Adding geography to the new economic geography: …brakman/Adding.pdfKeywords: new economic geography, multi-region simulations, empirics JEL classifications: F15, O18, R12, R11 Date

Journal of Economic Geography (2010) pp. 1–31 doi:10.1093/jeg/lbq003

Adding geography to the new economic geography:bridging the gap between theory and empiricsMaarten Bosker�y, Steven Brakman�, Harry Garretsen� and Marc Schrammz

�Department of Economics, University of Groningen, The NetherlandsyCorresponding author: Maarten Bosker, Department of International Economics and Business, Universityof Groningen, Landleven 5, Groningen, 9747 AD, The Netherlands. [email protected] School of Economics, Utrecht University, The Netherlands

AbstractFor reasons of analytical tractability, new economic geography (NEG) models treatgeography in a very simple way, focusing on stylized ‘unidimensional’ geographystructures (e.g. an equidistant or line economy). All the well-known NEG results arebased on these simple geography structures. When doing empirical work, thesesimplifying assumptions become problematic: it may very well be that the main NEGresults do not carry over to the heterogeneous geographical setting faced by theempirical researcher, making it inherently difficult to relate empirical results back toNEG theory. This article tries to bridge this gap by proposing an empirical strategy thatcombines estimation and simulation. First, we show by extensive simulation that many,but not all, conclusions from the simple unidimensional NEG models carry over whenusing more realistic geography structures. Second, we illustrate our proposed empiricalstrategy using a sample of European regions, combining estimation of structural NEGparameters with simulation of the underlying NEG model.

Keywords: new economic geography, multi-region simulations, empiricsJEL classifications: F15, O18, R12, R11Date submitted: 16 July 2007 Date accepted: 28 December 2009

1. Introduction

Theoretical economic geography models treat geography in a very stylized way(Neary, 2001, 551). Attention is largely confined to simple two-region models,multi-region models exhibiting a simple unidimensional spatial structure (e.g. allregions lying on a circle, all regions equidistant from each other, or all regions lying ona straight line), or to three-region models that do allow for different trade costs betweenregions but at the cost of having to assume that one region’s economic mass isexogenous.1

1 Examples of these simple two-region, unidimensional multi-region or three-region models are Fujita et al.(1999a, chapter 6) or Krugman (1993) both considering a ‘circle’ or ‘racetrack’ economy; Puga (1999) orTabuchi et al. (2005) both considering an ‘equidistant’ economy; Fujita et al. (1999b) or Krugman (1993)both considering a ‘line’ economy; and Krugman and Elizondo (1996) or Monfort and Nicolini (2000)considering three-region models.

A notable exception is the work by Behrens et al. (2007), which presents analytical results in a multi-region trade model with a somewhat more complex characterization of geography, for example atransportation network locally described by a tree, showing that in that case changes in transport costshave spatially limited effects.

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The reason for making these simplifying assumptions is analytical tractability.

Adding a more realistic, asymmetric, geography structure to an NEG model

would render the model analytically insolvable [see Behrens et al. (2007, 16), Fujita

and Mori (2005, 396) or Behrens and Thisse (2007, 461–462)]. Without imposing

such simple geography structures, the so-called three-ness effect (Behrens and

Thisse, 2007, 461) enters the picture introducing complex feedback effects into

the models that make them analytically intractable. As such, it is the assumption of

a simple geography structure that allows for the establishment of all the well-known

analytical results in the NEG literature (e.g. multiple equilibria and catastrophic

(de)agglomeration).2

When doing empirical or policy work, these simplifying assumptions become

problematic. It is unclear whether the conclusions from these simple models carry

over to the more heterogeneous asymmetric geographical setting faced by the empirical

researcher or policy maker in the real world [see also Fujita and Thisse (2009)

or Behrens and Thisse (2007, 461)]. For empirical work, it becomes difficult to

relate estimates of the structural model parameters based on multi-region or multi-

country data [see e.g. Redding and Venables (2004), Hanson (2005) or Brakman

et al. (2006)] back to the underlying theory. When doing policy work, it becomes

ambiguous to provide policy recommendations for the clearly asymmetric multi-region

setting in the real world on the basis of a stylized equidistant (and often two-region)

model.This work proposes an empirical strategy that combines estimation and simulation of

the underlying NEG model as a solution to the above-described ‘mismatch’ between

NEG theory and empirics. First, we assess, through simulation, the impact of adding

more geographical realism to a well-known NEG-model (Puga, 1999) that encompasses

several benchmark NEG-models.3 A particularly nice feature of that model is that it

presents analytical results for both the two-region and the equidistant multi-region

setting that naturally serve as the theoretical benchmark to which we can compare our

later empirical findings. Having such a theoretical benchmark has been stressed by

several authors [e.g. Krugman (1998, 15); Fujita and Krugman (2004, 158); Fujita and

Mori (2005, 396); Behrens and Thisse (2007, Section 3)]. It sets us apart from studies by

Forslid et al. (2002a, 2002b), Brocker (1998) and Venables and Gasiorek (1999) that all

resort to the simulation of a computable general equilibrium (CGE) model of an

asymmetric multi-region and/or multi sector world. Their results are difficult to connect

to theory as the properties of the CGE-models that are used for the simulations are

2 Puga and Venables (1997) do derive analytical results regarding the locational effects of small(asymmetric) trade cost changes around the stable symmetric equidistant M-region equilibrium in anNEG model with immobile labour. In all other cases than the stable symmetric equidistant equilibrium,they too rely exclusively on simulation to establish the effect of asymmetric trade costs on the spatialdistribution of economic activity.

3 The only other work that we know of that simulates an NEG model adding a more realistic depiction ofgeography is Stelder (2005). Stelder (2005) tries to replicate the actual spatial distribution of cities acrossEurope by simulating the Krugman (1991) ‘cum’ geography model. The paper does, however, not relateany of the simulation results back to the underlying theoretical model nor tries to link them to empiricalfindings, focusing instead on simulating the current spatial distribution of economic agglomerations asclosely as possible.

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generally not known,4 not even for the simple two-region or equidistant multi-region case.5

We show that the introduction of non-equidistant regions in the Puga (1999) modeldoes by and large not change the qualitative results from the benchmark equidistantmodel regarding the impact of a change in trade costs on the equilibrium degree ofagglomeration. With interregional labour mobility, a fall in trade costs will ultimatelyand catastrophically lead to complete agglomeration. Without interregional labourmobility, a fall in trade costs will also initially result in the emergence of agglomeration,but when trade costs continue to fall the degree of agglomeration will start to decreaseagain resulting in a return to more spreading. Moreover, agglomeration is notnecessarily catastrophic in the latter case; partial agglomeration can also arise. Theseresults are qualitatively in line with the benchmark equidistant model. A notabledifference between the long run equilibria in our non-equidistant and the equidistantmulti-region Puga (1999) model is that the same long run equilibrium (LRE) levelof agglomeration may go along with a different spatial distribution of economicactivity.

Having assessed the impact of adding more geographical realism to the multi-regionPuga (1999) model, we provide a (stylized) illustration of our proposed empiricalstrategy using a sample of European regions. First, we estimate the key structural NEGparameters. Next, and in contrast to Crozet (2004), Brakman et al. (2005) and Headand Mayer (2004), we do not relate these parameter estimates back to the stylized‘unidimensional’ (and mostly two-region) models to obtain NEG based predictionsregarding the effect of increased integration on the spatial distribution of economicactivity. Instead, we use the estimated parameters in combination with the currentdistribution of economic activity across EU regions and simulate the underlying‘asymmetric’ multi-region NEG model to derive empirically grounded, NEG-basedpredictions regarding the impact of increased European integration. In doing so, westay as closely as possible to the Puga (1999) model on which our estimates are based,and do not, for instance, introduce additional sectors or spreading forces to thesimulations. Although this would arguably bring the simulation exercise closer to thereality of the EU, we refrain from doing so as it would imply losing the link between ourempirics and the (simple) NEG model on which these are based.

2. The Puga (1999) model

2.1. Setup of the model

This section provides a brief description of the NEG-model introduced by Puga (1999).As mentioned earlier, we use this model as it captures two important benchmark NEG-models, that is, Krugman (1991) and Krugman and Venables (1995) as special cases.Also, Puga (1999) derives analytical results in the two-region case as well as in theequidistant multi-region case, which allows for a ready comparison to our simulation

4 Moreover, due to their usually much more elaborate setup, it would be quite difficult to estimate thestructural parameters of such an elaborate CGE model in the first place (either because the model’s datarequirements cannot be met or because of econometric difficulties in identifying the model’s structuralparameters).

5 ‘A most desirable model would be one that has solvability at the low dimensional setup and computabilityeven at the fairly high dimensional setup.’ (Fujita and Mori, 2005, 396).

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results in Sections 3 and 4. The model set up is as follows6: Consider a world consistingof M regions, each populated by Li workers and endowed with Ki units of arable land.Each region’s economy consists of two sectors: agriculture and industry. Labour is usedby both sectors and is perfectly mobile between sectors within a region and is eitherperfectly mobile or immobile between regions. Land on the other hand is used only bythe agricultural sector and is immobile between regions.7

2.1.1. Production.

The agricultural good is produced under perfect competition and free entry and exitusing Cobb-Douglas technology8 and is freely tradable between regions. The industrialsector produces heterogeneous varieties of a single good under monopolisticcompetition and free entry and exit, incurring so-called ‘iceberg’ trade costs whenshipped between regions (�ij� 1 goods have to be shipped from region i to let one goodarrive in region j). Industrial production technology is characterized by increasingreturns to scale, that is, production of a quantity x(h) of any variety h requires fixedcosts and variable costs, where � and �, the fixed and variable costs parameter,respectively, are assumed to be the same in each region, see Equation (1). This, togetherwith free entry and exit and profit maximization, ensures that in equilibrium, eachvariety is produced by a single firm in a single region. The production input is a Cobb–Douglas composite of labour and intermediates in the form of a compositemanufacturing good, with 0� m� 1 the Cobb–Douglas share of intermediates. Thecomposite manufacturing good in turn is specified as a CES-aggregate (with s41the elasticity of substitution across varieties) of all manufacturing varieties produced.The resulting minimum-cost function associated with the production of a quantity x(h)of variety h in region i can be written as:

CðhÞ ¼ q�i wM1��i ð�þ �xðhÞÞ ð1Þ

where qi is the price index of the composite manufacturing good and wMi the

manufacturing wage in region i.

2.1.2. Preferences.

Consumers have Cobb–Douglas preferences over the agricultural good and a CES-composite of manufacturing varieties (again with s41 the elasticity of substitutionacross varieties), where 0� g� 1 is the Cobb–Douglas share of the compositemanufacturing good. Specifying preferences this way ensures demand from each

6 We only set out the basics of the model. For the complete detailed exposition of the model, we refer toPuga (1999). We use the same notation as Puga (1999) for ease of exposition.

7 Defining the two sectors as being agriculture and industry is arbitrary. The main point is that one sectoruses an immobile (both between sectors and regions) factor of production, producing a homogenous goodthat is freely tradable between regions under perfect competition (here: agriculture, but one could alsothink of e.g. low-skill intensive manufacturing with low-skilled workers being the immobile factor ofproduction) and that the other sector employs a mobile (be it between sectors and/or regions) factor ofproduction, producing heterogeneous varieties of the same good that are costly to trade between regionsunder monopolistic competition.

8 Puga (1999) defines the agricultural sector somewhat more general. However, when deriving analyticalresults, he also resorts to the use of a Cobb–Douglas production function in agriculture, see p. 318 of hispaper.





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region for each manufacturing variety, which, together with the fact that each variety is

produced by a single firm in a single region, implies that trade takes place between

regions.

2.1.3. Equilibrium.

Having specified preferences over, and the production technologies of, the manufactur-

ing and agricultural good, the equilibrium conditions of the model can be calculated.

Profit maximization and free entry and exit determine the share of labour employed,

LAi , the wage level w

Ai , which equals the marginal product of labour, and the rent earned

per unit of land rðwAi Þ in the agricultural sector. The former two in turn pin down the

share of workers in manufacturing, &i. Given the assumed Cobb–Douglas production

function in agriculture, with labour share y, we have that:

&i ¼LMi

Li¼ 1�

LAi

Li¼ 1�

Ki

Li

�

wAi

� � 11��

ð2Þ

where 0� y� 1 denotes the Cobb–Douglas share of labour in agriculture, and LMi and

LAi the number of workers in manufacturing and agriculture, respectively. Equation (2)

shows that, in contrast to Krugman (1991), where agriculture uses only land9 (y¼ 0), or

to Krugman and Venables (1995), where agriculture employs only labour (y¼ 1), the

share of a region’s labour employed in manufacturing is endogenously determined in

this model. It increases with a region’s labour endowment and agricultural wage level

and decreases with a region’s land endowment and with the Cobb–Douglas share of

labour in agricultural production.

Consumer preferences in turn determine total demand for agricultural products in

region i as:

xAi ¼ ð1� �ÞYi ð3Þ

where Yi is total consumer income [see (9) below]. In the industrial sector, utility

maximization on behalf of the consumers, combined with profit maximization and

free entry and exit, gives the familiar result that all firms in region i set the same price

for their produced manufacturing variety as being a constant markup over marginal

costs:

pi ¼��

� � 1q�i w

Mið1��Þ ð4Þ

where qi is the price index of the composite manufacturing good in region i defined by:

qi ¼

Zj

�1��ij njpð1��Þj

0B@

1CA

11��

ð5Þ

9 Krugman (1991) does not call this immobile production factor land; he refers to it as being immobilelabour, that is, farmers.





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where ni denotes the number of firms in region i and

wMi ¼ ð1� �Þnipi

ð� � 1Þ

��ð�þ �xiÞ

� �� ð&iLiÞ

�1ð6Þ

is the manufacturing wage in region i.

Utility maximization also gives total demand for eachmanufacturing variety produced

(coming from both the home region i as well as foreign regions j), which is the same for

each variety in the same region due to the way consumer preferences are specified:

xi ¼

Zj

p��i ejqð��1Þj �1��ij ð7Þ

In Equation (7) demand from each foreign region j is multiplied by �ij, because (�ij–1) ofthe amount of products ordered from region i melts away in transit (the iceberg

assumption) and

ei ¼ �Yi þ �nipið� � 1Þ


� �ð8Þ

is total expenditure on manufacturing varieties in region i (the first term representingconsumer expenditure on final goods and the second term producer expenditure on

intermediates) where

Yi ¼ wAi 1� ið ÞLi þ wM

i iLi þ r wAi

� �Ki þ nii ð9Þ

is total consumer income consisting of workers’ wage income, landowners’ rents andentrepreneurs’ profits, respectively. Due to free entry and exit, these profits are driven

to zero (i¼ 0), thereby uniquely defining a firm’s equilibrium output at:

xi ¼ �ð� � 1Þ=� ð10Þ

Finally, to close the model, labour markets are assumed to clear:

Li ¼ LMi þ LA

i ¼ ð1� �Þnipið� � 1Þ


� �� wMi

� ��1þKi

�

wAi

� � 11��

ð11Þ

where the demand for labour in agriculture, LAi , follows from the assumption of Cobb–

Douglas technology in agriculture and the term between square brackets represents the

total manufacturing wage bill. Moreover, equating labour supply to labour demand in

the industrial sector gives an immediate relationship between the number of firms and

the number of workers in industry:

ni ¼&iLi

��ð1� �Þq�i wM��i

ð12Þ

2.2. Long Run Equilibrium and the degree of interregional labour mobility

Next, to solve for the Long Run Equilibrium (LRE), Puga (1999) distinguishes between

the case where labour is both interregionally and intersectorally mobile and the case

when it is only intersectorally mobile. Without interregional labour mobility, LRE is

reached when the distribution of labour between the agricultural and the industrial





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sector in each region is such that wages are equal in both sectors. This is ensured bylabour being perfectly mobile between sectors driving intersectoral wage differences to

zero. When instead labour is also interregionally mobile, not only intersectoral wagedifferences are driven to zero in all regions in equilibrium. Workers now also respond toreal wage (utility) differences between regions by moving to regions with higher real

wages (utility) until real wages are the same in all regions,10 hereby defining the LRE.In effect, the model (and its two variants) can be summarized by the following schemeor decision tree11:

a. Initial distribution of labour over regions and over sectors within each region.b. Labour moves between sectors within each region until sectoral wages are equal.c. Interregional labour mobility?

C1. NO: long run equilibriumC2. YES: short run equilibrium ! d.

d. Interregional real wage equality?

D1. NO: labour moves between regions in response to differences in real wages,with workers moving to those regions with higher real wages, hereby changing

the distribution of labour over the regions! process restarts at a. with this newdistribution of labour over regions and sectors.D2. YES: long run equilibrium

2.2.1. Interregional labour immobility.

The LRE in case of interregional labour immobility can be shown to be a solution{wi,qi} of three equations that have to hold in each region. In our case (when usingwage-worker space), these are, using the fact that in equilibrium wM

i ¼ wAi ¼ wi

12:

qi ¼��

� � 1

1

��ð1� �Þ

Xj

&jLjq��j w

1��ð1��Þj �1��ij

� !1=ð1��Þ

ð13Þ

wi ¼��

� � 1

� ��1q�=ð��1Þi

�

�ð� � 1Þ

Xj

ejq��1j �1��ij

!1=ð�ð1��ÞÞ

ð14Þ

ei ¼ �ðwiLi þ KirðwiÞÞ þ �=ð1� �Þwi&iLi ð15Þ

10 Note that in case of interregional labour, immobility real wages can possibly differ between regions.11 The model is actually static, which implies that the economy immediately adjusts to the LRE. The model

outline merely serves to get the intuition behind the model. Also, it is the way we find the LRE whensimulating the model.

12 Note that this equality does not hold in a region that is fully specialized in agriculture. In that case(potential), wages in manufacturing are always lower than in agriculture. The case of full specializationin industry is ruled out because of decreasing returns to labour in agriculture.





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where (13) is obtained by substituting (4) and (12) into (5), (14) by substituting (4) and(10) into (7) and (15) by substituting (4), (10) and (12) into (8).

2.2.2. Interregional labour mobility.

In case of interregional labour mobility, a solution to (13)–(15) merely constitutes ashort-run equilibrium (SRE). With interregional labour mobility, workers will alsomove between regions in response to real wage differences until interregional real wagedifferences that are possible to persist when workers are unable (or unwilling) to movebetween regions, are no longer present. More formally, the LRE solution {wi,qi} foreach region i has to adhere to the additional condition that real wages, !i, are equalacross all regions:

!i ¼ q��i wi ¼ ! 8i ð16Þ

Having specified the equilibrium equations, the main point of interest of any NEGmodel is to determine the equilibrium distribution of firms and people over the Mregions in the model and to establish how this distribution depends on the level ofeconomic integration modelled here by the level of trade costs, �ij.

2.3. Economic integration

This is the point where one has to start making simplifying assumptions about thegeography structure in order to be able to derive analytical results. In specific, Puga(1999) makes the following simplifying assumption: trade costs between each pair ofregions are the same and there are no costs of transporting goods within one’s ownregion, that is:

�ij ¼ �, if i 6¼ j and �ij ¼ 1, if i ¼ j ð17Þ

Assuming (17), he derives an interesting difference in the impact of regional integrationbetween the case when labour is both interregionally and intersectorally mobile and thecase when it is only mobile between sectors. This difference is best summarized byFigure 1a and b, respectively,13 that are obtained from a simulation of the symmetrictwo-region model. These two figures replicate Figures 2 and 6 in Puga (1999) and arealso known as the tomahawk and the bell shaped curve, respectively. They show thatthe assumption about interregional labour mobility can crucially affect the sensitivity ofthe spatial distribution of economic activity to increased levels of economicintegration.14 Starting from a relatively high level of trade costs (e.g. �¼ 1.7), increased

13 See Appendix A for the analytics behind these figures. The y-axis depicts the Herfindahl index,HI ¼

Pi �

2i (the sum of each region i’s squared share, �i, in total economic activity). In the two-region

case, this is similar to depicting one region’s share in total economic activity.14 Throughout the paper, we focus on the effect of increased integration (lower trade costs) on the stability

of the (initially symmetric) equilibrium distribution of economic activity. We do not pay explicitattention to the sustainability of an agglomerated equilibrium. Whereas agglomeration is a well-definedconcept when considering the simple two-region models (i.e. agglomeration being a situation with alleconomic activity in either of the two regions only), which spatial distributions of economic activity tocall agglomeration becomes more arbitrary in case of more than two regions. What is agglomeration andwhen is it sustainable is not as clear-cut as in the two-region case, so that we focus on symmetry breakingthroughout Section 3. Also, in case of interregional labour immobility, not even the simple two-regionmodel provides analytical results into the sustainability of an agglomerated equilibrium (see Puga, 1999).





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integration (moving from right to left along the x-axis) will in the case of interregionallabour mobility result in a sudden (catastrophic) change in the (economic) landscapecharacterized by a shift from perfect spreading to complete agglomeration. In case ofinterregional labour immobility, increased integration will also first result (but lesscatastrophically) in agglomeration, but now, as integration continues, the economyultimately moves back to perfect spreading.

This return to symmetry in case of interregional labour immobility is caused by thefact that the spreading force imposed by the increased difficulty with which firms haveto attract their workers from the agricultural sector is not weakened (as in case ofinterregional labour mobility) by the possibility to attract workers from the otherregion. As with ongoing economic integration trade costs become relatively small, thismeans that wage differences become more important as a cost factor in production.Eventually, the spreading forces (i.e. the lower wage level in the periphery) take overand industrial firms spread out over both regions again. This does not happen withinterregional labour mobility as the higher real wage levels in agglomerations keepattracting workers from the periphery (see also e.g. Helpman (1998), as to how not onlynon-traded production inputs—here the interregionally immobile labour force—butalso non-traded consumption goods can give rise to such a return to symmetry at lowlevels of trade costs).15

3. Beyond an equidistant setup

The results regarding the impact of increased levels of integration on the LRE, assummarized by Figure 1a and b, crucially depend on the assumption of an equidistantgeography structure (17). It is difficult to envisage such a geography structure with morethan three regions on a flat plain. More importantly, it is at odds with the real world,

15 Note that these conclusions do also depend on the model’s other structural parameters (see Appendix A).

Figure 1. Trade costs and the LRE in the two-region model.Notes: Simulation parameters as in Puga (1999): 333. In (a) m¼ 0.2, g¼ 0.1, y¼ 0.55 and s¼ 4and in (b) m¼ 0.3, g¼ 0.4, y¼ 0.94 and s¼ 4. The breakpoints, see appendix A, are �S¼ 1.6002in Figure 1a, and �S,1¼ 1.1839 and �S,2¼ 1.3887 in Figure 1b. a) Left panel: with labormobility, b) right panel: without labor mobility.





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where regions are related to each other by a more complicated geography structure:

�ij 6¼ � for all i,j ð18Þ

All empirical work within the new economic geography (NEG) literature, be it multi-country (Redding and Venables, 2004) or multi-region (Hanson, 2005; Brakman et al.,2006; Crozet, 2004; Breinlich, 2006; or Knaap, 2006) studies, imposes such a ‘multi-dimensional’ geography structure on the data. Different geography structures (tradecost specifications) have been used in empirical work (Bosker et al., 2007), but in allstudies trade costs depend on bilateral distances between regions and sometimes alsoincorporate the idea that ex- or importing to a region in a different country involvesextra trade costs (tariffs, language barriers, etc.). However, when discussing theimplication(s) of the estimated model parameters and for example trying to answerquestions like ‘where on the bell (tomahawk) are we?’, it is common practice to do thisusing the analytical insights obtained from stylized (but analytically solvable) NEGmodels that use a unidimensional geography structure (and mostly even the simplesttwo-region version of the underlying model); see for example Crozet (2004), Brakmanet al. (2005) or Head and Mayer (2004). It is this mismatch between estimation andinterpretation in terms of the underlying geography structure used that lies at the heartof our paper: given that the equilibrium properties of the estimated ‘multi-dimensional’NEG model are unknown, interpreting the estimation results using theoretical insightsfrom the stylized solvable ‘unidimensional’ models can be considered largely tentativeor even misleading. Or in the words of Behrens and Thisse (2007), ‘it is this challengethat constitutes one of the main theoretical and empirical challenges NEG and regionaleconomics will surely have to face. . .’ (Behrens and Thisse, 2007, 462).

The most elegant solution to this problem would of course be to develop ananalytically solvable version of an NEG-model with a multi-dimensional geographystructure. However, given the mathematical difficulties that are far from straightfor-ward (probably even impossible) to overcome,16 we propose a different strategy in thispaper: simulation. Instead of trying to explicitly solve for equilibrium using Equations(13)–(15), and also (16) in case of interregional labour mobility, making some necessarysimplifying assumptions in the process, one can also use these equations to simulatemodel outcomes. A major advantage of this is that it does not require any simplifyingassumptions about the geographical dependencies between regions. A drawback,however, of performing merely simulations is that one is never 100% certain whether ornot the results found are due to the particular parameter setting used in the simulationand whether or not the equilibrium solution found is unique or not. Given the fact thatthe symmetric equidistant version of the model with interregional labour mobility ischaracterized by multiple equilibria it is not unthinkable to also be a characteristic of amulti-region model with a multi-dimensional geography structure. However, we do notethat the introduction of more asymmetries to the model is likely to reduce themultiplicity of equilibria. For example Krugman (1993) shows this when consideringregions lying on a disc or line, and Fujita and Mori (1996) do the same when some

16 See also Behrens and Thisse (2007) who link the problem of solving an NEG model with an asymmetricgeography structure to the n-body problem in mechanics. An approach that is analytically viable in caseof an interregionally immobile labour force would be to start from the symmetric equidistant equilibriumat high-trade costs and derive the equilibrium location for any small trade cost changes around thatstarting point (see Puga and Venables, 1997).





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regions have an advantage in terms of ease of transportation (hubs). Also, in case ofJapan, Davis and Weinstein (2002) note that interregional asymmetries in physicalgeography (i.e. space required for a large city) severely limit the number of possibleequilibria when it comes to the possible location of Japanese cities.

We think that by extensive simulation, starting at different initial distributions oflabour and/or land over the regions and/or sectors, and using different modelparameters, one can get a good grasp of the model’s behaviour in the multi-region,multi-dimensional geography case. Even more so from an empiricist’s point of view,where the number of parameters to use is restricted to merely one set of parameters(those estimated) and only one initial distribution of labour and land (their currentactual distribution), hereby substantially limiting the number of simulations neededwhen performing robustness checks.

3.1. The simulation setup

The version of the model that we simulate consists of 194 regions, the number ofNUTSII17 regions that make up the 15 countries of the European Union before itseastward expansion in 2004 (this choice is made for sake of comparison to theillustration of our proposed empirical strategy in Section 4). To restrict our attention tothe introduction of more realistic geography structures, we initially deliberately assumethat all 194 regions are of equal size (i.e. Li¼Ki¼ 1/194 for each region i). Oursimulation model solves for the LRE in case of an interregionally immobile labour forceusing a sequentially iterative search algorithm that follows the schematic outline of themodel as presented in Section 2.2, where the algorithm stops whenever the nominalwages in each region change less than 0.00000001% between iterations. In case ofinterregional labour mobility, we also have to specify the way workers move in responseto real wage differences between regions (and subsequently solve for the equilibriumdistribution of labour between manufacturing and agriculture in order to have identicalwages within a region). Following Fujita et al. (1999), we assume that workers moveaccording to the following simple dynamics, which can be reconciled with for exampleevolutionary game theory [Weibull, 1995, see also the discussion in Baldwin et al.(2003)]19:

d�i=�i ¼ cð!i � �!Þ, with �! ¼Xj

�j!j ð19Þ

Where �i ¼ Li=P

j Lj, �! the average real wage per capita and c is a parametergoverning the speed at which people react to real wage differences.18 We define

17 Nomenclature of Territorial Units for Statistics, a division of the EU15 in regions for which statisticalinformation is collected by Eurostat. Excluding Luxembourg and the overseas territories of Portugal,Spain and France, the following 14 countries (nr. regions) are included in the sample: Belgium (11),Denmark (3), Germany (30), Greece (13), Spain (16), France (22), Ireland (2), Italy (20), TheNetherlands (12), Austria (9), Portugal (5), Finland (6), Sweden (8) and The United Kingdom (37).

18 These dynamics imply: �i, þ1 ¼ 1þ ð!i � �!Þ½ ��i, , where denotes a simulation run. Finally, wenormalize �i, in each simulation run to make sure that

Pi �i, ¼ 1.

19 One could in principle also allow for more realistic migration dynamics depending on for exampledistance and allow for country effects such as linguistic or cultural similarity. Allowing for more realisticmigration dynamics would in our view call for empirical estimates of the (relative) importance ofdistance or such country effects in determining migration flows. Interregional migration flows are





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equilibrium to be reached whenever the real wage in each region is less than0.00000001% of the average real wage per capita. We explicitly mention the stoppingcriterion used in our algorithm as we found the equilibrium solution quite sensitive(especially in case of interregional labour mobility) to its specification. With a lessstringent stopping criterion (e.g. 0.000001%) than the one we use in our baselinesimulations, the search algorithm may stop ‘too early’, presenting a SRE characterizedby partial agglomeration as the LRE (see also footnote 24). In general, we stress thatthe type of search algorithm used to find the LRE, that is, the way dynamics areartificially but necessarily introduced in an essentially static model, is of paramountimportance and can potentially give misleading results regarding the agglomerationpattern in the LRE [see e.g. Fowler (2007) and Brakman et al. (2009); for morediscussion on this, see also Section 3.2].

Next, we have to choose the parameter values for which to show the simulationoutcomes. Figure 1a and b already showed that our simulation model replicates thefindings in Puga (1999) using the same parameter values as in that paper (providingconfidence in our simulation algorithm). For our benchmark equidistant multi-regionsimulations, however, we use different parameter values, namely m¼ 0.6, g¼ 0.2,y¼ 0.55 and s¼ 5. This choice is made for the following important reason. Using thisset of model parameters, we can isolate the impact of the assumption made about theinterregional mobility of the labour force on the conclusions drawn regarding the effectof increased integration on the spatial distribution of economic activity. It precludes asituation where the choice of parameters is such that it results in (uninteresting) LREcharacterized by complete agglomeration or symmetry for all levels of trade costs ineither of the two interregional mobility scenarios [note: the latter is the case when usingthe same parameter values as in Puga (1999)20].

To provide a multi-region benchmark for the simulation results in the rest of thework, Figure 2a and b shows the effect of increased integration, using the above-mentioned parameter values, in case of the simplest equidistant 194-region version ofthe model where each region is initially endowed with the same amount of land andlabour (Li¼Ki¼ 1/194 for each region i). Because we are dealing with more than tworegions, the vertical axis depicts the Herfindahl index as our agglomeration measure(HI ¼

Pi �

2i , where �i denotes region i’s share in total economic activity. The advantage

notoriously hard to come by, so that obtaining such estimates is difficult. Using more elaboratemigration dynamics would therefore, while arguably more realistic, be arbitrarily specified instead ofempirically grounded. To avoid complexity, we decided to leave more elaborate specifications of themigration dynamics beyond the scope of this paper and stick to the simple migration dynamics in (19).We do note that some first attempts to introduce more realism in the migration dynamics did not changethe results reported in the following sections.

20 The reason for this difference is that the breakpoints not only depend on the model’s structuralparameters, but also on the number of regions, M, considered. Regarding the choice of structuralparameters, we found that being able to obtain the effect of increased integration in case of aninterregionally immobile labour force similar to Figure 1b, is quite sensitive to two of the structuralparameters, namely y and �. Either y or � needs to be set ‘large enough’. Instead of, as in Puga (1999),picking a high value of y, we decided for the latter option, where our choice is mainly driven by the factthat such a high share of labour in agriculture seems to be more at odds with reality than assuming a highshare of intermediates in final production (see e.g. Hummels, 2001, who document a large increase intrade in intermediates over the last decades). We note that y the share of land in agricultural productionmatters only because—following from our assumed production function in agriculture—it changes thewage elasticity of labour supply across sectors. A high value of y is really about making labour respondquite sensitively to wage differences between the agricultural and the manufacturing sector.





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of using the HI-index is that it allows us to distinguish between different levels ofagglomeration in a multi-region setting.21

Figure 2 shows that the effect of integration on the spatial distribution of industrialactivity is qualitatively similar to the effect shown in Figure 1 and depends crucially onthe assumption of whether or not labour is mobile between regions. In Figure 2a,labour is mobile between regions and, as in Figure 1a, ongoing integration results in asudden move from symmetry to agglomeration. In case of interregional labourimmobility, Figure 2b shows the same move from symmetry to agglomeration and backto symmetry as in Figure 1b, although here we find that the shift from symmetry toagglomeration is not gradual as in Figure 1b [see Puga (1999), footnote 18, for adiscussion of this result].

3.2. Introducing more realistic geography structures

Using Figure 2 as a benchmark, we now turn to introducing an asymmetric geographystructure to the model. Instead of assuming all regions equidistant to each other asin (17), we define the level of trade costs between region i and j as being pair specific,that is.

�ij ¼ �ji ¼ D�ijð1þ bBijÞ if i 6¼ j, and �ij ¼ 1 if i ¼ j ð20Þ

Figure 2. Trade costs and the LRE for 194 equidistant regions.Notes: Simulation parameters: m¼ 0.6, g¼ 0.2, y¼ 0.55, s¼ 5, M¼ 194. The breakpoints, seeAppendix A, are in (a) �S¼ 10.107 and in (b) �S,1¼ 3.2024 and �S,2¼ 5.9710. Stability is checkedby equally shocking half of the regions in terms of number of workers in Figure 2a or in termsof number of workers in manufacturing in Figure 2b. Given that we equally shock half theregions, agglomeration means an equal division of labour /firms over these 97 regions, that is,HI¼ 0.0103. If we instead equally shock R regions, these R regions will attract all footlooseactivity in equal proportion (with each region having a share 1/R of footloose economicactivity. The dashed line shows the value of the HI, 1/194, associated with a perfect spreadingequilibrium of footloose economic activity over the 194 regions. a) Left panel: with labormobility, b) right panel: without labor mobility.

21 Although there are other arguably preferable measures of agglomeration (see e.g. Bickenbach and Bode,2008), we deem the HI suitable when looking at the change in the degree of agglomeration in response tochanges in trade costs. A notable disadvantage of the HI is that it is essentially ‘spaceless’: the same HIcan be accompanied by a different spatial distribution of economic activity [see section 3.3].





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where Dij is the great-circle distance (in kilometers) between region i’s and region j’s

capital city, Bij an indicator function taking the value zero if two regions belong to the

same country and one if not, �� 0 is the so-called distance decay parameter and b� 0 a

parameter measuring the strength of the border impediments. Specifying trade costs this

way is common in empirical studies [see e.g. Anderson and van Wincoop (2004) and

Bosker et al. (2007)]. It captures the notion that trade costs increase with distance and it

also allows international trade to differ from intranational trade (due to either tangible

costs in the form of, for example tariffs, but also due to intangible costs such as

differences in language and culture).

Using (20) as our trade cost specification, we simulate the effect of ongoing

integration on the spatial distribution of economic activity for the following two

cases22:

a. Assuming no border effect, b¼ 0, and looking at the effect of lowering the

distance decay parameter � ! see Figure 3.b. Assuming no transport costs, that is, �¼ 0, and looking at the effect of lowering

the border effect,23 b ! see Figure 4.

The a-panels of Figures 3 and 4 show the results of increased integration for the long

run equilbrium (LRE) in case of an interregionally mobile labour force and the b-panels

when labour is immobile between regions. Comparing Figures 3 and 4 to the

benchmark equidistant case presented in Figure 2, we observe that the effect of ongoing

integration still crucially depends on the assumption whether or not the labour force is

interregionally mobile.Without interregional labour mobility (see Figures 3b and 4b), ongoing integration

will, as in the equidistant case, first result in increased agglomeration followed by a

Figure 3. Transport costs and the LRE for 194 non-equidistant regions.Notes: m¼ 0.6, g¼ 0.2, y¼ 0.55, s¼ 5 and b¼ 0. The dashed line shows the value of the HIassociated with a perfect spreading equilibrium, HI¼ 1/194. a) Left panel: with labor mobility,b) right panel: without labor mobility.

22 See Appendix B in Bosker et al. (2007) for an illustration of what happens when combining these twoeffects.

23 Note that the symmetric multi-region case (for which analytical results are available) is equivalent tohaving zero transport costs and only border effects when all regions are in different countries.





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return to symmetry with further integration. The shift from symmetry to agglomeration

and back to symmetry is however not as sudden as in the equidistant case (resembling

much more the bell-shaped curve as found when using Puga’s parameter settings, recall

Figure 1b). Moreover, complete agglomeration is never reached; manufacturing activity

is still present in several regions.With interregional labour mobility, ongoing integration in the form of decreasing

trade costs, as depicted in Figure 3a, also has a similar effect as in the equidistant case.

It results in a sudden (catastrophic) change in the economic landscape from symmetry

to complete agglomeration. With a positive border effect, as in Figure 4a, full

agglomeration is always the LRE outcome for any level of the border effect

shown here.24

Figure 4. The border effect and the LRE for 194 non-equidistant regions.Notes: m¼ 0.6, g¼ 0.2, y¼ 0.55, s¼ 5 and �¼ 0. The dashed line shows the value of the HIassociated with a perfect spreading equilibrium, HI¼ 1/194. a) Left panel: with labor mobility,b) right panel: without labor mobility.

24 The above results in case of interregional labour mobility are different from the findings in Stelder (2005)and Brakman et al. (2006) (the latter is also based on Stelder’s model but starting the simulationsfrom the actual distribution instead of an equal distribution of labour across regions). In these twopapers, multi-region simulations of the Krugman (1991) model (where labour is mobile betweenregions) with an asymmetric geography structure give rise to long run equilibria characterized byincomplete agglomeration, with the level of agglomeration increasing and the number of agglomeratedregions decreasing the lower trade costs. Here, we find that agglomeration forces are so strong in amodel with interregional labour mobility that, when the spreading equilibrium becomes unstable,each introduced asymmetry (here relative location, but one could also think of asymmetric initialendowments) always results in the one region that is the most favorable in terms of net asymmetriesattracting all industrial activity. That the above-mentioned papers find partial agglomerationwhen labour is interregionally mobile could possibly be explained by the particular geographystructure used in those papers. For example, the exponential distance decay function, resulting inhighly localized areas of relatively cheap trade, or the particular distance grid used in these papers[in Brakman et al. (2006) also the initial asymmetric interregional distribution of labour could play arole]. However, we think this is unlikely: the only way we are able to find partial agglomeration patternssimilar to those presented in the above-mentioned papers (even when using similar model parametersand the same distance decay function) is when using a higher stop criterion in our search algorithm(see pp. 11–12 for a discussion of the sensitivity of the simulated long run equilbrium to the stopcriterion). This suggests that these earlier papers could mistakenly be taking a short run for a longrun equilibrium.





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3.3. Same overall degree of agglomeration—but different spatial distribution

A major difference with the equidistant case is that the same level of agglomeration as

measured by the Herfindahl index does not necessarily mean the same spatial

distribution. This is especially so when there is interregional labour immobility as

illustrated by Figure 5. But also in case of interregional labour mobility, the same level

of agglomeration does not necessarily mean the same spatial distribution of economic

activity.25 In Figure 5, the left and the right panel show the spatial distribution of the

manufacturing sector obtained using the same parameters as in Figure 3 and the same

initial (equal) distribution of land and labour over all regions, but for two different

values of � that are chosen such that the distribution in both panels gives rise to the

same value of the Herfindahl index. That is, the left/right panel shows the distribution

on the right/left side of the bell in Figure 3b, corresponding to a lower/higher level of

economic integration respectively.In the simple equidistant models, and given the same initial symmetric distribution of

land and labour over the regions, these two distributions would be exactly the same. As

can be seen from Figure 5, this no longer holds when allowing for a more realistic

geography structure: the left panel shows a distribution with a group of centrally

located core regions (in Belgium, The Netherlands and Germany), surrounded by a ring

of ‘empty’, agricultural, regions but still some industrial activity in the peripheral

regions (Scandinavia and Mediterranean Europe). The right panel instead shows a

much more centralized group of core regions in Belgium and the Netherlands,

extending out into its immediate surrounding regions (the southern UK, northern

France and Germany) but with no longer any industrial activity in the peripheral

regions.More generally, we find, on the basis of more extensive simulations (not shown here),

that starting from a symmetric distribution of industrial activity, increased economic

integration has the following effect on the spatial distribution of economic activity.

At a certain level of integration, agglomeration starts, with a number of core regions

Figure 5. Similar agglomeration but different regional distribution.Notes: Simulation parameters as in Figure 3b. Left panel: �¼ 0.29. Right panel: �¼ 0.13.HI¼ 0.011.

25 See the Appendix of Bosker et al. (2007).





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attracting activity from nearby regions (creating an agglomeration shadow), still leavingsome level of industrial activity in the peripheral regions. As integration proceeds, thisprocess continues until the peripheral regions are completely specialized in agricultureand industrial activity only takes place in the centrally located core regions (hub effect).A further fall in trade costs eventually reverses this process, with industrial activitygradually spreading out from the core, at first to nearby regions (not to the peripheralones) and eventually reaching the peripheral regions again.

3.4. The importance of the geography structure imposed

Essentially, the way regional interactions in the economy are modelled, that is,the imposed geography structure crucially and predictably influences the wayintegration affects the distribution of economic activity [see also Behrens and Thisse(2007), Krugman (1993) or Puga and Venables (1997)].26 That is, in our case, thedistance matrix, Dij, and the border-dummy matrix, Bij, together determine theequilibrium outcomes whereas the parameters (� and b) in the trade cost function (20)determine the strength of the Dij and Bij effects. When only Dij is allowed to havean effect by setting the border parameter b equal to zero, agglomeration will alwaysbe in or around the most centrally located regions in case of interregional labourimmobility (see Figure 5) and in the most centrally located region in case ofinterregional labour mobility (i.e. Vlaams–Brabant in our case). Note that thiscorresponds to the hub effects found in, for example Puga and Venables (1997, Section4.2), Fujita and Mori (1996) or Krugman (1993): the best connected regions attractmost economic activity.

When instead only Bij is allowed to have an effect by setting � to zero, Figure 6 showswhat happens when border impediments are decreasing in case of an interregionallyimmobile labour force. Now agglomeration, if it occurs, will be in countries with manyregions relative to other countries, with the regions within these countries all having thesame share of footloose industrial activity. As can be seen when comparing the left andright panel of Figure 6, when the border effect becomes less important, ever fewercountries retain footloose activity. In case of interregional labour mobility (not shownhere), the largest country in terms of number of regions, that is, the United Kingdom inour case will eventually attract all industrial activity (again equally spread over theregions within the United Kingdom).27 Again this corresponds to results in, for examplePuga and Venables (1997, Section 4.1) regarding the effect of preferential tradingarrangements (captured here by preferential trading between regions in the samecountries).

To sum up this section, many of the qualitative conclusions obtained from the simplesymmetric NEG models do carry over when introducing a more realistic asymmetricgeography structure. Catastrophic agglomeration as a result of increased integrationremains a characteristic of the model with interregional labour mobility. Also in case of

26 If more asymmetries are introduced (as e.g. in the next section asymmetric initial distributions of labourand land), these will also play a crucial role.

27 Note that this shows the importance of the definition of a region. Using a different subdivision ofcountries into regions will have an impact on the simulation results when considering the importance ofborder effects.





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interregional labour immobility, the impact of increased integration shows a similarpattern in terms of the LRE agglomeration levels (first increasing and finallydecreasing) as in the simple symmetric models. However, as shown in this section,a big difference with the symmetric versions of the model is that the same level ofagglomeration (in terms of some agglomeration index) does not necessarily mean thesame spatial distribution of economic activity once a more realistic geography structureis added to the model. Finally, the simulated effects of increased integration dependcrucially (and predictably) on the type(s) of asymmetric geography structure imposed,hereby corroborating among others results in Krugman (1993), Puga and Venables(1997) or Behrens et al. (2007).

4. Bridging the gap between NEG theory and empirics—illustrating our proposed empirical strategy

Having established the effects of introducing non-equidistant regions in the Puga (1999)model, we now turn to the illustration of the empirical strategy—combining estimationwith simulation—that we propose to overcome the ‘mismatch’ between NEG theoryand empirics characterizing previous empirical work in NEG. Combining estimationand simulation provides a way to link structural estimates of the important NEGparameters back to the actual ‘multi-dimensional’ NEG model that underlies theseestimates instead of relating them to the stylized, analytically solvable equidistant(or even two-region) model.

4.1. Estimating the structural parameters

Our empirical illustration focuses on the 194 NUTSII regions of the 15 EU countriesthat formed the European Union before its eastward expansion in 2004. To illustratethe usefulness of our proposed strategy, we first obtain estimates of the structural modelparameters in the Puga (1999) model. Using data from Cambridge Econometrics oncompensation per employee and gross value added (GVA) for our sample of 194 EU15

Figure 6. Changing the border impediments Bij (Fig. 4b in more detail).Notes: Simulation parameters as in Figure 4. Left panel: b¼ 8. Right panel: b¼ 3.





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NUTS-II regions over the period 1992–2000,28 we obtain the estimates of s, � and b by

estimating, using NLS panel data techniques, the wage equation (in logs) shown in (14)

while substituting (20) for �ij.29 Our estimates of s and � are in line with other empirical

work on NEG (see e.g. Head and Mayer, 2004). We find a quite strong distance decay

(�¼ 0.102) indicating localized agglomeration forces.30 Parameter values of m and g are

calculated using data from Input–Output Tables provided by the OECD (edition 2002)

and y is calculated using Eurostat data on the compensation of employees and GVA in

the agricultural sector in the EU-15 for the year 1995. Table 1 shows the resulting

parameter estimates, together with the breakpoints (�s, �s,1 and �s,2) that would apply at

these parameter settings for our 194-region model if we would stick to the case of an

equidistant geography structure and land and labour (initially) equally distributed

across regions (in case of both interregional labour mobility and immobility,

respectively). Note that we set g at 0.944, which is manufacturing’s share in total

manufacturing, m, plus agricultural share’s economic activity, a, in the EU economy:

[m=ðmþ aÞ ¼ 0:335=ð0:335þ 0:02Þ ¼ 0:944]. This amounts to treating services as

exogenous and completely separate from the part of the economy (agriculture and

manufacturing) considered by the Puga (1999) model.31

Next, we use these parameters in the following simulation exercises while setting

b at 0.32 The asymmetric geography structure between regions is certainly not the only

28 Due to wage data availability, we use data at the NUTS I-level for Germany and London, which leavesus with 183 regions.

29 More specifically, we use the same estimation strategy as in Brakman et al. (2006), addressing theendogeneity inherent in the NEG wage equation by measuring market access at a higher level ofaggregation (NUTS I) following Hanson (2005). For more detail, see Brakman et al. (2006), Section 3:618–619. Like in Brakman et al. (2006), we set m¼ 0 in the estimation of the wage equation. First-naturegeography variables are omitted as explanatory variables, we do include country dummies.

30 Our estimated distance decay parameter is however in the lower range of distance decay coefficients foundin other empirical NEG or trade studies (see e.g. Head and Mayer, 2004 or Disdier and Head, 2008).

31 We thank an anonymous referee and Diego Puga for this suggestion. See Bosker et al. (2007) for the casewhen setting g at 0.335 (the share of manufacturing in total economic activity).

32 One can choose any parameter value for the border effect as one can be 99% sure that it lies within therange [�1.16� 1014, 1.16� 1014]. A possible reason for the insignificance of this parameter may be thatthe extent of the border effect differs substantially among different pairs of EU15 countries [Breinlich(2006) provides evidence on this].

Table 1 Structural parameter estimates

s 7.122

� 0.102

b 285.65

g 0.944

� 0.284

y 0.234

Labour interregionally mobile

�s such that: Symmetry never stable

Labour interregionally immobile

�s,1 and �s,2 such that: Symmetry always stable

Notes: In the estimation of the wage equation s and � are significant

(P value: 0.000). b is insignificant (P value: 1.000).





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real world asymmetry faced by the empirical researcher or policy maker. Instead, thecurrent (unequal) distribution of economic activity is also of paramount importance.Indeed, in reality, the observed spatial distribution of economic activity is very muchthe result of the interplay between relative (distance) and absolute (economic mass orsize) geography. To take account of this, we also introduce the true initial distributionof labour (total employment share) and land (arable land share), shown in Figure 7aand b, respectively, as additional asymmetries to the simulation exercises. This isdifferent from Section 3 where we initially endow each region with the same amount ofland and labour. In all our subsequent simulation results, we have used these regions’actual shares in employment and arable land as the initial (starting) values of thesimulation.33

4.2. Simulating the impact of ongoing EU integration

Having specified the simulation settings in the previous section, we now turn tosimulating the effect of ongoing integration. Hereby, we focus on ‘a decrease ininterregional transport costs’ (the EU e.g. supports the construction and upgrading oftransportation links) by looking at the effect of decreasing � on the spatial distributionof economic activity. In Appendix B, we also show the results when we instead considera ‘decrease in border impediments b’ (the EU stimulates the formation of an internalmarket by removing trade barriers, streamlining national regulations and removingborder controls). Figure 8 shows how the resulting long run equilibria depend on� when labour is either (a) interregionally mobile or (b) interregionally immobile.In both Figure 8a and b, the dashed line shows the value of the Herfindahl indexassociated with the actual, initial spatial distribution of economic activity across the

194 regions.

Figure 7. Adding economic mass: actual labour and land distributions. a) Left panel: totalemployment; b) right panel: arable land.

33 It is important to note that in the Puga (1999) model arable land is used to capture the idea that, whenintegration goes far enough, the cost of certain non-tradables, such as land or housing, becomes crucialand prevents the catastrophic results (see also e.g. Helpman, 1998).





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With interregional labour mobility (see left panel of Figure 8), we find that the

agglomeration forces in the model are so strong that we always end up with complete

agglomeration in the region Ile-de-France (Paris) that is, both centrally located and

initially already the region with the largest share of workers. Even when transport costs

are large (�41), these do not impose a spreading force large enough to have the economy

move towards a more equal distribution across the 194 regions.34 Only when transport

costs become irrelevant (�¼ 0) can industrial activity be found outside the Ile-de-France

region [distributed similarly as in case of no labour mobility and �¼ 0 (see Figure 10a)].Without interregional labour mobility (see Figure 8b), we again find a ‘bell-type’

agglomeration pattern, be it much less clearly a bell than in Figure 3b. Interestingly, in

the (long run) equilibrium the spatial distribution of manufacturing activity is always

more spread out than the current distribution across EU regions.35 Also, and to further

relate our estimation results back to the underlying multidimensional NEG model, we

can plug in the estimated value for � (0.102) to get an idea of what the (long run) NEG

equilibrium corresponding to the estimated parameter values in Table 1 looks like (see

the dot in Figure 8b). Figure 9 maps this distribution (Figure 9b) and compares it to the

actual distribution of manufacturing labour across the EU regions in our sample

(Figure 9a). In Figure 9c, fully coloured regions denote regions with a larger share in

manufacturing activity in Figure 9b than in Figure 9a (and the more so the darker

coloured), whereas dashed regions denote regions with a smaller share in manufacturing

activity in Figure 9b than in Figure 9a (and the more so the darker coloured).

Figure 8. Transport costs and the LRE when geography matters.Notes: Simulation parameters as in Table 1 and the simulations are started using the actualdistributions of arable land and total employment (see Figure 8). Left panel: interregionallabour mobility. Right panel: interregional labour immobility. The dashed line corresponds tothe HI (0.011) associated with the actual initial distribution of economic activity across our EUregions. The black dot in the Figure 8b denotes the long run equilibrium distribution associatedwith estimated value of �¼ 0.102 [see Table 1]. a) Left panel: with labor mobility, b) rightpanel: without labor mobility.

34 In Bosker et al. (2007), we show that when giving the manufacturing sector less weight in consumers’utility, the economy does spread out for high levels of transport costs. In that case, the economy willeventually spread out–—given the assumed production function in agriculture—according to thegeographic dispersion of arable land (i.e. people start moving to regions that offer them higher wages dueto the larger supply of arable land).

35 In Bosker et al. (2007), we show that when giving the manufacturing sector less weight in consumers’utility, the simulated long run distribution can also become more agglomerated than the current actualdistribution.





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This shows that in the simulated LRE the distribution of economic activity is indeed

more spread out. In particular, we see by looking at Figure 9c that compared to the

actual spatial distribution in Figure 9a, the peripheral regions within Europe, but also

generally within each country, gain in manufacturing activity mostly at the expense of

the established industrial centres. Taking this argument even further, we can also give a,

be it very tentative, prediction regarding the effect of increased integration on the

spatial distribution of economic activity that is based on taking our estimated model

parameters and the Puga (1999) model seriously.36

Figure 9. Interregional labour immobility: actual and simulated long run equilibrium.(a) Actual manufacturing labour; (b) LRE at �¼ 0.102; (c) % difference between (a) and (b).Notes: In the right panel, the simulation parameters as set as in Table 1 and �¼ 0.102 andstarting the simulation using the actual distributions of arable land and total employment(see Figure 7).

36 We certainly do not want to claim that this prediction is the best prediction, because our aim, recall theintroduction of our paper, is not to come up with the most realistic (NEG) model of the EU regions.Instead, our prediction is the prediction that would follow from consistently interpreting the estimatedNEG parameters taking the multidimensional (but still stylized) NEG model that underlies theseestimates seriously. It is thus first and foremost meant to illustrate what our suggested strategy as to theempirical use of NEG models in a world with asymmetric trade costs and other regional asymmetries(like labour or land distribution) would imply when a particular NEG model, in casu Puga (1999),is applied to a real world case. See also Section 4.3 on this issue.





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Given that Figure 9b depicts where we would end up on the bell given the estimated

structural parameters and the current distribution of land and labour across the EU

regions, Figure 10 shows that further integration (decreasing �) would result in an evenmore dispersed distribution of industrial activity. Note however that this return will not

mean going back to a completely symmetric distribution of footloose activity across EU

regions (in which case the HI would be about 0.005). Instead, when �¼ 0 the

distribution of manufacturing activity looks like the one depicted in Figure 10a.Compared to Figure 9b the peripheral regions gain even more by full integration,

with regions in Scandinavia, Greece, Scotland, Southern Italy and Portugal gainingmore industrial activity at the expense of Europe’s core regions in The Netherlands,

Germany, Northern Italy and the Southern UK.

4.3. Discussion

It is still worthwhile to ask how realistic the predictions are that follow from our

empirical application of the Puga (1999) model to the NUTSII EU regions. In case offree interregional labour mobility (except when trade is costless), the simulated LRE is

always characterized by one region (in our case Ile-de-France) attracting all

manufacturing activity. This is clearly not what we observe in the real world, where

the spatial distribution of industrial activity is characterized by partial agglomeration

(many regions with industrial activity but some more so than others). In that respect,

the simulation outcomes are closer to reality when we do not allow for interregionallabour mobility. In that case, the additional spreading force imposed by the increased

wage costs which firms face when attracting workers from the agricultural sector plays

an important role as it will not be weakened by the possibility to attract workers from

Figure 10. Simulated long run equilibrium no transport costs. a) Left panel: LRE at �¼ 0;b) right panel: extra difference (ppt) with (a).Notes: The simulation parameters are as in Table 1 with �¼ 0 and the simulation is based onthe actual distributions of arable land and total employment. (b) shows the extra % differencewith the actual distribution of manufacturing activity (as in Figure 9a) in ppt compared toFigure 9b. In (b), fully coloured regions denote regions with a larger difference compared to (b)(and the more so the darker coloured), whereas dashed regions denote regions with a smallerdifference compared to Figure 9b (and the more so the darker coloured).





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other regions. As a result, firms are at some point attracted by the lower wages in

peripheral regions, preventing them to cluster in one region only.As the empirical evidence points to relatively low-interregional labour mobility

within Europe, and even within European countries, we think that the simulation

results under the assumption of interregional labour immobility are more realistic [see

also Puga (2002)] than the extreme core-periphery pattern that shows up when allowing

for interregional labour mobility across EU regions [see Braunerhjelm et al. (2000) for a

detailed discussion on labour mobility in Europe or Obstfeld and Peri (1998) for

empirical evidence showing a much lower migration response to shocks in labour

demand in European countries compared to the United States].However, labour is in principle free to move within the EU. The fact that our

predictions based on the Puga (1999) model allowing for interregional labour mobility

are not able to come (even) close to the actual observed distribution of economic

activity37 no doubt points to the limitations of the model used and to the omission of

important additional spreading forces. One can think of an immobile service sector,

land consumption [e.g. the form of housing as in Helpman (1998)], transport costs in

agriculture (Fujita et al., 1999, chapter 5), commuting costs within agglomerations

(Tabuchi and Thisse, 2006) or more generally costs of migration (so that workers no

longer respond to any infinitesimally small interregional real wage difference).38 Also,

adding additional heterogeneity in, for example consumer preferences or regional

productivity could result in partially agglomerated model predictions that come closer

to the EU reality.But to round up our analysis and to restate our main aim, this article is not about

providing the ‘best’ NEG model for the EU. In fact, the empirical analysis of the

European NUTSII regions is only meant to illustrate the usefulness of our suggested

empirical strategy of combining estimation of NEG structural parameters with

simulation of the underlying theoretical NEG model. It offers a way to ‘bridge the

gap between (multidimensional) NEG empirics and (largely unidimensional) NEG

theory’. As such, our predictions for the degree of agglomeration in the EU presented in

Sections 4.1 and 4.2 may not be that realistic; they are the predictions that follow from

consistently interpreting the estimated NEG parameters while taking the multi-

dimensional (but still stylized) NEG model that underlies these estimates seriously. One

could easily argue that our model, or any (analytically solvable) NEG model for that

matter, is much too stylized to apply to a case like the EU regions, requiring much more

elaborate CGE models that incorporate, for example more sectors, transport costs in

agriculture or additional spreading forces instead [see e.g. Forslid et al. (2002a), Forslid

et al. (2002b), Brocker (1998) or Venables and Gasiorek (1999)]. This would constitute a

different analysis altogether than the one we present in this paper; and notably one

where the link between empirical outcomes and the underlying theory (our main

concern in this article) would be much weaker or even non-existent.

37 Also when allowing for only intranational labour mobility [see Appendix C], a strong core-peripherypattern shows up, but in that case within each country.

38 A simple way to gauge the effect of an increase in the strength of spreading forces within the simple setupof the Puga (1999) model, would be to increase the consumption share g in agriculture. See Bosker et al.(2007) for the results of setting g¼ 0.335.





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5. Conclusions

Most NEG models treat geography in a very simple way: attention is either confined toa simple two-region or to an equidistant multi-region world. As a result, the mainpredictions regarding the impact of, for example diminishing trade costs are based onthese simple models. In empirical work, these simplifying assumptions becomeproblematic as conclusions from these simple models may not carry over to theheterogeneous geographical setting faced by the empirical researcher or policy maker.This paper proposes an empirical strategy that combines estimation of the structuralNEG parameters with simulation of the underlying multi-dimensional NEG model tobridge this gap.

First, we assess, through extensive simulation, the effect of adding more realisticgeography structures to the NEG model of Puga (1999), one of the main NEG modelsthat encompasses several other core NEG models. We show that many, although notall, conclusions from the simple models do carry over to a multi-region setting withmore realistic geography structures. The effect of increased levels of integration on thelevel of agglomeration is very similar to that found in the simple equidistant (and oftentwo-region) models. With interregional labour mobility, agglomeration levels increasewith the level of integration, and, as in the equidistant model, this increase is mostlycatastrophic. Without interregional labour mobility, increased integration is accom-panied by a steady (not a catastrophic) increase in the level of agglomeration. And whenintegration proceeds even further this process is reversed, resulting in a return to anequal distribution of economic activity over all the regions, hereby confirming the bell-shaped pattern in the analytically solvable model. Although the qualitative results aresimilar to the simple equidistant models, a major difference that we find is that the samelevel of agglomeration—as measured by, for example the HI-index—can correspond tovery different spatial distributions, especially so when labour is interregionallyimmobile. Also, the results depend crucially (and predictably so) on the type(s) ofasymmetric geography structure imposed.

Second, having established the effect of introducing more realistic geographystructures to a multi-region NEG-model, we illustrate our proposed empirical strategyto bridge the gap between NEG theory and empirics using a sample of Europeanregions. First, we estimate the key structural NEG parameters. Next, we do not—asstandard in most empirical work in NEG—relate these parameter estimates back to thestylized equidistant (or two-region) models to obtain NEG-based predictions regardingthe effect of increased integration on the spatial distribution of economic activity.Instead, we use the estimated parameters in combination with the current distributionof economic activity across EU regions and simulate the underlying asymmetric multi-region NEG model to derive empirically grounded, theory-based predictions regardingthe impact of increased European integration.

We again find that the extent and spatial pattern of agglomeration crucially dependson the assumption about interregional labour mobility. In case of interregional labourmobility, the model’s predictions are probably too extreme suggesting a very strongcore-periphery model with all economic activity concentrated in Ile-de-France. Whenlabour is interregionally immobile (in our view not a completely far fetchedassumption in case of the EU), the model’s predictions become less extreme andpoint to a likely decrease in interregional disparities as a result of further EUintegration.





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Overall, we show the usefulness of our proposed empirical strategy in overcoming themismatch between NEG-theory and NEG-empirics that is present in all empiricalstudies that interpret estimates of structural NEG parameters in terms of a stylizedunidimensional NEG model. In our view, our proposed strategy of combiningestimation of structural NEG parameters with simulation of the underlying multi-dimensional NEG model does much more accurately link the empirical results back totheory. Hereby, it improves the researcher’s possibility to interpret the results and todraw conclusions about the empirical relevance of the assumed structural multi-dimensional NEG model that underlies his/her estimates.

Acknowledgements

We thank Joppe de Ree, Jacques Thisse and Seminar Participants at the 2006 North AmericanRegional Science Conference in Toronto and the 2007 Kiel workshop on Agglomeration andGrowth for helpful comments and suggestions. We are in particular grateful to three anonymousreferees and the editor, Diego Puga, whose comments have significantly improved our work.

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Appendix A

Breakpoints of the Puga (1999) model

Focusing on the two-region version of the model only [in Puga (1999), Appendixes A1and A2 shows the results for the M-region equidistant version of the model], we brieflysummarize the analytics behind Figure 1a and b.

In case of an interregionally mobile labour force (see Figure 1a), there exists aminimum level of transport costs at which a symmetric distribution of firms andworkers is a stable equilibrium, that is, symmetry is stable for levels of transport costs39:

�ij ¼ � � �S ¼ 1þ2ð2� � 1Þ½� þ �ð1� �Þ�

ð1� �Þfð1� �Þ½�ð1� �Þð1� �Þ � 1� � �2�g

� �1=ð��1Þ

ðA1Þ

where � is the wage elasticity of labour supply from a region’s agricultural to itsmanufacturing sector.40 Also, a maximum level of transport costs at whichagglomeration (i.e. with industrial production and the labour force located in onlyone region) is a stable equilibrium can be derived, that is, agglomeration is stable forlevels of transport costs smaller or equal to �B, being a (positive) solution to

�½�ð1��Þð1��Þ�1� �2ð1��Þ þð1� �Þð1� �Þ

1þ ��=ð1��Þð�2ð1��Þ � 1Þ

� �¼ 1 ðA2Þ

In case of an interregionally immobile labour force (see Figure 1b), the results arequite different. In that case, Puga (1999) shows that a symmetric distributionof industrial production is an unstable equilibrium for the following range oftransport costs: 05�S,15�5�S,251, with �S,1 and �S,2 the (positive) solutions of thefollowing quadratic expression41:

½�ð1� �Þ � 1�½ð1þ �Þð1þ �Þ þ ð1� �Þ��½�1��2

� 2f½�ð1þ �2Þ � 1�ð1þ �Þ � �ð1� �Þ½2ð� � 1Þ � ��g�1��

þ ð1� �Þ½�ð1� �Þ � 1�ð�þ 1� �Þ ¼ 0

ðA3Þ

and stable for levels of transport costs smaller than �S,1 and larger than �S,2.

39 This is the case provided that the denominator is larger than zero. If this does not hold, agglomeration isthe only stable equilibrium for all possible levels of transport costs.

40 Here, � ¼ �ð1� �Þ=�ð1� �Þ given the assumed Cobb–Douglas production function in agriculture.41 Note that in order for Equation (21) to have two solutions in the required range, the model parameters

have to adhere to some additional requirements [see Puga (1999) or Bosker (2009) for more details].





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Appendix B

The simulated effect of a decrease in border impediments

In Section 4.2, we focused on the effect of ‘a decrease in interregional transport costs’(modelled by decreasing �). In this Appendix, we instead show the effects of a ‘decreasein border impediments’ on the spatial distribution of economic activity in the EU (theEU, e.g. stimulates the formation of an internal market by removing trade barriers,streamlining national regulations, and removing border controls). As in Section 4.2, weuse the estimated structural parameters shown in Table 1 together with the actualdistribution of land and labour across our 194 EU regions, and simulate the effects of adecrease in border impediments by a decrease of the border parameter b. Figure A1shows the resulting long run equilibria in case of (a) an interregionally mobile and (b)an interregionally immobile labour force.

With interregional labour mobility, we find the same results as in Figure 8a whenconsidering a decrease of transport costs �: no matter how high the level of borderimpediments, the agglomeration forces are so strong that we always end up with fullagglomeration (in Ile-de-France). Again, only in case of full integration (no borderimpediments left, b¼ 0) do we find industrial activity outside the Ile-de-France region.In case of interregional labour immobility, Figure A1b shows that higher borderimpediments result in a long run distribution characterized by more agglomeration thanwhen these border impediments are absent.42 Also, it shows that, with the exception ofvery low values of the border impediments, an increase of the border impediments hasalmost no apparent effect on the spatial distribution of footloose activity (the

Figure A1. A decrease of border impediments and the long run equilibrium.Notes: Simulation parameters as in Table 1 and the simulations are started using the actualdistributions of arable land and total employment (see Figure 7). Left panel: interregionallabour mobility �¼ 0.102. Right panel: interregional labour immobility, �¼ 0.102. The dashedline corresponds to the HI (0.011) associated with the actual initial distribution of economicactivity across our EU regions. a) Left panel: with labor mobility, b) right panel: without labormobility.

42 Still the Herfindahl index of the simulated LR-distribution is always lower than that corresponding tothe actual distribution of manufacturing activity (see Figure 9a).





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correlation coefficient between the distribution at b¼ 1 and at b¼ 6 is almost equal toone). Note that this insensitivity of the simulated LRE distribution to changes in theborder parameter is very much consistent with our highly insignificant estimate of theborder parameter (see Table 1). Figure A2 shows the simulated long run distributioncorresponding to a very high degree of border impediments (b¼ 6) along with, for eachregion, the percentage difference in terms of manufacturing activity with the long rundistribution in the absence of such border impediments (see Figure 9b).

Compared to the case of no border impediments in Figure 9b, we observe that theincreased border impediments result in manufacturing activity to concentrate more intothe a priori large regions on a country-by-country basis (cf. Figure A2b with Figure 9a).The larger border impediments make the domestic market more important for firms’location decision resulting in them moving more reluctantly across internationalboundaries. Instead of moving towards the larger European industrial centres, theytend to move to the already established industrial centres within their home country.

Appendix C

Labour mobile but only within countries

As intranational labour mobility is much higher in Europe than international labourmobility, and to complement the discussion in Section 4.3, Figure A3 shows thesimulated LRE distribution of economic activity that results when allowing people tomove interregionally, but only so within their country of residence. In that case, peoplemove in response to real wage differences between regions within their own countryonly.

Figure A3 shows that in that case, and using the estimated parameters of Table 1, wewould find a strong core-periphery pattern within each country with generally the

Figure A2. The effect of increasing the border impediments (b¼ 6). a) Left panel: LRE atb¼ 6; b) right panel: difference (%) with (b), b¼ 0.Notes: The simulation parameters as set as in Table 1 with �¼ 0.102 and starting the simulationusing the actual distributions of arable land and total employment (see Figure 7). In (b), fullycoloured regions denote regions with a larger share of manufacturing activity compared toFigure 9b (and the more so the darker coloured), whereas dashed regions denote regions with ashare of manufacturing activity compared to Figure 9b (and the more so the darker coloured).





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region that initially already hosted most economic activity attracting all the country’seconomic activity (the only exception to this rule is Sweden, where the initially largestregion (Stockholm) loses its status to the within Europe much more centrally located,and also initially second largest Swedish region, Vastsverige.

Figure A3. The long run equilibrium assuming only intranational labour mobility.Notes: parameters are set as in Figure 9b. During the simulation, we fix each country’s shareof total EU working population, that is, Belgium, 3%; Denmark, 2%; Germany, 20%;Greece, 3%; Spain, 10%; France, 15%; Ireland, 1%; Italy, 15%; The Netherlands, 4%;Austria, 2%; Portugal, 3%; Finland, 1%; Sweden, 3% and the UK, 19%.





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Adding geography to the new economic geography: …brakman/Adding.pdfKeywords: new economic geography, multi-region simulations, empirics JEL classifications: F15, O18, R12, R11 Date

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