title: The socio-economic impact of projects financed by the Cohesion Fund : a modelling approach. Volume II, Computable general equilibrium models : Models of explicit distribution dynamics.

eurovoc_concepts:
Cohesion Fund
EU financing
EU regional policy
economic and social cohesion
economic consequence

text: European Union ®@0®°@©®[ηΜ Α@©Ώ© iÏDöQ©®< UQQ@ ©®La]®©D®m LPQÜLB A modelling approach Volume 2 Computable general equilibrium models lodels of explicit distribution dynamics m r ■ " · · * · * European Commission The socio-economic impact of projects financed by the Cohesion Fund A modelling approach Volume 2 Computable general equilibrium models Models of explicit distribution dynamics European Commission A great deal of additional information on the European Union is available on the Internet. It can be accessed through the Europa server (http://europa. eu. int). Cataloguing data can be found at the end of this publication. Luxembourg: Office for Official Publications of the European Communities, 1999 ISBN 92-828-3065-9 © European Communities, 1999 Reproduction is authorised provided the source is acknowledged. Printed in Italy Contents SECTION I : COMPUTABLE GENERAL EQUILIBRIUM MODELS 1. Introduction 2. The issues 3. Overview of the model 4. Data and Calibration 5. Simulations 5. 1. Base experiment : North-South Corridor (Ireland) 5. 2. Madrid Ring Road 5. 3. Rias-Bajas Motorway 5. 4. Tagus Crossing in Lisboa 5. 5. Egnatia Motorway 5. 6. Pathe Motorway 5. 7. Greece : Combined Effects of Egnatiaand Pathe motorway Simulations : summary and conclusions 6. Concluding Comments Appendix A1 (tables) Appendix A2 (Technical Appendix) References SECTION II : MODELS OF EXPLICIT DISTRIBUTION DYNAMICS A. Regional cohesion from local isolated actions - Historical outcomes 1. Introduction 2. Preliminaries on convergence and distributions 2. 1. Spatial dynamics 2. 2. The shape of distribution dynamics 3. Mobility and dynamics 4. Conclusions References Data Appendix Tables Figures Contents Page 5 7 9 13 17 23 24 31 36 41 46 52 56 58 61 63 69 75 79 81 81 83 83 85 91 97 99 101 104 113 Β. Regional cohesion from local isolated actions - Conditioning 1. Introduction 2. Conditioning and explaining distribution dynamics 2. 1. Some conditioning operations 2. 2. Conditioning schemes 3. Empirical results 4. Conclusions Technical Appendix References Tables Figures 165 165 167 168 170 173 177 179 183 185 187 Section I — Computable General Equilibrium Models SECTION I COMPUTABLE GENERAL EQUILIBRIUM MODELS Anthony J. Venables Department of Economics, London School of Economics with Michael Gasiorek School of European Studies, University of Sussex 1. Introduction This paper presents an analysis of the long run supply side effects of selected cohesion fund projects. These projects change the economic infrastructure of regions, and thereby change the attractiveness of these regions as a base for in vestment and production. We seek to answer the following questions. If we know how a project changes important characteristics of a regions' infrastructure, then how does this affect the at tractiveness of the region as a location for eco nomic activity? What are the consequent changes in the location of industry, and how do these changes in activity impact on wage levels and real income in different regions and in aggre gate? The methodology employed is to construct a computable general equilibrium model of the re gions under study, and use it to simulate the ef fects of cohesion fund projects. This methodolo gy is very different to that used in other parts of this study. The approach in these other parts of the study is to undertake a rich empirical analysis using time series data, but a very simple 're duced form' economic model. Here we take a di ametrically opposite approach. We build a model with a fully articulated micro-economic structure. The behaviour of consumers and of firms is mod elled, as are trade and transport links between regions. Producers are cost minimising, and will react to changes in cost levels caused by infra structure projects. The main innovation in the model is that we draw on developments in 'new economic geography' to capture 'linkages' be tween the actions of firms. That is, if a firm relo cates then it creates forward and backward link ages which may attract other firms to relocate with it, creating the possibility of cumulative cau sation in the performance of a region. The micro-economic detail built into the model al lows us to capture in a quite detailed way the ef fects of different projects. For example, the ef fects of a transport project will depend on pre cisely how it changes the transport network and changes transport costs on different links in the network. It will also depend on the characteristics of the regions that experience a change in trans port costs either internally, or to and from other regions. Different regions along and even some distance away from a transport project may be affected in quite subtle ways as the costs of sup ply to these regions is reduced, and so too are the market access costs of firms located in the regions. By working with a fully articulated micro- economic structure we can capture these effects, and measure their impact on a wide range of economic variables — output and employment in various industries, and wage rates and real in come levels. The benefits of the methodology employed in this section of the study are then that the micro-eco nomic structure incorporated in the model allows us to capture a high level of project detail, and thereby discriminate between different projects in a way which econometric analysis cannot. For example, two similar size transport project locat ed in the same region may have very different ef fects if they are filling in different links in a trans port system. The disadvantages of the methodol ogy are that the models are not subject to the same empirical testing and verification as are the other elements of this study. The model is fitted Introduction to data in the most accurate way possible, but the model structure — for example the behaviour of firms and households — is imposed and not subject to econometric testing. We see the approach developed in this part of the study as being complementary to the ap proaches in the study, and to standard cost ben efit analysis techniques. Our approach requires that a standard cost benefit analysis be under taken, in order to provide the detailed description of each project that is needed in the model. For example, we need to know, as input to the mod el, how a project changes the transport links be tween all pairs of regions in the country or coun tries under study. The approach developed here is perhaps best viewed as an extension of cost benefit analysis. It widens the scope of standard analysis to include the evaluation of changes — eg the relocation of industrial activity — that may be caused by a project, but that are outside the scope of standard cost benefit analysis. The plan of this part of the study is as follows. The main economic issues involved in the model ling approach are set out in part 2. Part 3 outlines the underlying economic model that is used, al though the full technical specification of the mod el is relegated to appendix A2. The model is fitted to three separate country/ country groups, namely Ireland, Greece, and Spain/ Portugal. Part 4 of the paper discusses data and calibra tion issues. In part 5 we outline the way in which a cohesion fund project can be represented with in the model, and present results from simulating the economic effects of six different projects. In a concluding section we discuss the overall poten tial of the approach, and some of the work — modelling and data work — needed for future development. Section I — Computable General Equilibrium Models 2, The Issues How does a regional expenditure such as an in frastructure project affect the recipient region and other neighbouring regions? Clearly, the first im pact of the project comes from its direct expendi ture — the demand it creates for construction workers and so on — but for a one-off capital project such effects are transient, and will not be the primary concern of this paper. The second set of effects flow from the supply changes asso ciated with the project. For example, a road pro ject offers a supply of services — lower cost trav el on the route — to users. These may induce a change in behaviour, for example, attracting new investments to particular regions. These invest ments will induce further economic changes, as they change the incentives for future investments, and as they work through the full equilibrium of the model, changing wages, household incomes and demands. The objective of this paper is to provide a way of quantifying these effects, both on individual regions and on the economy as a whole, of such projects. It is helpful to think of the effects of a project as consisting of three elements which we shall call direct, induced, and spillover. The direct benefits are those that accrue at unchanged activity levels in the economy. Taking as an example a road project, the direct benefits are simply the reduc tion in cost per journey on the road, times the ini tial number of journeys. The induced effects arise from the fact that the project may change the lev els of activities directly related to the project. For example, the project will increase the number of journeys undertaken. Spillover effects arise as the effects of the project ripple through the wider economy. The standard approach to evaluating these ef fects is illustrated in figure 2. 1. The number of journeys taken is measured on the horizontal ax is, and the marginal value of journeys on the ver tical. The curve DD is the demand curve for jour neys, measuring the private marginal value of journeys undertaken, and the horizontal line CC is the initial cost of making the journey, implying that X journeys are taken. The project has the ef fect of reducing the cost of the journey to C'C', and increasing the number of journeys taken to X'. The figure illustrates the direct and induced ef fects of the project. The direct effect is simply area a. The cost saving times the number of jour neys made. The induced effects depend on the marginal valuation curve. If the curve is DD, then the induced effects are area b. This measures the gap between marginal valuation and cost on the extra journeys induced by the project. Suppose however that there is some difference between marginal private valuations (as measured by DD) and marginal social valuations (as measured by DSDS). This increases the value of the induced ef fects, adding area cc to the benefit calculation. This effect has been illustrated as a positive ben efit (DSDS above DD), but could of course be negative (if DSDS were below DD), reducing the value of the project. The reason for reproducing this piece of standard analysis is make the point that the size of the in duced effect, (b+cc) depends crucially on the size of the project and on the presence of 'distor tions' — deviations between private and social marginal valuations. For a small project in an The issues Marginal value Ds D C' a c b c C D C Ds Journeys Figure 2. 1. undistorted economy the only welfare effects are the direct effects, area a, and induced effects are absent. We can see this from the figure by noting two things. First, in this case curve DD not DSDS is the marginal social valuation schedule (by as sumption). And second, the ratio of the area b to area a goes to zero as the size of the project (the cost reduction given by the gap between CC and C'C') gets small. The role of traditional cost benefit analysis has been to allow evaluations of projects where the assumptions of smallness and absence of distor tions are inapplicable. Cost- benefit analysis therefore incorporates both direct and induced effects. In undertaking a cost benefit analysis the question arises, how far away from the project should the analyst go in quantifying the induced effects? Does the evaluation look only at the change in the number of journeys, or also at con sequent changes in activity levels in other activi ties in the economy? Clearly a road project might substitute for rail travel and if rail is operating at a price greater then marginal cost then this is a source of induced welfare change which should be, and usually is, taken into the cost benefit analysis. But typically the analyst would not look for induced welfare effects of the road caused by its effects on some industry operating at a loca tion affected by the road, and still less effects on another industry supplying this industry, and so on. In other words, the analyst makes the judge ment that it is only necessary to look at induced benefits 'close to' the project, and that little is gained by looking at the wider 'spillover' effects elsewhere in the economy. This judgement is based on two beliefs. The first is that industries are unlikely to be sufficiently dis torted for an induced quantity change to have significant social value. And second, that quantity effects are likely to taper off quite rapidly as we move away from activities directly related to the project. And as we saw in our discussion of fig ure 2. 1, small quantity changes on activities which are not subject to significant distortions are of little social value. In this paper we go beyond traditional cost bene fit analysis in widening the scope of activities that are included in the analysis — in fact we widen right out to the full general equilibrium of the economy. Why do we differ from the traditional view and think that these effects are worth inves tigating? There are two reasons. The first is that there is increasing realisation throughout eco nomics of the importance of externalities and in creasing returns to scale. For example, in new growth theory much turns on externalities associ ated with accumulation of knowledge stocks or other accumulable inputs. In development eco nomics attention has been paid to externalities between the actions of different agents, and the consequent possibility of 'coordination failures' causing an economy to be trapped in a low level equilibrium. And in the 'new economic geogra- 10 Section I — Computable General Equilibrium Models phy' literature, externalities and other linkages have been shown to give rise to agglomeration forces, explaining city formation and industrial lo cation. 1 These externalities may be pecuniary, rather than technological. That is, they may be transmitted through market transactions, but transactions in which prices are not fully measur ing the marginal costs and benefits to the trans acting agents. What all these areas have in com mon is the view that wide ranges of economic activity may be affected by market failure and dis tortions, meaning that private and social valua tions of activities are not necessarily equal. Changes in activity levels of such activities are then not of zero social value, and should be brought into the cost benefit analysis. The second reason is related, and perhaps more important. Given the presence of externalities — technological or pecuniary — it is possible that 'cumulative causation' mechanisms may operate. This means that it may be the case that the ef fects of an economic change in one activity are not necessarily dampened as they spread through the economy, but could possibly be am plified. In this case the belief that a project will not have a significant impact on the scale of opera tion of other activities is unfounded. We have to look beyond induced effects, to wider the 'spillover effects' of the project through the econ omy. These cumulative causation mechanisms have long been seen as important in economic geog raphy and in development economics, (for exam ple in the work of Perroux (1955), Myrdal (1957), Hirschman (1958), Harris (1954) and Pred (1966)) but have received rather little attention from mainstream economics. This failure is largely due to the technical complexity associated with mod elling and quantifying them. To construct a satis factory model in which cumulative causation forces are present requires increasing returns to scale and imperfectly competitive market struc tures, and to apply them in a regional framework requires a multi-regional general equilibrium set ting. Such models are inherently complex, and are likely to give rise to multiple equilibria and complex dynamics. It is only in the last ten years or so that economists have developed tech niques which make analysis of these issues tractable, and only in the last five years or so that they have come to be applied to regional eco- ' For a stimulating discussion of these issues see Krugman (1995). nomics, in the so called 'new economic geogra phy' (see Krugman (1991a) for a statement of the issues and Krugman and Venables (1995, 1996) for details of the approach). The current paper is the first attempt to apply these models to a large data set and use them for policy analysis. What are the precise mechanisms which will gen erate these spillover effects through the econo my? One possibility is that there are technological externalities between firms — for example knowl edge spillovers of one sort or another — which create an interdependence between the locations of firms. If an infrastructure project attracts one firm to a location, then technological externalities of this type can lead to other firms being attract ed, and hence a process of cumulative causa tion. This mechanism may be important for some industries, but we exclude it from this study. There simply is not sufficient evidence of the im portance of the mechanism to make it a satisfac tory basis for modelling. A second mechanism arises through pecuniary externalities between firms. A pecuniary externali ty arises when firms interact through markets which are imperfectly competitive, and can best be thought of in terms of the concepts of forward and backward linkages put forward in the devel opment economics literature of the 1950s (for ex ample Hirschman, (1958)). To see the implica tions of this suppose that a location contains some firms in each of two vertically related indus tries — a downstream industry (eg car manufac ture) and an upstream industry (car parts). An in frastructure improvement raises the profitability of firms in this location, causing the entry of a fur ther firm. What then happens? In the standard world of neoclassical economics the entry re duces profits of existing firms. It does so by in creasing the intensity of product market competi tion, and also by bidding up the price of primary factors in the location. These negative effects have the effects of discouraging further entry and dampening down quantity changes. But if there are positive pecuniary externalities other forces come into play. Entry in the downstream industry may attract entry of supplier firms in the up stream industry — a backwards linkage. This in turn may cause the upstream industry to become more competitive or to offer a wider range of vari eties of intermediate product. If its effect is to re duce the price of intermediates to the down stream industry this is a forward linkage, and cre ates a pecuniary externality that may lead to fur- The issues 11 ther expansion of the downstream industry. We are therefore in a world of positive feedback. The initial change — entry of a downstream firm — may lead to amplified change, the entry of further downstream firms, rather the damped effects of standard theory. The phenomenon just described are simply the backward and forward linkages idea popular in the development economics literature of the 1950s (eg Hirschman (1985)). However, we now recognise the importance of market imperfec tions and pecuniary externalities in making the process work, (in a standard world of perfect competition and non-increasing returns to scale these linkages are of no value) and we now have ways of formally modelling, analysing and quanti fying the forces. In extreme cases these forces can lead to spatial agglomeration of activity. The positive feedback may be strong enough to cause most of a particular industry or set of in dustries to be drawn into a one location (see Venables (1996), Krugman and Venables (1995,96)). But even if the forces are not suffi ciently strong to cause agglomeration, we may nevertheless get amplification of economic changes, not dampening. This suggest the need for techniques which assess regional infrastruc ture projects to look at broader effects than those included in traditional cost benefit analysis, and to incorporate and evaluate these spillovers through sectors of the economy. Our analysis then, will incorporate increasing re turns to scale at the level of the firm and imper fect competition (in some, but not all sectors), and input-output linkages between industries so that there are potential forward and backward linkages. The combination of these forces gives rise to pecuniary externalities and spillovers, al though possibly rather weak ones. In the next section of the paper we present an overview of the model we employ, before turning, in section 4 to data and section 5 to experiments. 12 Section I — Computable General Equilibrium Models 3. Overview of the model In this section we outline the main elements of the model (a full description is given in the techni cal appendix). The same basic model structure is applied to each of the cohesion countries, al though at different levels of industrial and regional disaggregation. In the following description coun try specific details are given only for the model as applied to Spain and Portugal. 3. 1. Locations and endowments The first component of the model is a specifica tion of the geographical space within which eco nomic activity takes place. This takes the form of a set of 'regions', which are points in space linked by a transport network through which goods and services can be traded. Ideally a high level of regional disaggregation is required, and for the combined Spain+Portugal model we work with 22 regions. Each region has an endowment of primary fac tors — in the models we present here this takes the form of two types of labour (differentiated by skill class) and capital. These endowments are owned by a representative household in each lo cation which spends its income on final goods. We assume that capital is perfectly mobile be tween regions, and take the price of capital to be constant. We make two different assumptions for labour. For each experiment we report results both when labour is immobile between regions, and when labour is perfectly mobile. In the former case wage rates are determined by supply and demand in each location, this implying that re gional wage differences are possible and are not offset by migration between regions. In the latter case wage rates are the same in all regions, and are determined by supply and demand for labour in the country area as a whole. In addition to the regions within the country area under study, there are external trading partners. We simply assume two of these — the rest of the EU and the rest of the world. They are modelled much less fully than the internal regions, merely offering import supplies and export demands to the regions under study. 3. 2. Production There are a number of industries sectors in the economy (16 for the Spain/ Portugal model), and these are divided into two types; perfectly and imperfectly competitive industries. In perfectly competitive industries production takes place ac cording to constant returns to scale, and firms price at marginal cost. A single homogenous product type is produced by each of these indus tries in each region, although we allow for the possibility that each region's product type is dif ferentiated from that of other regions. (This is the 'Armington assumption' frequently employed in computable equilibrium models of international trade. Its effect is to prevent total regional spe cialisation occuring in these industries). Imperfectly competitive industries contain firms which operate under increasing returns to scale. In general, each industry will operate in each re- Overview of the model 13 gion, so each region contains some number of firms from each industry. We use the standard Dixit — Stiglitz representation of increasing re turns and imperfect competition. This involves a number of assumptions on the demand system (given in the appendix), and the assumptions that each firm is constrained to operate in a single re gion only, is assumed to produce a distinct vari ety of product, and to set price at a constant mark up over marginal cost. Although each firm produces its own variety of product, the varieties are assumed to be symmetric. That is, they are produced using the same technology, and face the same demand functions. Consequently, if they are sold at the same price, then they will achieve the same level of sales. All sectors of the economy use as inputs to pro duction the primary factors and intermediate goods. Corresponding to this, all sectors' output is used both as a final product, and as an inter mediate good. The details of intermediate goods useage and the destination (final or intermediate use) of output comes from the input output ma trix. A consequence of product differentiation combined with the symmetry assumption is that all firms at a particular location in a particular in dustry supply final demand and intermediate de mand in the same proportions. In experiments we report results both for cases where the number of firms is held constant, and where it is allowed to change. The former cap tures a 'short run' case where industrial location is assumed to be constant. The latter captures a 'long run' where entry and exit of firms has oc- cured in response to profit opportunities. In the short run the number of firms operating in each location is therefore equal to the base number. In the long run equilibrium the location of firms is determined by the zero abnormal profit condition which will hold for all industries and all regions. 3. 3. Inter-locational trade We want to capture the possibility that there is in- tra-industry trade in each industry and between all locations, and this follows from our modelling of product differentiation. The Dixit-Stiglitz formu lation implies that the representative consumer has preferences exhibiting 'love of variety', so will consume all available varieties of product. Since firms are operating at different locations and pro ducing distinct varieties, these preferences gen erate demand at each location for output pro duced in all other locations, and hence can pro duce the full set of inter-locational trade flows. Demands come not only from consumers, but al so from other firms demanding intermediate products, and we make an analogous assump tion for these intermediate goods demands. That is, firms benefit from having a wide range of inter mediate goods available, and their intermediate demands will draw on output from all locations The volumes of these inter-locational trade flows are regulated by transport costs between loca tions. A high level of transport costs between two regions will raise the price of products traded be tween regions, and reduce the level of trade on that segment of the network. An important Issue arises in measurement of these transport costs. Whereas a model of international trade would use data on trade international trade flows to in fer the trade costs consistent with these flows, disaggregated data on inter-regional trade flows is unavailable. We therefore have to follow the re verse methodology. We obtain estimates of the trade and transport costs between locations, on the basis of which the model generates all the in ter-regional trade flows. This issues is discussed more fully in section 4. 3. 4. International trade Regions in the model also serve as 'ports' — points through which exports and imports to the rest of the EU and rest of the world pass. Imports Imports are available at fixed world prices, and constitute an additional source of supply (addi tional to any local production) at each port loca tion. They can be shipped from port of entry to other regions in a manner exactly analogous to the inter-regional trade in domestically produced goods. Changes in the cost of bringing imports in through a port, or of shipping from the port to a final demand region, will cause substitution be tween ports, as final users may change the ports through which they import. This allows us to cap ture the effect of port improvements on port use- age. 14 Section I — Computable General Equilibrium Models Exports Each port also serves as a source of demand for domestically produced goods, as exports to the rest of the EU and rest of the world pass through the port. Just as consumer and intermediate de mand at a region can be met from other regions via inter- regional trade, so export demand at a port is met by domestic suppliers from many re gions, this bearing the usual inter-regional trade costs. As with imports, changes in the relative costs of using a particular port may cause changes in the volumes of exports going through the port, as exporters can substitute between the ports they use. We also assume that overall de mand for the total exports of each industry is a decreasing function of their price. The economy under study is therefore a price taker with re spect to imports, but not with respect to exports. The dimension of this model is quite high — for example, in the Spain/ Portugal model there are 22 regions plus 2 external trading partners, and 16 industries. High dimensionality is also created by the inter-regional trade flows. Since demand in any location will in general be met by supply from all other locations, there are 22 χ 22 such trade flows within each industry. Tractability is achieved by making use of various aggregation properties which are consistent with our Dixit-Stiglitz formu lation of product differentiation. In particular, it is possible to construct price indices for each in dustry at each location. These price indices sum marise (in an exact way) the prices of all varieties of product supplied, and act as the basis for con sumer choices and for firms input decisions. The structure described here is able to capture the effects we described earlier. For example, a reduction in transport costs on some point of the transport network will have a direct effect on prices of products in different regions. This changes firms sales (increasing sales of firms that benefit from the link, and reducing those of firms now facing increased competition from imports from another region) and, since firms are operat ing with price set above marginal cost, this changes profits. Entry and exit of firms may oc cur in response to these profit changes, and this entry and exit causes a further round of effects. Entry of a firm typically has four effects. It in creases competition, tending to reduce profits of other firms. It bids up factor prices, reducing profits. It increases demand for other firms sales of intermediates, the backwards linkage, raising profits in supplier industries in the location. And in so far as the new firm supplies intermediates, it reduces the price index of these products in the location, this raising the profitability of user firms. As we have already argued, the first two of these effects are 'neoclassical', tending to dampen in duced quantity effects. The last two are positive feedbacks, amplifying the changes caused by some initial shock. Overview of the model 15 4, Data and calibration The model sketched out above was fitted to da ta for three country/ country groups. A com bined Iberian model was constructed for Spain and Portugal, and separate single country mod els for Greece and Ireland. Each of these appli cations requires the same categories of data for the base data set. This section discusses first discusses the primary data requirements of the model, the procedures that were employed to ensure the internal consistency of the data, and the consistency of the data to each of the under lying computable general equilibrium models. Secondly for each of the countries included in this report, the primary data sources used and the procedures employed are discussed. In or der to provide background information on the re gional and industrial structure of each economy, some key features of each country's data are al so presented. 4. 1. Primary data requirements 4. 1. 1. Production For each country the model works with a num ber of regions and industries, and in each case three factors of production (two categories of labour — manual and non-manual; and capital). In the first instance therefore, it was necessary to collect data on either the value of production, or on value added in each sector. However, as the models are designed to deal with inter-re gional trade within a country the production da ta is required both by sector and by region. In principle regional data are available for the countries of the European Union at various lev els of regional disaggregation ranging from NUTSO to NUTS3; where NUTSO refers to the country and each of the subsequent categories provides finer levels of disaggregation. In prac tice there are serious restrictions on the amount of data that are available at the regional level. The problems here range from virtually the com plete absence of data (as in the case of Ireland), to incomplete data sets. The level of disaggre gation finally employed in this paper is the fol lowing: Spain - NUTS2 ("Communidades Au tonomas"); Portugal - NUTS2 (Regiones Au tonomas; Greece — own regional classification scheme (YPA which can be reconciled with the NUTS2 Ireland level of disaggregation); (NUTS3). The full details of the regional classifi cation used are given in Table 4. 1. The regions in bold are the regions used in the respective models. The level of industrial disaggregation was neces sarily determined by the completeness of the corresponding regional data set. For each coun try the level of Industrial disaggregation employed was: Spain & Portugal - Nace R17; Greece - again based on own classification scheme which comprises eight sectors; Ireland - three sectors. The precise industrial disaggregation employed is given in Table 4. 2. It is unfortunate that a disag gregation of manufacturing was not possible for Greece and Ireland. Data and calibration 17 TABLE 4. 1. Regional disaggregation by country Spain Portugal Greece Ireland NUTS1 NUTS2 NUTS1 NUTS2 NUTS1 NUTS2 NUTS1 NUTS3 Noroeste Continent Voreia Ellada Ireland Norte Centra Lisboa Alentejo Faro Islands Central Ellada Madei'a Azores Attiki Kriti Anatoliki Makedonia East Mid West South East South West Midlands West Border & Thraki Kentriki Makedonia Dytiki Makedonia Thessalia Ipeiros Ionia Nisi Dytiki Ellada Sterea Ellada Peloponnisos Voreio Aigaio Notio Aigaio Kriti Noreste Madrid Centro Este Sur Galicia Asturias Cantabria Pais Vasco Navarra Rioja Aragon Castilla Leon Castilla La Extremadura Valencia Baleares Catalunya Andalucía Murcia Ceuta Melilla Canarias TABLE 4. 2. Sectoral disaggregation by country Sector Agriculture Fuel and power Manufacturing Ferrous & non-ferrous metals Non-metallic metals and minerals Chemical products Metal, machinery, equipi, electrical goods Transport Food Textiles Printing Other Sen/ices Building & construction Market services Transport & communication Banking Other R17code Iberia Greece Ireland B01 B06 B02 B13 B15 B17 B24 B28 B36 B42 B47 B50 B03 B53 B58 B60 B69 B74 X X X X X X X X X X X X X X X X X X X X X X X X X X X Section I — Computable General Equilibrium Models 4. 1. 2. National Accounts data As discussed previously each model is a full gen eral equilibrium model of regional production and trade. This means that both intermediate produc tion and final goods production are explicitly modelled. With regard to intermediate goods production the primary data requirement was an input-output table which Included both the table of intermediate consumption as well as details on primary inputs. From this one can then derive the appropriate technical coefficients which are re quired for describing the intermediate demands and supplies of each sector. 4. 1. 3. Inter-regional trade costs Each of the models contains inter-regional trade within an open economy. This means that (changes in) patterns of trade between regions and production within each region as a result of changes in the policy environment are central to the concerns of the model. However, the data described above includes only information on production by sector and by region, but not on the value of trade between each region in each industry. Deriving this matrix is a central feature of the calibration procedure. Ideally this procedure requires information on transport costs between each region. Such data is not available, so these costs have to be inferred or estimated, and we do this on the basis of distance. We proceed in three stages. First we locate the primary centre of economic activity within each region and construct the matrix of distances be tween each pair of regions. Given the distance matrix, we then assume a relationship between distance and transport costs. Using this in the model we generate a pattern of gross trade flows between regions. For some countries there is da ta available on the volume of trade between re gions (although in units different from those of the model, and not always at the same level of re gional classification), and this was compared with the trade flows generated by the model. An itera tive procedure was then adopted to adjust the relationship between distance and transport costs until the model produced a reasonable replica of the data on trade volumes. Finally, we allowed the relationship between distance and trade volumes to vary across industries (while preserving aggregate trade flows) in order to cap ture different transport costs in different indus tries. We do this by using external trade data and production data (exports plus imports relative to total production for each industry) to measure the tradabality of the output of different industries. 4. 1. 4. Ports As discussed in the previous section, the models presented here include both inter-regional trade but also external trade. The external trade is limit ed to both intra and extra EC12 trade. However, as each country is broken down into a number of regions it is necessary to identify through which regions the external trade flows take place. Here too It is necessary to distinguish between differ ent types of "ports" which should include land, air and sea. With regard to air and sea traffic, data was obtained for each country on the volume of trade going through each port. With regard to ex ternal trade over land, data was obtained on the total volume of externally directed road and rail traffic. The form of this data does not able one to neatly identify ports. The procedure employed here, therefore, was to identify the regions which are contiguous with other countries, to calculate for each of these regions their share of total con tiguous regions' production, and then to allocate the land traffic accordingly. The final stage of the ports process was to sum the total volume of trade by type of traffic going out of each region, and then to calculate each region's share of total external traffic. 4. 1. 5. Miscellaneous In addition to the above for each country data was required on both intra and extra European trade for each sector, as well as a range of indus try specific parameters. These include the value added share in each sector; the shares of manual and non-manual labour in each sector; elasticities of substitution between capital and labour and between the different labour types. Table 4. 3 pro vides an example of the key industrial character istics required for the operation of the model, with the last column giving the share of value added in gross production, and the three preced ing columns giving the shares of each of the pri mary factors in value added. The data presented here was calculated on Spanish data. This pro vided the basis for the comparable data which was then required for the other countries. Hence where the data was required at a more aggregate level appropriate aggregation or averaging tech niques were employed. Data and calibration 19 TABLE 4. 3. Industry Characteristics R17code Capital share Labour share Value Added ν Sector Agriculture Fuel and power Manufacturing Ferrous & non-ferrous metals Non-metallic metals and minerals Chemical products Metal, machinery, equipi, electrical goods Transport Food Textiles Printing Other Services Building & construction Market services Transport & communication Banking Other B01 B06 B02 B13 B15 B17 B24 B28 B36 B42 B47 B50 B03 B53 B58 B60 B69 B74 0. 758 0. 698 0. 448 0. 535 0. 493 0. 389 0. 165 0. 594 0. 360 0. 408 0. 412 0. 446 0. 710 0. 542 0. 538 0. 739 Non-man. Man. 0. 116 0. 160 0. 144 0. 130 0. 264 0. 293 0. 267 0. 159 0. 160 0. 231 0. 171 0. 166 0. 116 0. 229 0. 416 0. 131 0. 126 0. 142 0. 409 0. 335 0. 243 0. 318 0. 568 0. 248 0. 480 0. 361 0. 418 0. 388 0. 174 0. 229 0. 046 0. 131 0. 552 0. 438 0. 260 0. 533 0. 389 0. 474 0. 300 0. 319 0. 458 0. 445 0. 443 0. 558 0. 668 0. 666 0. 761 0. 758 4. 2. Country data requirements 4. 2. 1. Iberia As listed in table 4. 1 the production data by in dustry and by region for Spain and Portugal was available at the Nace R17 level of classification for the year 1990. The principal source for this data was Eurostat, and in particular the Regio data bank. This includes eight manufacturing industries and eight other sectors, as listed in Table 2. At that level of industrial classification the data was available for 18 regions. Input-output tables were available at this level of sectoral disaggregation for the year 1990. The input output tables thus pro vided the vertical coefficients for each of the in dustries at the R17 level of disaggregation, and for the share of labour and capital in production. In order to check on the consistency of the coeffi cients thus calculated and in particular the shares of labour and capital, input-output tables for Ger many and the UK were also examined (ESA Na tional Accounts: Input-Output tables, 1980). The input-output tables also were used to calculate the share of value added in each industry. The share of the different types of labour in each sector were calculated on the basis of data avail able in the Eurostat Labour Force Survey for 1988. Where data were missing for certain sec tors best guess estimates were made. The exter nal trade data was derived from the COMEXT trade data base. Distance data was obtained from geographical sources and using own judge ments regarding main area of economic activity within each region. An adjustment was made for the Spanish - Portuguese border, to capture the historically very low levels of trade across the border. The source of the port data was Eurostat, Statistical Yearbook, Transport, communications, tourism (1991). Table 4. 4 provides details on the industrial and regional makeup of the Spanish economy, where the industrial classification has been aggregated to four sectors. The first four columns show the the share of region in the value added of each sector. The last four columns show for each re gion the share of each of the main sectors in that regions value added. From the table it can be seen that Murcia and Galicia are the most impor tant source of agricultural products as well as mining and electricity; Catalunya and Madrid are the most important manufacturing producers and services providers. With regard to the degree of specialisation within each region it can be seen that services are the most important sector in all regions, with manufacturing being the second most important area of activity in all but Extra- maduras and Alentejo. 20 Section I — Computable General Equilibrium Models TABLE 4. 4. Regional & sectoral shares in value added — Iberia Regional shares by sector Sectoral shares by region Region Agrie. Vlining & Elee. Manuf. Services Agrie. Mining & Elee. Manuf. Services galicia asturias cantabria paisvasco navarra rioja aragon madrid cas-leon cas-man extrema Catalunya cv anda mure canarias baleares Norte Centro Lisboa Alentejo Algarve 0. 108 0. 017 0. 015 0. 028 0. 014 0. 014 0. 029 0. 005 0. 081 0. 074 0. 041 0. 066 0. 068 0. 007 0. 225 0. 048 0. 030 0. 034 0. 030 0. 041 0. 017 0. 010 0. 077 0. 044 0. 004 0. 098 0. 005 0. 003 0. 027 0. 064 0. 074 0. 075 0. 034 0. 156 0. 077 0. 011 0. 113 0. 039 0. 034 0. 024 0. 009 0. 026 0. 003 0. 002 0. 041 0. 021 0. 014 0. 087 0. 024 0. 014 0. 035 0. 115 0. 047 0. 029 0. 005 0. 223 0. 096 0. 007 0. 080 0. 016 0. 011 0. 060 0. 021 0. 051 0. 003 0. 001 0. 045 0. 022 0. 012 0. 053 0. 013 0. 006 0. 029 0. 160 0. 045 0. 028 0. 015 0. 171 0. 091 0. 027 0. 126 0. 022 0. 041 0. 027 0. 009 0. 052 0. 003 0. 004 0. 118 0. 041 0. 067 0. 024 0. 051 0. 094 0. 053 0. 002 0. 089 0. 119 0. 146 0. 020 0. 041 0. 018 0. 102 0. 114 0. 051 0. 052 0. 123 0. 044 0. 256 0. 165 0. 089 0. 113 0. 020 0. 090 0. 019 0. 022 0. 051 0. 027 0. 086 0. 127 0. 126 0. 050 0. 049 0. 031 0. 054 0. 098 0. 060 0. 039 0. 040 0. 030 0. 045 0. 025 0. 199 0. 224 0. 278 0. 338 0. 384 0. 422 0. 281 0. 207 0. 231 0. 208 0. 084 0. 305 0. 257 0. 088 0. 162 0. 169 0. 082 0. 411 0. 386 0. 248 0. 216 0. 079 0. 594 0. 623 0. 635 0. 548 0. 546 0. 463 0. 616 0. 764 0. 594 0. 546 0. 644 0. 624 0. 653 0. 863 0. 681 0. 619 0. 807 0. 498 0. 451 0. 678 0. 483 0. 731 4. 2. 2. Greece Neither the industrial nor the regional disaggrega tion of the Greek data were available in any of the standard Eurostat classification schemes, we therefore used country team data from 1993 (NSSG: Accounts Division). The industrial data came disaggregated in the form listed in table 4. 11, and there was no formal correspondance obtainable between this classification scheme and the Nace R17. The correspondance listed in Table 4. 2 is therefore based on our best judge ment. Input-output data for Greece was unobtainable and therefore the technical coefficients derived from the Spanish input-output table were used as a proxy and had to be aggregated according ly. Similarly the Spanish data was employed to derive the share of value added in each sector, as well as the share of manual and non-manual labour in value added. Total trade (imports and exports) was available from the country team da ta, however data broken by sector proved un available (for example the Eurostat CD-ROM for 1992 and 1993 listed imports and exports but excluded services). The trade for each sector was thus interpolated on the basis of the Spanish shares of both intra and extra Imports/exports for each sector. Finally the port and flows data came from the country teams, and the distance matrix was derived from appropriate road maps. Table 4. 5 provides the key details on the industri al and regional makeup of the Greek economy. As with Table 4. 4 for Spain the first four columns show the the share of region in the value added of each sector; and the last four columns show for each region the share of each of the main sectors in that region's value added. 4. 2. 3. Ireland Regionally disaggregated Irish data was not avail able in a satisfactory and up to date form. The data used in this model is at the NUTS3 level and is for the year 1981. This data was only available at a highly disaggregated sectoral level (Agricul ture, Manufacturing and Services). As with Greece, input-ouput data was unobtainable and therefore the Spanish input-output coefficients were used as a proxy and had to be aggregated accordingly. Similarly the Spanish data was em ployed to derive the share of value added in each sector, as well as the share of manual and non- manual labour in value added. Data and calibration 21 TABLE 4. 5. Regional and sectoral shares in value added — Greece Regional shares by sector Sectoral shares by region Region Agrie. Mining & Elee. Manuf. Services Agrie. Mining & Elee. Manuf. Services East Macedonia & Thraki Central Macedonia West Macedonia Thessalia Ipiros Ionian Islands West Ellada East Ellada Ättika Peloponissos East Aegean Dodecanese & Cyclades Crete 0. 087 0. 199 0. 035 0. 127 0. 042 0. 023 0. 107 0. 091 0. 045 0. 121 0. 019 0. 019 0. 086 0. 097 0. 100 0. 213 0. 036 0. 020 0. 009 0. 040 0. 097 0. 212 0. 077 0. 017 0. 043 0. 040 0. 040 0. 201 0. 016 0. 066 0. 012 0. 005 0. 049 0. 113 0. 417 0. 047 0. 006 0. 009 0. 018 0. 039 0. 146 0. 022 0. 051 0. 023 0. 022 0. 047 0. 052 0. 440 0. 045 0. 017 0. 042 0. 055 0. 295 0. 207 0. 186 0. 327 0. 297 0. 208 0. 318 0. 214 0. 021 0. 343 0. 212 0. 101 0. 275 0. 091 0. 029 0. 312 0. 026 0. 039 0. 023 0. 033 0. 063 0. 028 0. 060 0. 052 0. 063 0. 035 0. 153 0. 234 0. 093 0. 190 0. 098 0. 056 0. 164 0. 296 0. 222 0. 150 0. 070 0. 054 0. 066 0. 461 0. 530 0. 407 0. 455 0. 561 0. 706 0. 482 0. 425 0. 729 0. 443 0. 649 0. 774 0. 618 Total trade for agriculture and manufacturing was available from the COM EXT trade data. Trade da ta from the OECD National Accounts (Main Ag gregates, 1960-86) was then obtained for the to tal value of trade in goods and services. The share of trade between intra and extra EC trade was then interpolated on the basis of the Spanish data, and then the value of trade in services was calculated accordingly. Finally the port data was obtained and the distance matrix was derived from appropriate road maps. Table 4. 6 provides the key details on the industri al and regional makeup of the Irish economy, and follows the same structure as the analogous ta bles for Iberia and Greece. TABLE 4. 6. Regional and sectoral shares in value added — Ireland Agriculture Manuf. Services Agriculture Manuf. Services East Mid West South East South West Midlands West Border 0. 113 0. 124 0. 191 0. 209 0. 111 0. 099 0. 153 0. 387 0. 090 0. 109 0. 145 0. 076 0. 061 0. 132 0. 471 0. 075 0. 080 0. 128 0. 052 0. 063 0. 132 0. 027 0. 142 0. 183 0. 142 0. 162 0. 147 0. 112 0. 357 0. 394 0. 402 0. 381 0. 424 0. 347 0. 368 0. 616 0. 464 0. 416 0. 477 0. 415 0. 506 0. 520 22 Section I — Computable General Equilibrium Models 5. Simulations In this section we outline the procedures that we follow to represent a cohesion fund project within the model, and then report results from simulat ing the economic effects of these projects. In to tal there are six experiments which we report, one for each of the countries in the model, each of which corresponds to an actual Cohesion Fund project which is being undertaken or is planned. The six experiments are: 1 : North-South road link (Ireland) 2: Madrid ring road (Spain) 3: Rias-Bajas motorway (Spain) 4: Tagus crossing (Portugal) 5: Egnatia motorway (Greece) 6: Pathe motorway (Greece) The detailed methodology employed in translat ing these projects into model experiments is out lined below in the first experiment we discuss (the North-South road link in Ireland). The report ing of subsequent experiments follows the same format but avoiding unnecessary repetition. Be fore outlining the methodology in some detail it is first important to outline some general considera tions. The experiments are all road projects, the direct effects of which are to reduce transport costs be tween and within regions. Our calibration of these costs was based on the distance between re gions, and we model a project as causing a re duction in the 'effective distance' between re gions. That is, if a given road project is expected to reduce travelling time between two regions by one hour, we can approximate this by reducing the effective distance between the regions by the average distance that could be travelled in that time, for example, 100 kilometres. Since trade costs were computed as a function of distance, this in turn translates back into a cost saving on the route. Implementing this procedure calls for a number of judgemental choices. First, given some infor mation on the project, how is this to be translat ed into an effective reduction in distance? Clearly time savings can be translated into effective dis tance reductions given estimates of average speeds. Rather more speculatively, kilometres of road improvement can be translated into an ef fective distance reduction, given estimates of av erage speeds with and without the project. As much detail as possible is needed from the cost benefit analysis of the study to provide the infor mation on which these calculations can be based. Second, what routes — links between regions — are affected by a particular road scheme? Pre sumably a road improvement in the Madrid region will change the effective distance between Galicia and Catalunya, but not between Catalunya and Valencia. Our decisions as to which routes are and are not affected is a matter of judgement, based essentially on looking at road maps. Third, what proportion of traffic on a route is af fected by a particular improvement? Clearly, not Simulations 23 all journeys are made by road transport, and oth er modes of transport are unaffected. Of road transport, some proportion of journeys within and through the Madrid region will use the Madrid ring road, but not all. We have to make judge ments on each of these numbers, and use these to deflate the effective distance reduction — so that a 100km distance reduction which is only used by half the journeys on the route is inter preted as a 50km distance reduction. Finally, the 'effective distance reduction' may be different for different industries. If we know that output in one industry is (and will continue to be) shipped exclusively by rail, then clearly the effec tive distance faced by firms in this industry is un changed by a road improvement. The model al lows us to take this into account, with the project impacting on different industries in different ways. But once again, the problem is getting hard infor mation on which to base any such unequal treat ment. Clearly then, a number of subjective and some what arbitrary descriptions of the project have gone into the design of our experiments, and this must be borne in mind in interpreting results. The underlying information on which our judgements are based comes from the relevant cost-benefit analyses but, unfortunately, the focus of these is rarely such to provide a clear picture of all the in formation needed. Given a representation of a particular project, we then use the model to simulate the effects of the project on the equilibrium. To assess the effects of the project we proceed in four stages. These four stages correspond to the direct, short run, medium run and long run effects as discussed in subsection 2 of the Modelling Report, Part 1, Section 2. These are described below: 1 : First, we compute the direct effects of the project. That is, holding constant inter-region al trade flows (and all other endogenous vari ables in the model), we find the value of the transport cost saving caused by the project. 2: Second, we compute the effects of the pro ject holding the location of firms and workers constant, but allowing the output and sales of these firms to change in response to changes in transport costs, with consequent changes in interregional trade flows. This approximates the induced effects of the project in so far as it permits changes in some endogenous vari ables, but ignores the possibility that the pro ject may cause industrial relocation. We shall call these changes the short run effects of the project. 3: Third, we also also allow the number of firms operating in each industry and in each region to change, but continue to hold the number of workers in each location constant. The changes in the number of firms occur in re sponse to short run changes in the level of profits and, as they occur, they further change the profits through the linkage and factor mar ket mechanisms. We shall call this stage of the experiment the medium run effects. 4: Finally, we also allow workers to move ¡n re sponse to induced changes in wages be tween regions. This stage of the experiment amounts to 'perfect' factor mobility, in so far as both labour and capital move to ensure equalisation of returns across all regions. We term this experiment the long run. Of course, the time connotations of these differ ent stages of the experiment are not to be taken literally, but follow the convention of letting more variables adjust to an economic change the longer the time horizon. We are now in a position to describe the projects studied and results obtained. 5. 1. Base experiment: North-South Road Corridor (Ireland) The North-South Road Corridor in Ireland com prises the national routes N1, N7, and N8. It leads from the North-Eastern border of Ireland (Dundalk) through Dublin to the South Coast (Cork). It is part of the National primary road net work, the major mode of internal transport which supports 90% of all passenger and goods traffic within Ireland. Commercial vehicles comprise about 1 of every 3 vehicles travelling on the North South Road Corridor. Evaluation of this base project includes seven distinct projects within this corridor, consisting mainly of by-passes. These projects are indicated on the schematic map which locates the seven subsections of the North South Road Corridor in 24 Section I — Computable General Equilibrium Models the context of the regional disaggregation used for Ireland. As can be seen from schematic Map 1. 1 the North-South Road corridor is primarily lo cated in the eastern part of Ireland, and most of the component parts are located within the East region. Table 1. 1 lists these seven projects as well as some more detailed information. Unless other wise specified the data reported in this table come from the cost-benefit analyses of the seven projects completed for the Commission of the European Communities in August, 1994. We have assigned numbers from 1 to 7 for indi vidual links within the corridor which will be used as reference numbers. Columns two, three, and four give the project number assigned by the Eu ropean Cohesion Fund, the title of the project, and the region in which the project is situated re spectively. In the next two columns, we have list ed the travel time on the section of the existing road before project improvement [t(0)] and travel time after improvement [t(N)j. Columns seven gives the distance of the road before the project improvements [D(O)]. Although the length of some of the road sections might be increased by the corresponding project (i. e. Drogheda by pass), the actual travel time is always decreased, due to an increase in average speed on the im proved road. Columns nine, ten, eleven, and twelve detail information from the cost-benefit analyses. Column nine specifies the scheme cost for each road link. Column ten reports the undis- counted values of time saved (over a twenty year period) for each road link in millions (ECU). Col umn eleven lists fuel cost savings (over 20 years) in millions (ECU); these values are sometimes negative in instances where increased average speed would lead to an increase of fuel utilised. The final column gives the cost benefit estimate of the internal rate of return for the project. TABLE 1. 1. North-South Road Corridor project details min km MECU Key Project Project Title Region Involved t(O) t(N) D(0) DS Cost Time Fuel Cost IRR 1 1 2 3 4 5 6 7 2 3 4 5 6 7 8 9 10 11 12 93/07/65/009 93/07/65/007 93/07/65/008 93/07/65/032 93/07/65/010 93/07/65/036 94/07/65/007 Dunleer- -Dundalk Drogheda by-pass Balbriggan by-pass Northern Cross Southern Cross Kildare by-pass Portlaoise by-pass Borders 27. 83 17. 32 27. 2 10. 27 67. 79 272. 62 - 4. 36 11 East 19. 6 14 20. 75 5. 93 81. 9 310. 86 - 1 3. 30 10 East 13. 07 7. 84 13. 55 5. 42 42. 59 314. 20 2. 81 20 East 21. 14 9. 14 9. 8 5. 56 74. 72 821. 21 12. 65 44 East 20. 11 8. 11 12. 5 7. 46 76. 87 703. 9 -7. 17 36 East 12 8. 19 11. 52 3. 66 56. 7 220. 69 3. 75 11 East/M 15. 35 9. 68 15. 44 5. 7 49. 14 186. 29 - 3. 13 10 The key input for our model is given 8, the effec tive distance saved. The formula used to calcu late the effective distance saved is the following: Distance of existing road Distance Saved = (1 - time travelled on the new road/ time travelled on the existing road)*- For example, the existing road of the Kildare by pass has a length of 11. 52 km. The time trav- Simulations 25 elied on the existing road is 12 minutes. The road improvement of the Kildare by-pass de creases the time travelled to 8. 19 minutes. This would reduce the distance travelled by. 3175 or roughly one-third. Thus, the distance saved would be. 3175 multiplied by 11. 52 km, which equals 3. 66 km. We see that, along the entire length of the road the effective distance reduc tion amounts to around 45kms. Calculating the effective distance saved comprises the first of the three judgemental choices outlined previ ously. Tables 1. 2 and 1. 3 illustrate the procedures em ployed for the second and third judgemental choices respectively which need to be made. In Table 1. 2 we list which projects affect which routes or links between any pair of regions. In compiling this matrix we have considered any possible road in the Irish National primary road network which could be used to link regions. From the matrix it can be readily seen that for this experiment it is the regions East and Borders which are the most heavily affected. This can al so be seen in the schematic map. TABLE 1. 2. Matrix of regions affected City of Reference Dublin Longford Waterford Cork Umerick Galway Dundalk Region East Midlands South East South West Mid West West Borders East Midlands South East South West Mid West West Borders 2,3,4,5,6 2,3,4,5,6,7 2,3,4,5,6,7 4,5,6,7 4,5,6,7 4,5 1,2,3,4,5 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1,2,3,4,6,7 1,2,3,4,5,6,7 1,2,3,4,6,7 1,2,3,4,6,7 1,2,3,4,5 1 Project components 2, 3, 4, 5 and 6 all lie within the East region. Though they are likely to affect some journeys within the East region, not every link is going to affect every single journey. Look ing at a detailed road map of this region, we can distinguish four main directions, North, North west, South-West, and South; these four direc tions correspond to six major roads (second schematic map). Travels to the North and North west profit from the Northern Cross Route, Dublin Ring (project 4) but are unaffected by any other subsection of the project. Similarly, travels to the South West are only affected by the Kil dare by-pass (project 6); the South Cross, Dublin Ring (project 5) is likely to influence solely jour neys from the South. Hence we also need to decide (judgemental choice 3) what proportion of traffic between any pair of regions or within a region is likely to be affected by any of the component parts of the experiment. This is captured by assigning a scaling factor to each of the component parts of the project. That factor may differ depending on which bilateral link between regions is being considered. For example, as can be seen from the schematic map, journeys between (parts of) the East and (parts of) the South-East are likely to be affected by project 7. However, clearly only a small fraction of journeys be tween the East and South-East are likely to be affected. It would therefore be unreasonable to reduce the effective distance between this pair of regions by the entire distance saved in pro ject 7, hence the scaling factor. As this proce dure involves difficult judgmental choices closely based on detailed road maps, the fac tors we employ are restricted to 0, 0. 25, 0. 5, 0. 75 and 1. The factors actually employed can be seen in Table 1. 3. 26 Section I — Computable General Equilibrium Models Map 1. 1 Map of Ireland, North-South Road Corridor WEST MID WEST BORDERS unclalk f o r ai —V 2 MIDLANDS EAST SOUTH EAST I e g p nH -f- City of Reference for a Region 1. 2. 3. North South Corridor Simulations 27 TABLE 1. 3. Weight attached to different projects on inter and intra regional travel Project Region 1 2 3 4 5 6 7 East / East East / Midlands East / South East East / South West East / Mid West East / West East / Borders Borders / Midlands Borders / South East Borders / South Borders / Mid West Borders / West Borders / Borders Midlands / Midlands 0 0 0 0 0 0 0. 5 0. 25 0. 5 0. 5 0. 5 0. 25 0. 5 0 0. 25 0. 25 0. 25 0 0 0 0. 5 0. 25 0. 5 0. 5 0. 5 0. 25 0 0 0. 25 0. 25 0. 25 0 0 0 0. 5 0. 25 0. 5 0. 5 0. 5 0. 25 0 0 0. 5 0. 5 0. 5 0. 5 0. 5 0. 5 1 0. 25 1 0. 5 0. 5 0. 25 0 0 0. 25 0. 25 0. 25 0. 25 0. 25 0. 25 0. 25 0 0. 25 0 0 0 0 0 0. 25 0. 5 0. 25 1 1 0 0. 25 0. 25 0. 25 0. 5 0. 5 0 0 0 0. 5 0. 25 1 1 0 0 0. 25 0. 25 0. 5 0. 5 0 0 0. 25 These weights were then used to calculate "the weighted effective distance saved" (WEDS) on all the intra-regional and inter-regional journeys. These distances saved are given in Table 1. 4. In order to get some idea of the size of this ex periment table 1. 5 gives the WEDS relative to the original distance matrix. TABLE 1. 4. Matrix of weighted effective distance saved City of Reference Dublin Longford Waterford Cork Limerick Galway Dundalk Region East Midlands South East South West Mid West West Borders East Midlands South East South West Mid West West Borders 8. 3975 12. 1625 1. 425 9. 8225 0 0 14. 005 14. 005 0 0 0 0 0 0 0 4. 645 0 0 0 0 0 19. 15 9. 135 20. 575 18. 27 18. 27 6. 795 5. 135 TABLE 1. 5. Weighted Effective Distance Saved relative to ori ginal distance City of Reference Dublin Longford Waterford Cork Limerick Galway Dundalk Region East Midlands South East South West Mid West West Borders East Midlands South East South West Mid West West Borders 0. 9 0. 94 0. 94 0. 94 0. 89 0. 98 0. 91 0. 94 0. 98 1. 00 1. 00 1. 00 1. 00 0. 96 9. 8225 1. 00 1. 00 1. 00 1. 00 1. 00 0. 94 0. 94 1. 00 1. 00 1. 00 1. 00 1. 00 0. 95 0. 89 1. 00 1. 00 1. 00 1. 00 1. 00 0. 84 0. 98 1. 00 1. 00 1. 00 1. 00 1. 00 0. 95 0. 91 0. 96 0. 94 0. 95 0. 84 0. 95 0. 92 28 Section I — Computable General Equilibrium Models Results: North-South Road Corridor (Ireland) We simulate the effects of the project for 4 cases. The direct effect reports the value of the project at unchanged levels of production, trade and trans port. The short run effects let prices, production, consumption, and hence trade flows adjust in re sponse to the project, but holds the number of firms and workers in each region constant. The medium run also lets the number of firms in each region change in response to changed profit op portunités. The long run also allows for some labour migration between regions in response to changes in regional wage differentials. The model computes values of all the endoge nous variables of the system for each of these cases. We only report a very small part of this output, concentrating on two sorts of variables. First are the welfare or real income changes gen erated by the project. And second, the changes in labour income (in nominal not real terms). This latter measure is useful because it gives a good indication of the impact of the project on demand for labour across different regions, although it is not of any direct welfare significance. Table 1. 6 reports the aggregate effects on the Irish economy of the North-South road link. The first row of the table gives the annual gains in mil lions of ECU, and the second expresses this as a proportion of the initial level of real Income. TABLE 1. 6. Real income consequence of North-South Road link, Ireland Direct effect Short run Medium run Long run mECU: % base real income: Relative to direct effect: 163 0. 91 1 165 0. 90 1. 01 184 1. 1 1. 13 183 1. 1 1. 12 Clearly, the absolute magnitude of the gains depend directly on the size of the effective distance reduc tions fed in as experiment, so the results are sensi tive to the judgements we have discussed above. The third row of the table expresses the real income change relative to the direct effect of the project and, as a pure ratio, is very much less sensitive to errors in our description of the project. It measures the extent to which the project generates additional gains — both close to the project and elsewhere in the economy — and hence captures 'spillovers'. We see from table 1. 6 that, in the medium and long run, these multipliers are of order 1. 12, indicating that the total benefit of the project exceeds its direct cost saving effect by around 12%. Table 1. 7 breaks out these changes by region. Several points can be made. First, all regions ex perience a real income gain from the project, al though the gain is largest in East and Border re gions. Second, the impact of the project on labour income — reflecting changes in demand for labour — is quite unequal, with gains occuring in only three of the regions. (Labour income and real income changes can move in different direc tions, both because of changes in regional costs of living, and because of changes in income ac cruing to capital in each region). The geographi cal impact is more clearly illustrated in map 1. 2. Clearly the positive impact is concentrated in the Border, Eastern and Midlands regions. TABLE 1. 7. Welfare and labour income changes by region Ireland % rea income change % change labour income Region Short run Med run Long run Short run Med run Long run East Mid West South East South West Midlands West Border 1. 19 0. 42 0. 57 0. 44 0. 88 0. 47 1. 38 1. 27 0. 53 0. 69 0. 53 1. 12 0. 54 1. 53 1. 24 0. 55 0. 70 0. 55 1. 12 0. 53 1. 52 1. 47 - 1. 28 - 1. 13 - 0. 91 0. 75 - 3. 27 2. 40 1. 76 - 0. 59 - 0. 29 - 0. 27 0. 87 - 1. 79 2. 83 1. 92 - 0. 90 - 0. 52 - 0. 59 0. 94 - 2. 10 3. 24 Simulations 29 Map 1. 2 North-South Corridor, Ireland WEST MID WEST BORDERS MIDLANDS EAST SOUTH WEST SOUTH EAST Figure 1. 2 Percentoge change in labour income Short run g j g H g a g g g g] Medium run* Long run Scole: lem to 17. 30 Section I — Computable General Equilibrium Models 5. 2. Madrid Ring Road The Madrid Ring Road provides a circular bypass for traffic travelling through Madrid. Evaluation of this base project includes three distinct projects within the Madrid Ring Road. The first is the Western section of the ring road. Sections 2 and 3 are the Northern sections of the ring road. Table 2. 1 lists these three projects and their rele vant information. The schematic Map 2. 1 locates the three sections of the Madrid Ring Road. TABLE 2. 1. Madrid Ring Road project details k m /h km MECU % Key Project Project Region AS(O) AS(N) D(0) D(N) DS Cost IRR 1 1 2 3 2 3 4 93/65/010 West Madrid 93/65/011 North Madrid 93/65/017 North Madrid 5 47 53 29 6 73 81 81 7 8 9 10 11 27. 8 20. 2 14. 99 136. 38 >20 12. 3 7. 715 7. 21 74. 17 >30 12. 5 7. 1 9. 96 93. 31 >30 The data reported in this table comes from the cost-benefit analysis of the three projects com pleted for the Commission of the European Communities in 1994. We have assigned num bers 1 to 3 for individual links within the ring road which will be used as reference numbers. Columns two, three, and four give the project number assigned by the European Cohesion Fund, the title of the project, and the region in which the project is situated respectively. In the next two columns, we have listed the average speed on the existing road [AS(0)] and average speed on the new road after improvement [AS(N)j. Columns seven and eight give the re spective distance of the roads before and after project improvement [D(0),D(N)j. The ninth col umn reports the effective distance saved. Columns ten and eleven detail information from the cost-benefit analysis. Column ten specifies the eligible cost for Cohesion Fund spending for each road link. The final column gives the cost- benefit analysis estimate of the internal rate of return for the project. The formula used to calcu late the effective distance saved for this experi ment was: Distance Saved = (Distance of existing road Distance of new road) + (1 — Average Speed on existing road/ Average speed on new road) * Distance of new road This formula gives in the first part the physical shortening of the road itself. The second part of the formula gives the effective distance saved on the new road due to an increase in average speed. Added together, these two parts of the formula capture the total effective distance saved. In Appendix A1 we detail the matrix of projects involved in journeys between and within regions, as well as the weights attached to the different projects on both inter and intra-regional travel. In constructing both of these tables we have con sidered any possible road in the major Spanish and Portuguese road network which could be used to link regions. Table 2. 2 gives the WEDS for each of the intra and inter-regional links, and Table 2. 3 gives the ratio of the WEDS to the origi nal distance matrix. Simulations 31 Map 2. 1 Madrid Ring Road Ùfr* *k. S : vsr^ ' ι A W\\ ^ ^ *Λ ^^ , ΨΤΪ Madrid i^ 7" * '. XJÉ χ Ι Μ Π ΡΓ ^ ¿W K' k l B Æ^ ^^ ^ ΑΟΥ. s <^j ;^ ^ ; QSf « * V* * 'J ^W ^ " * "^ *l« V Γ * * ^ ^V # < 4 li •i 1 Jr^U^ • » » \ ,^ \ /χί^νΛ 32 Section I — Computable General Equilibrium Models 3 Tabla 2 2) Malnx ol weighted distance saved In the Madrid Ring Road Ptojecls ( 93/65/010. 93/65/01 1. 93/65/017) Coruna Oviedo Galicia Asturias Santander Cantabria B13 Bilbao Pals Vasco B21 Pamplonajlogrono Navarra IRioja B22 ;B23 Zaragoza Aragon B24 Madrid Madrid B30 Valladolid CaslillaL 041 Albacete Castillala 042 Cáceres Extremad B43 Barcelona. Valencia Cataluna B51 Comuntda Andalucía ; B52 B61 Sevilla. lurcia Tenente Murcia Cananas B62. 670 Santander Cantabria IB 13 Bilbao ¡Pais Vasclß21 Pamplona. Navarra ¡B22 logrono ¡Rioja B23 Zaragoza ¡Aragon B24 Madrid ¡Madrid ¡B30 Valladolid|Ca>ullaL |B4I Albacete ¡Castillala !B42 Caceras j Extremad ι B43 Barcelona Cataluna B51 Valencia Comunlde B52 Savilla lAnda'lucla IBÖI Murcia ¡Murcia B82 Táñenle ¡Canaries >B70 Mallorca Baleares ¡853 Coimbra Icanlro 'C12 Évora Alentejo :C14 Faro ¡Algarve ¡CIS 0 0 0 0 0 0 18. 08 15535 , 0 0 18. 08 7. 405 18. 08 0 18. 08 0 0[ 0 0 0 0 0 0 0 0 16 OS 0 15 535 0 0 16 08 3. 7475 1β 08 0 1808 0 Ó 0 o| o. °i °¡. » o! ol o 0 0 l 0 à 12. 3325 o 0 0 0 0 ó 0 0 0 0 0 0 ° 0 0 0 °! 0 12. 3325 °l "I 32. 16, 0; 0 ol oí 0 0 0 o' 32. 1β| 32. 18: 32. 16! Ol 0 0 0 01 0 ol o o; o 0¡ 0 Oj 0 123325¡ 12. 3325 0| 0 o; o. 32. 16, 32. 18 Oj 0 0 0 01 0 01 0 ol 0 ol o 0| 0 o; o 321β| 32. 16 32. 1β! 32. 16 32. 16Ì 32. 16 0 0 0 0 0 0 0 4. 2925 4. 2925 °. 0 8. 04 0 6 0 0 0 0 0 8. 04 6. 04 8 04 16 00 16 00 123325 12. 3325 12 3325 12. 3325, 42925! 24. 12 24. 12 6. 041 11. 7875' 4 2925 604¡ 11. 76751 8041 11. 7675! 8 04| 1808 16 08 a 04 8. 04 604: 0 0 0 0 o! o¡ 4. 2925! 24. 12J °l 11. 7875· B04¡ 42925I 16. 081 37475I 16081 θ! 16081 0! θ! o¡ 0 0! 15535 15535 0 0 0 0, θ' 8 04¡ 11. 7875 0{ ■ θ' 0; 0 0 0 32. 16 32 16 32. 16 6 04 11. 7875 8 04i o] oj 8. 041 Õ] 01 01 ol 01 °! X' θ! 15 8351 3 7475' 0! 0. 0: 01 0' o' 0 0 0 0: 4 29251 42925Í 0 16 08; 16 08 0: 0 0 0. 0: 8. O4; 16 00 0 3 7475! 7495' ol 0 0 OÍ 01 11. 7675! 3. 7475; 0: 0' 0¡ 01 θ! 0 Ο Ο °! O1 θ! 8. 041 6. 04 : 804; OÍ 1808' 16 08 01 0 0. °¡ 01 0| 0, o; 0; 0, °1 0 0! ol 0: 0! Baleares B53 cu C12 ; Lisboa Ev0fa F Alentejo 'Algarve 16 06 0 0 0 0 0 8 04 0 0 0 0 0, 0: 16 06 0 0^ 0; 0 15 535 O θ] le. oaj 0; 16 081 0! 16 06 0 0· 0 0 0 0. 0. °¡ ° 0· 01 8 04J 11. 7875 O; O] o; o¡ ol oi ol 0' teoál o: 0! 0' 0 0 o' 0 0' Οι oi 16 08¡ 0. 3. 7475; Ο Ο 16. 08; ù' 16 08. o' ol 0 0 0 0 32 16 32 16 32. 16 6. 04 004 0 0 0 804 0 0 0 0 0 0 0 0 0 »1 s 32 IG 32 1Γ, 32 If β o«· 60. 1 Οι oi 0| 0 04 0 ol οι o! °l 0; 0 θ! O' 0 0 0 32 16 32 16 32. 16 8 04 8. 04 0 0 0 804 0 0 0 0 0 0 0 0 0 Tabla 2 3) WEDS relative lo original dislance Projects ( 93/65/010. 93Æ5/01 1. 93/65/017) ; Region ¡ ι 1 Coruna Galicia Oviedo iSanlanderiBilbao Asturias ¡Cantabria |pals Vasco B12 IB13 IB2I Pamplona Nava. TB B22 1 logrono | Rioja IB23 1 Zaragoza | Aragon ¡B24 Oviedo Aslunas 1B12 Santander1 Cantabria ¡013 Bilbao ;Pals Vasc'B21 Pamplona. Navarre :B22 logrono ¡Rioja ¡B23 Zaragoza ¡Aragon IB24 Madnd ¡Madrid ¡B30 Albacete ¡CaslillalaÉB42 Cacares ¡Extremad Í043 Barcelona. Cataluna ¡B51 Valencia 'Comunida¡B52 Sevilla 'Andalucía ιΒΘΙ Táñenla 'Canarias ·Β70 Mallorca ¡Baleares ¡B53 Coimbra Centro 'C12 Lisboa 'Lisboa I c i3 Évora Alentejo C14 Fero. Algarve ,C 15 1 1 1 1 1 1 1 1 1 11 1 11 1 11 1 11 1 11 1 0973596 0. 964348 0. 96862 0 96877648 0 969699 0963296 11 1 0981936 0. 97787 1 1 1 1 1 1 0 94664296 1 11 1 0. 983267 0. 979973 1 1 0. 98302 0. 97962 1 1 0. 99629 0991203 1 1 1 11 1 0. 969699 0966539 1 1 11 1 11 1 1 1 1 1 1 096426667 1 1 1 09598 1 1 1 096815842 0. 950521 0. 9459! 0967184 0. 96194 0. 966315 096426 0 95796 0. 965604 1 1 1 1 1 I 1 0. 986792 0. 988304 1 0. 987074 1 1 1 1 1 1 1 1 0. 991364 0991686 0991346 Madrid Madrid B30 IB4I 0 973596 0 964346 0 96662 0 966770 0 969699 0 963296 0 966792 0 800661 0 875026 0 967968 0 960311 0. 993088 0 977159 0 965058 0970605 1 0. 991555 0. 98005 0 970603 0 987535 0984235 0. 9666 ω ω Valladolid Castilla L 1 1 1 1 1 1 0 908304 0 875026 1 0971528 0975262 0992376 0. 970495 0. 97071 0 993691 1 0 985956 I 1 1 1 1 Albacelo Castillala B42 0 981936 097767 1 1 1 0967968 0 971526 1 I 1 1 1 1 1 0 981745 0995274 1 1 1 I 1 0 946643 0 950523 0. 94595 0987074 0 960311 0975262 0991242 1 1 1 1 0. 993006 0. 992376 1 0991242 1 1 1 1 1 1 0993550 0992091 0 993437 Caceras Extromad B43 Barcelona Cataluna B51 Valencia Sevilla. Murcia , Tenente Comunlda Andalucía iMurda ¡Canaries B52 B61 ,B62 ,B70 0 983267 0. 979975 0 96302 0 99629 0 97962 0 991203 1 1 C II !C12 C13 ¡Baleares ¡B53 0 909699 0988539 1 1 1 1 1 0977159 0 970495 0. 985056 0 970605 0 97071 0 993691 1 1 0 991555 1 1 1 1 0 90005 0 970603 1 Alentejo Algarve !ci4 ¡CIS 1 1 0 964267 0 9590 0 960156 0967184 0961941 0960315 0. 964267 0 957961 0 965604 0991364 0991686 0991346 1 1 0993558 0. 992891 0. 993437 1 1 0 983162 0982074 0. 977821 1 0. 909003 1 0 9B9259 1 0. 989659 09C9259 1 1 1 S1 σ Φ IO ■ IO 21 σ Φ IO co Results: Madrid ring road Table 2. 4 gives the real income effects of the project, and the ratio of the total to direct ef fects. These multipliers exceed 1. 50 in the medium and long run, indicating significant gains from induced changes in activity and in dustrial location. TABLE 2. 4. Real income consequence of Madrid ring road Direct effect Short run Medium run Long run mECU: % base real income: Relative to direct effect: 185 0. 045 1 230 0. 06 1. 24 282 0. 07 1. 52 287 0. 07 1. 55 The regional effects of the project are given in table 2. 5 and map 2. 2. Once again, there are real income gains for all regions, and these are largest in the Madrid region and Castille-Leon. The way in which the impact of the project spreads from the Madrid region is illustrated in the map. TABLE 2. 5. Welfare and labour income changes by region: Madrid ring road % real Income change % change labour Income Region Short run Med run Long run Short run Med run Long run Galicia Asturias Cantabria Pais Vasco Navarra Rioja Aragon Madrid Castil-Leon C-Mancha Extremadura Catalunya C. Valenciana Baleares Andalucía Murcia Canarias P-Norte P-Centro P-Lisboa P-Alentejo P-Algarve 0. 06 0. 07 0. 02 0. 07 0. 07 0. 09 0. 02 0. 16 0. 10 0. 04 0. 10 0. 01 0. 04 0. 06 0. 01 0. 00 0. 03 0. 05 0. 05 0. 05 0. 09 0. 09 0. 07 0. 08 0. 04 0. 08 0. 08 0. 09 0. 04 0. 17 0. 11 0. 06 0. 11 0. 03 0. 06 0. 08 0. 03 0. 00 0. 04 0. 06 0. 07 0. 06 0. 10 0. 10 0. 07 0. 08 0. 04 0. 08 0. 08 0. 09 0. 04 0. 17 0. 12 0. 06 0. 11 0. 03 0. 06 0. 08 0. 03 0. 00 0. 04 0. 06 0. 07 0. 06 0. 10 0. 10 0. 05 0. 08 - 0. 06 0. 05 0. 05 0. 10 0. 13 0. 20 - 0. 14 0. 15 0. 15 0. 20 - 0. 07 - 0. 07 0. 33 0. 23 0. 01 0. 19 - 0. 08 0. 00 0. 02 - 0. 07 - 0. 09 - 0. 04 0. 04 0. 04 0. 01 0. 07 0. 08 0. 54 0. 34 0. 05 0. 33 - 0. 10 0. 05 0. 09 - 0. 07 - 0. 29 0. 0 0. 08 0. 09 0. 10 0. 18 0. 20 0. 15 0. 24 - 0. 13 0. 17 0. 17 0. 23 - 0. 11 0. 61 0. 40 0. 04 0. 38 - 0. 16 0. 03 0. 10 - 0. 09 - 0. 32 - 0. 04 0. 09 0. 10 0. 11 0. 21 0. 23 34 Section I — Computable General Equilibrium Models Map 2. 2 Madrid Ring Road, Spain CASTILLA  LEON PAIS VASCO ASTURIAS GALICIA CATALUNA C A S T I L L A  LA M. BALEARES COMUNIDAD VALEN. EXTREMADURA ANDALUCÍA 1URCIA "□ er C A Ñ A R ES Figure 2. 2 Percentage ch ange in labour income Short run DSät^rSSSäSäl Medium run ®QQQQQ<&Q8tø Long run msm&smvM Scale: 5 cm to. 1% Simulations 35 5. 3. Rias Bajas Motorway The Rias Bajas Motorway improves the journey between Porrino and Camarzana, linking the re gions of Galicia and Castilla Leon. The first sec tion of the project extends from Porrino to Orense, and the second section extends from Orense San Ciprian to Camarzana. Table 3. 1 lists relevant information for the two sections, and schematic Map 3. 1 locates the project. TABLE 3. 1. Rias· -Bajas Motorway Project Details k m /h km MECU % Key Project No Project Region AS(0) AS(N) D(O) D(N) DS Cost IRR 1 2 3 4 5 6 7 8 9 10 11 1 94/65/002 Porrino- ~ Orense „ ,. Galicia 2 94/65/004 Orense- Camarzana Galic a- Castilla 61 81 85. 49 78. 8 26. 15 273. 84 9 61 81 183 183 45. 19 512. 64 The data reported in this table comes from the cost-benefit analysis of the project completed for the Commission of the European Communities in 1994. We have assigned numbers 1 and 2 for in dividual links which will be used as reference numbers. Columns two, three, and four give the project number assigned by the European Cohe sion Fund, the title of the project, and the region in which the project is situated respectively. In the next two columns, we have listed the average speed on the existing road [AS(0)] and average speed on the new road after improvement [AS(N)j. We have assumed that the increase in average speed for the second section was equal to that of the first section since we do not have the cost-benefit analysis for the second section. Columns seven and eight give the respective dis tance of the roads before and after project im provement [D(0),D(N)j. The ninth column reports the effective distance saved, using the methodol ogy outlined earlier. Columns ten and eleven de tail information from the cost-benefit analysis. Column ten specifies the eligible cost for Cohe sion spending for each road link. The final column gives the internal rate of return for the project; the internal rate of return for the second section was not available. In Appendix A1 we detail the matrix of projects involved in journeys between and within regions, as well as the weights attached to the different projects on both inter and ¡ntra-regional travel. In constructing both of these tables we have con sidered any possible road in the major Spanish and Portuguese road network which could be used to link regions. Table 3. 2 gives the WEDS for each of the intra and inter-regional links, and Table 3. 3 gives the ratio of the WEDS to the origi nal distance matrix. 36 Section I — Computable General Equilibrium Models Map 3. 1 Rias Bajas Motorway Project ASTURIAS GALICIA NORTE CENTRO LISBOA E V. D J. L i s b oa ALENTEJO ALGARVE EXTREMADURA ANDALUCÍA MURCIA CATALUNA CASTILLA-LA M. BALEARES COMUNIDAD VALEN. Simulations 37 Table 3. 2 Table 3. 3 II LU < O fi. O tl — υ υ o 11 = ο. ζ υ 3 s 5 2. 'C "C ti α c g o " υ m si t> Cl tf) < c « f i l: >U c | S "S c m O_co •a I Ό T3 c il Ό -D o a s co f. s. ο α &3·! s S s-s to ο. ω I f I" W Ü lU 3 o ¿ 2, 5 ε ,E CM Ο β — o υ o SS Q. Z O 3 ε δ s £ 5 e go ϋ o a 1 5- • ε ra o _ II CD u m E ϋ tu m S = = "C ■Ό Ό S S œ „S S ? α g-M rsl < CD f? S « ¿ gm Ë > ÏM Si m ο. ί S2 2 2 S 3. O < ( I. Õ o i Κ 5 5 5 2 S2 d i o' d o' o do d ö o l d :! M i r i i  e ; « ! « ! « ;« : ο ; ο ι « ι ο ;ο * η — c* η *» o — IN r» — r« — cx o Γ Ϊ ' ^ - Ι Γ » : «. ^ ·« Q ο co m co m. co co co co CD co m co O ! C O : 0:U ! O Ì O IO __. ____. _ ^. __. * "E S η ■ J. Ï " ί ^ 1! « ;¡ o » 3 C A S £ H " S 5 Í 53 S ; ! ¡ S Í ' S l| ï β « « 5 2* « «κ * o Ei . « l o · · · β. σι c jj α. z ce < 3 (j_o ^_ojj^^_9¡m_z_tj¿_;;<;< Ι" ·§Ι« s 3 If ï s *f f* S. β α u cu œ « e J β ™ ο u ™ >. «Β a > < u m > » v ì 5 (  a a O  j m u ¡ 5 g ·· 3 α 2 INI δ « - o < ï « ¡ ρ ο α ο ι < α > η > η η ·  ι η τ ο ι ρ ο β ·  κ ο η α ?? d d d ο d ο d ο d d d d d ο d ό ό ο ο ο ο » ^ ·Λ·ί> ο o r- «ο — *- »----ι — co m cam m com m o o u ο ,ϋ —( JS Ό' | 5:1 > £. ' Ι'! S if S Sf l í l i l l i l i ll S f i l i la Ü < U a 2 t t Í 2 U O ui O. O < 2 (JfD Z U D ί? = Φ m C · _ ■ f i t | r i i i 8 ? j i i ¡ i f ¡ i ¡ i ¡s •"IL ■ ^ « ? Œ™ ™ — · ■ · · 3 · "■ a o. « 51 β u O w m a. o. s j S > < u m > w a t  S au j  u i u. 38 Section I — Computable General Equilibrium Models Results: Rias Bajas motorway TABLE 3. 4. Real income consequence of Rias Bajas motorway Direct effect Short run Medium run Long run mECU: % base real income: Relative to direct effect: 121 0. 030 1 140 0. 034 1. 14 162 0. 04 1. 33 164 0. 04 1. 35 The gains from the project are given in the first row of table 3. 4, and the multipliers in the last row give the ratio of the total to the direct gain. Medium and long run gains exceed direct gains by a factor of around one-third. The regional pattern of gains is given in figure 3. 5. All regions gain, although the gains are heav ily concentrated in Galicia. This unequal regional impact is particularly apparent in the changes in labour income, see map 3. 2. TABLE 3. 5. Welfare and labour income changes by region Rias-Bajas motorway % real income change % change labour income Region Short run Med run Long run Short run Med run Long run Galicia Asturias Cantabria Pais Vasco Navarra Rioja Aragon Madrid Castil-Leon C-Mancha Extremadura Catalunya C. Valenciana Baleares Andalucía Murcia Canarias P-Norte P-Centro P-Lisboa P-Alentejo P-Algarve 0. 39 0. 00 0. 00 0. 00 0. 02 0. 03 0. 02 0. 03 0. 04 0. 03 0. 03 0. 02 0. 02 0. 03 0. 02 0. 00 0. 02 0. 00 0. 00 0. 00 0. 00 0. 00 0. 38 0. 00 0. 01 0. 01 0. 03 0. 04 0. 03 0. 04 0. 05 0. 03 0. 04 0. 03 0. 03 0. 04 0. 02 0. 00 0. 02 0. 00 0. 01 0. 00 - 0. 01 0. 01 0. 36 0. 01 0. 02 0. 01 0. 03 0. 04 0. 03 0. 04 0. 05 0. 03 0. 04 0. 03 0. 03 0. 04 0. 02 0. 00 0. 02 0. 00 0. 02 0. 00 0. 00 0. 00 1. 15 - 0. 12 - 0. 07 - 0. 08 - 0. 02 0. 00 - 0. 01 0. 00 0. 03 - 0. 04 0. 00 - 0. 01 - 0. 02 0. 00 - 0. 04 - 0. 08 - 0. 04 - 0. 09 - 0. 09 - 0. 09 - 0. 07 - 0. 08 1. 86 - 0. 14 - 0. 12 - 0. 09 - 0. 03 - 0. 02 0. 00 0. 01 0. 06 - 0. 01 0. 02 - 0. 02 - 0. 02 0. 01 - 0. 04 - 0. 15 - 0. 05 - 0. 16 - 0. 14 - 0. 14 - 0. 12 - 0. 11 2. 17 - 0. 13 - 0. 12 - 0. 11 - 0. 03 - 0. 01 - 0. 01 0. 01 0. 07 - 0. 03 0. 03 - 0. 04 - 0. 04 0. 01 - 0. 05 - 0. 24 - 0. 07 - 0. 17 - 0. 16 - 0. 15 - 0. 15 - 0. 14 Simulations 39 Map 3. 2 Rias Bajas Motorway, Spain ) GALICIA ί LI530A E V. D J J N ^ L· A L E I JO ALGARVE ~^^Λ CATALUNAl CASTILLA-LA M. I3ALEARE5 COMUNIDAD VALEN. FURCIA ANDALUCÍA "TEg CANARE5 Fie J re 3. 2 Pecentage eh ange in labour income Sh c rt run |:"■  '■ ·:ϊ'. :; v;i. ;^. ;;;j Me c i um run Le"C run See e: 5 cm to mxmmm mmmmm 1% , 40 Section I — Computable General Equilibrium Models 5. 4. Tagus Crossing in Lisboa Table 4. 1 lists relevant information for the bridge. The schematic map 4. 1 locates the Tagus Crossing. The Tagus Crossing in Lisboa, called the Montijo Bridge, provides a second bridge over the Tagus River in the Lisbon District. It shoulders traffic currently crossing the Tagus via the existing 25th of April Bridge, alleviating existing congestion. The data reported in this table comes from the cost-benefit analysis of the project completed for the Commission of the European Communities in September, 1993. Columns one, two, and three give the project number assigned by the Euro- TABLE 4. 1. Tagus Crossing, project details km/h km MECU % Project No Project Region AS(0) AS(N) D(0) D(N) DS Cost NPV BC-Ratlo IRR 1 2 3 4 5 6 7 8 9 10 11 12 94/10/65/005 Tagus Crossing Lisboa 22 14 18 10. 7 6. 5 122,710 426. 07 111. 4 9. 8 pean Cohesion Fund, the title of the project, and the region in which the project is situated respec tively. In the next two columns, we have listed the travel time on the existing bridge before project improvement [t(0)j and travel time with the new bridge [t(N)j. Columns seven and eight give the respective distances of the existing bridge, the 25th of April Bridge, and the new bridge, the Montijo Bridge [D(0),D(N)j. Columns nine, ten, eleven, and twelve detail information from the cost-benefit analysis. Column nine specifies the scheme cost (millions of ECU). Column ten gives the net present value in millions of ECU. Column eleven lists the ratio of benefit to cost. Finally, col umn twelve reports the internal rate of return. The formula used to calculate the effective distance saved is the following: Distance Saved = (1 — time travelled on the new bridge/ time travelled on the existing bridge) * Distance of existing bridge In this case, we have used the projected time savings, 8 minutes, to calculate the new travel time of 14 minutes; this compares to the old trav el time on the 25th of April Bridge, which is 22 minutes. This is based on 1998 projections, us ing working day traffic for commercial vehicles, assuming the main socioeconomic scenario of projected growth and the main toll scenario. In Appendix A1 we detail the matrix of projects involved in journeys between and within regions. The project was not weighted since a high pro portion of journeys passing through Lisboa would have to cross the Tagus River, hence every ele ment of the effective distance saved (EDS) matrix shows the same distance reduction (as in Table 4. 1). In constructing the table we have consid ered any possible road in the major Spanish and Portuguese road network which could be used to link regions. Table 4. 2 gives the ratio of the EDS to the original distance matrix. Simulations 41 Map 4. 1 Tagus Crossing ι ■ ■{■' ƒ ' i—\\ r ψ / / * A * < I ' >J II // S / \ */k~i Æ / r ^ Ø s b oa sk?"* A /A I i *+^?\ jut ¡P€\ s?v ·. \ \ί A M ^ ' ^^v. «· 42 Section I — Computable General Equilibrium Models Q? 3' 1^ Coruna (Galicia Oviedo Asturias Santander; Cantabria Bilbao 'Pais Vase Pamplona Navarra logrono ¡Rioja Zaragoza ¡Aragon Madrid ι Madrid ValladolidiCasüllaL Albacete pastillala Cacares ¡Extremad i BU B12 B13 B21 B22 B23 B24 B30 B41 B42 843 I B51 ¡Comunida B52 ' Andalucía I B61 ¡Murda B62 Canaries B70 Baleares B53 Norte C lí Centro C12 Lisboa C13 Alentejo C14 Algarve C I S" BarcelonajCataluna Valencia Sevilla Murda Tenente Mallorca Porto Coimbra Lisboa Evora Faro Table 4. 2) WEDS relativa to original distance, T afluí Crossing Projects ( 94/10Æ5/005) City or rel. : Region Conine i Oviedo Galida ¡Asturias 11 I B I2 Santander Cantabria B13 Bilbao Pals Vasco B21 Pamplona logrono ¡Zaragoza iMadrid Navarra Rioja Aragon Madrid B22 B23 | B 24 ¡B30 Valladolid ¡Albacete CeslillaL ¡CaslillaIa B4I IB42 Cáceres Barcelona,Valenda 'Sevilla iMurcia Extremad Cataluna ¡ComunJdaJAndaluda ¡Murcia B43 B51 ÌB52 ÌB6t ¡B62 ■ Tenorile ¡Mallorca 'Canaries ¡Baleares ¡B70 ¡B53 Porto Coimbra Norte. ¡Centro ¡CII. C12 0. 99) OBS 0 89: 0. 097 0. 997 0. 997 0. 998 Lisboa ¡Evora iFaro Lisboa ¡Alentejo ¡Algarve ÍC13 |C14 ÍC15 0. 987 0. 992 0992 0 993 0. 993 0. 993 0. 993 099 0 99 0. 992 0. 978 0. 995 0 993 0 9 66 0 993 0 9 97 0. 996 0 96 O. Øfle 0. 939 0 9 33 0. 975 0 9 78 0. 933 0 9 88 0. 978 0. 986 0986 0975 ω σ Φ •μ 'ro Results: Tagus crossing: The real income gain and multipliers for the pro ject are given in table 4. 3. In contrast to other projects, the multipliers are less than unity, indi cating that the overall effect of the project is smaller than its direct cost saving. The reason is that, while there are benefits from the effective distance reductions created by the project, these have little effect on output levels or on regional lo cation decisions of firms. TABLE 4. 3. Real income consequence of Tagus crossing Direct effect Short run Medium run Long run mECU: Relative to direct effect: 39. 2 1 35. 9 0. 917 39. 0 0. 997 36. 9 0. 943 Table 4. 4 reports these changes by region. Re sults are given for Portugal alone, because, al though the full Spain and Portugal model was used, effects on Spain were negligible. As we have already remarked, the effects are small, and, unsurprisingly are concentrated on the Lis bon region. This project, alone of those we studied, pro duced multipliers of less than unity. That is, allow ing for endogenous change in the output of firms (short run), the location of firms (medium run) and also the location of workers (long run) produces welfare benefits less than the direct cost saving (savings in transport costs) created by the pro ject. Although these multipliers are slightly less than unity, there is of course still a positive wel fare gain and growth of labour income in directly affected regions. The reason for the low multipliers in this case is very similar to the distinction between trade cre ation and trade diversion in the literature on cus toms unions and preferential trading arrange ments. The improved infrastructure creates trade, allowing productive factors in affected regions to be utilised more fully. But it may also divert trade — activities that would have taken place in an other region may relocate. If this other region has inherent advantages then it is possible that the relocation may not be welfare improving. We have no general theory outlining circumstances in which losses from trade diversion will exceed the gains from trade creation, although some authors have suggested that it is more likely to occur for regions that are 'peripheral', in the sense of hav ing the natural disadvantage of being a long way away from large markets. This seems to be what is happening in this case. TABLE 4. 4. Welfare and labour income changes by region: Tagus crossing % real Income change % change labour Income Region Short run Med run Long run Short run Med run Long run P-Norte P-Centro P-Lisboa P-Alentejo P-Algarve 0. 01 0. 02 0. 10 0. 03 0. 02 0. 01 0. 02 0. -1 0. 02 0. 02 0. 01 0. 02 0. 10 0. 02 0. 02 0. 0 0. 05 0. 48 0. 03 0. 03 - 0. 03 0. 02 0. 40 0. 00 0. 01 0. 00 0. 02 0. 21 0. 00 0. 01 44 Section I — Computable General Equilibrium Models Map 4. 2 Tagus Crossing, Portugal CASTILLA  LEON ASTURIAS GALICIA NORTE CENTRO LISBOA E V. D J. ALENTEJO ALGARVE CATALUNA CASTILLALA M. BALEARES COMUNIDAD VALEN. EXTREMADURA ANDALUCÍA MURCIA ¿ A N A R ES F i g u re 4. 2 P e r c e n t a ge c ha i ge in labour i n c o me S h o rt r un ESSE RBS8BSSÎH8 M e d i um r un L o n g· r un S c a l e: 1 0 cm to ^^^^^^m HI ■I 1% Simulations 45 5. 5. Egnatia Motorway, project details The Egnatia Motorway runs from Southwest to Northeast in Greece, linking Igoumenitsa to Or- mentio. The nine sections include the following links: Igoumenitsa-Pedini, Pedini-Panagia, Pana- gia-Kozani, Kozani-Klidi, Thessaloniki-Strimon, Strimon-N. Karvali, N. Karvali-Komotini, Komoti- ni-Kipi, and Ardanio-Ormentio. The location of these projects (as well as for the Pathe Motor way) can be seen in schematic Map 5. 1 The data reported in Table 5. 1 comes from the cost-benefit analysis of the project completed for the Commission of the European Communities in November, 1994. TABLE 5. 1. Egnatia Motorway, project details Aggregate information travel time time saved 1 2 DS 3 total length total cost 4 5 Projects 1 -9 16. 5 h 6. 5 h 374. 24 km 950 km 4301. 76 M E CU I Project information Key Project Title 2 Region 3 Igoumenitsa-Pedini Ipeiros Pedini-Panagia Ipeiros/Thessalia Panagia-Kozani Ipeiros/Dyt. Mkdnia Kozani-klidi Dyt. /Kent. Mkdnia Thessaloniki-Strimon Kent. Mkdnia Strimon-N. karvali Kent. Mkdnia N. Karvali-Komotini Anatoliki M. T. Komotini-Kipi Anatoliki M. T. 1 1 2 3 4 5 6 7 8 9 Ardanio-Ormentio Anatoliki M. T. 130 km D(N) 4 70 60 95 78 84 76 80 95 MECU Cost 6 663. 8 410. 87 562. 22 428. 65 402. 24 463. 19 308. 79 432. 71 630. 79 DS 5 27. 57 23. 64 37. 43 30. 73 33. 1 29. 94 31. 52 37. 43 51. 22 In the top section, we have given total travel time for the entire Egnatia motorway in the second column and total travel time saved in the third columns. Based on this, we computed total dis tance saved, which is listed in the fourth column. The fifth column gives the total length of the mo torway. The sixth column gives total scheme costs in millions of Ecu. 46 Section I — Computable General Equilibrium Models Map 5. 1 Pathe/Egnatia Motorway Project K o s t a n ia C^> Î «3 , , S^ | ΝΟΤΙΟ AIGAIO I «S. <? DITIKI ELLADA I e r j p n ri + C i ty of R e f e r e n ce f or a R e g i on 1. 2. 3 E g n a t ia M o t o r w ay l. ll. lll. P a t he M o t o r w ay Simulations 47 In the bottom section we have assigned num bers 1 through 9 for individual links which will be used as reference numbers. Columns two and three give the title of the project and the re gion in which the project is situated respective ly. Column four lists the distance in kilometers of each section. Column five lists distance saved for each link. In calculating the distance saved for each link, we have assumed constant time savings over the entire motorway. Thus, we have calculated distance saved on each link as a proportion of the overall distance saved, based on the length of the link. Column six gives the construction cost of each link in mil lions ECU. The formula used to calculate the effective dis tance saved is the following: Distance Saved = (1 — time travelled on new road/ time travelled on existing road) * Distance of existing road To compute distance saved for each link, we used the following: Distance Saved for link = Length of link/total length of motorway * total distance saved In Appendix A1 we detail the matrix of projects involved in journeys between and within regions, as well as the weights attached to the different projects on both inter and intra-regional travel. Table 5. 2 gives the WEDS for each of the intra and inter-regional links, and Table 5. 3 gives the ratio of the WEDS to the original distance matrix. 48 Section I — Computable General Equilibrium Models w 3 CD Table 5. 2) Malrix ol weighted effective dislance saved. Egnalia Motorway City of Reference ¡ ' A13 A14 Anatolokl M. T. |A11 Kent. Mkdnia Ι Λ 12 Dyt. Mkdnia Thessalia Ipeiros A21 loniaNisla :A22 Dytiki Ellada ¡A23 Slerèa Ellada ÍA24 Alllkl |A30 PeloponnlBO« IA25 East Aeg. Dodacanese | kriti IA43 Alexandr. Analoloki M. T A11 A12 Thessaloniki Kenl. Mkdnla kozani I Larissa Dyl. Mkdnia |Thessalla ¡Ipeiros ¡Ionia Nisia |Dytiki Ellada A13 ¡A14 llgoumenilsa iAgrinio ¡Paira |A21 |A22 JA23 Lamia ¡Alhen Slerca Ellada [Allikl A24 :A30 ■ Kalamata i Milliini 'Peloponnisos !E. Aeg. Ά 25 'Rodos Dodaca :lrakllo nese ! Krili | A 43 45. 80! 93. 48 93. 48 124. 21 93. 48 189. 21 189. 21 93. 48 93. 48 93. 48 93. 48 0. 00 0. 00 93. 48 0. 00 31. 92 47. 28 0. 00 '74. 26 88. 05 0. 00 16. 25 0. 00 0. 00 0. 00 0. Õ0 0. 00 124. 21 ¡ 47. 281 18. 72J o. ooj 41. 861 55. 64! o. ooj 0. 001 9. 381 0. 00 0. 00 0. 00 93. 48! 189. 211 189. 21! 0. 00 74. 26I 88. 05I 0. 00 0. 00 44. 32 41. 86. 55. 64J 44. 32! 0. 00I 26. 59I O. OO' O. Òo! 0. 00! O. OO! O. OOJ 0. 00; o. ooj 0. 00· 12. 80J 0. 00¡ O. OOJ 12. 80 O. 00I 0. 00 ò. oo; 0. 0Ò O. OOI 0. 00 O. Ool 12. 80 O. 00| 0. 001 0. 00; o. ool o. ooi 93. 48 0. 00 16. 25 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 93. 48' 0. 00' 0. 00 0. 00! 12. 80' 0. 00 O. OO' o. ooj O. OOI O. OOI 0. 00, 0. 00! o. ooi 93. 4B' 0. 00' 9. 36 0. 00! 0. 00' 0. 00, 0. 00' O. OOj 93. 48· 0. 00 0. 00' 0. 00: 12. 80' 0. 00 0. 00 0. 00: 0. 00; 0. 00¡ O. OOI O. OOI 0. 00( 0. 00' o. ooi o. ooj 0. 00! 0. 00! 0. 00· 0. 00 O. OO! o. ooj 0. 00' 0. 00 O. OO] O. OOJ Ó. 00! O. OOl 0. 00; 0. 00' 0. 00' 0. 00' 0. 00' 0. 00; 0. 00! 0. 00' O. OO' O. OOI o. ooj O. OOI 0. 00 0. 00 0. 00 0. 00 93. 48 0. 00 0. 00 0. 00 12. 80 0. 00 0. 00 0. 00 0. 00 0. 00 Õ. 00 0. 00 0. 00 Table 5. 3) WEDS relative lo original distance. Egnalia Motorway Cily of Reference Analoloki M. T. Kenl. Mkdnia Dyl. Mkdnia Thessalia Ipeiros Ionia Nisia Dytiki Ellada Slerea Ellada Alliki Peloponnisos East Aeg. Dodacanese Krili ¡ AH I A 12 JA13 ¡A14 U2I IA22 ¡A23 | A 24 |A30 ¡A25 ÌA43 Alexandr. Anatolokl M. T A11 Thessaloniki Kenl. Mkdnla A12 I Kozani Dyt. Mkdnia A13 Larissa Thessalia A14 0. 7 0. 79 0. 78 0. 47 0. 60 0. 71 0. 65 0. 72 0. 87 0. 82 0. 87 0. 90 1. 1 0. 79 0. 47 0. 86 0. 65 1 0. 79 0. 82 1 1 1 1 1 1 1 0. 60 0. 65 0. 88 1 0. 81 0. 85 0. 96 1 1 0. 98 1 1 1 • Igoumenitsa j Ipeiros ! A 21 ¡Agrinlo ¡Ionia Nisia !A22 |Palra ¡Dytiki Ellada lA23 lAlhen Lamia ¡Slerea Ellada 'Allikl ;A24 ¡A30 ¡Kalamata iMitilinl jPeloponnlsos ¡E. Aeg. !A25 ! ¡Rodos Iraklio |A43 0. 72 0. 82 0. 85 0. 8 0. 96 0. 87 0. 90 1 0. 98 0. 95 0. 97 0. 98 0. 65 0. 79 0. 81 0. 79 0. 85 1 1 0. 95 0. 97 1 1 1 0. 98 51 σ Φ Ol ro Q) σ Φ αϊ ω Results: Egnatia Motorway The real income gains of the project are given in table 5. 4, together with multipliers indicating medium and long run gains exceeding direct ef fects by approximately 15%. The cross regional distribution of these effects is given in table 5. 5. It should be noted that the real income gains are very substantial for some re gions — in particular E. Macedonia. The impact on E. Macedonia also shows up in the very sub stantial change in labour income. TABLE 5. 4. Real income consequence of Egnatia motorway improvements Direct effect Short run Medium run Long run mECU: 398 422 448 448 % base real income: Relative to direct effect: 0. 96 1 1. 1 1. 06 1. 2 1. 13 1. 2 1. 16 TABLE 5. 5. Welfare and labour income changes by region Egnatia motorway % real Income change % change labour income Region Short run Med run Long run Short run Med run Long run E. Macedonia C. Macedonia W. Macedonia Thessalia Ipiros Ionian Isl W. Ellada E. Ellada Ättika Peloponis E. Aegean Dodecanes Crete 6. 22 2. 40 2. 24 0. 43 2. 92 0. 95 0. 24 0. 30 0. 10 0. 20 0. 14 0. 14 0. 32 6. 34 2. 45 2. 35 0. 47 3. 04 1. 10 0. 31 0. 34 0. 15 0. 28 0. 23 0. 26 0. 43 6. 25 2. 47 2. 37 0. 48 3. 04 1. 12 0. 30 0. 34 0. 15 0. 27 0. 21 0. 22 0. 42 5. 42 0. 24 0. 80 -0. 56 1. 54 0. 99 -0. 52 -0. 46 -0. 46 -0. 50 -1. 24 -0. 92 -0. 44 15. 39 1. 36 2. 72 -0. 68 4. 73 3. 04 -0. 97 -0. 48 -0. 84 -1. 04 -2. 83 -2. 12 -0. 99 17. 77 2. 17 3. 35 -0. 49 5. 15 3. 25 -1. 47 -0. 76 -1. 34 -1. 75 -2. 69 -2. 21 -1. 24 50 Section I — Computable General Equilibrium Models Map 5. 2 Egnatia Motorway Mop 5. 2 Percentoge chonge in lobour income Short run Medium run Long run Scole: 1 / 2 cm lo Ì7. Simulations 51 5. 6. Pathe Motorway sa-Katerlni, Katerini-Thessaloniki, and Thessa- loniki-Promachon. The Pathe Motorway runs from South to North in Greece, linking Patras to Promachon. The nine sections include the following links: Patras-Ko rinth, Korinth-Athens, Athens-llliki, llliki-Molos, Maliakos Fixed Link, Karavomilos-Larissa, Laris- The data reported in Table 6. 1 comes from the cost-benefit analysis of the project completed for the Commission of the European Communities in November, 1994 and the location of the project can be seen on schematic Map 5. 1. TABLE 6. 1. Pathe Motorway, project details Aggregate information travel time time saved 1 2 DS 3 total length total cost 4 5 Projects l-IX 11. 5 h 2. 5 h 184. 78 km 850 km 3859. 9 M E CU Project information Key 1 I II III IV V VI VII VIII IX Project Title 2 Region 3 Patras-Korinth Korinth-Athens Athens-llliki llliki-Molos Maliakos Fixed Link Dyt. Ellada/Peloponnisos Peloponnisos/Attiki Attiki/Sterea Ellada Sterea Ellada Sterea Ellada Karavomilos-Larissa Thessalia Larissa-Katerini Katerini-Thessaloniki Thessaloniki-Promachon Thessalia/Kent. Mkdnia Kent. Mkdnia Kent. Mkdnia km D(N) 4 133 62 79 96 10 129 77 60 131 DS 5 28. 91 13. 45 17. 14 20. 83 2. 17 27. 99 16. 71 13. 02 28. 43 MECU Cost 6 827. 85 81. 26 0 571. 37 770. 96 661. 77 411. 89 0 499. 75 In the top section, we have given total travel time for the entire Pathe motorway in the second col umn and total travel time saved in the third col umn. Based on this, we computed total distance saved, which is listed in the fourth column. The fifth column gives the total length of the motor way. The sixth column gives total scheme costs in millions of ECU. In the bottom section we have assigned num bers 1 through 9 for individual links which will be used as reference numbers. Columns two and three give the title of the project and the region in which the project is situated respectively. Col umn four lists the distance in kilometers of each section. Column five lists distance saved for each link, and the procedure used here was the same as for the Egnatia motorway. Column six gives the construction cost of each link in mil lions ECU. In Appendix A1 we detail the matrix of projects involved in journeys between and within regions, as well as the weights attached to the different projects on both inter and intra-regional travel. Table 6. 2 gives the WEDS for each of the intra and inter-regional links, and Table 6. 3 gives the ratio of the WEDS to the original distance matrix. 52 Section I — Computable General Equilibrium Models Table 6. 2) Matrix ol weighted effective dislance saved. Palhe Molorway ' City ol Reference ! Analoloki M. T. |A11 Kent. Mkdnia 'A12 Dyt. Mkdnia ¡A13 Thessalia A14 Ipeiros U 21 Ionia Nisia ' A 22 Dylikl Ellada ,A23 Slerea Ellada ] A 24 Altikl 1A30 Peloponnlsos IA25 East Aeg. , Dodacanese j Krill 'A43 Alexandr. |Thessalonikl Analoloki M. T ¡Kent. Mkdnia A11 ¡Á12 Kozani Dyl. Mkdnia A13 O. OOI 0. 00' 29. 08! 0. 001 o. ool o. ool 43. 95 O. OO! 0. 00 0. 00 0. 00 58. 18 0. 00 0. 00' O. OO1 0. 00 88. 32 98. 74 128. 29 168. 65 0. 00 o. bo 126. 29 112. 081 68. 13! 0. 00, 0. 00: 74. 111 0. 00; 84. 52 40. 58 112. 0β| 68. 131 154. 44Ì 55. 25I 0. 00| 0. 00; 0. 00 O. OO· Larissa llgoumcnilsa lAgnnlo ¡Paira :Lamia lAlhen IKalamala IMililini Thessalia 'Ipeiros A14 ¡Ionia Nisia ¡Dytiki Ellada ¡Slerea Ellada ¡Allikl ¡Peloponnlsos 'E Aeg IA22 ·Α23 :A24 ¡A30 ■ ^A25 ' IA21 58. 161 43. 95! o. oo| 20. 99| 0. 00' 44. 70! 30. 16J 40. 58I 61. 13¡ 103. 49: o. ooj 0. 00! 61. 13Í 0 0 0! 0. 00! B8. 32! 98. 74' 126. 29! 168 65' 000! 0. 00' 7 4. 1 i: 84. 52: 112. 08' 154 44! O. OOj 0. 00· O. OO! 40. 58' 68. 13' 55 25! O. OOj 44. 70| 30. 16' 40. 58' 61. 13: 103 49¡ 0. 00' Ò. 00' 0. 00' O. OO' 40. 14' 0 0 0' 0. 00, O. OO! 0. 00: O. Oo! 42. 38' OOo! o. oo¡ 0. 00! 7. 23; o. oo¡ 39. 00; o. ool O. OOj O. OOj 0. 00! 11. 50, 34. 39: O. ooj 40. 141 42. 36: 39. 001 34. 39; 15. 3θ' 28. 911 O. OOI 0. 001 O. OOi 0. 00: 28. 91 42 36I 0. 00, 0. 00 0. 00; 0. 00' 0. 00' 0 00' 0. 00 0. 00· 0. 00; 0. 00' o. oo'i 0 0 0! 40. 14, 42. 36! 39. 00! 63. 30: O. OOi 6 73! : Irakiin :A43 !Dodacanese ÍKriti I 0. 00' O. OO1 o. ooj 0. 001 0. 00' 0. 001 O. OOi O. OOj o. ool O. OOi o. ooj O. OO, 0. 00! 0. 001 126. 29 O. OO! 112 08 O. OOJ 68. 13 O. OO 61 13 0. 0Ó' 40. 14 O. OOi 42 38 O. OOJ 39. 00 0. 00 63 30 0 OOi 0 00 O. OOI 6 73 o. ooj 0 00 0 001 0 00 0. 00! 0. 00 Table 6. 3) WEDS relative to original dislance, Pathe Motorway Cily ol Reference Ά 21 -A22 Anatolokl M. T. ÌA11 Kent. Mkdnia I A 12 Dyt. Mkdnia A13 Thessalia ¡A14 Ipeiros Ionia Nisia Dytiki Ellada ¡A23 Slerea Ellada A24 Attikl | A 30 Peloponnisos [Α25 East Aeg. ' Dodacanese. Krili. 'A43 σι co Alexandr. iThessalonikl IKozani jLarissa llgoumenilsa |Agrinio ¡Paira 'Lamia Alnen Anatolokl M. T I Kenl. Mkdnla Dyt. Mkdnia IThessalia ¡Ipeiros A11 ! A 12 ;A13 | A 14 |A21 'Ionia Nisia ! A 22 iDytlkl Ellada !A23 ¡A24 A30 'Sterea Ellada Attikl Kalamala IMililini ¡Peloponnisos !E. Aeg. •A25 ■ Rodos Dodacanese : Krili Uraklio •A43 1. 00 1. 00 1. 00 0. 82 1. 00 0. 87 1. 00 0. 71 1. 00 1. 00 1. 00 1. 00 0. 82 0. 71 1. 00 0. 88 1. 00 1. C0 1. 00 1. 00 1. 00 1. 00 1. 00 0. 87 0. 88 0. 86 1. 00 0. 92 0. 81 0. 76 0. 87 0. 79 0. 82 0. 79 0. 87 0. 84 0. 82 0. 80 0. 91 0. 83 1. 00 1. 00 1. 00 1. 00 1. Ό0 0. 72 1. 00 0. 78 1. 00 1. 00 0. 88 0. 81 1. 00 1. 00 0. 86 0. 76 1. 00 1. 00 1. 00 0. 87 1. 00 0. 87 0. 92 0. 79 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 0. 95 1. 00 1. 00 1. 00 1. 00 0. 94 0. 91 0. 91 0. 81 0. 82 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 0. 94 0. 92 0. 91 0. 85 1. 00 0. 91 1. 00 0. 90 0. 82 0. 79 0. S7 0. 84 0. 91 0. 91 0. 81 0. 82 0. B5 0. 88 1. 00 1. 00 1. 00 0. 82 ' 0. 80 0. 91 0. 83 1. 00 1. 00 1. 00 1. 00 0. 88 0. 77 1. 00 1. 00 0. 98 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 1. 00 0. 72 0. 78 0. 91 0. 90 0. 94 0. 92 0. 91 0. 85 1. 00 0. 98 1. 00 1. 00 1. 00 ^ Q) σ Φ σ> ro s1 Φ co Results: Pathe motorway The aggregate welfare effects and multipliers are given in table 6. 4. Clearly, this project is the largest of those under study, bringing substantial gains to the aggregate economy, and to the re gions as listed in table 6. 5 TABLE 6. 4. Real income consequence of Pathe motorway Direct effect Short run Medium run Long run mECU: 933 1098 1156 1157 % base real income: Relative to direct effect: 2. 33 1 2. 75 1. 17 2. 89 1. 24 2. 89 1. 24 TABLE 6. 5. Welfare and labour income changes by region: Pathe motorway % real income change % change labour income Region Short run Med run Long run Short run Med run Long run E. Macedonia C. Macedonia W. Macedonia Thessalia Ipiros Ionian Isl W. Ellada E. Ellada Ättika Peloponis E. Aegean Dodecanes Crete 2. 35 3. 89 1. 12 3. 13 0. 72 0. 94 1. 84 2. 45 2. 60 4. 12 0. 34 0. 39 1. 45 2. 51 3. 98 1. 34 3. 31 0. 92 1. 22 2. 02 2. 57 2. 69 4. 25 0. 56 0. 65 1. 71 2. 53 3. 99 1. 35 3. 33 0. 91 1. 18 2. 03 2. 59 2. 70 4. 27 0. 49 0. 55 1. 72 3. 05 3. 21 -2. 10 2. 53 -4. 86 -3. 57 -0. 59 1. 25 0. 72 0. 65 -8. 10 -6. 72 -0. 90 4. 44 4. 69 -1. 28 2. 91 -4. 19 -3. 17 0. 09 1. 77 1. 06 2. 06 -7. 23 -6. 36 0. 44 5. 08 5. 45 -1. 10 3. 39 -4. 34 -3. 31 -0. 03 1. 87 0. 83 1. 82 -7. 25 -6. 56 0. 24 54 Section I — Computable General Equilibrium Models Map 6. 2 Pathe Motorway KENTRIKI MKDNIA. ATQ L O K' N/1. T. j S Λ Map 6. 2 P e r c e n t a ge eh an ge ϊπ labour i n c o me Short run neMffliwasseos Medium run mmM Umm Long run Scale: 1 / 2 cm to llllllllllllllllllllllllllllll 17. Simulations 55 5. 7. Greece: combined effects of Egnatia and Pathe motorway projects Finally, we report the combined effect of the Eg natia and Pathe motorway projects. The aggre gate welfare effects are given in table 7. 1, and re gional effects in 7. 2. The main point to note from the combined exper iment is that there is a (weak) super-additivity property, in the sense that the combined experi ment yields larger welfare gains than the sum of the separate ones. For example, the medium run gain for East Macedonia of the two projects sep arately sums to 8. 85% of base real income. However, there is positive interaction between the projects, so the combined effect is a real in come gain of 9. 26% of base income. TABLE 7. 1. Real income consequence of Greek motorways Direct effect Short run Medium run Long run mECU: 1330. 8 1549 1639 1639 % base real income: Relative to direct effect: 3. 33 1 3. 87 1. 16 4. 09 1. 23 4. 09 1. 23 TABLE 7. 2. Welfare and labour income changes by region: Greek motorways % real Income change % change labour income Region Short run Med run Long run Short run Med run Long run E. Macedonia C. Macedonia W. Macedonia Thessalia Ipiros Ionian Isl W. Ellada E. Ellada Ättika Peloponis E. Aegean Dodecanes Crete 8. 91 6. 48 3. 33 3. 58 3. 60 1. 86 2. 11 2. 79 2. 74 4. 37 0. 54 0. 56 1. 84 9. 26 6. 63 3. 68 3. 80 3. 93 2. 29 2. 36 2. 95 2. 88 4. 57 0. 84 0. 94 2. 22 9. 11 6. 66 3. 71 3. 84 3. 95 2. 28 2. 36 2. 98 2. 89 4. 59 0. 72 0. 79 2. 22 19. 58 21. 19 24. 22 3. 87 0. 07 0. 10 - 0. 94 - 1. 06 2. 11 0. 32 - 0. 22 - 0. 91 -11. 30 - 8. 90 - 0. 43 6. 05 1. 29 2. 28 0. 30 - 0. 45 - 0. 84 1. 35 0. 24 1. 02 - 9. 71 - 8. 16 - 0. 49 7. 40 1. 98 2. 88 0. 44 - 0. 48 -1. 69 1. 18 - 0. 44 0. 12 - 9. 73 - 8. 63 - 0. 78 56 Section I — Computable General Equilibrium Models Map 7. 2 Egnatia and Pathe Motorways Combined ΝΟΤΙΟ AICAIO O Y T I KI M A K E D O N IA I P E I R OS [JO NIA NISIA] g l · —\ I OYTIKI ELLADA fPELOPONNISOS Mop 7. 2 P e r c e n t a ge c h a n ge in l a b o ur i n c o me S h o rt r un M e d i um r un Long r un S c a l e: 1 / 2 cm to t% Simulations 57 Simulations: summary and conclusions. From these simulation experiments, we can see how specific infrastructure projects create differ ent regional spillover effects. Using the models, we simulate the effects of the project, and calcu late the real income change in each region result ing from the project. We then compute the real income change relative to the direct effect of the project. This pure ratio is much less sensitive to errors than simply the real income change and, used as a multiplier, captures the additional gains of the project beyond the direct cost saving ef fect. The multiplier results are summarised in table 7. 3. Also, these experiments yield the change in labour income for each region resulting from each Cohesion Fund project. In the case of the Irish North-South Road Corri dor, the East and Border regions experience the largest real income gain, a natural result consid ering that the majority of the project links are sit uated in these regions. All regions have a real in come gain from the project. In terms of labour income, only the three regions in which the pro ject is geographically situated, the Border, East ern and Midlands regions, experience an in crease in labour income. This reflects the changes in labour demand. For all of the other Irish regions, labour income experiences a nega tive impact, a result of changes in regional costs of living and of changes in income accruing to capital in each region. The multipliers for this project are quite small, only rising to 1. 1 in the medium and long run. Similar to the Irish North-South Corridor, the Madrid ring road provides real income gains for all regions, with the largest in the Madrid and Castilla-Leon regions. The location of the Madrid ring road as a link for numerous motorways in Central Spain explains why a project located in one region can have fairly strong spillover effects throughout the regions of Spain and Portugal. In contrast, the Rias Bajas Motorway, located mainly in the region of Galicia, creates gains heavily concentrated in Galicia, although all re gions do experience some increase in real in come. The disproportionately large benefit to Galicia is shown particularly clearly by its in crease in labour income. The multipliers for both these projects are quite large, rising to 1. 55 for the Madrid ring road. The Tagus Crossing in Lisboa illustrates an infra structure project which mainly improves local transport, rather than affecting numerous re gions. In this project, obviously the Lisboa region gains the most with negligible effects on any of the Spanish regions. Unlike the other projects, the multipliers are less than unity, indicating that the overall effect of the project is smaller than its direct cost saving. This is due to the fact that the benefits from the effective distance reductions created by the project have only small effects on output and location decisions, and the possibility of some of the relocation is 'diversion' rather than 'creation' of activity. Both the Egnatia and the Pathe motorways pro vide examples of large scale infrastructure pro jects covering numerous regions, allowing the model to capture the extensive spillover effects. In the case of the Egnatia motorway, the real in come changes from the project are positive over all with extremely robust gains in East Macedo nia. The multipliers (the ratios of real income change relative to the direct effect of the project) indicate medium and long run gains exceeding direct effects by approximately 15 percent. The extreme increase in change in labour income for East Macedonia in the medium and long run cas es shows how dramatically an infrastructure pro ject can affect demand for labour. The Pathe mo torway is the largest of all the projects evaluated and offers particularly substantial gains to the ag gregate Greek economy and to particular re gions. Looking at the percentage change in real income, we also see that this project creates fair ly evenly distributed spillover effects on all regions in Greece, in contrast to some of the other pro jects studied. Finally, the Pathe and Egnatia mo torways taken together have a slight super-addi- tivity property; in other words, the combined ex periment results in larger welfare gains than the sum of the separate ones. In short, there is posi tive interaction between the projects. These simulated experiments demonstrate the differences in spillover effects resulting from infra structure projects of very different natures. They highlight how one project located in a single re gion, such as the Madrid ring road, can create large welfare benefits rippling through numerous regions, while another project also located in a single region, such as the Tagus Crossing, can have much more limited regional spillover effects. Furthermore, they offer explanations for how im proved transport networks can lead to gains in 58 Section I — Computable General Equilibrium Models welfare for all regions, but can adversely affect the labour income of some regions and positively affect the labour income of others. Finally, the ex periments give particularly useful insights into the effects of extremely large projects, such as the Pathe and Egnatia motorways, illustrating the possibility of positive interactions between infra structure projects. TABLE 7. 3 Project multipliers — real income change relative to direct effects Direct effect Short run Medium run Long run Ireland: North-South road link Madrid ring road Rias-Bajas motorway Tagus bridge Egnatia motorway Pathe motorway 1. 01 1. 24 1. 14 0. 92 1. 1 1. 17 1. 1 1. 52 1. 33 0. 997 1. 2 1. 24 1. 1 1. 55 1. 35 0. 94 1. 2 1. 24 A note on Rail projects So far, the model has been applied only to road projects but can be applied to other transport modes, providing that good descriptions of the forecast direct effects of the investments are available. The model does not contain within it a choice of transport mode by firms and individu als, so would be unable to capture endogenously a switch of mode, eg from road to rail. However, if the initial project evaluators provided estimates of this switch, then simulation could proceed on the basis of these estimates. The project description we would require would then include estimates of the time/ cost saving on rail journeys, the proportion of journeys taken on rail rather than road, and how this proportion is predicted to change. This information should ideally be available between all pairs of regions in the area under study, and disaggregated by user — private/ industrial, and within industry, by sec tor. The model would then use this as the basis for simulating the changes in trade flows, prof itability by region and by sector, and hence pro duction, relocation and employment effects cre ated by the investment. Simulations 59 6. Concluding comments The work undertaken in this part of the study il lustrates how a micro based economic model can be used to evaluate the effects of regional in frastructure of the type supported by the Cohe sion Fund. Results are derived for four projects, and illustrate both how the projects might affect aggregate economic welfare, and how the effects of the projects might be spread across regions. The main result is that welfare gains from infra structure projects seem to be significantly in creased by allowing for the full general equilibri um effects of the projects, and in particular by al lowing for the relocation or establishment of new firms. This suggests that traditional cost benefit analysis is too narrow in its scope, focusing as it does on partial equilibrium analysis of the local effects of the project. We have already discussed some of the strengths and weaknesses of the approach. The main strengths are the micro-economic detail in corporated in the model. This allows discrimina tion between projects according to their exact impact on the infrastructure system of the region. It also allows us to take seriously the concerns of many economic geographers — that there may be significant spillovers between activities, per haps giving rise to cumulative causation and ag glomeration of economic activity. The weakness of the approach is that we assume the model to be correct — it is not subject to rigorous empiri cal verification. The response to this is to under take sensitivity analysis — to see how sensitive results are to the selection of key parameters of the model, and perhaps also to assumed func tional forms and behavioural relationships. Our in vestigations in this direction indicate that our main results — the extra real income gains esti mated once relocation effects are included — seem to be quite robust, but more work remains to be done. As is evident to the reader, more work also needs to be done ¡n improving aspects of the data on which the model is calibrated. To fully exploit the potential of the model two di rections need to be pursued. The first is to en sure that good descriptions of the projects are available. The effects of a project will depend crit ically on which regions get improved transport links with which other regions, and it has not al ways been easy to assess this on the basis of available information. If good enough project de scriptions are available, the method can also be applied to transport modes other than roads. The model does not contain within it a choice of transport mode by firms and individuals, so would be unable to capture endogenously a switch of mode, eg from road to rail. However, if the initial project evaluators provided estimates of this switch, then simulation could proceed on the basis of these estimates. The project description we would require would then include estimates of the time/ cost saving on rail journeys the propor tion of journeys take on rail rather than other road, and how this proportion is predicted to change. This information should ideally be avail able between all pairs of regions in the area un der study, and disaggregated by user — private/ industrial, and within industry, by sector. The model would then use this as the basis for simu lating the changes in trade flows, profitability by region and by sector, and hence production, relo cation and employment effects created by the in vestment. Concluding Comments 61 Second, the modelling approach adopted here provides a 'big picture' of regions as a whole, and of the economic interaction between regions. This suggests that the model has more to offer for large projects — or series of projects — than it does for small. One of the distinctive features of this model is the presence of forward and back ward linkages between firms and following from that, the possibility that cumulative causation and agglomeraton of activity may occur. These forces have been operating in the experiments that we have undertaken but, because of the small scale of these experiments, these forces have inevitably been rather muted. If a major transport corridor is opened up, then what changes in economic ac tivity will this cause? If this corridor runs into ad joining higher wage economies, then what reloca tions of activity might occur? Application of this framework to larger scale forecasting of this type might be of interest. These points reinforce the view that model should be seen as complementary to the other techniques developed in this project, and to tra ditional cost benefit analysis. The model requires good cost benefit studies to inform the experi ments undertaken. But the model can also go beyond cost benefit, in giving a broader picture of the possible effects of projects on the eco nomic geography of an area as a whole. 62 Section I — Computable General Equilibrium Models Appendix A1 Tables Uitti of Refont «leetad, M. dia RtrKj Rl»d Prosea (93ΛΑΟ10. 93ÆMI t, Β3Λ5Λ17)) ary ot ret. Red on Pamplona logrono Riot« Aja pon B24 Zangola A/aoon VatatMd Abacate CaiBte^a Manch ComLrlrJadVarati JAL 1A3_ UT Τ3Γ DT" 1. 2. 3 2,3 1,2,3 1. 2,3 1. 2,3 1,2,3 12,3 i l i- TTT 1. 2. 3 1. 2. 3 Stvlla Andauda 061 1 1. 2,3 1,2,3 1,2,3 1,2,3 1,2,3 AJontoft JAL Oí O O 3 n O CD O Q. CD Mart* oí Ramona Aflecled. RlasB«)is Pro)«» ( Μ Λ Μ » 2. WÆiOCH) Crtv of ref. Region Cor\re øalda Bit CM ado A i m as B12 Santander Cantabria BI3 Bl bao Pali Vate B21 Pamplom Navarra. B22 lorjrono Rlora B23 B11 B12 B13 B21 B22 B23 B24 B30 &A\ \U2 B43 B51 B52 Ββΐ Ββ2 Gilda Art/Ii» Cantabria Pili Vasco Navarra RJofc Angón Madrid CintaLeón C a n u ti Manch Externa dun Cataluna Comxídad Valen AndeUd· Murdi Canaria« Bateara« Norte Cent* Unóoi Alentejo Atoa rv« M3 CU m cu 015 1 1 1 ,V 1 1 1 1 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 '■2 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 1 1 1 1 Zaraoon A/agon B24 Madid Madid B30 Vala dead Calli« La Bll Aliacela Ciilkele B42 Cacarea Extemadu B43 Barcelona C> launa BJ1 Velende Cenuri da B52 Sevlla Anoa Lda B61 Muda Muda B62 Cananei Tenerife Maiorca Baleares B53 Porlo Noria CU 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 1. 2 2 Cdnfjra Cento C12 Usboa Usboa CI3 Even Ajeníelo CH Faro Aloe rva CI5 1 1 1 1 I loor* r**, \φ leen. Bj^jjg inw i í t i_ >V>M C W l Í l Wi H2 U il l » il 3K mu tHM mm. "πτπ; m»»; cm»»M»x »il T i r o; -nm; tíHI! ort o li nrrtf ira: > TD CD CD CTI Coru» CM edo Santander BJbio Pampéona iOQVCQ Ζ Ι Γ Β Ο ΟΛ [Madrid Valadold Atecen Cicerfri Birc etone Vitenda S*MU Mirdi Tenerti e Mikxci Porto Cûiirtrt Uibo* Evora Faro Ü£E1_ ¿£Eü σ. CD O o 3 Ό C CT CD CD CD ΓΠ n Mattt oí Rodens ArTected, Tegua Crossing Project ( M/IOÆMX») Crfy ol ret. Redon Coruna CM edo Santander Blbao Pamplona Ιοςτοηο Ζ an gore Madrid Vale dold Arrecete Cáceres Bere elona Vatend ι Sevlla Murda Tenente Maiorca Porlo Cobrira Usto« Evon Faro Gelda A i t i li ι Cantabria Pats Vasco Navam Rlora Ara con Midrld CassiaLeon Caille* Mandi FjcTemaòjre Cataluna Comunidad Vilen AndaLde Murdi Cenadel Bile er es Norte Cento Usbos Ájentelo AJoerve BU B12 B13 B21 B22 B23 B24 B30 B41 W2 W3 BJ1 B52 Bel B«2 Bi3 C11 C12 CI3 CU C15 Coruna Gelda B11 Oviedo Ansias B12 Santander Cantabria B13 Blbeo Pelt Vise B21 Parroiora Navarra B22 logrono Rlota B23 Zaragoia Angón B2s Madid Madid B30 Valedold Ca ft laLe B4I AJbacete Catitela B« Cáceres Exlremedj B43 Barcelona Catalan« BS1 Velende Comurfda B52 Sevlla Anda Lda B61 Murda Murda B62 Canaries Tenerite Maiorca Beleeres B53 Perto Norie C II Coirrfcn Cento C12 Usboi Usbos C13 Evon AJenteto CU Firo Algerve CIS 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > "D δ1 CT CO - si Matrix of Projecta regioni affected, Egnatia Motorway City of Reference) Analoloki M. T. Kenl. Mkdnia Dyt. Mkdnia Thessalia Ipeiros lorua Nisia Dytiki Ellada Sterea Ellada Attikl Peloponnisos Kriti All A12 AI3 A14 A21 A22 AH A^4 A30 A2i A4J Matrix of Weigh 3 City qøieferenco Analoloki M. T. Kent. Mkdnia Dyt. Mkdnia Ipeiros Dytiki Ellada Sterea Ellada Attiki Peloponnisos Kriti All A li AU A14 A21 A22 A23 A74 AJO A25 A43 Alexandr. Analoloki A ll 7,8,9 Thessaloniki Kent. Mkdnia A12 5,6,7,8,9 4,5 Kozani Dyt. Mkdnia A13 4,5,6,7,8,9 4,5 3 Larissa Thessalia A!4 5,6,7. 8. 9 0 0 0 Igoumenilsa Ipeiros A2I 1,3,4,5,6,7,8,9 1,3,4 1. 3 1,2 1,2 Agrinio Ionia Nisia A22 1,3,4,5,6,7,8,9 1,3,4 1. 3 0 0 0 Patra Dytiki Ellada A23 5,6,7,8,9 0 1. 3 0 0 0 0 Lamia Slerea Ellada A24 5,6,7,8,9 0 0 0 1,2 0 0 0 Alhen Attiki A30 5,6,7,8,9 0 0 0 1,2 0 0 0 0 Kalamata A25 5,6,7,8,9 0 3 0 0 0 0 0 0 0 Krili A43 5,6. 7 8. 9 0 0 0 1,2 0 0 0 0 0 0 Alexandr. Anatolokl All 0. 75. 0. 25,0. 15 Thessaloniki Kent. Mkdnia A12. 1,0. 75,0. 5,0. 25,0. 25 0. 5,0. 5 Kozani Dyt. Mkdnia A13 1,1. 0. 75. 0. 5. 0. 25,0. 25 1. 0. 5 0. 5 Larissa Thessalia AM 1. 0. 75. 0. 5,0. 25. 0. 2 0 0 Igoumenitsa Ipeiros A21 Agrinio Ionia Nisia A22 Parra Dytiki Ellada A23 Lamia Sterea Ellada A24 Athen Attiki A30 1. 1. 1. 1,0. 75,0. 5,0. 25. 0. 25 0. 5,1,0. 75 0. 5. 0. 75 1. 1,1,1. 0. 75. 0. 5,0. 25,0. 25 1,1. 0. 75 1. 0. 75 1,0. 75,0. 5. 0. 25. 0. 25 0 0. 25,0. 25 1. 0. 75,0. 5,0. 25. 0. 2 0 0 1,0. 75. 0. 5. 0. 25. 0. 2 0 0 075. 025 0 0 0 0 0 0. 25. 0. 25 0 0 0 0 0. 25,0. 25 0 0 0 0 A25 Kriti A43 1. 0. 75. 0. 5. 0. 25,0. 25 0 1,0. 75. 0. 5 0 25 0 25 0 0. 25 0 0 0 0 0 0 0 0 0 0. 25. 0. 25 0 0 0 CO oo ω ω O o 3 "O ω CD m η Matrix of Project! regioni affected, Pithe Motorway Alexandr. Analoloki A ll Thessaloniki KenLMkdnia A12 Kozani DytMkdnii A13 vn. vin. ix Larissa Thessalia A14 vn,vnux vn. vnux 0 Igoumcnitsa Ipeiros A21 Agrinio Ionia Nitia A22 Patra Lami« Dytiki Ellada A23 Sterea Ellada A24 Alhcn Altiki A30 Kalamata Peloponnisot A25 V. V1 0 ν. νχνπ,νπι,Γχ v,vi,vn. vm,rx rv. v. vi, νπ,ντιυ rV. V. Vl,Vll. VD7,l Γαιν,ν,ντ,νιΐντη Ετ,ιν,ν,νι,νπ,νιη rv. v. vi IV. V. VI mjv. v. vi mjv. v. vi π,ιν,ν LD. IH ιη,ιν,ν irmiV. V,VT,VII,VTIUX ÍH,m. rv,v. vi,vn. vTJUx LB, m. rv. v. vi imu, rv. v. vi o U Iraki io Krili A43 m. iv,v,VT. vii. vm. tx mjv. v. vi, vii. vm. rx cy. v. v. vi m. rv,v,vi IDJV. V U m. rv. v Alexandr. Anitoloki Thessaloniki KcnLMkdni« A12 Kozani DylMkdni« A13 Igourocniua Ipeiros Agrinio Ionia Niti« A22 Lari ss« Thessilii AM 1. 1,1 1,1,0. 5 Dytiki Ellada 1. 1,1. 1,1 Sterea Ellada Λ24 0. 5,1,1. 1,1,1 0. 5. 1,1. 1,1. 0 5 Altiki Kalamata Pelo, 'ponniios Iraldio Kriti 1,1,1,1,1 ,1. 1. 1. 1. 0. 5 ,1. 1 ,1. 0. 75 1. 1,1. 1. 1,1. 1,1. 1 1. 1,1,1,1,1. 1,1,05 0. 5,0,5,0. 5. 0. 5,0. 5. 0. 5 1,1,1,1,1,0. 75 1,1. 1. 1,1,1 1,1. 1. 1,1,0. 5 City of Reference Analoloki M T. KcnLMkdni« Dyl· Mkdnia Thcssalii Ipeiros Ionia Nitia Dytiki Ellada Sterea Ellada Altiki Peloponnisos Krili A ll A12 A13 A14 A21 A22 A23 A25 Matrix of Wc i ¡dits City of Reference Anatolold M. T. KcnLMkdni» Dyl· Mkdnia Thessalia Ipeiros lont« Niti« Dytiki Ellid« Sterea Ellada Attiki Peloponnisos Kriti A ll A12 A13 Al 4 A21 A22 A23 A24 A30 A25 A4 3 Appendix A2 Technical Appendix The model There are L locations within the country or region under study, and I industries. The price and quantity of industry i composite output sold at lo cation í are denoted s', and z', respectively. De mand for each industry's output aggregate in each location, zi, is given by z'f=c, i + mi l+g'l+z(A)i+z(B)i (1) ci, denotes consumption demand, m', intermediate demand and gi government demand. If location (' is a 'port' then it also receives export demand. Divid ing this export demand according to two external 'countries', A and B, gives the terms z(A)i + z(B)'r. Consider a particular industry, i, for which the value of expenditure at location I is si z',. This demand can be met by domestic production from various locations, and by imports from ei ther A or Β which can come through various ports. The division of expenditure s', z', between these sources of supply is guided by a series of price indices, each taking the form of CES func tions of lower level prices. This process can also be viewed as the way in which the aggregates s'( and z', are constructed from underlying prices and quantities, and we start by outlining the ag gregation procedure. We then turn to the behav iour of the economic agents that give rise to this aggregation. A schematic overview is given in figure 1. FIGURE 1 Expenditure si z', Imports from A: r(A)\ Imports from B: r(B)i Ports j = 1. L: q(A)jf, y(A% Ports j = 1. L: q(B)¡„ y(B)j( Firms/varieties P¡. ,x¡„ Appendix A2 — Technical Appendix 69 The figure indicates that a given level of expendi ture on industry i at location i is first divided be tween domestic supply and imports from sources A and B. Prices of supply from each of these sources are given by r't , r(A)'e and r{B)[, and the price s\ is formed as a CES aggregate of these prices taking the form, 1-θ' δ(4"θ' + δ4ΓΚ + 5c π 1-θ 1/ 1-θ (2) The parameter θ' is the elasticity of import de mand with respect to the price of imports. For domestic production demand is further allo cated across locations and across varieties of dif ferentiated product. The division across locations is guided by price indices qje which give the price index in location I of products produced in j. The price index r'\ is defined as a CES function of these prices, country A (B) through port j is denoted q(A)'jf q(B)j,. These prices guide choice of entry port, and are the basis for the price indices r(A)', and r(B)'t defined as, ιΐ/(ι-ηΛ) 1-n„ ΣΚΉ -ιΐ<Ί-ηΒ (5) ΣΜΒ1 1-Tls H- H- ΆΑ (Tie) measure the elasticity of substitution be tween different ports, and aAj (afe;) are parameters giving the 'preference' of agents for imports through port j. This procedure amounts to the as sumption that purchasers discriminate imports by port according to an Armington type procedure. This structure translates into the following de mand system for the output of each domestic firm and for imports from each source. Denoting the quantity sold in location I by a single industry i firm located in region j, x\¡, the corresponding value of sales is, Ί1/1-η' Σ(4*) (3) x'liP'li = 1  ε '. W, ¿j! Q'jl Q i' J S (6) where a¡( is a preference parameter positioning the demand curve, and η' a measure of substi tutability between products from different sources. This stage corresponds to the Arming ton assumption of product differentiation by source. The final stage is allocation acaross individual va rieties. The prices of products p¡¡ are aggregated according to a CES ('Dixit Stiglitz') subutility function which defines qjc. It takes the form, 1/ h-ε' "ίΚΓ' (4) where rif is the number of symmetric varities of in dustry i output produced in location j, and ε' is the elasticity of demand for a single product variety. The two right hand flows in figure 1 location fs imports from A and B. Countries A and Β each supply a single variety of product in each indus try, but imports of this product can reach location I via different 'ports', this having the effect of dif ferentiating imports according to port of entry. The price at location i of industry i imports from For imports, the quantity imported from A through port j and sold in I is denoted yíA)¡(, with corresponding value, y(4Mr y(BÚ(B) Equations (6) and (7) make clear the roles of the various elasticities. Looking first at equation (6), ë is the compensated elasticity of demand for a single variety, (compensated meaning holding constant all higher level price indices). If the price of all products produced in location j change equiproportionately then qj, moves by the same proportion, and η' is the compensated elasticity of demand for products from j in aggregate. If the prices of all domestic products change equipro portionately, then r'i changes by the same pro portion, and Θ' gives the compensated elasticity of demand for domestic output of this industry. On the import side (equation (7)) r\A (ηβ ) measure 70 Section I — Computable General Equilibrium Models the compensated elasticity of demand for im ports through a single port of the price of ship ping through this port changes. If the prices of all imports from A (or B) change, then Θ' gives the compensated elasticity of demand for imports from this source. We shall assume that ε' > η', (ηΛ, ηβ) > θ''. If these conditions all hold with equality then the model reduces to a pure DixitStiglitz monopolistic com petition model (see equation (6)). η' < ε', θ' < ε' and r\A (η6) < ε' have the effect of lowering overall elasticities, so dampening down the quantity ef fects generated by price changes. Supply Domestic producers A single location I industry i producer has profits of the form, n'r^x'Jp'cjU+b^t -biti (8) where hi is the fixed input requirement and b', is the unit cost function. This uses intermediates and primary factors with fixed coefficients, so takes the form, bi^eßsi+^fkid'(w (9) where e>' is the input of intermediate j per unit output good i (which has price s[ in location l), fki is the input of factor k per unit output of good i, adjusted by industry and location specific tech nology parameter d'f, and the factor price at loca tion £ is wir. The unit cost of transport services is b°, and industry i incurs t\, of these in shipping a unit from »? to j. Transport technology has fixed coefficients, so b?=±ei°s'^f k0. ,k Wr (10) There are two sorts of industry in the model. The first is monopolistically competitive industries, in which there are increasing returns to scale, so hi > 0. Each firm produces its own variety of prod uct and prices are set according to a constant mark up over marginal cost, so p'A 1-1/ε' = b^ + b¡? fL (11) The long run number of firms in these industries, ni, is determined by free entry and exit, ie by the condition that firm scale is sufficient for the mark up revenue earned in equation (11) to cover fixed costs. We shall sometimes look at short run ex periments in which the number of firms is held constant at the base level. The second industry type is perfect competition. In these industries there are constant returns to scale, hi  0, and a single homogenous product produced at each location. We can assume pro duction is taking place in a single representative firm (η) = 1), which sets price equal to marginal (=average) cost, b p U ò í + b ° íL (12) Importers Imports are supplied from two countries, A and B, each supplying a single variety (i. e. , the num ber is held constant and normalised at unity). Border prices for imports in each industry from each country are exogenously set at p{A)' (p(B)'). Imports incur internal distribution costs of the same form as do local products, and an addition al port services requirement of xj per unit for entry through port j. The price at location I of industry i products supplied from foreign country A (B) through port j, q(A)¡(, {q(B)¡f), are therefore given by q{A)j(=p(B)+b°(t>( + ^), (13) Demand Consumers The location i representative consumer is en dowed with quantity vk of the /rth factor, and solves a multistage optimisation problem, with expenditure, and subexpenditure functions de fined as follows. At the first stage the consumer divides expenditure between industries. The bud get constraint is, ,Π«' =0*) wk,vk + J \ JX (14) Appendix A2 — Technical Appendix 71 The right hand side is total income, made up from factor income plus any pure profits, and net of taxation levied at rate tx. The left hand side is the expenditure function, where u, is utility, si is the price index of industry i products in location i, and ω' are expenditure shares in the Cobb- Douglas functional form. ^);(s<+b° Η(*Ί+>ή= (17) 1-λ' Solving the consumer's first stage optimization problem gives expenditure on each industry, where λ' is the elasticity of demand for exports in industry i and the parameters ßjy, ßß/ position the demand curves. : w ' ( l  f x) w,vk + Ση'π'> (15) Government Further stages of the consumer's problem are solved in the manner given above. That is, the consumers' expenditure is divided between do mestic production and imports from A and B. Demand for domestic output is divided between regions and then individual varieties. Demand for imports is divided between ports. Exports Quantities of industry i output exported through port j to countries A and Β are denoted, z(A)'¡, (z(ß)j). The price of these exports are sj + b°j τ) where s¡ is the price index of industry i products in location i, and b^cj is the additional charge in curred shipping through the port. These prices determine both the overall level of exports in each industry and the ports through which they are shipped. We proceed in the usual way by defining a price index for exports of industry i to location A (B) taking the form: ή- ΣΚνΗ+0<°τ'< σ(β)' Σ(Μ5;+ί,°τ'/ 1/(1-1Λ) 1 - 1 ,4 (16) 1 / ( 1 - 1 Β) 1-1β Government receives tax income on income (equivalent^ final expenditure) in the location, and external grants ss. It spends revenue on pur chasing output from each industry in each loca tion, gi. We let the tax rate adjust to put the gov- erment on its budget constraint, that is, tx solves fx Y^wk vk +Y4ril'. π', L I + s s =XXs'^· (18) The government expenditure falling on industry i in location I is divided between different sources of supply in the usual way. Intermediate demands Intermediate demands in location ( come from local production and transport costs incurred on shipping local production and exports giving mf=X ν b<+£; y J V J 'Σ4 + ek0 > xljti, ' I L ^|Î(H+1KJM)+ (19) \ I + ζ The value of demands for exports through each port are then given by, These demands are divided between domestic production, and imports, regions, varieties, and ports according to the procedure outlined above. 72 Section I — Computable General Equilibrium Models General equilibrium Wage rates adjust to clear factor markets. Supply of factor k in location i is denoted vk. Demand for the factor comes from local production and transport costs incurred on shipping local pro duction and exports. Equating supply and de mand gives, f 1 vk -Σ i n\ fki \ f "'+Σ*ί/ V +ί"0Σχ^ι rkO Í £ ( H+ iK ) M )+ (20> ' V i Appendix A2 — Technical Appendix 73 References Armington, P. (1969) "A theory of demand for products distinguished by place of production" Interna tional Monetary Fund Staff Papers 16 (March): 159-78 Brown, D. and Stern, R. (1989) "U. S. -Canada bilateral tariff elimination: The role of product differentiation and market structure" in Feenstra R. ed. Trade policies for international competitiveness Buckley, P. (1992) "A transportation-orientated interregional computable general equilibrium model of the United States" Annals of Regional Science 26 (4) 331 -348 Burniaux, J. , Waelbroeck, J. (1992) "Preliminary results of two experimental models of general equilibri um with imperfect competition" Journal of Policy Modelling 14 (1) 65-92 Corden, W. (1980) "Economies of scale and customs union theory" Journal of Political Economy 93: 15- 145 Cox, D. and Harris R. , (1985) "Trade liberalization and industrial organization: some estimates for Cana da" Journal of Political Economy 93 115-45 Dixon, P. , Parmenter, Β. , Sutton, J. , and Vincent, D. ORANI: A multisectorial model of the Australian Economy Dixit, A. K. and J. E. Stiglitz, (1977), 'Monopolistic competition and optimum product diversity,'. American Economic Review, 67, 297-308. Gasiorek, M. , Smith, A. and Venables, Α. , (1991) "Completing the internal market in the EC: Factor de mands and comparative advantage in Winters, L. and Venables, A. eds. European integration: Trade and industry Ginsburgh, V. (1990) "In the Cournot-Walras general equilibrium model there may be "more to gain" by changing the numeraire than by eliminating imperfections; a two good economy example" in Srinivasan and Mercenier eds. General Equilibrium Modelling for Developing Countries Harris, C, (1954) 'The market as a factor in the localization of industry in the United States', Regional Science and Urban Economics, 18, 87-124. Hirschman, A. (1958), The strategy of economic development', New Haven, Yale University Press. References 75 Higgs, P. , Parmenter, Β. and Rimmer, R. (1988) "A hybrid top down, bottom up regional computable general equilibrium model" International Regional Science Review 11 (3) 317328 Jones, R. and Whalley, J. (1989) "A Canadian Regional general equilibrium model and some applica tions" Journal of Urban Economics 25 368404 Kehoe, Τ and Kehoe, P. (1994) "A primer on Static applied general equilibrium models" Federal Reserve Bank of Minneapolis Quarterly Review 18 (2) Spring Kehoe, Τ and Kehoe, P. (1994a) "Capturing NAFTA's impact with applied general equilibrium models" Federal Reserve Bank of Minneapolis Quarterly Review 18 (2) Spring Kehoe, T, Polo, C. and Sancho, F. , (1994b) "An Evaluation of the performance of an applied general equilibrium model of the Spanish economy" Economic Theory 6 (1) 115141 Kimbell, L. and Harrison, G. (1984) "General equilibrium analysis of regional fiscal incidence" In Scarf, H. and Shoven, J. Applied General Equilibrium Analysis Krugman, P. (1979) "Increasing returns, monopolistic competition and international trade" Journal of In ternational Economics 9 468480 Krugman, P. (1980) "Scale economies, product differentiation,and the pattern of trade" American Eco nomic Review 70 950959 Krugman, P. (1991) "Increasing returns and economic" Journal of Political Economy, 99, 183199 Krugman, P. (1991) Geography and Trade, MIT press, Cambridge Krugman, P. (1995) Development, geography and economic theory, MIT press, Cambridge Krugman, P. and A. J. Venables (1995), 'Globalisation and the inequality of nations', Quarterly Journal of Economics, CX, 857880 Krugman, P. and A. J. Venables (1996), 'Integration, specialisation and adjustment', European Economic Review, 40, 959967. Lolos, S. , SuwaEisenmann, Α. , Zonzilos, N. , and Bourguignon F. , (1995) "Evaluating the CSF with an extended computable general equilibrium model  The case of Greece (19881995)" Journal of policy modelling π (2) 177197 Mercenier, J. (1995) "Can 1992 reduce unemployment in Europe  on welfare and employment effects of Europe move to a single market" Journal of Policy Modelling 17(1)1 37 Morgan, W. , Mutti, J. , and Partridge, M. (1989) "A regional general equilibrium model of the United States  tax effects on factor movements and regional production" fîewëw of Economics and Statistics 71 (4) 626635 Myrdal, G. (1957), Economic Theory and Underdeveloped regions, Duckworth, London. Norman, N. (1990) "Assessing trade and welfare effects of trade liberalization: a comparison of alterna tive approaches to CGE modelling with imperfect competition" European Economic Review 34 72551 Perroux, F. (1955) 'Note sur la notion de pole de croissance', Economie Applique, 8. Polo, C. and Sancho F. , (1993) "Insights or forecasts  an evaluation of a computable general equilibrium 76 Section I — Computable General Equilibrium Models model of Spain" Journal of Forecasting 12 (5) 437-448 Pred, A. (1966), The spatial dynamics of US urban-industrial growth, MIT press Cambridge Scarf, H. and Shoven, J. (1984) Applied General Equilibrium Analysis Shoven, J. and Whalley, J. (1992) Applying general equilibrium Shoven, J. and Whalley, J. (1984) "Applied general equilibrium models of taxation and international trade: an introduction and survey" Journal of Economic Literature 22 1007-51 Smith, A. and Venables, A. (1988) "Completing the internal market in the EC: some industrial simula tions" European Economic Review 32 1501 -25 Venables, A. J. (1995) 'Equilibrium locations of vertically linked industries', International Economic Review, 37, 341-359. Whalley, J. (1985a) Trade Liberalization among Major World Trading Areas Whalley, J. (1985b) "Hidden challenges in recent applied general equilibrium exercises" in Piggot, J. and Whalley, J. eds. New developments in applied general equilibrium analysis References 77 SECTION II MODELS OF EXPLICIT DISTRIBUTION DYNAMICS Danny T. Quah Department of Economics, London School of Economics Α. REGIONAL COHESION FROM LOCAL ISOLATED ACTIONS HISTORICAL OUTCOMES 1. Introduction Regions in the European Union—as do all geo graphical units—spread out on a two-dimension al map (Fig. 1). The economic performance of each region can be represented as a height above that map. Connecting those heights across space, the result is a mathematical sur face over the physical geography of Europe. Then, regional distribution dynamics are vibra tions over time in this surface. This paper and its companion Quah [24] provide a framework for understanding and quantifying such regional, spatial uctuations. The framework is designed with a number of specific, targeted goals: First, we are interested here in the dynam ics of cohesion and equality across the Cohesion regions in Europe. 1 The term cohesion could, in general, mean a range of possibilities. In the cur rent work, for concreteness, I take it to mean equality in the cross-section distribution of in comes. In ways to be made precise below, cohe sion will have both static and dynamic aspects. Knowing how one region behaves in isolation — whether it converges towards a steady-state growth path, or how it responds to public and in frastructure! investment within it, and so on—is, for my purposes, irrelevant (important and inter esting though such issues might be). Instead, I seek here to characterize whether the entire cross-section of regions is tending over time to wards Income equality. If there is no tendency to wards cohesion, I wish to understand what struc tures might produce that. Second, I seek to characterize prospects for mo bility within the regional income distribution: even if cohesion were not to obtain, do poorer regions see the possibility of overtaking those initially richer? If not, why not? What economic policies might lead to such regional overtaking? These first two goals can be summarized as a technical need for a model of explicit distribution dynamics or medd, where one seeks to under stand the evolution of the entire cross-section distribution. 2 By contrast, standard regression analysis considers only average or representative behavior, and reveals nothing about what hap pens to the whole distribution. Third, I am interested in the dynamic effects of lo cal, isolated regional actions. Those actions can take one of two possible forms. One is that of changing the structure of a region and that region alone. Examples of these might include varying the stock of public capital, the quality of the envi ronment, and other infrastructural characteristics of that region. The other form is that of changing how a region is related to other regions. Exam ples of these might include interregional trans portation, factor mobility, and merchandise trade. More generally, such actions provide spatial inter dependence and linkages, and induce dynamic spillovers across regions. The goals I have just described necessitate going beyond the technical tools extant in the econom- 1 The Cohesion regions are regions In the four Cohesion countries Greece, Spain, Ireland, and Portugal. For data reasons, the results for Ireland are not yet available at time of writing—they will be pro vided when the Irish data are ready. 2 This medd terminology was Introduced in Quah [25]. That a medd differs from, say, convergence-regression models had been empha sized In Friedman [10], Hart [11], and Quah [17]. Introduction 81 ics literature. Convergence regression and σ convergence analyses (e. g. , Barro and Salai Martin [1], de la Fuente and Vives [6], and Salai Martin [26], among others) cannot reveal evolving distribution dynamics: they cannot show the mo bility prospects in intradistribution behavior, and they cannot uncover the longrun, limiting shape of the crosssection regional income distribution. The same is true of most timeseries applications to regional analyses (e. g. , Blanchard and Katz [3], Carlino and Mills [4], and Decressin and Fatás Π). 1 Previous work with medds (e. g. , Desdoigts [8], Lamo [12], Magrini [13], Neven and Gouyette [14], and Quah [16, 17, 18, 19]) have shortcom ings as well. They allow, in general, neither study ing interregional linkages explicitly nor consider ing the effects of structural changes of a local, isolated nature. Expanding on the last of these statements, while earlier medds have proved useful for measuring the dynamics of crosssection distributions, they cannot directly be used for tracing through the effects of alternative scenarios. While these med ds have provided the most useful answers on whether or not convergence might occur, they have been unable to address the issue of why whatever is the case is, in fact, so. Thus, they can give no answer to what changes might be needed to bring about or speed up cohesion. 1 Bean [2] and Pissarides and Wasmer [15] improve on these by seek ing to working explicitly with multiple regions. I seek to provide medds that allow this and, therefore, overcome the shortcomings of earlier medds. For this, I build on conditioning ideas for medds earlier used in Quah [20]. The extension, however, is elaborate; it is detailed in Quah [24]. The current paper lays only groundwork for ana lyzing such distribution dynamics—despite this, the paper is already quite lengthy, and so it seemed best to defer the conditioning analysis to the companion paper. In beginning from basics, this paper also uncovers relevant stylized facts on convergence across Cohesion regions: it compares them to the distribution dynamic regu larities across countries in the world and across other regional units in Europe as a whole. Section 2 introduces the idea of looking at evolv ing distributions, and examines the dynamic regu larities on regional income distributions across the Cohesion economies. Because it is instructive to do so, I carry along a parallel analysis of the world's crosscountry, Europewide, and selected nonCohesion EU member state income distribu tions: similarities and differences are Immediately manifest between Cohesion regions on the one hand and countries around the world and regions across Europe more broadly on the other. The worldwide and Europewide patterns of growth and convergence give a useful benchmark against which to compare Cohesion countries' experi ences. The comparison sheds light on where rela tive successes and failures have occurred. Section 3 develops further dynamics, and exam ines intradistribution mobility properties and longer horizon tendencies. Section 4 then concludes. 82 Section II — Models of Explicit Distribution Dynamics 2, Preliminaries on convergence and distributions I now examine what actually happened in the Co hesion economies over the 1980s. In the course of doing this, I develop technical ideas on distrib ution dynamics, and show how such dynamics can be interpreted to analyze cohesion. 2. 1 Spatial dynamics Begin with Fig. 2. el (Greece), Fig. 2. es (Spain), Fig. 2. pt (Portugal), and Fig. 2. ep (Spain and Por tugal together)—these are the real-world Cohe sion counterparts of the hypothetical Fig. 1 : the vertical axis graphs per capita GDP in thousands of ECUs in each NUTS3 location. 1 Each of these figures tracks a single Cohesion nation over time; the last combines the physically contiguous Spain and Portugal. (For Spanish NUTS3s In Fig. 2, Las Palmas and Tenerife have been excluded to provide greater resolution on the mainland lo cations. ) To emphasize the physical spatial dimension, the base in each of these pictures is formed from longitude and latitude measurements. Regional political boundaries—which would add to the clutter in the pictures—have been removed. 1 The convention—using. el to denote Greece,. es Spain,. pt Portugal, and. ep Spain and Portugal together—Is one that I will continue be low. In addition, for the collection of all countries across the world I will use. w; for the collection of all NUTS2s across Europe I will use. E12 (since this refers to the earlier 12 European Community mem ber states for which I have data); and finally, for all NUTS3s across the Cohesion economies, I will use. c. When no ambiguity can arise, I will use the term economy to refer to either a NUTS3 location, a NUTS2 location, or an entire nation-state. In addition, for conve nience, I will refer to the 18 Portuguese administrative districts as NUTS3 throughout. Complete data details are given in the Data Ap pendix below. These pictures reveal information on the dynamic spatial patterns of regional growth in the Cohe sion economies. Fig. 2. el for Greece shows the richness of Viotia in the center, and the dramatic rise of Lassithi in the extreme southeast and of Kavala in the northeast. Viotia already had per capita GDP of 5264 ECUs in 1980; that in creased to 7332 in 1989. Lassithi grew from per capita GDP of 2511 ECUs in 1980 to 6008 in 1989, while that in Kavala grew from 2794 ECUs in 1980 to 5256 in 1989. By comparison, Greek average per capita GDP was 2660 ECUs in 1980, and 4350 in 1989 (an annual growth rate of 5. 4%). Thus, Viotia was already twice as rich as the Greek average in 1980; it remained much richer than average in 1989, although its annual growth rate of only 3. 7% was one of the lowest among Greek NUTS3s. Lassithi and Kavala be gan from around the average but then pulled ahead to be respectively 40% and 20% richer by the end of the decade. (The numbers used here were computed from NUTS3 data on populations and nominal in comes, as described in the Data Appendix. The reader should keep in mind that these are all computed in ECUs. Comparison with related cal culations off a different database might be help ful. Summers and Heston [29] (and updates) pro vides a much-studied dataset of annual per capi ta incomes for over 120 countries, recorded since 1950 in constant (1985) US dollars. The fig ures for Greece there show $5901 in 1980 and $6734 in 1989, giving an annual growth rate of 1. 4%. For later use I also record here that the Summers-Heston figures for Spain show $7390 in 1980 and $9238 in 1989, so that the annual Preliminaries on convergence and distributions 83 growth rate is 2. 4%; those for Portugal, $4982 in 1980 and $6575 in 1989, with the implied annual growth rate thus 3. 0%. We see below that in our dataset, Spanish per capita GDP in ECUs grew at an annual rate of 8. 7% (from 4100 ECUs in 1980 to 9020 ECUs in 1989). Portuguese per capita GDP in ECUs grew at an annual rate of 8. 9% (from 2170 ECUs in 1980 to 4860 ECUs in 1989). Across all 119 Cohesion NUTS3s, per capita GDP was 3060 ECUs in 1980 and 6300 ECUs in 1989, thus growing at an annual rate of 8. 0%. For the 140 NUTS2 locations across the earlier 12 European Community member states, per capita GDP was 6235 PPSs in 1980 and 14488 PPSs in 1990, implying an annual growth rate of 8. 4%. While conducting all the analysis in a constant value, as in the Summers-Heston da ta, has its advantages, for the current work the ECU figures allow easy comparison across Co hesion NUTS3 locations. The more intricate cal culations below will, in any case, be done relative to national averages and so nothing is lost by us ing ECU numbers. ) The poorest regions are not as easily seen in the figure, but can nevertheless also be detected, loannina and Arta in the west had the lowest per capita GDP in 1989 (3150 and 3171 ECUs re spectively); they had begun below average (2053 and 1853 in 1983), but were certainly not the poorest at the beginning of the sample: Rodopl in the extreme northeast and Thesprotia in the far west had per capita GDP of only 1742 and 1792 ECUs respectively in 1983. However, not all that were poor remained poor, and not all that were rich remained rich. Evritania, Zakinthos, Dodekanissos, Kyklades, Iraklio, and Lassithi were all NUTS3s that began below the Greek average in 1980 and ended up above in 1989. In particular, Lassithi In the southeast and Dodekanissos in the extreme east grew at annual rates of 9. 7% and 9. 0% respectively, almost dou ble the national rate. By contrast, Pela, in the north, went from per capita GDP 2816 ECUs in 1980 (6% above the Greek average) to 4284 ECUs in 1989 (1. 5% below). In the central east, Evia, the lowest-growth Greek NUTS3, had per capita GDP 3722 ECUs in 1980 and 4938 ECUs in 1989, an annual growth rate of only 3. 1 %, less than two-thirds of the Greek average. These data reveal both persistence and mobility: some NUTS3S that were already rich 'emained rich, and some that were already poor remained poor. Some NUTS3s that were originally poor be came rich; others that were originally rich be came poor. Summarizing further, it is apparent that in Greece the west is, in general, poorest, but pockets of relative economic success and failure may be found in all different parts of the country. Relative successes and failures are not just static, but show important dynamic dimen sions. For Spain, Fig. 2. es shows first the growth suc cess of the country as a whole. Spanish per capi ta GDP rose from 4100 ECUs in 1980 to 9020 in 1989, an annual growth rate of 8. 7%. While the Spanish average has, thus, performed better than the Greek average, some individual NUTS3s in Spain have done even better. Tarragona in the northwest had the highest per capita GDP in 1989: per capita GDP in Tarragona had risen from 5755 ECUs in 1980 to 14637 in 1989, an annual growth rate of 10. 3%—Tarragona further increased its lead over the average. Alava, in the north, the richest NUTS3 in 1980 had its per capita GDP rise from 6243 to 12105 ECUs in 1989—this, however, was an annual growth rate of only 7. 3%, lower than that of the average. Badajoz, in the southwest, was the poorest Spanish NUTS3 in 1989 with per capita GDP of only 4886 ECUs. (This still exceeded both the Greek and Portuguese 1989 averages of 4350 and 4860 ECUs respectively). In 1980, this NUTS3 location had per capita GDP of 2494 ECUs, again, the lowest in Spain: the implied an nual growth rate for Badajoz was thus 7. 4%, slightly higher than that of Alava, the richest NUTS3in 1980. Just as with Greece, Spanish NUTS3s also show transitions between relative poor and rich. As a relative success, Valencia in the east had 1980 per capita GDP of 3940 ECUs, below the Span ish average, but grew to have 1989 per capita GDP of 9059 ECUs, above the average. Valen cia's annual growth rate was 9. 2% over this peri od. By contrast, its physical neighbor Alicante grew at only 7. 5% per annum, its per capita GDP growing from 4100 ECUs in 1980 (at the Spanish average) to only 8070 ECUs in 1989 (11 % below the average). Asturias in the north and Valladolid in the centre both began the decade above the Spanish average but ended up below, with annu al growth rates of 7. 3% and 7. 6% respectively. 84 Section II — Models of Explicit Distribution Dynamics The Spanish NUTS3s showing fastest growth were Cáceres in the west and Tenerife. It Is useful to note that Cáceres borders on Badajoz, and that both share a boundary with Portalegre, one of Portugal's relative growth successes. Together, Cáceres and Badajoz were among the poorest NUTS3s in Spain in 1980. But Cáceres grew subsequently at an annual rate of 11. 0%, while, to its immediate south, Badajoz—with growth of only 7. 5%—was Spain's single poorest NUTS3 in 1989. Not only did these two neighboring loca tions show different dynamics, but Avila with growth of only 7. 3%, sits right on Caceres's northern border. This example shows that suc cessful growth need not be spatially concentrat ed across NUTS3s. At the same time, however, geographically-localized pockets of relative slow growth can be discerned: La Coruna (7. 7%), Lu go (7. 2%), Asturias (7. 3%), Burgos (7. 6%), and Cantabria (7. 8%) are all relatively slow-growth NUTS3S, and all in the north of Spain. Portugal has only 18 NUTS3 locations; Fig. 2. pt is thus correspondingly sparse. As already re ported above, Portuguese per capita GDP grew at 8. 9% per annum, the highest aggregate growth rate among all the Cohesion economies. Lisboa, in the west, consistently remained the richest NUTS3 location in Portugal: between 1980 and 1989 Lisboan per capita GDP in creased from 3131 to 8211 ECUs, an annual growth rate of 10. 7%, faster than the growth of the Portuguese national average. Portalegre, in the east and bordering on Cáceres and Badajoz in Spain, grew from a per capita GDP in 1980 of 1856 ECUs (below the Portuguese average then of 2170 ECUs) to 5350 ECUs in 1989 {above the Portuguese average of 4860). Finally, Fig. 2. ep puts together in one picture the NUTS3 locations of the physically contiguous Spain and Portugal. The lessons on Spain and Portugal from above simply repeat, with the added emphasis on the relative poverty in the west. Summarizing the results of the discussion thus far, we have seen that there is great diversity in income and growth performance across the NUTS3 locations in the Cohesion countries. This variation is observed not just across the coun tries, but also within each of them. Moreover, the range of variation can be either large or small in geographically-localized areas. Both mobility and persistence are observed: some originally poor NUTS3s became rich; and some originally rich ones, poor. At the same time, some initially rich NUTS3s remained rich; and some initially poor ones remained poor. 2. 2. The shape of distribution dynamics The analysis above, while Informative for details, has limitations. Without placing more structure on the investigation, it is dicult to distinguish underly ing regularities from Isolated, one-off outcomes. What has been noted above is consistent with a range of possibilities: Fig. 3 shows just one of these possibilities. Fig. 3 plots on its horizontal axis the progress of time; on its vertical axis, per capita GDP or in come. The figure shows at time t a hypothetical Income distribution across locations. As drawn, that distribution at r shows most locations having a middle level of income; there are few in the up per tail (the very rich), and few in the lower tail (the very poor). There is one such distribution at each time point. Fig. 3 gives for t+s, again hypothetical^, a differ ent distribution from that at f. This later distribu tion shows a "twin peaks" character: there is a clustering of the very rich and a clustering of the very poor; the middle income class of economies has vanished. Technically, the distribution at t+s is said to show a bimodal shape; the sequence of distributions between f to t+s shows an "emerging twin peaks" property. Fig. 3 also draws in arrows that show intra-distri bution transitions (or churning). Some economies rich at t+s had already been so at t. Similarly, oth ers poor at t+s began also poor at f. However, there are other economies —indicated by the criss-crossing arrows in the figure—that transited from being poor to being rich and conversely from rich to poor. This picture is one that shows mobility and per sistence simultaneously. Thus, Fig. 3 is potentially representative of experience in the Cohesion economies. At the same time, however, the figure shows some features that might not be factual. Most prominent, the twin-peaks shape there car ries the implication of polarization between rich Preliminaries on convergence and distributions 85 and poor: the division between the rich, cluster ing together, and the poor, similarly clustering, is stark in Fig. 3. This, in one interpretation, is the precise opposite of cohesion. There is, of course, no logical necessity that only two peaks appear at t+s. In general, distributions later in time might show even more peaks. Then, stratification is a more apposite description than polarization. But the intuition remains: distinct multi-tier income classes form and then separate from one another. Is this occurring in the Cohe sion economies? Note, moreover, that time t+s need not be a time period that has already transpired. It could in stead be some future time: we then need to ask, Can "emerging twin peaks" properties be detect ed in already-extant data, if only indirectly? If the shape at t+s cannot yet be observed, we need a model to give guidance on the likely possibilities for that future. Looking at the raw data alone will not suce. It is this task to which I now turn. Fig. 4 shows point-in-time snapshots of income distributions across countries in the world, across NUTS2S Europe-wide, across all Cohesion NUTS3S taken together, across NUTS3s in each Cohesion country, and finally across NUTS3s grouping together Spain and Portugal. Aside from the first three, Fig. 4. w, Fig. 4. E12, and Fig. 4. C, these pictures match the earlier ones on spatial dynamics given in Fig. 2. Take first the picture for countries in the world, Fig. 4. W. To prepare these estimates of cross country income distributions, I took all 105 coun tries for which per capita GDP data were avail able between 1961 and 1988. Dividing per capita GDP in each year by that year's population- weighted average across these economies year gives relative incomes (relative to the world's per capita income). For each of the years 1961, 1970, 1980, and 1988, I then found the cross country relative income distribution. 1 The densi ties of these distributions are given in the figure with relative income values on the horizontal axis. Follow the progression in the densities across the (nearly) decennial intervals: it is apparent that these data show the emerging twin-peaks prop erty. 2 In 1961, the cross-country income distribu tion showed a significant peak at about 1 and a small "shoulder" at about 3. By 1988, the loca tion of that significant peak had fallen to below 0. 5 while the "shoulder" had magnified into a second peak and, moreover, had risen in location to almost 3. 5. Not only have the peaks become more pronounced, they have also grown more distant from each other, with corresponding in crease in the disparity between rich and poor. We conclude that the "emerging twin-peaks" property of Fig. 3 is not entirely whimsical: the world's economies have, in reality, polarized. This conclusion is in stark contrast to the mes sage given in Fig. 4. E12 for European NUTS2s. To begin, note that Fig. 4. E12 differs from Fig. 4. W in two ways. First, the time separation be tween the observations on income distributions is much shorter, only three years rather than ap proximately 10. Second, the units of measure ment are in thousands of PPS units (GDP per in habitant in purchasing power standardized units), not relative to a weighted average. However, Fig. 4. E12 shows a marked single central tendency in the distribution sequence, a tendency that per sists throughout the observed sample—the miss ing twin-peakedness here cannot be mechanical ly explained by either of the two differences men tioned. Although in Fig. 4. E12 there is a spread ing out of the distribution, that can be explained entirely as an overall growth effect. If one had plotted not the distributions in PPS units, but in stead had normalized each observation by the Europe-wide per capita income, the resulting dis tribution sequence would then have uctuated on ly imperceptibly over the sample period. What then about the 119 Cohesion NUTS3 economies? Fig. 4. c shows the counterpart to the cross-country Fig. 4. w and the Europe-wide Fig. 4. E12. Again, note two differences in Fig. 4. c's construction relative to Fig. 4. w before be ginning on its implications: first, the income distri butions are given for only three-year intervals and over only the 1980s. Second, the underlying data are per capita incomes in ECUs rather than ratios of incomes relative to an average: the horizontal axis is now in units of thousand ECUs, rather than income ratios. 1 I estimated the densities corresponding to these distributions using a Gaussian kernel with automatic bandwidth chosen as in Silverman [27, 3. 4. 2], restricting the domain to be non-negative. Using earlier data than those here, Quah [17] had provided a first preliminary observation on these emerging twin peaks. See also the more recent discussion in Quah [21]. 86 Section II — Models of Explicit Distribution Dynamics The reason for the second difference is, as be fore, to maintain comparability across Cohesion nation states. 1 The reason for the first difference is data availibility: the Cohesion data are ob served only over a much shorter timespan than the Summers-Heston cross-country data. This shorter timespan makes apparent the need for some model, before one can speak on the un derlying dynamic regularities in these data—the t+s of Fig. 3 is likely outside the time-range of ob servations. Like Fig. 4. E12, the Cohesion Fig. 4. c does nor show the twin-peaks property. Instead, the most prominent feature is the spreading out of in comes over time; the single peak remains at about 5000 ECUs over the decade. The standard deviation of these cross-NUTS3 income distribu tions-see Table 1. c-was 1120 ECUs in 1980, increasing steadily to 1200 ECUs in 1983, 1720 ECUs in 1986, and then 2730 ECUs in 1989: the standard deviation in 1989 was 2. 4 times that in 1980. An alternative measure of spread is the in- ter-quartile range, i. e. , the distance between top and bottom 25th percentiles of the distribution: the value for this in Fig. 4. c in 1989 was 2. 6 times that in 1980 (it rose from 1510 ECUs in 1980 to 3900 ECUs in 1989). Average per capita GDP across these Cohesion economies only about doubled between 1980 and 1989. If Fig. 4. c had been calculated from relative incomes— as had been Fig. 4. w—the in- ter-quartile range would have increased by a fac tor of 125. 4%, the standard deviation by 118. 4%. Across countries, the four panels of Fig. 4. W show an increase in inter-quartile range of 143. 4% and in standard deviation by 117. 0%. This, at first, appears similar to the Cohesion case. However, for the world, this increase oc curred over 27 years, three times longer than the 9 years covered in the Cohesion case. Contrast both of these with what happened across Europe-wide NUTS2s in Fig. 4. E12 and Table 1. E12: here, the standard deviation and the inter-quartile range doubled between 1980 and 1989, but the weighted average also increased, and by an even greater 212%. Thus, normalizing by this weighted average, the spread of the Eu rope-wide NUTS2 income distribution actually fell. Calculating the cross-country Fig. 4. w without first normalizing to rel ative incomes, one sees the same twin-peaks emergence, with even more of a spreading out across income values. Thus the conclusion only strengthens when income levels are analyzed rather than ratios. To look deeper into what happened here, Tables 1. fr, 1. it, and 1. uk, provide statistics on France, Italy, and the UK, respectively, taking each of these nonCohesion EU member states in isola tion. France is overall the richest of these three in regional average and median. It has seen its re gional interquartile range increase by 50% over the 1980s, while the standard deviation more than doubled. In this time, however, its overall well-being (measured by either median or weight ed average), again, more than doubled. Italy and the UK, in either average or median income, ex perienced the same relative change as France. While in Italy inter-quartile range and standard deviation increased roughly in step with this scale growth, the UK showed regional spread increas es three times their initial magnitude. Thus, it is the UK that has seen the furthest deterioration in regional cohesion. We will see below, moreover, that this increase in inequality has taken a very particular form. To summarize, while the Cohesion NUTS3 economies do not show the same emerging twin-peaks feature as do the world's economies (at least not obviously), the historical growth rate in disparity between rich and poor locations has been much larger in the Cohesion economies than for both countries across the world and NUTS2 disaggregates across Europe more broadly. The rest of Fig. 4 provides counterparts to Fig. 4. C, for each of the Cohesion countries, for Spain and Portugal together, and then finally for a cou ple of non Cohesion EU member states. The re sults for Greece Fig. 4. el and Spain Fig. 4. es re peat the single-peakedness and the spreading- out over time of Fig. 4. c. Details, however, differ. Normalized by nation av erages, from 1980 through 1989 the Greek NUTS3S inter-quartile range increased by a factor of 128% while the standard deviation felt to onfy 89% of its original value. 2 Across Spain NUTS3s, the inter-quartile range increased by a factor of 106% and the standard deviation by a factor of 109%. Unsurprisingly, the inter-quartile range and standard deviations do not always move in the same direction. The fact that —as for Greek NUTS3s— the standard deviation falls while the inter-quartile range rises only indicates the ex- Below, In Fig. 5 and associated tables, I will come back to the ab solute, rather than relative, magnitudes on these measures. Preliminaries on convergence and distributions 87 treme rieh and poor being pulled in, strongly, to wards the middle. By contrast, Spain's NUTS3 income distributions—relative to the nation aver age—seem merely to replicate in shape over time. The panels in Fig. 4. pt for Portugal show a bi- modality early in the decade that then gradually disappears. However, the data for Portugal com prise only a small number of observations, and a reader might not wish to read too much into this. By contrast, the increase in spread again mani fests clearly. Normalizing as before by nation av erage so that we consider relative magnitudes, the Portuguese NUTS3 inter-quartile range in creased by a factor of 112% from 1980 to 1989; the standard deviation, by a factor of 143%. By these measures, therefore, the increase in spread or the decrease in cohesion in Portugal was by far the largest of any of the Cohesion naiions. 1 The final figure on the Cohesion economies Fig. 4. ep shows income distributions across the con tiguous nations Spain and Portugal. Its gross fea tures combine those of Spain and Portugal sepa rately (although there is no mechanical reason, from the construction of these distributions, why they should). Relative to the integrated Spanish- Portuguese average, the 1989 inter-quartile range fell to only 86% of the 1980 value; while, over the same time, the standard deviation in creased by a factor of 105%. This is the opposite to the pattern observed for Greek NUTS3s: for the combined Spain/Portugal, the extreme rich and poor are pulled apart, rather than drawn into the middle, while the already-middle NUTS3 con gregate ever more tightly in the middle. Next, I turn to results for a couple of non-Cohe sion EU member states: Fig. 4. fr for France and Fig. 4. it for Italy. (The UK's 11 NUTSIs provided too small a sample for useful analysis here. ) Like the previous figures, the most marked feature is a spreading out over time of the cross-section dis tribution. In the evidence presented here, there might appear some slight tendencies towards a polarization, but if so, such tendencies do not leap out at the observer. Thus, these figures do not, by themselves, suggest significant differ- enees for France and Italy that, aside from their being richer overall, would set them apart from the Cohesion economies. Below, however, we will see such disparities emerge. Summarizing Fig. 4's lessons, we see that the twin-peaks feature did not emerge across the Cohesion NUTS3 economies in the same way that it did across countries in the world. On the other hand, the spreading out of rich and poor has been much faster and more dramatic across Cohesions NUTS3s compared to either countries across the world or NUTS2s across Europe generally. The pattern of that spreading out differs across the Cohesion nations: it is Portugal that has displayed this increasing in equality most strongly, while Greece has seen the opposite, an increased cohesion among its NUTS3S. To interpret the different dynamic behaviour of in ter-quartile range and standard deviation, I used above the idea that the extreme rich and poor move in different directions relative to the rest of the distribution. Tukey boxplots —given in Fig. 5—provide a convenient way to see this. (Tukey boxplots are well described in, e. g. , Cleveland [5]. ) Begin with Fig. 5. w: time appears on the horizon tal axis while the vertical axis maps income val ues. A single boxplot appears for each of the years 1961, 1970, 1980, and 1988 (repeating the time periods from Fig. 4. w above). Take the box- plot for 1961 : coming down from above, the box itself begins at the top quartile (i. e. , the 75th per centile) of the 1961 income distribution, and ends at the bottom quartile (i. e. , the 25th percentile). The height of the box is therefore also the in terquartile range: as already Indicated above, it denotes a measure of spread in the distribution. By construction, therefore, the middle 50% of the distribution lies entirely within the box. If the inter quartile range is large—the box is tall—the mid dle 50% of the distribution is relatively spread out. By contrast, if the interquartile range is small—the box is short—the middle 50% is tight ly compressed together. There is a common misperception that smaller sample sizes will me chanically produce evidence of greater spreads or higher variability: thus, Portugal might show this increase in spread only because it has fewer NUTS3s than Greece or Spain. Recall, however, that while smaller sample sizes, in general, do imply more statistically variable estimates, the estimates themselves are not biased upwards or downwards. The horizontal bar that appears, at varying loca tions, somewhere inside the box is the median or 50th percentile of the income distribution. This is one measure of the location of the distribution. The upwards and downwards distance from the median to the top and bottom of the box provide Section II — Models of Explicit Distribution Dynamics information on the shape of the income distribu tion. If these distances differ, then the distribution is skewed or asymmetric. Thin vertical lines emanate from the box both up wards and downwards: these end at what are known as upper and lower adjacent values, re spectively. If the interquartile range is r, then the upper adjacent value is the largest income value observed that is no greater than the top quartile plus 1. 5 χ r. Similarly, the lower quartile is the lowest income observed that is no smaller than the bottom quartile minus 1. 5 χ r. Finally, upper and lower outside values are those observations in the original distribution that lie outside the upper and lower adjacent values. These are outliers, and are individually Indicated by asterisks. Of course, upper and lower outside values might not exist—the adjacent values might already be the extreme points in a particular real ization. Fig. 5. W shows that the expanse of the world's crosscountry relative income distribution has ac tually remained stable over the three decades un der study. What happened, instead, is a spread ing out of the middle: the interquartile range and the top quartile both increased. With them, the upper adjacent value rose to cover progressively more of the cross section of relative incomes. 1 While, at the beginning of the sample, ten economies showed upper outside values, by the end of the sample only two did so. Those two need not, of course, have been among the origi nal ten: to study that systematically, one needs to analyze intradistribution properties. Those prop erties are considered In the next section. The matching counterparts in Fig. 4 and Fig. 5 use exactly the same underlying data. However, they emphasize different empirical regularities. The emerging twinpeaks feature is striking in Fig. 4. W, but is far from obvious in Fig. 5. w. The spreading out of the middle is apparent in Fig. 5. w; it appears in amended form as a vanishing of the middleincome class of economies in Fig. 4. W. Table 1 is usefully studied simultaneously with Fig. 5: the table contains numerical values that match certain features in Fig. 5. The increase in In none of the boxplots in this paper did lower outside values exist: this is unsurprising given that the income data are all positive. the interquartile range as well as the spreading apart of top and bottom quartiles is clearly seen in Table 1. w. Similarly, the much slower growth in the standard deviation σ indicates that most of the spreading out in the distribution occurred nor in its tails—for then σ would have increased more dramatically. Fig. 5. E12 gives the sequence of boxplots for the 140 Europewide NUTS2s. Recall that the units of income here are thousands of PPSs per capi ta. As already remarked above, what is most no table here is the maintenance of shape and loca tion in the crosssection distribution, subject only to the natural scaling. Fig. 5. c gives the sequence of boxplots for the 119 Cohesion NUTS3s; Table 1. c gives corre sponding numerical values. (Recall that as in Fig. 4 the underlying data for all Cohesion income ob servations are in thousands of ECUs. ) The spreading apart in the Cohesion NUTS3s income distribution has two distinct sources: on the one hand the middle, and on the other the extremes. The contribution of the former has exceeded that of the latter. We see this from the increase both in the interquartile range and in the standard devia tion (again from Table 1. c and the earlier discus sion surrounding Fig. 4. c). The same conclusion follows also from Fig. 5. c: that the middle has contributed more to the increasing spread mani fests in the upper outside values here being pro gressively swallowed by the advancing upper ad jacent value. Finally, Table 1. c makes clear that the interquartile range is increasing due to a rising top quartile, not a falling bottom quartile. Thus, across the Cohesion NUTS3s, inequality has been increasing —but that increase has been due primarily to the rich pulling away from the poor, while the position of the poor has not significantly changed. Turn now to the individual Cohesion countries. In Greece, the middle has spread but not dramati cally: the interquartile range increased by a fac tor of 209%, while the median increased by a comparable factor of 180%. Moreover, most of the rise in the interquartile range occurred be tween 1986 and 1989; up through 1986, that range had actually fallen. The standard deviation showed the same general movement, but less so: σ increased from 570 ECUs in 1980 to 830 ECUs ¡η 1989. However, relative to either the weighted average (i. e. , Greek per capita income) or the NUTS3 median, σ actually fell. We con Preliminaries on convergence and distributions 89 elude, therefore, that Greece has shown high cohesion—certainly the highest of all the individ ual Cohesion countries, as we will see further below. The earlier discussion surrounding Fig. 4. es had concluded, tentatively, that Spain's increase in dispersion matches almost exactly its overall growth: the distribution simply replicated to scale. Fig. 5. es and Table Les confirm that conclusion. The increase in the interquartile range is by al most exactly the same factor as that in σ, in the weighted average (i. e. , Spanish per capita in come), or in the NUTS3 median. In Fig. 5. es ei ther no outliers appear, or they are very close to and track the adjacent values. Turning to Portugal, Fig. 5. pt and Table 1. pt con firm our earlier conclusion that Portugal is the Cohesion nation that has shown the greatest in crease in NUTS3 inequality. In Fig. 5. pt, the in terquartile range increased, but the outliers did so even further. Table 1. pt shows that the in terquartile range and σ increased faster than both the weighted average (i. e. , Portuguese per capita income) and the NUTS3 median. Finally on the Cohesion economies, Fig. 5. ep and Table 1. ep provide simply a combination of our conclusions on Spain and Portugal, recognizing that there are about three times the number of observations on Spain as there are on Portugal: nothing surprising emerges. Turn now to some non-Cohesion EU member states. Fig. 5. fr, Fig. 5. it, and Fig. 5. uk give Tukey boxplots for France, Italy, and the UK respectively. These now show interesting differences both within the non-Cohesion group and in comparison with the Cohesion economies. As previously already noted, the spreading out over time of the cross sections is evident. But the character of that in these creasing economies. Both France and the UK show signifi cant outliers, in the form of leading regions, pulling away from the others. (Regional income distribu tion across the UK was so tight in 1980 that the main box in the Tukey boxplot for that year does not even show on the graph. ) The tails of the French and UK distributions also spread apart. In Italy, by contrast, the spreading out involved pri marily regions in the middle of the distribution itself. inequality differed across To summarize this subsection, I note that a clear picture has emerged. In aggregate, Portugal has grown the fastest, closely followed by Spain; Greece has in aggregate grown slowest. This ranking is replicated in tendencies away from co hesion within each nation. Spain's aggregate growth performance, while practically as good as Portugal's, did not prevent Spain from maintain ing cohesion across its NUTS3s. Greece, slow- growing in aggregate, fostered cohesion even more successfully than did Spain. Analysis of non-Cohesion EU member states showed a vari ety of dynamic behaviour: although an increasing inequality was everywhere evident, the nature of that increase differed across member states. 90 Section II — Models of Explicit Distribution Dynamics 3. Mobility and dynamics Thus far we have discussed only point-in-time snapshots of cohesion, either across the world, across all of Europe, or across the Cohesion economies. This section takes the next step: it investigates intra-distribution dynamics and long- run tendencies. In terms of Fig. 3, this section considers two features there: first, the transitional arrows in bold, and second, t+s being outside the sample, possibly arbitrarily far outside. It will be convenient hereafter to take observations rel ative to the larger, encompassing unit: thus, all cross-country incomes are normalized by the world average; all NUTS2 measures by the Eu rope-wide average; and all NUTS3 measures by the member-state average: these will be denoted just as relative incomes. Fig. 6 shows cross-profile dynamics: it illustrates when economies overtake one another, fall be hind, or pull ahead. 1 In Fig. 6 the vertical axis is the log of relative incomes. Each curve in the figure shows the situation at a given point in time. The lowest curve is that for the earliest time period; proceeding upwards, we encounter curves for progressively later periods in time. The lowest curve, moreover, is construct ed to be monotone rising: at that earliest time pe riod, the cross section of economies is sorted in increasing order. This ordering is then maintained throughout the time periods considered. Obvi ously, the character of the upper plots depends on the initial period when the ordering is taken. The change in character of the plots through time, however, does not. The idea for such a picture comes from Dolado et al [ In the cross-profile plot, increasing choppiness, increasing jaggedness, or increasing variation through time indicate intra-distribution churning. If, over time, each cross profile always monotonl- cally increases, then income rankings are invari ant. More information appears, however, than just rank ordering: the slope of the cross-profile plot also shows the income distance across rich and poor. Table 2 contains numerical measures of those features just described. In the first column, s l o pe measures how much, on average, (the log of relative) incomes rise as one proceeds rightwards across economies in a given cross- profile curve. If s l o pe has value x, then "being 10 economies richer" means having income e'°* times higher. This slope information —ignoring identities in the cross section —can show not much more than the point-in-time snapshots of the previous section. Indeed, the first two columns of Table 2 only repeat our earlier conclu sions. Across Portugal, NUTS3 inequality is greatest; it is lower in Spain, and even lower in Greece. The e10x measure is relative to the ab solute position of the entire cross section: across the Cohesion economies, it shows comparative stability through time. However, the most striking feature of Fig. 6 is not this stability. Rather, it is the change in choppi ness through time in the cross-profile plots. In Fig. 6. W by 1988 local peaks —around economies ranked 26th, 47th, 62nd poorest in 1961—had appeared: these turn out to be Ko rea, Taiwan, and Singapore respectively. By con trast, Malawi (3rd poorest in 1961), Mali (9th), Mobility and dynamics 91 Uganda (14th), Chad (22nd), Ghana (27th), the Philippines (41st), Mozambique (42nd), Papua New Guinea (49th), Guyana (56th), Jamaica (63rd), Costa Rica (69th), Chile (78th), Argentina (85th), Venezuela (95th), and New Zealand (102nd), among others, had experienced eco nomically significant relative declines by 1988. The columns s e r C o rr and 2V a r tn in Table 2 more systematically record such increasing choppiness. Take (I) to denote the sequence giv en by the cross-profile ranking, i. e. , (1) indexes the poorest economy in the earliest period, (2) the next poorest economy, and so on. For a giv en time period, the measure s e r C o rr is then the first-order serial correlation coecient of se quential changes across the given ordering (/). If y are the units on the vertical axis, sequential changes are defined as: A * y ( , ) = y(, ) - y(, _ i ). Letting EA*y denote average A*ym, then s e r C o rr is: £(A»y(/)-EA*y)(A*y(M)-EA*y) V / Because it is a correlation coecient, serCorr is always between -1 and +1. It measures the serial correlation in changes: thus, even for a monoto ne increasing cross-profile plot, s e r C o rr is nev er guaranteed to be non-negative. If the crossprofile plot is a straight line (of whatever slope), then s e r C o rr is zero. In general, howev er, s e r C o rr differs from zero, and becomes in creasingly negative as the crossprofile plot be comes progressively choppier. The measure 2V a r t n, by contrast, measures mean-square variation. For a cross-profile com prising Ν economies, 2v a r tn is defined as Κ2)~1Σ(Δ>)-Δ>-1>)2· Like s e r C o r r, the measure 2V a r :n is zero when the cross-profile plot is a straight line. How ever, 2Vartn is always non-negative; it increases (potentially without bound) when the cross-profile plot shows greater variation. Finally, (as with serCorr, the measure 2v a r tn can be directly compared across different cross-section samples since it is normalized by sample size). Unsurprisingly, both measures of choppiness in Table 2 generally increase over time in each of the cross-section samples. The serial-correlation measure s e r C o rr stabilizes rapidly in Table 2. E12 (Europe-wide NUTS2s), Table 2. c (all Co hesion NUTS3S), and Table 2. el (Greece), but continues to increase in Tables 2. w (the world economies), 2. es (Spain), 2,pt (Portugal), and 2. ep (combined Spain/Portugal). For Greece, the variation measure 2v a r tn again stabilizes quick ly; in all other samples, 2V a r tn shows ongoing increase. Not only is Greece the cross section that shows greatest cohesion, it is also that whose dynamics display the most rapid settling down to a regular pattern. Of course, this does not mean that the Greek cohesion profile has frozen in time: Fig. 6. el shows the churning continuing. It is just that the pattern of such churning characteristics is stable. Across the 140 European NUTS2s, on the other hand, the outstanding feature is persistence: there is little ongoing overtaking and falling be hind. After normalization, the relative income dis tribution sequence is practically frozen, both in external shape and in (the little) intra-distribution movement. Comparing the dynamics of s e r C o rr and 2V a r tn in the other cross sections, Portugal stands out, again as the extreme opposite to the dynamics in Greece. [I have omitted cross-profiles for France, Italy, and the UK. They do not appear informative be yond the other evidence presented. ] The cross-profile dynamics in Fig. 6 and Table 2 have given a first, preliminary look at the impor tance of Fig. 3's transition arrows: they, however, do not yet show any deep underlying regularities in the data. I turn therefore to two more represen tations of intra-distribution churning: first, transi tion probability matrices in Table 3; and second, stochastic kernels in Fig. 7. (For studying growth and convergence, these have featured promi nently in a series of studies beginning with Quah [16] and extending through Quah [20,· 23]. ) 92 Section II — Models of Explicit Distribution Dynamics Consider again the emerging twin peaks picture Fig. 3. In practice, for some f, we do observe which economies were where in the income dis tribution at f and then where in the income distri bution they went at r+1. (In this example, I have used a transition interval of 1. ) Therefore I can simply count the number of transitions across those different parts of the income distribution, and then average across all observed transitions, to uncover the underlying regularities. As a first step, to make this operational, I need to say what I mean by where in the income distribu tion an economy begins and goes. Table 3. w makes a start at this. It assumes that the interest ing where's are between 0 and 1/4 of the distrib ution's weighted average, between 1/4 and 1/2, and so on. Call these individual ranges the states of the transition process. Table 3. w is then an ex ample of a transition probability matrix. As select ed here, its states are proportionally-defined. The first row of Table 3. w notes that for the world's economies, 470 total state-year pairs be gan in the poorest state (between 0 and 1/4). Of those initial 470 observations, after one year 6% transited to the next higher income state, namely that between 1/4 and 1/2 of the distribution's weighed average. The other 94% remained in the original poorest state. Contrast this with the third row: 733 state-year pairs began in the middleincome state, that be tween 1/2 and 1. After one year, 92% remained there; 4% transited to a richer state and 4% tran sited to a poorer state. The diagonal of a transition probability matrix thus describes persistence: it shows the likeli hood of remaining in a particular state when one starts there. The smaller is the diagonal, the more intra-distribution dynamics there are. Suppose that the system described by a transi tion probability matrix continues in its evolution. If nothing structural were to change, then the sys tem could eventually reach a long-run steady state. The row labeled "Ergodic" describes that hypothetical long-run situation: it gives the distri bution across states that would be achieved in the long run. For the world's economies, as shown in Table 3. w, that ergodic distribution is one that is twin-peaked. There is, first, a peak in that state extending up to the value 1, and then again in that state extending up to the value 4; the state between those peaks has strictly lower probability. This twin-peakedness is related to but differs from that observed earlier in Fig. 4. w. The twin peaks in that earlier picture were for the year 1988; the twin peaks just noted in Table 3. w are for a hypothetical long-run steady state. In thetermsgiven in Fig. 3, the time period t+s is now arbitrarily far outside our observed sample for the ergodic distribution of Table 3. w, while t+s equals just 1988 in Fig. 4. w. These calculations show that the emerging twin- peaks property for the world's economies is symptomatic of a deeper, underlying regularity, not just something that happened over our given sample. However, such characterizations also need not be especially robust. Table 3. w. u inves tigates the outcome if the states —which were earlier taken arbitrarily—are redefined, again arbi trarily, to be such that the rightmost column is (al most) uniform. I will refer below to such a transi tion probability matrix as having its states uni formly-defined. The implied ergodic distribution again shows a dip in the middle, but the "peaks" are now at the extreme ends—the lower peak occurs below the value 1/4 rather than between 1/2 and 1; similarly, the higher peak now falls outside the value 4. 5 rather than below 4. The reason for this pattern of results is not mys terious. The division into discrete states is arbi trary, and in general allows only a distorted pic ture of the underlying dynamics. By exploring a number of different possible discretizations, the researcher might succeed in imparting confi dence into a particular set of findings. However, such a happy result cannot be guaranteed in general. There need, moreover, be no reason for taking a single period to be the transition inter val—the implied ergodic distribution could well differ for different transition probability matrices estimated over different transition intervals. 1 The stochastic kernels of Fig. 7 provide one way of removing arbitrariness in the state discretiza tion. Instead of a state being just a fixed interval, say (1/4, 1/2], now let the states be all possible intervals, including those infinitesimally small. (Technically, extend the state space to the natural Borei sigma-algebra. ) The transition probability This is a well-studied problem. See, e. g. , Singer and Spilerman [28] and its references. Mobility and dynamics 93 matrix, with its finite number of rows and columns, is now replaced by a stochastic kernel. A useful way to think of the latter is that it is a transition probability matrix with a continuum of rows and columns. For the world's economies, Fig. 7. w and Fig. 7. w15 display stochastic kernels across 5-year and 15-year transition intervals. 1 The companion Fig. 7. W. C and Fig. 7. w. c15 show contours of the stochastic kernels, with contours chosen to high light the kernels' critical features in each case. To interpret these, take as an example Fig. 7. W15. Stand at any point on the period t axis, and then look in a straight line, parallel to the pe riod r+15 axis. What is traced out on the surface of the kernel is a probability density: it is always non-negative and integrates to 1. The more likely transition possibilities manifest as higher values on this line. (In the same way, looking across a given row of a transition probability matrix one sees a vector of non-negative numbers that add up to 1, and where the most likely outcomes are indicated by the highest numbers in this vector. ) Just as with a transition probability matrix, the 45-degree diagonal in a stochastic kernel indi cates persistence properties: the more pro nounced the surface along that diagonal, the more persistence there is in the distribution. The lower is that diagonal, the greater is intra-distribu tion churning. If the stochastic kernel were to have its ridge twisted counter-clockwise from the 45-degree diagonal, then an initial distribution is transformed over time with the rich becoming poor and the poor, rich. If the stochastic kernel were to have its ridge parallel to the period f axis, then cohesion occurs—over time, both poor and rich converge towards the middle. By contrast, when clusters appear along the 45-degree diag onal, then they describe dynamics that are ab sorbing—entering those income states engen ders an increase in persistence. An emerging twin-peaks property for the income distribution is typically captured by similar peaks appearing in the stochastic kernel. This corre spondence, however, is only suggestive rather than strict; it is possible to have twin peaks in These kernels were estimated with an Epanechnikov kernel using an automatic bandwidth choice following Silverman [27, 4. 3. 2]. As de scribed in Quah [22], the kernels are also graphed so that where more observations are available, the resolution is correspondingly finer—more grid lines are drawn. When the surface is mostly white space, the precision of the estimate Is low. one without their appearing in the other. For in stance, imagine independent and identically ob servations drawn from a bimodal distribution: the kernel then comprises two ridges parallel to each other and to the period-f axis. Alternatively, if in the kernel one of the clusters dominates the oth er, then the ergodic distribution could be single- peaked (as will happen in the Portuguese case below). Fig. 7. W and Fig. 7. w15 highlight the twin-peaks dynamics already observed earlier for the world's economies: they do this now without the arbi trariness of Table 3. w. I conclude from these that it is the transition probability matrix of Table 3. w that gives the more accurate message than that in Table 3. w. u. Of course, there is no a priori rea son that the proportionally-defined states are al ways better than the uniformly-defined ones. In stead, the message here is that one should look first at stochastic kernels, and then possibly aug ment the information in them by studying an ap propriately-defined discrete transition probability matrix. With this intuition, we can now turn to Europe and the Cohesion economies. Fig. 7. E12 through Fig. 7. it (and their companion contour plots Fig. 7. E12. C through Fig. 7. it. c) present stochastic kernels for first the 140 Europe-wide NUTS2s, then all 119 Cohesion NUTS3s, then for individ ual nation states, their constituent NUTS3s, the NUTS3S combining Spain and Portugal, and then for France and Italy, two non-Cohesion EU mem ber states. (The UK NUTS1 economies are too few in number to support any further analysis reli ably, and so I have omitted them. ) Table 3. E12 through Table 3. it present counterpart uniformly- defined state transition probability matrices, esti mated with a one-year transition interval. (Experi mentation showed that these were the ones most accurately representing the message from the stochastic kernels. ) Across the 140 Europe-wide NUTS2s, the pic ture that emerges from the stochastic kernel and transition probabilty analysis simply repeats the earlier lesson: there is great stability and persis tence in these regional income distributions. Not much can be observed to change. The message alters interestingly, however, when we turn to the finer NUTS3 disaggregates. Across all 119 Cohesion economies, the domi nant feature in Fig. 7. c and Fig. 7. c. c is persis- 94 Section II — Models of Explicit Distribution Dynamics tence. Tendency towards cohesion is not appar ent. Table 3. cu shows an implied ergodic distrib ution that is weighted more towards the relatively poor. The Cohesion economies do not show a dynamic tendency towards cohesion: if anything, there will be Increasingly more that are poor rela tive to the (weighted) average. For Greece, all of Fig. 7. el, Fig. 7. el. c, and Table 3. el. u repeat the optimistic economic message from earlier. The ridge in the stochastic kernel is twisted counter-clockwise; the ergodic distribu tion in the transition probability matrix is weighted towards the rich relative to the (population- weighted) average. Greece shows dynamic ten dencies towards cohesion, and more in it can be expect to be relatively better off over time. In Spain, the stochastic kernel in Fig. 7. es and Fig. 7. es. c shows a counterclockwise distortion in the ridge mostly at the extremes; that distor tion occurs more at the upper extreme than at the lower. This says that there exist dynamics to wards cohesion, with the average (showing a tendency for) catching up with the very rich. However, while that is happening, the relatively poor do not climb towards the average enough. Table 3. es. u still shows the ergodic distribution weighted more towards the relatively poor. From Fig. 7. pt and Fig. 7. pt. c, Portuguese NUTS3S show tendencies away from cohesion, and towards twin-peaks dynamics. However, the upper peak is imprecisely estimated —note the predominant white space on it. As earlier de scribed in a footnote, this means that few obser vations were actually made there, and the preci sion of the estimate is low. Indeed, Table 3. pt. u shows that It is the lower peak that dominates: the ergodic distribution is weighted towards the relatively poor, and more strongly than in the oth er Cohesion economies. The Spain and Portugal combined NUTS3s give the strongest evidence for emerging twin peaks. The stochastic kernel in Fig. 7. ep and Fig. 7. ep. c shows a pronounced twin peaks along the 45- degree line. It is evident, however, from Fig. 7. ep that it is the lower peak that dominates. Table 3. ep. u shows weighting in the ergodic distribu-. tion towards the relatively poor, although not to the extent as seen for Portugal alone. Recall again that Spanish per capita income levels have been about double those of Portugal. Thus, while not all those relatively poor in the ergodic distrib ution represent only Portuguese NUTS3s, both Portugal's average income relative to Spain's, and its own internal dynamics suggest that Por tuguese NUTS3s do account for most of that lower part of that ergodic distribution. Finally, turn France and Italy in Fig. 7. fr, Fig. 7. fr. c, Fig. 7. it, and Fig. 7. it. c. The most striking obser vation here is the polarization emerging in Italy, a feature that had been already suggested by the earlier findings, although less obviously. For France, on the other hand, we see that the mea sured increasing inequality is due primarily to a small set of leading regions. The bulk of the re gional distribution actually has seen high cohe sion. Mobility and dynamics 95 4, Conclusion This paper has studied the empirics on cohesion across the Cohesion economies. It concludes that cohesion has been highest in Greece, lowest in Portugal, and intermediate in Spain. This char acterization holds across a range of ways of as sessing cohesion. It holds for both static and dy namic considerations. growing only roughly in step with overall growth. But in France and the UK this increase in inequal ity is due primarily to only a small number of lead ing regions; Italy, on the other hand, shows an emerging polarization, even if its overall measures of regional cohesion do not increase dramatically through time. The ranking is reversed for Cohesion nation- state's aggregate growth performances: Portugal has grown fastest, Spain slightly slower, and Greece some way behind. In levels, Spain has had the highest per capita income—on average double that of Portugal's. Greece began the 1980s slightly ahead of Portugal, but fell behind the latter soon after that. In the world, the cross-section of countries has shown a tendency towards polarization—a clus tering of the rich separating from a clustering of the poor—or, alternatively, emerging twin peaks. While the Cohesion economies do not show such polarization, the relative gap between rich and poor here has increased faster than has that across countries in the world. Our parallel study of the 140 Europe-wide NUTS2S provides an interesting methodological lesson: most of the interesting changes across Europe are simply hidden at gross levels of dis aggregation. This becomes especially clear when individual non-Cohesion EU member states are studied: the UK shows the greatest increasing re gional disparity, with that in France and Italy One immediate lesson from this is that regional disaggregates down to only Europe-wide, NUTS2 level do not reveal interesting intricate dy namics in regional income distributions. Those richer dynamics emerge only at either Europe- wide NUTS3 level, or by concentrating on what happens within each member state. For the lat ter, however, the small number of observations disallows further more elaborate analysis. A more serious study of convergence and regional devel opments across Europe will benefit greatly from finer levels of disaggregation than is currently available. In developing the empirical regularities in the Co hesion and European data, this paper has Intro duced a number of technical devices useful for studying income distribution dynamics: snapshot pictures of densities through time; inter-quartile ranges and standard deviations; Tukey boxplots; cross-profile plots; and transition probability ma trices, stochastic kernels, and ergodic distribu tions. The sequel to this paper (Quah [24]) builds on these ideas to consider what might explain — and potentially alter—these observed patterns of cohesion. Conclusion 97 References 1] Barro, Robert J. and Sala-i-Martin, Xavier. (1991), "Convergence Across States and Regions", Brookings Papers on Economic Activity, 1:107-182, April. [2] Bean, Charles R. (1997), "The Impact of Cohesion Fund Spending on Regional Output and Employ ment in the Presence of Interregional Spillovers", Working paper, CEP, March. [3] Blanchard, Olivier Jean and Katz, Lawrence F. (1992), "Regional Evolutions", Brookings Papers on Economic Activity, 1:1 -75, April. [4] Carlino, Gerald A. and Mills, Leonard, (1993), "Are US Regional Incomes Converging? A Time Se ries Analysis", Journal of Monetary Economics, 32(2):335-346, November. [5] Cleveland, William S. (1993), Visualizing Data, Hobart Press, Summit NJ, USA. [6] de la Fuente, Angel and Vives, Xavier. (1995), "Infrastructure and Education as Instruments of Re gional Policy: Evidence from Spain", Economic Policy, (20): 13-51, April. [7] Decressin, Jörg and Fatás, Antonio. (1995), "Regional Labor Market Dynamics in Europe", Euro pean Economic Review, 39(9): 1627-1655, December. [8] Desdoigts, Alain. Changes in the World Income Distribution: À NonParametric Approach to Chal lenge the Neoclassical Convergence Argument. PhD thesis, European University Institute, Florence, June 1994. [9] Dolado, Juan J. , González-Páramo, José Manuel, and Roldan, José Maria. (1994), "Convergencia Económica Entre las Provincias Españolas: Evidencia Empírica (1955-1989)", Moneda y Crédito, (198):81-119. [10] Friedman, Milton. (1992), "Do Old Fallacies Ever Die?", Journal of Economic Literature, 30(4):2129- 2132, December. [11] Hart, Peter E. (1995), "Galtonian Regression Across Countries and the Convergence of Productivi ty", Oxford Bulletin of Economics and Statistics, 57(3):287-293, August. [12] Lamo, Ana R. Cross-section Distribution Dynamics. PhD thesis, LSE, February 1996. [13] Magrini, Stefano. (1995), "Income Disparities among European Regions", Working paper, Geogra phy Department, LSE, London, November. References 99 [14] Neven, Damien J. and Gouyette, Claudine. (1994), "Regional Convergence in the European Com munity", Discussion Paper 914, CEPR, London, February. [15] Pissarides, Christopher A. and Wasmer, Etienne. (1997), "The Impact of Cohesion Fund Spending: Regional Labour Market Issues", Working paper, CEP, April. [16] Quah, Danny. (1993), "Empirical Cross-Section Dynamics in Economic Growth", European Eco nomic Review, 37(2/3):426-434, April. [17] Quah, Danny. (1993), "Galton's Fallacy and Tests of the Convergence Hypothesis", The Scandina vian Journal of Economics, 95(4):427-443, December. [18] Quah, Danny. (1996), "Convergence Empirics Across Economies with (Some) Capital Mobility", Journal of Economic Growth, 1(1):95-124, March. [19] Quah, Danny. (1996), "Empirics for Economic Growth and Convergence", European Economic Re view, 40(6): 1353-1375, June. [20] Quah, Danny. (1996), "Regional Convergence Clusters across Europe", European Economic Review, 40(3-5):951-958, April. [21] Quah, Danny. (1996), "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics", Economic Journal, 106(437): 1045-1055, July. [22] Quah, Danny. (1997), "The tsrf Reference Manual", Technical report, Economics Department, LSE, December. [23] Quah, Danny. (1997), "Empirics for Growth and Distribution: Polarization, Stratification, and Conver gence Clubs", Journal of Economic Growth, 2(1):27-59, March. [24] Quah, Danny. (1997), "Regional Cohesion from Local Isolated Actions: II. Conditioning", Working paper, Economics Department, LSE, December. [25] Quah, Danny. (1998), "Convergence as Distribution Dynamics (With or Without Growth)", in Bald win, Richard, Cohen, Daniel, Sapir, Andre, and Venables, Anthony, (eds. ), Regional Integration. Cambridge University Press, Forthcoming. [26] Sala-i-Martin, Xavier X. (1996), "Regional Cohesion: Evidence and Theories of Regional Growth and Convergence", European Economic Review, 40(6):1325-1352, June. [27] Silverman, Bernard W. (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall, New York NY 10001. [28] Singer, Burton and Spilerman, Seymour. (1976), "Some Methodological Issues in the Analysis of Longtitudinal Surveys", Annals of Economic and Social Measurement, 5:447-474. [29] Summers, Robert and Heston, Alan. (1991), "The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988", Quarterly Journal of Economics, 106(2):327-368, May. 100 Section II — Models of Explicit Distribution Dynamics Data Appendix The data used above are, except where stated to be publicly available, collected by private com mission, under the general supervision of Robert Leonardi at LSE's Economic and Social Cohesion Laboratory. The regional disaggregates used attempt to con form to Eurostat nomenclature of statistical terri torial units referred to as NUTS (pronounced as spelt). These territorial units, in principle, partition into successive, strict refinements: thus, any NUTS-1 territorial unit contains an integral number of NUTS-2 units each of which, in turn, contains an integral number of NUTS-3 units, and so on. To gain a rough idea of the degree of regional disintegration analyzed in the text, it is useful to note some further NUTS facts. In 1992 Commis sion terminology, NUTS-1 units were also called European Community Regions; NUTS-2 units, Basic Administrative Units; and NUTS-3 units, Subdivisions of Basic Administrative Units. Within each member state, however, terminology dif fered. France, Italy, and Greece referred to NUTS-2 units as regions. By contrast the UK called NUTS-1 units regions —consistent with Commission usage —while Ireland called its NUTS-3 units regions. Greece calls its NUTS-3 units nomi (singular nomos); Spain, districts; and Portugal, provinces. In the text, I have used the term location, or NUTS3 to refer to these. The term economy, by contrast, is used for NUTS3 locations, countries, or any other coherent eco nomic unit, without ambiguity. When I refer to Europe-wide NUTS2 economies above, the data are from Eurostat, and comprise regional disaggregates in the 12 European Com munity member states: Belgium, Denmark, Ger many, Greece, Spain, France, Ireland, Italy, Lux embourg, the Netherlands, and the UK. For Bel gium, I used all 9 NUTS2s. For Germany, I used 31 NUTS2s: data were available for none of the formerly East German NUTS2 disaggregates. For Greece, Spain, and Italy—Greece and Spain are two of the four Cohesion economies also investi gated using NUTS3 data-1 used all 13, 18, and 20 NUTS2 disaggregates. This study has not been able to obtain disaggregate Irish data NUTS3 levels. According to Eurostat, no NUTS2 disaggregates are defined for Ireland. Thus, for the Europe-wide analysis, I used observations on all of Ireland. For Denmark, by contrast, Eurostat does define NUTS2 disaggregates. However, no data were available on them, and so I have omit ted Denmark altogether from the study. Of the 26 NUTS2 disaggregates in France, none of the four overseas departments have made any data avail able. I have thus confined analysis to the 22 NUTS2, noting further that Corse has no Income data available before 1982. The Grand Duchy of Luxembourg is treated as a NUTS2 disaggregate for the purposes here. Of the 12 NUTS2S in the Netherlands, t h r e e- Overijssel, Gelderland, and Flevoland —have in come data only from 1986. I confined the analysis, therefore, to the 9 remaining disag gregates. Portugal is another Cohesion econo my, studied using our NUTS3 disaggregate da ta: in the Europe-wide analysis, I would have used all its 7 NUTS2s. However, two of these— Data Appendix 101 Acores and Madeira—had no data available, so that the study used only the 5 remaining NUTS2S. Finally, the UK has 35 NUTS2 disaggregates in the Eurostat definition. However, for all of these, data were missing for 1975, 1976, 1978, 1980, 1982, 1983, 1985, and 1986. Thus, I used the 11 NUTSIs instead: for the purposes here, grouping them with the other 129 NUTS2s already de scribed above. It is these 140 locations that I refer to as European or Europe-wide in the text. For the Europe-wide analysis, I use GDP per in habitant measured in PPS (purchasing power standard), as defined by Eurostat. These units are comparable to ECUs, with a slight correction. Turn now to the even more finely-disaggregated analysis. Greece has 51 NUTS3 economies; Spain, 50; Portugal 18. The specific NUTS-3 lo cations used were: Greece Aitoloakarnania, Attiki, Boiotia, Euboia, Eurutania, Fthiotida, Fokida, Argolida, Arkadia, Achaia, Heia, Korinthia, Lakonia, Messinia, Zakynthos, Kerkyra, Kefallinia, Leukada, Arta, Thesprotia, loannina, Prebeza, Karditsa, Larisa, Magnisia, Trikala, Grebena, Drama, Imathia, Thes saloniki, Kavala, Kastoria, Kilkis, Kozani, Pella, Pieria, Serres, Florina, Xalkidiki, Evros, Xanthi, Rodopi, Dodekanisa, Kyklades, Lesvos, Samos, Chios, Irak- leio, Lasithi, Rethumno, Chania Spain Almería, Cadiz, Cordoba, Granada, Huelva, Jaén, Malaga, Sevilla, Huesca, Teruel, Zaragoza, Asturias, Baleares, Las Palmas, Tenerife, Cantabria, Avila, Burgos, Leon, Palencia, Salamanca, Segovia, Soria, Valladolid, Zamora, Al bacete, Ciudad Real, Cuenca, Guadala jara, Toledo, Barcelona, Gerona, Lérida, Tarragona, Alicante, Castellón, Valencia, Badajoz, Cáceres, La Coruna, Lugo, Orense, Pontevedra, Madrid, Murcia, Navarra, Alava, Guipúzcoa, Vizcaya, La Rioja Portugal Aveiro, Beja, Braga, Bragança, Castelo Branco, Coimbra, Evora, Faro, Guarda, Leiria, Lisboa, Portalegre, Porto, Santarém, Setúbal, Viana Do Castelo, Vila Real, Viseu For Spain, NUTS3 income data had been collect ed as GDP per inhabitant in ECUs. For Greece and Portugal, on the other hand, NUTS3 income data were collected in drachma and escudos, re spectively, at current prices. I used Eurostat's an nual ECU/local currency exchange rates. For Greece, census data provided NUTS3 population figures for 1971, 1981, and 1991 ; the local Greek data team estimated corresponding figures for the intervening years. In Portugal, data on resi dent population were available at NUTS3 level. For Spain I used total employed population to proxy the total population—to the extent that re gional unemployment rates varied significantly over time, some of the calculations above might be misleading. We can assess the magnitude of that error from the following. I can calculate, us ing the weights implied by NUTS3 employed population rather than the correct weights im plied by (the unobserved) NUTS3 population, av erage per capita GDP in Spain; data on average per capita GDP are, however, directly available and so can be compared with my calculated numbers. My calculations for this national aver age give 4100 ECUs in 1980, 4680 ECUs in 1983, 6180 ECUs in 1986, and 9020 ECUs in 1989. The direct measures, instead, are 4070 ECUs in 1980, 4630 ECUs in 1983, 6090 ECUs in 1986, and 8880 ECUs in 1989. As expected, my numbers are biased upwards; the errors are 0. 73% in 1980, 1. 07% in 1983, 1. 46% in 1986, and 1. 55% in 1989. Thus, there is evidence that the approximation is only imperfect, and deterio rating over time—it is, however, not egregiously bad. Moreover, to the extent that different regions are affected in the same way by this approxima tion, the cross-Spain calculations will show a smaller margin of error. To produce Fig. 2, I downloaded longitude and ( U R L ): latitude data from the nameserver h t tp : / / w w w. d m a. g o v / g n s / h t m l/ on the US Government Department of Defense Mapping Agency's Web page. The Summers-Heston data on cross-country comparisons were described in Summers and Heston [29]. Updates to the data since then have been distributed on the World Wide Web (e. g. , (URL): h t tp : / /www. nber. h a r v a r d. edu/). The per capita income figures I used above were those for real GDP per capita in constant dollars, chain indexed and expressed in international prices, base 1985 (series RGDPCH). 102 Section II — Models of Explicit Distribution Dynamics All textual and logical information used above were first encoded in p e rl scripts. Another p e rl program read that information, and wrote out segments of tsrf code. The author's tsrf econometrics shell interpreted these ma- chinewritten segments together with other tsrf code written by a human (the author) to then generate all the calculations and graphs in the paper. This shell figures prominently in the analy- sis above. A 130-page manual for the shell is available as Quah [22]; all the C and bison code—close to 3Mbyt. es—for it is available from the author's Web page (URL on the cover page above), or alternatively from h t t p : / / e c o n. l s e. a c. u k/ d q u a h / d / t s r f /. Data Appendix 103 TABLE 1. W: Cross-country income distributions* (105 economies, relative to world per capita income) Weighted Average Median Bottom quartile /Median Top Quartile /Median Inter-quartile Range 1961 1970 1980 1988 2. 35 3. 10 3. 73 4. 16 0. 65 0. 63 0. 77 0. 67 0. 60 0. 57 0. 39 0. 42 2. 11 2. 26 2. 22 2. 52 0. 99 1. 07 1. 41 1. 42 1. 00 1. 03 1. 08 1. 17 ' The symbol σ denotes standard deviation. The "weighted average" column is in thousands of 1985 US dollars; the median, the interquartile range, and σ are measured as fractions of the world's per capita income. TABLE 1. E12: Europe-wide NUTS2 income distributions* (140 NUTS2S, Thousand PPSs) Weighted Average 6. 36 8. 42 10. 76 13. 46 1980 1983 1986 1989 Bottom quartile /Median Top Quartile /Median Inter-quartile Range 5. 82 7. 97 10. 25 12. 69 0. 79 0. 80 0. 75 0. 79 1. 20 1. 16 1. 16 1. 16 2. 36 2. 87 4. 14 4. 60 σ 1. 82 2. 47 3. 09 3. 65 * The symbol σ denotes standard deviation. Unlike in Table 1. w, here the columns under weighted average, median, interquartile range, and aare all In thousands of PPSs. TABLE 1. C: Cohesion income distributions* (119 NUTS3S, Thousand ECUs) Weighted Average Median Bottom quartile /Median Top Quartile /Median Inter-quartile Range 1980 1983 1986 1989 3. 06 3. 70 4. 49 6. 30 2. 80 3. 70 3. 94 4. 93 0. 77 0. 79 0. 80 0. 78 1. 31 1. 18 1. 38 1. 57 1. 51 1. 44 2. 28 3. 90 1. 12 1. 20 1. 72 2. 73 ' The symbol σ denotes standard deviation. Unlike in Table 1. w, here the columns under weighted average, median, interquartile range, and aare all in thousands of ECUs. 1 04 Section II — Models of Explicit Distribution Dynamics TABLE 1. EL: Greek NUTS3 income distributions* (51 NUTS3S, Thousand ECUs) Weighted Average Median Bottom quartile /Median Top Quartile /Median Inter-quartile Range 1980 1983 1986 1989 2. 66 3. 56 3. 56 4. 35 2. 32 3. 39 3. 35 4. 19 ' See notes under Table 1. c. 0. 92 0. 86 0. 92 0. 85 1. 15 1. 12 1. 13 1. 11 0. 53 0. 88 0. 72 1. 11 0. 57 0. 76 0. 64 0. 83 TABLE 1. ES: Spanish NUTS3 income distributions* (50 NUTS3S, Thousand ECUs) Weighted Average Median Bottom quartile /Median Top Quartile /Median Inter-quartile Range 1980 1983 1986 1989 4. 10 4. 68 6. 18 9. 02 3. 94 4. 47 5. 87 8. 17 0. 85 0. 84 0. 80 0. 85 1. 19 1. 15 1. 16 1. 23 1. 35 1. 39 2. 06 3. 14 * See notes under Table 1. c. σ 0. 85 1. 06 1. 43 2. 04 TABLE 1. PT: Portuguese NUTS3 income distributions* 18 NUTS3S, Thousand ECUs) Weighted Average 2. 17 2. 72 3. 52 4. 86 1980 1983 1986 1989 * See notes under Table 1. c. Bottom quartile /Median Top Quartile /Median Inter-quartile Range 1. 83 2. 23 2. 29 2. 64 0. 67 0. 71 0. 83 0. 94 1. 11 1. 08 1. 32 1. 70 0. 80 0. 81 1. 12 2. 01 0. 53 0. 66 1. 08 1. 70 Tables 105 TABLE 1. EP Spanish/Portuguese NUTS3 income (68 NUTS3S, Thousand ECUs) distributions* Weighted Average Median Bottom quartile /Median Top Quartile /Median Inter-quartile Range 1980 1983 1986 1989 3. 24 3. 78 4. 94 7. 21 3. 43 3. 90 4. 92 7. 33 0. 72 0. 72 0. 80 0. 73 1. 30 1. 28 1. 27 1. 25 1. 99 2. 18 2. 32 3. 82 1. 25 1. 41 1. 96 2. 92 * See notes under Table 1. c. TABLE 1. FR: French NUTS2 income distributions* (22 NUTS2S, Thousand ECUs) Weighted Average 7. 42 9. 71 12. 14 15. 02 1980 1983 1986 1989 * See notes under Table 1. c. Bottom quartile /Median Top Quartile /Median Inter-quartile Range 6. 42 8. 47 10. 51 13. 07 0. 90 0. 94 0. 95 0. 94 1. 06 1. 08 1. 08 1. 06 0. 98 1. 18 1. 43 1. 59 0. 97 1. 37 1. 78 2. 26 TABLE 1. IT: Italian NUTS2 income distributions* (20 NUTS2S, Thousand ECUs) Weighted Average 6. 38 8. 57 11. 03 13. 86 Median 6. 68 8. 86 11. 29 13. 90 1980 1983 1986 1989 * See notes under Table 1 c. Bottom quartile /Median Top Quartile /Median nter-quartile Range 0. 68 0. 68 0. 68 0. 70 1. 09 1. 09 1. 12 1. 14 2. 72 3. 64 4. 94 6. 12 1. 50 1. 94 2. 64 3. 39 TABLE 1. UK: UK NUTS1 income distributions* (11 NUTS1S, Thousand ECUs) Weighted Average 6. 03 8. 33 10. 88 13. 77 Median 5. 58 7. 72 10. 10 12. 52 1980 1983 1986 1989 * See notes under Table 1. ( Bottom quartile /Median Top Quartile /Median Inter-quartile Range 0. 96 0. 95 0. 92 0. 94 1. 03 1. 03 1. 02 1. 04 0. 39 0. 63 1. 05 1. 24 0. 58 0. 81 1. 11 1. 53 106 Section II — Models of Explicit Distribution Dynamics TABLE 2. W: World cross-profile dynamics* (105 economies, relative to world per capita income) Slope 0. 028 0. 031 0. 031 0. 032 1961 1970 1980 1988 e10* 1. 32 1. 36 1. 36 1. 37 serCorr -0. 017 -0. 523 -0. 530 -0. 583 2V a r tn 0. 055 0. 489 0. 822 1. 168 r If Slope is x, then "being 10 economies richer" means having income that is e'°* times higher; this ratio is also given in Next, s e r C o rr is the firstorder "serial" correlation coecient between "first-differences" in the cross-profile (taking the tion as sequential in the given ordering), this need not be positive, even at the beginning of the analysis. Finally, 2Var mean square "change" in those "f rst-differences" (again, "change" Indicating sequentially in the cross section). the Table, cross sec- tn is the TABLE 2. E12: European cross-profile dynamics* (140 NUTS2S, relative to Europe-wide per capita income) S l o pe 0. 008 0. 008 0. 008 0. 012 1982 1983 1986 1989 e,a* 1. 08 1. 08 1. 08 1. 07 s e r C o rr 0. 427 - 0. 0 98 -0. 576 -0. 406 0. 020 0. 053 0. 140 0. 153 See notes under Table 2,w. This table begins at 1982 rather than 1980 because of missing observations for Corse in France. TABLE 2. C (119NUTS3S, : Cohesion cross-profile dynamics* relative to Cohesion per capita income) Slope 0. 011 0. 009 0. 011 0. 012 1980 1983 1986 1989 * See notes under Table 2. w. e1Q* 1. 12 1. 09 1. 12 1. 13 serCorr 2V a r tn 0. 463 -0. 483 -0. 426 -0. 456 0. 021 0. 281 0. 319 0. 420 Tables 107 TABLE 2. EL. Greek cross-profile dynamics* (51 NUTS3s, relative to Greek per capita income) Slope 0. 012 0. 010 0. 008 0. 009 1980 1983 1986 1989 * See notes under Table 2. w. e,Q* 1. 13 1. 10 1. 08 1. 09 serCorr -'. 'aren 0. 295 -0. 523 -0. 494 0. 498 0. 040 0. 351 0. 275 0. 323 TABLE 2. ES. Spanish cross-profile dynamics* (50 NUTS3S, relative to Spanish per capita income) Slope 0. 014 0. 015 0. 015 0. 015 1980 1983 1986 1989 * See notes under Table 2. w. e'°* 1. 15 1. 16 1. 16 1. 16 serCorr -vartn 0. 177 -0. 442 -0. 542 -0. 534 0. 026 0. 152 0. 246 0. 246 TABLE 2. PT. Portuguese cross-profile dynamics* (18 NUTS3s, relative to Portuguese per capita income) Slope 0. 054 0. 051 0. 051 0. 056 1980 1983 1986 1989 * See notes under Table 2. w. e,a* 1. 72 1. 66 1. 66 1. 75 serCorr -". "art n 0. 460 -0. 525 -0. 653 -0. 788 0. 053 0. 195 0. 661 0. 885 TABLE 2. EP. Spanish/Portuguese cross-profile dynamics* (68 NUTS3s, relative to Es/Pt per capita income) Slope 0. 021 0. 020 0. 021 0. 023 1980 1983 1986 1989 * See notes under Table 2. w. e,Q* 1. 23 1. 22 1. 23 1. 26 serCorr •Varen 0. 477 -0. 529 -0. 643 -0. 734 0. 030 0. 177 0. 405 0. 495 108 Section II — Models of Explicit Distribution Dynamics TABLE 3. W. P. Cross-country income dynamics* (105 economies, relative to world per capita income, 1961-1988) Grid. (0,1/4,1/2,1,2, 4,oo) 1/4 0. 94 0. 06 1/2 0. 06 0. 89 0. 04 (Number) (470) (620) (733) (416) (553) (43) 0. 05 0. 92 0. 05 Ergodic 0. 16 0. 16 0. 19 Upper Endpoint: 1 2 4 0= 0. 04 0. 94 0. 01 0. 16 0. 02 0. 99 0. 02 0. 30 0. 98 0. 02 The table shows transition dynamics over a single-year horizon. The cells are arrayed In increasing order, so that the lower right- hand portion of the table shows transitions from the rich to the rich. The numbers in parentheses in the rightmost column are the number of economy/year pairs beginning in a particular cell. Cells showing 0 to two decimal places are left blank; rows might not add to 1 because of rounding. TABLE 3. W. U. Cross-country income dynamics* (105 economies, relative to world per capita income, 1961-1988) Grid. (0. 00, 0. 25, 0. 43, 0. 70,1. 08, 2. 52, «,) Upper Endpoint: 0. 70 1. 08 2. 52 „ 0. 25 0. 94 0. 08 0. 43 0. 06 0. 90 0. 04 (Number) (467) (474) (475) (475) (474) (470) 0. 02 0. 91 0. 05 Ergodic 0. 21 0. 16 0. 10 0. 06 0. 90 0. 03 0. 11 0. 05 0. 94 0. 01 0. 15 0. 03 0. 99 0. 27 * See notes under Table 3. w. p. This table differs only In that the grid is automatically chosen to give an (almost) uniform rightmost column. Tables 109 TABLE 3. C. P. Cohesion income dynamics* (119 NUTS3S, relative to Cohesion average per capita income 1980-1990) Grid. (0,1/2, 3/4,1,5/4, 3/2, <*>) 1/2 0. 96 0. 05 3/4 0. 04 0. 82 0. 17 (Number) ( 77) (273) (325) (243) (136) (136) Ergodic 0. 27 0. 22 t See notes under Table 3,w. p. Upper Endpoint: 1 5/4 3/2 0. 12 0. 73 0. 14 0. 01 0. 18 0. 01 0. 10 0. 80 0. 08 0. 13 0. 07 0. 84 0. 08 0. 10 0. 08 0. 91 0. 09 TABLE 3. C. U. Cohesion income dynamics* (119 NUTS3S, relative to Cohesion average per capita income ,1980-1990) Grid. (0. 00, 0. 63, 0. 77, 0. 92,1. 09,1. 38, °°) Upper Endpoint: (Number) (179) (197) (213) (209) (198) (194) 0. 63 0. 92 0. 19 0. 77 0. 07 0. 63 0. 24 0. 01 0. 92 0. 01 0. 16 0. 61 0. 19 Ergodic 0. 38 0. 16 0. 13 1. 09 1. 38 0. 02 0. 14 0. 67 0. 13 0. 01 0. 11 0. 01 0. 12 0. 78 0. 09 0. 11 0. 09 0. 90 0. 10 * See notes under Table 3. w. p column. This table differs only in that the grid is automatically chosen to give ar (almost) uniform rightmost TABLE 3. E12. European income dynamics* (140 NUTS2S, relative to Europe-wide average per capita income, 1980-1989) Grid. (0. 00, 0. 64, 0. 87, 0. 95,1. 05,1. 17, °°) Upper Endpoint: (Number) (247) (232) (231) (227) (233) (228) 0. 64 0. 91 0. 03 0. 87 0. 02 0. 91 0. 07 0. 95 0. 02 0. 07 0. 81 0. 11 Ergodic 0. 05 0. 18 0. 23 1. 05 0. 05 0. 12 0. 84 0. 08 0. 27 1. 17 0. 04 0. 86 0. 08 0. 15 0. 06 0. 92 0. 12 ι See notes under Table 3. w. p. This table differs only in that the grid is automatically chosen to give an (almost) uniform rightmost column. 110 Section II — Models of Explicit Distribution Dynamics TABLE 3. EL. Greek income dynamics* (51 NUTS3s, relative to Greek average per capita income, Grid. (0. 00, 0. 81, 0. 88, 0. 95, 1. 03,1. 12,oo) 1980-1990) (Number) (85) (87) (87) (83) (85) (83) 0. 81 0. 66 0. 21 0. 06 0. 88 0. 28 0. 45 0. 17 0. 06 Ergodic 0. 09 0. 11 Upper Endpoint: 0. 95 0. 05 0. 26 0. 44 0. 19 0. 04 0. 14 1. 03 0. 01 0. 07 0. 25 0. 57 0. 16 0. 02 0. 20 1. 12 oo 0. 07 0. 17 0. 55 0. 22 0. 21 0. 01 0. 01 0. 01 0. 25 0. 76 0. 24 * See notes under Table 3. w. p. This table differs only in that the grid is automatically chosen to give an (almost) uniform rightmost column. TABLE 3. ES. Spanish income dynamics* 50 NUTS3S, relative to Spanish average per capita income, 1980-1990) Grid. (0. 00, 0. 74, 0. 83, 0. 94,1. 06,1. 21, oo) Upper Endpoint: 0. 94 1. 06 1. 21 0. 74 0. 90 0. 14 0. 83 0. 10 0. 67 0. 23 (Number) (82) (83) (82) (86) (84) (83) 0. 18 0. 66 0. 16 Ergodic 0. 33 0. 22 0. 17 0. 11 0. 70 0. 19 0. 01 0. 12 0. 14 0. 69 0. 11 0. 08 0. 12 0. 88 0. 08 f See notes under Table 3. w. p. This table differs only in that the grid is automatically chosen to give an (almost) uniform rightmost column. TABLE 3. PT. Portuguese income dynamics* (18 NUTS3S, relative to Portuguese average per capita income, 1980-1990) Grid. (0. 00, 0. 53, 0. 58, 0. 76, 0. 86,1. 03, oo) Upper Endpoint: (Number) (28) (29) (31) (32) 0. 03 (30) Ergodic 0. 53 0. 79 0. 31 0. 06 0. 20 0. 41 0. 58 0. 18 0. 55 0. 19 0. 06 0. 63 0. 24 0. 76 0. 04 0. 14 0. 68 0. 09 0. 13 0. 17 0. 86 1. 03 0. 06 0. 66 0. 06 0. 19(30) 0. 10 0. 05 0. 90 0. 06 ι See notes under Table 3. w. p This table differs only in that the grid is automatically chosen to give an (almost) uniform rightmost column. Tables 111 TABLE 3. EP. Spanish/Portuguese income dynamics* (68 NUTS3S, relative to Es/Pt average per capita income, 19801990) Grid. (0. 00, 0. 60, 0. 90,1. 04,1. 22,1. 43, oo) Upper Endpoint: (Number) 0. 60 0. 90 1. 04 1. 22 1. 43 (113) (112) (114) (110) (118) (113) 0. 93 0. 07 0. 08 0. 80 0. 15 0. 12 0. 72 0. 13 0. 18 0. 72 Ergodic 0. 28 0. 25 0. 19 0. 14 0. 15 0. 01 0. 10 0. 76 0. 08 0. 12 0. 87 0. 09 0. 06 ' See notes under Table 3. w. p. This table differs only in that the grid is automatically chosen to give Ï an (almost) uniform rightmost column. TABLE 3. FR. French income dynamics* (22 NUTS2S, relative to Europewide average per capita income, 19801990) Grid. (0. 00, 0. 91, 0. 96, 1. 00,1. 04, 1. 11, oo) Upper Endpoint: (Number) 0. 91 0. 96 1. 00 1. 04 1. 11 (33) (39) (35) (36) (38) (37) 0. 91 0. 09 0. 18 0. 69 0. 17 0. 13 0. 71 0. 11 0. 22 0. 72 0. 16 Ergodic 0. 46 0. 23 0. 17 0. 09 0. 06 0. 79 0. 05 0. 11 0. 89 0. 03 0. 02 ι See notes under Table 3. w. p. This table differs only n that the grid is automatically chosen to give an (almost) uniform rightmost column. TABLE 3. IT. Italian income dynamics* (20 NUTS2s, relative to Europewide average per capita income, 19801990) Grid. (0. 00, 0. 70, 0. 78,1. 08, 1. 16,1. 20,oo) Upper Endpoint: 1. 08 1. 16 1. 20 oo 0. 70 0. 85 0. 18 0. 78 0. 15 0. 76 0. 06 (Number) (33) (34) (34) (35) (32) (32) 0. 06 0. 88 0. 03 Ergodic 0. 11 0. 10 0. 10 0. 06 0. 77 0. 16 0. 20 0. 20 0. 78 0. 06 0. 25 0. 06 0. 94 0. 25 ' See notes under Table 3. w. p. This table differs only n that the grid is automatically chosen to give an (almost) uniform rightmost column. 1 12 Section II — Models of Explicit Distribution Dynamics Fig. 1 : Regional spatial distribution dynamics per capita Income Region j physical geography Figures 113 Fig. 2. el: Greek regional (spatial) dynamics 1980:1 1983:1 1986:1 1989: ! H) ^ 20 lon9'tode f f 114 Section II — Models of Explicit Distribution Dynamics Fig. 2. es: Spanish regional (spatial) dynamics 1980:1 1983:1 f Hi ! Ui 1986:1 1989:1 Figures 115 Fig. 2. pt: Portuguese regional (spatial) dynamics 1980:1 1983:1 f TJ Ij V) S ^ ^ S. ^ t o öe 1986:1 1 989:1 f V) 9 \ ° o ^ - 'de V^. &8 o n>de 116 Section II — Models of Explicit Distribution Dynamics Fig. 2. ep: Combined Spain/Portugal regional (spatial) dynamics 1980:1 1983:1 f li Vi 1986:1 1 9 8 9 :1 6" : ¡ t u de Figures 117 Fig. 3: Emerging twin peaks increasing incomes income distributions t + s time 118 Section II — Models of Explicit Distribution Dynamics Fig. 4. w: Densities of relative (per capita) Incomes across 105 countries (b): 1970 (c): 1980 0 2 4 6 (d): 1988 Figures 119 Fig. 4. E12: Densities of (per capita) incomes across 140 Europe-wide NUTS2s 20 30 20 30 (a): 1980 (b): 1983 10 20 30 (c): 1986 10 (d): 1989 20 30 120 Section II — Models of Explicit Distribution Dynamics Fig. 4. c: Densities of (per capita) incomes across 119 Cohesion NUTS3s (a): 1980 0 5 (b): 1983 10 15 20 10 15 20 (c): 1986 (d): 1989 Figures 121 Fig. 4. el: Densities of (per capita) incomes across Greek NUTS3s 0 2 4 (a): 1980 6 8 10 (b): 1983 (c): 1986 2 0 4 (d): 1989 6 8 10 122 Section II — Models of Explicit Distribution Dynamics Fig. 4. es: Densities of (per capita) incomes across Spanish NUTS3s 0 5 10 15 20 0 5 10 15 20 (a): 1980 (b): 1983 0 5 10 15 20 0 5 10 IS 20 (c): 1986 (d): 1989 Figures 123 Fig. 4. pt: Densities of (per capita) incomes across Portuguese NUTS3s 0 2 4 6 (a): 1980 0 2 4 (b): 1983 6 4 0 2 (c): 1986 68 10 12 0 2 46 (d): 1989 124 Section II — Models of Explicit Distribution Dynamics Fig. 4. ep: Densities of (per capita) Incomes across Spanish/Portuguese NUTS3s 0 5 10 15 20 0 5 10 15 20 (a): 1980 (b): 1983 0 5 10 15 20 0 5 10 15 20 (c): 1986 (d): 1989 Figures 125 Fig. 4. fr: Densities of (per capita) incomes across French NUTS2s 10 20 JO 40 (a): 1980 10 (b): 1983 20 30 40 0. 12 0. 10 0. 08 - - 0. 06 0. 04 0. 02 / \ / \ - - 0. 12 0. 10 0. 08 0. 06 0. 04 0. 02 /\ / Χ 10 (c): 1986 20 30 40 10 (d): 1989 20 30 40 126 Section II — Models of Explicit Distribution Dynamics Fig. 4. it: Densities of (per capita) incomes across Italian NUTS2s o to (a): 1980 0 10 (b): 1983 20 30 (c): 1986 (d): 1989 Figures 127 Fig. 5. w: Tukey boxplots, relative (per capita) incomes across 105 countries 4- 3- 1- 60 — ι— 70 80 90 1961,1970,1980,1988 128 Section II — Models of Explicit Distribution Dynamics Fig. 5. E12: Tukey boxplots, (per capita) incomes across 140 Europe-wide NUTS2s 20- 15- 10- 5- 7'8 80 82 S 86~ " Ί— 88 —ι— 90 1980,1983,1986,1989 Figures 129 Fig. 5. c: Tukey boxplots, (per capita) incomes across 119 Cohesion NUTS3s I 1 ι ι * ί t * i * * * * t 14- 12- 10- 8- 6- 4- 2- L 8 0 7 8 J ι 82 ι 84 8 6 88 ι 90 1980,1983,1986,1989 130 Section II — Models of Explicit Distribution Dynamics Fig. 5. el: Tukey boxplots, (per capita) incomes across Greek NUTS3s J I I I I L 5- 3- —ι— 80 78 —ι 82 1— 84 —ι— 86 ~ ~ ]— 88 ~90~ 1980,1983,1986,1989 Figures 131 Fig. 5. es: Tukey boxplots, (per capita) incomes across Spanish NUTS3s J I I L 14- 12- 10- 6- 4- 78 80 82 84 86 88 90~ 1980,1983,1986,1989 132 Section II — Models of Explicit Distribution Dynamics Fig. 5. pt: Tukey boxplots, (per capita) incomes across Portuguese NUTS3s J I I I I L 8- 6- 4- 78 —ι 80 1 82 1 84 1 86 Γ 88 90 1980,1983,1986,1989 Figures 133 Fig. 5. ep: Tukey boxplots, (per capita) incomes across Spanish/Portuguese NUTS3s 1 1 1 1 , i 14- 12- 10- 8- 6- 4- 2- 7 8 8 0 1 82 I 84 6 8 88 90 1980,1983,1986,1989 134 Section II — Models of Explicit Distribution Dynamics Fig. 5. fr: Tukey boxplots, (per capita) incomes across French NUTS2s 20- 1980,1983,1986,1989 Figures 135 Fig. 5. it: Tukey boxplots, (per capita) incomes across Italian NUTS2s 15- 10- 5- 78 —ι 80 1 82 1 84 1 86 1— 88 90 1980,1983,1986,1989 136 Section II — Models of Explicit Distribution Dynamics Fig. 5. uk: Tukey boxplots, (per capita) incomes across UK NUTS1 s l i l i lí * 16- 14- 12- 10- 8- * : 3 J [ * l 78 80 82 84 86 88 90 i l * Γ i lí 1980,1983,1986,1989 Figures 137 Fig. 6. w: Cross profile dynamics across 105 Countries upwards: 1961, 1970, 1980, 1988 138 Section II — Models of Explicit Distribution Dynamics Fig. 6. E12: Cross profile dynamics across 140 Europe-wide NUTS2s 20 40 60 80 100 120 140 upwards: 1982, 1983, 1986, 1989 Figures 139 Fig. 6. c: Cross profile dynamics across 119 NUTS3s 20 40 60 80 100 upwards: 1980, 1983, 1986, 1989 140 Section II — Models of Explicit Distribution Dynamics Fig. 6. el: Cross profile dynamics across Greek NUTS3s 10 20 30 40 50 upwards: 1961, 1970, 1980, 1988 Figures 141 Fig. 6. es: Cross profile dynamics across Spanish NUTS3s 10 20 30 40 50 upwards: 1961, 1970, 1980, 1988 142 Section II — Models of Explicit Distribution Dynamics Fig. 6. pt: Cross profile dynamics across Portuguese NUTS3s 5 10 15 upwards: 1961, 1970, 1980, 1988 Figures 143 Fig. 6. ep: Cross profile dynamics across Spanish/Portuguese NUTS3s 20 40 60 upwards: 1961, 1970, 1980, 1988 144 Section II — Models of Explicit Distribution Dynamics Fig. 7. w: Relative Income Dynamics across 105 Countries 5-year-Horizon Figures 145 Fig. 7. W. C: Relative Income Dynamics across 105 Countries 5-yearHorizon T3 O •ι—I SH CD CU 1 2 Period t + 5 3 Contour plot at levels 0. 325, 0. 475, 0. 625 146 Section II — Models of Explicit Distribution Dynamics Fig. 7. w15: Relative Income Dynamics across 105 Countries 15-yearHorizon Figures 147 Fig. 7. W. C15: Relative Income Dynamics across 105 Countries 15yearHorizon O •r-H S-, P L, 1 2 3 Period ¿+ 15 Contour plot at levels 0. 2, 0. 35, 0. 5 148 Section II — Models of Explicit Distribution Dynamics Fig. 7. E12: Relative Income Dynamics across 140 Europe-wide NUTS2s 5-year-Horizon 0·° p en( Figures 149 Fig. 7. E12. C: Relative Income Dynamics across 140 Europewide NUTS2s 5-year-Horizon 1. 4  J ^y^ i / ■40 O •rH u CD Cu 1. 2 1. 0 0. 8 0. 6 / / / / / / / / / / / // / / / / / / / / / / - /ι ι ι / Ι ι /l I 1 1 1 1 I , , , I , , , 1 , , ," 0. 6 0. 8 1. 0 1. 2 1. 4 Period ¿ + 5 Contour plot at levels 0. 5, 1. 5, 2. 0 150 Section II — Models of Explicit Distribution Dynamics Fig. 7. c: Relative Income Dynamics across 119 NUTS3s 5-year-Horizon r ^. 6 ° p V >d Figures 151 Fig. 7. C. C: Relative Income Dynamics across 119 NUTS3s 5-year-Horizon / // 1 ~ / / y ^ / ~ ~ ~\ / / - 1. 6 - 1. 4 - 1. 2 • t —t o s-, cu 1. 0 - / / / // // / 0. 8 - 0. 6 i / f / //y - - - / \ ι K 1/ l/ 1 I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0. 6 0. 8 1. 0 1. 2 Period t + 5 1. 4 1. 6 Contour plot at levels 0. 7, 0. 9, 1. 1 152 Section II — Models of Explicit Distribution Dynamics Fig. 7. el: Relative Income Dynamics across Greek NUTS3s 5-year-Horizon 0. 8 U-Pe r i( Figures 153 Fig. 7. el. c: Relative Income Dynamics across Greek NUTS3s 5-year-Horizon 0. 8 0. 9 1. 0 1. 1 P e r i od t + 5 1. 2 1. 3 Contour plot at levels 0. 50, 1. 50, 2. 00 154 Section II — Models of Explicit Distribution Dynamics Fig. 7. es: Relative Income Dynamics across Spanish NUTS3s 5-yearHorizon Figures 155 Fig. 7. es. c: Relative Income Dynamics across Spanish NUTS3s 5-year-Horizon T3 O • i—l 5-1 CD CU 0. 8 1. 0 Period t + 5 1. 2 Contour plot at levels 1. 50, 1. 75, 2. 00 156 Section II — Models of Explicit Distribution Dynamics Fig. 7. pt: Relative Income Dynamics across Portuguese NUTS3s 5-year-Horizon Figures 157 Fig. 7. pt. c: Relative Income Dynamics across Portuguese NUTS3s 5-yearHorizon 0. 6 0. 8 1. 0 1. 2 1. 4 Period έ + 5 Contour plot at levels 0. 50, 0. 75, 1. 00 158 Section II — Models of Explicit Distribution Dynamics Fig. 7. ep: Relative Income Dynamics across Spanish/Portuguese NUTS3s 5-yearHorizon 4 0·6 pen°( 0· Figures 159 Fig. 7. ep. c: Relative Income Dynamics across Spanish/Portuguese NUTS3s 5-yearHorizon 0. 4 0. 6 0. 8 1. 0 Period ¿ + 5 1. 2 1. 4 1. 6 Contour plot at levels 0. 50, 1. 00, 1. 50 160 Section II — Models of Explicit Distribution Dynamics Fig. 7. fr: Relative Income Dynamics across French NUTS2s 5-year-Horizon Figures 161 Fig. 7. fr. c: Relative Income Dynamics across French NUTS2s 5-yearHorizon T3 O 'u, CD CU 1. 0 1. 2 P e r i od t + 5 1. 4. 6 Contour plot at levels 0. 50, 1. 00, 1. 50 162 Section II — Models of Explicit Distribution Dynamics Fig. 7. it: Relative Income Dynamics across Italian NUTS2s 5-year-Horizon Figures 163 Fig. 7. it. c: Relative Income Dynamics across Italian NUTS2s 5-year-Horizon 0. 8 1. 0 1. 2 P e r i od t + 5 Contour plot at levels 0. 50, 1. 00, 1. 50 164 Section II — Models of Explicit Distribution Dynamics Β. REGIONAL COHESION FROM LOCAL ISOLATED ACTIONS CONDITIONING 1. Introduction Patterns of growth and convergence across the world and across the Cohesion economies Greece, Spain, (Ireland,) and Portugal have changed through time. A previous paper Quah [14] documented that over the 1980s: (vil) The emerging twinpeaks property—polariza tion into a twotier (or, in general, multitier) grouping —is observed across the world's cross section of countries. It does not occur, however, across the Cohesion economies. (i) The collection of Cohesion NUTS3s has grown more unequal; that increase In unequality has occurred at a rate faster than that seen across the world's countries. 1 (¡i) While Greece has grown slowest in aggregate, its NUTS3S have shown the greatest static and dynamic cohesion. (iii) Portugal and Spain have, in aggregate, individ ually grown at relatively high rates; Spain having started with average per capita in come already double that in Portugal, has re mained about twice as rich as its neighbour. (¡v) Spain's regional inequalities have kept pace with its aggregate growth; Portugal's have increased more than proportionally. (v) Greek average per capita income, initially high er than that of Portugal's, rapidly fell behind the latter. (vi) If the trend were to continue, the crossCohe sion NUTS3 income distribution will progres sively be skewed towards the relatively poor. The terminology I use here and the underlying data are also de scribed in detail in that paper. (viii) The emerging twinpeaks property also does not occur across Europe as a whole. In stead, the situation across Europe Is remark ably stable and persistent: one observes nei ther marked changes in the external shape of the distributions nor great intradistribution mobility. However, that the interesting dy namic features in the Cohesion economies are not observed in Europe as a whole might be due simply to their being hidden except at fine levels of disaggregation. (ix) Reinforcing this last point, regional distribution dynamics within specific non Cohesion EU member states showed marked differences. While gross measures of regional inequalities across France and Italy are roughly compara ble and those for the UK somewhat higher, the sources of these and of patterns of in equality dynamics across these nonCohesion EU member states differ. France and the UK highlight the strong performance of a small number of leading regions; Italy shows the pronounced pattern of twinpeaks polarization seen also across countries in the world. This paper evaluates a number of alternative ex planations for these observations. Because the objects to be explained are (income) distributions and how they evolve over time, standard econo metric techniques need not directly apply. Introduction 165 Moreover, among the possible mechanisms I wish to study are spillovers across elements in the income distribution, where those spillovers may change in character through time—as trans portation infrastructures and communication pos sibilities change. 1 The principal contribution of this paper is to point the way forwards, to where more research along these lines will provide useful insight. Neverthe less, some concrete results are already available below. The guiding principle in this paper's analy sis has been to clarify the distribution dynamics of regional incomes. Doing so allows an overall picture not easily obtained when the analysis fo cuses on fine details. By the same token, howev er, knowledge about some fine details will be un available in this approach. Thus, for example, while the conditioning schemes developed here contain some econom ic structure, such structure is minimal. The pro jections presented below for conditioning on public and private investment cannot carry a di 1 Other work relevant for this are, e. g. , Brock and Durlauf [3] and Roehner [15]. Although the underlying motivations are similar, the details and approaches there differ from what I use below. Traditional statistical research on spatial processes, e. g. , Cliff and Ord [5], often ignore dynamics, which are critical in the current work. rect structural interpretation: but they do, correct ly, generate the appropriate conditional distribu tions. Thus, one can perform simple dynamic simulations based on historical patterns of invest ment. For instance, we will see that both public and private investment have played some role in income's dynamic evolution. The strongest ef fects for Greece have come from private invest ment in individual regions. The strongest effects for Spain have come from both individual region private investment and, interestingly, public (pro ductive) investment in neighbouring regions. The way the analysis has been performed here concentrates on the regional distributional dimen sion to an extent that aggregate national econo my outcomes can be assessed only with a great deal of imprecision. Statistically, this is because the modelling has left few unconstrained degrees of freedom for understanding aggregate dynam ics. Combining those aggregate concerns with the distributional ones studied below would be of great interest, but will have to be left for future work. The remainder of this paper is organized as fol lows. Section 2 develops the conceptual ideas underlying the analysis. Section 3 illustrates em pirical application on real-world economies. Sec tion 4 then briefly concludes. 166 Section II — Models of Explicit Distribution Dynamics 2. Conditioning and explaining distribution dynamics Explaining distribution dynamics is conceptually the same as analyzing the effects of conditioning. In conventional regression analysis, the re searcher asks if a variable Ζ explains the variable Y (when X is already in the regression) by examin ing whether the two conditional expectations E(Y | X,Z) and E(Y | Z) differ. When these expecta tions are linear, this is equivalent to asking If in E(Y | X,Z) = ßX+yZ the regression coeficiente γ equal zero. There is no reason, however, why the researcher should be interested only in equality between the conditional expectations Ely \ X, Z) and Ely \ Z). More generally, the researcher might wish to in vestigate equality between the conditional distrib utions of By | XT) and E{Y | X). When, further, X is taken to be null, then the researcher is studying the relation between the conditional distribution (that in V | Z) and the unconditional distribution (that in V). Were interest to lie only in whether Y \ Ζ and Y have the same distributions, then standard statis tical approaches that examine equality between two distributions can shed useful light. Here, however, I ask not just whether V | Ζ and Y have the same distributions; I wish also to see how Y has been transformed into Y \ Z. In the same way, researchers studying the linear conditional ex pectation Ely | Χ,Ζ) = βΧ + γΖ ask not just if γ is zero, but also for its direction and magnitude. How one distribution (that in Y) transforms into another (that in V | Z) canbe described mathe matically by an operator mapping distributions to distributions. When that operator is the identity map, then we can say that the distributions of Y and V | Ζ are identical, and that Ζ does not ex plain Y. In such circumstances, altering Ζ does not affect the distribution of V. Note that the two distributions in V and Υ | Ζ can be identical even if the operator transforming V to V | Ζ is not the identity. (For instance, let Y have the normal distribution with mean 0 and positive variance, and let V | Ζ be 1xV. ) Thus, asking for V > Y | Ζ be the identity map is stronger than what standard statistical tests (e. g. , Kolmogorov Smirnov and related) examine for equality in dis tributions. It turns out that we have already encountered a mathematical operator that transforms distribu tions to distributions, namely the stochastic ker nel. In traditional Markov process theory, the sto chastic kernel has been used to study transitions through time—as exploited also in the earlier pa per, Quah [14]. However, there is no technical reason why it cannot serve double duty: the sto chastic kernel can model evolving distributions, and thus the effects of conditioning, not just across time but more generally. The empirical results below will repeatedly apply this insight of examining an appropriatelycon structed stochastic kernel. To build intuition, the next subsection looks at some hypothetical but simple examples of conditioning. Subsection 2. 2 develops an operational formalism—that of con ditioning schemes—that will be used for the em pirical section to follow. Conditioning and explaining distribution dynamics 167 The earlier paper Quah [14] discussed interpreta tion of different shapes in stochastic kernels. Those interpretations were what happened over time; they apply directly, however, to the current more general setup. They thus provide insight In to the effects of arbitrary conditioning on the dy namics of income distributions. problematic as it is an endogenous outcome, rather than an exogenous part of the environ ment). Finally, as the communication of economic values becomes easier—perhaps because of technical change and ongoing dematerialization (Quah [10])—physical distance might become ir relevant altogether. 2. 1 Some conditioning operations Specific examples will provide concrete intuition on the conditioning analysis below. A. Spatial dynamics First, take conditioning across space. The eco nomic idea is simple: spillovers occur across economies that are physically close to each oth er. With Lugo, Asturias, and Cantabria being clustered together—and physically contiguous— in the north of Spain, do developments in one of them lead to parallel developments in another? Or the opposite, so that improving infrastructure in, for instance, Cantabria draws economic activi ty into it and away from Asturia? How rapidly do any such spatial spillovers occur? A closelyrelated idea is that these spillovers might be localized to political or administrative entitles. Thus, developments in Badajoz might have spillover effects on Cáceres because both of them happen to be part of the Extremadura NUTS2 of Spain, but not with any of the other abutting NUTS3s—Huelva, Sevilla, or Cordoba (in the Andalucía NUTS2, although still in Spain); or Beja, Evora, or Portalegre (in Portugal). Com plications arise, moreover, when a single NUTS3 is divided between different NUTS2s: e. g. , Se túbal between Lisboa e Vale do Tejo and Alente jo, or Viseu between Norte and Centro in Portu gal. A third idea is that the notion of physical close ness might not at all be the right notion of close ness for considering spillovers. Two NUTS3s might abut one another, but if transportation be tween them is dicult while transportation to a noncontiguous third—Madrid, say—is easier be cause highways exist around the latter but not between the former, then it is that economic dis tance that is relevant, not physical distance. Thus, volume of trade between economies might better measure closeness (although this too is Such dynamic spatial effects can be studied as follows. Consider the artificial examples given in Fig. 1. They illustrate the dispersion across space of economic activity. Here, there is only a 1di mensional geography depicted on the horizontal axis, while economic activity is measured by Y on the vertical axis. Locations s0, s,, through s5— representative of many other locations in this hy pothetical example—have per capita incomes in them given by the heights of the respective points vertically above them. I have also drawn ¡n a horizontal line denoting the average level of economic activity across all locations. For conve nience, I will take this average to equal 1. Take first Fig. 1. a. The income distribution across economies is a twopoint distribution with one half at one height Y0, and onehalf at the other YV Suppose that over time the spatial distribution just shifts horizontally, i. e. , s0 at time period f takes value V0 when r is even and V, when f is odd. What emerges then is a picture of alternate rises and falls in per capita income across neigh boring locations. Suppose the researcher hypothesizes, incorrect ly, that spillovers across neighbors are positive, i. e, one's income is close to one's neighbors' in comes. In the example, of course, reality is the opposite. But nevertheless, on this guess, the re searcher proceeds by asking how taking an economy's income relative to the average of its immediate neighbors changes the distribution of Y. If spillovers were positive, this would move every economy's income to just the crosssec tional average: the income distribution across economies would collapse to just a single point at the average. Thus, the mapping from the origi nal distribution in Vto the conditional one in Y \ Ζ takes the twopoint distribution on {Y0, V·,} into the degenerate distribution on (ΥΛ+Υ0)/2 = 1. If the spillovers were positive but not complete, then the conditioning mapping takes the original twopoint distribution only to something more concentrated about 1, not to a distribution entire ly on 1. 168 Section II — Models of Explicit Distribution Dynamics What the researcher observes, however, is the opposite, as illustrated in Fig. 1. a. Conditioning across immediate neighbours in the way just de scribed actually pulls apart the distribution — shown as downwards and upwards movements in the representative points initially at (s2, YQ) and (s3, ΥΊ). Thus the mapping from Y to Y | Z—the latter being the conditional that is incorrectly con structed by the researcher—gives a resulting dis tribution even more unequal than the original. The researcher discovers from this that spillovers are actually negative across physical neighbours in the data. Suppose, on the other hand, the researcher were working with data generated as in Fig. 1. t, where uctuations through time take the form of clock wise and counterclockwise rotations of the data about the fixed point (s2, Y2). As before, Y2 the average equals 1. Here, the ratio of (sy, Yj) relative to the average of its two physical neighbours is always unity. The distribution of the researcher- constructed conditional Y \ Ζ is, thus, now de generate on the point 1. The researcher con cludes correctly that spillovers are positive across physical neighbors. B. Convergence-club dynamics Fig. 2 shows yet different dynamics, intended now to illustrate the behaviour of convergence clubs. 1 The horizontal axis denotes time and the vertical axis income Y. The points vertically aligned show the incomes at a given time period of a cross section of economies $. In Fig. 2. 1 the cross section converges over time: cohesion improves across the entire cross sec tion. By contrast, in Fig. 2. 2 the cross section po a nd %. The disparity larizes into two clusters <€0 between the poor club %0 and the rich club % Increases over time while, simultaneously, cohe sion within each of the clubs improves. Except for the lack of intra-distribution crossings, the picture emerging from such a scenario is exactly the twin-peaks dynamics described in Quah [11]. This example can thus also be viewed as giving, in general, a multltier or stratified cross section of economies. Quah [13] describes how member ship in such convergence clubs might be en dogenously determined through economic con siderations. Convergence clubs had been studied in Baumöl [1] and DeLong [6]. More recently, Quah (9, 13, 11, 12] has related them to "emerging twinpeaks" dynamics. How can conditioning help a researcher under stand the emerging twin peaks here? In Fig. 2. 2 the researcher would find that taking the ratio of an economy's income to the average of its fellow club members' would remove the twin-peaks feature from the income distribution dynamics. The resulting income dynamics would then look exactly as in Fig. 2. 1. The pattern of polarization is therefore understood as working through club membership. In more general specifications, club memberships could change through time; indi vidual economies might work on getting into bet ter clubs; convergence clubs could start up, dis solve, and reconstitute in altered form. The intu ition just discussed, however, would remain: con ditioning on fellow club members explains the observed dynamic pattern of stratification. In Fig. 2, unlike in Fig. 1, what matters for club membership is completely unrelated to spatial distance. Instead what matters might be separa tion in levels of development, one's trading part ners (e. g. , Ben-David [2] or Quah [12]), or sophis tication of technological practice (e. g. , Quah [13]). Finding the natural set of associated economies for conditioning is then more subtle than just looking at physically neighbouring economies. C. Summary The examples above are highly artificial, but that is intentional, for it makes precise what condition ing for distribution dynamics is, and how it mat ters. It is the operator mapping Y to V | Ζ that gives insight for understanding the nature of spillovers across space, time, or even more gen erally. Some conceptual generalizations are immediate. When transportation costs vary across economies or patterns of trade change, the hori zontal axis in Fig. 1 might need to be replaced or augmented by some notion of relevant economic distance. When it is not only an economy's im mediate neighbours that matter, the researcher needs to study conditioning subsets more com plex than just "the neighbors one on each side" as naively depicted in Fig. 1. When one member of the conditioning subset matters more than others, developments in that one economy should be weighted more heavily in constructing the conditioning information. Taking equally weighted local averages, after all, is just a special case of kernel smoothing in nonparametric esti Conditioning and explaining distribution dynamics 169 matlon. When transportation infrastructures change over time, both the conditioning subset's members and the weighting used in a condition ing operation might need to vary correspondingly. (ii) %(?) a subset of $, and (iii) ßj/r) a set of probability weights on $, The range of possible conditioning operations that map Y > Y \ Ζ is large. Thus, the range of possible explanations we can consider for ob served distribution dynamics is correspondingly extensive. Within that range, however, a number of features are important. Improvements within an economy, other things equal, should affect its own income: thus the weight assigned itself in a conditioning operation —perhaps with a time lag—should matter. Improvements across partic ular configurations of economies should affect the strength of interaction across the relevant subset of economies: thus the conditioning oper ation should allow such actions to affect cross economy spillovers. The next section describes a simple but exible way of narrowing the focus while maintaining the prominence of the features described above. It is this method that is subsequently investigated in the empirical section. one such triple for each / in ¿£ and each f. Subset %(?) is the collection of economies associated with / at time f: for convenience, I will refer to these as coalitions, clubs, or groupings. In the examples of Fig. 1, %{f) is ( M; /+1} for all f. In more general situations, ^ ( f) will change over time. In Fig. 2, it is whichever of ^0 or ^, the economy is in at time r. By probability weights in cj,(f) I mean simply a col lection of nonnegative numbers that sum to 1. I require further that given %(f), weights GJ,(f) can be positive only on ^,(Γ) (alternatively, given weights GStf)· define %(£) to be that subset of $ getting positive weights in G7,(f)). Thus GJ,(f) de cides the relative importance of different economies in %(f) for the distinguished economy / at time r. Finally, r,(f) is the lag in time: it indi cates the delay with which developments in the associated economies in ^/f) affect /,(?), as medi ated through the weights G7,(f). Since τ/lf) can be a positive constant, I's associated economies ^,(ί) can include / itself. 2. 2 Conditioning schemes The presentation here will be technical for effi ciency in presenting the ideas used below. How ever, to follow the empirical discussions to follow, readers can skip this subsection if they are willing to extrapolate (carefully) from intuition previously developed above. The conditioning schemes considered in this pa per all build on taking weighted averages. Ex tending to more general possibilities is conceptu ally straightforward, if potentially arduous. Denote the entire set of economies under con sideration by $. A subset of $ will be indicated by % C $; different economies in <€ will be indexed by / in %. Time proceeds as f = 0, 1, 2 De note per capita income in economy / at time t by //(f); denote its conditional version by Vj(f). Write Y and / to denote the collections of all Y,(f)'s and Yi[t)'s respectively. A conditioning scheme © is a collection of triples: (i) T/(f) an integer, Sometimes, it will be convenient to use a scaled version of the probability weights ωβ), i. e. , just a collection of non-negative numbers with nonzero sum. I will denote such a collection by ω,(ΐ). The probability weights fi7,(f) can always be construct ed from an ω,(ί), so referring to the latter is with out loss. A conditioning scheme 3 can depend on sample information, and so is in general random. As de fined above, such a scheme is not as tight as it could be. There is, for instance, redundancy in the information contained in %{t) once a>,{t) or C7,(f) is given. However, this exibility will make eco nomic description more straightforward: some times it will be easier just to give coft); other times, it will be easier to describe ct>,(f) taking %(f) as fixed. (For instance, one can just say let cotf) be investment-output ratios or populations across different economies, and not repeat that there is normalization by the cross-section average. ) The lag τ,(ί) is taken to be a scalar integer. In gen eral, of course, different elements in %(?) could af fect / with different delay, so that r,(f) couldthen- have the same cardinality as C7,(f). Such an exten sion is conceptually easy, but exploring its added 170 Section II — Models of Explicit Distribution Dynamics insights will have to be left for future work. More over, typically, r,(f) will be just a positive constant. Since r is written as a function of / and t, clearly, %(ί) and öT,(f) can, in general, vary with the lag as well. Following the analyses surrounding Fig. 1 and Fig. 2, say that the conditioning scheme δ for Y implies the conditional version / by Y,(t)^(Y,(t),Yi(t)). (1) where Y,(t)= ]T aj¡(t)Yj(tT,(t)), (2) y ¡n VM and φ: U2 > IR is a function that is allowed to vary with what the researcher wishes to model. In the current work, the function φ is naturally tak en to be the ratio of its first argument to its sec ond: then V | S comprises per capita incomes relative to one's neighbours, appropriately weight ed. (If equation (2) is replaced on its righthand side by the exponential of the conditional expec tation of Y,{t) conditioned on information set g, then Yi(t) is just the exponential of the expecta tions error log(V/f))  log(Vfc) b Yffì) = log(V,(f)) E (logVffl) I S). ) When <β,(ί) = { / - 1; /+1} for all f and ®,{t) is {1/2,1/2}, equations (1) and (2) give the condi tional version of Y calculated for the spatial ex ample in Fig. 1. When %{t) is <€0 or % in Fig. 2, depending on which club the economy / is in at time f, and αφ) is all 1 's, then equations (1 ) and (2) give the conditional version of Y described for the convergence-club example there. To develop more intuition, it is useful to provide explicit examples of alternate conditioning schemes 3. Fix τ,(ί) = τ <0; take %(f) = {/}, i. e. , just the economy itself; define coff) = {1 on %(ί) and 0 elsewhere}; and let φ equal its second ar gument. Then the operator mapping Y —> / is just the usual Markov stochastic kernel for -r-period transitions. The next example generalizes Fig. 1 to a more re alistic situation. Let φ be the ratio; fix r,(f) = 0; take %(f) = % (0) to be the set of economies physically contiguous with / (excluding / itself); and let co,(t) be the set of population sizes at time f - T,(f) in each of the economies in %(0). Then b Yi(t) is the per capita income in all contiguous economies abutting on /; ?,{t) is per capita income in / relative to that in the surrounding economies. Graphically, this describes the relative variation in heights in a spatial plot of per capita incomes across economies (e. g. , Fig. 2 in Quah [14]). The operator mapping Y -> e /describes how much of that variation is explained by spatial agglomer ation. Taking τ/ί) to be a negative integer rather than zero allows this spatial agglomeration to oc cur with a lag. A conditioning scheme © can also be used to describe trade blocs across economies, whether those blocs be explicitly designed or left only im plicit. Again, let φ be the ratio, and let r,(f) = (f-T) for Ta given fixed date, which might be set to the beginning, middle, or end of the sample. Take %(f) to be the top η trading partners with econo my / at time f-r,(f) = Τ as defined by imports (or exports or exports plus imports). Then define a>i(t) to be the shares of the economies of ω,(ί) in I's trade accounts, again as defined by imports (or exports or exports plus imports). The operator mapping Y -> /then describes the importance of trade in bringing about convergence or cohesion across economies. 1 The lag r,(f) can also be set, not to give a con stant difference in f-T,(f), but itself to be a con stant. Then, when / trades more with economy j in %(f), the weight accorded j in equation (2) cor respondingly rises. If previously; did not figure as a significant trading partner, but has since risen to be one, then both % and ω, will evolve through time—% to admit economy j, and ω, to adjust the weight applying to j. As one final perturbation in this trading-bloc example, one could also let %(ί) be not I's top η trading partners but instead that group of top trading partners such together their total share in I's trade accounts exceeds fraction ƒ· Above, I have already permitted weights ω,(ί) to vary with sample information when I constructed those weights from population sizes. One can al so take cü)(f) to be, say, investment-output ratios, so that the conditional version of Y is now de fined by relative investments. ' Quah [12] has presented an analysis of world cross-country growth along precisely these lines. Conditioning and explaining distribution dynamics 171 Communication or transporation across particu lar elements of the cross section also fall readily in our framework. Suppose, for instance, that 77,(1") measures the number of telephone lines in / at time f. Suppose, further, that one wants to see if such communication channels facilitate cohe sion. Take %(Γ) to be $ for all / and f, and let they th entry of coff) be i7,(f)1/2 χ r/,(f)1/2. Different conditioning schemes can be com bined, A rich range of auxiliary information can be used to determine the weights tuff). Finally, in all the examples above, the researcher can also es timate coecients (e. g. , the 1/2 exponent in the telephone lines example), rather than impose them a priori. Finally, one might be interested in conditioning schemes where the elements of the crosssec tion distribution need have not obvious, immedi atly observable relation. As an example, consider when one is interested in the distribution dynam ics of the nonCohesion European economies, conditional on hypothesized changes in the distri bution dynamics of the Cohesion economies. Sure, some nonCohesion regions are contigu ous with some Cohesion ones, but many are not. Then it is natural for the researcher to hypothe size that the two distinct blocs should be related based on historical comovements: the grouping % for each nonCohesion / can then be con structed by looking at those Cohesion economies that, in the past, have been most highly correlated (both negatively and positively) with /. Both negative and positive correlations have to be considered as it might be exactly the diverging or growing apart of different regions that is critical. It is this Idea that will be used be low to analyze the impact of Cohesion changes on the nonCohesion European economies. While the approach is general, circumspection ¡s called for in coming up with alternative definitions of groupings and linkages across regions. A use ful rigorous formulation derives from using an ab stract notion of distance to define neighbor hoods, groupings, and coalitions: simply consti tute neighbourhoods from all those economies "close together" in the appropriate distance con cept. Concrete examples of this would be when a researcher studies regional economies that are contiguous one with the other, or considers those economies that high volumes of trade Interlink, but not others. The researcher defines coalitions C I to comprise those elements in a space that fall within a particular topological neighbourhood of/. While this formulation helps clarify the logic of the ideas here, not all the natural groupings that econ omists use can be easily accommodated. For in stance, the grouping defined by "those stochastic processes most strongly correlated with each oth er"—a concept close to that just described earli er—need not be a neighborhood ¡n a metric space. This is because correlation (or covariance) is not a monotone transformation of the metric im plied by the covariance inner product, even among zeromean stochastic processes having fi nite second moments. Nevertheless, the "strongest correlations" idea is a natural one for many economic applications, and we use it below. 172 Section II — Models of Explicit Distribution Dynamics 3. Empirical results I now apply the theoretical ideas of the previous section to explaining observed patterns of growth and convergence. The empirical analyses I un dertake here are simple and restrictive; despite this, however, we will see that they already pro vide much information. More elaborate Investiga tion is deferred to subsequent work. First, consider economies across the world. From the discussion in Quah [14], we have seen that the prominent feature in cross-country income distributions is an emerging twin peaks. Explain ing that feature is, in the current perspective, equivalent to obtaining a conditional version of per capita incomes Y such that that emerging twin-peaks characteristic goes away. Fig. 3 shows the results here of spatial condition ing: I calculate the conditional version of V by tak ing its ratio relative to the population-weighted average over geographically contiguous neigh bors. Fig. 3 gives, in order, the sequence of (con ditioned) income distributions over time; the cor responding sequence of Tukey box plots; and fi nally the stochastic kernel mapping unconditional to spatiallyconditioned distributions. Fig. 3. d—the sequence of densities—shows that the "emerg ing twin peaks" property is no longer present. Fig. 3. b, the sequence of Tukey boxplots, shows that outliers in the cross section remain—a num ber of economies are inordinately rich relative to their physical neighbors—but most of the income distribution is now tightly packed together be tween the top and bottom quartiles. Moreover, that interquartile range continues to decline over time. The stochastic kernel in Fig. 3. s shows dramati cally the change from unconditional to spatially- conditioned distributions. Although varying in height, the principal ridge in this figure lies parallel to the axis marked "Original". Thus, spatial condi tioning has twisted the kernel counter-clockwise to an extent where most of the inequality has been explained away. Fig. 4 considers conditioning not across space, but across trading partners. 1 Comparing the ex panse of tradeand spatially-conditioned distribu tions, we see that trade is the stronger factor ex plaining observed cross-country income distribu tion dynamics: the remaining outliers are much smaller in magnitude. Although details differ from the spatially-conditioned kernel, the transforming stochastic kernel in Fig. 4. s again shows the strong counter-clockwise twist away from the 45- degree diagonal. The prominent ridge rises and falls, but lies parallel to the "Original" axis. Turn to the situation for Europe. 2 Fig. 5 considers conditioning across space. First, Fig. 5. d pre sents snapshot plots of income densities across the 140 NUTS2 economies. Although the distrib ution appears a little skewed to the right, the bulk of the density seems centered symmetrically on the average of unity. The boxplots in Fig. 5. b make this particularly clear: upper and lower out- ' The weights used were trade shares (exports plus Imports) of the top trading partners such that their total exceeded 50% In 1994. The underlying trade data were obtained from the IMF's Direction of Trade Statistics. 2 As in Quah [14], Europe refers to NUTS2 economies from 12 Euro pean Community member states; the Data Appendix there provides more details. Empirical results 173 liers exist here, but the 25th to 75th percentiles are located close to the mean. Lower and upper adjacent values are compactly situated at within 0. 5 and 1. 5 times average income levels. The transforming stochastic kernel Fig. 5. s shows the now-familiar counterclockwise twist away from the 45-degree diagonal. Except at very high-in come levels—where NUTS2s still stand out from their physical neighbors —European NUTS2s have their economic performance well-explained by those around them. Spatial spillovers matter a great deal across Europe. Turn now to the Cohesion economies: Fig. 6 through to Fig. 8 analyze spatial conditioning, i. e. , % is the group of physically contiguous locations. The outstanding feature across all three is how the transforming stochastic kernels in Fig. 6. s, Fig. 7. S, Fig. 8. s, again all twist counter-ciockwise in all the Cohesion economies. The effect is par ticularly pronounced for Spain, where the kernel is almost parallel to the "Original" axis. Portugal, however, again appears to show the least tendency towards cohesion. The boxplots Fig. 8. b show that even after spatial conditioning, the dynamic tendency towards increasing in equality remains present. The transforming sto chastic kernel here Fig. 8. s shows a slight clock wise reversal-rather than counter-clockwise—on the very highest parts of the income distribution, reinforcing the interpretation just given for the boxplots. For the non-Cohesion EU member states of France and Italy, the importance of spatial condi tioning varies. (Again, for the UK I have been able to obtain data for too few regional disaggregates for this analysis to be reliable. ) In France, the per formance of physical neighbours shows little spillover effect where regions have become most unequal. The small set of leading regions do not seem to have their economic performance carry over to the physically surrounding areas. By con trast, Italy's convergence dynamics are strongly in uenced by spatial spillovers. The stochastic kernel in Fig. 10. s, in particular, shows that al most the entire emergingpolarization features can be attributed to regional spillover dynamics. A further natural possibility is to investigate spatial spillover dynamics across the Cohesion economies and then into France, Italy, and the UK—just as in the Europe-wide study above, but here focusing only on selected economies. More over, the idea of spillovers from Cohesion spend ing into non-Cohesion member states is itself ap pealing and interesting. However, such a study is sensible only when one looks at the entire physi cal geography in the EU, incorporating simultane ously all the regions in between—only then would the experiment be likely to give accurate an swers. The analysis here, where I have looked at individual economies, reveals instead the inherent dynamic spillover possibilities within the respec tive member states, and thus gives some guid ance on the likelihood of overall spillovers, but without using an artificial configuration of Cohe sion and non-Cohesion economies together. The issue is suciently interesting and important, however, that I have investigated an alternative mechanism for these spillover dynamics from the Cohesion economies into France, Italy, and the UK. For each non-Cohesion economy, I con struct groupings of aliated Cohesion economies based on high absolute correlations in historical growth rates between those Cohesion regions and the particular non-Cohesion one. The moti vation here is that, absent better information, the natural groupings are between those economies that have historically moved most strongly to gether or, alternatively, most strongly apart. Changes in the dynamics of the Cohesion economies in these groupings will then imply changes in the dynamics of the non Cohesion ones. This therefore allows us some Idea about the magnitude and direction of the spillover ef fects. Since it is absolute correlations that are taken, the groupings that emerge might comprise those that are positively correlated or negatively corre lated or a mixture—it is the historical data that will decide. 1 Using these endogenously determined groupings (weighted by population), I construct the distribution dynamics among the non-Cohe sion economies, conditioning on hypothetical changes in the Cohesion ones. 2 Putting this another way, there is nothing in the analysis that me chanically restricts the distribution dynamics of the non-Cohesion economies towards either higher or lower equality. I have experimented with groupings determined either by total size of grouping or by a minimum absolute correlation. Within reason, the results are Invariant across specifications: for instance, when I take the maximum grouping to be 10 Cohesion economies to each non- Cohesion economy, I get visually indistinguishable results from when I set the minimum absolute correlation to be 0. 5 (although, of course, the groupings themselves then differ). The results I give be low are for minimum absolute correlation set to 0. 5. 174 Section II — Models of Explicit Distribution Dynamics A normalization was needed here because all the non-Cohesion economies have incomes in Pur chasing Power Standard (PPS) units while the Cohesion ones are in ECUs. I used PPS data for each Cohesion member state, calculated ECU aggregate member state data from the NUTS3 economies in those same member states, and then derived the appropriate correction from the different series. I applied these corrections to the ECU data for the Cohesion economies to obtain comparable PPS per capita incomes for the Co hesion and non-Cohesion economies. Per capita incomes were then taken relative to the Europe- wide average, and it is these relative incomes that are used for the analysis. Fig. 11. sk shows the stochastic kernel describing the conditioning operation: it illustrates the change in the distributions across the non-Cohe sion economies, conditioning on the distribution dynamics in the Cohesion regions. It is striking in the Figure how the kernel twists sharply counter clockwise relative to the 45 degree line: Fig. 11. sk suggests that when the Cohesion economies tend towards greater equality among themselves and have their incomes increased, so will the non-Cohesion ones. 1 Moreover, it is the relatively poor non-Cohesion economies that benefit most from these hypothesized changes in the Cohesion economies. I turn finally to conditioning schemes that exploit measures of public and private investment. Such data are available only at NUTS2 levels of disag gregation for Greece and Spain, although Portu gal admits NUTS3 disaggregation. For Portugal, I used total private investment (from Contas Nacionas, Banco de Portugal) for the 18 NUTS3 economies from 1980 through 1991, as the measure of disaggregate private investment. Two potential measures of public investment are available. The first comprises investments by central administrative units at market prices. For these, however, observations before 1990 do not exist. The second comprises investments by mu nicipalities, again at market prices. Observations on these exist from 1979, although data for the three years 1987-1989 are missing. I chose to use the second, linearly interpolating between It is important to note that this conditioning exercise by itself does not shed light on whether, in light of contemplated policy changes, convergence will necessarily occur between the Cohesion and non- Cohesion economies: for that question, more extensive data on the relations between the groups would be needed. 1986 and 1990. What I refer to as investment be low are then these NUTS3 private and public in vestments, normalized to thousand ECUs per capita. In both Greece and Spain, private investment is not disaggregated further sectorally beyond NUTS2. For Spain, I used total productive invest ment by the public administrations as the mea sure of public investment. (Other measures are available, but this is much the largest overall. I decided—after some experimentation— that de tails might change if other measures were con sidered, but the overall picture on distribution dy namics would remain. ) All data were first convert ed to units of ECUs per capita in each NUTS2 re gion. I then apportioned investments into NUTS3 locations by population: since no other informa tion is available, the assumption here is that pub lic and private investments are done uniformly per capita within NUTS2 locations. Next, I computed conditional distributions by pro jecting log per capita GDP on log public and pri vate investments—current, lagged, and future— and measures specific to the individual region as well as population-weighted averages across physically contiguous regions. These kinds of two-sided lag distributions had previously been used for conditioning in, e. g. , Quah [9]: they clearly bear no economic interpretation, although they do produce the appropriate conditional dis tributions. Tables 1,2, and 3 show the estimated regression coefficients for Greece, Spain, and Portugal (see table notes for detailed description). A useful summary statistic in such two-sided projections is the sum of regression coecients within each bloc of regressors. In all cases, the bloc If, the lo cation-specific private investment, has a positive sum. For Greece, it is only this bloc that shows a positive sum effect. For Spain, the same bloc If shows a positive sum as well, but then l^j, the neighboring public investment, does so even more strongly. The case of Portugal is intermedi ate between Greece and Spain: the neighboring public-investment bloc l^j shows a positive sum, but with low estimated precision. Fig. 12, Fig. 13, and Fig. 14 show the results of this investment conditioning scheme for distribu tion dynamics in the three Cohesion economies. For Greece, Fig. 12. s displays the stochastic ker nel of the conditioning operation; Fig. 12. dyn Empirical results 175 shows the dynamic stochastic kernel, over a five- year horizon, of the conditional incomes data. From Fig. 12. s we see that investment condition ing helps but not a great deal for understanding Greek income distribution dynamics: the bulk of the transformation kernel remains clustered around the 45-degree line. However, turning to Fig. 12. dyn, we see that maintaining historical patterns of investment, the natural tendency for cohesion in Greece manifests. The propensity for cohesion here is strong. Spain has the opposite tendencies. Fig. 13. s shows that the kernel transforming unconditional to investment-conditioned is now largely parallel to the "Original" axis: public investment, spilling over across neighbouring regions, plays an im portant role in explaining Spanish cohesion. Fig. 13. dyn repeats the message that the Spanish economy itself has no necessarily built-in propen sity towards cohesion. It is public investment spillovers that have successfully maintained such tendencies in that economy. Portugal provides an interesting case. Invest ment, both location-specific private and neigh boring public, has had a strong effect for pro moting social cohesion: the transformation sto chastic kernel in Fig. 14. s is largely parallel to the "Original" axis. The rotation of probability mass in the stochastic kernel here is even stronger than that for Spain. The dynamics in Fig. 14. dyn shows intricate patterns: at low in come levels, investment in Portugal has quick and dramatic effects for promoting cohesion. That effect is muted as incomes rise, and then disappears after a threshold (high) level of devel opment. 176 Section II — Models of Explicit Distribution Dynamics 4, Conclusion This paper has developed an empirical procedure to assess alternative explanations for income dis tribution dynamics. The method allows one to account for the differing patterns of growth and convergence that are observed across economies. The paper finds that positive spatial spillovers ac count for a large part of income inequality dy namics across both Europe as a whole and the Cohesion economies in particular. In Europe, In general, spatial spillovers matter a lot. Across the world, both spatial location and trade relations have mattered for determining cross country income distribution dynamics: the "emerging twinpeaks" property can be explained by these. France and Italy—a couple of sample non-Cohe sion EU member states— provide a peek at the range of spatial spillover dynamics that might be possible across Europe. The patterns of regional inequalities within them differ: France shows a small set of well-performing regions pulling away from the others; Italy shows an emerging polar ization. Just as these patterns differ, so too the importance of spatial spillovers in the different economies. In France, spatial spillovers matter hardly at all, while such spillovers account for a great portion of the twinpeaked distribution dy namics in Italy. data across all the economies in Europe. Such data are not yet available: therefore, the study ex plored instead spillovers based on historical co- movements between the Cohesion and non-Co hesion regions. The results from this investigation are intriguing. Should the Cohesion economies see their incomes increase and experience higher tendencies towards greater equality, so will the non-Cohesion economies of France, Italy, and the UK experience similar outcomes. Moreover, it is the relatively poor non-Cohesion economies that will benefit most from improving conditions in the Cohesion economies. In Greece, private investment in individual regions is likely to continue its ongoing dynamic role in promoting cohesion. In Spain, the same variable has mattered, but importantly so has public pro ductive investment in neighbouring regions- spillovers matter a great deal there. The case for Portugal is intermediate between that for Greece and Spain. Here, the dynamic effects of invest ment alter Intricately at different levels of develop ment: the cohesion impact of investment is strongest at low income levels; the effect is mut ed as incomes rise, and then disappears after a threshold income level is attained. The theoretical analysis has developed an empirical methodology potentially much richer than what has just been exploited above. Extending the latter, therefore, is on the Immediate research agenda. To get an idea of the magnitude and direction of spillover dynamics from Cohesion economies to the non-Cohesion ones, the study would have benefited from complete and exhaustive regional This study has demonstrated the importance of recognizing the similarities and the differences, the possibilities and the pitfalls, of using locally-isolat ed Cohesion policies across EU member states Conclusion 177 and Cohesion economies. Member states differ in the dynamic tendencies for regional inequalities al ready embedded in existing economic structures. Decisions on where to focus subsequent policy actions need to be informed by putting together knowledge on such dynamic tendencies with clear understanding on what policy goals are most immediate. For instance, going for overall aggre gate growth in some specific Cohesion economies could do a lot to improve convergence prospects; in others, the opposite may result. Thus, this paper argues and demonstrates the importance of careful, case-by-case analysis for analyzing the effects of locally-isolated actions in the Cohesion economies. It has done so by doc umenting explicitly the intricate and subtle distrib ution dynamics across Cohesion and non-Cohe sion EU member states. It has shown the possi bility, in certain economies, of an emerging re gional polarization that also characterizes coun tries across the world. 178 Section II — Models of Explicit Distribution Dynamics Technical Appendix In this technical appendix, I describe first the use of stochastic kernels in dynamic modelling of Markov models. Then I consider how the ideas differ for modelling conditioning effects more generally (answer: hardly at all). Let F, denote the distribution of incomes across economies at time f. We seek first a probability model or econometric equation for F that de scribes Fs evolution over time. Such a model is what underlies, for instance, the stochastic kernel descriptions of transition dynamics in Quah [14, Section 3]. Take Ft as realizations of a random element in a space of income distributions. 1 The underlying state space of incomes is then the measurable space (IR, îft), i. e. , the real line IR together with the collection i)t of its Borei sets. Let B(IR, Í)?) denote the Banach space of bounded flnitelyadditive set functions on (IR, Si) endowed with total variation norm: V¿nnB(LR,3i): \μ | = s u p ^ ( / 4y) |, where the supremum in this definition is taken over all [A¡ :j = 1, 2 n) finite measurable parti tions of LR. The framework derives from Futia [7] and Stokey and Lucas [16, Ch. 8]. The mathematics here, in turn, can be found in most advanced texts on probability and functional analysis. A simple version of these ideas was first exploited for crosscountry growth empirics In Quah |8|. Empirical distributions on IR can be identified with probability measures on (IR, ?lì); those are, in turn, just countablyadditive elements in B(IR, ffi) as signing value 1 to the entire space IR. Let S3 de note the Borei σalgebra generated by the open subsets (relative to total variation norm topology) of B(IR, 3Ì). Then (B, 33) is another measurable space. Note that Β includes more than just probability measures: an arbitrary element μ in Β could be negative; p(U) need not be 1 ; and μ need not be σadditive. On the other hand, a collection of probability measures is never a linear space: that collection does not include a zero element; If λ^ and λ2 are probability measures, then λ,  λ2 and λ, + λ2 are not; neither is χλ^ a probability measure for χ e IR except at χ = 1. By contrast, the set of bounded finitelyadditive set functions certainly is a linear space, and as described above, easily given a norm and then made Banach. Why embed probability measures in a Banach space as we have done here? A first reason is so that distances can be defined between probabili ty measures; it then makes sense to talk about two measures —and their associated distribu tions— getting closer to one another. A small step from there is to define open sets of probabil ity measures, and thereby induce (Borei) σalge bras on probability measures. Such σalgebras then allow modelling random elements drawn from collections of probability measures, and thus from collections of distributions. The data of interest when modelling the dynamics of distribu Technical Appendix 179 tions are precisely random elements ;aking val ues that are probability measures. μ and ν is a mapping ΜψΜ tying: (U,m)>[0, 1]saf/s Associated with F, is a measure λ, in (B, 33). If (Ω, g, Pr) is the underlying probability space, then λ, is the value of an îsV33measurable map Λ( : (Ω, is) H> (B, B). As f evolves, the sequence {Af : r} is a Bvalued stochastic process. (i) Vy in U, the restriction Μ(μΛ/ι (y ■) is a probabil ity measure; (ii) VA in 3Î, the restriction M^M (·, A) is ^mea surable; We wish to obtain an econometric equation for λ, of the form: (iii) y A in % we have μ(Α) = ¡Μ{μν) (y A) dv(y). λ, = Τ* (λ, 1 -1 < (3) where Τ is an operator that maps the oroduct of measures together with generalized disturbances u to probability measures. (Why the * appears will be clarified below. ) Equation (3) is a stochastic difference equation, intended to correspond to the wellknown autoregression. It is exactly what we want, an econometric equation describing the evolution of the distribution of incomes across economies. Just as in autoregression analysis, one might look for those tendencies by taking repeated convolutions of 7"*, setting u to "zero": Τ*(λι+$_νθ) = Τ*(τ*(λ{+5_2,θ),θ) Τ* Τ *(τ\. (τ*(λ(,ο),ο,). ο),ο), (4) with the result being a proxy for λ(+5. Conver gence in economy incomes towards equality might be represented by (4) tending as s » °° to wards a degenerate point mass. The world parti tioning in the long run into rich and poor might be represented as (4) tending towards a twopoint measure. Stratification in the long run manifests in (4) tending towards a multimodal measure. The speed of convergence of the evolving mea sures {λ,+s : s > 1} can be found from the spec tral characteristics of the operator 7*. A wealth of Interesting questions on distribution dynamics can, therefore, be addressed in this analysis. To see why this is useful, first consider (¡ii). In an initial period, for given y, there issome fraction dv(y) of economies with incomes close to y. Count up all economies in that group who turn out to have their incomes subsequently fall in a given i)imeasurable subset A c IR. When nor malized to be a fraction of the total number of economies, this count is precisely M(y, A) (where the (μ, ν) subscript can now be deleted without loss of clarity). Fix A, weight the count Mly, A) by dvly), and sum over all possible y's, i. e. , evaluate the Integral f Mly, A) dv(y). This gives the fraction of economies that end up in state A regardless of their initial income levels. If this equals μΙ/\) for all measurable subsets A, then μ must be the measure associated with the subsequent income distribution. In other words, the stochastic kernel M is a complete description of transitions from state y to any other portion of the underlying state space IR. Conditions (i) and (ii) simply guarantee that the in terpretation of (iii) is valid. By (il), the right hand side of (iii) is welldefined as a Lebesgue integral. By (i), the right hand side of (iii) is a weighted av erage of probability measures Mly, ■), and thus is itself a probability measure. In (4) we are interested in cases where u is set to zero. Thus, without loss, redefine (3) so that u does not appear. Let b(IR, ili) be the Banach space under sup norm of bounded measurable functions on (IR, i){). Fix a stochastic kernel M and define the operator Τ mapping b(IR, ί)ΐ) to it self by To understand the structure of T, begin from the following. V/inb(R,SH),VyinR: (Tf)(y) = jf( x)M{y,dx). Stochastic kernel definition Lef μ and ν be elements of Β that are probability measures on (IR, 5){). A stochastic kernel relating Since Mly, ■) is a probability measure, the image Ti can be interpreted as a forwards conditional expectation. For example, if all economies in the cross section begin with incomes y, and we take 180 Section II — Models of Explicit Distribution Dynamics ƒ to be the identify map, then (T f)(y) = ¡ xM (y, dx) is next period's average Income ¡n the cross section, conditional on all economies having in come y in the current period. Clearly, Τ is a bounded linear operator. Denote the adjoint of Τ by T*. By Riesz Representation Theorem, the dual space of b(IR, ili) is just B(1R, ϊ)ί) (our original collection of bounded finitely ad ditive set functions on i){); thus T* is a bounded linear operator mapping B(1R, ili) to itself. It turns out that T* is also exactly the mapping in (iii) of the Stochastic Kernel Definition, i. e. , Vv probability measures in B,\/A in ί)ί : (T*v){A)=ÏM{y,A)dv(A). (This is Immediate from writing the lefthand side as Two useful implications follow: first, instead of studying M directly we can Investigate the struc ture in V. Second, this gives an underlying model for equation (3), and clarifies how exactly it is that T* carries intradistribution dynamics. Thus, for instance, T* contains strictly more information than just means and variances (say) evolving through time. What about when analyzing the effects of condi tioning more generally? Let Y be the (possibly ar tificial) random variable having distribution F, and let Y | Ζ denote the (again, possibly artificial) ran dom variable having distribution Fz. Implicit in the definition of Υ | Ζ is some kind of conditioning scheme as described for example in Section 2 above. Call the associated measures λ0 and λζ respectively. In equation (3), replace λ, on the left hand side by λ2 and λΜ on the right by λ0. The rest of the analysis above then goes through without change. {T*v)(A) = jtAd(T*v)(y) = j(T1/,)(y)dv(y) (adjoint) = ¡ïïlA(x)M(y,dx) dv [y) (definition of 7") = \M[y,Á)dv{y), (calculation) with 1„ the indicator function for A Technical Appendix 181 References [I] Baumol, William J. (1986), "Productivity Growth, Convergence, and Welfare", American Economic Review, 76(5): 1072-85, December. [2] Ben-David, Dan. (1994), "Convergence Clubs and Diverging Economies", Working Paper 922, CEPR, February. [3] Brock, William A. and Durlauf, Steven N. (1995), "Discrete Choice with Social Interactions", Working paper, University of Wisconsin, Madison, April. [4] Chamberlain, Gary. (1984), "Panel Data", in Griliches, Zvi and Intriligator, Michael D. , (eds. ), Hand book of Econometrics vol. II, chapter 22, pages 1247- 1318. Elsevier North-Holland, Amsterdam. [5] Cliff, A. D. and Ord, J. K. (1981), Spatial Processes: Models and Applications, Pion Limited, London NW2 5JN. [6] DeLong, J. Bradford. (1988), "Productivity Growth, Convergence, and Welfare: A Comment", Amer ican Economic Review, 78(5): 1138-55, December. [7] Futia, Carl. (1982), "Invariant Distributions and the Limiting Behavior of Markovian Economic Mod els", Econometrica, 50(1):377-408, January. [8] Quah, Danny. (1993), "Empirical Cross-Section Dynamics in Economic Growth", European Eco nomic Review, 37(2/3):426-434, April. [9] Quah, Danny. (1996), "Convergence Empirics Across Economies with (Some) Capital Mobility", Journal of Economic Growth, 1(1):95-124, March. [10] Quah, Danny. (1996), "The Invisible Hand and The Weightless Economy", Occasional Paper 12, Centre for Economic Performance, LSE, London, May. [II] Quah, Danny. (1996), "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics", Economic Journal, 106(437):1045-1055, July. [12] Quah, Danny. (1997), "Empirics for Growth and Distribution: Polarization, Stratification, and Conver gence Clubs", Journal of Economic Growth, 2(1):27-59, March. References 183 [13] Quah, Danny. (1997), "Ideas Determining Convergence Clubs", Working paper, Economics Depart ment, LSE, October. [14] Quah, Danny. (1997), "Regional Cohesion from Local Isolated Actions: I. Historical Outcomes", Working paper, Economics Department, LSE, December. [15] Roehner, Bertrand M. (1993), "Trade and Space-Time Correlation Functions in Dynamic Random Field Models", Working paper, Laboratoire de Physique Théorique et Hautes Energies, Université Paris. [16] Stokey, Nancy L. and (with Edward C. Prescott), Robert E. Lucas Jr. (1989), Recursive Methods in Economic Dynamics, Harvard University Press, Cambridge MA. 1 84 Section II — Models of Explicit Distribution Dynamics TABLE 1. Greece, log relative income Conditioning Regressions (Twosided Projections^ Coefficient Robust S. E. /'rj(D ¡M /TVH η' /??/(+1 ) 4(D 'S(+1) 0. 10 0. 36 0. 41 0. 15 0. 03 0. 17 0. 10 0. 48 0. 56 0. 23 0. 09 0. 17 0. 06 0. 09 0. 11 0. 14 0. 21 0. 18 0. 06 0. 11 0. 13 0. 15 0. 21 0. 18 1 Robust S. E. in the table denotes the White heteroskedasticltyconsistent standard error estimate. The regression was calculated over 612 observations (51 NUTS3 locations over 12 years from 1981 through 1992); the R2 was 12%. The conditioning vari ables in these projections are a constant and investment. The latter is denoted by /, and further delineated by superscripts (u) and (r) for public and private respectively; time shift (1) and (+1) for oneperiod lag and lead respectively; subscripts; and Í, for individual regionspecific and populationweighted average across physical neighbors. The projections are computed by ordi nary least squares. Panel data models of individual heterogeneity (e. g. , Chamberlain [4]) eschew calculating these kinds of pro jections for recovering consistent estimates of structural coeficients. Here, however, I seek only the conditional distribution, and this projection—under mild regularllty conditions—delivers exactly that. TABLE 2. Spain, log relative income Conditioning Regressions (Two-sided Projections)* Coefficient Robust S. E. /7Ή) M 'i ή' (+1) /?(-1) ή >?(+1) /ί?,(-1) 'ti /$(+1) 1% H) M '■il '#(+1) -0. 06 -0. 01 -0. 24 -0. 05 0. 06 0. 27 0. 13 0. 01 0. 16 0. 20 -0. 13 -0. 08 0. 06 0. 09 0. 06 0. 10 0. 13 0. 10 0. 06 0. 08 0. 06 0. 10 0. 15 0. 11 * Robust S. E. in the table denotes the White heteroskedasticity-consistent standard error estimate. The regression was calculated over 550 observations (50 NUTS3 locations over 11 years from 1980 through 1990); thefl2 was 41%. See also notes to Table 1. Tables 185 TABLE 3. Portugal, log relative income Conditioning Regressions (Twosided Projections)* Coefficient Robust S. E. C M) ¡(υ) 'i /7V1) /?(1) ή ή(+Λ) /f^(-1) '■6/ Æ/M) 4 Η) #,(+D 0. 16 0. 07 0. 19 0. 10 0. 16 0. 14 0. 31 0. 11 0. 32 0. 37 0. 11 0. 34 0. 14 0. 19 0. 15 0. 09 0. 13 0. 12 0. 19 0. 37 0. 24 0. 28 0. 38 0. 21 * Robust S. E. in the table denotes the White heteroskedastlcityconsistent standard error estimate. The regression was calculated over 162 observations (18 NUTS3 locations over 9 years from 1981 through 1989); the R2 was 62%. See also notes to Table 1. 1 86 Section II — Models of Explicit Distribution Dynamics Fig. 1. a: Spatial conditioning, a onedimensional geography (apart)Y y Vi Yo Average = 1 So Si S2 S3 S4 space Fig. 1. t: Spatial conditioning, a onedimensional geography (together) Y Υ Λ Yz Yl ï Vi Vo Average = 1 Η t So Si S2 S3 S. } Η 1- space Figures 187 Y V Fig. 2. 1 : Convergence, oneworld :<e Fig. 2. 2: Convergence, twocoalition polarization ■ HOQ U \D ï % ^0 Section II — Models of Explicit Distribution Dynamics Fig. 3. d: Densities of relative (per capita) incomes across 105 countries Spatial conditioning 0 2 4 (b): 1970 6 8 10 12 0 2 4 6 (c): 1980 0 2 4 6 β 10 12 (d): 1988 Figures 189 Fig. 3. b: Boxplots, relative (per capita) incomes across 105 countries Spatial conditioning 1961,1970,1980,1988 190 Section II — Models of Explicit Distribution Dynamics Fig. 3. s: Stochastic kernel, relative (per capita) incomes across 105 Countries Spatial conditioning Figures 191 Fig. 4. d: Densities of relative (per capita) incomes across 105 countries Trade conditioning (a): 1961 (b): 1970 0 1 2 34 0 1 2 34 (c): 1980 (d): 1988 192 Section II — Models of Explicit Distribution Dynamics Fig. 4. b: Boxplots, relative (per capita) incomes across 105 countries Trade conditioning 3- 2- 1- CM " Ί— 60 ~ ι— 70 80 90 1961,1970,1980,1988 Figures 193 Fig. 4. s: Stochastic kernel, relative (per capita) incomes across 105 Countries Trade conditioning 194 Section II — Models of Explicit Distribution Dynamics Fig. 5. d: Densities of relative (per capita) incomes Europe-wide Spatial conditioning (a): 1980 (b): 1983 (c): 1986 (d): 1989 Figures 195 Fig. 5. b: Boxplots, relative (per capita) incomes Europe-wide Spatial conditioning j l_ 2. Ο Ι. 5- 1. Ο Ο. 5- — ι— 80 — ι— 82 — ι— 84 — ι— 86 — ι— 88 — ι— 90 78 1980,1983,1986,1989 196 Section II — Models of Explicit Distribution Dynamics Fig. 5. s: Stochastic kernel, relative (per capita) incomes Europe-wide Spatial conditioning 0-6 %°^C' Figures 197 Fig. 6. d: Densities of relative (per capita) incomes across Greece Spatial conditioning (a): 1980 (b): 1983 (c): 1986 (d): 1988 198 Section II — Models of Explicit Distribution Dynamics Fig. 6. b: Boxplots, relative (per capita) incomes across Greece Spatial conditioning 1. 6-. 4- 1. 2- 1. Ο Ο. 8- 78 80 82 84 β ο7 88 90 1980,1983,1986,1989 Figures 199 Fig. 6. s: Stochastic kernel, relative (per capita) incomes across Greece Spatial conditioning 200 Section II — Models of Explicit Distribution Dynamics Fig. 7. d: Densities of relative (per capita) incomes across Spain Spatial conditioning 0. 0 0. 5 1. 0 1. 5 2. 0 2. 5 (a): 1980 0. 5 0. 0 (b): 1983 1. 0 1. 5 2. 0 2. 5 OJ 0. 0 (c): 1986 1. 0 t. 5 2. 0 2. 5 0. 5 0. 0 (d): 1988 1. 0 1. 5 2. 0 2. 5 Figures 201 Fig. 7. b: Boxplots, relative (per capita) incomes across Spain Spatial conditioning j ι ι ι L 1. 4 1. 2 1. Ο Ο. 8 78 —ι 1 1 1 Γ 80 82 84 86 8ë 90 1 9 8 0 , 1 9 8 3 , 1 9 8 6 , 1 9 89 202 Section II — Models of Explicit Distribution Dynamics Fig. 7. s: Stochastic kernel, relative (per capita) incomes across Spain Spatial conditioning u- 5p# Figures 203 Fig. 8. d: Densities of relative (per capita) incomes across Portugal Spatial conditioning (b): 1983 (c): 1986 (d): 1988 2 3 0 204 Section II — Models of Explicit Distribution Dynamics Fig. 8. b: Boxplots, relative (per capita) incomes across Portugal Spatial conditioning ι ι ι ι 1. 6- 1. 4- 1. 2- 1. Ο Ο. 8- 0. 6- 0. 4- 7 8 8 0 ι 82 ι 84 8 6 ι 88 ι 90 1980,1983,1986,1989 Figures 205 Fig. 8. s: Stochastic kernel, relative (per capita) incomes across Portugal Spatial conditioning 0. 6 °ξβ^ 206 Section II — Models of Explicit Distribution Dynamics Fig. 9. b: Boxplots, relative (per capita) incomes across France Spatial conditioning. 6- 1. 4- 1. 2- 1. Ο Ο. 8- 78 80 82 84 86~ 88 90 1 9 8 0 , 1 9 8 3 , 1 9 8 6 , 1 9 89 Figures 207 Fig. 9. d: Densities of relative (per capita) incomes across France Spatial conditioning (a): 1980 (b): 1983 (c): 1986 (d): 1988 208 Section II — Models of Explicit Distribution Dynamics Fig. 9. s: Stochastic kernel, relative (per capita) incomes across France Spatial conditioning 0. 8 s pa t ia lC°n' Figures 209 Fig. 10. d: Densities of relative (per capita) incomes across Italy Spatial conditioning (a): 1980 (b): 1983 (c): 1986 (d): 1988 210 Section II — Models of Explicit Distribution Dynamics Fig. 10. b: Boxplots, relative (per capita) incomes across Italy Spatial conditioning J I L 1. 2- 1. Ο Ο. 8- 78 — ι— 80 —r~ 82 —ι— 84 — ι— 86 88 ~ ι— 90 1980,1983,1986,1989 Figures 211 Fig. 10. s: Stochastic kernel, relative (per capita) incomes across Italy Spatial conditioning δ) 1 ν A U SPat 212 Section II — Models of Explicit Distribution Dynamics Fig. 11. sk: Conditioning stochastic kernel, Non Cohesion conditioned on Cohesion <5 3 δ5 0 dl1. rCO^ Figures 213 Fig. 12. s: Stochastic kernel, relative (per capita) incomes across Greece Investment conditioning 214 Section II — Models of Explicit Distribution Dynamics Fig. 12. dyn: Relative (per capita) incomes across Greece Investment conditioning dynamic stochastic kernel α ι ·0 1l 'í + 5 0. 8 °-9 re'-'°d Figures 215 Fig. 13. s: Stochastic kernel, relative (per capita) incomes across Spain Investment conditioning 0. 8 lnves tC< 216 Section II — Models of Explicit Distribution Dynamics Fig. 13. dyn: Relative (per capita) incomes across Spain Investment conditioning dynamic stochastic kernel Figures 217 Fig. 14. s: Stochastic kernel, relative (per capita) incomes across Portugal Investment conditioning r 0- o^tC< 218 Section II — Models of Explicit Distribution Dynamics Fig. 14. dyn: Relative (per capita) incomes across Portugal investment conditioning dynamic stochastic kernel Figures 219 European Commission The socio-economic impact of projects financed by the Cohesion Fund — A modelling approach Volume 2: Computable general equilibrium models — Models of explicit distribution dynamics Luxembourg: Office for Official Publications of the European Communities 1999 — 219 pp. — 21 χ 29. 7 cm ISBN 92-828-3065-9 (Volume 2) ISBN 92-828-3064-0 (Volume 1) ISBN 92-828-3066-7 (Volume 3) ISBN 92-828-7238-6 (Volumes 1, 2 and 3) Price (excluding VAT) in Luxembourg: EUR 86 (Volumes 1, 2 and 3) Venta · Salg · Verkauf · Πωλήσεις · Sales · Vente · Vendita · Verkoop · Venda · Myynti · Försäljning BELGIQUE/BELGIË Jean De Lannoy Avenue du Roi 202/Koningslaan 202 B1190 Bruxelles/Brussel Tél. 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