Regional Science and Urban Economics 37 (2007) 457  465
www.elsevier.com/locate/regec
Regional economics: A new economic
geography perspective&
a a,b,c,
N
Kristian Behrens , Jacques-François Thisse
a
CORE, Université Catholique de Louvain, Belgium
b
CERAS, Ecole Nationale des Ponts et Chaussées, France
c
CEPR, United Kingdom
Received 5 August 2006; accepted 19 October 2006
Available online 12 April 2007
Abstract
We show that the concepts and tools developed in new economic geography may be used to revisit several
problems in regional economics. In particular, we want to stress the following two points: (i) what do we mean
by a region and (ii) what kind of interactions between regions do we want to study and how to model them? We
conclude by discussing a few open problems that should be explored in more detail for regional economics to
become a richer body of knowledge.
© 2007 Elsevier B.V. All rights reserved.
JEL classification: R1
Keywords: Regions; Regional economics; New economic geography
1. Introduction
This journal has been launched in 1972 under the title Regional and Urban Economics, which
is almost the name of the JEL-classification entry R. The first point we wish to make is that, by the
time this journal was launched, urban economics was already a well-established field drawing on
new concepts and tools. By contrast, the scientific status of regional economics was less clear in
&
We thank a referee, Richard Arnott, Wilfried Koch and Giordano Mion for helpful comments and suggestions. Kristian
Behrens gratefully acknowledges financial support from the European Commission under the Marie Curie Fellowship
MEIF-CT-2005-024266.
N
Corresponding author. CERAS, Ecole Nationale des Ponts et Chaussées, France.
E-mail addresses: [e-mail] (K. Behrens), [e-mail] (J.-F. Thisse).
0166-0462/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.regsciurbeco.2006.10.001
458 K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465
that regional concepts, models and techniques were too often a mere extension of those used at the
national level, with an additional index identifying the different regions (see, e.g., interregional
input output matrices or the Harrod Domar model of regional growth).1 The Samuelsonian
emphasis put on trade theory also acted as an impediment to the further development of regional
economics, the trade of goods being viewed as a substitute to the mobility of factors. Today,
thanks to the surge of new economic geography (in short, NEG), it is time to re-think regional
economics. This is what we wish to do in this note.
It is worth stressing from the outset that, in order to talk even halfway sensibly about regional
economics, it is necessary to tackle the following two questions: (i) what do we mean by a region;
and (ii) what kind of interactions between regions do we want to study and how to model them?
Regarding the first question, we find it crucial to develop a better understanding of how the
spatial scale of the analysis matters for the economic results. Too often, economists use
interchangeably different, yet equally unclear, words such as locations, regions or places without
being aware that they often correspond to different spatial units. In doing so, they run the risk of
drawing implications that are valid at a certain level of spatial aggregation but not at another.2
Furthermore, using vague definitions of the spatial unit of analysis reduces the scientific contents
of the theory in the Popperian sense, as the empirical results can always be contested in light of the
theory on the sole basis that variables are not measured at the appropriate spatial scale.
As to the second question, regardless of what is meant by a region, the concept is useful if and
only if a region is part of a broader network through which various types of interactions occur.
Without taking this aspect into account, one may wonder what the difference between regional
economics and the macroeconomics of a closed economy would be. When there is a single region,
the economy is a-spatial and there is nothing interesting to be said in terms of spatial analysis.
Hence, any meaningful discussion of regional issues requires at least two regions in which
economic decisions are made. Furthermore, if we do not want the analysis to be confined to trade
theory, we must also account explicitly for the mobility of agents  firms and/or consumers  as
well as for the existence of transport costs, which are the two main ingredients of location theory.
In the first two sections, we briefly review what we know and do not know about those two
questions. We conclude in Section 4 by discussing a few open problems that should be explored in
more detail for regional economics to reach the level of generality one expects for such an
important field.
2. What is a region?
Since the early days of regional economics, there have been many definitions for and approaches
to the concept of a region, Lösch (1938) being probably the most stimulating contribution. In its
broadest sense, the term  region is used to describe a bundle of places such that any two places
belonging to the same region are, in a way or another, similar. Yet, the multiplicity of definitions
reflects the fact that the concept of similarity to be used does not suggest itself. This difficulty may be
formalized in a very rigorous, but largely unnoticed, way.
Observe first that a set of regions always involves a partition of some geographical space that
contains a  large number of places  a place being the elementary spatial unit. Keeping this in
1
A noticeable exception is the work of Takayama and Judge (1971), which has led to a large body of extensions and
real-world applications.
2
For example, Rosenthal and Strange (2001) show that the nature of agglomeration forces differs depending on the
spatial scale of the analysis (zipcode, county level, state level).
K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465 459
mind, a well-known result in set theory is that there is a one-to-one correspondence between the
family of partitions in a set and the family of equivalence relations of the same set (Halmos, 1965).
Recall that an equivalence relation in a set is a reflexive, symmetric and transitive relation.
Intuitively, one may think of an equivalence relation as a generalization of the concept of equality
to that of similarity: (i) an object is always similar to itself (reflexivity); (ii) if one object is similar to
another, the latter is similar to the former (symmetry); and (iii) two objects similar to a third one are
themselves similar (transitivity).
Accordingly, using a particular regional system amounts to working with a special equivalence
relation defined on the space of reference. This result has two important implications: (i) any place
belongs to a single region and (ii) two places belonging to the same region are considered as being
identical from the standpoint of the equivalence relation, whereas two places belonging to two distinct
regions are not. It is now easy to understand why there is no general agreement on what a region should
be: the number of equivalence relations that can be defined in a space is  huge . Thus, depending on
the point of view selected by the analyst, the regional system, whence the shape and number of
regions, may vary. Consequently, a given area cannot be considered as a region per se. Whether or not
it is part of a regional system ultimately depends on the equivalence relation that is being used.
This difficulty should not come as a surprise as defining a regional system bears some
resemblance with the problem of aggregation in economic theory. In this respect, it is well known
how poorly representative the so-called  representative consumer may be (Kirman, 1992).
Likewise, the word  industry is still in search of a well-defined theoretical meaning (Triffin,
1940). Grouping locations within the same spatial entity, called a region, gives rise to similar
difficulties. It is, therefore, probably hopeless to give a clear and precise answer to our first
question, which is essentially an empirical one. When we talk about a region, we must be happy
with the same theoretical vagueness that we encounter when using the concept of industry. Note
that both involve some  intermediate level of aggregation between the macro and the micro.
It should be clear from the foregoing discussion that the main challenge in defining a regional
system lies more in the empirical application one has in mind. From a purely empirical point of
view, the concept of region one retains is often intrinsically linked to the availability of data.
Hence, the question of the spatial scale of analysis, though already problematic in theory,
becomes even more dramatic in applied research. However, such a difficulty does not dispense the
analyst from seeking meaningful empirical solutions (see, e.g. Magrini, 2004; McMillen and
Smith, 2003). On the one hand, the question of the size of regions no longer matters because it is
often dictated by administrative classifications (e.g., the NUTS regional classification of the EU).
On the other hand, one is tempted to twist theory so that it fits into the available statistical
classifications. One additional problem is that, due to the nature of the data available, space must
often be represented by a discrete set of points. Yet, when there are too many points, aggregation
becomes necessary and gives rise to another problem, known as the MAUP (Movable Areal Unit
Problem).3 Some new techniques should alleviate the MAUP problem. In particular, the use of
geographical information systems and the increasing availability of micro-spatial data should
allow for less reliance on arbitrarily determined regional boundaries.4
3
Economists and geographers do not seem to be aware that mathematicians have extensively studied the possible errors
that may emerge from the aggregation of data. In this perspective, Francis et al. (2007) consider and compare various
aggregation error measures, identify some effective (and some ineffective) aggregation error measures, and discuss some
open research areas.
4
For example, Duranton and Overman (2005) start from a continuous space approach to determine the degree of spatial
concentration of various industrial sectors, whereas Mori et al. (2005) propose an index of industrial location that can be
decomposed into components representing localization at various levels of spatial aggregation.
460 K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465
3. The relationship between regional economics and NEG
The idea of spatial interaction is central to regional economics. Broadly defined, spatial
interaction refers to a wide array of flows subject to various types of spatial frictions, such as
traded goods, migrations, capital movements, interregional grants, remittances, and the
interregional transmission of knowledge and business cycle effects. So far, the bulk of NEG
has been restricted to the movements of goods and of some agents only.
As argued in the foregoing section, defining clearly and delineating precisely a region appears
to be a difficult, not to say impossible, task. Keeping this in mind, we assume from now on that
regions may be viewed as units where economic activity takes place. In light of this (vague)
definition, it becomes crucial for the analysis to account for the fact that where things happen is
endogenously determined in a regional system. In this respect, traditional regional economics
often fails to grasp such an issue by taking the location of production factors as given, very much
as in trade theory.
How can (or should) a regional system be formally represented is still a matter of debate.
Firstly, one may consider that there is a discrete set of regions. Alternatively, one may assume that
there is a continuum of regions. Although the second approach may seem more appropriate when
we want to work at a very disaggregate spatial level, it seems natural to think of a regional system
as being formed by a finite set of regions. Furthermore, NEG shows that even when location
spaces are continuous, economic activity usually clusters into a few places.5 This leads us to
believe that the operationally feasible and theoretically desirable representation of a regional
system is in terms of a graph. Note that this is the approach that has been chosen for a long time in
location theory (Beckmann and Thisse, 1986). Indeed, graphs offer a natural representation of
finite systems of agents/nodes which interact with each other through links. It also fits well the
intermediate spatial scale considered in regional economics.
In a spatial economy with a finite number of regions, we know from Starrett s Spatial
Impossibility Theorem that the competitive market mechanism breaks down when the mobility of
firms and/or households is combined with the transport costs of goods between regions. Hence,
unless strong spatial heterogeneities are assumed to be given a priori, the question of where
economic activity occurs and why cannot be readily addressed within the competitive framework.
As argued by Krugman (1995), this probably explains why spatial economic issues have been for
so long at the periphery of mainstream economics. Note, in passing, that a major implication of
the Spatial Impossibility Theorem is that some forms of imperfect competition are likely to be
necessary to handle regional issues. It is no surprise, therefore, that the surge of NEG took place a
few years after the revival of monopolistic competition and industrial organization, from which
NEG borrows many ideas and concepts.
Since the pioneering work of Krugman (1991), NEG has become a fast-growing field (Fujita
et al., 1999; Baldwin et al., 2003; Ottaviano and Thisse, 2004). It provides a full-fledged general
equilibrium approach with strong microeconomic underpinnings in which regional disparities
may or may not emerge endogenously, depending on the values of some structural parameters. In
this respect, it seems fair to say that NEG is the first successful attempt made to explain why
5
To be sure, the initial strategy used in NEG was in terms of two regions. However, later developments have shown
that the basic ideas remain applicable to continuous space models (see, e.g. Fujita et al., 1999; Picard and Tabuchi, 2003).
In this context, a precise definition of a region is not really needed since regions appear endogenously as clusters of
activities. In such a context, regions become even more of a relative concept because they are subject to changes in the
economic environment.
K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465 461
a priori similar regions do not experience the same level of economic development. When
compared to earlier attempts made in regional economics, one appealing feature of NEG is that it
has very strong connections with several branches of modern economics, including industrial
organization and urban economics, but also with the new theories of growth and development. In
particular, NEG and endogenous growth theory share the same framework, using monopolistic
competition, increasing returns and spillovers. This suggests the existence of a high potential for
cross-fertilization, which is being explored in recent contributions (Baldwin and Martin, 2004).
Another striking aspect of NEG is the very large number of empirical investigations it has
triggered (Head and Mayer, 2004). However, if empirical papers deal with many regions (and
sectors), theory has focused almost exclusively on two regions (and sectors). Although such simple
settings have proven to be valuable to our understanding of spatial phenomena, they offer in
general a fairly poor basis for deriving testable predictions (Behrens et al., 2005a). In addition, it is
far from being clear that we can extrapolate the predictions and results derived from two-region
models to a multi-regional system. Quite the opposite: the answer is probably no although this is
not really recognized by the profession. Note that such  dimensionality issues are reminiscent of
fairly old debates in trade theory. As concisely emphasized by Deardorff (1984, p.468), the
Heckscher Ohlin theorem  is derived from a model of only two of each of goods, countries, and
factors of production. It is unclear what the theorem says should be true in the real world where
there are many of all three . This inevitably affects applied work, since most  papers that claim to
present tests of the hypothesis have used intuitive but inappropriate generalizations of the
two × two model to deal with a multidimensional reality (Bowen et al., 1987, p.791). The
dimensionality issue is likely to be part of the explanation for the  moderate support provided by
the numerous attempts made to test the theoretical predictions of NEG (Head and Mayer, 2004).
A last remark is in order. NEG models typically rest on very specific models of monopolistic
competition, mainly the one by Dixit and Stiglitz. Therefore, such models lack the level of
generality that characterizes standard general equilibrium theory. Hence, it is fair to say that NEG
models have so far the scientific status of examples. We are fully aware of the many conceptual
and technical difficulties encountered in building general equilibrium models with imperfect
competition and increasing returns, so that working with a general model is probably out of reach.
Yet, for NEG and regional economics to achieve the status of economic theories, it is necessary,
we believe, to explore alternative formulations of monopolistic competition, and to check whether
its main conclusions remain valid within such frameworks.6
4. From two to many regions
In many scientific fields, the passage from one to two dimensions raises fundamental
conceptual difficulties. In NEG, it is the apparently innocuous passage from two to three regions.
The reason for this is that when there are just two regions, there is only one way in which these
regions can interact, namely directly; whereas with three regions, there are two ways in which
these regions can interact, namely directly and indirectly. In other words, in multi-regional
systems the so-called  three-ness effect enters the picture and introduces complex feedbacks into
6
Ottaviano et al. (2002) revisit the core periphery model within an alternative monopolistic competition model
featuring price competition effects and quasi-linear preferences. They show that the main conclusions of NEG are robust
with respect to these changes. Behrens and Murata (in press) propose an alternative framework of monopolistic
competition with both price competition and income effects. Its future application to NEG may constitute another step in
the direction of exploring the robustness of this theory.
462 K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465
the models, which significantly complicates the analysis. Dealing with these spatial
interdependencies constitutes one of the main theoretical and empirical challenges NEG and
regional economics will surely have to face in the future.7
4.1. Theory
If multi-regional trade models already pose a formidable challenge to theoretical analysis in the
presence of spatial frictions, it is easy to figure out that matters become even worse when
production factors and purchasing power are geographically mobile. But why should one bother
about the existence of many regions instead of two?
In addition to the need for a better theoretical understanding of spatial interdependencies to
guide the empirical analysis, as emphasized in the foregoing, the new fundamental ingredient that
a multi-regional setting brings about is that the accessibility to markets varies across regions. In
other words, spatial frictions between any two regions are likely to be different, which means that
the relative position of the region within the whole network of interactions matters. In this respect,
it is worth recalling that even the simplest firm location model accounts for the fact that the access
to several markets is the key-issue faced by a firm making its locational choice (Beckmann and
Thisse, 1986). Although location theory accurately stresses this fact, most trade theorists are still
reluctant to the idea of assuming that different countries have a different access to each other.
Instead, they keep working largely in settings in, which market accessibility does not really
matters. Yet, armchair empirical evidence shows that a good access to markets is a major
determinant for the location of economic activity (Gallup et al., 1999).
The concept of accessibility is not a new one, and has been introduced into regional economics
and trade under the form of market potential (Harris, 1954) and the gravity equation (Tinbergen,
1962). Both of these initially a-theoretical concepts have rapidly become fundamental applied
tools and have, subsequently, triggered a good deal of theoretical work (Anderson and van
Wincoop, 2003; Head and Mayer, 2004). Behrens et al. (2005a,b) offer a recent attempt at
developing a multi-regional system with endogenous firm locations, and they derive testable
empirical implications. In particular, they show that accessibility crucially matters for predicting
how local market size affects industrial location: only when accessibility is appropriately  filtered
out of the data can one assess the link between regional market size and the structure of trade and
location.
Another key insight one can derive only in a multi-region economy is that any change in the
underlying parameters has in general complex impacts which vary in non-trivial ways with the
properties of the graph representing the spatial economy. As argued in the foregoing, when there
are only two regions, any change in structural parameters necessarily affects directly either one of
the two regions, or both. On the contrary, when there are more than two regions, any change in
parameters that directly involves only two regions now generates spatial spill-over effects that are
unlikely to leave the remaining regions unaffected. This in turn further affects the other regions
and so on.8
7
The difficulty encountered by economists in solving the dimensionality problem is reminiscent of the n-body problem
in mechanics, which is solved for n = 2 but not for an arbitrary number of bodies.
8
For example, Behrens et al. (2005b) show that the welfare impacts associated with changes in transport costs can only
be unambiguously signed in a multi-regional economy when the underlying graph has locally the structure of a tree. In
the remaining cases, the indirect feedback effects induced by the loops of the graph do not allow for any clear-cut
conclusions to be drawn.
K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465 463
4.2. Empirics
Accounting for the complex chains of indirect spatial effects is of even greater importance in
applied work, since the empirical analyst necessarily faces a multi-dimensional reality. The
gravity equation offers a good illustration of this. Indeed, almost all previous work has estimated
the gravity equation on a two-by-two basis, thus implicitly assuming that what happens between
two regions can be isolated from the rest of the economy. Anderson and van Wincoop (2003) have
recently shown that doing so, i.e. failure to take into account the whole structure of the regional
trading system, yields biased estimates and incorrect conclusions. Although some authors have
proposed to capture the spatial interdependence in the gravity equation by using regional fixed
effects instead of Anderson and van Wincoop s procedure, it is our contention that this is not fully
correct. It seems, indeed, fairly unlikely from a theoretical point of view that the whole structure
of regional interdependence can be reduced to a mere scalar measure without leading to a
significant loss of information.
An alternative road that empirical regional economics should consider is structural spatial
econometrics. Although spatial econometric techniques have been around for some time
(Anselin, 1988; Lee, 2004), their rigorous theory-based application to multi-regional trading,
growth, and NEG systems is practically non-existent. This is surprising for two reasons.
Firstly, spatial econometrics seems to be the natural empirical complement to the graph
theoretic approach we have highlighted in the foregoing. It is, indeed, well known that every
graph can be represented in matrix form. Hence, there is a natural relationship between the
weight matrices used in spatial econometrics, to summarize the spatial interdependence in the
sample, and the underlying graph of the regional economic system. Theory-based modeling
should allow for this underlying structure to endogenously appear in the analysis, therefore
obviating the need for too often ad hoc specifications of such matrices. Secondly, as recently
argued by Anderson and van Wincoop (2004, p.713), spatial econometric techniques allow
for richer error structures, and  [i]mproved econometric techniques based on careful
consideration of the error structure are likely to pay off. Introducing errors into spatial
models usually gives rise to complex patterns of correlation, which have to be handled with
adequate tools.
The main reason explaining the relative neglect of spatial econometrics in regional
economics is that it seems difficult to bridge the gap between the theoretical models and the
spatial econometric specification, and to derive structural estimating equations which explicitly
account for spatial interdependence in explanatory variables and error terms. That these
difficulties can be overcome has been recently shown by Ertur and Koch (2007), who derive a
structural estimating equation from a neoclassical growth model with spatially correlated
knowledge spillovers.
A second alternative for future applied work is to recognize that the numerical calibration
and computation of multi-region models may pay off. Several recent multi-country studies
indeed calibrate their models on real-world data and investigate their behavior with the help of
counterfactuals (Eaton and Kortum, 2002; Del Gatto et al., 2006). Whether such an approach is
possible at the interregional level crucially hinges on the availability of data. Yet, the increasing
availability of high-quality micro-geographic data sets should allow one to push the analysis
further in this direction.
Last, natural experiments (or quasi-experiments) that provide exogenous changes in key
explanatory variables may prove useful for analyzing spatial phenomena (see, e.g., Meyer, 1995,
for a discussion of natural experiments). Unfortunately, unlike in other fields like labor
464 K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465
economics, migration and education, natural spatial experiments at a larger regional or
interregional scale are rare and, therefore, difficult to exploit in a systematic way.9
To sum-up: although urban systems have attracted the attention of economists for a long
time (see, e.g. Henderson, 1988), the study of regional systems has been far too neglected.
What makes this subject a real future challenge are the following two reasons: (i) new tools
have to be found and applied to build a theoretical framework involving many regions,
whereas (ii) the empirical analysis of regional systems requires further and sophisticated
developments in spatial econometrics and numerical calibration. Beyond its own interest, the
emergence of trading blocks and the gradual removal of national borders make it more and
more important to have at one s disposal a well-developed body of regional economics if we
want to understand better that particular form of economic integration and its potential
consequences.
References
Anderson, J.E., van Wincoop, E., 2003. Gravity with gravitas: a solution to the border puzzle. American Economic Review
93, 170 192.
Anderson, J.E., van Wincoop, E., 2004. Trade costs. Journal of Economic Literature 42, 691 751.
Anselin, L., 1988. Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, Dordrecht.
Baldwin, R.E., Martin, Ph., 2004. Agglomeration and regional growth. In: Henderson, J.V., Thisse, J.-F. (Eds.), Handbook
of Regional and Urban Economics, vol. 4. North Holland, Amsterdam, pp. 2671 2711.
Baldwin, R.E., Forslid, R., Martin, Ph., Ottaviano, G.I.P., Robert-Nicoud, F., 2003. Economic Geography and Public
Policy. Princeton University Press, Princeton, NJ.
Beckmann, M.J., Thisse, J.-F., 1986. The location of production activities. In: Nijkamp, P. (Ed.), Handbook of Regional
and Urban Economics, vol. 1. North-Holland, Amsterdam, pp. 21 95.
Behrens, K., Murata, Y., 2007. General equilibrium models of monopolistic competition: a new approach. Journal of
Economic Theory, forthcoming (doi:10.1016/jet.2006.10.001).
Behrens, K., Lamorgese, A.R., Ottaviano, G.I.P., Tabuchi, T., 2005a. Testing the  home market effect in a multi-country
world. CORE Discussion Paper 2005/55. Université catholique de Louvain.
Behrens, K., Lamorgese, A.R., Ottaniviano, G.I.P., Tabuchi, T., 2007b. Changes in transport and non-transport costs: local
vs global impacts in a spatial network. Regional Science and Urban Economics, forthcoming.
Bosker, M., Brackman, S., Garretsen, H., Schramm, M., 2007. Looking for multiple equilibria when geography matters:
German city growth and WWII shock. Journal of Urban Economics 61, 152 169.
Bowen, H.P., Leamer, E.E., Sveikauskas, L., 1987. Multicountry, multifactor tests of the factor abundance theory.
American Economic Review 77, 791 809.
Davis, D.R., Weinstein, D.E., 2002. Bones, bombs, and break points: the geography of economic activity. American
Economic Review 92, 1269 1289.
Deardorff, A.V., 1984. Testing trade theories and predicting trade flows. In: Jones, R.W., Kenen, P.B. (Eds.), Handbook of
International Economics, vol. 1. North Holland, Amsterdam, pp. 467 517.
Del Gatto, M., Mion, G., Ottaviano, G.I.P., 2006, Trade integration, firm selection and the costs of non-Europe.
Mimeographed, UniversitÄ… di Bologna.
Duranton, G., Overman, H.G., 2005. Testing for localisation using micro-geographic data. Review of Economic Studies 72,
1077 1106.
Eaton, J., Kortum, S., 2002. Technology, geography, and trade. Econometrica 70, 1741 1779.
Ertur, C., Koch, W., in press. Growth, technological interdependence and spatial externalities: theory and evidence. Journal
of Applied Econometrics.
9
Redding and Sturm (2005) take the German reunification as a natural experiment and study its impact on the
economic performance and development of border cities in West Germany. Davis and Weinstein (2002) and Bosker et al.
(2007) consider shocks to urban structure due to strategic bombing as natural experiments and investigate the inertia in
the location and size distribution of cities.
K. Behrens, J.-F. Thisse / Regional Science and Urban Economics 37 (2007) 457 465 465
Fujita, M., Krugman, P., Venables, A.J., 1999. The spatial economy. Cities, Regions and International Trade. The MIT
Press, Cambridge, MA.
Francis, R.L., Lowe, T.J., Rayo, B., Tamir, A., 2007. Aggregation error for location models: survey and analysis. Annals of
Operation Research, forthcoming.
Gallup, J.L., Sachs, J.D., Mellinger, A., 1999. Geography and economic development. International Regional Science
Review 22, 179 232.
Halmos, P.R., 1965. Axiomatic Set Theory. Van Nostram, Princeton, NJ.
Harris, C., 1954. The market as a factor in the localization of industry in the United States. Annals of the Association of
American Geographers 64, 315 348.
Head, K., Mayer, T., 2004. The empirics of agglomeration and trade. In: Henderson, J.V., Thisse, J.-F. (Eds.), Handbook of
Regional and Urban Economics, vol. 4. North Holland, Amsterdam, pp. 609 2669.
Henderson, J.V., 1988. Urban development. Theory, Fact and Illusion. Oxford University Press, Oxford.
Kirman, A., 1992. Whom and what does the representative individual represent? Journal of Economic Perspectives 6,
117 136.
Krugman, P.R., 1991. Increasing returns and economic geography. Journal of Political Economy 99, 483 499.
Krugman, P.R., 1995. Development, Geography, and Economic Theory. The MIT Press, Cambridge, MA.
Lee, L.-F., 2004. Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models.
Econometrica 72, 1899 1925.
Lösch, A., 1938. The nature of economic regions. Southern Economic Journal 5, 71 78.
Magrini, S., 2004. Regional (di)concergence. In: Henderson, J.V., Thisse, J.-F. (Eds.), Handbook of Regional and Urban
Economics, vol. 4. North Holland, Amsterdam, pp. 2741 2796.
McMillen, D.P., Smith, S.C., 2003. The number of subcenters in large urban areas. Journal of Urban Economics 53,
321 338.
Meyer, B.D., 1995. Natural and quasi-experiments in economics. Journal of Business and Economic Statistics 13,
151 161.
Mori, T., Nishikimi, K., Smith, T.E., 2005. A divergence statistics for industrial localization. Review of Economics and
Statistics 87, 635 651.
Ottaviano, G.I.P., Thisse, J.-F., 2004. Agglomeration and economic geography. In: Henderson, J.V., Thisse, J.-F. (Eds.),
Handbook of Regional and Urban Economics, vol. 4. North-Holland, Amsterdam, pp. 2564 2608.
Ottaviano, G.I.P., Tabuchi, T., Thisse, J.-F., 2002. Agglomeration and trade revisited. International Economic Review 43,
409 436.
Picard, P.M., Tabuchi, T., 2003. Natural agglomeration. CORE Discussion Paper 2003/101. Université catholique de
Louvain.
Redding, S., Sturm, D.M., 2005. The costs of remoteness: evidence from German division and reunification. CEPR
Discussion Paper, vol. 5015.
Rosenthal, S.S., Strange, W.C., 2001. The determinants of agglomeration. Journal of Urban Economics 50, 191 229.
Takayama, T., Judge, G.G., 1971. Spatial and Temporal Price and Allocation Models. North Holland, Amsterdam.
Tinbergen, J., 1962. Shaping the World Economy: Suggestions for an International Economic Policy. Twentieth Century
Fund, New York.
Triffin, R., 1940. Monopolistic Competition and General Equilibrium Theory. Harvard University Press, Cambridge, MA.