman tests. Comparing estimatesobtained from using only these two instruments to those of our baseline specifica-tion (Column 1 of Tables 1 and 2) yields a χ2(8)-distributed Hausman test statisticof 0.710, with a p-value of 0.99, so we fail to reject the null of valid overiden-tifying restrictions (other specifications yield similar results). Another test we car-ried out was the Sargan test, applied to single-equation IV estimates of the growthequation (these estimates were very close to those obtained with 3SLS). For thebaseline specification, the χ2(9)-distributed Sargan test statistic bears a value of11.24, with a p-value of 0.26, so we again fail to reject the null of valid overiden-tifying restrictions in the IV specification of the growth equation, increasing ourconfidence in the validity of the instruments.42

39 Note that the Staiger–Stock rule of thumb for weak instruments, which states that first stageF-statistics should be greater than 10, applies only to the case of one endogenous regressor. Wehave two endogenous regressors in our application. Further, Shea’s R2 statistics, available uponrequest, bore high magnitudes, alleviating concerns about weak instruments.

40 We are grateful to an anonymous referee for pointing this out. In fact, equation-by-equationOLS estimates were remarkably similar to SUR estimates, and equation-by-equation IV estimateswere very similar to 3SLS estimates (on the other hand, SUR estimates do differ in magnitudefrom 3SLS estimates, so accounting for the endogeneity of openness and the interaction termdoes matter). Single equation results are available upon request.

41 We do not perform Hausman tests to test for the presence of endogeneity, as is commonlydone. Rather, we use them as tests of the overidentifying restrictions. Under the null of validoveridentifying restrictions, the 3SLS estimates using all instruments are consistent and efficient.3SLS estimates using only a subset of “maintained” instruments are consistent but not efficientunder the null. This can serve as a basis for testing the validity of the overidentifying restric-tions using a Hausman test.

42 Tests of overidentification tend to have low power in the presence of other specification prob-lems. The Hausman test, for instance, relies on specifying at least two valid instruments, often avery strong assumption. While we should not overinterpret these tests, the results remain encour-aging. Moreover, similar tests appeared in ASW, who also concluded that the geographic deter-minants of openness were excludable from the growth regression, suggesting they were validinstruments. Related to this, Frankel and Romer (1999) showed that an instrumental variable


4.1.3. Robustness

Our baseline results hold up when using the updated PWT 6.0 dataset for theperiod 1960–1998, despite the loss of 15 data points (Tables 1 and 2, columns4–6). Due to this smaller sample, estimates are sometimes less statistically signifi-cant, but the pattern of signs and the magnitude of the coefficients are unchangedcompared to the 1960–1989 dataset. Therefore, we are confident that our estimatesof the border effects on growth would be qualitatively unchanged if we were to usecoefficients from the updated dataset. As explained above, we refrain from usingestimates obtained from the smaller dataset as this would result in a loss of 15countries, in particular Germany.

The second robustness issue that we examine relates to our measure of openness.In an important paper, Alcala and Ciccone (2004) have argued that commonlyused volume measures of trade openness, obtained by taking the ratio of importsplus exports in exchange rate US dollars to GDP in exchange rate US dollar, maybe inappropriate. The explanation is quite simple. Suppose that trade opennessraises productivity, but does so more in the tradable than in the nontradable sec-tor (a plausible assumption). This will lead to a rise in the relative price of non-tradables, and a fall in conventionally measured openness under the assumptionsthat the demand for nontradables is relatively inelastic, because it may raise thedenominator of the conventional measure of openness more than the numerator.So one may observe trade-induced productivity increases going hand in hand witha decline in conventional measures of openness. Alcala and Ciccone propose analternative measure, “real openness”, defined as the ratio of imports plus exportsin exchange rate US$ to GDP in PPP US$. This alternative measure will addressthe problem, since the denominator now corrects for international differences inthe price of nontradable goods.

Tables 4 and 5 (columns 1 and 2) present 3SLS estimates of our baseline modelusing Alcala and Ciccone’s “real openness” measure, still using version 5.6 of PWTfor the 1960–1989 period.43 In both specifications with and without controls, ourresults on growth are confirmed and strengthened. Column 2 of Table 4 reveals aneffect of openness on growth that has increased by 50% compared to the corre-sponding entry in Table 1. The magnitude and significance of the interaction termhas also increased, while the magnitude of the coefficient on the log of popula-tion has decreased somewhat. In Table 5, while the effect of country size on open-ness still has a negative sign, its statistical significance and magnitude have fallen.Again, these results based on an alternative measure of openness suggest our base-line coefficients are quite robust, and may even understate the effect of opennesson growth.

The last robustness check that we perform consists of testing our theory in apanel rather than a cross-sectional context. While the cross-sectional approach is

constructed from the geographic determinants of trade volumes were excludable from a regres-sion of income levels on trade volumes.

43 We thank Antonio Ciccone for providing us with the data.


Table 4. Growth equation—robustness checks (estimator: 3SLS).

Alcala-Ciccone openness measure 4 Decade panel (1960–2000)

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

Log population 1.174 (0.293)** 0.447 (0.205)** 0.761 (0.144)** 0.437 (0.144)**Open*log Pop −0.019 (0.009)** −0.012 (0.006)** −0.009 (0.002)** −0.005 (0.002)**Openness 0.233 (0.074)** 0.122 (0.050)** 0.096 (0.019)** 0.055 (0.019)**Log per capitaincome 1960 −0.489 (0.267)* −1.514 (0.269)** 0.167 (0.112) −1.056 (0.227)**Fertility rate −0.343 (0.128)** −0.408 (0.109)**Male human capital 1.619 (0.467)** 0.341 (0.249)Female human capital −1.229 (0.489)** −0.232 (0.294)Governmentconsumption ratio −0.060 (0.021)** −0.032 (0.012)**Investment rate 0.083 (0.027)** 0.094 (0.016)**# Countries (# periods) 88 (1) 88 (1) 99 (4) 79 (4)

Standard errors in parentheses; ∗: significant at 10%; ∗∗: significant at 5%.Notes: (a) The R2 is not well-defined for 3SLS regressions and is not reported.(b) The regression in column 4 includes period fixed effects (output omitted). Other regressions include anintercept term (output omitted).

Table 5. Openness equation–robustness checks (estimator: 3SLS).

Alcala–Ciccone openness measure 4 Decade panel (1960-2000)

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

Log population −7.692 (1.852)** −1.895 (2.293) −10.364 (1.218)** −8.541 (1.741)**Log per capitaincome 1960 11.608 (3.275)** 10.761 (3.288)** 8.570 (1.742)** 2.781 (2.038)Log land area −7.302 (1.854)** −5.611 (1.454)**Terms of trade shocks 17.399 (179.445) 38.631 (12.662)**Oil dummy 6.263 (19.024) 11.128 (9.927)Landlock dummy −0.138 (7.921) −3.869 (6.130)Island dummy −0.776 (6.830) 0.132 (5.622)# Countries (# periods) 88 (1) 88 (1) 99 (4) 79 (4)

Standard errors in parentheses; *: significant at 10%; **: significant at 5%.Notes: (a) The R2 is not well-defined for 3SLS regressions and is not reported.(b) The regression in column 4 includes period fixed effects (output omitted). Other regressions include anintercept term (output omitted).

preferable to capture the long term relationship between growth, openness andcountry size, and is now usual in the literature linking trade and productivity, apanel approach using decade averages may provide efficiency gains while still main-taining a relatively long horizon. We used the latest version of the PWT (version6.1) and construct a panel of four decades spanning 1960–2000.

We formulated a system of equations with two equations per period (one for thedetermination of growth and the other for trade openness), and constrained slopecoefficients to equality across periods. We then ran 3SLS on this eight equation


system.44 Results are displayed in Tables 4 and 5 (columns 3 and 4). Once again,our results are qualitatively unchanged. In the growth equation (column 4 ofTable 4), estimates on openness, log population and their interaction are very closeto those obtained in the corresponding entry of Table 1 (column 4), and similarlyfor the effect of country size on openness in Table 5.

4.2. The Effects of Hypothetical Mergers

4.2.1. Effects on Expected 1960–1989 Growth

The parameter estimates presented in Tables 1 and 2 can be used to calculate,for pairs of adjacent countries, what their growth rate would have been had theyformed a single country over the sample period under consideration.45 Namely, wecan now calculate the impact of specific borders on growth, under alternative defi-nitions of political integration. As described above, under a “size merger”, which isreflected in equation (37), a political merger simply entails full access to the neigh-bor’s markets, without any change in the home country’s Wat and Zat variables.Under “full integration”, reflected in equation (39), both hypothetically mergedcountries share the same initial incomes, W m

at and Zmat , and therefore the same

growth rate under political integration. Since there is no a priori reason to preferone definition over the other, we calculate the effect of borders under both defini-tions, and further decompose this effect into the direct positive effect of an increasein country size, the indirect negative effect via openness reduction, the ambiguouseffect via the interaction term, and the steady-state determination effect.

Table 6 shows summary statistics for these various effects based on 123 hypo-thetical pairwise mergers. A salient feature of these statistics is the wide disper-sion of the various effects. The pure size effect on growth, �G, has a standarddeviation of 0.377 and a positive mean of 0.123 percentage points of growthannually, suggesting that the average country would have benefitted from merg-ing with a neighbor based on increased size alone (interestingly, even a countryat the 25th percentile would benefit slightly). Indeed, the direct effect of size ongrowth, on average, more than outweighs the indirect effect via openness reduc-tion (while the interaction effect is on average very close to zero). Under a fullintegration scenario, however, a typical country would have lost slightly, on theorder of �Gm = −0.112 percentage points of annual growth. Since the differ-ence between �Gm and �G is equal to the steady-state determination effect, thelatter is on average negative (and equal to −0.235). Therefore, borders shield the

44 For further details on panel-3SLS estimators, see Wacziarg (2001).45 We also considered mergers between proximate islands and up to five neighboring countries,

such as the United Kingdom and Ireland, or the United Kingdom and France. Our results per-tain to a total of 123 hypothetical mergers of country pairs (i.e. 246 merger experiments).


Table 6. Summary statistics of the effects of border removals (based on Tables 1 and 2, column (1) estimates).

Variable Mean Std. dev. 25th pctile 50th pctile 75th pctile Min Max

Observed averagegrowth 2.127 1.671 1.059 2.252 3.013 −1.231 6.580Fitted growth 2.167 1.369 1.138 2.059 2.995 −0.006 6.150Direct effect of size 0.745 0.743 0.149 0.480 1.158 0.005 3.452Indirect effect viaopenness reduction −0.601 0.600 −0.934 −0.387 −0.120 −2.784 −0.004Effect via change ininteraction term −0.021 0.405 −0.025 0.028 0.102 −2.400 1.056Steady-statedetermination effect −0.235 0.678 −0.507 −0.077 0.066 −3.442 2.350�G (size merger) 0.123 0.377 0.028 0.088 0.250 −1.733 1.367�Gm (full integration) −0.112 0.914 −0.363 −0.004 0.187 −4.965 3.350Openness equivalent(size merger) 10.184 22.517 1.140 5.306 13.873 −40.281 184.332Openness equivalent(full integration) 0.403 43.089 −16.308 −0.344 12.085 −144.379 315.772�Ge (size mergerwith residual effect) 0.097 0.524 0.016 0.083 0.236 −4.214 1.511�Gme (full integrationwith residual effect) −0.092 1.047 −0.427 −0.024 0.249 −4.036 4.220�SSY (level effect,size merger), % 10.976 33.623 2.454 7.847 22.355 −154.651 121.956�SSY m (level effect,full integration), % −2.068 83.400 −19.665 2.131 22.824 −421.068 325.630

Notes: (a) Summary statistics based on 246 effects calculated from 123 hypothetical political mergers.(b) �G (size merger) is the sum of the direct effect of size, the indirect effect via openness reduction, andthe effect via the change in the interaction term.(c) �Gm (full integration) is the sum of �G (size merger) and the steady-state determination effect.(d) The openness equivalent is the percentage point increase in the trade to GDP ratio needed to achievea change in growth equivalent to merging with a neighbor (equation 37 in text).(e) �Ge is �G plus the residual effect, as explained in Section 3.3 and Appendix 3.(f) �Gme is �Gm plus the residual effect, as explained in Section 3.3 and Appendix 3.(g)�SSY and�SSY m are the steady-state level effects of a “size merger” and “full integration”, respectively.

average country from slow growing neighbors. However, the median effect, equalto −0.077, is closer to zero.46

46 This is not surprising. Since the steady-state determination effect is obtained largely from pop-ulation weighted average of steady-state determinants, when two countries consider merging thepoorer one will stand to gain from better steady-state determinants, while the richer one willstand to lose. Thus, we should see roughly half the sample of 246 effects display positive effects,and the other half negative ones (this is only roughly true because under integration some vari-ables, such as the landlocked country dummy and land area, are not simply averages of theunderlying variables for the two merging countries). While the median effect is expected to beclose to zero, the average effect is negative: the countries with positive effects display effectssmaller in absolute value than those that suffer negative effects. This could reflect the fact thatthe former set of countries (the ones with worse steady-state determinants) is composed of

362 SPOLAORE AND WACZIARGF

ract

ion

-2 -1.5 -1 -.5 0 .5 1 1.5

0

.2

.4

Figure 1. Total effect of size merger on growth.

There is a wide dispersion of these effects around their mean. This suggests thatthese simple summary statistics mask relevant country-specific features of the bor-der effect on growth. The percentiles presented in Table 6 more information onthe distribution of the effects, and Figures 1 to 8 provide an even more com-plete picture. They plot the distributions of the estimated effects. The total sizeeffect �G is generally positive but moderate, in most cases smaller than 0.5 per-centage points of annual growth. The effect of full political integration �Gm ismore symmetrically distributed around zero, with slightly fatter tails. Turning tothe decomposed effects confirms previous observations, namely that the interactionterm effect is tightly distributed around zero, while the steady-state determinationeffect is slightly skewed, with a negative mean.

4.2.2. An Example: France and Italy

While these summary statistics and plotted distributions are useful, they are nosubstitute for the estimates obtained individually for each pair of adjacent coun-tries. A close examination of these specific estimates reveals that their magnitudesare very sensible and that their signs are as expected. Small countries merging

relatively large countries in population terms, for which merging with a small neighbor doesnot represent a large change in steady-state determinants.

BORDERS AND GROWTH 363F

ract

ion

-5 -4 -3 -2 -1 0 1 2 3 4 5

0

.1

.2

.3

.4

Figure 2. Total effect of full integration on growth.

Fra

ctio

n

0 .5 1 1.5 2 2.5 3 3.5

0

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.3

Figure 3. Direct size effect.

with large markets and poor countries merging with neighbors that exhibit supe-rior steady-state determinants tend to gain. Large countries like the US tend to beindifferent to merging with small neighbors like Canada. The magnitudes of thegains and losses are commensurate with relative sizes and relative incomes.


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ion

-3 -2.5 -2 -1.5 -1 -.5 0

0

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.3

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Fra

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0

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Fra

ctio

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(Truncated at 200% of trade to GDP for readability)

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0

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Figure 7. Openness equivalent—size merger.


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(Truncated at 200% of trade to GDP for readability)

-100 -50 0 50 100 150 200

0

.1

.2

.3

Figure 8. Openness equivalent—full integration.

To illustrate the results, we can examine more specifically the example of Franceand Italy (Table 7). The effect on France from merging with Italy would have beenquite large and positive. We estimate that the total size effect would have resultedin a gain of 0.281 points of growth annually for France. To achieve a similarincrease in growth via openness, France would have had to increase her trade toGDP ratio by 27.79 percentage points (for comparison, the average trade to GDPratio of France over the sample period was 36%). Since Italy started with a lowerlevel of per capita income than France in 1960, but has a higher estimated steady-state income level given its observed steady-state determinants, France would alsohave gained from the steady-state determination effect. This effect alone wouldhave accounted for �Gm −�G =0.492 additional points of growth.47

Turning to the effect on Italy from merging with France, it follows from whatprecedes that the steady-state determination effect would have been negative forItaly. Moreover, the positive size effect of a merger on Italian growth, equal to0.237, would not have been sufficient to outweigh the negative steady-state deter-mination effect. Under full integration, Italy would have lost −0.316 points ofgrowth annually. A possible interpretation of these results is that, if France and

47 This is another way of saying that Italy was a faster growing country than France over thetime period covered in the sample. In fact, the average observed annual growth rate of per capitaincome in Italy over the 1960–1989 period was 3.40%, while for France it was 2.94%. Our modelpredicts that, if France and Italy had merged, their unified growth rate over this period wouldhave been 3.15% per year (under “full integration”).


Table 7. An example: France and Italy (based on Tables 1 and 2, column (1) estimates).

Effect on (country a): France Italy

of merging with (country b): Italy France

Observed growth (country a) 2.936 3.404Fitted growth (country a) 2.374 3.464Direct effect of size 0.491 0.451Indirect effect via openness −0.396 −0.364Effect via change in interaction term 0.186 0.149Steady-state determination effect 0.492 −0.553�G (“size merger”) 0.281 0.237�Gm (“full integration”) 0.773 −0.316Openness equivalent (“size merger”) 27.789 24.300Openness equivalent (“full integration”) 76.423 −32.492�Ge (“size merger” with residual effect) 0.294 0.265�Gme (“full integration” with residual effect) 0.474 0.006�SSY (steady-state level effect of a “size merger”) (%) 25.099 21.122�SSY m (steady-state level effect of “full integration”) (%) 57.011 −15.894

Notes: (a) �G (size merger) is the sum of the direct effect of size, the indirect effect via openness reduction,and the effect via the change in the interaction term(b) �Gm (full integration) is the sum of �G (size merger) and the steady-state determination effect.(c) The openness equivalent is the percentage point increase in the trade to GDP ratio needed to achieve achange in growth equivalent to merging with a neighbor (equation 37 in text).(d) �Ge is �G plus the residual effect, as explained in Section 3.3 and Appendix 3.(e) �Gme is �Gm plus the residual effect, as explained in Section 3.3 and Appendix 3.(f)�SSY and�SSYm are the steady-state level effects of a “size merger” and “full integration”, respectively.

Italy could somehow have achieved the more restrictive form of political integra-tion implied by the “size merger” definition, i.e. a removal of the border withoutchanges in national savings rates, human capital, etc., both could have benefited interms of growth.

Interested readers can ponder upon the estimated effects of their favorite hypo-thetical political merger among the 246 examples listed in Table 8.

4.2.3. Residual Effects

Section 3.3 above outlined a methodology to include the residuals from the growthand openness regressions into our analysis. Table 8 (columns 9 and 10) presentsestimates of �Gme and �Ge as in equations A.9 and A.10. The distribution ofthese effects is also displayed in Figures 9 and 10. Interestingly, the results donot change as much as expected given that the explained portions of growth andopenness in the baseline regressions are only 60 and 50%, respectively. The sim-ple correlation of �G with and without the residual effect is 0.737, while the


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Fra

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Figure 10. Effect of full integration on growth—with residual.

corresponding figure for �Gm is 0.640. Out of 246 mergers, accounting for theresidual leads to a change in the sign of the effect in 31 cases for �G (12.6% ofthe cases) and 75 cases for �Gm (30.1%).48

48 In general, accounting for the residual effect has a much smaller effect on estimates of puresize mergers than it does on estimates of full integration, because the former only involves the


ract

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-150 -100 -50 0 50 100 150

0

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Figure 11. Effect of size merger on steady-state income (%).

Again, the case of France and Italy is illustrative (Table 7). Since France’sexplained annual growth falls short of its observed growth by 0.56 points, whileItaly’s observed and explained growth are about equal, accounting for the resid-ual in the merger experiment is now slightly beneficial to Italy—which would havegained both under a size merger and full integration.

4.2.4. Effects on Steady-State Income Levels

Columns 11 and 12 of Table 8 presents, for each country pair, the estimated effectof a merger on the steady-state income level of country a, while the last row ofTable 6 presents summary statistics for the steady-state level effects (the distri-bution of these level effects is displayed in Figures 11 and 12 for a size mergerand full integration, respectively). On average, size mergers would raise a country’ssteady-state income level by 10.98 percentage points and full integration wouldreduce it by 2.07 percentage points. These averages reflect the generally positiveeffect of a size merger and the ambiguous effect of full integration. However,they again mask considerable case-specific differences. The effect of full integra-tion ranges from −421.07 percentage points (the effect on Malta from mergingwith Algeria—a small rich country merging with a relatively large poor country)to 325.63 percentage points (the effect on Papua New Guinea from merging with

residual from the openness regression (multiplied by the coefficient on openness in the growthregression), while the latter involves the population weighted average of the residual from thegrowth regression. See equations (A.9) and (A.10).


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ion

-400 -300 -200 -100 0 100 200 300

0

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Figure 12. Effect of full integration on steady-state income (%).

Australia—a small poor country merging with a rich country with five times itspopulation). Logically, large effects such as these are found in cases where neigh-bors have very different sizes and income determinants.

More moderate effects are found in regions that are homogeneous in terms ofincome and size. For example, Table 7 shows that a size merger between Franceand Italy would have raised both countries’ steady-state income levels by 25.1 per-centage points for France and 21.12 points for Italy. Full integration would havereduced Italy’s steady-state income by 15.89 percentage points. This partly reflectscompounding the negative growth effect on Italy of full integration with France,as discussed earlier. The merger would raise France’s steady-state income by 57.01points, reflecting Italy’s superior steady-state determinants.

4.3. Convergent Interests in Political Integration

An interesting application of our framework is to examine pairs of countries inwhich both would have benefited from merging politically. As suggested above, it ismuch easier for two countries to have convergent interests in a size merger thanin full integration, because the effect of the former is far more likely to be posi-tive for any given country. Out of the 123 political mergers we considered in thispaper, 94 entail growth gains for both country a and country b based on a sizemerger alone, and only six cases did the trade reduction effect dominate in bothcountries—so that both would have experienced reduced growth under a merger.These cases pertain to pairs of very small and already open countries, such as Sin-gapore and Hong Kong or Jamaica and Haiti. Taken at face value, these resultssuggest that it would be mutually beneficial for most country pairs to grant each


Table 9. Pairs of countries that would both have gained from full political integration (�Gm >0 for bothcountries).

Argentina ChileBolivia BrazilBrazil ColombiaBrazil GuyanaBrazil ParaguayBrazil PeruCanada U.S.AColombia PeruDenmark Federal Republic of GermanyFrance Federal Republic of GermanyIndia PakistanIndia Sri LankaIndonesia MalaysiaMali Niger

other access to their markets, though the reduction of formal and informal barriersto trade in goods.

An interesting question that arises from these results is whether the extent of theborder effects can be used to predict the emergence of regional trading arrange-ments (RTAs). The literature on RTAs has so far focused on their effects on tradevolumes, not growth (Viner, 1950; Vousden, 1990). In principle, one could lookat the extent of the growth effects of “size mergers” and predict that pairs withlarge mutual gains will enter into RTAs. However, the potential effects on eco-nomic growth of granting reciprocal market access are not the only reason coun-tries enter into RTAs: there are a myriad political factors, lying beyond the scopeof this paper, affecting their emergence. Moreover, one limitation of our approachis that we only consider mergers between two countries, whereas proposed RTAsoften involve more than two countries (our methodology could be easily extendedto consider the growth impact of such arrangements). For these reasons, we wouldurge caution in using our results to predict the emergence of trade blocks, thoughthis is a promising avenue for future research.

In contrast to size mergers, in only 14 cases would both countries in a mergingpair have benefited (in terms of economic growth) from full integration.49 Thesepairs are listed in Table 9. Salient examples include Argentina and Chile, Franceand Germany, Canada and the US, India and Pakistan, as well as several countrypairs involving Brazil. Of course, many more cases would entail a winner and aloser among the merging pair. Ninety two cases out of 123 entail exactly one coun-try that would have gained from full political integration, while the other wouldhave lost, and in the remaining 17 cases both countries would have lost. The con-clusion is that, in 109 of the 123 cases we considered, borders shield at least onecountry from the other’s slower growth.

49 All of these pairs are also composed of countries that would both have benefited from sizemergers with each other.


An implication of these observations is that, when unions of country pairs areconsidered, it may be easier to gain mutual support for a form of political inte-gration that shields countries from having to share their Zat and Wat variables butfocuses instead on taking advantage of scale effects, through the formation of freetrade areas and the reduction of physical trading costs.

5. Conclusion

This paper provides a theoretical framework to understand the relationshipbetween political borders and growth. We suggested that, whenever scale effectsare present, political borders affect steady-state per capita income levels and tran-sitional growth rates by reducing the extent of the market. We also pointed outthat, in a world of more than two countries, the removal of only one border willresult in trade reduction from the merging countries vis-a-vis the rest of the world,with correspondingly adverse effects on growth and income. We examined formalconditions under which the extent of the market effect dominates the trade reduc-tion effect, and discussed situations in which countries might differ in more thatjust size and openness levels.

We then derived an empirical specification directly from the theoretical model,and found strong empirical support for the predictions of our theory. Baselineparameter estimates from this empirical model were used to estimate, for specificcountries, the growth effects of merging with another country. We have applied thisframework to 123 pairs of adjacent countries and proximate islands. We found thatfull political integration with a neighbor would have a slight negative impact onthe average country. This type of political integration, which entails full averag-ing of steady-state determinants across merging pairs, generally involves a winnerand a loser—in only 14 of 123 cases would a merger have raised both country’sgrowth rate. In contrast, countries would in general benefit from expanding theextent of their markets through deep economic integration with their neighbors,as shown by the prevalence of positive estimated effects under “size mergers”. Alimited form of integration that entails access to markets and a reduction of tradecosts, to take advantage of scale effects, seems more likely to benefit both countriesin a pair than a form of integration that results in uniform growth determinantsacross country pairs.

Our framework can be extended in several directions. First, we have limited ourinvestigation to hypothetical mergers involving only two countries. However, ourframework is readily applicable to studying the growth effects of more than onepolitical border. We could apply our methodology, for example, to the removal ofall borders within Europe, in order to study the growth implications of propos-als for European political integration. Our results for France and Germany sug-gest that both would have benefited, in terms of growth, from merging politically.Whether European countries would have benefited from the removal of all intra-European borders is an open and equally interesting question.


Second, our estimation method focuses exclusively on growth and income lev-els. There are obviously many other reasons, beyond growth, why countries wouldwant to merge or stay separate. We can interpret our estimates of the growtheffects of borders, whenever they are negative, as the amount of growth a countryis willing to forego in order to avoid the noneconomic costs of sharing a sin-gle polity with a neighbor. These may include increases in cultural, ethnic, reli-gious or linguistic heterogeneity. Future work could relate changes in heterogeneityresulting from political integration to the magnitude of the growth costs or bene-fits. One interesting hypothesis to test is whether countries that remained separatedespite potential growth effects of merging, have done so because political integra-tion would have entailed large increases in heterogeneity.

Appendix 1

Derivation of Equation (5)

At each time t , the resource constraint for each input i ∈ [0,W ] produced in aregion i belonging to a specific country a of size Sa is:

Sa xia(t)+∑n �=a

Sn fin(t)= Ki (t). (A.1)

Equations (4) and (A.1) imply that each region in country a will use the sameamount of domestically produced input i :

xia(t)= Ki (t)

Sa +∑n �=a Sn(1− ξa − ξn)

α1−α

. (A.2)

On the other hand, each region of a country b �= a will purchase the followingamount of input i produced in country a:

fib(t)= (1− ξa − ξb)α

1−α Ki (t)


α1−α

(A.3)

By substituting (A.2) into (4) we obtain equation (5).

Derivation of Equation (8)

Equation (8) is obtained from equation (3) by substituting domestically producedand imported intermediate inputs with their equilibrium values, as specified inequations (A.2) and (A.3), and the levels of capital with their steady-state val-ues, using the fact that all regions belonging to the same country n have the same


steady-state level of capital K ssn , given by equation (7), that is:

K ssn =

(α

ρ

) 11−α

⎡⎣Sn +

∑n �=m

Sm(1− ξa − ξn)α

1−α

⎤⎦ . (A.4)

Therefore, we have:

yssi =

∫ W

0(xss

ji )αd j = Sa(x

ssa )

α +∑

n �=aSn(1− ξa − ξn)

α( f ssn )

α. (A.5)

In steady state domestically produced inputs are given by

xssa = K ss

a


α1−α

=(α

ρ

) 11−α

(A.6)

while imported inputs are given by

f ssn = (1− ξa − ξn)

α1−α K ss

n

Sn +∑m �=n Sn(1− ξn − ξm)

α1−α

=(α

ρ

) 11−α

(1− ξa − ξn)α

1−α . (A.7)

Hence we have:

yssi = Sa

(α

ρ

) α1−α +

∑n �=a


(α

ρ

) α1−α [(1− ξa − ξn)

α1−α ]α

=(α

ρ

) α1−α [

Sa +∑

n �=aSn(1− ξa − ξn)

α1−α

]. (A.8)

Appendix 2

The reduced form parameters in equation (36) are:

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

γ0 =β0 +β2α0γ1 =β1

γ2 =β3 +β2α1 +β4α0γ3 =β4α1γ4 =β4α2γ5 =β4γ6 =β2α2γ7 =β5

µi t = εi +β2νi t


Appendix 3

A. Alternative treatment of the error term

Instead of computing the expected effect of a size merger on growth ignoring theerror term (equation 37), we can compute:

�Geabt ≡� log

yat

yat−τ

= log(

Smt

Sat


4Wat +γ5νat]

(A.9)

and replace γ2, γ3, γ4 and νat with their regression estimates in computing theempirical �Ge

abt . In equation (A.9), the superscript “e” indicates that the residualterms are taken into account. Note that since the error term of the growth regres-sion, µat , is assumed to be unchanged between the merged and unmerged states,it gets differenced away from equation (A.9). 50

Things are more interesting when we turn to “full integration”. We can nowtreat the error terms as additional (unobserved) growth determinants, and computethe empirical �Gme

abt directly using the appropriate population weighted averages ofthe estimated residuals:

�Gmeabt ≡� log

yat

yat−τ

= log(

Smt

Sat


4Wat +γ5νat]

+γ1 logymt−τyat−τ

+ [γ ′

6 +γ ′4 log Smt

][Wmt − Wat ]

+γ ′7 [Zmt − Zat ]+ (νmt −νat ) [γ5 log Smt ]+µmt −µat , (A.10)

where νmt and µmt are the population weighted averages of νat and νbt and µat

and µbt . Again, this equation involves the same terms as equation (A.9), with thesteady-state determination effect (including that which results from merging theestimated unexplained portion of growth) added on.

B. The effect of mergers on steady-state income levels

Theory delivers a growth equation of the following form, based on equation (9):

logyat

yat−τ=λ (

log yssa − log yat−τ

)+ εat , (A.11)

50 The only reason νat remains in this equation is the nonlinearity of the effect of country size ongrowth brought forth by the interaction term between openness and size in the growth equation.


where yat is current income per capita, yat−τ is initial income per capita, and yssa is

(unobserved) income in steady-state.51 Assume that the steady-state level of incometakes the form:

log yssa = δ1 + δ2 Oat + δ3 log Sat + δ4 Oat log Sat + δ′5 Zat . (A.12)

This specification choice for log yssa reflects the fact that the right-hand side vari-

ables of empirical growth regressions (except initial income) are to be interpretedas the determinants of the steady-state level of income in the neoclassical growthmodel. On the other hand, our actual growth specification is that of equation (34):

logyat

yat−τ=β0 +β1 log yat−τ +β2 Oat +β3 log Sat

+β4 Oat log Sat +β ′5 Zat + εat . (A.13)

Substituting equation (A.12) into equation (A.11), we can write:

logyat

yat−τ=λδ1 +λδ2 Oat +λδ3 log Sat

+λδ4 Oat log Sat +λδ′5 Zat −λ log yat−τ + εat . (A.14)

Thus, we can recover:52

log yssa =−β0

β1− β2

β1Oat − β3

β1log Sat − β4

β1Oat log Sat − 1

β1β ′

5 Zat . (A.15)

This provides a methodology for backing out the effects of political mergers onsteady-state income levels. The percentage change in the steady-state income levelof country a after merging with country b can be computed in terms of thereduced form parameters defined in Appendix 2, under the two scenarios underconsideration—a pure size merger or full political integration:

�Y SSabt ≡ E(� log yss

a |Sat , Smt ,Wat)

=− 1γ1

logSmt

Sat

[γ2 +γ3 log (Sat Smt )+γ ′

4Wat]

(A.16)

and:

�Y SSmabt ≡ E

(� log yss

a |Sat , Smt ,Wat ,Wmt , Zat , Zmt)

=− 1γ1

[logSmt

Sat

(γ2 +γ3 log (Sat Smt )+γ ′

4Wat)

+ (γ ′

4 log Smt +γ ′6

)(Wmt − Wat )+γ ′

7 (Zmt − Zat )]. (A.17)

Equations (A.16) and (A.17) are the analogs to equations (37) and (39), respec-tively, applied to income levels rather than growth. Note that equation (A.16)

51 See Barro and Sala-i-Martin (1995), p. 37 and p. 82 for a derivation of this standard specifica-tion in the context of the neoclassical growth model.

52 Note that β1, the conditional convergence coefficient, is negative.


implies that �Y SSabt is simply −1/γ1 times �Gabt —hence, since γ1 = β1 is neg-ative, the effect of a size merger on steady-state income will have the same signas its effect on economic growth. However, the signs of �Y SSm

abt and �Gmabt may

differ. This is because we have:

�Gmabt =γ1

(log

ymt−τyat−τ

−�Y SSmabt

)(A.18)

A country a that has a positive steady-state level effect �Y SSmabt of full integra-

tion may display a negative growth effect �Gmabt simply because it has a sufficiently

low initial level of income relative to country b (and hence enjoys relatively fastgrowth holding the steady-state level of income constant). This is because initialincome is one of the growth determinants used to calculate the effect of borders ongrowth under “full integration”: an initially poor country on its own would growfast due to the forces of convergence (holding steady-state determinants constant)but under the merged state might find itself with a higher initial income level (sincethe initial incomes of merging countries get averaged under this scenario), resultingin lower transitional growth.

Acknowledgments

We thank David Baron, Antonio Ciccone, Oded Galor, Herschel Grossman, Thor-valdur Gylfason, Peter Howitt, Larry Jones, Pravin Krishna, Jeffrey Sachs, DavidWeil, Asaf Zussman, an anonymous associate editor and an anonymous referee,as well as seminar participants at UC Berkeley, Brown, Claremont McKenna,Cornell, Duke, Ente Einaudi, the Hoover Institution, UC Irvine, UC San Diego,Stockholm University, the Stockholm School of Economics, Stanford, Tufts, VeniceInternational University, and a CEPR conference at the University of Modena foruseful comments. Any remaining errors are ours. Jessica Seddon Wallack providedexcellent research assistance.

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