TRADE AND THE SPATIAL DISTRIBUTION OF
TRANSPORT INFRASTRUCTURE∗
Gabriel J. Felbermayr†and Alexander Tarasov‡This version: May 2016

Abstract
The distribution of transport infrastructure across space is the outcome of deliberate government planning that reflects a desire to unlock the welfare gains from regional economic
integration. Yet, despite being one of the oldest government activities, the economic forces
shaping the endogenous emergence of infrastructure have not been rigorously studied. This
paper provides a stylized analytical framework of open economies in which planners decidenon-cooperatively on transport infrastructure investments across continuous space. Allowing for intra- and inter national trade, the resulting equilibrium investment schedule features
underinvestment that turns out particularly severe in border regions and that is amplified
by the presence of discrete border costs. In European data, the mechanism explains abouta fifth of the border effect identified in a conventionally specified gravity regression. The
framework sheds light on the welfare costs of second best investment schedules, on the effects of intercontinental trade or of privatized infrastructure provision.
JEL Codes: F11, R42, R13
Keywords: International Trade, Infrastructure Investment, Economic Geography, Border Effect.
∗

We thank Kristian Behrens, Holger Breinlich, Lorenzo Caliendo, Kerem Cosar, Dalia Marin, Philippe Martin,
Pierre Picard, Diego Puga, Esteban Rossi-Hansberg, Philip Ushchev, seminar participants at the universities of
Zurich, St. Gallen, Konstanz, Tübingen, Giessen, TU Darmstadt, Linz, Rotterdam, Luxembourg, Ifo Munich,
Paris School of Economics, Nottingham, Hohenheim, Milano, and the European University Institute, at theConference of the Society of Economic Dynamics (SED) in Warshaw, the Congress of the European Economic
Association (Geneva), the European Trade Study Group (Munich), the 17th Conference of the SFB/TR (Munich),
the Congress of the German Economic Association (Hamburg), and the workshop “Imperfect Competition andSpatial Economics: Theoretical and Empirical Aspects” (Saint-Petersburg) for valuable comments and discussions.
Alexander Tarasov is grateful to the Deutsche Forschungsgemeinschaft through SFB/TR 15 for financial support.
†
Address: Ifo Institute for Economic Research at the University of Munich, Poschingerstraße 5, 81679 München,
Germany. Tel.: +49(0)89/9224-1428. Email: felbermayr@ifo.de.
‡
National Research University Higher School of Economics, Faculty of Economics, Shabolovka 26, 119049,
Moscow, Russia. E-mail: atarasov@hse.ru.

1Introduction

The provision of transport infrastructure is one of the oldest and most basic government activities. The roads built by the Inca in South America or by the Romans in Europe bear testimony
to this fact. Indeed, any known civilization has devoted resources to the construction of roads;
presumably with the objective to unlock the welfare gains from regional integration.1 On average, OECD countries spend about 1% of GDP on inland transportation infrastructure andmaintenance. This amounts to about 3% of countries’ public budgets. Emerging or transition
economies spend up to 10% of their budgets on transport infrastructure.2
A large mostly empirical literature demonstrates the important role of infrastructure on
trade costs, trade flows, and welfare. It makes massive efforts to address the suspected endogeneity of infrastructure but does not model the processes that determine these costs. So, in
their authoritative handbook chapter, Redding and Turner (2014) ask for “further research ...
examining the political economy of transport infrastructure investments”. The present paper isa first step towards endogenizing the spatial distribution of transport infrastructure.3
In this paper we focus on land-borne transportation, by far the most important mode for
intracontinental trade in the EU or in North America. Much transport infrastructure spending isdecided in a decentralized manner, in particular in the EU, where only about 1% of total spending
is at the Union level and central planning is limited to a small number of projects. For this reason,
we assume that welfare-maximizing national governments allocate infrastructure spending overspace in a non-cooperative fashion. However, while political space is fragmented, consumers
demand goods from all locations in our continuous, linear, two-country economy. National
governments do not internalize the benefits from reductions in domestic transportation costs that
accrue to foreign consumers. Clearly, in such a setup, there is inefficiently low global investment
in infrastructure. More interestingly, however, underinvestment has a spatial structure: it isparticularly severe in border regions, where the positive externality of domestic investment on
foreign welfare is largest.
As a consequence, trade across national borders entails higher transportation costs than trade
within countries, holding bilateral distances and market sizes constant. This effect materializes
even in the absence of discrete border costs caused by tariffs or non-tariff measures. However,1

A fascinating account of the history of road construction and operation is provided by Lay (1992).
ITF-OECD (2012), p. 4. These investment costs pale in comparison to total social road transport costs(including time costs and externalities), which have been estimated to amount to 20-25% of GDP (Persson andSong, 2010).
3
We formalize the non-cooperative behavior of welfare-maximizing national governments in continuous space.
However, we argue that our main results generalize to the median voter model.
22the effect is magnified by the existence of such costs. The endogenous emergence of broad borderzones may contribute towards explaining the empirical fact that international borders tend to
restrict international trade much more severely than what observable border costs together withplausible trade elasticities would suggest (Anderson and van Wincoop, 2003).
We employ data on intra-EU trade flows and transportation costs to discipline a calibrationof our stylized model. We use the theory to simulate a data set of bilateral intranational
and international trade flows, and apply a conventional gravity model. The obtained bordereffect significantly overestimates the true border costs; about half of the bias is due to omitting
infrastructure; the second half is a statistical artefact that arises from the high correlation
between distance and border. Hence, it appears that endogenous infrastructure investment can
explain part of the border effect.
To advance our theoretical understanding of the mechanisms shaping transport infrastructure provision we start by proposing a useful mapping between the spatial distribution of infrastructure spending within an interval into transportation costs between the two endpointsof this interval. This mapping is consistent with the concave relationship between geographicaldistance and transport costs documented in the data. The link between infrastructure investment over space and transportation costs is shaped by the elasticity of substitution between
investment at different locations. We embed this structure into a simple model of intra- and international trade, where each location produces a unique differentiated product which is subject
to transportation costs.
We find that the optimal infrastructure investment at some point in space is not only determined by local conditions at that point, but also – and predominantly – by the situation in otherlocations that produce and demand goods which transit through that point. The enlargementof a country – e.g., the reunification of Germany – leads to a reallocation of investment awayfrom formerly central regions towards the former border. A higher degree of substitutability between investments at different addresses has an ambiguous effect on investment while a higher
elasticity of substitution between goods produced at different location reduces investment.
Using actual data on EU trade flows, we provide econometric support for the role of transport
infrastructure in shaping the border effect. Employing road distance or, even better, travel time,
as proxies for transportation costs instead of great-circle distance, the estimated trade-inhibiting
effect of the border falls by about a quarter. We provide various sensitivity checks to make surethat our empirical result is not driven by reverse causation.
We extend our analysis by adding a non-contiguous country which supplies and demands
goods to and from our two-country continent. We find that an increase in the economic mass3

of this overseas trading partner induces a reallocation of spending towards coastal regions andaway from the hinterland, strengthening the border effect.
Our main result is robust to a number of model variations. First, we discuss how privately
operated toll roads would change our results. Second, we study a special case where governments
outsource the design and operation of roads to domestic private monopolists but regulate thefee system. These firms care only about profits and not about welfare. However, the central
issue leading to inefficient investment variation persists: the monopolists underinvest more inlocations close to the border where the positive externality on foreign infrastructure operatorsis largest. Third, we argue that allowing for labor mobility does not undo underinvestment at
the border relative to first best. However, whether the non-cooperative equilibrium features abimodal investment pattern depends on the size of discrete border costs. Fourth, we demonstratethat our central planner results are similar to the outcome expected from a median voter model.
Our paper is related to at least four important strands of literature. First, it connectswith papers that study the importance of geographical frictions and transportation costs for
trade and welfare. Typically, the literature has treated those costs as exogenous. Limao and
Venables (2001) find that up to 60 percent of the cross-country variation in transport costs
is due to transport infrastructure and that high cost of land-borne transportation is a more
relevant trade barrier than the costs of maritime transportation. Venables (2005) argues that
infrastructure explains a larger share of spatial income inequality than sheer geography. Many
existing papers assume that countries (or regions) do not have a geographical extension. Recent
work provides more spatial detail, but continues to treat infrastructure as exogenous. Cosar and
Demir (2014) show that the upgrading of motorways in Turkey significantly increases exports oftransport-intensive goods of landlocked cities. Allen and Arkolakis (2014) incorporate realistic
topographical features into a spatial model of trade. They find that the introduction of the US
interstate highway system has reduced the costs of a coast-to-coast shipment by about a third.
Duranton et al. (2014) use data on US interstate highways to show that highways within cities
cause them to specialize in sectors that have high weight to value ratios. Using a multi-region
general equilibrium model of trade, Donaldson (2014) and Donaldson and Hornbeck (2015)
analyze the welfare gains from railroads in India and the United States, respectively. They findthat improved market access through reduced transport costs creates trade and generates welfare
gains, but that it also leads to trade diversion. Behar and Venables (2011) and Redding andTurner (2014) provide excellent surveys. While they cite empirical work on the determinants oftransportation costs, they do not provide theoretical references on their endogenous emergence.
Second, our paper is related to a small literature that endogenizes transportation costs,
4

usually by introducing a proper transportation sector. Using an economic geography model,
Behrens and Picard (2011) show that the prices for transporting differentiated goods increase in
the degree of spatial specialization of the economy and that this channel dampens core-periphery
patterns. While their model has a competitive transport sector, Hummels et al. (2009) provide
evidence that monopolistic market structure in the transport sector restricts trade. These papers
do not analyze the endogenous emergence of road infrastructure.
Third, our paper is related to literature that jointly considers international and intranational
aspects of trade. Courant and Deardorff (1992) emphasize the importance of trade withincountries for trade patterns across countries. Rossi-Hansberg (2005) studies the effects of smallborder costs on the regional distribution of workers within a country and assesses the implicationsof the equilibrium population distribution on intra- versus international trade flows. However,
his focus is not on infrastructure investment.
Fourth, our paper relates to work on the border puzzle. Transport costs are usually related
to geographical distance while the border effect is attributed to some lumpy cost that materializes when crossing a border. Anderson and van Wincoop (2003) estimate that the US-Canadianborder reduces international trade relative to intranational trade by a factor of 4.7.4 Explanations for fixed border costs abound. Among other things, they are related to informational costs(Casella and Rauch, 2003), networks (Combes et al., 2005), or exchange rates (Rose and van
Wincoop, 2001). Border effects exist also within countries, where the above explanations do not
help.5 Our setup shows that border effects can arise even in the absence of explicit costs at theborder.
The structure of the paper is as follows. Section 2 presents some stylized facts on thetransportation sector that inform our modeling choices. Section 3 explains our formulation of
the mapping between the spatial distribution of infrastructure investment and transport costs.
Section 4 sets up the general equilibrium environment which motivates intra- and international
trade and analyzes the optimal infrastructure investment schedule in a closed economy. Section
5 moves to a setting of two symmetric open economies and derives our core results on the
4

Prior to Anderson and van Wincoop (2003), McCallum (1995) compares trade flows within Canada to flows
between Canadian provinces and U.S. states, controlling for distance and regional GDPs. Everything else equal,crossing the border reduces trade by a factor as high as 22. For Europe, Nitsch (2000) finds that on average
intranational trade is about 10 times higher than international one. Nitsch arrives at his results after controllingfor cultural proximity (language), along other conventional gravity covariates. Wei (1996) constructs measures forimports of countries to themselves and compares this with imports from a statistically identical foreign country.
He finds that the former magnitude is 2.5 times larger than the latter. Helliwell (1998) offers a comprehensive
overview of the pre Anderson and van Wincoop state of the econometric literature.
5
Okubo (2004) shows a border effect for trade between Japanese regions, Wolf (2000) for the US, and Combes
et al. (2005) for their sample of French departments.

5

endogenous emergence of border regions. Section 6 provides empirical evidence supporting ouranalysis while Section 7 discusses several extensions. Section 8 concludes.

2

Stylized facts

Here, we present some stylized facts on transportation costs and transport infrastructure.
Fact 1: Transport costs vary across space. Direct data on transportation costs is scarce.
Representative marginal costs for freight transportation amount to 1.54 Euro per kilometer on
average around 2008 in the United Kingdom. Fuel (including taxes) and travel time accountfor 44% and 38% of the total, respectively (Braconier et al., 2013). Combes and Lafourcade(2005) provide generalized transportation cost data for a sample of 8742 French city pairs in
1993. Average road transportation costs are 5.16 French Francs per kilometer.6 The dataalso reveals a strong degree of variation in bilateral transportation costs: transportation costsat the 5% percentile are 4.54 while at the 95% percentile they are 5.86 per kilometer. The
standard deviation is 0.43. Looking at the average per kilometer cost of transiting one of the
94 French departments,7 one discovers an even higher standard deviation of 1.12. Only part ofthis variation is explained by variables such as economic activity, density, or topography.8
Fact 2: Transport costs are non-convex in distance.

Usually, in economic geographymodels (Fujita et al., 1999), transportation costs are modeled as exponential functions of distance.9 However, the data reject convexity. Figure 1 provides an illustration based on data
by Combes and Lafourcade (2005). Regressing the log of transportation costs between capitalsof French départements on the log of geographical distance reveals an elasticity of 0.90 with astandard error of 0.02. The hypothesis of the elasticity being equal to unity is rejected at the
1% level.10
6Assuming an inflation rate of 3% a year and applying the FF/Euro conversion rate of 6.55957, this would
amount to about 1.25 Euro in 2008 current prices.
7
To obtain a measure of transit costs, we average total variable transport costs per kilometer between neighboring departements, using the neighbors’ area as weights.
8
In Appendix C (Table 9), we relate average transit costs to GDP, area and population of the respective
department, the ruggedness of territory, and to geographical remoteness. We find that average transportation
costs are higher in geologically difficult, less densely populated and poorer departments. Everything else equal,
they are also higher in less central regions. Geography explains about 16% of transport cost variation; adding
GDP, area and population drives the explanatory power of the model up to 58%. Hence, such a ‘naive’ model
leaves about 40% of variance unexplained.
9
See McCann (2005) for criticism.
10
Using robust regression methods to punish outliers leads to an elasticity of 0.92, still different from 1.00 at
the 1% level. The same holds true if one restricts the sample to distances below 200, 150 or 100 km.

60generalized transportation costs, in FF
500
1000

1500

Figure 1: Transportation costs and distance: a concave relationship

0

100

200

300

distance in km

Notes. Generalized transportation costs between capitals of French departements in French Francs (1993) as afunction of geographical distance in km.

Fact 3: Infrastructure investment and transportation costs are closely related.

Alarge empirical literature, already discussed in the introduction, establishes a close link between
infrastructure investment, transportation costs, and the benefits of economic integration; see
Limao and Venables (2001) on cross-country evidence, Allen and Arkolakis (2014) or Duranton
et al. (2014) on US interstate highways, Donaldson (2014) and Donaldson and Hornbeck (2015)
on railroads in India and the US, respectively, or Cosar and Demir (2015) on roads in Turkey.
Fact 4: Intracontinental trade flows are mostly land-borne. Table 1 reports data formerchandise trade within NAFTA and Europe. In 2010, between 72 and 75% of the value of
total regional trade is transported on roads or railways. Measured by tonnage, the shares arelower as much bulk transportation is water-borne. While the importance of air-borne traffic isincreasing, it still is almost irrelevant in intracontinental trade.
Fact 5: Transport infrastructure is publicly provided. Infrastructure and maintenancespending on roads amounts to about 1% of GDP across OECD countries (average across 20012009).11 Countries with difficult territory (such as Japan, Switzerland or Italy) have higher than
average spending. Almost all spending on roads and railways is financed by governments, even
11OECD Economic Outlook 91 database. There is some disagreement about measurement; the Congressional
Budget Office puts total public spending for transportation and water infrastructure between 1.2% and 1.5% of
GDP in the 1956-2007 period.

7

Table 1: Intercontinental merchandise trade by transport mode: NAFTA and EU

Truck
Rail
Air
Water
Pipeline
Other
Total

North America
valueweightbn. USD % mio. tons %
557
61
187
29
131
14
134
21
45
5
1
0
81
9
210
32
63
7
106
16
40
4
9
1
918
100
646
100

French intra-EU tradevalue
weightbn. EUR % mio. tons %
338
69
200
59
15
3
15
4
22
4
0
0
70
14
77
23
n.a.
n.a.
n.a.
n.a.
45
9
45
13
491
100
336
100

Notes: Data refer to 2010 (except French quantity information: 2006).

Sources:

US department of transportation, Freight Facts and Figures 2011, Table 2.8.,
www.ops.fhwa.dot.gov\freight\freight analysis\nat freight stats\docs\11factsfigures\index.htm
andCommissariat

dudevelopment

durable,www.statistiques.developpement-

durable.gouv.fr\transports\873.html.

if private public partnership agreements are becoming increasingly popular.12
Fact 6: Regional governments influence interregional infrastructure projects substantially.

Within countries, there is a substantial amount of centralization of infrastructure

planning and spending. Nonetheless, local governments matter, too. In the US, about 90% of
all spending on infrastructure and equipment falls on the local or state level, but federal transfers have become quite important over time (Congressional Budget Office, 2010). In Europe,
member states decide almost exclusively on their own about transport infrastructure investment
projects. There is some coordination at the Union level through the so called Trans-European
Transport Network, but the budget has been limited to about 1 billion Euro per year over the
2007-2013 spending period. This is less than 1% of overall spending on infrastructure in the EU(120 billion Euro).13
Fact 7: Distance elasticities and border effects in gravity models.

A voluminous

empirical literature finds that geographical distance restricts trade flows; see Head and Mayer(2014). In their meta analysis across appropriately specified gravity models, the authors find a
median elasticity of trade flows with respect to great circle distance of about -1.1 and a median
12

Applying conventional discount and depreciation rates to the flow investment data, the present value of thestock of public transport infrastructure amounts to between 10% and 20% of GDP in most countries.
13
http://ec.europa.eu/transport/infrastructure/tentec/tentec-portal/site/en/abouttent.htm.
In the period
2014-2020, centralized spending rises about threefold. However, this still keeps decentralized spending at about
97% of total spending.

8border effect (i.e., the trade inhibiting effect of a border as compared to trade within a country)of -1.6. In our empirical application using very recent European data, the distance elasticity isalso -1.1, but the border effect is -0.8.14

3

Modeling transportation costs

Models of international trade and economic geography typically employ Samuelson’s (1952)
iceberg trade costs assumption: in order to receive one unit of the good at some location x,
T (x, z) ≥ 1 units of that good have to leave the factory at location z.15 A share 1 − T (x, z)−1of the good ‘melts’ in transport; the share T (x, z)−1 arrives at x when one unit of the goodis shipped at z. This formulation represents a dramatic simplification (McCann, 2005). But
it has proved convenient, because it makes the introduction of a specific transportation sector
redundant.
In this paper, we stick to the iceberg formulation, but we let transportation costs between
two addresses x and z depend on cumulative infrastructure investment. Public infrastructure
investment refers to the process of investing some resource at specific locations s with the aimof reducing transportation costs.16 We assume that the set of geographic locations, S, is given
by an interval, [0, s̄], where s̄ characterizes the geographical size of the economy. In contrast
to a circular economy, the linear specification appears preferable since it features a natural
periphery.17
We model the effectively available stock of infrastructure over some interval [x, z] ∈ S using
a constant elasticity of substitution aggregator function
Z z
I (x, z) =

i (s)

1−δ

 1
1−δ
ds
, δ > 1, x ≤ z,(1)xwhere i (s) is the level/stock of infrastructure at location s ∈ [x, z] and δ > 1 is a constant technology parameter (which will turn out to be the elasticity of substitution between investments
at different locations). I (x, z) increases in distance. This formulation has the natural implication that spreading a constant investment budget B over increasing distance z − x lowers the14

We describe the data, methodology and results in Section 6 but mention our findings here, because they will
inform the numerical illustrations of our theory.
15
A popular specification in continuous space is T (x, z) = ea|x−z| , with a > 0; see Krugman (1991) or Fujita etal. (1999).
16
Our model is static; hence, we use the terms infrastructure investment and stock of infrastructure interchangeably.
17
Unlike in a symmetric circular economy, in a linear economy, symmetry in terms of endowments or available
technologies does not entail symmetry in infrastructure investments.

9

available stock of I (x, z) . Note also that if i(s) is equal to zero on some subset (with a positive
measure) of [x, z], then the available stock of infrastructure over the whole interval [x, z] is zero.
The costs of transporting a product from z to x is linked to infrastructure byT (x, z) =1
1+
|I (x, z)|1−δδ−1γ, δ > 1, γ > 0, x ≤ z.

(2)

Transportation costs are symmetric in the sense that delivering a product from x to z costs thesame as delivering a product from z to x. The parameter γ governs the effect of the total stockof infrastructure on transportation costs.
The choice of functional forms (1) and (2) proves convenient, as will become transparent
below. Moreover, the formulation has properties long discussed (but rarely formally modelled
in a general equilibrium context) by transport economists (Winston, 1985, or Gramlich, 1994).
Lemma 1

Generalized iceberg trade costs T (x, z) have the following properties:(i) T (x, z) ≥ 1 with T (x, x) = 1 and T (x, y)T (y, z) ≥ T (x, z).
(ii) T (x, z) = (1 + a|z − x|)γ , if i (s) is a constant ı̄ over the interval [x, z], and a = ı̄1−δ / (δ − 1).
(iii) T (x, z) = ∞, if i (s) = 0 on some subset (with a positive measure) of [x, z].
(iv) T (x, z) is increasing in distance: i.e. for fixed x a more distant location z results in higher
transportation costs. Moreover, if i(s) is a differentiable function on S, T (x, z) is concavein distance if the distance-induced increment to the trade cost gradient is outweighed by
an improvement in infrastructure. That is, if (γ − 1) [a (z)]2 / (T (x, z))1/γ < i0 (z) i (z)−δ
where a (z) = i (z)1−δ / (δ − 1).
(v) The (interregional) elasticity of substitution between infrastructure investment at different
locations is 0 < 1/δ < 1, so that investments at different locations are gross complements.
(vi) Investment smoothing property: if investment costs do not vary across locations, then the
cost-efficient way to achieve some exogenous target level of transportation costs involves aflat spatial investment profilenhio1/(δ−1)
i (s) = (z − x) / (δ − 1) T̄ 1/γ − 1.
where T̄ > 1 is the target level of iceberg transportation costs.

10

Proof

The first three properties directly follow from the definition of the trade costs in(2). The last three properties are proved in Appendix A.
Property (i) establishes that, for any x, y, and z, the triangle inequality holds: T (x, y)T (y, z) ≥T (x, z) (the strict inequality holds, if x, y, and z represent different locations). So, it is cheaper
to transport products directly to a destination address, rather than through some intermediate
address.
Property (ii) shows that equation (2) collapses to the specification almost exclusively used inempirical gravity models (with a = 1); see Head and Mayer (2014). Our specification also allows
for concavity of transportation costs with respect to distance documented in the data. Icebergtransportation costs are concave in distance, as long as the component of dT (x, z) /dz driven byvariation in infrastructure investment outweighs the pure distance component of dT (x, z) /dz(see property (iv) in the above lemma). Hence, in general, whether T (x, z) is concave in distancedepends on the spatial allocation of infrastructure investment and the values of γ and δ.
Properties (v) and (vi) exploit an isomorphism between (2) and the usual representation ofutility in an optimal growth model. The parameter δ measures the ease with which infrastructure
investment at some address can substitute for investment at another place. The restriction δ > 1
ensures that investments at different places are gross complements: investment at some address
makes investment at some other place more worthwhile, which seems realistic and is consistent
with the data.18

4

Infrastructure investment and intraregional trade

In a first step, we incorporate our modeling of transportation costs and infrastructure into a
simple model of intranational trade. Later we introduce inter national trade.

4.1

Geographical space and goods space

We assume that, at each location s ∈ S, there is a representative household who inelasticallysupplies m (s) > 0 units of labor. The total endowment of labor in the economy is then equalR
to s∈S m(s)ds, which we define as L.
Each location produces both a homogeneous agricultural and a spatially differentiated industrial good. Consumers consume both goods and perceive industrial goods produced at specific18
We do not allow for incremental transport costs incurred at address s to depend on the volume of traffictransiting through s. Actually, in equilibrium, the contrary will hold: more traffic at s will encourage the planner
to invest more in infrastructure, thereby driving down the gradient of T. This lowers the incremental trade costs
at s for all units of goods that transit through s.

11

locations as imperfect substitutes. There are no costs of transporting the agricultural good.
Moreover, the agricultural good serves as an input into infrastructure provision.19 Each location s is home of consumers and producers. We denote addresses of consumers by x andaddresses of producers by z.
We assume that locations may differ with respect to topological circumstances. Specifically, infrastructure at address s is produced according to a linear production function i (s) =b (s) /q (s), where b (s) denotes the input of the agricultural good used for infrastructure investment, and 1/q (s) > 0 measures the rate at which that resource is transformed into infrastructure.
We restrict q (s) to be continuously differentiable. Feasibility of an investment policy i (s) reR
quires s∈S q (s) i (s) ≤ B, where B is the amount of agricultural good invested in infrastructure
and will be endogenously determined by government policy.

4.2

Consumption

The utility function of a representative household at location x is a monotone transformation of a
Cobb-Douglas aggregate over the homogeneous agricultural good and a Dixit-Stiglitz aggregate
over industrial goods: αρU (x) = cA (x) (1−α)(1−ρ)

Z

I

ρ

c (x, z) dz

 1

1−ρ

,

(3)

z∈S

with α ∈ (0, 1) , 0 < ρ < 1, where cA (x) denotes the total quantity of the agricultural good
consumed at address x and cI (x, z) is the quantity of an industrial variety produced at addressz and consumed at x.20
Let Y n (x) denote household x0 s net income in terms of a numeraire to be defined below.
R
Then, the budget constraint of household x is Y n (x) = cA (x) pA (x) + z∈S cI (x, z) pI (x, z) dz,
where pA (x) is the price of the agricultural good at location x and pI (x, z) is the price of avariety imported from location z and consumed at x.
The utility maximization problem implies that the demand functions for the agricultural
19
The assumption of a freely tradable agricultural good which is produced at every location is frequently used inmodels of economic geography. It provides tractability as wages are equalized across space (in nominal terms). An
alternative/equivalent way to model infrastructure provision is to assume that the only input into infrastructureis labor, which in turn is perfectly mobile between locations (within an economy). But consumption takes place atthe place of origin. This will equalize wages across locations (which is in the present model done by the presenceof the homogenous agricultural good) making the presence of the agricultural good redundant.
20
Notice that U (x) is a positive monotonic transformation U (x) = [Ũ (x)]ρ/((1−α)(1−ρ)) of the usual Cobbα  I
1−αDouglas formulation Ũ (x) = cA (x)u (x). The transformation makes the theoretical analysis of themodel more tractable (without qualitatively changing the main conclusions).

12

good and a certain variety of the industrial good are respectivelycA (x) =αY n (x)pI (x, z)−σ
I
n
,
and
c
(x,
z)
=
(1
−
α)
Y
(x)
pA (x)P I (x)1−σ(4)where σ ≡ 1/ (1 − ρ) andIZ

P (x) =I1−σp (x, z)

 1

1−σ

dz

(5)

z∈S

is the price index for industrial goods at location x.
The indirect utility attainable at prices pA (x), pI (x, z) and income Y n (x) can be writtenas
−αρ/((1−α)(1−ρ))  I
1−σ nV (x) = A pA (x)P (x)(Y (x))ρ/((1−α)(1−ρ)) ,(6)

ρ/(1−ρ)where A ≡ αα/(1−α) (1 − α).

4.3

Production

At each location z ∈ S, the agricultural and the industrial good are produced under conditionsof perfect competition. The only input of production is labor. Production functions for thetwo types of goods are linear y A (z) = blA (z) and y I (z) = lI (z), where b > 0 is a productivity
parameter common to all locations. Output quantities are denoted by y A (z) and y I (z), andlabor inputs by lA (z) and lI (z) , respectively.
We assume that, within addresses, workers are perfectly mobile across agricultural and industrial firms. This in turn implies that pA (z) = w (z) /b and pI (z) = w (z), where w (z) is thewage rate (expressed in units of numeraire) at address z. Industrial goods bear transportation
costs. We assume that there are no trade costs other than transportation costs.21 Hence, thec.i.f. prices faced by consumers differ from the f.o.b. (ex-factory) prices. In particular, a household at x faces the price pI (x, z) = pI (z) T (x, z) for a variety of the industrial good imported
from location z. In contrast, the agricultural good can be transported freely.

4.4

Equilibrium

In this paper, we impose a non-full-specialization (NFS) assumption: there is always a strictly
positive quantity of agricultural production at each location. The NFS assumption introduces
factor price equalization in terms of the agricultural good.22 We may therefore choose the21

In Section 5, when we consider international trade, we will introduce a discrete trade friction at the border.
Relaxing the NFS assumption would allow to study the interaction between infrastructure investment policies
and regional specialization patterns. This is an interesting issue that raises additional complications. It is therefore
22

13

agricultural good as the numeraire and set pA (z) = 1 for all z ∈ S. Since pA (z) = 1 for any z,
we drop the superscripts A and I in the following.
As the price of the agricultural good is normalized to unity, the wage rate at location z, w(z),is equal to b. The gross income at location x in terms of the numeraire is then Y (x) = bm (x).
Finally, from our assumption on technology, the c.i.f. prices of industrial goods are p (x, z) =bT (x, z) .
The government imposes a lump-sum tax with rate t, which is assumed identical acrossaddresses s ∈ S. Thus, the net income at location x, Y n (x), is (1 − t)bm (x). Total tax income
isZm (s) ds = btL.

B = bts∈S c

Substituting the expressions for net household income and for the price index, we can now
rewrite the indirect utility function in (6) as
V (x) = Ω(1 − t)(σ−1)/(1−α)

Z

1−σ

m̃ (x)T (x, z)


dz ,

(7)

z∈S

where m̃ (x) = m (x)(σ−1)/(1−α) and Ω ≡ αα/(1−α) (1 − α) bα/(1−α)

4.5ρ/(1−ρ)is a constant.

The choice of infrastructure investment

In this section, we characterize optimal policies {ia (s), ta }s∈S in a closed economy. The social
planner chooses the infrastructure investment and the tax rate to maximize total welfare – thesum of individual utilities – in the economy. Ignoring the irrelevant constant, we have({ia (x) , ta }x∈S = arg max (1 − t)

 1−α Z

Z

)

σ−1

q (x) i (x) dx ≤ btLm̃ (x) v(x)dx

,

(8)

x∈S

x∈S

where
Z
v(x) =T (x, z)1−σ dz.

(9)

z∈S

A sufficient condition for concavity of the objective function in (8) is
1 + (γ (δ − 1))−1 > σ > 2 − α.
left to future research.

14

(10)

The first inequality means that T (x, z)1−σ is concave with respect to infrastructure investments,
implying that the consumption utility, v(x), is concave in infrastructure investments as well.23
The second inequality, which would be always met if σ ≥ 2, implies that the objective function
is concave in v(x). As a result, the objective function is concave with respect to infrastructure
investments.24
Next, we characterize the solution of the planner’s problem. Note that, without loss ofgenerality, we find the solution among continuous functions on [0, s̄]. That is, social welfare is
maximized with respect to ia (x), where ia (x) is continuous.
Proposition 1

The optimal allocation of infrastructure spending across space and the opti-

mal tax rate chosen by a social planner under autarky are implicitly determined by the following
system of equations:ia (x)δ =ta =
bγ (1 − α) (1 − ta )L  L
φ (x) + φR (x) ,q(x)Ras∈S q (s) i (s) ds
,
bL

(11)
(12)

where φL (x) and φR (x) denote aggregate marginal utilities from investing to the left or the rightof x, respectively, and are defined as
Rx

0 m̃ (s)

L

 
R s̄
x

φ (x) =

Proof
R t a 1−δ γ(1−σ)−1dr
dt ds
s i (r)Rs∈S m̃ (s) v(s)ds

R s̄
φR (x) =1
1 + δ−1x m̃ (s)

 
Rx
0

1
1 + δ−1R,R s a 1−δ γ(1−σ)−1dr
dt ds
t i (r)s∈S m̃ (s) v(s)ds.

In the Appendix.

The investment at location x is higher, the larger the sum φL (x)+φR (x) or the lower the costof infrastructure at the location, q(x). In the next proposition, we summarize some additional
properties of the optimal infrastructure investment function, ia (x), and the consumption utility,v(x).
Proposition 2
23

The optimal infrastructure investment function, ia (x), and the consumptionγ(1−σ)1
The function 1 + δ−1x1−δis strictly concave on [0, ∞) if and only if γ(σ − 1) (δ − 1) < 1. In turn,

T (x, z)1−σ is concave with respect to infrastructure investment.
24
Our results are qualitatively robust to changes in the functional form of the transportation costs as long as
T (x, z)1−σ is concave in i (s), s ∈ [x, z], and has an unbounded derivative at i(s) = 0.

15

utility, v(x), have the following properties:(i) The infrastructure investments are zero at the borders of the region: ia (s̄) = ia (0).
(ii) If q(x) is continuously differentiable, ia (x) is increasing in the neighborhood of zero anddecreasing in the neighborhood of one: specifically, (ia (x))0x=0 = ∞ and (ia (x))0x=s̄ = −∞.
(iii) If there is no variation in the cost of infrastructure investment and the household size
across the locations: q(x) = q and m(x) = m for any x ∈ S, then v(x) and ia (x) aresymmetric around x = s̄/2 and have a hump shape with maximum at x = s̄/2.
Proof

The first property immediately follows from the definitions of φL (x) and φR (x).

Specifically, we have that φL (s̄) = φL (0) = φR (s̄) = φR (0) = 0. The last two properties are
established in the Appendix.
According to the proposition, if there is no variation in the cost of infrastructure and inhousehold size, the optimal infrastructure is symmetric around the middle point of the [0, s̄]interval. So, transportation costs in central parts of the country are lower than in peripheral
parts and, thereby, households located closer to the middle point have higher indirect utility.
The intuition is that, at the optimum, the sum of marginal benefits from investment needs tobe equalized to the constant cost of investment at each location and this is achieved by higher
investment in central locations.

4.6

Comparative statics

The optimal infrastructure investment at location x is implicitly determined byai (x) =!1/δRγ (1 − α) bL − s∈S q (s) ia (s) ds
LR
φ (x) + φ (x)
q(x)

(13)

≡ ia (x, I a , ) ,where I a represents the infrastructure profile in the economy and  is the set of parameters in
the model. Thus, changes in ia (x) due to changes in  are implicitly determined by∂ia (x)∂ia (x, I a , ) ∂ia (x, I a , ) ∂I a
=
+
.
∂
∂
∂I a
∂

(14)

The first term in the right-hand side of (14) captures the direct effect of  on ia (x), while thesecond term stands for the indirect effects.
16Figure 2: Closed economy equilibrium investment loci: comparative statics(a) Moving s̄ from 500 to 700(b) Moving γ from 0.86 to 0.7

180

180

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20

0

20

0

100

200

300

400

500

600

0

700

(c) Moving σ from 2.7 to 2.0

0

50

100

150

200

250

300

350

400

450

500

(d) Moving δ from 1.65 to 1.5
180

250

160

200

140

120

150
100

80

100
60

40

50
20

0

0

0

50

100

150

200

250

300

350

400

450

500

0

50

100

150

200

250

300

350

400

450

500

Notes. Solid black curve: default investment distribution with σ = 2.7, δ = 1.65, γ = 0.86, α = 0.5, q(x) =q = 1, m(x) = m = 1000, b = 1, and s̄ = 500. Dashed red curves: distributions resulting from alternative
parameterizations. See Table 2 for calibration details.

Proposition 3

Changes in the parameters in the model have the following effects on the

optimal infrastructure profile in a closed economy:.
(i) A rise in b increases ia (x) for all x.
(ii) Assuming that m(x) = m for all x, a rise in m increases ia (x) for all x.
(iii) Assuming that q(x) = q for all x, a rise in q decreases ia (x) for all x.
(iv) Assuming that m(x) = m for all x, a rise in s̄ has a positive direct effect on ia (x) forx close to the right border and has an ambiguous impact on the investments at the otherlocations. If in addition q(x) = q for all x, then a rise in s̄ has a positive direct effect onia (x) for all x ∈ S.
Proof

In the Appendix.

17

While parts (i) to (iii) of Proposition 3 account for direct and indirect effects, part (iv)
describes only the direct effect of an increase in s̄ (which, holding population density constant,amounts to an enlargement of a country, such as the reunification of Germany in 1990). Figure2(a) provides a numerical illustration of the overall effect of a rise in s̄ on the infrastructure
profile.25 Enlargement of a country diverts investment away from locations sufficiently far fromthe added territory. This is consistent with the German post-reunification experience.26
The formal analysis of the comparative statics with respect to γ, δ, and σ is not tractable;
so, we turn to numerical experiments. A lower value of γ makes the dependence of transportation costs on infrastructure investments weaker. Therefore, the returns from investing ininfrastructure at all locations are smaller, leading to lower ia (x) at all locations (Figure 2(b)).
Lower σ makes the varieties of the differentiated product less substitutable, increasing the benefits of intra- and international trade. As a result, incentives to invest in infrastructure go up
and, therefore, ia (x) rises ((Figure 2(c)). In contrast, changing δ has an ambiguous impact on
infrastructure investment. With the chosen parameterization, a decrease in δ from 1.65 to 1.5
makes investments at different locations more easily substitutable. This decreases infrastructure
investments at all locations and also lowers the spatial variance of investment (Figure 2(d)).

5Infrastructure investment and inter national trade

Now, we assume that the world economy consists of two independent countries, each with its
own government that decides on infrastructure investment in a non-cooperative way. However,consumers demand goods from all over the world. Thus, we have a situation with ‘globalized
markets, but regional politics’. Otherwise, we maintain all earlier assumptions. To start with,
we assume that countries are symmetric. In particular, the world geography is described by the[0, 2s̄]-interval, where locations from [0, s̄] and (s̄, 2s̄] represent the home and the foreign country,
respectively. To isolate a pure border effect on the equilibrium infrastructure profile we assume
away any variation in the costs of infrastructure and in household size across locations: i.e.,q(x) = q and m(x) = m for all x ∈ [0, 2s̄].27 Finally, we suppose that trade between locations indifferent countries is subject to an exogenous discrete (i.e., independent from distance) borderfriction denoted by τ ≥ 1. That is, the cost of delivering one unit of a product produced at
25

In the figure we consider a discrete variation of the model that has similar properties as the continuous model(see more on the choice of the parameterization in Section 5.3).
26
See the information on

www.bmvi.de/SharedDocs/DE/Artikel/StB/entwicklung-der-autobahnen-in-deutschland-seit-derwiedervereinigung.html.
27

The framework can be easily extended to the case when q(x) and m(x) are symmetric around x = s̄.

18foreign location z to domestic location x is τ T (x, z), where T (x, z) is modeled as before.

5.1

World planner problem

We start with a description of the first-best situation, in which economic and political spacecoincide. Such a world planner problem is characterized as follows:
(
w

w

 1−α
σ−1

Z 2s̄

{i (x) , t }x∈[0,2s̄] = arg max (1 − t)i(x),tv(x)dx)Z 2s̄
i (x) dx ≤ 2bLt

q

0

,

(15)

0

where v(x) is utility at address x given by v(x) =

R 2s̄
0

τ (1−σ)ind(x,z) T (x, z)1−σ dz (the indicatorfunction, ind(x, z), is equal to 1 if locations t and s belong to different countries and 0 otherwise)and L is population size in each country.28 The world planner problem looks very similar to thesocial planner problem in the case of a closed economy. The only difference is that geographicalspace is now given by the [0, 2s̄]-interval and trade between locations in different countries incurs
extra costs. Hence, we can formulate the following proposition.
Proposition 4

The optimal allocation of infrastructure spending across the world geography

and the optimal tax rate chosen by the world planner are implicitly determined by the following
system of equations:
iw (x)δ =tw =
2bLγ (1 − α) (1 − tw ) L,w
φ (x, τ ) + φR,w (x, τ ) ,q
R 2s̄ w
q 0 i (s) ds
,
2bL

(16)
(17)

where

R x R 2s̄φL,w (x, τ ) =0xτ (1−σ)ind(t,s)



1
1 + δ−1

R t w 1−δ γ(1−σ)−1dr
dt ds
s i (r),v(s)dsR 2s̄ R x (1−σ)ind(t,s) 
R s w 1−δ γ(1−σ)−11
dt ds
1 + δ−1 t i (r)
dr
x
0 τ
.
R 2s̄
v(s)ds0
R 2s̄0

φR,w (x, τ ) =Proof

The proof is exactly the same as that for Proposition 1.

When τ is equal to unity, the properties of the world planner solution are the same as those
R 2s̄
R 2s̄
The constraint in the maximization problem is q 0 i (x) dx ≤ bt 0 m (x) dx = 2bs̄m = 2bL, where L is thesize of the countries.
28

19

for the autarky planner case; see Proposition 2. In particular, the infrastructure profile has ahump shape with maximum at s̄. However, when τ > 1, the infrastructure profile chosen by theworld planner has a double-hump shape (see details in the Appendix). At Home it is decreasingaround the border s̄, at Foreign it is increasing. Due to the presence of the border friction, theinfrastructure profile in the countries is skewed towards internal locations compared to the casewith no border friction.

5.2

Global economics, regional politics

We assume that two independent governments play a Nash game and set their infrastructure
investment schedules non-cooperatively.
The game is defined as Γ = (I, Ui , Θi ) , where I = {H, F } represents the set of countries, Θi iscountry i’s strategy set (i ∈ I), and Ui is country i’s payoff functional defined on ΘH ×ΘF . In thecontext of the present framework, Home’s strategy set, ΘH , is given by iH (x), tH x∈[0,s̄] , whereR s̄
iH (x) ≥ 0, 0 iH (x) dx ≤ bLtH /q, and tH ∈ [0, 1]. Similarly, ΘF is the set of iF (x), tF x∈[s̄,2s̄] ,R 2s̄
where iF (x) ≥ 0, s̄ iF (x) dx ≤ bLtF /q, and tF ∈ [0, 1]. Here, iH (x) and iF (x) are continuous on [0, s̄] and [s̄, 2s̄], respectively. Finally, the countries’ payoffs are represented by thecorresponding countries’ total welfare functions.29
Since the countries are symmetric, in the following analysis we focus on the home country
only. Given the infrastructure profile and the tax rate in the foreign country, the social planner29

As the Nash equilibrium in the above game, we consider the limit of the Nash equilibrium in the corresponding
discrete approximation Γn = (I, Uin , Θin ) (in other words, the equilibrium in game Γ is considered as the limit(n → ∞) of the equilibrium in game Γn ). To formulate Γn , we consider a uniform partition of the [0, 2s̄]-interval
given by {xi }i=0..2n , where x0 = 0, xn = s̄, and x2n = 2s̄. In this case,of strategies of the home country,
Pthe setHΘHn in country i is given by iH (xi ), tH i=0..n , where iH (xi ) ≥ 0, ni(x
) 4n ≤ bLtH /q, and tH ∈ [0, 1]
i=0
 Fi(here, 4n = s̄/n is the partition size). In the same way, ΘF n is the set of i (xi ), tF i=[n+1,2n] (without lossPFof generality, we assume that location n belongs to the home country), where iF (xi ) ≥ 0, 2ni=n+1 i (xi ) 4n ≤FFbLt /q, and t ∈ [0, 1]. The countries’ payoffs are then the following:

UHn

=

H

(1 − t )

n
X

! 1−α
σ−1

v(xi )4n

,

i=0

UF n

=

F

(1 − t )

2n
X

! 1−α
σ−1
v(xi )4n

,

i=n+1

where
v(xi ) =2nXτ (1−σ)I(xi ,xj ) T (xi , xj )1−σ 4n .

j=0

It is straightforward to see that the game Γn has a Nash equilibrium in pure strategies. This is due to the fact thatthe strategy sets are non-empty, convex, and compact subsets of a metric vector space and the payoff functions
are continuous on ΘHn × ΘF n and concave in the own strategy of a player: i.e., Uin is concave on Θin .

20

at home solves the following maximization problem:
(
)
Z s̄
 1−α
Z s̄
σ−1
H
H
i (x), t x∈[0,s̄] = arg max (1 − t)v(x)dxqi (x) dx ≤ bLt ,t,i(x)

where

0

Z 2s̄
v(x) =(18)0τ (1−σ)I(x,z) T (x, z)1−σ dz.

0

As agents consume both domestic and foreign products, consumption utility, v(x), depends not
only on domestic infrastructure investment, but also on the foreign investment. As a result,foreign infrastructure investment affects the choice of infrastructure investment in the homecountry, and vice versa. The next lemma describes the best response of the home social planner
given a certain infrastructure profile in the foreign country.

Given an infrastructure profile in the foreign country, iF (x) x∈(s̄,2s̄] , the homesocial planner chooses an infrastructure investment schedule and a tax rate, iH (x), tH x∈[0,s̄] ,Lemma 2such that the following equations are satisfied:
iH (x)δ =tH=

bLγ (1 − α) (1 − tH )  LRφ̃ (x, τ ) + φ̃ (x, τ ) ,q
R s̄ Hq 0 i (x) dx
,
bL

where

R x R s̄ γ(1−σ)−1 
Rt H
1−δ
dr
dt ds
x
0
s i (r)Lφ̃ (x, τ ) =R s̄
0 v(s)dsγ(1−σ)−1 RR
R s̄ H
Rt F
2s̄
x
1−δ
1−δ
1
1
1−σ
1 + δ−1 s i (r)τ
dr + δ−1 s̄ i (r)
dr
dt ds
s̄
0
+
, and
R s̄
v(s)ds0γ(1−σ)−1 
R s̄ R x 
Rs H
1−δ
1
dt ds
dr
x
0 1 + δ−1 t i (r)Rφ̃ (x, τ ) =.
R s̄
0 v(s)ds
Proof1
1 + δ−1

In the Appendix.

The optimal infrastructure profile in an open economy has a similar form as the one ofLa closed economy. The main difference is the expression for φ̃ (x, τ ) which represents theaggregate marginal welfare gains from a rise in iH (x) to the left of location x. The reason
is that infrastructure investments at location x affect the transportation costs from all foreign21

locations to the locations on the left of x (as the foreign country is located on the right of x). This
leads to additional welfare gains from a rise in infrastructure investment at location x comparedto the closed economy case. As a result, in contrast to the closed economy case, iH (x) is strictly
greater than zero at x = s̄ if and only if iF (x) is strictly positive in some right neighborhoodLof x = s̄. If iF (x) is equal to zero in some right neighborhood of x = s̄, then φ̃ (x) is exactly
the same function as in the case of a closed economy, because the transportation costs fromforeign locations are infinitely high. Finally, as in the closed economy case, the infrastructure
investment at location x = 0 is zero: iH (0) = 0.
In the symmetric Nash equilibrium of the game, countries’ equilibrium infrastructure profiles
are symmetric around x = s̄, such that iF (x) = iH (2s̄ − x) for x ∈ [s̄, 2s̄]. Using Lemma 2, wemay formulate the next proposition.
Proposition 5

In the symmetric Nash equilibrium, the equilibrium home infrastructure

profile and tax rate are implicitly determined by the following system of equations:
iH (x)δ =tH
where φ̃
Proof

L,N

=


bLγ (1 − α) (1 − tH )  L,NR,Nφ̃ (x, τ ) + φ̃
(x, τ ) ,q
R s̄ Hq 0 i (x) dx,bLL(x, τ ) = φ̃ (x, τ ) and φ̃

R,NR(x, τ ) = φ̃ (x, τ ) from Lemma 2 and iF (r) = iH (2s̄ − r).

The proof directly follows from Lemma 2 and the fact that in the symmetric equi-

librium iF (x) = iH (2s̄ − x).
In the symmetric equilibrium, there always exists some left (right) neighborhood of x = s̄
where iH (x) (iF (x)) is strictly greater than zero. Indeed, if it is not true, then iH (x) is equal
to zero around x = s̄. This implies that iF (x) is equal to zero around x = s̄ as well (dueto symmetry). As a result, there is no trade with the foreign country and the equilibrium
infrastructure profile corresponds to the optimal infrastructure profile in the closed economy,
which is, as was shown, strictly positive for any x ∈ (0, s̄). This constitutes a contradiction.
Thus, we can conclude that, in contrast to the closed economy case, the infrastructure investment
at x = s̄ is strictly positive due to the possibility of trade with the foreign country. Specifically,iH (s̄)δ =bLγ (1 − α) (1 − tH ) L,Nφ̃ (s̄, τ ) > 0.
q

Next, we explore the behavior of the infrastructure profile around the border. The following
proposition holds.
22

Proposition 6

0
In the symmetric Nash equilibrium, iH (x) x=0 = ∞ and0iH (x) x=s̄ isnegative, but finite.
Proof

In the Appendix.

In the presence of a foreign country, the distribution of infrastructure investment has moremass in regions closer to the border (compared to the closed economy case). Nevertheless, the00infrastructure profile still is hump-shaped (as iH (x) x=0 > 0 and iH (x) x=s̄ < 0). Hence,
investment close to the border is lower than in central locations. Compared to the first-bestsolution, the non-cooperative solution features underinvestment at the border. This outcome
is purely based on a network externality: local governments do not internalize the benefits
from reductions in domestic transportation costs that accrue to foreign consumers, and theseunaccounted benefits are largest the closer a location is to the border. Note that, since there isa numeraire product, there are no terms-of-trade effects on the optimal choice of infrastructure
profile.30
Another possible explanation for low investment close to national borders may coincide withgeographical frictions such as mountain ranges or rivers. In this case, investment is low becauseof high investment costs, and not due to the network externality. We explore the quantitativerole of this possibility in Section 5.6.
We now discuss how discrete border costs τ affect the endogenous allocation of infrastructure
spending within economies and how failing to account for infrastructure biases the border effectmeasured in the traditional econometric specifications of the gravity model. Focusing on direct
effects of changes in τ on infrastructure investment, we explore how τ changes the infrastructure
profile at given total spending.31 The following proposition holds:
Proposition 7

The direct effect of a rise in τ is a decrease in iH (x) in some left neigh-borhood of the border and an increase in iH (x) at locations that are relatively far from thatborder.
Proof

In the Appendix.

The existence of explicit border costs τ skews the equilibrium infrastructure profile awayfrom the border as gains from trade with the foreign country are lower and the marginal returns
30

In principle, instead of setting non-cooperative tariffs, governments can use infrastructure investment strategically to manipulate the cost of delivering goods over space. Higher transport costs close to the border increase theprice of imports, reducing their demand. This can improve the terms of trade. The optimal tariff being positivein a non-cooperative tariff game, governments can restrict investment around international borders. However,this mechanism is broken by the presence of an active linear outside sector.
31
In the numerical exercise below, we take account of indirect effects. Quantitatively, they are of absolutely
minor importance.

23

from investing around the border are smaller. This offers a natural explanation for the large
border effect observed in the data. Indeed, a rise in τ not only increases the trade costs with theforeign country, but also decreases the stock of infrastructure around the border. As a result,
the trade trade cost effect of the discrete border cost is larger than the one implied by τ alone.

5.3

Calibration and numerical illustrations

To provide numerical illustrations and some ideas about the relevance of our mechanism, wecalibrate our model. We think it is useful to discipline our numerical exercise with the help ofavailable data, but we are fully aware of the fact that our framework is too stylized to provide
a full empirical analysis of the spatial distribution of infrastructure investment in Europe. We
work with a discrete formulation of our model (see Appendix B for details) and set parameterssuch that the model replicates some key moments estimated on European data.
For the calibration, we normalize some parameters. Particularly crucial parameters such as
δ, γ and τ are set such that the model replicates key moments obtained from EU data. Assuming
symmetry within countries (m(x) = m, q(x) = q), and noting that per capita income b and thecost of infrastructure q affect investment only through bL/q (where L = ms̄), we set m(x)to 1000 and normalize q = 1 and b = 1. To guarantee enough variation in distance between
locations generated by the model, we set s̄ at 500. We set the share of income spent on the
agricultural product, α, to 0.5.32
We set parameters δ, γ, τ such that the model replicates key empirical moments. To thisend, we apply a gravity equation of the typeln Xij = µ1 ln Dij + µ2 Bij + exi + imj + ij ,(19)

to data generated by our model and to actual data. Xij represents trade volumes from locationi to j, Dij denotes the distance between the locations, Bij is a border dummy that is equal to
one if i and j belong to different countries, exi and imj are exporter and importer fixed effects,and ij is the error term. We use European trade data to estimate the empirical counterpart of(19); see Section 6. This yields estimates µ̂1 = −1.1 and µ̂2 = −0.8. We parameterize the modelsuch that the trade data generated from it produces exactly the same values for µ1 and µ2 as
those obtained from real data. The parameter γ is chosen such that the generated elasticity
of internal transportation costs with respect to distance matches the value of 0.9 estimated in
32

In Table 4 we report robustness checks pertaining to these choices.

24

Table 2: Calibration strategy(a) Normalizations
Value Explanation
1000 arbitrary choice500
arbitrary choice1symmetry
1
symmetry
0.5
arbitrary choice(b) Parameters calibrated to match EU data
Parameter Value Momentγ
0.86 Distance elasticity of transport costs in French data
(Combes and Lafourcade, 2005): 0.9
δ1.65 Distance elasticity µ1 estimated in EU trade data: -1.1
τ
1.32 Border effect µ2 estimated in EU trade data: -0.8
σ2.70 Set to satisfy (10) given calibrated values of γ, δ, τ

Parameter
m(x)
s̄
b
q(x)
α

French data.33 We use parameter restriction (10) to set the elasticity of substitution σ at the
maximum admissible level.
Table 2 summarizes the calibration strategy and outcomes. The border friction implies an
ad valorem tax equivalent of 32%, which is a reasonable magnitude compared with estimatespresented in Anderson and van Wincoop (2004). The interregional elasticity of substitution is1/δ = 0.61, implying a fairly strong degree of complementarity of investments between different
locations. The parameter governing the curvature of the transportation cost – distance relationship is γ = 0.86. Finally, the maximum value of σ that satisfies the parameter restriction (10)
is 2.7.34 We use this parameterization as our benchmark configuration.
We are now ready to run numerical exercises. We start with the counterfactual situation
where τ is equal to unity. Figure 3 compares optimal schedules for infrastructure investment andaggregate price levels, denoting the outcome under autarky by ia (x), the world-planner solution
by iw (x), and non-cooperative Nash outcome by (iH (x), iF (x)). In line with our analyticalresults, the world-planner schedule has a unique maximum at the location of the border, while
the non-cooperative schedule has a double-hump shape with underinvestment around the border(compared to the world-planner outcome). This shape generates a border effect even without
33

We do not match spending on infrastructure investment t, because due to the one-period nature of our modeli(x) measures capital stocks while the empirical value of t discussed in Section 2 refers to the flow of (gross)investment.
34
This is a low value compared to findings in the literature; see Costinot and Rodriguez-Clare (2014) for asurvey. As equation (10) is only a sufficient condition, we can set σ at higher levels, but may end up violating the(unknown) necessary condition for the existence of an interior solution. We work with σ = 3.4 in the robustness
checks below.

25having any discrete border costs.
Figure 3: Infrastructure investment and price levels across space in the absence of explicit(discrete) border frictions (i.e., τ = 1)(a) Investment(b) Price levels

Notes. ia (x), iw (x), and iH (x) refer to the autarky, central-planer, and non-cooperative optimal infrastructure
investment distributions. Similarly for price levels. See Table 2 for the parameterization and Table 3 for numericalresults.

Panel b in Figure 3 depicts the distribution of the price index across locations in the autarky,
world-planner, and Nash outcomes. In our framework, the price index at location x depends
on the ‘remoteness’ of the location (which determines the level of ‘global’ trade) and the levelof infrastructure in the neighborhood (which determines the level of ‘local’ trade). Thus, inthe world-planner outcome the price index is the lowest at the border, since the border is theleast remote location in the world economy and the infrastructure investment is the highest
there. In contrast, in the Nash equilibrium the price index has the lowest value at some internal
location, rather than at the border (meaning that the local effect is stronger than the globalone). This is caused by the skewness of the infrastructure profile towards internal locations in
the Nash outcome. If we decrease the geographical size of countries s̄ (making ‘local’ trade lessimportant), the lowest value of the price index will be closer to the border.
Given our parameterization, Table 3 shows that underinvestment in border regions is quantitatively quite substantial, while global underinvestment is not. Compared to the first-bestsituation (row (2)), the non-cooperative outcome (row (3)) displays an investment gap of 49%
at the border (compare 88.5 to 172.9). Overall spending on infrastructure investment (measured
by the equilibrium tax rate), falls only 7% short of the first-best. Compared to autarky, investment is about 5% higher in the first-best situation but about 2% lower in the Nash equilibrium.
26

Table 3: Autarky versus first-best and Nash outcomes under trade(1)
border inv.
i (500)(2)
max. inv.
arg max i (x)(3)
tax ratet

Autarky: τ = ∞(1) ta , ia (x)
0.0
250
13.4%
No discrete border frictions: τ = 1 (counterfactual)(2) tw , iw (x)
172.9
500
14.1%
H
H
(3) t , i (x)
88.5
296
13.1%
Discrete border frictions: τ = 1.32 (data)(4) tw , iw (x)
117.6
322
13.8%
(5) tH , iH (x)
63.6
276
13.2%

(4)
real income
E [W ](5)inequality
V [ln W ] , %1.00001,691.07071.05631.67
1.20

1.04191.03351.24
1.14

Notes: The parameterization is as in Figure 3. Two symmetric countries, S = [0, 1000].
Autarky welfare is normalized to unity.

Real net per capita income at location x being given by W (x)= (1 − t)b/P (x), we use averagereal per capita income, E[W ], as a measure of welfare (in Table 3 we normalize autarky welfare
to unity). The gains from trade are about 7.1% when the infrastructure investment schedule
is first-best and about 5.6% when it is Nash; the cost of non-cooperation therefore amounts toabout 1.4% of autarky welfare, or, equivalently to 20% of the gains from trade achievable wheninvestment is first-best.35 Interestingly, inequality (as measured by the variance of the log ofreal net income multiplied by 100) is almost identical in autarky and in the first-best situation,
but is substantially lower in Nash, where the income differential between the border region andthe periphery is much smaller.36
In Figure 4 we set τ = 1.32. The world planner spends 4.5% more on infrastructure thancountry-level governments would, while the shortfall of investment at the border is around 46%.
The welfare loss (the difference between the average real per capita income in the first-best
and non-cooperative outcome) constitute around 0.8%. This suggests that lower border frictions
increase the welfare loss from infrastructure misallocation (when τ = 1, the loss is around 1.3%).
The fall in the real income at the border is more substantial (around 8.7%), suggesting that the35
If we fix overall spending to the first-best level, but allow independent governments to decide about the spatial
distribution of this spending, the welfare losses become minor. This outcome is robust across different parameterization, suggesting that welfare losses arising in case of the Nash equilibrium are mainly due to insufficientfinance (a lower tax rate), rather than the distribution of infrastructure itself. The border investment is higher
when overall spending is forced to be at the first-best level, but it still falls short from the optimum substantially.
36
At first glance, the implied tax rate of about 13% might seem high compared to the flow of public spending
in relation to GDP as reported in Section 2, Fact 5. Note, however, that the fact refers to the flow of investment
while in our static model flows and stocks are indistinguishable. Translating the flows into stocks, one would
obtain much higher values that are not unreasonably high relative to the outcomes reported in column (3) of
Table 3.

27

welfare loss from underinvestment in infrastructure can be larger, if a country has more than one
border. The border cost decreases average real per capita income by around 2%. The presenceof the border cost τ also changes the distribution of the price index (see panel b of Figure 4).
If there is a border friction, the prices of the foreign varieties rise compared to the prices of thelocal varieties and, infrastructure investment moves away from the border. As a result, the priceindex achieves its minimum in more remote (from the border) locations. In the extreme casewith prohibitive border costs, we have the autarky case where the price index has a U -shapewith the minimum at the central location.
Figure 4: How higher discrete border costs change the distribution of infrastructure investment
and price levels across space(a) Investment(b) Price levels

Notes. iH (x) and iF (x) refer to the non-cooperative (Nash) infrastructure investment distributions, and iH0 (x)and iF 0 (x) show the same loci with a higher border cost. See Table 2 for the parameterization and Table 3 fornumerical results.

To assess the role of infrastructure in explaining the border effect, we perform the following
experiment. We set the infrastructure investment i(x) at all locations to its average value underthe benchmark parameterization ī (which is 131.8). In this case, the distribution of infrastructure
is flat and does not affect the size of the border effect. All other parameters and variables remain
fixed. Then, we simulate trade volumes within and between countries and estimate the bordereffect generated by the model. We find that the estimate of µ2 drops from 0.80 to 0.65. Thismeans that the variation in infrastructure investments explains around 19% of the border effect.
The rest is explained by the border friction τ and the correlation between the border dummy
and distance generated by the model.37 In other words, the border effect identified in a gravity
37

That correlation amounts to 71%. It arises from the fact, that pairs of locations characterized by short28

Table 4: Robustness checks

Benchmark:
(1)
(2)
(3)
(4)

m(x) = 1000, s̄ = 500,
n = 100, σ = 2.7m(x) = 10000s̄ = 700n = 70σ = 3.4

(1)
γ

(2)
δ

(3)
τ

(4)
4W

(5)
Inf ra

0.86

1.65

1.32

0.8%

19%

0.85
0.86
0.86
0.80

1.50
1.69
1.66
1.83

1.35
1.31
1.32
1.12

0.7%
0.9%
0.9%
1%

13%
21%
20%
22%

Notes: We fix the moments measured in European and French data, modify our choiceof free parameters, and obtain new calibrated values for γ, δ, τ , (columns (1), (2), (3)).
Columns (4) and (5) show the welfare costs resulting from an inefficient infrastructure
investment, and the relative importance of infrastructure in explaining the border effect,
respectively.

model that ignores variation in transport infrastructure over space is biased upward by 19%.
The discrete border friction τ = 1.32 explains about 59% of the border effect, and 22% is dueto the correlation between the border dummy and distance.38
We also perform robustness checks regarding the chosen values of m(x), s̄, n, and σ. In
particular, we change the value of one of these parameters, re-calibrate the model, and assess
the role of infrastructure in explaining the border effect as well as the size of welfare losses.
Table 4 summarizes the results. As can be seen, a rise in the population density (see row (1) inthe table) barely changes the calibrated values of γ and τ and the welfare losses. The value of δ
decreases from 1.65 to 1.50. Since the value of δ falls, the variation in infrastructure investments
becomes less important and, consequently, the role of infrastructure in explaining the bordereffect becomes less pronounced. In contrast, an increase in the geographical size of countriess̄ (row (2)) raises the value of δ and, thereby, increases the role of infrastructure. The valuesof γ and τ and the welfare losses do not substantially change. A decrease in the number ofinternal regions n from 100 to 70 (row (3)) has a minor impact on the values of the calibrated
parameters, welfare losses, and the role of infrastructure. Finally, a rise in σ (row (4)) has asubstantial impact on the calibrated values of the parameters (especially, on τ ), while the impact
on the role of infrastructure and welfare losses is small. The role of infrastructure increases from
19% to 22% and the welfare losses increase from 0.8% to 1%.
distances tend to be within-country and, thus, have a border dummy of zero while the opposite is true for long
distances.
38
This as a statistical artefact that arises from the high correlation between distances and the border dummy.
It implies that if i(x) = ī and τ = 1, the model still generates a statistical border effect.

29

5.4

The role of country asymmetries

We study asymmetries with respect to countries’ populations (given area), or with respect toareas (holding population constant). Figure 5 illustrates these cases, where Home is always
assumed the ‘bigger’ country, and we distinguish between cases with and without an explicit
discrete border friction τ . In panels a and c, both countries have the same geographical extension,
but Home has a higher population (and, hence, a higher density). Specifically, we set mH (x) =1100 and mF (x) = 900.39 In panels b and d, Home has a larger geographical extension, but
the same density m(x) as Foreign. The figures show that, regardless of whether or not there
is a discrete border cost and regardless of the nature of the asymmetry, the larger country
wishes to invest more (in the sense that the mode of the distribution is higher). However, incontrast to the symmetric case, the planner solution involves a concentration of investment inthe ‘bigger’ economy; with an explicit border friction, the planner solution can even be bimodal(panel d). In all cases, the Nash equilibrium yields global underinvestment, including at theborder. However, the spatial structure differs across scenarios.40 The ‘bigger’ country severely
underinvests, but the ‘smaller’ one may overinvest relative to the planner solution. This isparticularly pronounced when the source of asymmetry is density; in this case, the location withthe strongest underinvestment typically is an interior location in Home. When asymmetry iscaused by geographical size, the extent of underinvestment is strongest in the border region.
Interestingly, overinvestment in Foreign under Nash implies that the smaller country may
gain from non-cooperation (assuming away any transfers between countries in the first-best
outcome). In panel c, in the first-best outcome, average real per capita income at Foreign is7.04, while in the Nash outcome it is 8.37, i.e., non-cooperation outperforms cooperation byaround 19%. In contrast, Home’s average income is 9.74 the first-best outcome, while it 9%
lower under Nash (8.87). Hence, asymmetry in population density across countries may increase
the welfare losses (caused by the misallocation of infrastructure in the Nash equilibrium) of thelarger country and decrease those of the smaller country (that may even gain). Thus, underasymmetry, welfare effects of non-cooperation are substantially more substantial than in thesymmetric case (where the average welfare loss was just about 0.8%). A similar observation
emerges in panel d, where Home’s welfare loss under Nash relative to the first-best is around
2.7%, while Foreign gains around 6% from non-cooperation.41
39

Compared to the benchmark configuration with mH (x) = mF (x) = 1000, world income expressed in the
numeraire is the same.
40
In the Nash equilibrium, the infrastructure investment profile has a discontinuity at the border (caused by
the asymmetry between the countries).
41
We also consider the case when both countries have the same total income with Home being larger in a30

Figure 5: The distribution of infrastructure investment when Home is ‘bigger’ than Foreign(a) Population size (τ = 1)(b) Geographical size (τ = 1)(c) Population size (τ = 1.32)(d) Geographical size (τ = 1.32)

Notes. iH (x) and iF (x) refer to the non-cooperative and iw (x) to the central-planer and optimal infrastructure
investment distributions. The default parameterization follows Table 2. Panels (a) and (c): m(x) is 1100 and 900
for domestic and foreign locations, respectively. In the non-cooperative outcome with τ = 1.32, the tax rate is
13.2% in Home and 13.3% in Foreign. Average real per capita income is 8.87 and 8.37, respectively. The levelof inequality is 1.15 and 1.13. Panels (b) and (d): The geographical size of Home and Foreign is 750 and 250,
respectively. In the non-cooperative outcome with τ = 1.32, the tax rate at Home and Foreign is 13.8% and12.0%, respectively. Average real per capita income is 8.87 and 8.08, respectively. The level of inequality is 1.16
and 1.01.

5.5Intercontinental trade

So far, we have studied a world of two countries which are connected by land-borne trade. Now
we study how the emergence of inter continental trade affects the intracontinental distribution
geographical size, but less densely populated (the world total income remains fixed). In this case, we findthat Foreign loses from non-cooperation, while Home gains. This suggests that the effect of population density
on welfare losses is stronger than that of the geographical area. A number of robustness checks confirm thisconclusion.

31

of infrastructure investment, trade, welfare, and the size of the border effect. We do this byassuming that there is a third country, call it rest of the world (RoW), which supplies anddemands goods to and from Home and Foreign via a harbor that is located at address 0 in
Home. We also assume that RoW’s supply and demand capacity is exogenous to the outcomesin Home and Foreign. In particular, we do not model the spatial extension of RoW, and treat
it as a mass point at location 0.
By construction, this constellation creates a coastal country (Home) and a hinterland (Foreign). It also breaks symmetry between Home and Foreign, as any location in Home now ismore central than any region in Foreign, even with a uniform distribution of infrastructure investment: on average, consumer prices will be lower in Home than in Foreign. However, withendogenous infrastructure investment, there will be additional effects that tend to exacerbate
inequality both between Home and Foreign as well as within them.42
Panels (a) and (b) in Figure 6 show how the intracontinental infrastructure investment
distribution changes due to the emergence of intercontinental trade with RoW. In panel (a)RoW is considered to produce the same number of varieties as Home and Foreign together (thatis, it has the mass of 1000). In this case, the share of trade volumes from RoW to Home andForeign in the total income of those countries constitutes around 10%,43 reflecting the share ofimports (in total income) of EU from the rest of the world in 2010. In Home, there will be a
massive reallocation of spending towards the coastal locations where imports from RoW crowdout varieties from locations within Home and Foreign. Investment falls rapidly with increasing
distance from the harbor and is lower than in the benchmark case (intracontinental trade only)
in about 80% of all locations in Home. In particular, Home will invest substantially less at theborder with Foreign. With the infrastructure schedule dramatically more skewed in Home, thedistribution of real wages will also become more uneven, so that trade with RoW makes Homea more unequal economy.
Simulations show that in Foreign, now a hinterland, incentives for investment barely change,
because there are two competing factors: On the one hand, all else equal, the presence of
RoW should result in more investment. On the other hand, this effect is mitigated by theremoteness of RoW and the reallocation of infrastructure investment in Home away from theborder with Foreign. However, the emergence of RoW increases the intracontinental bordereffect, because it diverts investment away from the border zone. This means that, in a standard
42

Another application of this model variant may be to poor coastal countries in Africa, which trade mostlyintercontinentally, and where intracontinental infrastructure and trade are underdeveloped.
43
Such a low share (taking into account the size of RoW) is explained by the remoteness of RoW and the factthat only (1 − α) share of total income is spent on industrial goods.

32Figure 6: Overseas trade and the distribution of intracontinental transport infrastructure
investment(a) “Large RoW”(b) “Small RoW”

Notes. iH (x) and iF (x) refer to the Nash infrastructure investment distributions without a third country,
while iH0 (x) and iF 0 (x) refer to those when there is trade with a third country (rest of the world: RoW). The
parameterization is as follows: σ = 2.7, δ = 1.65, γ = 0.86, α = 0.5, q(x) = q = 1, b = 1, τ = 1.32, m(x) = 1000
for all locations at Home and Foreign, and s̄ = 500. In Panel (a) RoW has the mass of 1000, in (b) it has themass of 40.

gravity equation, the estimated border dummy should grow larger with the increasing importanceof intercontinental trade despite the fact that border related trade costs have not changed.
Specifically, under the benchmark parameterization the presence of RoW increases the size ofthe border effect by around 24% (from −0.8 to −0.99).
In panel (b) of Figure 6, we consider a case where RoW is much smaller than Home andForeign (with a mass of 40). In this case, the infrastructure profile at Home still has a humpshape. However, there is more investment in coastal areas and less in the hinterland comparedto the benchmark case (of intracontinental trade only).
A rise in trade with RoW increases welfare in the coastal country but has minor effects
in the hinterland (Foreign), where inequality also remains essentially unchanged. In contrast,
trade with RoW has a substantial non-monotonic effect on inequality in Home. When the size of
RoW is small, inequality in Home decreases (since the distribution of the infrastructure becomesflatter (see panel b in Figure 6)). When RoW is big, inequality rises, as the infrastructure profile
is highly skewed towards the border with RoW (see panel a in Figure 6). Table 5 summarizes
the effects of trade with RoW on Home and Foreign under the benchmark parameterization.

33

Table 5: Overseas trade: Inequality and WelfareHome

Foreign

WelfareInequality

Tax rate

WelfareInequality

Tax rate

Size of RoW is 0:

1.0000

1.14

13.2%

1.0000

1.14

13.2%

Size of RoW is 40:

1.0243

0.26

13.2%

1.0000

1.14

13.2%

Size of RoW is 1000:

1.4658

33.62

11.2%

0.9949

1.25

13.1%

Notes: Calibration as in Table 2; Rest of the World (‘RoW’) is modeled as a mass point
at location 0. When the size of RoW is zero, welfare is normalized to unity.

5.6

The role of “natural” borders

As we discussed in Section 5.2, infrastructure underinvestment around national borders can bealso explained by the fact that borders could endogenously arise in mountain regions or close torivers. In this case, low investment is caused by high cost of investing in transport infrastructure
rather than by the political externality emphasized in our theory. In this section, we performseveral numerical experiments that allow us to assess this mechanism quantitatively. In contrast
to the calibration exercise summarized by Table 2 (where the cost of investing in infrastructure
q(x) is flat), we numerically explore the case where q(x) is higher around the border. Specifically,
we assume that q(x) equals 2 (and then 2.5) on some interval of locations around the border,
while at all other locations q(x) remains equal to unity as in the benchmark case. In otherwords, q(x) is assumed to be a step function. As the length of such an interval we consider 5%(and then 10%) of the total geographical size of each country. We then recalibrate the model
matching the same moments in the data and decompose the effect of infrastructure on the bordereffect into the political and the “natural” border mechanisms.
Table 6 summarizes our findings. In particular, column (1) reports the calibrated values ofτ for different scenarios (the calibrated values of γ and δ have barely changed). An exogenous
border friction τ and higher costs of investing in border regions have similar effects. Thus, arise in the cost or the length of the interval where the cost is higher leads to a lower calibrated
value of τ . For instance, when q(x) is equal 2 on the 5% border interval, the value of τ drops
from 1.32 to 1.22. Thus, difficult territory in border regions plays the same role as an exogenous
border friction.
As before, to isolate the role of infrastructure in determining the border effect, we assume aflat distribution of infrastructure (keeping all other parameters fixed) and compute the bordereffect generated by the model. Column (2) reports the results. Not surprisingly the role of34

Table 6: The role of “natural” borders

Benchmark:
(1)
(2)
(3)
(4)

(1)
τ
1.32
1.22
1.14
1.18
1.08

(2)
Inf ra: T E
19%
36%
50%
44%
62%

(3)
Inf ra: P M E
19%
17%
14%
16%
13%

q(x) = 1 everythere
q(x) = 2 on 5%
q(x) = 2 on 10%
q(x) = 2.5 on 5%
q(x) = 2.5 on 10%
Notes: We assume that q(x) is higher on some interval around the border. The rows
report the chosen values of q(x) and the length of the interval as a percentage of thetotal geographical size of a country. Column (1) reports the calibrated values of τ ineach case. Columns (2) and (3) report the overall role of infrastructure in explaining
the border effect and the role of the political mechanism, respectively. TE : total effect;
PME : effect attributable to the political mechanism.

infrastructure substantially increases. In the benchmark case, the distribution of infrastructure
explains around 19% of the border effect, that share goes up significantly when the difficulty ofgeography is higher in border regions.
We then explore the pure role of the political mechanism (PME) in explaining the bordereffect. Given the calibrated values of the parameters derived in the case when q(x) is a step
function, we make q(x) a flat function (setting q(x) to its average value everywhere), find the
optimal distribution of infrastructure in this case and then compute the border effect generated
by the model. The difference (as a percentage of the actual border effect) between the bordereffect derived when only q(x) is flat and the one derived when the whole infrastructure profile isflat is considered as the pure effect of the political mechanism. That is, we try to understand by
how much the border effect rises compared to the case when the infrastructure profile is flat, if we
add only the political mechanism (assuming away the differences in topology across locations).
Column (3) in Table 6 reports the findings. As can be seen, the role of the political mechanism
is smaller compared to the benchmark case, but nevertheless remains relatively substantial. In
the benchmark specification, the political mechanism accounts for 19% of the border effect, inthe presence of the “natural” border, it accounts for 13% − 17%. In particular, the magnitudeof the network effect falls, when the value of q(x) around the border or the length of the borderinterval rises. Overall, the calibration results suggest that a more difficult geography aroundthe border which roughly doubles the role of infrastructure in restricting trade leads to a slight
reduction in the relative role of the political mechanism by about 2 percentage points. Hence,the political mechanism loses significance as natural border barriers grow, but – at least withour calibration – the effect is relatively small.
35

Finally, we also assess how the presence of a natural border can affect the welfare loss
associated with the misallocation of infrastructure investment. As in Section 5.3, we consider
the difference between the average real per capita income in the first-best and non-cooperative
outcome assuming now that q(x) is equal to 2.5 on the 10% border interval (rather than beingflat). In this case, the welfare loss is about 1%, which is slightly higher than that in thebenchmark case, 0.8%. Note that similar results take place if we decrease the population sizearound the border instead of increasing the cost of infrastructure investment. In particular, if
we decrease the population size from 1000 to 400 on the 10% border interval (keeping q(x) flatas in the benchmark) and then calibrate the model44 , the welfare loss is around 1.6%, which is
twice as high as in the benchmark case.

6

Supporting evidence

Two important prediction of our theoretical model are: (i) locations within jurisdictions are
better connected by transport infrastructure than locations lying in two different jurisdictions,and (ii) inefficiently low infrastructure investment in border regions explains part of the so calledborder effect. In this section we use data from the European Union to provide some supporting
evidence for these hypotheses.
Data.

We use data provided by Pisu and Braconnier (2013) on bilateral minimum road dis-

tances and minimum travel times between 220 cities in 22 countries in continental Europe.45
The data come from Bing Maps Route Service and relate to the year 2012. The authors provide
population weighted proxies at the country-pair level which we use in our analysis. We merge
this information with bilateral trade data for the year of 2010 provided in the World Input
Output Database (WIOD) project (Timmer et al., 2015). Crucially, that data base provides
accurate measures for domestic trade within countries. Unfortunately, there is no information
on Switzerland, so that our analysis rests on 212 = 441 country pairs. We focus on the 16
non-service sectors contained in WIOD. Finally, we obtain CES weighted geographical distancemeasures (based on great-circle distances), common language and contiguity measures fromMayer and Zignago (2011).46
44

Compared to the case when q(x) is equal to 2.5 on the 10% border interval, the calibrated values of theparameters barely change. For instance, the value of τ is equal to 1.09.
45
The countries are: Austria, Belgium, Bulgaria, Czech Republic, Denmark, Estonia, France, Germany, Greece,
Italy, Hungary, Latvia, Lithuania, Luxembourg, Netherlands, Poland, Portugal, Romania, Slovenia, Slovak Republic, Spain, Switzerland.
46
Head and Mayer (2002) show that measuring distance between countries by a geometric (CES) average of
distances between major cities dramatically reduces the border effects in European data. These authors, however,36Straight-line distance, road distance, and travel time.

We start by showing direct evi-

dence on relative underinvestment in European border regions. The left-hand diagram in Figure
7 shows that the ratio of road distance to the straight-line distance (the so called divergence)is on average higher between cities in different countries than between cities within the same
country. Intranational road trips are 9% longer than what the great-circle (bird-flight) distancewould indicate; inter national road trips are 30% longer. The difference is statistically significant
at the 1% level. As the mid panel in Figure 7 shows, the average travel speed on domestic roads
is 88 km/h while it is 100 km/h on international road trips; the difference again being significant
at the 1% level. However, this disadvantage for domestic trips does not outweigh the advantageof shorter connections. The hypothetical speed of traffic for overcoming the bird-flight distanceis 83 km/h in domestic links versus 77 km/h in international links. This difference is statisticallysignificant at the 5% level.47
Figure 7: Distance versus travel time in intra- and international bilateral links

100
0

0

50

50

100
50
0
International Intranational

Avg. direct speed (km/h)
150

150

Avg. road speed (km/h)

100

150

Avg. excess distance (%)

International Intranational

International Intranational

Notes. Average excess distance is the %-ratio between road distance and bird-flight distance, both in km. Avg.
road speed denotes the average travel speed on the fastest road connection, in km/h, while avg. direct speed
refers to the average theoretical speed on the most direct (= bird-flight distance), in km/h.

Table 7 conditions the difference between domestic and international trips on distance andalso controls for destination and origin fixed effects. Column (1) reports a simple linear regressionthat correlates the log of travel time (in minutes) and the log of geographical (great-circle)
distance. The obtained elasticity is 0.96. Moreover, column (2) shows that travel time is
do not account for real transportation costs.
47
Note that the hypothetical travel speed on the bird-flight distance is given by the ratio between the travel
speed on the road and the excess length of the road trip over the bird-flight distance.

37

Table 7: Bird-flight distance, road distance, and travel time across EU countries(1)(2)
log travel time

Dep.var.:Border (0,1)
ln bird-flight distance

0.959***(0.0137)(3)(4)
log road distance

0.282***(0.0418)
0.893***(0.0128)

1.041***(0.0113)(5)(6)
log travel time

0.217***(0.0325)0.990***(0.00945)

ln road distance

0.0799***(0.0232)

Constant-0.0795(0.0890)0.344***(0.0837)-0.0253(0.0727)0.300***(0.0613)0.924***(0.0104)-0.0721(0.0682)

R-squared

0.983

0.986

0.992

0.994

0.994

0.905***(0.00987)
0.0526(0.0657)
0.994

Notes: OLS regressions. All regressions contain complete sets of separate exporter and importer fixed
effects. Robust standard errors (clustered at the pair-level) in parentheses, *** p < 0.01, ** p < 0.05, *p < 0.1. N = 441.

significantly larger between different countries than within countries, the difference being equal
to about 28%. Including the dummy variable for domestic connections brings down the elasticityof travel time with respect to distance to 0.89, again hinting at some concavity in the relationshipbetween distance and trade costs.48 Columns (3) and (4) repeat this exercise, but use the log ofroad distance (in km/h) as the dependent variable. It turns out that road distances that crossa political border are longer by some 22%, controlling for bird-flight distance. Finally, columns(5) and (6) show that domestic travel time is longer by 8% given road distances.
The border effect.

Finally, we turn to an investigation of the border effect. To this end, we

use a generalization of equation (19)Xijs = exp [µ1 ln Tij + µ2 Bij + exis + imjs + ijs ] ,where s indicates the sector. Bilateral trade costs are Tij and Bij , where the latter is a dummythat takes value one for an inter national and value zero for an intranational transaction. Tij =(1 + Dij )δ0 eδ1 CLij +δ2 CON Tij models trade costs as a function of distance-related transportation
costs Dij , common language CLij and contiguity CON Tij . Dij can either be the weighted
great-circle distance between i and j, or the shortest (similarly weighted) road distance, or
the minimum (similarly weighted) travel time. Following current practice, we estimate Poisson
48

The hypothesis of a unitary elasticity is rejected at the 1% level.

38

Table 8: The border effect and the role of infrastructure: Poisson models(1)
Dep.var.:SampleBorder (0,1)
ln great-circle distance

PPML-0.804***(0.170)-1.112***(0.128)ln road distance

(2)
full
PPML
-0.547***(0.180)-1.171***(0.123)ln travel time
Common language (0,1)
Contiguity (0,1)
Constant

Observations
R-squared

(3)
(4)
(5)
(6)
aggregate tradenon-contingent pairs
PPML
PGMM
PGMM
PGMM-IV-0.422** -2.063*** -1.546*** -1.411***(0.176)(0.458)(0.428)(0.462)-1.204***(0.135)0.761***(0.132)0.326**(0.157)14.92***(0.881)0.840***(0.134)0.215(0.154)15.58***(0.872)-1.361***(0.124)0.841***(0.125)0.134(0.141)16.07***(0.802)

441
0.989

441
0.990

441
0.991

-0.295(0.414)-1.365***(0.139)-0.145(0.355)-1.443***(0.163)-0.134(0.367)17.66***(0.835)17.66***(0.835)18.03***(0.834)

377
0.977

377
0.977

377

(7)

(8)
(9)
sectoral trade
full
PPML
PPML
PPML
-0.775*** -0.503*** -0.391***(0.0915)(0.101)(0.101)-1.142***(0.0674)-1.211***(0.0693)-1.391***(0.0713)0.763***
0.843**
0.841***(0.0803)(0.0793)(0.0792)
0.320***
0.200**
0.131(0.0845)(0.0843)(0.0816)
12.49*** 13.24*** 13.63***(0.780)(0.788)(0.758)
7,004
0.959

7,004
0.961

7,004
0.961

Notes: Pseudo Maximum Likelihood (PPML) or Generalized Methods of Moments (PGMMs) estimations of Poisson moels. All models contain complete
sets of separate exporter and importer fixed effects (exporter × sector, importer × sector effects in case of sectoral trade data). Robust standard errors inparentheses, *** p < 0.01, ** p < 0.05, * p < 0.1.

models, as this setup is best suited do deal with zero trade flows and heteroskedasticity arisingfrom additive error terms.49
Column (1) of Table 8 reports a frequently observed pattern in gravity models: the tradeelasticity of bird-flight distance is close to −1, and a common language or a adjacency (contiguity) have strongly positive effects on trade flows. The estimated border effect is −0.804, signallingthat international trade flows are by about 55% (1 − exp(−0.804) = 0.55) smaller than intranational ones, holding other trade determinants (such as market sizes, multilateral distances – allcaptured by fixed effects – geographical distance, contiguity, and common language) constant.50
Using the log of road distance or travel time instead of great-circle distance as a proxy oftransportation costs (columns (2) and (3)), the estimated border effect increases from −0.804 to−0.547 and to −0.422, respectively. Hence, international trade is only by 42% and 34% smaller,
respectively, than intranational trade, holding other determinants of trade constant.51 Hence,49
See Head and Mayer (2014). As a default, we use a Poisson pseudo maximum likelihood estimator (PPML),
but for the instrumental variable estimation we estimate the Poisson model using a a generalized methods ofmoments (PGMM) approach. Note that results do not qualitatively depend on using the Poisson approach.
Log-linear OLS models yield qualitatively similar results; see Table 10 in the Appendix.
50
The measured border effect seems small compared to earlier findings in the literature, e.g., by Nitsch (2000).
This has several reasons: First, we use the more consistent distance measure proposed by Head and Mayer (2002),
which has been shown to shrink the border effect in a sample of European data from the early 1990s (see footnote
46). Second, the use of PPML yields a substantially smaller border effect than OLS, which dominated the earlier
literature; compare Table 10 in the Appendix. Third, thanks to the WIOD project, we have more accurate
information on within-country trade. And fourth, our data refers to a very recent period (2010) and lower bordereffects probably simply show the effects of ongoing economic integration in the EU.
51
1 − exp (−0.547) = 0.42, and 1 − exp(−0.422) = 0.34, respectively.

39

it appears that, in Europe, using proxies of transportation costs that account for the quality of
infrastructure brings down the estimated border effect by between 24% and 38%.
Sensitivity Analysis.

Treating borders as exogenous to sectoral trade shocks ijs , the iden-tification assumption underlying our analysis can be stated as cov ( ijs , Tij | Bij , exis , imis ) = 0.
A high realization of ijs could incite countries i and j to invest into reducing Tij , which could
bias the distance effect µ1 away from zero. How this affects our coefficient of interest, µ2 , isnot obvious, though. Tij depends on investment Ii and Ij , but also on investment by countries
k 6= i, j located on the shortest travel route between i and j. So, if i and j boost investment due
to a positive shock in ijs , they also lower Tii and Tjj , which increases Xii and Xjj , and thiscontributes to moving µ2 upwards at given Ik .
To contain the danger of biased results, we restrict the sample to non-contingent countries,
the transport links between which are importantly shaped by countries other than the trade
partners themselves. We also instrument trade costs Tij by the weighted sum of Tkk , where
k belongs to the set K of countries through which any transport from i to j has to transit.
The assumption is that the covariance of bilateral, sectoral trade shocks ijs and infrastructure
investment Ik , k 6= i, j is zero. More precisely, we focus on travel time and apply the average
travel speeds measured in within-country k ∈ K links to the great-circle distance from i to j.
The partial correlation between this instrument and actual travel time Tij is 0.46. Columns (4)to (5) of Table 8 show the results. First, note that excluding the 61 contingent pairs strongly
increases the absolute value of the border effect (column (4)).52 Second, replacing great-circle
distance by travel time lowers the absolute value of the border effect quite significantly (column(5)).53 Third, instrumenting travel time further slightly reduces the absolute value of the bordereffect but increases that of travel time (column (6)).
Next, we turn from aggregate to sectoral data. Columns (7) to (9) show that our argument
remains robust. Estimated coefficients change only minimally. If we drop all trade relationshipsof any country that account for more than 5% of total sector-level trade and which are, thus
presumably important enough to affect investment decisions, we find a substantially higher
border effect, but replacing great-circle distance by road distance or travel time shrinks theeffect; see Table 11 in the Appendix.54
52

The common language dummy turns insignificant as we have only very few non-contingent countries with
common language in the sample.
53
A similar result obtains when using road distance; see Table 11 in the Appendix. Interestingly, the elasticityof trade with respect to travel time is almost unchanged by restricting the sample to non-contingent pairs.
54
Table 12 in the Appendix runs sector-level regressions and finds statistically significant border effects in 12
out of 16 sectors. In all of these sectors, the border effect is (algebraically) smaller when road distance or travel40

Finally, we also check whether our results are driven by the recent eastward enlargementof the EU. Excluding the 10 new eastern European EU member countries present in our data,
we find an algebraically smaller border effect. Still, the measured border effect changes upon
replacing great-circle distance by road distance or travel time in the way suggested by our model.

7

Extensions and robustness analysis

In this section, we discuss some potential extensions of the framework.

7.1

Toll roads

Today, many countries operate public toll tax systems for freight traffic. The share of interregional highways subject to decentrally administered toll systems ranges from 6 percent in the
U.S. to 52 percent in France. Countries such as Germany and Austria have centrally administered distance dependent road pricing for lorries. User fees may be contingent on a wide arrayof factors such as the situation of the environment (e.g., smog), the degree of congestion, thetime at which a road is traveled, and so on.
How a toll system affects the main argument in this paper depends very much on its specificdesign. Here we study a particularly interesting and relevant configuration. Suppose governments decide on the infrastructure allocation across space, but rather than taxing consumers
through lump-sum taxes, they tax road users per unit of distance. Further assume that the tax
varies continuously on the space of addresses and that it works just as our iceberg transportation
costs, albeit with the shaved transported good not lost but transferred into the governments
coffers and redistributed to households. In that case, the government has two margins of action:
it sets a distribution of fees, f (s), where s ∈ [0, s̄], and decides on the infrastructure allocation,
R s̄
i (s) . Total income from fees will be B = 0 f (s) R̄ (s) ds, where R̄ (s) measures total traffic
through location s. Note that R (s) depends on the domestic and on the foreign distribution of
infrastructure. If the government is free to spend B on whatever infrastructure distribution it
prefers, and does not impose any additional tax, it will find it optimal to make fees dependent
on the distance to the border, with higher fees the closer the border. Moreover, it will concentrate its spending as before in the central regions of the jurisdiction. The reason for this result
is identical to the one discussed above: The government cares only about home welfare, thus
taxing foreigners and transferring the receipts to home citizens is a welcome option.
time is used instead of great-circle distance.

41

If governments are not allowed to spend toll income on places other than those where theincome has been generated, there will be a direct link between infrastructure investment andtransit volume, f (s) R̄ (s) /q (s) = i (s) . Governments will then set f (s) such that native welfare
is maximized. By imposing high fees in border regions, governments tax foreign consumers morestrongly than domestic ones; however, the implied high investment volumes are of little value
for domestic consumers. By imposing high fees in the center, governments affect domestic
consumers, but also achieve high utility for them. The implied distribution of infrastructureneed not exhibit excessive spatial variation, but it still can; the exact outcome depending onunderlying model parameters.

7.2

Private-public partnerships (PPP)

Since ancient times, governments have asked private agents to construct and operate roads orrailways and allowed them to take fees for road usage. In England, from the 17th century
on, Parliament entrusted private companies with concessions to run certain road connections;around 1830 there were about 48,000 km of so called turnpike roads; see Lay (1992). The system
was also used in the US. Currently, cash-strapped governments around the world use various
types of PPP to finance the construction of transport links.
We provide a simple model of such a situation. Each government in the two countries auctions
the exclusive right to run a road segment which coincides with the space of the government’s
jurisdiction. The firm with the highest bid gets the license. In a competitive auction, theequilibrium bid amounts to exactly the profits that the would-be monopolist can achieve. In
principle, the government can let the monopolist choose the preferred investment schedule i (s)and a fee structure f (s) . Or it can regulate either i (s) or f (s) . Here, we consider an example
where two contiguous countries each entrust a private monopolist to choose an optimal iM (s),given a regulated user fee p per unit of traffic.
The monopolist in Home sets iM (s) to maximize profits
M

π i



Z s̄

Z s̄
R̄(x)dx −=p0q(x)iM (x)dx,

(20)

0

where R̄(x) is the measure of the total traffic through location x, iM (x) is infrastructure investment at location x, and q(x) denotes the associated cost per unit of investment.55
55

In the above specification, we assume that the government pays a fixed price p per unit of the traffic to themonopolist and finances this with a lump-sum tax. This assumption removes the distortive effects of p on theinfrastructure profile.

42

Total traffic through location x is given byZ x Z 2s̄
0

x

x


R(y, z)dz dy,

R(y, z)dz dy +R̄(x) =
whereZ 2s̄ Z x0

Y (z)T (y, z)1−σR(y, z) = (1 − α)(1 − t ) R s̄.
1−σdv
0 T (v, z)M

Here, R(y, z) is interpreted as the traffic from y to z: a quantity measure of trade in products
produced at y and transported to z. It is determined by demand at location z and the transportation costs from y to z. Note that in general R(y, z) is not equal to R(z, y). Finally, tM is
the income tax imposed by the government to finance the infrastructure investments and Y (z)is the gross income at location z. We assume that the monopolist takes the income tax andthe location sizes as given. As in the benchmark case, the monopolists at Home and Foreignchoose the corresponding infrastructure investments non-cooperatively. In the symmetric Nashequilibrium with no asymmetries in the cost of infrastructure and the location size, the domestic
infrastructure profile (in case of the interior solution) is given byı̃M (x)δ =
pγ(1 − α)(1 − t̃M )(σ − 1)  L,MR,Mφ̃(x) + φ̃
(x) ,
q

L,M

R,M

where as before φ̃(x) (φ̃(x)) represents the aggregate marginal profits due to a rise intraffic from the right (the left) to the left (the right) of location x.
Similar to the social-planner scenario, the monopolist infrastructure profile has a hump shape
in autarky and is skewed towards the border with the foreign country in the open economy
case. It is also straightforward to show that the presence of costs associated with crossing theborder will redistribute the infrastructure away from the border, amplifying the border effect.
However, there is a conceptual difference between iH (s) and iM (s) . Under certain parameter
constellations, the monopolist finds it optimal to chose zero investment in peripheral locations.
This is because higher investment in s has two effects on total traffic. On the one hand, traffic
through s goes up, increasing total traffic. On the other hand, traffic through other regions goes
down because of the corresponding changes in the price indices (a substitution or trade diversion
effect). This tends to decrease total traffic. In some cases the negative effect prevails over the
positive one, so that iM (s) = 0. In contrast, the social planner sets i (s) > 0 for all s excepts = 0.
Figure 8 shows the optimal infrastructure distributions chosen by the monopolists under43

autarky (panel a), and under international trade (panel b), and compares them with the Nashsocial-planner or the first-best solutions. The parameterization is benchmark with τ = 1 and thefee p is set such that the monopolist and social-planner scenarios yield the same overall investment. As can be seen, the monopolist chooses investment schedules that exhibit substantiallymore spatial variation than the one picked by the social planner. Moreover, as discussed above,
there is zero investment at peripheral locations in both panels. In the case of international trade,the monopolist invests much more around the border even compared to the first-best outcome.
This can generate a smaller or even no border effect, but comes at cost of zero investments inmany peripheral locations (that are in fact driven into autarky).
Figure 8: Equilibrium investment loci: social planner vs. monopolist.
(a) Autarky(b) Trade

Notes. Solid black curves (iM (x) and iM H (x)) refer to investment profile resulting from non-cooperative monopolists. Dashed red curves (ia (x) and iH (x)) refer to (non-cooperative Nash) solutions. The parameterization
is as follows: σ = 2.7, δ = 1.65, γ = 0.86, τ = 1, α = 0.5, q(x) = q = 1, b = 1, m(x) = 1000 for all locations, ands̄ = 500. In Figure (a), p = 0.4. Spending on infrastructure (in terms of the tax rate) in this case is 13.4 percent.
In Figure (b), p = 0.275. Spending on infrastructure in each country in the Nash equilibrium is 13.1 percent.

7.3

Internal labor mobility

In the model we assume away the effects of internal labor mobility on the infrastructure profile.
Here we offer some discussion. First, note that the underinvestment problem in border regions
relative to the first-best occurs regardless of the form of a (non-degenerate) distribution of
economic activity. This is because the share of non-internalized benefits of investment are
higher the closer one gets to the border, regardless of distributional details.
In contrast, how the endogenous adjustment of infrastructure investment shapes the distribution of economic activity and the size of the border effect, is hard to determine analytically44

as the social planner needs to internalize the effects of infrastructure on the endogenous population density. Moreover, multiple equilibria are possible. At the same time, the intuition behind
the impact of labor mobility on the equilibrium infrastructure profile seems to be relatively
straightforward.
With internal labor mobility (associated with some adjustment costs to avoid extreme solutions), the equilibrium can be considered as the outcome of the following multi-stage variation of
the model. The economy starts with some distribution of population, which results in a certain
distribution of infrastructure investment chosen by the social planner. Then, given this infrastructure profile, agents decide about their location and, as a result, the population distributionchanges. Given the new distribution of population, the social planner adjusts the distributionof infrastructure and continues doing so until convergence.
To understand the potential effects of labor mobility on the infrastructure profile in the above
variation of the model, we distinguish between high and low border frictions, and we assume auniform distribution of population as the initial one. With relatively high border costs, after the
first stage, the distribution of the price index will have a U -shaped form with the minimum atsome internal location that is relatively close to the central one (see panel b in Figure 4). In thiscase, at the second stage the population will move away from the border to benefit from lower
aggregate prices at internal locations. This in turn will move the infrastructure distribution
even further from the border as well and so on. As a result, labor mobility will magnify theconcentration of infrastructure around internal locations and, therefore, increase the magnitudeof the border effect. The opposite happens when the border frictions are low. When the bordercost is low, after the first stage the price indexes will be the lowest relatively close to the border(but not necessarily at the border as showed by the simulations), implying that the population
will move closer to the border. This will lead to more investment around the border and so on.
In this case, labor mobility will magnify the concentration of infrastructure around the border
and, thereby, decrease the magnitude of the border effect. However, underinvestment in Nashrelative to the first-best in border regions will remain, regardless of the distribution of economic
activity.
The reasoning above suggests that there can exist a certain threshold value of the border costτ̂ such that if τ > τ̂ , labor mobility increases the border effect, otherwise the opposite happens.
Further (perhaps, quantitative) analysis is needed to explore the actual effect of labor mobility on
infrastructure investments. Meanwhile, if the infrastructure investments were initiated/started
in the past when the border costs were quite high, then in the model with labor mobility one
might expect a higher border effect, rather than a lower one.
45

7.4

The political economy of infrastructure investment

An alternative way of modelling the endogenous infrastructure distribution is a majority rulevoting system. For any distribution of the transport infrastructure, each household derives a certain utility level which is represented by its indirect utility function. As a result, each household
has its own preferences over the continuum of infrastructure distributions that are determinedby the geographical location of this household: a household prefers more infrastructure investments around its location. For instance, for a household located at the periphery (x = 0),
the optimal infrastructure profile on [0, s̄] is a decreasing curve with maximum at x = 0. It is
possible to show that the household preferences defined above are single peaked. As a result,the political equilibrium infrastructure profile is the profile chosen by the median voter, whichis the household located at x = s̄/2. So, in the absence of asymmetries across locations, themedian household will choose a hump shaped profile with maximum at s̄/2. In other words, themedian voter solution is qualitatively equivalent to the social planner solution. Thus, all thequalitative results derived in the paper can be extended to the framework with a majority rulevoting system.

8

Conclusions

This paper develops a simple theoretical model where consumers demand goods from the entire
world, but the world is fragmented into jurisdictions which set infrastructure investment schedules in a non-cooperative way. Governments care only for the welfare of their own constituency
and ignore the effects that their decisions have on foreign consumers; this basic externality leads
to global underinvestment. The lower the geographical distance of a location is to the politicalborder, the bigger is the externality since a larger share of the benefits caused by investment
accrues to foreign consumers. Hence, the externality has a spatial structure: infrastructure underinvestment is stronger in poltically peripheral regions of jurisdictions rather than in central
ones.
The local lack of infrastructure investment makes imports from other countries more expensive than imports from other regions from the same country, even if geographical distance orincomes of trading partners are the same. Our infrastructure story may therefore contributetowards unpacking trade costs and explaining the border effect first highlighted by McCallum(1995) and since then discussed in a voluminous empirical literature.
We use intra- and international trade flows data from Europe to calibrate the model. We

46

find that about 20% of the empirically observable border effect is due to low infrastructure
investment around national borders. In our simulations, the border effect is magnified by the
emergence of intercontinental trade and appears larger, when countries are asymmetric withrespect to their sizes. We argue that privatization of construction and operation of roads may
not undo the border underinvestment problem; similarly, it also emerges under a majority voting
system.
Information from the Bing Maps Route Service allows us to show that international roaddistances are about 22% longer than intranational ones and that travel is 28% longer, holding
bird-flight distance constant. The econometrically identified border effect falls from -0.80 in aconventional setup to -0.55 when road distance is used rather than bird-flight distance. Hence,using transportation cost proxies that account for infrastructure brings down the border effect,
as implied by our theoretical argument.
Future work should endogenize the distribution of economic activity by allowing intranationalmigration of workers or/and firms. Moreover, to carry out a full-fledged quantitative analysis,
it would be needed to conduct the analysis on a plane rather than a line with realistic topology
as in Allen and Arkolakis (2014); this is a non-trivial generalization, since it requires not only
to characterize optimal investment schedules for given routes, but also to solve for the layout of
optimal transportation networks.

47

References
Allen, T. and C. Arkolakis (2014). Trade and the Topography of the Spatial Economy. Quarterly
Journal of Economics, 129(3): 1085-1140.
Anderson, J.E. and E. van Wincoop (2004). Trade costs. Journal of Economic Literature, 42:
691-751.
Anderson, J.E. and E. van Wincoop, E. (2003). Gravity with Gravitas: A Solution to the Border
Puzzle. American Economic Review 93(1): 170-92.
Behar, A. and A. Venables (2011). Transport Costs and International Trade. In: de Palma, A.,
R. Lindsey, E. Quinet, and R. Vickerman, eds., A Handbook Of Transport Economics, Edgar
Elgar.
Behrens, K., P. Picard (2011). Transportation, freight rates, and economic geography. Journalof International Economics 85(2): 280-291.
Casella, A., and J. Rauch, Overcoming Informational Barriers to International Resource Allocation: Prices and Ties, Economic Journal 113(1): 21-42.
Chen, N. (2004). Intra-national versus international trade in the European Union: why donational borders matter? Journal of International Economics 63(1): 93-118.
Combes, P-P., M. Lafourcade and T. Mayer, 2005. The Trade Creating Effects of Business andSocial Networks: Evidence from France, Journal of International Economics 66:1-29.
Combes, P-P. and M. Lafourcade, 2005. Transport Costs. Measures, Determinants, and Regional
Policy Implications for France. Journal of Economic Geography 5:319-349.
Congressional Budget Office, 2010. Public Spending on Transportation and Water Infrastructure.
US Congress, Washington, DC.
Cosar, K. and B. Demir (2015). Domestic Road Infrastructure and International Trade: Evidence
from Turkey, Journal of Development Economics, forthcoming.
Costinot, A. and A. Rodriguez-Clare (2014), Trade Theory with Numbers: Quantifying theConsequences of Globalization, Handbook of International Economics, Vol. 4, Chapter 4, Gita
Gopinath, Elhanan Helpman, and Kenneth Rogoff (eds.), Elsevier: Holland.

48

Courant, P.N., and A.V. Deardorff (1992). International Trade with Lumpy Countries. Journalof Political Economy 100(1): 198-210.
Donaldson, D. (2014). Railroads and Raj: Estimating the Impact of Transportation Infrastructure. American Review of Economics, forthcoming.
Donaldson, D., and R. Hornbeck, Railroads and American Economic Growth: a “Market Access”
Approach, Quarterly Journal of Economics, forthcoming.
Duranton, G., P. Morrow, and M. A. Turner (2014). Roads and Trade: Evidence from the US.
The Review of Economic Studies 81 (2): 681-724.
Gramlich, E.M. (1994). Infrastructure Investment: A Review Essay. Journal of Economic Literature 32(3): 1176-1196.
Head, K., and T. Mayer (2014), ”Gravity Equations: Workhorse, Toolkit, and Cookbook”,
Handbook of International Economics, Vol. 4, Chapter 3, Gita Gopinath, Elhanan Helpman,
and Kenneth Rogoff (eds.), Elsevier: Holland.
Head, K., and T. Mayer (2002), Illusory Border Effects: Distance mismeasurement inflates
estimates of home bias in trade, CEPII Working Paper 2002-1.
Helliwell, J.F. (1998). How Much Do National Borders Matter? The Brookings Institution.
Hummels, D., V. Lugovskyy and A. Skiba (2009). The trade reducing effects of market powerin international shipping, Journal of Development Economics 89: 84–97.
ITF-OECD (International Transport Forum) (2012), Statistics Brief-Infrastructure Investment,
Paris.
Krugman, P. (1991). Increasing Returns and Economic Geography. Journal of Political Economy
99: 383-499.
Fujita, M., P.R. Krugman, and A.J. Venables (1999). The Spatial Economy. Cambridge, MA:
MIT Press.
Lay, M.G. (1992), Ways of the World: A History of the World’s Roads and of the Vehicles That
Used Them, New Brunswick: Rutgers University Press.
Limao, N., and A.J. Venables (2001). Infrastructure, Geographical Disadvantage, Transport
Costs, and Trade. World Bank Economic Review 15(3): 451-479.
49

Mayer, T., and S. Zignago (2011), Notes on CEPII’s distance measures: the GeoDist Database,
CEPII Working Paper 2011-25.
McCallum, J. (1995). National Borders Matter: Canada-U.S. Regional Trade Patterns. American
Economic Review 85(3): 615-23.
McCann, Ph. (2005). Transport costs and new economic geography. Journal of Economic Geography 5: 305–318.
Milgrom, P., and C. Shannon (1994). Monotone Comparative Statics. Econometrica 62(1): 157180.
Nitsch, V. (2000). National Borders and International Trade. Evidence from the European Union.
Canadian Journal of Economics 33(4): 1091-1105.
Okubo, T. (2004). Border Effect in the Japanese Market – A Gravity Model Analysis. Journalof the Japanese and International Economies 18: 1-11.
Persson, J. and D. Song (2010), The Land Transport Sector: Policy and Performance, OECD
Economics Department Working Papers, No. 817, OECD Publishing.
Pisu, M. and H. Braconier (2013), Road Connectivity and the Border Effect: Evidence from
Europe, GEP Research Paper Series 2013/06.
Rose, A.K., and E. van Wincoop (2001). National Money as a Barrier to International Trade:
The Real Case for Currency Union. American Economic Review 91(2): 386-390.
Rossi-Hansberg, E. (2005). A Spatial Theory of Trade. American Economic Review 95(5): 14641491.
Samuelson, P. (1952). The Transfer Problem and Transport Costs: the Terms of Trade when
Impediments are Absent. Economic Journal 62: 278–304.
Timmer, M., E. Dietzenbacher, B. Los, R. Stehrer, G. de Vries (2015), “An Illustrated User
Guide to the World Input-Output Database: the Case of Global Automotive Production”,
Review of International Economics, doi: 10.1111/roie.12178.
Wei, S. (1996). Intra-National versus International Trade: How Stubborn are Nations in Global
Integration? NBER Working Paper 553.

50

Winston, C. (1985). Conceptual Developments in the Economics of Transportation: An Interpretative Survey. Journal of Economic Literature 23: 57-94.
Wolf, H. (2000). Intranational Home Bias in Trade. Review of Economics and Statistics 82(4):112-128.
Venables, A. (2005). Spatial disparities in developing countries: cities, regions, and international
trade. Journal of Economic Geography 5(1): 3 - 21.

51

Appendix A: Proofs
In the Appendix, we provide all the necessary proofs for the lemmas and propositions in the paper.

Proof of Lemma 1
Property (i)For three different locations x, y, and z such that x < y < z,
T (x, y)T (y, z)

=
=
>
=

γ
Z z
1
1−δ
i (s)
ds
δ−1 y
x
!γ
Z y
Z z
Z y
Z z
1
1
1
1−δ
1−δ
1−δ
1−δ
1+
i (s)
ds +
i (s)
ds +
i (s)
ds
i (s)
ds
2
δ−1 x
δ−1 y
(δ − 1) x
y
γ

Z y
Z z
1
1
1−δ
1−δ
i (s)
ds +
i (s)
ds
1+
δ−1 x
δ−1 y

γ
Z z
1
1−δ
1+
i (s)
ds
= T (x, z).
δ−1 x

1+

1
δ−1

Z y

1−δ

i (s)

γ 
ds
1+

Property (iv)
The behavior of T (x, z) with respect to geographical distance can be checked by looking at the derivativeof T (x, z) with respect to z. Specifically, we have thatT (x, z)

=

1+

1
δ−1

Z z



Tz (x, z)=Tzz (x, z)

=

⇐⇒

1
γ 1+
δ−1

1−δ

i (s)

γ
ds

,

x

Z z

γ−1

i
1 h
1−δ
i (z)
> 0,
δ−1
x


h
i2

1−δ
1

γ−1
Z z
δ−1 i (z)
1


1−δ
−δ
γ 1+
i (s)
ds
− i (z) i0 (z) ≷ 0Rz
(γ − 1)
1−δ
1
δ−1 x
1 + δ−1i(s)dsx(γ − 1)
1/γ(T (x, z))

i (s)

1−δ

1−δ

i (z)
δ−1

ds

!2
−δ

≷ i0 (z) i (z).

The left-hand side shows the effect of a marginal increase in distance on Tz (x, z) under the assumption that i (z + dz) = i (z) . It reflects variation in trade costs due to an increase in distance, holding
infrastructure constant. The right-hand side makes the opposite assumption and reports the change inTz (x, z) due to the difference in infrastructure investment between z and z + dz, holding the sheer costsof distance constant. T (x, z) is convex (as in Krugman), if the left-hand side dominates.

52

Property (v)00

We compute the elasticity of substitution between investment at two different locations s0 , s ∈ [x, z] asfollows−

d ln [i (s0 ) /i (s00 )],(x,z) ∂T (x,z)
d ln ∂T∂i(s0 ) / ∂i(s00 )where for any s ∈ [x, z]
γ−1

Z z
∂T (x, z) d.
1−δ1−δi (s) .
i (s)
ds
≡γ 1+
∂i (s)
δ−1 x
As a result, the elasticity of substitution is given by−d ln [i (s0 ) /i (s00 )]1= < 1.
000−dδ ln |i (s ) /i (s )|δProperty (vi)
The Lagrangian for the cost minimizing problem can be written as follows:
Z zΛ ({i (s)} , λ) = q

i (s) ds + λ 1 +

x

1
δ−1

Z z
i (s)

1−δ

ds − T̄

1/γ


,

x

where q is the cost of infrastructure investment at location s. It is straightforward to see that the firstorder conditions imply that, for any two locations k, l ∈ [x, z],i (k) = i (l) .
Taking into account the budget constraint, we derive thatnhio1/(δ−1)
i (k) = i (l) = (z − x) / (δ − 1) T̄ 1/γ − 1.

Proof of Proposition 1
To find the optimal infrastructure investments on [0, s̄], we first formulate and analyze a discrete modification of the social planner’s maximization problem (which approximates the actual continuous maximization problem). Remember that the social planner solves({ia (x) , ta }x∈S = arg max (1 − t)

 1−α
Z
σ−1

Z

q (x) i (x) dx ≤ btLm̃ (x) v(x)dx
x∈S

x∈S

53

)
.

whereZv(x)=T (x, z)

1−σ

dz

z∈S

=

Z s̄ 
1+
0

Z x
=
0

1
δ−1

Z z

1
1+
δ−1

Z x

1−δ

i (s)

γ(1−σ)
dz

ds

x
1−δ

i (s)

γ(1−σ)Z s̄ 
dz +
1+
ds
x

z

1
δ−1

Z z

1−δ

i (s)

γ(1−σ)dz.
dsx

In the discrete version of the problem, we assume that the geography of the economy consists of npoints (transportation hubs) uniformly distributed on [0, s̄]: 0 = x1 < x2 .. < xn = s̄. We define thedistance between location xi and xi+1 by 4n : that is, x2 − x1 = ...xn − xn−1 = 4n . We also assume thatthe transportation costs between two locations, xi and xj , depend on the level of infrastructure at thelocation of the producer and the intermediate locations between xi and xj (not including the location of
the consumer) and the distance between the locations determined by 4n .56 Specifically, if a product issent from xi to xj (xi < xj ), the transportation costs are
j−1

T (xi , xj ) =

1 X
1−δ
1+
i (xk )
4n
δ−1

!γ
.

k=i

We then formulate the social planner’s problem in the case of the discrete geography in the followingway:{ia (xi ) , ta }i=1..n = arg max




n
X

(1 − t)m̃ (xi ) v(xi )4n


! 1−α
σ−1 

,

(21)



i=1

subject tonXq (xi ) i (xi ) 4n ≤ btL,

(22)

i(xi ) ≥ 0, i = 1..n.

(23)

i=1

Here,

Pi−1




v(xi ) = 4n 
 P
n


k=1

k=i+1

1
1 + δ−11
1 + δ−1i−1P!γ(1−σ)1−δi (xj )

4n

+




,
!γ(1−σ)kP1−δi (x )
4
+1 

j=k

j

(24)

n

j=i+1

where the first term in the brackets describes the welfare derived from trade with locations on the left
side of xi , the second term describes the welfare derived from trade with locations on the right side of56

The fact that the transportation costs between xi and xj do not include the level of infrastructure investment
at the destination location (the location of the consumer) means non-symmetric transport costs. However, taking
the limit (n → ∞) will imply symmetric transport costs between any locations, as in this case the contributionof the infrastructure of a single location into the total transport costs will be negligible.

54

xi , and one stands for the transportation costs from xi to xi (that are normalized to unity). In this case,the social planner’s problem is to choose the level of transportation infrastructure at each location xithat maximizes the social welfare. This maximization problem is the approximation of the maximization
problem in the main text (see (8)). Specifically, taking the limit (n → ∞), one can derive the actual
maximization problem described in the main text. This in turn implies that the solution of the continuous
maximization problem is the limit of the solution of the discrete problem (when n → ∞).
Note that the existence of the global maximum in the above discrete maximization problem follows
from the continuity of the objective function and the fact that the objective function is maximized on thecompact subset of Rn (which is given by the constraints in (22) and (23)). Moreover, it is straightforwardγ(1−σ)Pk
1−δ
1to show that if γ(σ − 1)(δ − 1) < 1 (as assumed in the paper), 1 + δ−1
4nis
j=i+1 i (xj )a concave function in i (x) = {i (xj )}j=1..n for any i and k. This in turn implies that ṽ(xi ) is concave
in i (x) as the sum of concave functions, but not strictly concave, as v(xi ) does not depend on i(xi ).
Pn
However, it is straightforward to show that i=1 m̃ (xi ) v(xi ) is strictly concave with respect to i (x).
Finally, since (1 − α) / (σ − 1) is assumed to be strictly less than one, the objective function in (21) isstrictly concave in infrastructure investments, i(x).
Next, we formulate the corresponding Lagrange function that can be written as follows:Λ ≡ (1 − t) 4n

n
X

! 1−α
σ−1
− λ0

m̃ (xi ) v(xi )

i=1

n
X

!
q (xi ) i (xi ) 4n −btL ,i=1

where λ0 is the Lagrange multiplier of the corresponding constraint. The necessary and sufficient condition
for the global maximum is that∂Λ∂i (xi )∂Λ∂t=0, i = 1..n,=0.

Next, we find the expression for ∂Λ/∂i (xi ). Specifically,∂Λ(1 − t) (1 − α)=4n∂i (xi )
σ−1

4n

n
X

m̃ (xl ) v(xl )! 1−ασ−1 −1 nX

l=10m̃ (xl ) (v(xl ))i(xi ) − λ0 4n q (xi ) .

(25)

l=1

One can show that0(v(xl ))i(xi )=2(4n ) γ(σ − 1)i(xi )

−δ

i
X
k=1

0
(v(xl ))i(xi )=2(4n ) γ(σ − 1)i(xi )

−δ

n
X
k=i

0

(v(xl ))i(xi )

=

P
1 l−1
1−δ
1+
i (xj )4n
δ − 1 j=k!γ(1−σ)−1

k
P
1
1−δ
i (xj )4n1+
δ − 1 j=l+1

0

if i < l,!γ(1−σ)−1
if i > l,if i = l.

55

As a result,

P
P
3
i−1
 n
(4n ) γ(1−α)(1−t)
l=1 m̃ (xl )
k=ii(xi )δ
∂Λ∂i (xi )=(4n
3 (1−α)(1−t) Pn
l=i+1
i(xi )δ

(4n )1
1 + δ−1kP!γ(1−σ)−1 
1−δi (xj )

4n



j=l+1

(26)

1− 1−ασ−1
l=1 m̃ (xl ) v(xl ))

Pn


Pi
m̃ (xl ) 

1
1 + δ−1

k=1

+
(4n

l−1
P

!γ(1−σ)−1 i (xj )

1−δ

4n



j=k

1− 1−ασ−1
l=1 m̃ (xl ) v(xl ))Pn−λ0 4n q (xi ) .
Finally,
∂Λ
∂t
λ0

− 4n

=

n
X

! 1−α
σ−1
+ λ0 bL = 0 ⇐⇒m̃ (xl ) v(xl )

l=1

(4n

=

Pn

l=1 m̃ (xl ) v(xl ))

1−α
σ−1

.

bL

(27)

∂Λ
Note that since ∂i(x|i(xi )=0 = ∞ (because of γ(σ − 1)(δ − 1) < 1), ia (xi ) is strictly greater thani)zero for all i = 1..n. That is, the global maximum {ia (xi ) , ta }i=1..n does not include zero investments
and, therefore, solves the following system of equations

Pi−1
a

l=1

δ

q(xi )i (xi )4n bLγ (1 − α) (1 − ta )Pnm̃ (xl ) 

=

4n


(28)

i=1 m̃ (xi ) v(xi )

l=i+1


Pi
m̃ (xl ) 

k=1+
q (xi ) ia (xi ) 4n1−δia (xj )

j=l+1

Pn
Pn

n
X

1
1 + δ−1k=i!γ(1−σ)−1 kP

1
1 + δ−1l−1P!γ(1−σ)−1 
1−δia (xj )

4n



j=k

Pn

i=1 m̃ (xi ) v(xi ),= bta L.

i=1

As the solution of the continuous maximization problem is the limit of the solution of the discrete
problem (when n → ∞), it is straightforward to see that the optimal infrastructure investment functionia (x) and the tax rate ta solve
δ

=

ta

=

ia (x)

bLγ (1 − α) (1 − ta )  L
φ (x) + φR (x) ,
q(x)
R s̄
q (s) ia (s) ds
0
,
b

56

whereR t a 1−δ γ(1−σ)−1
1
1
+
i
(r)
dr
dt
ds
δ−1 s
x
,
R s̄
m̃ (s) v(s)ds0 R s a 1−δ γ(1−σ)−1
R s̄
Rx
1
m̃ (s) 0 1 + δ−1 t i (r)
dr
dt ds
x
.
R s̄
m̃ (s) v(s)ds0Rxm̃ (s)0φL (x)=

φR (x)=

R s̄ 

Proof of Proposition 2
Property (ii)Note that the derivative of ia (x) with respect to x can be written as follows:δ−1q(x)δia (x)

0

0 
0 
⇐⇒
φL (x) + φR (x)

0 
0 
δ
bLγ (1 − α) (1 − ta ) φL (x) + φR (x)− q 0 (x)ia (x)δ= bLγ (1 − α) (1 − ta )0=

(ia (x)) + q 0 (x)ia (x)(ia (x))



.

δ−1

q(x)δia (x)We have that





0
φL (x)

0
φR (x)m̃ (x)

 
R s̄
x

1
1 + δ−1

Rt

i (r)
x

1−δ

dr

γ(1−σ)−1=R s̄−m̃ (x)

 
Rx
0

1
1 + δ−1

Rx
t

1−δ

i (r)

dr



γ(1−σ)−1
Rx
Rx
1−δ
1
dt − 0 m̃ (s) 1 + δ−1
ds
i
(r)
dr
s

,
m̃ (s) v(s)dsγ(1−σ)−1

Rs
R s̄
1−δ
1
dt + x m̃ (s) 1 + δ−1
i
(r)
dr
ds
x

0
γ(1−σ)−1

=

R s̄
0

.

m̃ (s) v(s)ds

It is straightforward to see that0 
0φL (0) + φR (0)

0 
0
φL (1) + φR (1)



> 0,
< 0.
δ

δ

Since q 0 (x) is continuous on [0, s̄] and ia (0) = ia (s̄) = 0, q 0 (0)ia (0) = q 0 (s̄)ia (s̄) = 0. This in turnimmediately implies that
0

= ∞

0

= −∞.

(ia (0))(ia (s̄))Property (iii)First, we show that ia (x) is symmetric around x = s̄/2. To do so, we use the fact that the objectivefunction of the planner’s problem is strictly concave, implying that there is a unique solution of (11).

57Indeed, if there are two different solutions of (11), then there are two different stationary points, which
is not possible with a strictly concave objective function. It is straightforward to see that if there is novariation in the cost of infrastructure investment and the household size across the locations: q(x) = q
and m(x) = m for any x ∈ [0, s̄], symmetric investments indeed solve (11). Taking into account theuniqueness of the solution, we can conclude that the symmetric infrastructure profile delivers the global
maximum of the maximization problem. Finally, if ia (x) is symmetric around x = s̄/2, the transportation
costs are symmetric and, thereby, v(x) is symmetric as well (this immediately follows from the definitionof v(x) (see (9)).
Next, we prove that ia (x) has a hump shape with the peak at x = s̄/2. Note that the optimal
investment profile can be considered as a unique fixed point of a certain functional J : E −→ E. Here,
E is the subset of the space of symmetric (around x = s̄/2) continuous functions on [0, s̄], which isdetermined by the constraints in the maximization problem. Specifically, the functional is given by
J(ia (x)) =



1/δ
bLγ (1 − α) (1 − ta )  L
φ (x) + φR (x)
,
q

where

R t a 1−δ γ(1−σ)−1
dt
ds
i
(r)
dr
s
0
x
,
R s̄
v(s)ds0R s a 1−δ γ(1−σ)−1R s̄ R x 
1
dt
ds
i
(r)
dr
1
+
δ−1 t
x
0
.
R s̄
v(s)ds0R x R s̄ φL (x)=

φR (x)=

1
1 + δ−1

We then show that if ia (x) has a hump shape with the peak at x = s̄/2, then J(ia (x)) has a humpshape. This in turn means that the fixed point of the functional has a hump shape. That is, the optimal
investment profile has a hump shape.
Consider a function ia1 (x) ∈ E that has a hump shape. We define ia2 (x) as the value of the functional
at ia1 (x): i.e., ia2 (x) = J(ia1 (x)). Next, we prove that ia2 (x) has a hump shape. To show this, we consider
the derivative of ia2 (x). It is straightforward to see thatia2 (x)δ−10(ia2 (x)) = 2

bLγ (1 − α) (1 − ta )
H(x),
R s̄
qδ
v(s)ds0

whereZ s̄ 
H(x) =

1+
x

1
δ−1

Z z

1−δ

ia1 (s)γ(1−σ)−1
ds

Z x
dz −

x

1+
0

1
δ−1

Z x

ia1 (s)1−δγ(1−σ)−1
ds

dz.

z

The first thing to notice is that H(s̄/2) = 0 (which follows from the symmetry of ia1 (x)). Consider

58

any x < s̄/2, then the function H(x) can be written as follows:
Z 2x 
H(x)

1+

=
x

1
δ−1

Z s̄ 
1+
+
2x

Z z

1−δ

ia1 (s)γ(1−σ)−1
Z x
1+
ds
dz −
0

x

1
δ−1

Z z

1−δ

ia1 (s)γ(1−σ)−1dsdzzγ(1−σ)−1

1−δ

ds

1
δ−1

Z z

ia1 (s)

Z x

1
δ−1

dz,

x

where
Z s̄ 
1+2x1−δ

ia1 (s)γ(1−σ)−1dz > 0.
dsx

Note that as ia1 (s) is symmetric around x = s̄/2 and has a hump shape at s̄/2, for any 4 ∈ (0, x]
ia1 (x + 4) > ia1 (x − 4) .
This in turn means that for any 4 ∈ (0, x],
1+

Z x+4

1
δ−1

1−δ

ia1 (s)ds < 1 +

x

1
δ−1

Z x

ia1 (s)

1−δ

ds,

x−4

implying that
1
1+
δ−1

Z x+4

!γ(1−σ)−11−δ
ia1 (s)
ds


> 1+

x

1
δ−1

γ(1−σ)−1Z x1−δia1 (s)ds,x−4

as γ(1 − σ) − 1 is negative. As a result, it is straightforward to see that
Z 2x 
1+
x

1
δ−1

Z z

ia1 (s)1−δγ(1−σ)−1
Z x
ds
dz >
1+

x

0

1
δ−1

Z x

1−δ

ia1 (s)γ(1−σ)−1
ds
dz.

z

That is, for any x < s̄/2, H(x) > 0. Similarly, it is possible to show that for any x > s̄/2, H(x) < 0.
0Thus, (ia2 (x)) is strictly greater than zero 0 on x ∈ [0, s̄/2) and strictly less than zero on (s̄/2, 1]. Thismeans that ia2 (x) has a hump shape. Therefore, the solution of (11) has a hump shape.
Finally, we show that v(x) has a hump shape as well. We have that

0

v (x)

=

Z x
1+
0

=
=

1
δ−1

γ(σ − 1)i (x)
δ−1

1−δ

γ(σ − 1)i (x)
δ−1

1−δ

Z x
i (s)

1−δ

γ(1−σ)Z s̄ 
ds
dz +
1+

z

x

1
1+
δ−1

Z z
i (s)

1−δ

x

Z z

1−δ

i (s)

dz

γ(1−σ)−1
Z x
ds
dz −
1+

Z x

x

0

1
δ−1

H(x).

Taking into account the properties of H(x), we can conclude that v(x) has a hump shape.

59!0γ(1−σ)dsx

Z s̄ 

1
δ−1

z

!

γ(1−σ)−11−δ
ia1 (s)dsdz

Proof of Proposition 3
Recall that when m(x) = m and q(x) = q, the optimal infrastructure profile ia (x) maximizes the following
function (up to an irrelevant constant):

W (I, A) =


Z
1−A

(1−α)/(σ−1),v(x)dx Zi (x) dxx∈Sx∈S

where I = {i (x)}x∈{0,s̄} and A = q/bL (where L = ms̄). The partial derivative of W (I, A) with respect
to A is given by∂W (I, A)
=−
∂A
0

00

Z

0

(1−α)/(σ−1)< 0.
v(x)dx Zi (x) dxx∈Sx∈S

We say that I % I if and only if i (x) ≥ i (x) for all x ∈ S. It is straightforward to see that if I 0 % I 00 ,
then

00

∂W (I 0 , A)
∂W (I 00 , A)≤
for any A.
∂A∂A

The latter follows from the fact that v(x) is increasing in infrastructure investment. Thus, W (I, A) is
submodular and satisfies single crossing property. This in turn implies that a rise in A decreases the
optimal infrastructure profile I a (see details in Milgrom and Shannon, 1994). That is, ia (x) falls for allx. This proves statements (i)-(iii) in Proposition 3.
As noted above, if m(x) is the same at all locations, then L = ms̄ and
!
R s̄
 1/δ
γ (1 − α) (bms̄ − 0 q (s) ia (s) ds)  LRφ (x) + φ (x)
.
q(x)

a

i (x) =In this case, the partial derivative of ia (x) with respect to s̄ is given by (here we use the fact thatia (s̄) = 0)

Z s̄
0


γ (1 − α) a∂ia (x)
1−δ
L
R
L
R
a
=
(i (x))
φ (x) + φ (x) (bms̄ −q (s) i (s) ds) + bm φ (x) + φ (x)
.
∂s̄
q(x)δ
s̄
0
The derivatives of φL (x) and φR (x) with respect to s̄ are given byRx0

φj (x) s̄ =0

1
1 + δ−1

R s̄ a 1−δ γ(1−σ)−1i (r)drds − v(s̄)φj (x)s,
R s̄
v(s)ds0where j ∈ {L, R}. Thus,R s̄ aγ(1−σ)−11i (r)1−δ dr )ds
(1+ δ−1sRs̄∂i (x)bmγ (1 − α) a1−δ v(s)ds
0


 .
=
(i (x))
a
)
L
R
∂s̄
q(x)δ
R s̄
+ φ (x) + φ (x) 1 − s̄v(s̄)(1−tv(s)dsa2s̄(1−ta )

Rx
0

0

0
As can be seen, if x is sufficiently close to s̄, then φj (x) s̄ > 0 (as φj (s̄) = 0) and, thereby, ∂ia (x) /∂s̄ > 0.

60

Moreover, if the cost of infrastructure is uniform,∂ia (x)> 0 for all x.
∂s̄This is due to fact that if q(x) = q for all x, v(x) is symmetric around x = s̄/2 and has a hump shape.
As a result, v(s̄) ≤ v(s) for any s ∈ S. This in turn means thatZ s̄v(s)ds> s̄v(s̄) =⇒01−s̄v(s̄)(1 − ta )R s̄v(s)ds0> 0.

The World Planner Solution
Recall that the world planner solution is given byδiw (x) =
2bLγ (1 − α) (1 − tw )  L,w
φ (x, τ ) + φR,w (x, τ ) ,
q

where


R t w 1−δ γ(1−σ)−11(1−σ)I(t,s)
i
(r)
dr
dt
ds
τ
1
+
δ−1 s
0
x
,
R 2s̄
v(s)ds0R 2s̄ R x (1−σ)I(t,s) 
R s w 1−δ γ(1−σ)−1
1
dr
dt ds
τ
1 + δ−1 t i (r)
x
0
.
R 2s̄
v(s)ds0R x R 2s̄φL,w (x, τ )=φR,w (x, τ )=The derivative of φL,w (x, τ ) with respect to x is given by

φL,w (x, τ )

0

=

x

R 2s̄
x


R t w 1−δ γ(1−σ)−1
R x (1−σ)I(x,s) 
R x w 1−δ γ(1−σ)−11
1
τ (1−σ)I(t,x) 1 + δ−1
i
(r)
dr
dt
−
τ
dr
ds
1
+
δ−1 s i (r)
x
0
.
R 2s̄
v(s)ds0

Similarly,
0
φR,w (x, τ ) =x
R x (1−σ)I(t,x) R x w 1−δ γ(1−σ)−1R 2s̄ (1−σ)I(x,s) 
R s w 1−δ γ(1−σ)−1
1
1
1
+
− 0 τ
1 + δ−1
i
(r)
dr
dt
+
τ
dr
ds
δ−1 x i (r)
t
x
.
R 2s̄
v(s)ds061This implies that if τ > 1, thenlimx→s̄−0τ0φL,w (x, τ ) =x

R 1−σ 2s̄s̄

1
1 + δ−1

R t w 1−δ γ(1−σ)−1R s̄ 
R s̄ w 1−δ γ(1−σ)−1
1
i
(r)
dr
dt
−
1
+
dr
ds
δ−1 s i (r)s̄0< 0, andR 2s̄
v(s)ds00
lim φR,w (x, τ ) =x→s̄−0R s̄ 

− 0x

R s̄ w 1−δ γ(1−σ)−1
R s w 1−δ γ(1−σ)−1R 
1
1
1−σ 2s̄
1 + δ−1
i
(r)
dr
dr
dt
+
τ
1
+
ds
δ−1 s̄ i (r)
t
s̄
< 0.
R 2s̄
v(s)ds000In the same way, one can show that limx→s̄+0 φL,w (x, τ )and limx→s̄+0 φR,w (x, τ )are positive.
xx

As a result, the infrastructure profile has a double-hump shape. At Home, it is decreasing around s̄, atForeign it is increasing.

Proof of Lemma 2
As in the proof of Proposition 1, we first formulate and analyze a discrete modification of the social
planner’s maximization problem, which approximates the actual continuos maximization problem, andthen take the limit. Recall that the home social planner solves
(
)
Z s̄
 1−α
Z s̄
σ−1
H
i (x), tH x∈[0,s̄] = arg max (1 − t)v(x)dxqi (x) dx ≤ bLtH ,t,i(x)

0

0

where
Z 2s̄
v(x)

=

τ (1−σ)I(x,z) T (x, z)

1−σ

dz

0

Rx
=

0

γ(1−σ)γ(1−σ)Rx
Rz
R s̄ 
1−δ
1−δ
1
1
i
(r)
dr
dz
+
i
(r)
dr
dz
1
+
1 + δ−1
δ−1 x
z
x
.

γ(1−σ)
R
R
R
2s̄
s̄
z F
1−δ
1−δ
1
1
+τ 1−σ s̄ 1 + δ−1
i
(s)
ds
+
i
(s)
ds
dz
δ−1 s̄
x

To formulate the corresponding discrete maximization problem, we consider a uniform partition of
the [0, 2s̄]-interval given by {xi }i=0..2n , where x0 = 0, xn = s̄, and x2n = 2s̄. Then, the discrete analogueof the continuos maximization problem can be written as follows (without loss of generality, we assume
that location n belongs to the home country):


! 1−α
σ−1 
n

X
H
i (xi ), tH i=0..n = arg max (1 − t)v(xi )4n,t,i(xi ) 
i=062

subject toqnXi (xi ) 4n ≤ bLt.

i=0

where

1+

Pi−1

1
1 + δ−1k=0v(xi ) = 4n
+τ 1−σi−1P!γ(1−σ)1−δi (xj )

4n

+

j=k

P2n

k=n+1

1
1 + δ−1nPi (xj )

j=i+1

1−δ

Pn

k=i+1

1
4n + δ−11
1 + δ−1kP!γ(1−σ)kP

1−δi (xj )4nj=i+1

!γ(1−σ)iF (xj )

1−δ

4n

j=n+1

and 4n = 1/n.
The first order conditions are given by∂Λ
∂i (xi )∂Λ∂t=0, i = 0..n,=0,where Λ is the corresponding Lagrange function. It is straightforward to see that∂Λ∂i (xi )

=

∂Λ
∂t

=

n
X

(1 − t) (1 − α)
σ−1
−

n
X

! 1−α
σ−1 −14nv(xi )4n

i=0

n
X

0

(v(xl ))i(xi ) − λ0 4n q,

l=0

! 1−α
σ−1
v(xi )4n+ λ0 bL.

i=0

We have that for i < l,02(v(xl ))i(xi ) = (4n ) γ(σ − 1)i(xi )−δ

i
X
k=0

P
1 l−1
1−δ
1+
i (xj )4n
δ − 1 j=k!γ(1−σ)−1,

for i > l,02(v(xl ))i(xi ) = (4n ) γ(σ − 1)i(xi )−δ

n
X
k=i

2

−δ 1−σ+(4n ) γ(σ−1)i(xi )

τ

2n
X
k=n+1

k
P
1
1−δ
i (xj )4n1+
δ − 1 j=l+1!γ(1−σ)−1

n
k
P
P
1
1
1−δ
1−δ
1+
i (xj )4n +iF (xj )4nδ − 1 j=l+1
δ − 1 j=n+1

0

Finally, (v(xl ))i(xi ) = 0 if i = l.

63!γ(1−σ)−1.

Thus, the optimal infrastructure profile, iH (xi ) i=0..n , solves the following system of equations:Pi−1δqiH (xi )=4n bLγ (1 − α) (1 − tH )Pi−1 P2n1−σ
l=0
k=n+1 τ

l=0


P
 n

k=i

!γ(1−σ)−1 kP

1
1 + δ−1

1−δiH (xj )

4n



j=l+1

Pn

i=0 v(xi )1
1 + δ−1nP

1−δiH (xj )

j=l+1

+

1
4n + δ−1!γ(1−σ)−1 

k
P

1−δ

iF (xj )

4n



j=n+1

Pn

i=0 v(xi )

Pn

l=i+1


P
 i

k=0

+

1
1 + δ−1l−1P!γ(1−σ)−1 
1−δiH (xj )

4n



j=k

Pn

i=0 v(xi ).

Taking the limit, we obtain the solution of the continuous maximization problem:δγ(1−σ)−1 
Rt H
1−δ
i (r)
dr
dt ds
s
0
x
=
R s̄
v(s)ds0 γ(1−σ)−1 
Rs H
R s̄ R x
1−δ
1
dt ds
dr
1 + δ−1 t i (r)
x
0
+
.
R s̄
v(s)ds0γ(1−σ)−1 RR 2s̄ R s̄ H
Rt F
1−δ
1−δ
1
1
1−σ x
1 + δ−1 s i (r)τ
dr + δ−1 s̄ i (r)
dr
dt ds
0
s̄
+
.
R s̄
v(s)ds0R x R s̄ qiH (x)bLγ (1 − α) (1 − tH )1
1 + δ−1

Finally, the optimal tax rate solves
tH =

R s̄
q 0 iH (s) ds.
bL

Proof of Proposition 6
From the expression for iH (x), we can see thatδ−1

δiH (x)iH (x)

0

=

0
R,N
bLγ (1 − α) (1 − tH )  L,Nφ̃
(x, τ ) + φ̃
(x, τ ) .
q

It is straightforward to see that
 R,N
0
φ̃
(x, τ )

> 0 and

x=0

 R,N
0
φ̃
(x, τ )
x=s̄

64

< 0.

Consider the derivative of φ̃L,N(x, τ ) with respect to x. We have thatγ(1−σ)−1γ(1−σ)−1
Rt H
Rx H
Rx
1−δ
1−δ
1
i
(r)
dr
dt
i
(r)
dr
ds
1
+
δ−1 s
x
x
0
=
−
R s̄
R s̄
v(s)dsv(s)ds00γ(1−σ)−1R s̄ H
Rt H
R 2s̄
1−δ
1−δ
1
1
i
(r)
dr
+
i
(2s̄
−
r)
dr
dt
τ 1−σ s̄ 1 + δ−1
δ−1 s̄
x.
+
R s̄
v(s)ds0
R s̄ 

 L,N0φ̃
(x, τ )

1
1 + δ−1

 L,N 0
As can be inferred from the above expression, φ̃(x)> 0. Moreover, as τ 1−σ ≤ 1,

x=0

τ 1−σ

Z 2s̄ 
1+
s̄

1
δ−1

Z t

1−δ

iH (2s̄ − r)γ(1−σ)−1dr

Z s̄ 
dt−

s̄

1+
0

1
δ−1

Z s̄

iH (r)1−δγ(1−σ)−1ds ≤ 0,drs L,N 00δ−1= 0) and(x)≤ 0. Hence, we can conclude that iH (x) x=0 = ∞ (as iH (0)implying that φ̃
x=s̄

0
δ−1
H
H
i (x) x=s̄ is negative, but finite (as i (s̄)> 0).

Proof of Proposition 7
Recall that the infrastructure profile is determined byδiH (x) =R,NbLγ (1 − α) (1 − tH )  L,Nφ̃
(x, τ ) + φ̃
(x, τ ) .
q

It is straightforward to see that if there are additional transport costs for products produced in the foreigncountry, thenγ(1−σ)−1 
Rt H
1−δ
1
dt ds
i
(r)
dr
1
+
δ−1 s
0
x




R R 2s̄R s̄ R s̄
1−σ1−σ1−σ s̄
T
(s,
z)
dz
ds
+
τ
T
(s,
z)
dz
ds
0
0
0
s̄

γ(1−σ)−1 
R s̄ HRt H
R x R 2s̄ 
1−δ
1−δ
1
1
dt ds
τ 1−σ 0
i
(r)
dr
+
i
(2
−
r)
dr
1
+
δ−1 s
δ−1 s̄
s̄




,
+
R s̄ R 2s̄
R s̄ R s̄
1−σ1−σ
T (s, z)dz ds + τ 1−σ 0 s̄ T (s, z)
dz ds
0
0

γ(1−σ)−1 
R s̄ R x 
Rs H
1−δ
1
1
+
i
(r)
dr
dt ds
δ−1 t
0
x

 .
R s̄ R 2s̄
R s̄ R s̄
1−σ1−σ
T (s, z)dz ds + τ 1−σ 0 s̄ T (s, z)
dz ds
0
0

R x R s̄ 

φ̃

φ̃

φ̃

L,N

R,N

(x, τ )=(x, τ )=

Therefore, to explore the direct effect of τ on iH (x), we need to analyze how changes in τ affect
 L,N
0
R,N
R,N
(x, τ ) + φ̃
(x, τ ). Specifically, we find that the sign of φ̃(x, τ ) + φ̃
(x, τ )
is the sameL,Nτ

as the sign of the following expression (remember that taking the derivative, we ignore all the indirect65effects):d

Z x

R(x) ≡

Z s̄ 
1+
x

0

Z s̄

Z x
1+

+
x

Z x

0

Z 2s̄ 

−
0

s̄

1
δ−1


γ(1−σ)−1 ! Z s̄ Z 2s̄
Z t
1
1−σ
1−δ
H
T (s, z)
dz ds
i (r)
dr
dt ds
δ−1 s
s̄
0

γ(1−σ)−1 ! Z s̄ Z 2s̄
Z s
1−σ
1−δ
H
dt ds
T (s, z)
dz ds
i (r)
dr

1
1+
δ−1

t

0

Z s̄

H

i (r)

1−δ

s

1
dr +
δ−1

Z t

H

s̄
1−δ

i (2s̄ − r)s̄γ(1−σ)−1dr!

Z s̄ Z s̄
T (s, z)

dt ds
0

0

As can be seen, R(x) is negative in some left neighborhood of x = s̄, implying that iH (x) falls for all
R s̄
x from this neighborhood. Finally, as 0 iH (x) dx remains the same, iH (x) must rise at some locations
that are relatively far from the border.

66

1−σ


dz ds.

Appendix B: Discrete variant of the model
To match the moments, we consider a discrete version of our framework. We assume that there are 2nlocations uniformly distributed on [0, 2s̄], with n locations in each country. We define 4n = 2s̄/(2n − 1)as the distance between any two adjacent locations. In discrete space, the costs of transportation costs
between i and j (i < j) arej−1

T (i, j) =

4n X
1−δ
1+
i (k)
δ−1

!γ
,

(29)

k=i

which can be rewritten as
T (i, j) =1 + 4n (j − i)

1
δ−1

Pj−1

k=i i (k)

j−i

1−δ

!γ
,

such that transportation costs from i and j are determined by the product of distance between i and j
and the average level of infrastructure between the locations. For sufficiently large n, the above discrete
version of the model approximates the continuous specification (see the proof of Lemma 2 in the Appendix
for more details). In our exercise we set n at 100, meaning that there are 100 regions within eachcountry which trade with each other and foreign locations. Note that given n = 100 and s̄ = 500, thediscrete version of the model does not perfectly approximate the continuous one and, therefore, should
be considered as a discrete variation of the benchmark continuous model which is used to fit the data.57

57

In (29) T (i, j) does not depend on the level of infrastructure at location j. The reason behind is that whenn approaches infinity, it is not quantitatively important whether i(j)1−δ is included into the definition of T (i, j)
or not. In our exercise we found that when n is equal to 100, the inclusion of i(j)1−δ into T (i, j) does notsubstantially affect the calibrated values of the parameters and the quantitative implications of the model.

67

Appendix C: Further empirical results
Table 9: Explaining variance in transportation costs in France
Dep. var.: Ln variable transport costs per km for transits through a département
(1)
(2)
(3)
(4)
(5)
(6)
ln distance to Paris
0.034**(0.015)ln GTC to Paris
0.039**(0.015)ln geography
0.041*** 0.029*** 0.032***0.020**
0.004
0.001(0.013)(0.011)(0.010)(0.008)(0.011)(0.011)ln GDP-0.048***(0.013)ln population-0.186***(0.050)0.167***(0.056)ln area (km2)
Constant

1.590***(0.009)2.026***(0.118)1.112***(0.334)-0.028(0.052)-0.002(0.059)-0.019(0.048)-0.006(0.056)-0.018(0.047)-0.007(0.055)0.087***(0.013)0.068***(0.015)0.067***(0.014)1.110***(0.299)1.059**(0.285)0.967***(0.288)

N
94
94
94
94
94
94
2
adj.R
0.158
0.289
0.333
0.583
0.609
0.616
F − stat.
10.06
9.443
10.66
41.91
41.25
45.17
RM SE
0.097
0.090
0.088
0.070
0.068
0.067
∗∗∗
∗∗
∗
Robust standard errors in parentheses,
p < 0.01, p < 0.05, p < 0.1.
GTC: generalized transport cost. “Geography” measures the difference between the points ofhighest and lowest altitude above sea level in a departement.

68

Table 10: The border effect and the role of infrastructure: OLS regressions(1)
Dep.var.:Border (0,1)
ln bird-flight distance(2)
aggregate trade-1.419***(0.333)-1.707***(0.136)ln road distance-1.003***(0.335)

Common language (0,1)
Constant(4)(5)
sectoral trade(6)-0.784**(0.334)-1.092***(0.144)-2.069***(0.0521)-0.614***(0.148)-0.405***(0.148)-1.708***(0.147)ln travel timeContiguity (0,1)(3)-2.053***(0.0551)0.130(0.135)-0.189(0.171)18.36***(0.909)0.117(0.146)-0.0959(0.169)18.76***(1.015)-1.917***(0.136)0.0400(0.127)-0.0201(0.171)19.06***(0.868)

441
0.949

441
0.949

441
0.950

Observations
R-squared

0.122**(0.0563)-0.276***(0.0760)
16.33***(0.476)

0.124**(0.0590)-0.161**(0.0761)
16.70***(0.502)-2.255***(0.0560)
0.0781(0.0565)-0.0689(0.0766)
16.74***(0.478)

6,975
0.894

6,975
0.893

6,975
0.892

Notes: OLS regressions. All models contain complete sets of separate exporter and importer fixed effects (exporter* sector, importer * sector effects in case of sectoral trade data). Robust standard errors in parentheses, ***p < 0.01, ** p < 0.05, * p < 0.1.

69

70
377
0.997

17.66***(0.837)-0.295(0.415)-2.063***(0.459)-1.204***(0.135)377
0.998

17.90***(0.784)-0.168(0.404)-1.264***(0.126)-1.626***(0.457)377
0.997

17.69***(0.744)-1.365***(0.140)-0.145(0.355)-1.546***(0.428)121
0.993

0.893***(0.147)0.152(0.180)15.59***(0.824)-0.687***(0.170)-1.079***(0.138)121
0.993

0.917***(0.152)0.147(0.174)15.34***(0.775)-1.021***(0.129)-0.584***(0.180)121
0.994-1.248***(0.120)0.892***(0.136)0.0277(0.141)16.01***(0.653)-0.422***(0.162)

5,324
0.999

0.244
(0.166)0.643***(0.0741)
11.20***(0.438)-2.767***(0.164)-0.580***(0.0607)

5,324
0.999

0.295*(0.163)0.652***(0.0745)
11.08***(0.424)-0.564***(0.0582)-2.634***(0.165)

5,324
0.999

-0.724***(0.0607)0.303*(0.161)0.567***(0.0740)
11.60***(0.405)-2.473***(0.165)

(7)
(8)
(9)
Small trade links only
Sectoral data

Notes: Poisson Pseudo Maximum Likelihood estimations. All models contain complete sets of separate exporter and importer fixed effects(exporter × sector, importer × sector effects in case of sectoral trade data). All models contain a common language dummy and a contiguity
dummy (not shown). Robust standard errors in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1. N = 441, R2 between 0.90% and 0.99%.

Observations
R-squared

Constant

Contiguity (0,1)

Common language (0,1)

ln travel timeln road distanceln great circle-distanceBorder (0,1)

(1)
(2)
(3)
(4)
(5)
(6)
Non-contingent pairs only
“Old” EU members only
Aggregate data

Table 11: Sensitivity analysis

71-1.207(0.787)-1.930***(0.526)(2)(1)-2.084***(0.408)-0.948***(0.229)-1.147(0.756)-1.938***(0.502)(2)(1)-2.263***(0.377)-0.747***(0.213)-1.260*(0.725)-2.087***(0.529)-2.346***(0.347)-0.807***(0.205)(2)Mining-1.016***(0.273)-1.244***(0.218)(3)-1.158***(0.289)-1.043***(0.224)(3)-1.416***(0.254)-0.972***(0.221)(3)
Food

0.697*(0.407)-1.418***(0.188)(4)

0.509(0.393)-1.181***(0.167)(4)

0.137(0.326)-1.030***(0.140)(4)
Textiles

1.022*(0.563)-1.419***(0.262)(5)0.923*(0.540)-1.330***(0.234)(5)

0.462(0.499)-1.131***(0.211)(5)
Leather-1.407***(0.237)-0.986***(0.172)(6)-1.513***(0.235)-0.842***(0.160)(6)-1.652***(0.201)-0.837***(0.150)(6)
Wood-1.316***(0.242)-1.170***(0.200)(7)-0.657(0.548)-1.385***(0.458)0.0241(0.248)-0.848***(0.156)0.268(0.278)-0.938***(0.166)-0.585(0.607)-1.319***(0.461)0.357(0.283)-1.092***(0.168)Z = ln travel time
(8)(9)

-0.788(0.583)-1.052**(0.410)Z = ln road distance(8)(9)-1.460***(0.247)-0.966***(0.189)(7)-1.680***(0.214)-0.913***(0.185)Z = ln bird-flight distance
(7)
(8)
(9)
Paper
Fuels
Chemicals-0.167(0.232)-1.290***(0.142)(10)-0.341(0.230)-1.069***(0.143)(10)-0.676***(0.221)-0.899***(0.150)(10)
Plastics-1.349***(0.227)-1.392***(0.180)(11)-1.501***(0.247)-1.169***(0.182)(11)-1.701***(0.216)-1.176***(0.179)(11)
Non-metals-0.368*(0.194)-1.456***(0.161)(12)-0.540***(0.207)-1.217***(0.165)(12)-0.742***(0.189)-1.212***(0.169)(12)
Metals-0.755***(0.155)-0.971***(0.109)(13)-0.874***(0.148)-0.819***(0.104)(13)-1.110***(0.155)-0.694***(0.115)(13)
Machinery-0.114(0.198)-1.113***(0.126)(14)-0.224(0.192)-0.968***(0.114)(14)-0.528***(0.190)-0.780***(0.123)(14)
Electrical-0.302(0.253)-0.784***(0.171)(15)-0.315(0.242)-0.738***(0.148)(15)-0.509**(0.235)-0.638***(0.153)(15)
Transport-0.335(0.206)-1.557***(0.129)(16)-0.519**(0.209)-1.315***(0.129)(16)-0.966***(0.227)-1.060***(0.164)

(16)
Other

Notes: Poisson Pseudo Maximum Likelihood estimations. All models contain complete sets of separate exporter and importer fixed effects (exporter * sector, importer * sector effects in case of sectoral trade data). All models contain acommon language dummy and a contiguity dummy (not shown). Robust standard errors in parentheses, *** p < 0.01, ** p < 0.05, * p < 0.1. N = 441, R2 between 0.90% and 0.99%.

Z

BorderZ

BorderZ

Border(1)
Agriculture

Table 12: The border effect infrastructure - sector by sector: PPML regressions