European Integration and Domestic Regions: A Numerical Simulation Analysis

Does European economic integration create more inequality between domestic regions, or is the opposite true? We show that a general answer to this question does not exist, and that the outcome depends on the liberalization scenario. In order to examine the impact of European and international integration on the regions, the paper develops a numerical simulation model with nine countries and 90 regions. Eastward extension of European integration is beneficial for old as well as new member countries, but within countries the impact varies across regions. Reduction in distance-related trade costs is particularly good for the European peripheries. Each liberalization scenario has a distinct impact on the spatial income distribution, and there is no general rule telling that integration causes more or less agglomeration.


Introduction *
How does European integration affect domestic regions? This question is urgent not only for those directly affected but also for policy makers: regional support constitutes a main component of the common policies of the European Union. In the -2013 Framework of the EU, 36% of total funds is allocated to such "cohesion activities". 1 While Greece, Ireland, Portugal and Spain were the main beneficiaries of EU regional support during the years preceding the 2004 enlargement, regions in the new member states have now taken over this role.
On this background, it is of considerable interest to know whether integration as such tends to widen or narrow the core-periphery gaps inside countries. If the latter was to be true, European integration would by itself be a good regional policy, and the case for budget support would be weaker. Ederveen et al. (2006) find that EU structural funds are only effective in regions that are open or have good institutional quality. For EU policy, especially in the context of the EU Neighbourhood Policy (see e.g. Dodini and Fantini 2006), an urgent issue is whether there is an "agglomeration shadow" whereby regions outside the enlarged EU are worse off.
A growing body of evidence (see e.g. World Bank 2000, Römisch 2003, Landesmann and Römisch 2006 suggests that regional inequality is on the rise in new member states. According to a recent comprehensive assessment (Melchior 2008a) covering 36 countries in Europe and beyond, there is no doubt: During 1995-2005, there was a substantial increase in domestic regional inequality within all Central and Eastern European countries. Given that East-West European free trade agreements and EU enlargement has been implemented during the last decade, an issue is therefore whether integration as such has been a cause for the observed increase in regional inequality. Or is it, on the contrary, the case that European integration promotes regional convergence within countries?
Existing research provides no clear answers about whether international integration promotes convergence or divergence between domestic regions. In section 2, we review some empirical work as well as some recent theoretical contributions within the new economic geography (NEG) and conclude that the answer to our main question is ambiguous in terms of theory as well as empirics. In this paper, we argue that there is no general answer to this question, and searching for such a general rule is barking under the wrong tree.
As an illustration, some of our results suggest that East-West regional integration will have an uneven impact on western and eastern regions within former member states and the new members. In the new member states, for example, western regions may be more stimulated by integration. Whether this contributes to more or less regional inequality, depends on the initial pattern of regional inequality. Furthermore, we show that the east-west impact of integration is quite different with other forms of international trade integration, for example multilateral trade liberalization of the WTO (World Trade Organization) type, or reduction in distance-related trade costs (such as transport costs). Hence the impact of international integration on domestic regional inequality depends on the type of integration as well as the initial income distribution. European regions have been affected by various stages of European integration, multilateral integration through WTO, and reductions in transport costs. We cannot expect that all these forms of integration have similar effects on domestic regions.
In order to address such integration effects, we should not only ask whether there will be spatial agglomeration of economic activity, but where this agglomeration will be. Will international integration stimulate growth in the north, south, east or west of a country, or its central areas? In order to address such issues, we need models of sufficient dimensionality: with a sufficient number of countries, and with distinct regions within each country. In trade theory and the new economic geography (NEG), the issues have mainly been addressed using low-dimensional models with three or four regions (see Section 2 for references). Many questions about European integration and domestic regions can however not be addressed within such models. Concluding their survey of the new economic geography (NEG), Fujita and Mori (2005) consider the development of higher-dimensional spatial models as one of the top priorities for future research in the field. 2 The ambition in this paper is therefore to develop a higher-dimensional model for the study of European integration, in order to highlight the issue and develop a platform for empirical work in the field. In this way, we try to move from economic geography to geographical economics, by developing a model that is directly applicable to the empirical analysis of spatial development patterns in Europe. As another contribution in a related field, Stelder (2005) uses a large-scale NEG model to examine the location of cities in Europe.
Except for this contribution we are not aware of similar large-scale models, although some regional CGE (Computable General Equilibrium) models may be partly related although these are mainly focusing on the national level only (see e.g. Bröcker and Schneider 2002). Multi-regional modeling has certainly been used also in the NEG context; see e.g. Fujita et al. (1999), but then mainly to answer questions about "whether" there will be agglomeration.
In the current paper, we extend this by focusing more on the "where" question, and derive implications that can be applied to the map and used directly in the empirical study of geographical patterns of change in Europe. For example, we ask whether integration will have different impact in the west and in the east, within Europe as a whole and within each country.
In Section 2, we survey some recent research in the field. In Section 3, we discuss and motivate the theoretical modeling approach chosen and define the integration scenarios to be examined. We present the technical properties of the theoretical model and examine the behaviour of the model in a low-dimensional setting, before proceeding to the higherdimensional numerical simulations. In section 4, we present the results from the modeling of various stages of regional and international integration affecting European regions. Some concluding remarks are presented in Section 5.

International integration and domestic regions: Some recent research
The new economic geography (NEG) (see Ottaviano and Thisse 2004or Fujita and Mori 2005or Fujita et al. 1999 for overviews, or Puga 1999 for a synthesis of some core models) provides a new micro-foundation for examining regional inequality. Some NEG contributions have also examined the relationship between international integration and domestic inequalities. In models of economic geography there is typically a centrifugal force working against agglomeration, and a centripetal force promoting a more uneven coreperiphery pattern. Appearing in various shapes and embedded in different models, the standard engine for agglomeration is often the so-called "home market effect" demonstrated by Krugman (1980): Industries with economies of scale and imperfect competition tend to be located where market access is better. In Krugman (1980) it was the home market that created better market access, but it may also be a more favourable geographical location.
If workers are allowed to migrate in response to real wage differences, as in Krugman (1991), it amplifies market size differences, and regional inequality will increase. In this model, the centrifugal force is that workers in the "agricultural" sector are immobile and maintain an incentive to locate firms close to peripheral demand. Allowing labour to migrate between domestic regions but not internationally, it may then be studied how migration and domestic agglomeration is affected by international trade integration. Within such a framework, Paluzie (2001) and Monfort and Nicolini (2000) find that international liberalisation makes domestic agglomeration more likely. Monfort and Ypersele (2003) obtained similar results in a model without labour migration but with vertical linkages between industries. It is well known in the new economic geography literature (see e.g. Puga 1999) that the NEG labour migration model and the model with vertical inter-industry linkages of Krugman and Venables (1995) produce rather similar results.
The results outlined above are derived in models where domestic regions are symmetrically placed related to foreign countries or region, so there is no geographical coreperiphery pattern. Crozet and Sobeyran (2004) also examined the asymmetric case where one domestic region is closer to the outside world. Now the conclusion about integration and regions is reversed: International integration promotes development in the border region. 3 A similar conclusion was obtained by Krugman and Livas Elizondo (1996), who replace the centripetal force working against concentration: When agglomeration is dampened by domestic congestion costs instead of immobile farmers, international integration also leads to less domestic concentration. 4 What is the intuition behind these results? International integration makes intranational trade less important and this weakens the forces for concentration as well as for dispersion: -It weakens the "monopoly" of the domestic core region by facilitating the periphery's trade with the outside world, and this may promote convergence. The intuition may also be expressed as follows: It is borders that create the backwardness of some border regions, and when borders are made less important, domestic core-periphery patterns are weakened.
-On the other hand, increased demand from abroad also strengthens the incentive for agglomeration. In models where domestic real wage differences are ruled out since they lead to labour migration, international integration is then more likely to produce agglomeration.
3 Another contribution considering spatial asymmetries, regions and international trade is Behrens et al. (2006). Using a model with two countries each having two regions, they show, among other things, how the probabilities of agglomeration in the two countries are interdependent. 4 See also Alonso-Villar (2005). Behrens (2003) also shows that some of these results depend on the Dixit-Stiglitz modelling approach where the firms' mill prices are unaffected by trade costs and changes in competition. If changes in competition lead to changes in prices, the share of trade costs in total costs may change, and this may change the results.
From the still limited amount of theoretical research on this issue, it is therefore ambiguous whether international integration promotes convergence or divergence between domestic regions.
This ambiguity also applies to empirics. Some evidence indicates that international integration leads to more inequality: Summing up the results from a large-scale United Nations research project, Kanbur and Venables (2007, 209) conclude that "trade has on balance increased spatial disparities". Hanson (see e.g. Hanson 2003) has examined the impact of NAFTA on wages in Mexico and found that integration led to greater regional wage dispersion but a gain for more skilled labour close to the U.S. border. 5 Egger et al. (2005) found that export openness increased regional inequality with respect to real wages in Central and Eastern Europe. This evidence is important; it is however not a direct test of the mechanisms described in the theoretical models above.
On the other hand, there is also evidence suggesting that international integration promotes regional convergence: - Crozet and Soubeyran (2004) interpret their evidence about labour migration in Romania as support for the hypothesis that European integration has been to the advantage of border regions, as predicted by their model.
- Redding and Sturm (2005) found that the division of Germany during 1945-1990 had a particularly negative impact on border regions; thus indicating that disintegration contributed to stronger core-periphery pattern. They also found signs of recovery for border regions after reunification.
Hence also empirically, some contributions suggest convergence and others divergence. 6 Based on earlier research, the impact of international integration on domestic regions is therefore ambiguous theoretically as well as empirically.
Except for the border region of Crozet and Soubeyran (2004), the theoretical models referred to above are essentially similar to trade bloc models containing three or four regions, with a limited spatial structure. It is therefore of interest to examine the issue in models where geographical location and distance plays a larger role. In order to obtain this, one needs greater dimensionality. Melchior (2000), using a 49-region multilateral version of the home market effect (HME) model of Krugman (1980), distinguishes between "spatial" trade costs (such as transport costs) and non-spatial trade costs (such as tariffs) and found that "spatial liberalisation" tends to promote more centralisation, while reductions in non-spatial trade costs tend to have the opposite effect. The distinction between spatial and non-spatial trade costs is also examined by Behrens et al. (2007), who study agglomeration effects with gated regions, and it will be an important element in the modelling undertaken here. Spatial trade costs allow the forces of geography and distance to work properly, while non-spatial costs allow the modelling of countries and trade blocs. When the two types are combined, one generally obtains effects that are distinct from those that apply with each of them alone.

A synthetic European space
In the theoretical analysis, we use a two-dimensional rectangular grid of 9 countries divided into 90 regions. Diagram 1 illustrates this "synthetic" European space: The map in Diagram 1 captures some aspects of the true European space but we should nevertheless be aware of the limitations: -There is no outside world so the model will tend to overestimate the isolation of regions at the borders of the landscape. Given that e.g. regions in the Russian Far East is now benefiting from more intensive trade with China, USA and others, this is a limitation.
-The landscape is stylized and misses many features of true geography, which has more countries, oceans, lakes, mountains, climatic differences and so on. For example, the results for "W1" may not be appropriate in order to assess the impact of European integration on Nordic regions. The North-South dimension is limited and allows limited analysis of e.g. EU enlargement towards the South and North. This is a deliberate choice since our focus here is particularly on the East-West dimension.
Neary (2001,551) also calls for two-dimensional extensions of NEG models but fears they will be "long on trigonometry and short on elegance"! With a richer landscape it is inevitably the case that the effects and results are also more complex. By choosing the rectangular grid rather than true geography, it is nevertheless easier to see the principal results in a stylized way. In order to show how the core model affects the results, we shall also proceed in two steps, by exploring the model properties in a low-dimensional setting before proceeding to the 90-region landscape.

Scenarios and trade costs
A core feature of the approach used here is that we include some trade costs that are a function of distance, and others that are independent of distance. We call the first spatial trade costs, and the second non-spatial. As shown by Melchior (2000); when the two types are present simultaneously one obtains effects on the spatial distribution of activity or incomes that are not present when each is considered in isolation. We may think of spatial trade costs as transport costs, but it could also be the case that policy-shaped barriers or regulations have a spatial dimension. For example, if geographical distance also reflects institutional similarity it could be that standards and regulations are more similar in countries and regions that are close to each other and their protective impact could then be correlated with distance. The relationship between transport costs and distance is also not 7 Before choosing this format, we also experimented with a more geographically realistic approach using up to more than 500 regions, using true regional map coordinates. It is however an illusion that the model is much more realistic even if the coordinates are true: After all, it is only theory. With a more stylised landscape, it is easier to interpret the results and we avoid some technical computation problems that are present in models with larger scale and variable region size. straightforward: while e.g. the costs of road transportation in Europe may be monotonously increasing with distance, this may not be so clear for long-distance sea freight. Similarly, we may think of trade policy barriers as non-spatial and this is certainly the case for e.g. a Most-Favoured Nation (MFN) tariff applying to all countries. But if countries form trade blocs with their neighbours only, there may also be a correlation between trade policy barriers and distance. In the analysis here, trade costs represent distribution costs in general, and it is an empirical issue which trade costs are spatial and non-spatial. In the European context, the European internal market is a large-scale project containing thousands of reforms, of which some may be spatial and others non-spatial.
In the model simulations, trade costs always include a spatial as well as a non-spatial component: -Spatial trade costs are present within as well as between nations. We use the notation d ij =β d *D ij /D max . Here D ij is the "geographical" distance in Diagram 1; varying from one between adjacent regions up to the maximum, D max ≈14.03. We divide by D max so the right hand side ratio is maximum equal to one. β d is a scaling factor, which we use to scale up or down the magnitude of spatial trade costs.
-We assume that there are non-spatial trade costs present between all regions, also within nations. We use three levels; within nations (t domestic ), between regions in different nations but within the same trade bloc (t rta , where the rta subscript refers to some regional trade agreement), and between regions in different nations that have made no special integration agreement (t mfn , where mfn refers to Most Favoured Nation). We always assume t domestic <t rta <t mfn and for simplicity we let the level for regional integration be midway between the domestic and MFN barriers. If we had allowed t domestic =t rta countries would not exist any more. Since international trade costs are always higher than the domestic ones, countries continue to matter in all scenarios.
We will simulate the following ten scenarios: 1. A base case without any regional integration agreements (BASE). The results are not reported in detail, but it is used as a yardstick for comparing the results of regional integration.
2. Western integration (WEST): A regional integration agreement is formed among the four countries to the west (W1-W4). This is meant to represent the earlier stages of integration  (2008a) it is shown that higher regional inequality invariably corresponds to a larger income gap between capital regions and the country average, and this applies to Central as well as Eastern European countries.

The choice of model
Models of the new trade theory and NEG are well-suited for our purpose since in such models, industrial location or income levels are affected by market access. The archetype version of this argument is the "home market effect" (HME) model of Krugman ( (2004,2663) conclude that the relationship between market access and wages is more robustly supported than the relationship between market access and the structure of production. Empirical research therefore strengthens the case for models with endogenous wages rather than net trade effects. In this paper, we therefore depart from Krugman's idea about nominal wage effects and develop a multilateralised version which we call the "wage gap model". In the analysis, we compare this to a multilateral version of the HME model and argue that the wage gap model is indeed a plausible alternative.
A multilateral version of the HME model was applied to the analysis of spatial inequality by Melchior (1997Melchior ( , 2000 or more recently Behrens et al. (2005Behrens et al. ( , 2007. 8 In the multi-region setting, the HME model has the advantage of simplicity: It has a simple matrixform solution so numerical exercises can be carried out with little technical difficulty. Hence the model has some of the virtues requested by Fujita and Mori in their quest for developing high-dimensional models (2005,396); "A most desirable model would be one that has solvability at the low dimensional setup and computability even at the fairly high dimensional setup." The drawback, however, is that for the HME model, a solution with positive production in all regions only exists within a restricted range of parameter values. Helpman and Krugman (1985, Chapter 10.3) showed that even in the two-region case, the range with positive production in both regions is limited in the HME model. In the case with many regions, this problem is severely aggravated. The implication for numerical modeling is that the model is "sustainable" only for quite high levels of trade costs, limited region size differences, and a high elasticity of substitution. This severely limits the applicability of the HME model in high-dimensional modeling. Another limitation of the HME model is the somewhat arbitrary assumptions about the numeraire sector. This sector is sometimes referred to as "agriculture", but it is empirically not very plausible that there is completely free trade for agriculture but not manufacturing. As shown by Davis (1998) (and discussed further in Fujita et al. 1999, Chapter 7), the HME disappears if trade costs are equal in the two sectors. 9 In spite of these limitations of the HME model, the model demonstrates in an extreme form a powerful mechanism that is present also in other models and crucial in the whole NEG literature.
Based on these arguments, we choose in this paper to develop an alternative model with endogenous wage differences instead of net export effects. Following Krugman (1980) and dropping the numeraire sector in the HME model, we obtain a model where wage differences are driven by differences in market access. Dispensing with sector differences and collapsing the economy into one sector, using one sector and one factor of production only, we can think of this as a "sector average" for the economy. To this we may later add other features: Sector differences in trade costs or technology, adding more production factors and so on. 10 Ideally, we would like to have net trade effects as well as wage effects simultaneously, but -given the dimensionality of the model -we start with wage effects only.
We call this the wage gap model since differences in market access are reflected in the form of different nominal and real wages. While this is our main approach, we shall also retain the HME model as part of the analysis and compare the two models: Are the wage effects in the wage gap model just a mirror of the net export effects in the HME model? As we shall see, this is sometimes but not always the case.
An alterative choice might have been to use NEG models along the lines of Krugman (1991) or Krugman and Venables (1995). While these models have some interesting properties, they generally generate multiple equilibria and even in the simple two-region case the analysis of stability can be demanding. For the purpose at hand, with 90 regions, we deliberately avoid models with multiple equilibria. 11 With many possible equilibria and no yeardstick to choose between them, it may be difficult to evaluate the results coming from 9 Also if we replace the numeraire sector with another "Dixit-Stiglitz sector" with trade costs, the HME effect may disappear and the pattern of specialization and trade will depend on differences in elasticities and trade costs across the two sectors. As shown by Venables (1999) in a two-dimensional setting (a circular plain), a complex "chess-board-like" pattern of alternating specialization may then occur. 10 For example, the model of Markusen and Venables (1998) adds a Heckscher-Ohlin type supply-side to the HME model so that market access differences will affect wages as well as net exports. Exploring how this model performs in a higher-dimensional setting is a task for future research. In a higher-dimensional setting, the technical challenge increases with the number of unknowns, e.g. two factor prices for each country rather than one. 11 With two regions, we obtain bifurcations and the well-known "Tomahawk diagram" (see e.g. Fujita et al. 1999, 68). With 90 regions, "star wars" would be a possibility! numerical simulations. For the purpose of analyzing European regional income distributions, we are also interested in a model which allows for a continuum of possible outcomes rather than catastrophic agglomeration in one region. European peripheral regions are generally not empty, but they have lower nominal and real incomes and we would like the model to capture this. Nevertheless, our choice is mainly for technical reasons and an interesting extension might be to develop more multi-region application of the NEG models with ad hoc dynamics, labour migration or externalities.

Properties of the wage gap model: Are wage effects and net export effects similar?
In Appendix A, the technical details of the model are presented. Here we shall illustrate some of the properties of the model. We start by examining the model in a lowdimensional setting, before proceeding to the 90-region simulations.
Some basic properties of the wage gap model are: -Since there is only one sector in the economy overall trade has to be balanced so there is only intra-intra-industry trade. 12 -Given that trade is balanced, domestic consumption and production of the differentiated goods must be equal. For this reason, the number of firms will be proportional to country size.
-Wage levels will however differ and for this reason the value of production and consumption will also differ across countries.
-Welfare is equal to the nominal wage divided by the price level; i.e. for region i per capita welfare will be X i =w i /P i . Regions with a favourable location close to markets will have lower price levels. In general, we will see from the results that effects via the price levels are larger than the nominal wage changes.
In Appendix A, we also include the HME model as a parallel case which we use as a yardstick for comparison and a useful contrast that sheds light on the results. In the following, we shall also compare the two models since it usefully sheds light on how net export effects and wage effects may differ. Given that net export effects play a key role in most NEG models, this exercise has broader relevance.
Does the wage gap model live up to the requirement of low-dimensional solvability and high-dimensional computability? Based on our experience, the answer is generally yes with respect to computability. The model has a solution although we cannot guarantee that it has always a positive and real solution for all possible parameter values. In the simulations undertaken, the model was well-behaved with positive solutions. Hence the model seems well-behaved in terms of computability. Solvability for low dimensions is trickier: Although an explicit analytical can be found for the case of two regions and with the elasticity of substitution ε=2 (see end of Appendix A), this solution is not very user-friendly and one has to use numerical methods to check its properties.
As a first illustration, we may use this analytical solution for two regions in order to shed some light on the properties of the wage gap model. In Diagram two, we assume that region 1 is twice as large as region 2; i.e. the labour endowment ratio L=L 1 /L 2 =2. Diagram 2 shows the wage ratio w 1 /w 2 when trade costs are varied. In this low-dimension case, there is only one type of trade costs, t 12 =t 21 =t. Here trade costs vary from zero (t=1) and 300% (t=4). At high levels of trade costs, we can (using the expression for w in Appendix A) find that the wage ratio converges to L 1/3 ; in this case approximately 1.26. When trade costs are lowered, the wage gap is gradually eliminated. Some implications of this are: -In the two-region case, reduction in trade costs reduces the wage difference between large and small countries/regions. There is a monotonous relationship and not an "inverse U" relationship as in some NEG models. Hence this is a NEG model without bifurcations.
-For a given size distribution of regions, there is an upper bound on the nominal wage inequality when t increases; in the case with two regions and ε=2 it is equal to L 1/3 . Observe however that since the limit value is a function of L, there is no upper limit on the wage ratio when L increases.
-The HME model has the paradoxical property that while agglomeration is created by differences in market access, the effect becomes stronger when these differences are reduced. In this sense the wage gap model is more plausible: Trade liberalization reduces the wage gap. Furthermore, the difference between price indexes must also be reduced when differences in market access disappear, so liberalization will lead to converging welfare levels. Hence small countries must gain more from trade liberalization, while in the HME model the welfare gain from liberalization is proportional across countries.
-Compared to the HME model, the wage gap model is well-behaved with positive solutions for a larger range of parameter values. Although negative and complex roots can also be observed, the problem is marginal compared to the HME model.
According to this first check, it therefore appears that the wage gap model is more plausible then the HME model, by being better-behaved and by eliminating the paradoxical outcomes of the HME model at low levels of trade costs.
In order to examine further some properties that are relevant for spatial modeling, we next compare the two models using a "Hotelling" world where regions of equal size are The HME model (Diagram 3), produces a duocentric or bipolar pattern of manufacturing agglomeration, where regions 2 and 6 have higher levels of "manufacturing" production, and the peripheral regions 1 and 7 lower. The central regions 3-5 have average levels of production (=1/N), but they have a better geographical location and therefore the welfare levels of regions 2 through 6 are equal. In this model, reduction of trade costs leaves production in the central regions unaffected but increases the gap between regions 2,6 and 1,7. For sufficiently low trade costs, the peripheral regions 1,7 will be deindustrialised. 13 Now consider the wage gap model to the right, in Diagram 4. It produces a smooth monocentric core-periphery pattern without distinct agglomerations. Nominal wages (the curve in the middle) are slightly higher in the central regions, but price levels are also lower so the welfare (real wage) gaps are even higher. The "duocentric" pattern is however visible in the lowest curve for domestic sales: Due to lower wages in the peripheral regions, and lower price levels in the central regions, regions 2 and 6 now export less and become more closed, with a higher share of production sold domestically. This is diametrically opposite to the HME model where the 2,6 regions are "big traders".
In the two models, the welfare results are similar in the sense that they are both monocentric. This may indicate that welfare predictions may be considered as more robust and less dependent on modeling assumptions than predictions about agglomeration or wage changes. To some extent, we may be more agnostic about whether the main impact is on the net trade pattern or income as long as the welfare effects are more comparable.
For empirical analysis, a useful property of the wage gap model is that it offers predictions about nominal variables: nominal wage effects may differ from welfare results and frequently, price level effects are more important than nominal changes and appropriate handling of the real/nominal distinction may be quite important. Nominal changes are not "nuisance" that should be cleaned away to approach the real things; they may be important for understanding change.
Using simulations with the HME model, Melchior (2000) found that the relative magnitude of "spatial" and "non-spatial" trade costs determined whether a duocentric or (in a two-dimensional model) "manufacturing belt" outcome occurred, or a more centralized outcome. With a higher level of non-spatial trade costs, a centralized pattern may be the outcome even in the HME model. In order to illustrate this, we add a non-spatial trade cost that applies to sales to all other regions, together with the spatial or transport-cost type of trade costs. We then examine what happens when either type of trade costs is changed.
Diagrams 5 and 6 show the outcomes in the HME model (the number of firms) and the wage gap model (the nominal wage), respectively. 14 13 When t ε-1 =2 the peripheral regions will have zero production. For example, with ε=5 the peripheries will be deindustrialised for t lower than 1.19.
14 In both diagrams we use ε=5, spatial trade costs that are 1/6*distance (i.e. =100% between the peripheral regions which have distance 6), and in the "high" curve in the graph non-spatial trade costs=0.2 for sales in all regions except own region. Hence spatial trade costs now increase linearly with distance. Total trade costs with other regions are then 1+1/6*distance+0.2. In Diagram 6 non-spatial trade costs=0 for the "low" curve. With these value, however, regions 1 and 7 obtain negative production in the HME model, so in Diagram 5 we use nonspatial costs at 0.05 for the "low" curve. In both cases, the introduction of non-spatial trade costs creates a more even distribution. In the HME model, there is a radical change from the duocentric to a monocentric pattern of agglomeration, and the sharp inequality between the two regions at each end of the line and the rest has disappeared. In the wage gap model, the wage distribution is still monocentric but with less inequality than before. There is a significant increase in the nominal wages of the peripheral regions, and reduced nominal wages in the central regions. Changes in welfare are similar but more modest.
If we reverse the sequence in both models, moving from "with" to "without" in the diagrams, it is evident that, a reduction in non-spatial trade costs will create more regional inequality. In the HME model, liberalization will also promote a movement from a "monocentric" pattern of agglomeration to the duocentric or bipolar pattern that obtains in the HME model without non-spatial trade costs. 15 Now turn to the reduction of spatial trade costs: We start from the situation described by the "with" curve in Diagrams 5 and 6, and reduce the spatial trade costs only. 16 Diagrams 7 and 8 show the outcome, for the HME and the wage gap models respectively: 15 Observe that we still have no country borders, so we only have regions but no countries. In the simulations to be undertaken, we also let regions form countries, and in that context the impact of spatial liberalization may be modified. 16 We reduce the scaling parameter for spatial trade costs from 1/6 to 0.05. Contrary to the case with non-spatial liberalization where the outcome was similar, the impact of liberalization in the two models is now diametrically opposite: In the HME model, spatial trade liberalization leads to a stronger core-periphery pattern, while in the wage gap model the opposite is the case. Spatial liberalization weakens the centrifugal force of the model; peripheries can now be served from the central areas and there is no wage adjustment stopping the relocation of production toward the centre. But in the wage gap model, spatial trade liberalization is to the advantage of the peripheral regions. Later, we shall see that this also applies in the simulations with our stylized European map.
These results show that the modeling approach may be crucial for some of the results in spatial models. In our simulations, we should therefore be aware about the sensitivity of results to the modeling assumptions, and in particular the model choice. In general, we consider the results from the wage gap model as more intuitive since the model is technically more well-behaved, and is does not have the counterintuitive properties related to the impact of trade liberalization. Nevertheless, we cannot exclude the possibility that "duocentric" outcomes and the net export effects of the HME model, with stronger relocation effects, are empirically relevant. We shall therefore carry out simulations also with the HME model, and check whether results differ between the two modeling approaches.
In the simulations, we use different levels of trade costs in order to check the sensitivity of results with respect to the levels of trade costs. There is generally no "U-shape" in our model so that agglomeration is stronger at intermediate levels of trade costs; it is nevertheless possible that integration effects depend on the level of trade costs. A reason for this is that trade liberalization is generally not neutral with respect to the ratio between spatial and non-spatial trade costs. An illustration is the following: Assume that trade costs to a neighbour region a are t a1 =1+0.2+0.2=1.4; where the two terms equal to 0.2 represent spatial and non-spatial trade costs, respectively. To a region b twice as far away, we assume that trade costs are t b1 =1+0.4+0.2=1.6, since distance costs are doubled. Now cut both types of trade costs by half, so that new trade costs are t a2 =1.2 and t b2 =1.3. We see that t a1 /t b1 <t a2 /t b2 . A proportional reduction in all trade costs thus tends to make spatial trade costs relatively less important, and this might affect the model outcome.
In Table B1, Appendix B, we show the parameter values used in the various simulations. We call these "High", "Main" and "Low" and we will generally report only results from the "Main" alternative with an intermediate level of trade costs. Table B2 shows the average level of trade costs for trade between regions in different countries in one of the scenarios (the WEST scenario). We see that the average level of trade cost is around 25% in the "Low" scenario, around 50% in the "Main scenario" and around 200% in the "High" scenario. In spite of the suggestion by Anderson and van Wijnkoop (2003) that total trade costs broadly defined, including distribution costs, could be as high as 170%, we consider the level in our "High" scenario as somewhat exaggerated. However, that is the level required if all regions are to have positive production in all scenarios in the HME model. We include this in order to be able to run simulations with the HME model in parallel to the wage gap model. We wish to include HME simulations in order to check whether the regional patterns of sector agglomeration effects are similar to outcome in the wage gap model.
In the analysis, our main concern is about changes from one scenario to another.
Hence we are interested in e.g. how the change from WEST to WIDER affects income and welfare. The main purpose is not to explain the current income distribution in Europe, but to examine how this is affected by changes in market access. Hence we do not try to calibrate the model to some actual distribution, but choose a configuration of parameter values that appears plausible and technically feasible, and then examine changes from there. Using the wage gap model, we obtain an income distribution similar to diagram 4, with modestly higher wages and welfare in the central regions of the rectangular grid. Diagram 9 shows welfare levels in the "base case" before any regional blocs are formed, with intermediate level of trade costs.
We observe a core-periphery pattern with lower welfare particularly in regions far to the west and east. Observe also the high welfare level in E1, due to the market access advantage of larger country size. Given that this situation without integration might represent the post-war situation in the 1940s and 1950s, it is evident that there was communism in the Soviet Union. In the model used here, results are driven by market forces and it is therefore inadequate to explain welfare changes during the Soviet period. For the Soviet/ COMECON period, the results may therefore be of limited relevance. For Western Europe (the four countries W1-W4), however, the pattern with peripheries in the west and higher incomes in W3+W4 is quite plausible in the light of empirical research (see e.g. Combes andOverman 2004 or Dall'erba 2005), although the true European map is certainly richer than ours.
From this starting point, we examine how regional distribution is affected in the 10 scenarios. In tables B3-B5 in Appendix B, we show correlation coefficients between results using different levels of trade costs. We also show how results with the HME model,  (Table B3), and changes in welfare from scenario WEST to WIDER are correlated with coefficients at 0.95-0.99 (Table B4).
-For the HME model, domestic sales (i.e. in own region) is an appropriate indicator also for per capita welfare (see Appendix A). Hence we observe from Table B3 that welfare in the HME model with WIDER is highly correlated with welfare in the wage gap model (absolute value of correlation coefficient=0.97), and this also applies to the welfare change (0.98, see Table B4).
-For production levels in the HME model, however, correlations with results from the wage gap model are still significant but in most cases lower. For example, with high trade costs, the number of firms under WIDER using the HME model, and the wages obtained using the wage model, are positively correlated with a coefficient of 0.56. Hence the spatial pattern of change is partly different in the two models.
In Table B5, we show such correlations for more scenarios and they confirm that production or net trade effects in the HME model is often less correlated with all other results. In some cases, results from the HME and wage gap models are even opposite. These are shown by shaded cells in Table B5. These cases are nevertheless exceptions and in the majority of cases, the direction of the effects is similar in the two models. Base on the comparison, we conclude: -The HME model and the wage gap model behave qualitatively similarly for scenarios with European regional integration; in the sense that welfare results, and production vs.
wages, are positively correlated.
-For the SPATIAL scenario where distance-related trade costs are reduced, the two models give opposite predictions, as in Diagrams 7-8.
-For EASTOPEN, the HME model suggests that unilateral liberalization gives a welfare loss while the opposite is the case for the wage gap model. This illustrates that the wage gap model is more "trade-friendly" than the HME model, where unilateral protectionism may sometimes improve welfare.
Hence in some cases, the results depend on the type of model used. It is ultimately an empirical issue what is true, although -as argued -we have more faith in the wage gap model as an average effect across sectors for the whole economy.
This concludes our methodological examination of the model. The challenge for numerical modeling is to show that results are not only stories with limited generality based on some arbitrary parameter values. We believe to have shown that the results that are presented in the following are more than this. They hold for a wide range of parameter values, and we have illuminated some of the model mechanisms that create the results.

Model simulation results
The numerical modeling results are intended as a point of departure for empirical examination of the issues. Therefore, a wide variety of scenarios and results are included.
We will here only briefly sum up some main results. In Appendix C, Tables C1-C18 and the corresponding Diagrams C1-C18 we report results from scenarios 2-10. We only report results for the wage gap model with an intermediate level of trade costs. 18 For each scenario, the tables include nominal wage levels and welfare levels, and changes in these from some other scenario (specified in the tables, often the WEST scenario). For each table, there is a corresponding grey-scale map graph which shows changes for each region, with some key words in the header. We generally do not repeat much detail in the main text so the readers are invited to use these graphs in Appendix C as an intuitive visualization of the results.
The results encompass standard results about regional integration from the new trade theory (see e.g. Baldwin and Venables 1995 for an overview) where participating countries gain and outsiders may sometimes lose. As shown in this literature, an "agglomeration shadow" may fall on non-participants close to the trade bloc. In standard HME or NEG models, this effect is driven by net export effects and so-called "productionshifting". In the wage gap model, there is no such production-shifting and the agglomeration shadow takes the form of lower nominal and real wages. Another new feature in our analysis is that positive and negative effects vary across regions inside countries.
The results clearly indicate that there is no unambiguous conclusion about how international integration affects domestic regions. All our scenarios represent international integration, but the impact on regions is different in each case. By the same reasoning, we cannot expect any unambiguous conclusion about regional inequality: International integration may lead to convergence in some cases, and divergence in others. Our analysis has therefore provided the "non-answer" we were searching for: There is no unambiguous rule, and searching for a universal answer is like barking under the wrong tree.
Our simulations include four regional integration scenarios; WEST, WIDER, EAST-WEST and EAST. In all the four cases, all the participating regions unambiguously gain in terms of welfare. Hence also in the case of widening integration from 4 to 6 and 7, the old members improve real wages. The gains are to some extent unevenly distributed: -In WEST, there is a larger gain for regions that are close to the centre of the WEST area, around the point where the four countries all border to each other. 18 Results from other scenarios used in the robustness checks in Tables B3-B5 can be provided upon request.
-In WIDER, the gain is larger in the new member states. For these, the gain is larger in the western regions, but for the old members W1-W4, the opposite is the case. Hence EAST-WEST is better for W3 and W4 than for W1 and W2, and better for eastern regions in these countries. EAST-WEST moves the centre of gravity in the regional integration area to the east.
-EAST-WEST gives a strong welfare gain for the new participant (E2) and modest positive effects for all the old participants, with a slightly better outcome for regions closer to the new participant. According to this, present participants of European integration have no reason to fear further enlargement.
-With Eastern integration (EAST), 19 the larger country E1 generally gains less than the other two since without integration, it already benefits from its large country advantage. In the wage gap model, integration is better for the small countries by creating wage convergence.
In some, but not all cases, the welfare gain from integration is accompanied by a nominal wage increase as well. This is however not always the case, as seen in Appendix C.
In a non-spatial model of regional integration, the "agglomeration shadow" or negative impact on outsiders apply to all countries outside. In our case, the integration shadow is clearly visible but it is stronger in outside regions close to the trade bloc that is formed. In the WEST scenario, the negative impact on wages as well as welfare is larger for Central/ Eastern European regions close to the WEST bloc, and weaker for remote regions.
There is however a negative impact for all outside regions. This applies also to the impact of WIDER and EAST-WEST on the outsiders.
The results on European regional integration show that eastward widening of the trade bloc gradually moves the "centre of gravity" eastward, while former members also gain from integration. Since the centre of gravity then gets closer and closer to the centre of the rectangular grid, the benefits of integration will be strongly correlated with any measure of "market potential". This strengthens the case for market potential approaches in the study of European integration (see e.g. Brülhart et al. 2004). Such a correlation between market potential and the impact of integration is however not present in all scenarios. For the "iron curtain" (IRON) scenario, WTO and especially SPATIAL (reduced distance costs) there may actually be a negative correlation, at least with simple market potential measure of the types introduced by Harris (1954): -While the "iron curtain" is bad for welfare all over Europe, it is particularly adverse for regions close to the curtain itself; in western regions in Central Europe, or eastern regions in WEST.
-The WTO scenario is especially positive for countries and regions that do not participate in regional trade blocs. When "multilateral trade liberalization" (WTO) is undertaken in the presence of WEST, it is particularly positive for regions outside but close to WEST. But also members of the regional bloc gain from such liberalization. WTO liberalization erodes the European trade preferences and thereby dampens trade policy discrimination.
-Reductions in spatial trade costs have a powerful equalising effect by being more positive for peripheral regions along the border of the rectangular space, in particular the regions far to the west and to the east. Observe that in this case the HME model and the wage gap model gives different predictions, and our simulation results are along the lines with the pattern shown in Diagram 8.
Hence the spatial impact of different types of integration varies, and some trade reforms will lead to more income growth in regions with a lower market potential in the sense of Harris (1954).
Finally, observe that if capital cities are "hubs" so that business has to take place via the capital (scenario CAPITAL), it strongly boosts the real wage level in capital regions. 20 In our Russia-like country E1, the hub effect is particularly severe for regions to the far east.
For these regions, even some of their trade with neighbour regions has to pass through the capital, and this creates a sharp increase in trade costs. The hub effect is also more severe and negative for some regions in north-west E2 and north-west Eurasian E3: These regions can no longer exploit their geographical proximity to Europe but have to ship some of their goods indirectly via capitals. On the other hand, north-west E3 and south-east E3 are in fact relatively better off since the hub effect implies a rebalancing of regions within the two countries, by eliminating some of the geographical relative disadvantages. Hub-and-spoke effect inside countries tend to eliminate the east-west and north-south differences in the impact of various policies, since all peripheries in the country become peripheral, wherever they are located. If the distance to the capital is larger, as for eastern E3 in our map, the impact is worse.
Central European countries C1-C2 are strongly affected in a number of different scenarios, be it as part of a European integration scheme, or being in the shadow outside trade blocs to the west or to the east, or benefiting from "preference erosion" due to WTO liberalization, or being trapped closed to the iron curtain. Hence not only armies have rolled over Central Europe; our results suggest that the forces of economic geography are also strong compared to the more "quiet corners" to the west and to the east.

Concluding remarks
The main purpose of this paper has been to provide an extended theoretical underpinning for the empirical study of European integration and regional income gaps in Europe. Carrying out such empirical work is an extensive task that has been left for future research. The model simulations show a number of different scenarios and a task for empirical analysis is to determine the relevance of each scenario. During the last decades, different trade reforms have occurred simultaneously (e.g. EU integration, East-West trade agreements, WTO or GATT liberalization, dissolution of the Soviet Union, fall of the iron curtain etc.). In the context of Central and Eastern Europe, a challenge is the phenomenon of "transition" which may imply that there is an extended period of institutional change from the former planning system to the market economy. Although the most dramatic change probably had occurred by the mid-1990s, some effects of this change may be long-lasting and possibly overshadow other events.
Our analysis captures some mechanisms but certainly not all, and the development of European regions is certainly affected by other aspects that are not addressed by the model. Input-output effects constitute a core feature in regional CGE (computable general equilibrium) models that have been constructed for some European countries (see e.g. Bröcker and Schneider 2002). 21 While our model has nine countries, it leaves out the rest of the world and this is surely a shortcoming. For example, the industrial change of Germany is surely affected by competition from Asia, which is left out in our framework. Hence the results should be interpreted with these reservations in mind.
In spite of these limitations, the results provide a rich set of hypotheses about the spatial and regional impact of integration in Europe, which will hopefully be of use in further research in the field. The scenarios shed light on different policy events and give predictions about nominal as well as real income changes and their spatial variation. In Melchior (2008b) we use the results derived here as a platform for empirical analysis of European regions during 1995-2005.

Appendix A: The modelling framework
We present the model here in a form which encompasses both models used in the numerical simulations; the wage gap model (which is the main approach) and the home market effect (HME) model (which is used for comparison and as a supplement to shed light on trade effects).
There are N regions. Each region, indexed i or j, has a single factor of production; labour, with endowment L i 22 and wage w i . The total income of the economy is therefore Y i =w i L i . In order to keep notation simple, we use only one set of subscripts (not for regions and countries separately). Trade costs are expressed as a mark-up on marginal costs so t ij ≥1, e.g. a trade cost of 10% implies t ij =1.1. For the purpose of the analysis here, we also allow non-zero trade costs in the home market, so t ii may be larger than 1. 24 For example, some Russian regions are huge with low population density, and it would be implausible to assume that internal trade costs are zero. While zero domestic trade costs are normally assumed in theoretical applications, it is technically no problem to have non-zero trade costs. We assume that t ij >t jj ; i.e. inter-regional trade may be thought to include the intra-regional cost plus some additional inter-regional cost. This assumption is plausible but also needed for the model to be well behaved.
We assume standard CES (constant elasticity of substitution) demand functions, so demand for a variety from region i in market j is equal to x ij = p ij -ε P j ε-1 D j where p ij is the price of a variety from region i in market j, ε is the elasticity of substitution between varieties (with the standard assumption ε>1), P j is the CES price index in region j, and D j is the total value of manufactured goods sold in market j (we revert to how this is determined). With monopolistic competition, firms maximise profits π i =-fw i + Σ j (p ij -w i ct ij )x ij , and we obtain the standard pricing condition p ij =[ε/(ε-1)] w i ct ij . Furthermore, free entry and exit imply that total profits have to 22 For the purpose of empirical analysis, it may sometimes be useful to think of this as "efficiency units" rather than population, in order to adjust for different productivities in the economy. 23 We consider it simpler in terms of notation to express trade costs as a mark-up on marginal costs rather than the usual iceberg formulation where goods melt away in transport. The results are similar. 24 In the results presented in the text, we have assumed zero trade costs within each region. Simulations including such trade costs, for example as a function of land area or population density, were however also tried and we therefore express the model in a form which allows this possibility.
equal sunk costs f, and as a consequence the total value of sales for a firm in region i will be εfw i . Now write v ij = x ij p ij for the value of sales of an individual firm from region i in some market j. Dividing v ij by v jj , we can express the sales v ij in some market j as a function of the home market sales v jj of firms in that market: Using the demand functions and the pricing condition, we obtain v ij = v jj * (w i /w j ) 1-ε (t ij /t jj ) 1-ε . Using this, the total sales of a firm in region i, ∑ j v ij =εfw i , can be written as or, moving the common term w i to the right hand side, For the N regions, we have N equations with 2N unknowns (v ii , w i ). In order to express this in matrix form, we define T expresses the relative trade costs in all markets, relative to domestic supply. Using this, the equation system above can be written as where Diag (w i with v ii (i.e. the home market sales of firms in each region) as elements, and [w i ε ] N×1 is a vector with w i ε as diagonal elements.
The sales of all firms in market j must add up to D j ; i.e.
∑ i n i v ij =D j . n i is the number of manufacturing firms in region i, and since there is no firm heterogeneity, and no sunk exports costs, all firms will sell a (large or small) positive amount in any market. Expressing all v ij 's in terms of home market sales as above, we can put w i and v ii on the right hand side and obtain the system of N equations Combining (1) and (2) we have 2N equations with 3N unknowns (n i , v ii and w i ). By adding more structure we can reduce the number of unknowns to 2N and solve the system. The wage gap model and the HME model represent two alternative approaches: In the wage gap model, we assume that manufacturing is the only sector in the economy. Then the whole income is spent on manufactured goods so we have D i =w i L i .
Given that firm size is determined (see above) and assuming full employment, the number of manufacturing firms must be n i = w i L i /(εfw i )= L i /(εf). Thereby eliminating the unknowns n i , we obtain a system with 2N unknowns that may be solved. Equation (2) then simplifies to: This is however a non-linear system where no explicit analytical solution can be found. 25 We therefore use numerical simulation in order to determine the outcome.  Observe also that the nominal level of wages, prices and sales is not determined and may be scaled up or down. We therefore have to normalise all results since the numerical results may end up at different levels. Since productivity is unchanged throughout the "events" we simulate, we normalise the average wage to equal one.
A second option, frequently used in the literature and referred to as the HME model, is to add a "numeraire sector" in which labour produces a homogeneous good with constant returns to scale. Assuming that one unit of labour produces one unit of output of the homogeneous good and that such goods are traded at zero trade costs, wages per efficiency unit in the regions must be equalised as long as all regions produce the homogeneous good.
Using the homogeneous good as numeraire, wages everywhere must then equal one; w i =1 for all i. The version here is a slightly modified and multilateralised version of the "home market effect model" of Krugman (1980). We must also address how consumption is divided between the two types of goods; using a Cobb-Douglas upper-tier function with consumption share α for manufacturing, total demand for manufacturing becomes D j = αL j (since total income is now L j ). In the multilateral version, equation (1)  Using the solutions for v ii , we can then also solve for the number of firms, and it can be shown that, ceteris paribus, large countries will have a higher than proportionate share of manufacturing.
In the wage gap model, the advantage of better market access is realised in the form of a higher nominal wage per efficiency unit, whereas in the home market effect model, the From (2b) we can find the solution for [n i ] and substitute into (3b). The components T'×(T') -1 then cancel out and we obtain the expression Since the inverse of a diagonal matrix is a diagonal matrix with inverse diagonal elements, we can also write We observe that for region i, welfare is positively related to home market size L i , and inversely related to the home market sales of firms (v ii ) as well as domestic trade costs (t ii ). 27 The intuition is that -in economically large regions that have a higher share of production, consumers buy a larger fraction of goods from domestic producers and thereby pay less trade costs (since t ij >t jj ) -domestic trade costs increase prices and reduce welfare -if firms sell a large share of production domestically, it reflects that inter-regional trade costs are high and that reduces welfare.
In this model, the world total number of firms is constant (=∑ i L i /(εf)) so there is no welfare effect of changes in the number of varieties.
In the wage gap model, welfare depends on nominal wages as well as the price level.
Welfare can then be measured directly by the CES quantity aggregator or utility function (1-ε) . Since total consumption equals total income; i.e. for region i we have X i P i =w i L i , we simply obtain that per capita welfare is equal to In most simulation results presented in the paper, we assume that L i =1 for all regions and that there are no domestic trade costs, t ii =1. In that case, we can directly use v ii as an index of welfare.