Agglomeration and Regional Unemployment Disparities: A Theoretical Analysis with Reference to the European Union

Südekum, Jens Book — Digitized Version Agglomeration and Regional Unemployment Disparities: A Theoretical Analysis with Reference to the European Union cege-Schriften, No. 6 Provided in Cooperation with: Peter Lang International Academic Publishers Suggested Citation: Südekum, Jens (2003) : Agglomeration and Regional Unemployment Disparities: A Theoretical Analysis with Reference to the European Union, cege-Schriften, No. 6, ISBN 978-3-631-75686-7, Peter Lang International Academic Publishers, Berlin, https://doi.org/10.3726/b14155 This Version is available at: https://hdl.handle.net/10419/182693 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Agglomeration and Regional Unemployment Disparities CEGE-SCHRIFTEN Jens Südekum In the European Union, unemployment rates differ markedly across regions, both within and across nations. This study presents a coherent theoretical approach to explain the emergence and persistence of such regional unemployment disparities. The analysis builds on the wage curve literature, and on regional agglomeration theories like the new economic geography. These theoretical strings are combined and extended, in order to provide a unified framework. Jens Südekum was born in Goslar, Germany, in 1975. Since 1996 he studied economics at the University of Göttingen and the University of California at Los Angeles (UCLA). He received his diploma in 2000 and his PhD in Economics from the University of Göttingen in 2003. CEGE-SCHRIFTEN Jens Südekum Agglomeration and Regional Unemployment Disparities Agglomeration and Regional Unemployment Disparities e4&-Schriften Center for Globalization and Europeanization of the Economy Zentrum fiir Globolisierung und Europiiisierung der Wirtschoft Georg-August-Universitiit Gottingen Band 6 Herousgegeben von Wolfgang Benner, Giinter Gobisch, Jiirg Gii6efeldt, Helmut Hesse, Hons-Joachim Jarchow, Renate Ohr, Helga Pollok, Peter Riihmonn, Hermann Sautter, Stefan Tangermonn und Wilhelm H. Wacker Verantwortlicher Herausgeber fiir diesen Band: Peter Riihmann • PETER LANG Frankfurt om Main • Berlin • Bern • Bruxelles • New York • Oxford • Wien Jens Sudekum Agglomeration and Regional Unemployment Disparities A Theoretical Analysis with Reference to the European Union £ PETER LANG Europiiischer Verlag der Wissenschaften Open Access: The online version of this publication is published on www.peterlang.com and www.econstor.eu under the international Creative Commons License CC-BY 4.0. Learn more on how you can use and share this work: http://creativecommons. org/licenses/by/4.0. This book is available Open Access thanks to the kind support of ZBW – Leibniz-Informationszentrum Wirtschaft. ISBN 978-3-631-75686-7 (eBook) Bibliographic Information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the internet at <http://dnb.ddb.de>. Q) :£ Zugl.: GOttingen, Univ., Diss., 2003 Gedruckt auf alterungsbestlindigem, sliurefreiem Papier. D7 ISSN 1617-741X ISBN3-631-51745-9 US-ISBN 0-8204-6521-6 © Peter Lang GmbH Europliischer Verlag der Wissenschaften Frankfurt am Main 2003 All rights reserved. All parts of this publication are protected by copyright. Any utilisation outside the strict limits of the copyright law, without the permission of the publisher, is forbidden and liable to prosecution. This applies in particular to reproductions, translations, microfilming, and storage and processing in electronic retrieval systems. Printed in Germany I 2 4 5 6 7 www.peterlang.de Foreword 5 Foreword of the editor Unemployment rates differ dramatically within the European Union. On a national level, these differences are typically explained by different national labour market institutions, economic policies, and country specific shocks. However, when looking at the European Union on the level ofregions, one can have doubts if it is really useful to think about unemployment only in national dimensions. Within most EU countries, there are marked, if not dramatic intra-national unemployment disparities. Moreover, unemployment in Europe tends to be organized in a transnational spatial pattern. On average, unemployment rates are low in the so called "European banana", i.e. in the economic core belt in the middle of the continent, where production and income are highly agglomerated. Vice versa, unemployment rates are extraordinarily high in the peripheral regions at the outside borders ofEU-15. In view of this, it seems necessary to reach out for some alternative theoretical approach, where differences in unemployment rates across jurisdictions are not primarily explained by institutional differences, which are mostly negligible for regions within the same country. It rather seems more adequate to attribute interand intra-national unemployment disparities to purely geographical factors. Recently, there was a rapidly growing interest in theoretical explanations for regional income disparities. Most notably, the "new economic geography" has shown how a core-periphery-structure of economic activity can endogenously emerge and persist within an integrated economic area. However, this literature does not incorporate an explicit analysis of labour market institutions and abstracts from unemployment. On the other hand, theories that explicitly aim at regional unemployment disparities, e.g. the wage curve theory, do not take into account the arguments for agglomeration and regional core-periphery patterns. This gap in the literature is the starting point of the present study by Jens Suedekum. After a careful review of the wage curve literature and the new regional divergence theories, he combines essential elements of these different strings and offers a coherent theoretical analysis of interand intra-national unemployment disparities. He shows how trans-national unemployment clusters can emerge due to agglomeration economies, and he thereby shifts the focus away from institutional differences towards geographical factors as the main determinant for unemployment differences across administrative units. Even though the technical level of the book is advanced in some parts, the reader can always follow the economic intuition of the arguments. The study of Jens Suedekum in my view is a substantial contribution to the literature, and it can also inspire fruitful further research in this important area. Peter Ruehmann Goettingen, July 2003 Table of contents List of tables, figures and maps Chapter A Map Al: MapA2: Table Al: Table A2: MapA3: Figure A4: MapA5: MapA6: Map A7a: MapA7b: Figure A8: MapA9: MapAl0: Figure Al I: Figure A12: Figure A13: Chapter B Figure Bl: Figure B2: Figure B3: Chapter C Figure Cl: Figure C2: GDP per head by region (PPS), 1999 GDP per person employed (EURO), 1999 Disparities in GDP per head in PPS by region within Member States, 1989-1999 Transition probability matrices of GDP per capita (PPS) and unemployment rates of European NUTS2-regions relative to EU-15 average Unemployment rate by region (2000) Disparities in unemployment, EU-15 I 970-1999 Cumulative employment growth 1976-1998 Population density by NUTS3-region, 1999 Crude rate of total population change, average 1995-1997 Crude rate of net migration, average 1995-1997 Features of regions with population decline in EU-15, 1993-1998 Education level by region, 2000 European patent applications, average 1997 to 1999 West Germany -Gross wage bill per employee in % of national average, 1970-1999 West GermanyUnemployment rates in North and South, 1967-1999 West Germany -Net internal migration 1988-1999 The wage setting curve in the ELMM Equilibrium in the ELMM Adjustment in the ELMM The wage curve Full equilibrium in the BIO-model 13 22 23 25 27 30 31 33 35 36 37 38 40 41 43 43 44 58 63 65 73 80 14 Chapter D Figure Dl: Figure D2: Figure D3: Figure D4: Figure D5: Figure D6: Table D1: Table D2: Figure D7: Figure D8: Figure D9: Figure D10: Figure D1 l: Chapter E Figure El: Figure E2: Figure E3: Figure E4: Figure E5: Chapter F Figure Fl: Figure F2: Figure F3: Figure F4: Table of contents Sustainability of a core-periphery structure The stability of the symmetric equilibrium The bifurcation diagram of the Krugman-model Location of the industrial sector in the Krugman/Venables-model Real wages in the Krugman/Venables-model The Helpman-model Income, size and cost-of-living in US metropolitan areas The correlation matrix Relative CPI \jlz/\j/ 1 as a function ofy Real wage quotient ro2/ro 1 as a function ofy Stability of the symmetric equilibrium Different scenarios of symmetry breaking The bifurcation diagram of our NEG-model 108 110 111 115 116 119 125 126 130 131 134 134-135 136 Equilibrium in the closed economy 146 Product market equilibrium in both regions 153 Equilibrium in the two-region economy with immobile agents 154 Total agglomeration with perfectly mobile labour 156 Distribution of the labour force with intrinsic regional preferences 158 Migration in a neoclassical two-region model 174 Migration in a two-region model with an aggregate extemality 178 The determination ofµ* 20 I The determination ofµ* with endogenous wz, 1 205 Introduction Introduction 15 One of the best ways to understand how the international economy works is to start by looking at what happens inside nations. (Paul Krugman) If we had to describe the economic geography of the European Union (EU-15) in only one phrase, we would say that there is a high degree of spatial agglomeration of economic activity in the EU-area and very pronounced core-periphery divides along various economic dimensions. There are marked differences in per capita output and income levels across European regions. People from the richest European regions have e.g. an average real purchasing power about five times higher than people from the poorest areas. Spatial divides and regional disparities are even larger with respect to other indicators of economic activity. In this book, we will specifically be concerned with regional unemployment rates. In the European Union today, regions with practically full employment and regions with excessive mass unemployment coexist. In many cases, they even coexist within the same country. Germany, Italy and Spain are the most prominent examples of national economies, where some regions have unemployment rates below 5 per cent, whereas others are stuck with figures well above 20 per cent. Such spatial unemployment disparities within and across countries exist for decades. In recent years, they even tended to increase. In chapter A of this book we will give an overview about the spatial structure of economic activity in the European Union. We will argue that regional unemployment rates in the EU follow a quite distinct, trans-national pattern and closely resemble the core-periphery-structure of regional GDP per capita. Regional unemployment rates are low in the rich core regions of the European Union, where population, production and income are agglomerated. On the contrary, high unemployment rates are found in the sparsely populated and economically peripheral regions with low levels of output and income per capita. The main aim of this book is to explain this stylised fact. More specifically, we aim to explain the spatial structure of regional unemployment rates within an integrated economic area in relation to the corresponding spatial structure of output and income. This is a largely unexplored issue in economic theory. Theorizing about unemployment has always been one of the most prominent tasks for macroeconomists, who predominantly think about the phenomenon of unemployment in its national dimension. Actually, different schools of thought within macroeconomics are still distinguished by the way how they think about the emergence of unemployment, especially in relation to the rate of inflation, and by the 16 Introduction the implications they derive for economic policy. Regional issues traditionally play a minor role in this debate. However, regional labour market analysis has gained some prominence during the last ten years. One useful regional approach comes from David Blanchflower and Andrew Oswald ( 1990, 1996). These two authors have compiled a great deal of empirical evidence about regional labour markets and claim to have distilled an "empirical law" of economics from the data, according to which "doubling the unemployment rate of some region will drive down the regional wage level by roughly ten per cent". This law, known as the wage curve, and the theoretical work that is associated with it, will play an important role for our analysis. In order to justify the existence of a wage curve theoretically, one has to work with concepts of imperfect competition in the labour market. So do Blanchflower/Oswald in the theoretical parts of their work, which is build on one specific macroeconomic approach that is often labelled the "European labour market model (ELMM)". This important macroeconomic precursor will be introduced and discussed in chapter B of this book. Chapter C will then be devoted to the theory of the wage curve, that in many respects is the regional pendant of the ELMM. The wage curve theory is useful for our purposes, since it draws an inherent link between key labour market variables on a regional level, the unemployment rate and the real wage level. But the existing wage curve models alone are insufficient to account for the observed spatial agglomeration of economic activity in the EU. The existing literature is useful to understand how regional unemployment rates develop if the corresponding regional levels of wages, output and income are exogenously given. But wage curve theory is ill-equipped to address why there are so pronounced disparities in the real world. Economic agglomeration theories are the second string in the literature that is related to our theoretical analysis. It is known since Alfred Marshall ( 1890) that there are forces in the world that push for spatial concentration of economic activity in only a few locations or regions within an economy. Again, such spatial and regional issues traditionally have been neglected by mainstream economists. Of course, important contributions have been made in location economics, in urban and regional economics in the course of more than a century.1 But all in all, this field of economics has eked a shadow existence within the discipline. This has dramatically changed in the last years. The revival of interest in spatial and regional issues as a piece of mainstream economics is somehow symbolised by the seminal contributions of Krugman (1980, 199la,b) that led to the theories known as "new trade theory (NTT)" and "new economic geography (NEG)". Especially 1 Location economics is actually seen as a "German tradition" and dates back to Heinrich von Thiinen (1826), and followed by several other German writers such as Weber (1909), Christaller (1966), Loesch (1954). For a brief overview of some history of economic thought see Fujita/KrugmanNenables (I 999), ch. 2+3. Introduction 17 the latter can be seen as a modem theory of regional agglomeration that explicitly addresses why core-periphery divides of economic activity can endogenously emerge and persist within an integrated area. Chapter D will be devoted to the discussion of regional agglomeration theories, with special emphasis on NEG. The core model of Krugman (1991a) will be introduced, and the main developments of this theory will be traced until the current research frontier. Still we conclude that there are several unexplored and open issues. One of these issues, which is not directly related to the analysis of regional unemployment disparities, concerns unrealistic predictions that current NEGmodels make about the development of regional costs-of-living during the process of regional agglomeration. This issue is taken up in chapter D, where we derive an own model that improves on the current state of art in the NEG-literature. The main critique we formulate against the new agglomeration theories, however, is that they have nothing to say about unemployment. All standard models ofNTT and NEG assume that labour markets always automatically clear. The phenomenon of regional unemployment disparities can thus not be analysed with these models. This neglect is peculiar, given that regional differences in unemployment rates are at least as pronounced, if not even more dramatic, than income disparities in the EU-15. The chapters E and F we will therefore propose theoretical frameworks that attempt to close this gap in economic theory. In chapter E we will marry a wage curve, which is thought of as a labour market equilibrium curve, with a product market that exhibits the essential features of the new regional agglomeration theories. The innovation that comes from this model is twofold: Firstly, it can be seen as a general equilibrium model with a wage curve, where the regional disparities can develop endogenously. And secondly, the model can be seen as an attempt to introduce the element of unemployment to the new regional agglomeration theones. The main result of our model framework is that the spatial structure of unemployment follows the spatial agglomeration pattern of overall economic activity. Large core regions with high per capita income levels have low unemployment rates. Vice versa, small regions with low income levels have high unemployment rates. Hence, our theoretical framework implies results that are consistent with the stylised facts about regional unemployment disparities and regional agglomeration in the EU. Chapter F will specifically address the issue of labour mobility. If there are intranational economic disparities, what happens if people migrate from the blurring to the blooming areas? Is labour mobility an adjustment force that gradually leads to an erosion of existing disparities? Or do differences even get larger and more pronounced when workers migrate? The conventional viewpoint on this matter, known from the neoclassical theory of factor migration, is that labour mobility will lead to a convergence of wages and income levels. But even slight departures 18 Introduction from the neoclassical world lead to fundamentally different conclusions about the impacts and effects of interregional labour mobility. We will specifically be concerned with the issue of selective labour migration. There are good theoretical and empirical reasons to assume that the group of workers who are mobile across space mainly consists of young and well educated individuals. The economic consequences of this selective labour migration are then derived using two alternative theoretical models. In the first version, we abstracts from endogenous agglomeration forces and formulate a straightforward neoclassical approach with a Cobb-Douglas production function. Still the model shows that high skilled labour migration will lead to a regional divergence process with respect to the real incomes of immobile low-skilled workers. In a second version, we again introduce endogenous agglomeration economies and show that selective migration and localised increasing returns are two distinct, but complementary arguments why labour mobility leads to regional divergence instead of convergence. Both frameworks of chapter F are then taken further to analyse the implications of national union wage setting for regional unemployment outcomes. The models specifically address intra-national unemployment disparities that arise because of undifferentiated union wage setting irrespective of regional productivity differentials. The regional unemployment disparities that arise are magnified through selective labour migration. All in all, the models of chapter F constitute an alternative, but complementary view about the relation of regional agglomeration and regional unemployment. The book will be finished by some concluding remarks and a very brief discussion of some policy issues. A) Spatial economic disparities within the European Union Spatial economic disparities within the European Union: The evidence 19 Al) Preface: Level of spatial disaggregation and the choice of territorial units At what level of spatial disaggregation should we measure the magnitude and the development of regional disparities over time? Mainly for reasons of data availability one is constrained to choose among different stages of administrative units. The statistical office of the European commission (Eurostat) has developed the NUTS-division scheme (NUTS="Nomenclature of Statistical Territorial Units"). Herein, four levels of gradation are distinguished: the level NUTS0 is identical with the 15 current member countries of the European Union. Below this, there are 77 subordinate NUTS!, 211 NUTS2 and 1031 NUTS3 in the EU-15. These units respectively correspond to the German jurisdiction levels Bundeslander, Regierungsbezirke and Landkreise. Aggregate economic analysis traditionally is concerned with the national (=NUTS0) level. There are good reasons for this, since nations are mostly well defined entities with a coherent institutional and political structure for which data availability is usually warranted. Furthermore, the development of aggregate theories requires that the area under consideration must be large enough in order to "convexify undeniable human indivisibilities and micro fixed costs" (Boldrin/Canova, 2001 :212), i.e. to allow the abstraction from several microeconomic influences that macroeconomic theory necessarily has to make. The large NUTS0-regions surely have this desired property. For an illustration of spatial economic disparities within the EU-I 5, however, NUTS0regions are too unspecific. It will become apparent in this chapter that economic activity is often utterly unequal within member countries. Moreover, for today's European Union, one would have to rely on an unsatisfactorily low number of 15 observations, which even comprise cases that are hardly comparable at all (e.g. Luxemburg versus Germany). Therefore it makes sense to choose some smaller unit size to document the economic geography of the European Union. By using a more disaggregated NUTS-level, one can "gain variance" and base intraEuropean illustrations on a higher number of observations. Secondly, by using smaller spatial units, the problem of comparability is moderated, since the differences in size of the single NUTS2-regions are of course much smaller than for the single NUTS0-regions. However, one should also be aware of different problems when disaggregation is pushed too far. NUTS3 areas e.g. might simply be too divergent in their underlying characteristics, natural endowments and historical preconditions as to conduct a meaningful comparison between them. Moreover, data problems and measurement errors can arise because of the entanglement of the single regions. For example, the 20 Spatial economic disparities within the European Union GDP per employee can be overstated in urban NUTS3-regions through daily commuters who live in surrounding areas. In other words, the territorial units must be numerous enough, the spatial areas must at least be roughly comparable, and also large enough to cope with the problems mentioned above. A commonly accepted level of disaggregation for documenting economic and social cohesion (and also for the conduct of European regional policy) is the NUTS2-level.1 Germany consists of 40 NUTS2 regions, whereas whole Denmark and Luxemburg are considered to be a single NUTS2.2 A2) Gross domestic product (GDP) We will first consider the geographical distribution of GDP per capita across European NUTS2 regions measured in purchasing power standards (PPS) for the average of the years 1997-1999 . Later we trace out the development over the last decades. GDP per capita is the most prominent indicator for measuring income inequalities within the EU, also heavily used for the conduct of European regional policies (see Suedekum, 2002a). From a theoretical point of view this measure might be problematic, since it measures output, not the disposable income level of the regional population. But for our documentation of stylized facts, we stick to this commonly used variable. A2.1.) GDP of European NUTS2-regions, 1997-1999 Europe's richest NUTS2 region is Inner London with an income level of 246.3 relative to EU-15 (=100), followed by Brussels (223.1), Hamburg (183.4) and Luxemburg (179. 7). At the other extreme, one finds regions like Ipeiros in Greece (47.3), Extremadura in Spain (50.3) or the Acores in Portugal (52.2). Put differently, individuals from the richest European regions have an average real purchasing power that is about five times higher than for inhabitants of the poorest areas. But income differences by no means only occur across the EU-15 member states. Also within countries there are substantial differences: the earnings in Hamburg are about three times higher than in Dessau (63.2), albeit the two regions are less than 300 kilometers apart. Other extreme examples include Lombardia (136.5) versus Calabria (61.9) in Italy, or Ile de France (154.1) versus Languedoc1 Note however the critique of Boldrin/Canova (2001 :212) who imply that NUTS2 are too small and too inherently different. 2 A full list of all European NUTS2 regions, including various economic summary statistics can be found in the Cohesion Report of the EU Commission (2001), available under http://www.europa.eu. in ti comm/regional po Ii cy/ sources/ doco ffi c/ offi cial/reports/pdf/taba en. pdf Spatial economic disparities within the European Union 21 Rousillon (77.2).3 Cornwall in the UK (66.6) or Hainaut in Belgium (71.8) are also substantially poorer than their corresponding capital regions. A more comprehensive picture on regional income disparities in the EU is presented in map A I. The prospective accession countries from Eastern Europe are included in this map, so that the regional GDP levels are relative to the EU-27 average. It can be seen that most entrant regions have incomes even below the poorest current member regions. But we want to focus here solely on the EU-15. The map illustrates that the regional distribution of GDP per capita follows a quite distinct spatial pattern: the rich regions are located roughly in the middle of the continent, in the so-called "European Banana", ranging from Southern UK over Benelux, East France and West Germany up to Northern Italy. Surrounding the economic core belt is a group of regions with medium per capita incomes, e.g. North-West Germany, Northern UK, Scandinavia as well as large parts of France. The economically lagging parts of Europe are all at the outside borders of EU-I 5. Most notably these are Southern Italy, East Germany, the Burgenland (AT), Greece and nearly all of Spain and Portugal. Together this group is eligible for structural funding from the EU Commission under "objective I" until at least 2006, i.e. they match the criterion that their GDP per capita falls short of 75% of the EU-15 average.4 The image of a "core -periphery" structure in the spatial distribution of GDP remains unchanged when we consider GDP per employed person (map A2).5 This measure more directly reflects the productivity level in European regions through adjusting for different employment rates. The image of the economic backwardness of Portugal and Spain is magnified to some degree, whereas the situation looks somehow more friendly for the case of Southern Italy. All in all, however, the magnitude and the geographic structure of spatial divides presented in this figure complements the impression from map A I. A2.2.) Regional convergence versus divergence in Europe The illustration of the descriptive cross-section evidence does not cope with the development of relative regional income levels over time. Has the difference between the richest and the poorest regions been narrowing, or did the disparities tend to grow over the last years? 3 This excludes the French overseas departments that are even poorer (SS. l ). 4 For an overview of European regional policy see e.g. Boldrin/Canova (2001), Suedekum (2002a), Puga (2002) 5 Due to data limitations, the map only traces NUTS! (or even NUTS0) regions. 22 Spatial economic disparities within the European Union Map Al: GDP per head by region (PPS), 1999 Index, EUR-27 = I 00 r <. )() D :w50 5075 • 15 • 100 • 100 - 125 • , J:!5 ' '"""' '"-- - ~-- Spatial economic disparities within the European Union 29 Map A3: Unemployment rate by r eg ion, 2000 % or labour force D .t:. 4.95 - 11 ,1 15 • 7. 81 -1,S$ -I0. 7.5 - 1075136.5 -- 1163 BU R -2 7, 9.J S1andard d('~ i11tion 5 7J , ..... .._ _ __ _,_ ~-.,- t ll't 30 Spatial economic disparities within the European Union Regional unemployment rates in fact closely resemble the "core-periphery" structure ofregional GDP per capita that has been described above. Low unemployment is centered around the "European Banana", i.e. in Southern UK, Netherlands, Flanders, Southern Germany and Northern Italy. Similarly, all areas with mass unemployment belong to the poor peripheral parts of EU-15, the so called "objective I "-regions: Southern Italy, East Germany, South and East Spain, Northern Finland.8 Most medium income regions also belong to the group with intermediate unemployment rates. Thus, the membership of a single region to one of the three "clubs" (Banana, objective I, intermediate) seems to be a more reliable indicator for the regional unemployment rate than the pure assignment to some EU member country. This notion is supported e.g. by Overman/Puga (2002), who find that "the unemployment outcomes of individual regions are much closer to the outcomes of their neighbors, than to the average outcomes of other regions within the same EU-member state". This "neighboring effect" leads them to conclude that unemployment clusters have been shaped within EU-15, and that there is truly a spatial dimension in European unemployment. The relation between income per capita and unemployment rate is surely not oneby-one, as several counterexamples are at hand: Portugal entirely consists of poor regions, especially when considering GDP per employed person. Portuguese unemployment on the other hand is low by European standards. Greek unemployment is also not as high as one might expect given its GDP figures. One might therefore put it this way: belonging to the "objective l "-group is a necessary, but not a sufficient condition for exhibiting extreme regional unemployment rates of above 15 per cent or so. Nevertheless, the average unemployment rate for all "objective !"-regions is markedly higher than the EU-15 average (15.8 vs. 9.7 for 1999). There are also some rather rich central regions with quite high unemployment rates (e.g. Nord-Pas de Calais in France). But the general conclusion, that the spatial pattern of unemployment rates resembles the spatial pattern of GDP per capita, seems hardly disputable. 8 This view is supported e.g. by CER (1998). They report that "the high unemployment regions in Europe have a low per capita income (30% below the EU average) and a similar production structure, in which manufacturing represents a lower than average share of output and is characterized by technologically stagnant industries such as food, mining, leather and apparel. On the contrary, the low unemployment regions are characterized by a I 0% higher than average per capita income and a production structure in which manufacturing is prominent and diversified, with a prevalence of industries such as machinery, precision instruments and electronics". Spatial economic disparities within the European Union 31 A3.2.) Convergence versus divergence of regional unemployment rates Looking at the history and the development ofregional unemployment rate disparities within Western Europe, one finds much clearer evidence for regional divergence than it was the case for regional GDP per capita levels. At first glance this can be seen in fig.A4, which indicates a strong upward trend of the regional unemployment disparities since the 1970s, measured by the weighted standard deviation of all regions now belonging to EU-I 5. Both regional as well as national differences rose pro-cyclically with the overall unemployment rate of EU- ! 5, but the rise of regional disparities has been more pronounced. Since the mid 1980s, regional unemployment disparities rose only moderately on average, but surely revealed no sign of deterioration. The OECD (2000:32) subscribes to this view as it points out that "variation in regional unemployment rates increased in many countries during the 1970s and early 1980s. [. .. } This variation generally remained stable or increased between 1985 and 1997." Fig. A4: Disparities in unemployment, EU15 1970-99; EU27 1998-99 % labour force 12 10 8 Starnlard deviation of 6 u~ploymenl rate (by region),... __ _ ,,,,--~--...._ .//' EU2~ / "' 4 ~ .,,- ,J , • - ... - .... / .,/ .. 2 / ,, .. · · · · ~ Standard dBVlal.Dn of unemployment · · rate (by Member State) 12 10 8 6 4 2 O'----------------------~o 1m1~1~1m1~1~1~1~1~,~~oo However, there is also evidence for another process that can not be revealed by using simplistic summary statistics like standard deviations. Overman/Puga (2002) 32 Spatial economic disparities within the European Union show that regional unemployment in the EU was subject to a process of polarization since the mid 1980s. The transition probability matrix for unemployment rates of European NUTS2 regions relative to the EU-15 average at times 1986 and 1996, that is reported in table A2c), illustrates this fact. There has been a quite high degree of persistence for the group of regions with very high and very low unemployment rates. That is, regions with low (high) unemployment rates in 1986 mostly belonged to the same group in 1996. This inertia, however, was absent for many regions who belonged to the group with intermediate unemployment rates in 1986. The degree of persistence for the three sub-groups with relative unemployment rates ranging from 0.6 to 1.3 is substantially lower than for the other two groups. Many regions with intermediate unemployment levels in 1986 moved to either of the two extremes. For example, several Italian, French and Spanish regions that used to have relative unemployment rates somewhere around the EU average experienced a significant deterioration since 1986, whereas some other regions from the same countries saw their unemployment rates drop substantially. As Overman/Puga (2002) show, this polarization process led to the geographical configuration of unemployment that we have described above, where areas with high and low unemployment were not divided by national borders, but distinguished by cross-country unemployment clusters. To obtain a better understanding of this evolution, it is helpful to distinguish what has driven this polarization process. Unemployment rates by definition change either because of changes in the size of the labour force (i.e. labour supply changes), or changes in employment (i.e. labour demand), or a combination of the two. It seems thus natural to look for regional employment growth patterns, as well as for population changes and migration flows within EU-15 in the next section. A4) Other regional indicators A4.l.) Employment growth An influential study on regional employment growth in Europe comes from Martin/Tyler (2000). The authors look at the evolution of cumulative relative employment growth, defined as the cumulative annual change in the log of regional employment minus the cumulative annual change in the log of Europe-16 employment, which consists of the usual EU-15 countries plus Norway. The study comprises annual data for the period 1975-98, the disaggregation corresponds whenever possible to the NUTS2 level. This measure thus captures the cumulative differential employment growth experience of the regions. The authors show that there has been marked regional divergence in employment growth within virtually all countries, particularly during the 1980s. Although one Spatial economic disparities within the European Union Percent -more lhan 10.0 - Oto9 .9 • -9.9to -o., -le ss t han -1 0.0 I : no data avf!l il ab le ... 33 I I 0 500 km Map AS : Cumulative employment growth. 1976-98 (from MartinfTyler, 2000) 34 Spatial economic disparities within the European Union can also single out three groups of countries that faced different employment growth at the national level,9 the most distinguishing feature for the time period under consideration is the substantial intra-national divergence in cumulative employment growth. The degree of regional divergence varies across countries. It is particularly large in Italy, Spain, the UK and Greece. In these states, there has been a difference of 50% or more between the cumulative employment growth of leading and lagging regions (Martin/Tyler, 2000:605 ff.). From a bird's perspective, these regional evolutions again follow a specific geographical pattern (see map A5). The economic core belt (the "European banana") is again visible in this picture and reveals by and large cumulative employment growth well above the European average. With a few outliners and exceptions, the poor peripheral regions of the EU (the "objective l" -regions) constituted the area with slow employment growth. In between, there is again the group of regions with intermediate income levels and unemployment rates, which on average also faced employment growth of medium strength. The regional characteristics 'low unemployment rate' and 'strong employment growth' thus tended to coincide. In relation to the results from the last section, it follows that the polarization process of regional unemployment rates was mainly driven by differential intra-national employment growth paths. This result is supported by Overman/Puga (2002), who find that regions that recently ended up with relatively low unemployment had relatively high employment growth over the last decades. The authors therefore conclude that " [. . .} contrary to labour force changes, employment changes have worked for polarization [ of unemployment rates}. It is employment changes that have driven high unemployment regions to their high rates and low unemployment regions to their low rates". A4.2.) Population Density, Population Changes and Migration In the same vein, one can show that population changes and migration on average have worked against unemployment polarization, since most regions that ended up with relatively low unemployment revealed relatively high labour force growth. An increase in labour supply translates into more unemployment if it outperforms growth in labour demand. However, the evidence indicates that the opposite has happened in the last decade: the increase in labour demand has been stronger than the increase in labour supply for the regions with good performance in reducing unemployment. 9 Martin/Tyler (2000) show that five states (Ireland, Luxemburg, Netherlands, Austria and Norway) had national employment growth rates significantly above the Europe-16 average, a second group consisting of the large EU-core countries West Germany, France, Italy and UK as well as of Belgium and Denmark exhibited employment growth rate in line with the European average. On the bottom of the scale, employment growth has been markedly below average in the geographically remote countries Spain, Portugal, Greece, Sweden and Finland. Spatial economic disparities within the European Union 35 Map A6; Population density by 'UTS3 r eg ion, 1999 ln h:ib1t ; 111l sfkm: EU R,27 11 2 § < IO I0-15 2!-- 50 El . E CY 19')8 CJ 50· 100 -100 -100 - 200500 Sourc.: f::uro:."1af 1md ~SI - 5001000 - >..., IOIJO _____ ..... 36 Spatial economic disparities within the European Union .,.,-·~ ~--~~- - ~·~~ :~ 1 '(_ ~ Map A7a: Crude rate oflolal population change, average I995-1997 I 0 0 3 -' 6 - >(, no1J,o1;j ~~(.1"""11 Wi'lle., S-r~q!11-ut NI TS, 1 li>{l hlUT'SO .... Spatial economic disparities within the European Union Map A7b: Crude r ate of net migration , average 1995-1997 [:::J <" Ill ,., oo - 00 /5 - ,s 50 - ,, .o t7 r,o,1a1,1 Sd";ll'!,,l_>r,, Wd-{.'5. ~-:Qfl;in,i· MITS l Ila NUISO 37 38 Spatial economic disparities within the European Union To assess the regional dimension of labour supply in Europe, it is instructive to look first at the population density across regions in the EU-15. Map A6 does so on a rather disaggregated basis, for NUTS3 units in the year 1999. The strong concentration in the "European banana" becomes particularly obvious in this map. It is fair to say that there is a strong agglomeration of labour supply in the economic core belt ofEU-15. The peripheral parts ofEU-15 on the contrary are characterized by a much lower population density. Moreover, there is indication that the poor and sparsely populated areas within EU15 have even lost inhabitants over the last years. This is most evidently so for East Germany, Northern Spain and Southern Italy, as can be seen in map 7a. The population decline is due both to natural processes as well as to emigration, depicted in map 7b. According to that, East Germany is subject to a rather large wave of emigration, 10 whereas the Spanish population decline apparently has had mainly other causes. The greatest population gains were recorded in Ireland, Southern France, and Southern UK. The latter area together with some West German regions has received the largest waves of immigration. Fig.A8: Features of regions with population decJin in EU 15, 199398 -40 -JO -20 - 10 0 10 w 30 Population 65+ (o/o) Population, 1998 Population 15-6-4 (%) Population <15 (%) Seivice employment(%) In dus tri al employment(%) Employment &M unemplOymeo t, 1 999 Ag rl cullur aJ employment(%) Unemployment rate(%) GD P per head (PPS) GOP , 1997 P op ulation density -40 -30 -20 -10 0 10 20 30 % differen ce from EU 15 average 10 with one exception: the substantial wave of immigration to the region "Brandenburg" is a singularity due to a sub-urbanization process of the Berlin area. Spatial economic disparities within the European Union 45 A6) Summing up the evidence In this last section, we want to summarize the combined descriptive evidence from the sections A2)-A5) in form of some stylised facts. • The area of EU-15 can roughly be divided into three groups: The economic core belt "European Banana", the poor and peripheral "objective I "-regions, and the "intermediates". The important economic indicators that we have considered reveal a spatial pattern that more or less clearly follows this division scheme. • Regions in the European Banana reveal on average high levels of GDP per capita and GDP per employee, low unemployment rates, high employment growth rates, a high population density, net inward migration, a relatively skilled labour force and high innovative activity. • The "objective l "-regions on the contrary have low income levels, high unemployment rates, low employment growth, a low population density with an even declining tendency, as well as a labour force with a high fraction of low skilled workers. Innovation activities are almost negligible. • The "intermediates" lie in between the two groups with respect to all economic indicators under consideration. • There has been a convergence process of national income levels, but no regional income convergence over the last decade. Quite contrarily, regional incomes have even (strongly) diverged in some European countries. For the EU as a whole, the time period since 1989 was characterised by a persistence of regional income disparities. • High and low unemployment areas in the EU are not divided by national borders, but distinguished by cross-country unemployment clusters. These clusters emerged through a polarization process of unemployment rates that was driven by differential employment growth paths of core and peripheral regions within the EU. • The situation in West Germany, which has been subject to a special examination, is also characterised by large and persistent regional disparities. The area in the south has both lower unemployment rates and higher earnings than the area in the north, which is lagging behind in both respects since approximately 15 years. Internal migration in West Germany went from the North to the South. B) The ,,European labour market model" Macroeconomic theories of unemJ>loyment and the "European labour market model Bl) Introduction 47 We try to understand the structure of unemployment rates across space in relation to the phenomenon of regional agglomeration. We thus need theoretical background from various fields in economics. We need a theoretical framework to analyse the issue of unemployment, with special reference to its regional dimension, a theory of regional agglomeration, and finally we need to combine the two. We shall at first start with the theory of unemployment in this chapter. In the introduction it was already said that our analysis will build on a specific regional labour market approach that was pioneered by Blanchflower/Oswald (1990, 1996), and that is comprehensively labelled the wage curve. This regional theory is closely linked to one specific macroeconomic approach which is known as the "European labour market model (ELMM)" or the "imperfect competition approach to macroeconomics". The purpose of this chapter is to introduce this macroeconomic model, since many essential features of the wage curve theory are built directly on it. In order to demonstrate how the ELMM relates to the long history of economic thought in macroeconomics, we intend to give at first a very brief overview of major developments in macroeconomics over the last century or so, with a special emphasis on theoretical explanations for the phenomenon of unemployment. This historical sketch that is provided in section B2 is by no means an attempt to survey all that has been done in this field. It only tries to present some essential ideas of a few major contributions in a very simplified manner. With this historical information it is easier to see what is actually new about the "imperfect competition approach" to macroeconomics which is then presented afterwards in section B3. B2) A brief historical overview about macroeconomics B2.1) The 'classics' The very traditional perspective in macroeconomics comes from the so called 'classics·. In their view, the real and the monetary sphere of an economy can be completely separated from each other. Inflation is interpreted as a purely monetary phenomenon, with the rate of inflation given only by the growth rate of money supply. The real sector on the other hands is seen as a system of perfectly competitive markets which all tend to clear because of the invisible hand of the market. 48 The ,,European labour market model" B2.2) Keynes and the neoclassical synthesis This consensus view of the economy as a whole, however, was put heavily under strain with the occurrence of the Great Depression in the late 1920s. It was impossible to explain this event with the traditional economic models at hand, since they were not ready to address why there could be persistent and involuntary mass unemployment in an economy. In this historical period, the macroeconomic theory of Keynes ( 1936) appeared. The contribution of Keynes was to show that economies can be in an equilibrium where full employment is not reached, because the prevailing level of effective demand is insufficient to render full utilization of existing production capacities. In other words, there exists the possibility of involuntary unemployment in the economy. It is still subject to ongoing and possibly never ending debates what exactly is at the root of involuntary unemployment in the view of Keynes himself. 1 But the most influential interpretation following the General Theory, that came to dominate macroeconomic theory and policy for a very long period of time, was the neoclassical synthesis. This Keynesian theory is crucially based on nominal wage rigidity, i.e. market failures on the labour market . The demand side in this model was modelled in the fashion of the famous IS/LMmodel (Hicks, 193 7). Economists then added a neoclassical production function and a standard neoclassical labour market to the analysis, but (in the name of Keynes) imposed nominal wages to be downwardly rigid. This was then seen as the major source of unemployment, since real wages were prevented to adjust to market clearing levels by these nominal rigidities. 2 The important implication for economic policy that comes from this well-known model is that the government can effectively achieve increases in production and employment through demand side policies (i.e. expansionary fiscal or monetary policy). As long as workers (or respectively, unions) are only concerned with nominal wages in a situation in which involuntary unemployment exists, the government can stimulate aggregate demand and hereby increase the price level. With nominal wages given, this translates into falling real wages and induces an increase in economic activity, possibly to a level where full employment is restored. If taken further, an interpretation of the (modified) Phillips-curve in the pure vein of the neoclassical synthesis can be based on this logic: with nominal wage inertia, the government can determine the price level through inflationary policies, thereby the real wage and hence the level of employment in this economy.3 In other words, the government is subject to a downward sloping schedule in the 1 For an overview of the debate about "what Keynes really meant", see Kromphardt (1991), p. 168-179. 2 For a comprehensive representation of the model see Jarchow (1998), chapter IV. 3 For this interpretation of the Phillips-curve within the neoclassical synthesis see Carlin/Soscice (1990), ch. 1.2; Felderer/Homburg (1993), S. 265 ff .. The ,,European labour market model" 49 inflation/unemployment rate-space from which it can choose a desired combination. Although the concept of the Philipps-curve traditionally has been introduced in a different manner into the Keynesian system, 4 this simplifying notion illustrates the main channels of the neoclassical synthesis. Effectively the model predicts that quantity adjustments were needed in this economy to restore equilibrium, because of sluggish nominal variables. Thus, if demand from the private sector is insufficient to render full capacity utilization and prices can not adjust so as to restore equilibrium, the government can step in and take maintenance for low unemployment at the cost of higher inflation. B2.3) Friedman and the 'natural rate of unemployment' This neoclassical synthesis was widely accepted in economic theory and policy during the first 20 to 25 years in the post-war period. However, the Keynesian orthodoxy was gradually challenged by political and economic developments and by advances in economic theory. In the beginning of the 1970s, major industrial countries saw inflation and unemployment rise simultaneously in the aftermath of the oil crisis. This development, called stagflation, was inconsistent with the conventional Phillips-curve. But prior to this, several scholars have criticised the Keynesian orthodoxy also from a theoretical point of view. In particular Milton Friedman (1968) emphasised that the validity of the Keynesian system effectively rested on money illusion by the workers. In the mechanism outlined above, expansionary fiscal or monetary policy drives up the price level, i.e. it causes inflation. This has only positive employment effects as long as nominal wages are rigid, so that real wages fall and restore full employment. But why should nominal wages remain constant in view of positive inflation? This would require that workers do not recognize the inflation pressure brought about by the government policy, and that they base labour supply decisions on nominal rather than on real wages. Friedman's argument was that this confusion of nominal with real wages can only be true in the short run, because workers might have incomplete information about inflation and might thus do not instantaneously perceive a fall in real wages. 4 Usually, the Phillips-curve was introduced in a pure ad-hoc way based on Phillips's (I 958) empirical observation that the level of unemployment and growth rate of money wages was negatively correlated. The theoretical concept of the modified Phillips-curve included mark-up pricing (normal costs pricing) on the firms part. If firms set prices simply as mark-ups over wage costs, and wage increases depend negatively on the rate of unemployment (see Lipsey, 1960), a negative correlation between the unemployment rate and the rate of inflation is implied (Samuelson/ Solow, 1960). Thus, the rate of price and the rate of wage increases were identical, but the nominal wages is not necessarily rigid. For the introduction of an ad hoc Phillips-curve in this spirit into the neoclassical synthesis see Carlin/Soscice ( 1990:69 fl). 50 The ,,European labour market model" Once they do, however, workers will adapt their nominal wage claims so as to restore the level of real wages that was prevailing before the policy intervention. Unemployment will thereby also move back to its old level. Effectively, all that has changed is that prices and nominal wages are now on a higher level after the political intervention. In the long run, there is no trade-off between inflation and unemployment, but rather a vertical Philipps-curve above some unemployment rate that Friedman called the 'natural rate of unemployment'. This natural rate according to Friedman (1968) is "[. . .]the level which would be ground out by the Walrasian system of general equilibrium equations, provided that there is imbedded in them the actual structural characteristics of the labour and commodity markets, including market imperfections, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labour availabilities, the costs of mobility, and so on" . In the long-run, unemployment is thus determined in the "classical" way, i.e. on a competitive labour market where unemployment is either voluntary or due to rigidities and the malfunctioning of labour market institutions. With the use of macroeconomic demand management policies, policymakers can keep unemployment below this natural level only at the cost of steadily accelerating inflation, which led to the name of a "non-accelerating inflation rate of unemployment (NAIRU)" as a synonym. Put differently, demand side policies can not be used systematically to reduce unemployment, they are neutral in the long-run and have only short term real effects when agents confuse nominal and real wages. B2.4) 'New classical macroeconomics' and rational expectations The short term effects of monetary and fiscal policy in the Friedman-model were due to the workers' temporary misconception of nominal and real wages. This was brought about by systematically wrong expectations about inflation, which in the Friedman-model were formed in an adaptive way. In the 1970s and 1980s, however, the 'new classical macroeconomics' appeared that questioned this construction and urged for a more radical reassessment of macroeconomics. Economic agents build expectations about future developments. Since the future is by definition uncertain, no agent can make predictions that are always absolutely correct, as there is always the possibility for stochastic and unexpected events. But the proponents of the 'new classical macroeconomics', most notably Robert Lucas, Thomas Sargent, and Edward Prescott, believed that agents will not make systematic errors. Friedman's use of adaptive expectations that left room for short run policy effects was replaced with the construction of rational expectations. This means that agents incorporate all available information that is at their disposal at any moment into their expectation formation. The consequence is that workers, when faced with inflationary government policies, would not misperceive nominal and real wages, but would correctly expect The ,,European labour market model" 51 falling real wages. Consequently, there is no room for the sort run mechanism a la Friedman, but inflationary policies are offset right away by changes in nominal wages in order to maintain the prevailing level of real wages. Put differently, because of rational expectations, output and employment in the models of new classical macroeconomics are permanently at the natural rate, except maybe for random disturbances (Lucas, 1972). The inherently stable economic system leaves no room for stabilization policy. Any attempt by policymakers to influence the output level via macroeconomic policies would only lead to inflation, or to a complete crowding out of private activities. The · new classical macroeconomics' can be viewed at as a modern and mathematically more articulate version of the pre-Keynesian classical economics. Both rest essentially on Walrasian general equilibrium theory with perfect competition and instantaneous price adjustments mandated by an imaginary auctioneer, and the · new classical' school has added rational expectations to this model. As it is well known, the W alrasian price tatonnement process leads to the clearing of all markets in the economy, including the labour market. The principal problem of the 'new classics' is thus more or less the same as it has been for the · old classics'. General equilibrium theory needs to answer why there can be business cycle fluctuations in a model where output is always at its natural level and agents have rational expectations.5 How can the observed short-run fluctuations of output and employment be explained in such an environment? Similarly, also the 'new classical macroeconomics' would have to come up with a convincing story why something like the Great Depression can unravel when markets work that perfectly.6 One way to deal with business cycle fluctuations in the context of 'new classical macroeconomics' was developed in the early 1980s and became known as "real business cycle theory (RBC)". RBC-models, pioneered by Kydland/Prescott ( 1982), are market clearing models with agents who form rational expectations. Fluctuations in output and employment are seen as resulting from exogenous technological shocks hitting the production function, and thereby the marginal productivity of labour. Agents in these models decide on intertemporal labour supply paths by equating the obtainable wage rate (the marginal product of labour) with the value of leisure. In view of adverse technological shocks, agents may find it optimal to engage in leisure or non-market activities, as falling wages can fall short of reservation wages. A typical RBC-model thus implies that output is always at its natural level, and this level fluctuates due to technological shocks. These models are therefore often called "equilibrium business cycle models". Any unemployment is entirely voluntary and simply determined by the optimal intertemporal allocation of time. But the use of the term "voluntary unemploy5 This puzzle was already noticed by Hayek (1933), p. 33 for the old general equilibrium theory. 6 For this debate see e.g. Lucas ( 1980), Tobin ( 1977) and Modigliani ( 1977). 52 The ,,European labour market model" ment" needs some further classification. Recorded unemployment rates by definition only include such persons who actively seek for jobs, i.e. no persons who have chosen not to belong to the labour force. However, this critique does not necessarily flaw the predictions of RBC-models and all other classical models that view unemployment as "voluntary". Firstly, these models might refer to a broader measure of joblessness ( e.g. the "non-employment rate") that also includes labour force drop-outs that in principal are interested in accepting a job, but not at going wage rates. And secondly, unemployed workers in reality have some degrees of freedom to signal job search activities, even though they are currently not interested to work. The main implication of classical and RBC models is simply that unemployment can not be viewed at as a phenomenon where individuals would be willing to accept jobs at going wage rates, but receive no job offers and thus remain unwillingly unemployed. B2.5) The Keynesian response The 'new classical' model of macroeconomics as well as RBC-models make extreme assumptions with respect to the rationality of agents and their state of knowledge, but also with respect to the functioning of markets. In particular, the models rest very heavily on the instantaneous price adjustments brought about by the Walrasian auctioneer. The first wave of Keynesian criticism against the new classical model was mainly concerned with the artificiality of the price tatonnement. What are the implications for the economy if this process is not functioning? Recall that in theory the Walrasian auctioneering process works such that some initial price vector for all commodities in the economy is announced, all market participants signal the quantities they are willing to buy and sell at these prices, the auctioneer calculates excess demands and excess supplies on all markets, and calls out a new pricing vector that brings quantitative supply and demand closer together. This process is repeated until the market clearing price vector is found. Only then do transactions take place, at the equilibrium prices that equilibrate supply and demand on all markets. Criticism against the artificiality of this theoretical construct was articulated by Clower ( 1965) and Leijonhufvud (1967, 1968) even before the emergence of the 'new classical' macroeconomics, with the original intention of "re-interpreting Keynes" in opposition against the neoclassical synthesis. Their works, however, where the precursors to much of the Neo-Keynesian critique in the 1970s, e.g. by Malinveaud ( 1977). Central to this literature was the analysis of economic systems when an auctioneer is absent and transactions take place at "wrong" prices.7 7 For a comprehensive overview of this school of Neo-Keynesian economics see Felderer/Homburg (I 993:287ff.) or Carlin/Soscice (I 990: I 06 ff.). The ,,European labour market model" 53 Clower (1965) has emphasised that it is highly artificial to assume that transactions only take place once the market clearing price vector is announced. In reality, there is continuous trading also at non-market clearing prices. Because markets do not instantaneously clear, agents face quantity constraints on some markets, which via a budget constraint also affects economic plans with respect to other markets. For example, if an initial price vector exists where the wage rate is higher than the theoretical market clearing level, agents can not sell the desired amount of labour, but rather face a quantity constraint on the labour market. Nevertheless, trading already starts at this pricing vectors and agents do not wait for an imaginary auctioneer to calculate market-clearing prices. Because agents supply less labour than intended, they can also not realize their desired consumption plans. They are forced to demand a lower quantity of goods, because actual income is below desired income. This is the essence of the "dual decision hypothesis". Agents first form desired economic plans. After having perceived quantity constraints, they have to adjust to market conditions and choose their actual economic plans. These actual plans are the optimal household decisions subject to the quantity constraints at the given non market-clearing price vector. The critical question is then whether there exist market forces that realign prices such that agents can gradually come to realize their desired economic plans. As shown by Dreze (I 975), this is difficult or even impossible if there is no auctioneer and all agents are atomistic. In other words, an economy might be trapped in a sub-optimal equilibrium where markets do not clear, because the Pareto-optimal Walrasian equilibrium is unknown to single agents and an adjustment process can not be triggered. Leijonhufvud (1967) emphasised that at best it takes a considerable amount of time for an economy to converge from a Keynesian equilibrium with quantity constraints towards the Walrasian general equilibrium. During the transition, there is room for government action, including the exploitation of multiplier effects through stabilization policy. To sum up, this first wave ofNeo-Keynesian economics with the so-called "fixedprice models" was concerned with the analysis of non-Walrasian equilibria.8 Involuntary unemployment can follow in these models, just as there is room for macroeconomic policy under some circumstances.9 It must, however, be stressed that the theoretical framework in this version of Keynesian economics was one of 8 Felderer/Homburg ( 1993:300) point out that the term "fixed-price" might be misleading. It means nothing more that there is no tiitonnement and no price auctioneer. 9 In particular Malinvaud ( 1977) was concerned with the distinction of 'classical' versus 'Keynesian' unemployment, i.e. with the question if rising real wages lead to more unemployment because of the neoclassical labour cost argument, or to less unemployment because of a boost in demand. Governments should therefore thoroughly analyse if unemployment is 'classical' or 'Keynesian· before taking any action. 54 The ,,European labour market model" atomistic agents and perfect competition on goods and labour markets. The bottom-line message was that within this very conventional market system, economies can still end up in sub-optimal equilibria with unemployment, because price adjustments do not work well. B3) The "European labour market model (ELMM)" During the late 1980s, a different macroeconomic approach was developed mainly in Europe that was popularised under the name ELMM, or "imperfect competition approach to macroeconomics". It is generally considered to be an approach in the Keynesian tradition, which is supported by the following citation that comes from one of its most famous adherents "My interpretation of the empirical evidence is that the magnitude and persistence of changes in statistically recorded unemployment are too large to be explained as variations in search or frictional unemployment, intertemporal substitution of leisure or a misinterpretation among economic agents regarding inflation or relative price and wage changes in the context of market-clearing models. The apparent unhappiness of many unemployed workers do not suggest that they have simply, in an optimal fashion, reallocated leisure in response to perceived temporal or intertemporal wage changes. [. . .] My inference from all this is that market-clearing approaches to the labour market cannot possibly be appropriate for an analysis of shortand medium-term macroeconomic developments. " Lindbeck (1992:209f.) Probably all Neo-Keynesians would subscribe to this viewpoint. But the new school departed from the "fixed-price model" described above, since there was a growing dissatisfaction with its micro-foundations. It appeared as if this literature has examined the properties of Walrasian systems with price rigidities, described non-Walrasian equilibria and classified 'new classical macroeconomics· as a very special case, where the prevailing price vector happens to be the market-clearing one. But this theory did not point to the origins and sources of price stickiness. 10 Moreover and more importantly, the use of perfect competition as the reference system of markets became increasingly unsatisfactory to economists. In particular for European countries it seemed much more appropriate to acknowledge that 10 This issue was later developed in much more detail in a different string of"Neo Keynesianism" that was concerned to formulate rigid micro-foundations for price stickiness in the context of Walrasian market-clearing models (menu costs etc.). For an overview of this literature see Gordon ( 1990). The ,,European labour market model" 61 the labour demand curve. 16 Its shape is determined entirely by the marginal product of labour (MPL ), i.e. by the properties of the underlying production function. If the capital stock is fixed and the production function exhibits neoclassical features, one would typically expect that labour faces diminishing marginal returns. If this is so, the PS curve under perfect competition becomes a downward sloping curve in the real wage/employment rate-space. With a low employment rate, the marginal product of labour is high. Product market equilibrium is obtained at a high real wage level. As the economy comes closer to full employment, labour faces diminishing returns, and product market equilibrium is only compatible with a lower real wage. However, it is subject to considerable dispute if marginal costs are indeed rising on an aggregate level (e.g. Blanchard/Fisher, 1989:463 ff.). For several reasons it is also conceivable that the MPL is actually constant. This will particularly be the case if the production function is such that capital and labour are used in fixed proportions. If this is the case, as in Blanchard/Katz (I 997:55), the real wage consistent with product market equilibrium is independent of the employment rate. The PS curve is then simply a horizontal line in figure Bl. The curve would also be horizontal if labour is seen as the only variable output, and constant marginal returns are assumed. But no matter if the PS curve is flat or downward sloping, the general equilibrium in this economy would lie at the intersection point of the PS curve with the upward sloping WS curve (at point B in figure B2). At this point, a combination of the real wage and the employment rate prevails that is consistent with equilibrium in both the product and the labour market. 17 We will come back to the case with perfect competit1on when discussing the wage curve approach of Blachflower/Oswald (1996). But now we tum to the (probably) empirically more relevant and the theoretically more interesting case with imperfect product market competition. 16 Under perfect competition the terminology PS curve it not fully appropriate, since the firm sector has no market power to set prices. However, the labelling is chosen in order to highlight the analogy with the imperfect competition case. 17 The issue of market clearing is this more is a bit more complex and requires some discussion. Since there is excess supply in the labour market, by Walras' law there must be excess demand on some other market. As Lindbeck (1992: 192) has put it, there is indeed 'notional' excess demand in the product market, since workers are income constrained because of unemployment. They can not demand as much goods as they would desire based on full employment considerations, i.e. at the Walrasian equilibrium represented by point C in fig. B2. The 'dual decision' hypothesis of Clower ( 1965) thus pops up again. However, perfect competition in the product market here simply means that there is no additional quantity rationing stemming from market power in the goods market. 62 The ,,European labour market model" b) Imperfect competition in the product market With imperfect competition, firms have market power and can actively set prices. Suppose that there is a large number of firms in the economy, each producing a distinct but symmetrical good under monopolistic competition. Each firm now maximizes profits subject to a downward sloping demand curve for its specific product. For simplicity we assume that labour is the only variable input of the firm. Profits are given by 1r = p(Y(N))Y(N)-wN (B.2) where Y(N) describes the short run production function for any firm, depending only on employment N. The downward sloping demand function is given by p(Y(N)). Maximizing (B.2) with respect to N yields the familiar rule that prices are a mark-up over marginal costs, which by definition is equal to the nominal wage divided by the MPL I w p=-- -- 1-1/a MPL (B.3) cr is simply the absolute value of the price elasticity of demand. To arrive at an expression for the PS curve under imperfect competition, we simply have to rearrange (B.3) in order to obtain w = (1-1/a)MPL p (B.4) The slope of the PS curve in the real wage/employment rate-space depends on two factors: a) whether the MPL is constant or declining in the aggregate employment rate, and b) whether the demand elasticity is a function of aggregate employment or not. As far as the MPL is concerned, the same consideration apply as for the case with perfect competition. Labour might face diminishing returns if the capital stock becomes a binding factor, but the evidence for this proposition in aggregate data seems scant. With respect to the demand elasticity cr, matters are also controversial. It has become common to work with iso-elastic demand functions e.g. of a CES-type. With these functions, the slope of the PS curve is entirely determined by the slope of the MPL. But some authors have argued that demand elasticity tends to be a pro-cyclical variable (Bils 1987, 1989). If this is so, the markup (l-l/crr 1 is decreasing in the employment rate and not constant. The ,,European labour market model" 63 Neither theory nor empirical evidence are fully decisive on the slope of the PS curve under imperfect competition, since neither the slope of the marginal cost curve nor the behaviour of the mark-up is known on an aggregate level. For most insights of the ELMM it is, however, not essential whether the PS curve is horizontal or downward sloping. B3.4) Equilibrium in the ELMM For simplicity and expositional purposes we will work with a flat PS curve. This slope can follow either because both the MPL and the demand elasticity cr are constant, or if the MPL is declining whereas cr is rising in ( 1-U). We will consider here the former possibility. Figure B2 graphically summarizes the ELMM, and highlights the differences between a competitive Walrasian equilibrium (point C), and the equilibrium points with imperfect competition in both product and labour markets (A), or only in the labour market (B). The Walrasian equilibrium with perfect competition in goods and labour markets is simply at the intersection of labour supply (LS) and labour demand (MPL). Of course, full employment is rendered under this competitive general equilibrium. But we have argued above that this Pareto-optimal situation might not develop, because of systematic market imperfections. Figure B2: Equilibrium in the ELMM Real wag LS w/p (1-1/cr) (w/p)*1---'------------, _ ____,. PS WSL---- I I I I I I U* :+=--+ I I I I 1-U* Employment rate (1-U) Product market equilibrium with perfect competition in the goods market is graphically described by the labour demand curve (MPL). For the imperfect competition case, the pricing behaviour of firms must be taken into account that is described by equation (B.4). The PS curve, the "labour demand determined real wage", will lie below the MPL. Equilibrium in the imperfectly competitive labour market is described by the upward sloping WS curve. For a general equilibrium, both the labour and the product market need to be in equilibrium. 64 The ,,European labour market model" With imperfections in both markets this is the case at point A. The real wage (w/p)* must be equal to the level that is determined by the PS curve. The associated unemployment rate U* can be called the "equilibrium rate of unemployment" (Carlin/Soskice, 1990), or, in reminiscence to Friedman's expression, even the "natural rate of unemployment" (Blanchard/Katz, 1997). 18 It is important to understand in what respect U* is an equilibrium rate of unemployment. Probably the best way to think about this issue has been proposed by Layard/Nickell/Jackman (1991 :8 ff.). They put strongest emphasis on the fact that equilibrium in the imperfect competition approach does not imply market clearing. It only means that private economic plans are compatible with each other, and that a system will return to the equilibrium configuration in case of a random disturbance. The WS and the PS curves represent such private plans. The WS curve represents how nominal wages are set in relation to goods prices in the labour market. The PS curve shows how firms on goods markets set output prices in relation to costs (i.e. nominal wages). Both priceand wage setters make their economic plans in real terms, and accordingly use their nominal action parameters. Suppose the WS curve is based on a monopoly union model. The union's bargaining power, and hence the real wage claim, positively depends on the employment rate. The union claims a nominal wage so as to achieve the desired level of the real wage, taking into account ( or forming expectations about) the prevailing price level. Equally, price setters are only concerned with the real value of their profits. They set prices in relation to the nominal wage in pursue of their economic plans in real terms. Only at the equilibrium level (w/p )* are the private economic plans compatible with each other. The adjustment mechanism that brings about the consistency of the real claims is the level of unemployment. The working of the ELMM can be seen best when considering an example. In figure B3 the general equilibrium is given by point A. This point represents the constellation of real wage and (un)employment, where output claims of firms and union are compatible. Suppose the union expects output prices to rise by 2% in the next year. Since the economy is in its long-run steady state in point A, the unions will claim nominal wage increases also equal to 2 %. The real wage is thus constant, as well as the real level of profits and the unemployment rate. Now suppose that a shock pulls the economy out off the equilibrium constellation A and to some point D that is associated with an unemployment rate Uo below the equilibrium level. The low unemployment positively affects the union's bargaining power. With adaptive expectations, the union expects inflation to remain at 2% in the next period. But at U0 the union will want to increase nominal wage by 18 One can see that the equilibrium rate of unemployment is lower with perfect than with imperfect product market competition. This is of course due to the fact that imperfect competition in the product market imply quantity rationing from firms, and thus lower labour demand. The ,,European labour market model" 65 more than 2%, say by 5%, in order to reach the desired real wage level (w/p)0. However, this real wage level would put the real profits under strain. Recall that firms set prices as a mark-up over wages, and the equilibrium conditions for the product market are only satisfied at the real wage level (w/p)*. At point D there is an inconsistency of economic plans. Put differently, the desired real wage income and the desired real profit level do exceed real output. Since this is not possible, an adjustment needs to occur that brings the competing claims of firms and unions for real output shares in line again. This will occur at first through a change in output prices. Typically the timing of the pricing decisions is assumed to be the following: first the union make the nominal wage claim based on expectations about future inflation and unemployment. Afterwards, pricing decisions of firms are made on the basis of the nominal wage claim, which then determine the actual rate inflation. 19 Since the firms seeks to maintain their real level of profits, they react to the nominal wage claim and increase prices also by 5% instead of 2%. With inflation equal to 5%, the real wage level is consistent again with product market equilibrium. Graphically this situation is given at point E in fig. 83, where the equilibrium real wage (w/p)* prevails, but on a higher nominal level than before. Figure B3: Adjustment in the ELMM Real wage w/p (w/p)o ws1.----- LS PS U* --i----------------~- Employment 1-U* 1-Uo I rate (1-U) At point E, unemployment is still at the level U0 below the natural rate U*. If in the next period the union still seeks to increase real wages, it would now have to claim nominal wage increases of more than 5%. Again, firms would respond by 19 In case the WS curve is based on efficiency wages rather than on a union model, both nominal wages and output prices are set simultaneously by firms that just need to bring together goods market considerations and motivation objectives. The timing of pricing decisions is discussed more intensively in Carlin/Soskice ( 1990: 163). 66 The ,,European labour market model" price increases proportional to the nominal wage increase. The ELMM thus predicts that unemployment can be kept below the natural rate only at the costs of accelerating inflation. Similarly, unemployment rates can remain above U* only in association with permanently falling inflation. Only at the equilibrium A are real wages claimed by unions and firms compatible with each other, and there is no need for a change in the rate of inflation. The unemployment rate U* can therefore be understood as the non-accelerating inflation rate of unemployment (NAIRU). However, note that inflation at U* does not necessarily have to be zero. It is just implied that the rate of change of nominal wages and output prices is identical. But will the system be endogenously driven back to the equilibrium value U* after an exogenous shock? In other words, are there endogenous forces that bring unemployment back from U0 to U*? So far we have only shown that maintaining unemployment at U0 imposes costs in form of an accelerating wage-price spiral. But unemployment dynamics have not been explicitly spelled out. Many authors such as Carlin/Soskice (1990) or Lindbeck ( 1992) are in fact not very explicit about this issue. However, a long-run convergence of unemployment to its natural level U* is the only economically plausible possibility. Otherwise, as pointed out by Layard/Nickell/Jackman ( 1991 : l 2f. ), there would be an everlasting wage-price spiral. The intuition for the transition from U0 to U* is easier to provide in the context of efficiency wage models at the core of the WS curve. Since here both wage and price setting is actually done by firms, real wages and (un)employment are determined simultaneously. The combination of an unemployment rate U0 and a real wage (w/p)* as in point Eis not sustainable, because unemployment is too low for given real wages to assure the optimal level of worker morale and effort. The firm sector will thus fire workers until the economy is at the equilibrium rate of joblessness, U*. In the context of a union model, firms do not set nominal wages. They set nominal prices in relation to the unions' wage claims. But they also choose the level of employment. Because we have assumed a flat MPL curve, firms can not speculate on a higher marginal productivity of workers at a lower employment rate. If the PS curve were to slope downwards, it would again be easy to see how the economy would converge to its long-run steady state at point A. But the basic trade-off implied by a downward-sloping labour demand curve, that plays a very prominent role in other collective bargaining models such as McDonald/Solow ( 1981 ), is absent with this linear technology. However, there is no reason to believe that firms will keep on reacting to excessive nominal wage increases only with rising output prices. There will also be a reduction in employment to the equilibrium level (1-U*) in order to avoid the wage-price-spiral. The equilibrium combination of unemployment U* and real wages (w/p)* is thus going to prevail in the long-run. In the short-run, unemployment can differ from its natural level. But changes in inflation and subsequent changes in employment The ,,European labour market model" 67 will gradually restore the general equilibrium, which is characterised by a consistency of claims for real output shares of wage and price setters. 83.5.) Some further issues of the ELMM Is the ELMM really a Keynesian model? Since we have placed the ELMM in the tradition of Neo-Keynesianism in the brief history of economic thought that was presented in section B2, one might somehow be biased to say that the ELMM is Keynesian. This is correct insofar as it is by nature a non-market clearing approach with involuntary unemployment.20 However, the model also has a NAIRU and a long-run vertical Phillips-curve as an integral part, which sounds pretty familiar from Friedman's (1968) classical model. It would thus probably be most appropriate to view the ELMM as a model with both Keynesian and classical features. For the remainder of this chapter, we want to illustrate this claim a little bit further by comparing the ELMM directly with the Friedman-model and other essential approaches introduced in this chapter. Even though both the ELMM and the Friedman-model imply the existence of a "natural" rate of unemployment at which inflation is remaining constant, there are still some notable differences. Most notably, these are the underlying microfoundations and the general concept about how the labour market works. This can be seen best by an example that highlights the differences: Both the Friedman-model and the ELMM share the policy implication that a deprivation of union bargaining power would lead to a lower equilibrium rate of unemployment. In the Friedman-model this would directly reduce the NAIRU, which is reflecting structural characteristics of the labour market. In the ELMM, lower union bargaining power ceteris paribus shifts down the WS curve, so that the intersection with the PS curve occurs at a lower level of U. However, the ELMM would still not imply that the deprivation of union power would transform the labour market into a perfectly competitive ideal. As argued in section B3.1., there are additional arguments that are inherent to the labour market itself why wage underbidding and perfect competition among workers will not occur: efficiency wage considerations as well as inevitable tum-over costs on which insiders can rely also without unions. The ELMM derives from a fundamentally different view with respect to the working of labour markets. Friedman's reference model is a Walrasian system with perfect product and labour markets. The equilibrium rate of unemployment is thus seen as a measure of market malfunctioning, or as the degree of deviation 20 This does by the way not imply that all observed unemployment in industrialized economies is entirely involuntary. Lindbeck (1992) points out, that the ELMM might just describe the rationing process of in a primary labour market. Individuals who are kept away from · good jobs· still have to decide whether they accept jobs in an unregulated and usually flexible secondary labour market that can more realistically be described in the usual fashion as a market with perfect competition. It is easy to see how institutions and welfare state arrangements play a role for this individual decision problem. 68 The ,,European labour market model" from the desirable ideal of perfect competition. The ELMM on the other hand acknowledges that the labour market is systematically, by its very nature, characterised by imperfect competition and has no endogenous tendency to clear. Differences between the ELMM and the Friedman-model also concern the endogenous inflation-unemployment dynamics. Recall that the initial inflationary impulse in Friedman (1968) comes from a monetary injection that stimulates aggregate demand. Short run real effects arise because workers on instance misperceive higher nominal wages with higher real wages. The lower unemployment can only be sustained if authorities keep on injecting money into the economy and systematically keep on confusing the individuals' perceptions. The mechanisms of the short-run trade-off between unemployment and inflation in the ELMM are fundamentally different. If unemployment is below its natural level (e.g. because of a demand stimulus), inflationary pressure arises because the bargaining positions of wage and price setters have shifted. Through inflation and employment changes, the real claims on output shares are brought back in line again. Monetary accommodation is not at all needed for this inflation mechanism, nor is the explicit introduction of money. Inflation in the ELMM is not a monetary phenomenon, but is rather stemming from the "battle of the mark-ups" (Layard/Nickell, 1986) between wage and price setters. The similarities between Friedman and the ELMM are more or less exhausted with the common result that unemployment can be kept below the equilibrium rate only at the cost of accelerating inflation, and with the use of adaptive expectations. Both approaches do not work with the extreme construction of rational expectations as 'new classical macroeconomics'. If this were the case in the ELMM, the inflation-unemployment dynamics we have just spelled out would not develop. The economy would rather always be at the equilibrium constellation U* and (w/p)*. Note, however, that the use of rational expectations does not imply that the emergence of equilibrium unemployment vanishes. The underlying causes, the market imperfections in labour and goods markets, are more general and do not hinge on the type of expectation formation. It should be mentioned that the ELMM can be used as a framework to analyse the impact of various exogenous shocks or policy interventions on real wages and unemployment. Among the issues that have been analysed in the vein of the ELMM are structural change, a change in labour productivity, employment subsidies, taxation, profit-sharing schemes, monetary and fiscal policy etc. 21 We have argued in this chapter that the main motivation for developing the ELMM has been the insight that labour markets in the real world can not, or at least should not be modelled as a perfectly competitive market. There is "some21 For an extensive coverage of policy implications of the ELMM, see: Layard/Nickell/Jackman (1991); Blanchard/Katz (1997); Bean (1994); and various others. The ,,European labour market model" 69 thing special" about the labour market (Solow, 1990). Approaches with imperfect competition seemingly are more appropriate for describing labour markets from a theoretical point of view. Stated in more technical terms, the major insight of the ELMM has been the replacement of a standard competitive labour supply function with an upward sloping WS curve, which has required micro-foundations radically different from the usual neoclassical ones. The economic arguments that are at the root of the WS curve also apply to the wage curve on the basis of regions, to which we tum now. The wage curve 77 utility from wage income Wr, but disutility from work-effort er. Utility V, is assumed to be linear. V, = w,-e,. (C.2) Effort at work is assumed to be a technologically fixed number er> 0. Individuals can choose to "shirk" at work and spend zero effort er=0. Shirking individuals run the risk of being detected and then fired. The exogenous detection and firing probability (I-yr) < l is Jess than perfect. Once fired, an individual enters the pool of the unemployed. Yet, following Shapiro/Stiglitz (1984), there is also some exogenous destruction rate of firms Rr > 0 that likewise leads to an inflow from employment to unemployment. For simplicity, we assume that unemployed persons have no source ofincome.5 The unemployed have a chance Ur of re-entering into a job. This endogenous variable depicts the flow from unemployment back into the pool of the employed. In the steady state equilibrium, the two labour market flows must be equal. Given that nobody will shirk in equilibrium, we can write this condition as Rr N, = a, (Lr-E,), where L, is the labour force and Er is employment. The definition of the unemployment rate is Ur= 1Er!Lr. This determines the function a, to be a,= (R, / Ur) - R,. Thus, the outflow probability from unemployment is decreasing in the regional unemployment rate Ur. With these assumptions, the ( expected) utility of an unemployed individual (V ur) is given by Vu,= a, (w, - e,). (C.3) Non-shirking employed workers and shirkers have utility levels Yenr and Yesr respectively Venr = w,- e, Vesr =r, Wr + (1-r,)(a,(w,- e,)). (C.4) (C.5) The firm has an interest to prevent shirking and will thus pay efficiency wages that are just sufficient to ensure equal utility for shirkers and non-shirkers, i.e. Yesr=Yenr• Equating (C.4) and (C.5) yields after some manipulations the following expression 5 In most parts of the efficiency wage framework of BIO, they assume that regions might differ with respect to the level of unemployment benefits. We do not consider these cases, because it is irrelevant for most continental European countries. Unemployment benefits are generally not differentiated across regions. We therefore have assumed that unemployment benefits b, are equalized on the level b,=O. This normalization, however, is only for analytical simplification. 78 The wage curve w =e + r, e, ' ' (l-y,)(1-a,(U,)) (C.6) Equation (C.6) is the regional wage curve and can be interpreted as the aggregate non-shirking condition in region r. It shows the efficiency wage that is sufficient to prevent shirking for any given unemployment rate, and given the structural parameters e, and y,. The graphical representation of (C.6) qualitatively looks like in figure C 1: the required efficiency wage is lower, the higher is the regional unemployment rate U,. The intuition for this result is clear. At any given shirking detection probability, individuals become more reluctant to shirk when the unemployment rate is high. Becoming unemployed is perceived to be a strong penalty. Consequently, firms do not have to rely on a wage premium to prevent their incumbent workforces from shirking. As the regional unemployment rate decreases, becoming unemployed is less of a threat for single workers, and shirking becomes a more viable option. To prevent shirking, firms pay efficiency wages w, > e,, since workers then put stronger value on their specific, well-paid jobs and abstain from shirking. The required efficiency wage is higher at any level of U, the higher is the disutility of effort e, and the lower is the shirking detection rate (1-y,).6 What B/O essentially do is to bring this aggregate non-shirking condition in a two-region context. They assume that both regions are structurally identical, meaning that R,, e, and y, are the same in both regions.7 This implies that both regions face the same wage curve, i.e. the same labour market equilibrium curve given by equation (C.6). BIO then analyse what happens if one region is intrinsically more attractive than the other, e.g. because of climatic and cultural circumstances. This region offers an utility supplement ~ to each individual who lives and works there. They show that regardless of~. both regions will still face exactly the same equilibrium locus with respect to unemployment and wages, the identical wage curve fig. Cl. This 6 With perfect infonnation on workers effort (yr=0), the finn would only need to pay wr=er for any unemployment rate to prevent shirking. Note further that with imperfect monitoring (y,>0), full employment is not possible in equilibrium, since ur<l requires that U,>R/(l+Rr)- Put differently, the required efficiency wage would have to become infinite. 7 One might potentially introduce differences in the structural parameters er and Yr across regions. These differences might e.g. be thought of as differences in labour market institutions, although the disutility level of effort or shirking detection rates are typically not the kind of institutions that seem directly relevant labour market comparisons. Model extensions are conceivable where Yr is influenced by regional employment protection laws, or er is some sort of reservation wage dependent on regional welfare state arrangements. But the same argument as for unemployment benefits applies: usually the degree of institutional variation across regions within the same country is very little in continental Europe. The wage curve 79 can be seen by considering the equilibrium condition (value of shirking equal to value of non-shirking) for the intrinsically attractive region. Wr-e + q = y(wr+;) + (}-Yr) { ar (Wre)+ q} In the process of substitution, the term ~ will cancel out, and the attractive region will face the same labour market equilibrium locus (C.6) as the unattractive region. But, as will be become more clear in the next section, BIO also assume mobile workers. If the "economic variables" w, and U, were the same in both regions, workers would want to move to the intrinsically more attractive area, since here they are rewarded with an utility bonus ~- BIO (1996:69) show that in an interregional equilibrium, which is characterized by a situation where there is no incentive for further migration, the attractive region will exhibit a higher expected unemployment rate and a lower expected wage. In other words, the intrinsically unattractive region has to compensate for its missing amenities by offering better "economic" values. The unattractive region will thus be located on the upper left part of the wage curve in fig. C 1. The attractive region on the other hand will find itself on the lower right tail of the wage curve. In observable regional data, a negative correlation between regional unemployment rates and wages is visible, since both areas are located on the same wage curve. C3.2) General equilibrium in the BlanchflowerlOswald-model This notion already gives an idea of how BIO will establish the stability of the wage curve as a long-run equilibrium curve. But these implications will only become fully visible when moving to a general equilibrium characterization of this economy. The wage curve in figure Cl only represents "one half' of equilibrium, analogous to the WS curve in the ELMM. It needs to be determined exactly where on the wage curve the single regions r=l and r=2 will end up. This will be a matter of goods market equilibrium. So, the full equilibrium in the BIO-model is also determined by joint equilibrium on labour and goods market, in full analogy to the ELMM. BIO assume that each of the two regions produces a distinct tradable commodity under constant returns to scale and perfect competition. The product market equilibrium they derive is therefore qualitatively identical to the case from section 83.3a). They assume that the production function for the regional tradable good Y, is given by Y, = f(N,,K,). Capital (K,) is assumed to be an essential input of production, for which the price i is determined on world markets. Labour and capital in both regions have to be used in fixed proportions. Firms in both regions will thus face the following minimum cost function C, C, (Y,., w,, i) = }J,1.~ { w,N, I Y,. + iK, I Y,.} = Y,. c, ( w,, i) (C. 7) 80 The wage curve Under this limitational production function with constant returns to scale, total minimum costs are simply the product of minimum unit cost (er) times the quantity of output Yr. Perfect competition implies that minimum unit costs Cr(Wr,i) need to equal the product price Pr in order for profits to be zero. The goods market equilibrium is given by the condition Pr= Cr(Wr, i). The product prices p1 and p2 for the two regional commodities Y1 and Y2 again ground out from a Walrasian tatonnement process, and are thus given to any single firm. Without loss of generality, B/O normalize the given product price for the good that is exclusively produced in region 1 to unity. The price of the product from region 2 is denoted p. Equilibrium in goods markets then requires that 1 = c1( w1,i) and p=c2( w2,i ). General equilibrium in either region is reached when product and labour market are jointly in equilibrium. Since both regions face the same wage curve locus, the graphical representation of the general equilibrium in both regions can be illustrated in only one diagram, fig. C2. Figure C2: Full equilibrium in the Blanchflower/Oswald-model Wr o = c, (w,. i) Wage curve u, The horizontal curves represent the product market equilibrium conditions for region 1 and 2 at the given output prices 1 and p. Full equilibrium in either region is obtained at the intersection points with the wage curve, i.e. at points A and B. At point A, firms make zero super-normal profits and shirking is deterred in region 1. The same is true for region 2 at point B. If the parameter constellation is such that p2<p1 (p<l ), nominal wages are higher and unemployment is lower in region 1. Note that with freely tradable goods, workers from both regions face the same consumer price index, and nominal wage differences are thus equal to real wage differences. Hence, for this constellation of exogenous product prices in fig. C2, region 1 is advantaged over region 2 along The wage curve 81 two dimensions: the real wage is higher in region 1, and the unemployment rate is lower. But for a full interregional equilibrium, also all migration incentives must have vanished. In the situation depicted in the diagram, this is not yet the case. Individuals from region 2 have an incentive to move to region 1. BIO (1996:81) are not very explicit about the technological effects on labour productivity and wages if migration occurs. This will of course crucially depend on the properties of the underlying production function. If firms can adjust the essential capital input proportionally with the additional stock of workers, the MPL, and ultimately the zero profit curves in fig. CI would remain unchanged. The incentive for migration would remain constant, as the regional wage gap is independent of the number of migrants and only depends on the exogenous product prices. Matters are different if the capital stock can not be adjusted. Under this circumstance, every additional worker has a marginal productivity of zero, since the technology is limitational. However, the total amount of labour (measured e.g. in working hours) that is technologically efficient for the given capital stock can simply be shared among a higher number of workers. The total wage income in both regions would thus remain constant, but the wage per worker in region I and 2 would converge through labour migration. Migration would thus lead to convergence of per capita remunerations and ultimately to an erosion of the wage curve relation.8 However, BIO partly avoid these discussions about technological effects of migration by going back to their construction with intrinsic regional characteristics that was mentioned earlier. Recall that they have developed the implications of differences in the intrinsic attractiveness of regions. In partial equilibrium, these intrinsic differences were exogenous. Now they endogenise the utility supplement ~ and make it negatively proportional to the population density of a region. In other words, as workers move into region I because of the better economic situation, the place becomes gradually crowded and thereby unattractive. With this construction of congestion, it is possible to construct general equilibria with the zero-migration condition satisfied. These will look like figure C2. Regions one the "bad side" of the wage curve will compensate individuals with inherent regional amenities, in this case by the fact that there is little congestion. In terms of the observable economic variables w and U, however, a wage curve is visible in the data. The regional values ofw and Udo not collapse into one point, because the compensating amenities make up for the regional differences in wages and unemployment. The wage curve is thus seen as a long-run equilibrium phenomenon, because single regions are placed at different points along the labour market equilibrium schedule. Regional wages and regional unemployment are 8 A more detailed discussion about the effects of migration in a model with a neoclassical production function is provided in chapter F. 82 The wage curve negatively correlated in equilibrium, and these regional disparities persist and show no tendency to vanish. C 3.3) Critique of the Blanchflower/Oswald-model Even though B/O intended to depart from the work of Harris/Todaro ( 1970), both models share some important common characteristics. Both subscribe to the idea of an equilibrium with compensating differentials, which is reached when incentives for migration have vanished. In the Harris/Todaro-world, unemployment rates and wages together form an equilibrium of compensating differentials and therefore are positively correlated. In the world with a wage curve, intrinsic regional amenities make up for the combination of unemployment and wages, which now are negatively correlated. The first critique against the Blanchflower/Oswald-model is that the substantial origin of regional differences remains an open issue. Regions are assumed to produce different final goods and sell them at different exogenous product prices under perfect competition. Thus, two principally identical regions still manufacture different commodities, which consequently leads to disparate regional development. The whole analysis is incapable of pointing to the very reason for regional differences in depth. Why can regions with low selling goods not switch over and manufacture better commodities? What is the reason that one local entity produces a "better" good than the other, which ultimately is rewarded with a lower unemployment rate and a higher wage? These questions remain unanswered. The second problematic aspect with exogenously given product prices is the apparent identification of regions with sectors, or at least with specific products. Because this identification is much more explicitly developed in the Blien-model that will be discussed in the next section, this critique will be postponed to a later point. The third critique concerns the analysis of labour mobility. As noted before, all individuals have a principle interest to move to the region with the "better" final product, which has both lower unemployment and higher real wages. If nothing else is added, the wage curve relation in the BIO-model would erode, and it would not be a stable long-run equilibrium relation as the authors imply. But BIO assume, in an "ad-hoc" way, that regional preferences are operating as an opposing factor. The critical point with this ad-hoc-construction is that the long-run stability of the wage curve (the main contention of B/O) crucially hinges on it. From a theoretical point of view, this does not seem fully convincing. Blien (2001:96ff.) points to another critical aspect: within the general equilibrium model, the original causality of the wage curve running from unemployment to wages suddenly has changed without explicit notice. The wage curve theory meant to provide rationale for negative wage effects of unemployment. But in the model of B/O, now exogenous product prices determine a wage rate via the zero profit condition for firms. Only in a secondary step is unemployment determined, The wage curve 83 but in an unusual way such that high wages are now associated with low unemployment. We subscribe to the critique of Blien, even though one can think of regional wages and unemployment rates as being simultaneously determined. It is still one more representation of the fact that essentially everything is driven by the exogenously given product prices in the model ofB/O. C 4) The model of Blien (2001) To cope with several critical aspects of the BIO-model, Blien (2001) presents an own approach to wage curve theory. This concerns both the partial equilibrium foundations of the wage curve, and the integration of the wage curve into a full model with a product market. C4.1.) Partial labour market equilibrium in the Blien-model Blien's motivation to base the wage curve on different micro-foundations are unrealistic features of the Shapiro/Stiglitz-world. Individuals in reality do not decide just whether to shirk completely or to provide full work effort. Moreover, strict legislation on dismissal policies often prevent firms from firing shirking individuals in Europe, specifically because the definition of shirking is difficult to formulate in reality. Therefore Blien 's main idea is that firms do not try to solve an "information problem" stemming from imperfect monitoring possibilities. Instead, they solve an "enforcement problem" and try to use efficiency wages to motivate employees to spend more work effort. His partial equilibrium model of the wage curve is inclined by the labour turnover approach of efficiency wage theory, and specifically builds on work by Schlicht ( 1978). The core idea of this approach is that individuals do not simply decide whether to supply full work effort or to shirk completely, but that the chosen effort level is a continuous function. Consider some individual worker, who has a job at some firmj. The worker's effort is given by the following function A (C.8) with oA I awi >O, oA/oUr>O. The worker will spend more effort the higher is the wage of firm j relative to some exogenous market wage w, and the higher is the unemployment rate is the respective region of residence. The intuition for the derivatives is straightforward: The penalty of loosing the particular job is greater for the worker the better she is paid at the particular firm j, and the worse are the outside prospects approximated by the regional unemployment rate. Work effort is an insurance for the worker against an individual lay-off. Therefore, the worker will spend more effort the higher is her interest in remaining employed at this particular firm. 84 The wage curve The firm's problem is to maximize profits, taking into account the effects of efficiency wages on workers' performance. When aggregating over the wage setting decisions of identical firms in region r, Blien (2001) ultimately also arrives at a wage curve relation. We just present the analytical expression of the wage curve that is given by equation (C.9) or In w, = In w - /J In Ur + /J In U w (}fl w, =--/JU, (C.9) U, and w, are regional values of unemployment rate and wages, whereas (} and w are exogenously given values of national averages. Equation (C.9) is also a negatively sloped (non-linear) wage curve that can be graphed like in fig.Cl. It analogously provides the labour market equilibrium relation for every region. C4.2.) The product market and general equilibrium in the Blien-model To move towards a full interregional general equilibrium model, Blien needs to specify the product market conditions. He assumes that each region is specialised in a single, distinct product or industry, just like B/O. But he adds a dynamic component to the product markets, by applying the idea of product cycles. Let demand and supply for the good of region r be given by the following two simple equations P, = ab Y, P,= M w,/D, ( demand curve) (supply curve) (C.10) (C.l 1) a, b are exogenous parameters for the demand side. M is also exogenous and captures a mark-up of prices over wages to pay for the rental rate of capital. Y, is regional income, D, is labour productivity, defined as D, = Y,/N,, where Nr is employment. Upon substitution, one can obtain the following expression. a M N =-----w r bD, bD; r (C.12) Under the use of the definition of the unemployment rate Ur = (L, -N,) / L, this expression can be rewritten as Mw a U =I+--'---- , bL,D; bL,D, (C.13) The wage curve 85 If we think of the wage w, as being exogenously given, equation (C.13) could be used to analyse the impacts of productivity improvements on unemployment.9 This type of analysis has been introduced by Appelbaum/Schettkat ( 1995). Their main result can be summarized as follows: A productivity improvement leads to an increase in employment, if the elasticity of demand on the product market is greater than one. Similarly, unemployment will increase in response to productivity improvements if product demand reacts inelastic. 10 The idea of product cycles enters in the following way. New products tend to face largely unsatisfied demand, and their price elasticity therefore is high. But specific products age over time, demand becomes largely satisfied. Price elasticities decline, and productivity improvements and lower prices do not translate any longer into an increase in total production. Think of the regional consequences of product cycles, if the single regions are completely specialized. The regional development is then driven by the dynamics of the market for the region-specific product. Blien (2001) assumes that improvements in labour productivity are exogenously given and identical for all regions. This has different effects on the single regions, depending on the state of the specific products within the cycle. Those who specialize in old products will be harmed, as higher productivity effectively leads to more unemployment. The opposite is true for regions with young products at the beginning of the cycle. There is a high elasticity of demand for the specific commodity, and productivity improvements (=falling prices) translate into higher employment. Equation (C.13) is the "second half' of full equilibrium, since it characterises the product market equilibrium and is a representation of labour demand. Graphically this is an upward sloping line in the (U,w)-space. For full equilibrium, equations (C.9) and (C.13) need to be integrated. Upon substitution, we obtain the following implicit function Z Z=U, M wiJPu-P a ------,~'-+---1=0 bl, D; bl,D, (C.14) The central insight of the product market dynamics remains unchanged: Whether productivity improvements at given wages decrease or increase the regional unemployment rate depends on the elasticity of product demand. But now the wage curve comes into play. Changes in unemployment will have wage effects, which in tum will again influence labour demand. For example, if there are productivity improvements and inelastic product demand, unemployment will increase. Due to 9 Be aware that since M is a fixed number, the relative factor intensity is assumed to remain constant even with improved labour productivity. 10 See Blien (2001: 120 ff.) for a formal elaboration. 86 The wage curve the wage curve, the necessity to pay efficiency wages is relaxed to some extend and equilibrium wages fall. This drop in wages then stimulates labour demand and consequently lowers unemployment, but to a smaller extend than the initial loss. 11 The final scope now is to integrate these ideas into a full interregional equilibrium. So far, Blien (2001) has shown how product market dynamics drive the equilibrium values of wages and unemployment rates for the single regions. In the long run, however, individuals from regions specialized in the production of commodities at the end of the product cycle do have an incentive to emigrate to booming areas. Recall that BIO have argued that individuals in lagging locations are compensated by "non-economic" amenities, and that the wage curve is thereby stable over time. Blien pursues a different path here. He acknowledges that workers will move to those areas where wages are high and unemployment is low. But he rightly points out that migration is not an instantaneous reaction to small differences in economic variables. It is a costly and slow process. Blien argues that migration will gradually take place in response to regional inequalities. Because of this, the regional disparities will slowly fade away, other things being equal. The wage curve is thus not a long-run equilibrium curve in his model, but rather one of temporary short-run equilibrium. But he does not present a formal integration of this argument into his model. He just states the principal tendency of the wage curve to erode due to labour mobility. In regional data, however, wage curve relationship is visible, because the equilibrating forces are weak, and frequent impulses from product markets keep the labour market in motion permanently. A wage curve that is detected in the data is a representations of permanent disequilibrium and sluggish adjustment in the labour market. C 4.3) Critique of the Blien-model The main innovation of the Blien-model is the integration of a dynamic element, the product cycle, into the model. By this construction, a boom for a region has the same origin as a possible subsequent downturn: the state within the product cycle. This dynamic element has great merits compared to the rather static approach of B/O with exogenously given product prices. By inspection, one can think of various examples where the economic situation of a region was inevitably linked to one very characteristic product: shipbuilding in the German harbour cities in the North, coalmining in the Ruhr area, and so on. But the identification of 11 One can see this argument more clearly by analysing the impacts of a demand shock on unemployment with and without wage reactions. The derivative 8U/8b in equation (C. 13) gives the unemployment reaction if wages are fixed, the same derivative for (5) shows the reactions if wages are endogenously determined by the wage curve reaction. One can show that with fixed wages reactions are more drastic. The wage curve hence smoothes out some effects, since wages move in the opposite direction as unemployment. New economic geography 93 "new trade theory" (NTT) of Krugman (1980). Ever since Krugman (1991 a,b ), NEG became a rapidly growing field of interest in academic economics. Various other models have appeared that elaborated on different agglomeration and dispersion forces, used different model assumptions, worked with different solution techniques etc. We will highlight and survey some distinguishing ideas and modelling strategies in section D6 and discuss the most recent developments in the field of NEG. Still, we come to the conclusion that the state of the art in NEG still has left various open and unsettled issues, out of which we concentrate on two. The first one directly concerns the main topic of this book. NEG models almost without exception assume full employment and automatic labour market clearing. They are therefore incapable of analysing regional unemployment disparities. This neglect will be taken up in chapter E, where we try to pull the pieces of regional agglomeration theory and regional unemployment together. However, the neglect of unemployment is not the only omission of NEG as it stands today. In section D7 we point to another strange implication of the Krugman-model that is at odds with real world evidence. The standard NEG-model predicts that the industrial agglomeration centres have lower overall costs-ofliving than rural peripheral areas. This empirically unsatisfactory result has not been addressed in the literature so far. We therefore take up this issue and develop an own NEG-approach that is capable of reproducing the main results of the Krugman-model, but that has more reasonable implications with respect to regional costs-of-living. This issue is a bit off-topic with respect to the analysis of regional unemployment disparities. Nevertheless, it improves the state of art in agglomeration theories, which are "one half' of our theoretical backbones. Therefore the model developed in section D7 should be seen as an additional and complementary contribution that comes from this book. D2) Scale economies, externalities and market competition Increasing returns to scale describe a situation in which an increase in the output level implies a decrease in the average costs per output unit. One can distinguish between "internal" and "external" economies of scale (Scitovsky, 1954 ). The former concept refers to the case where a single firm faces a downward sloping average cost curve when increasing its own output level. This type of scale economies arises e.g. if production incurs fixed costs and marginal costs are constant. Internal scale economies at the plant level play a dominant role in the Dixit-Stiglitzmodel and therefore also in NEG. It is clear that internal scale economies are inconsistent with perfect competition, since merging production of two atomistic firms would always be dominant over separating production activities. The DixitStiglitz-model of increasing returns therefore works with monopolistic competition: each firm produces a distinct commodity under increasing returns. The single varieties are linked in the sense that consumers can substitute between these single 94 New economic geography goods. The elegant feature of the Dixit-Stiglitz-model', that allows for many of its derivations, is the critical assumption that all single commodities enter symmetrically into the utility function of the representative consumer and that the elasticity of substitution between commodities is constant. The concept of "external" increasing returns on the other hand refers to the case that scale economies arise on an aggregate (spatial or industry) level, making average costs per output unit a decreasing function of aggregate output. One can distinguish between pure and pecuniary externalities. With pure (technological) externalities, an increase in aggregate output changes the technological relation between input and output for each firm, i.e. it affects the production function on the micro level. Typically, the aggregate externality enters the production function through some term capturing the total factor productivity A. Consider e.g. the production function of a single firm to be where yi is firm output, k and n are the firms capital stock and employment respectively, and Y is some aggregate variable (e.g. aggregate output) beyond disposal of any single firm. An increase in Y has a positive effect on the total factor productivity A and thus on the firm's output y for given input levels of k and n. Since the aggregate externality enters parametrically into the function y, this type of increasing returns is consistent with perfect competition (Chipman, 1970). This modelling strategy has a long tradition in particular in the first wave of endogenous growth theory, where the aggregate externality represents e.g. some form of "learning-by-doing" (Arrow, 1962), when A is a function of the aggregate capital stock K, or a human capital externality (Lucas, 1988), where A is increasing in the aggregate stock of human capital.5 Pecuniary externalities, or pecuniary external economies of scale, are instead transmitted through the market price mechanism and do not influence the relation between inputs and outputs (i.e. the production function) on the level of single firms. An increase in aggregate output rather has impacts on goods or factor prices e.g. through a "love-for-variety effect" on the consumer side, or through a greater variety of industrial inputs. This reasoning is often labelled a "market linkage" or "market interdependence" and is the second essential feature of the Dixit-Stiglitzmodel of monopolistic competition. This seminal model thus works with internal scale economies on the plant level, as well as with a pecuniary externality on an aggregate level. The details of this proposition will become clear below when we 5 For an overview of this first wave of endogenous growth theory, also in opposition to the second wave of "innovation based" growth models, see Romer (1994). Essentially the effort of this string of theory was to look for ways to overcome the "tragedy of diminishing returns" inherent to neoclassical production functions, but inconsistent with real world evidence on income convergence. New economic geography 95 discuss the core model of NEG, which is essentially a spatial version of the DixitStiglitz framework. To sum up, increasing returns to scale usually require that markets are imperfect. Marshall (1890) was probably not fully aware of this requirement when he developed three distinct arguments why economic activity tends to push for spatial agglomeration. To these intuitive arguments we tum next. D3) The Marshallian agglomeration economies The three Marshallian arguments for industrial agglomeration can be labelled in modem terminology as follows. Agglomeration of economic activity ensures a) the availability of large markets for specialized inputs, b) the presence of knowledge spillovers, and c) forward and backward linkages stemming from a large market size for final products. In this section, we will briefly introduce the main ideas for either of these forces, as well as introduce another argument from endogenous growth theory. a) Large markets for specialized inputs In simple neoclassical models, input factors are mostly homogenous. This means that all workers are assumed to be identical, with no differences in skill, education etc. In modem real-world societies, however, production processes are highly sophisticated and require very specialized skills and intermediate inputs. These are not easily available everywhere. For example, computer specialists are concentrated in Silicon Valley and hard to find in Nebraska. Financial market insiders live in London or Frankfurt, not in Finland. Modem firms thus have an incentive to locate where such specialized human capital is available. On the other hands, specialists in any industry have an incentive to move to areas where there is not only one potential employer, but a high number of them. Thus, there is a reciprocal advantage for local concentration: skilled workers go where firms are, and firms go where workers are. Note that this 'cumulative causation' mechanism particularly applies to high skilled workers. For many low skilled professions, there is often not THE place to go. But this does not mean that low skilled workers would not to gain from local concentration of specialists in their region. For example, if many sophisticated specialists pool in some region A, also the low skilled workers from that area will benefit, because different types of labour are complementary (Matsuyama, 1995). Theoretical issues on the labour pooling argument come e.g. from Krugman ( 1991 b ). Evidence for the empirical relevance of the argument has been provided e.g. by Audretsch/Feldmann (1996). Formally, the presence of a large pool of specialized inputs can be seen as a pecuniary external scale economy for any single firm, since being close to large factor markets enables firms to hire specific inputs at lower costs. 96 New economic geography b) Knowledge spillovers and externalities A different argument why firms from the same industry like to cluster together are external knowledge flows and spillovers that require personal proximity. For example, it is easier to gather information about competitors, about sector specific news, to make deals, to negotiate contracts etc. if many firms from the same industry cluster in the same location. Essentially, the argument can be expressed in formal terms like in section D2, where we have introduced the purely external form of increasing returns. Knowledge spill-overs imply that firms have an advantage when operating in some location A with a high density of firms from the same industry rather than in isolation. The pooling advantages shift the efficiency frontier of any single firm through a total factor productivity term as described above. The use of pure externalities is therefore convenient if one is preoccupied to maintain a market structure of perfect competition. F /K/V and Krugman (1991 b ), however, criticize its use as a modelling strategy that "looks like assuming one's conclusion". Since spill-overs are not market-mediated but exogenously imposed, the concept lacks some theoretical substance and might suffer from "ad-hocery". This does not imply that it is irrelevant. 6 But the availability of imperfect competition models like the Dixit-Stiglitz-approach at least made it possible from a theoretical point of view to advance to other approaches of increasing returns that were more sufficing. c) Market size effects and linkages The last of the classical Marshallian arguments for agglomeration are linkages stemming from large markets for final products. This third mechanism is actually at the core of the Dixit-Stiglitz-model and thus of NTT and NEG. It will be discussed in much more detail below. Nevertheless we want to briefly describe its intuition here. The linkage argument heavily rests on two essential assumptions: firstly, there are internal economies of scale at the plant level through the existence of fixed costs that restrict firms to only one location. And secondly, it is assumed that there exist transportation costs for final goods. Firms thus have an incentive to locate close to large markets with many customers nearby in order to economize on transportation costs.7 Similarly, customers also like to be close to the firms, because they enjoy a greater variety of local consumption goods for which prices are not blown up by transportation costs. Additional linkages can arise within the production sector, as some firms might use the products of other firms as intermediate inputs. 6 In particular urban economists have stressed the importance of external knowledge spill-overs for the shaping of cities and urban locations. See also Ciccone/Hall (1996) 7 Transportation costs are relevant for the firm even if they are fully rolled over on prices, simply because demand and thereby profits will drop if prices are blown up by transportation costs. New economic geography 97 If this is the case, the finn sector has a motive to concentrate spatially, since increasing returns ensure a greater variety of inputs that are available locally and do not need to be costly imported. It is straightforward to see how 'cumulative causation' can result: since finns like to go where customers are, and customers (=workers) like to go where finns are located, there is an endogenous centripetal tendency. We will develop further on this agglomeration channel when we discuss the core model of NEG. d) Growth and innovation Not belonging to the canonical Marshallian arguments for agglomeration, but still an interesting perspective comes from the so called "new growth theory". The second wave of endogenous growth theory also builds on the Dixit-Stiglitz-model, i.e. on imperfect competition in goods markets and increasing returns to scale.8 It is viewing growth as a phenomenon of innovation and technological and structural change, not mainly as a phenomenon of accumulation. Contrary to old growth theories, technological progress is no longer seen as something that is ,,falling from the sky", but rather as the result of specific (and mostly private) R&Dinvestments. The innovators must thus firstly have rents in order to finance these investments, and secondly they must be able to extract temporary monopoly rents in case of a successful innovation. Both these requirements illustrate why a model set-up with monopolistic competition is much more appropriate than one with perfect competition and zero profits if one thinks about these Schumpetrian processes. In spatial tenns, the temporary monopoly rents accrue in the location where the innovation has been made. The newly created technological knowledge spills only imperfectly into other regions. If this logic is then combined with a tendency of increasing returns in the R&D-sector, it follows that innovation activities will reveal a high tendency towards spatial concentration. This concentration will perpetuate growth in those regions where the innovative research centres are located, and the diffusion of this growth into other regions will be imperfect. Because of that, the centre regions again have more resources available to invest in further, and even more sophisticated R&D. Growth and agglomeration might then end up in a cumulative causation mechanism, since they are mutually reinforcing processes (Martin/Ottaviano, 2001). This view is supported e.g. Audretsch/Feldman (1996), who show that in the US the geographical structures of innovation and production are quite similar, but that the innovation sector is stronger concentrated. In section A4.4.) we have shown that the same is true for the EU, where there is also a heavy spatial concentration of innovation in only a few European NUTSII-regions (EU-Commission, 2001). The considerations from this section 8 Famous adherents of this class of "innovation based growth models" are Romer (1990) and Grossman/Helpman ( 1991 ). 98 New economic geography highlight why the high spatial concentration of innovation might be a primary concern of policymakers interested in territorial equity. The arguments presented in this section all claim that there are advantages from spatial concentration of economic activity, and may be labelled centripetal forces. None of the stories can be reconciled with the standard neoclassical paradigms ( except to some extent the pure externality argument b ). But of course there are not only centripetal forces in the world, but also centrifugal forces. D4) Centrifugal forces and other location factors If the world were only characterised by agglomeration forces, economic activity would only take place in one single location in the world. This is of course nonsensical. The degree of core-periphery divides observed in the real world suggests that centripetal tendencies might be quite strong. But of course there are also opposing dispersion forces. Together they will determine the spatial equilibrium structure of an economy, and a high degree of equilibrium agglomeration simply reflects that agglomeration forces are strong relative to dispersion forces. Furthermore, the economic landscape in the real world is not only determined by the balance of "pure" centrifugal and centripetal tendencies, but is also influenced by other factors, and subject to considerable inertial forces. a) "Pure" centrifugal forces The dispersion forces used in the seminal NEG-model of Krugman (1991 a), but also in most other standard NEG-models like e.g. Venables (1996) or Puga ( 1999), is local immobility of demand in conjunction with transportation costs for final goods. The argument rests on the fact that some individuals (consumers) are assumed to be regionally immobile and inevitably tied to specific locations. They typically engage in some sort of basic production activity under constant returns and perfect competition, generally labelled "agriculture". They nevertheless demand also commodities that are produced by the manufacturing sector. The increasing returns in this sector push for concentration in only one location (the "centre"). But the demand from peripheral farmers is opposing this tendency. Since manufacturing firms are interested in satisfying also this demand segment, it is ambiguous whether the increasing returns outweigh the transportation costs that are necessary when the "peripheral" demand is served through exports. This centrifugal force is typical for NEG-models. Its use is driving many of the results of NEG-models that will become apparent below. But demand immobility is by no means the only conceivable dispersion force. Actually, old location theorists like Isard (1956) or Weber (1909) have claimed that probably the most important boundary for spatial economic concentration is the limited availability of usable land and housing opportunities. Suppose that the housing stock in any region is fixed. In the process of agglomeration in one specific location, housing prices will be bid up. At some point will the agglomeration New economic geography 99 advantages stemming from increasing returns not make up any more for the high housing and land prices. Surprisingly, however, most standard NEG-models neglect this highly relevant and plausible dispersion force. An exception is Helpman ( 1998), who explicitly sets up a model where increasing returns explicitly face housing scarcity. Further arguments against spatial agglomeration are congestion costs, broadly defined. Metropolis areas might be characterised by high crime rates, pollution, the lack of traditional social networks and personal interactions, and all sorts of other sociological factors. But individuals are surely heterogeneous with respect to the weight they put on these congestion costs in their respective utility functions. Some individuals might even perceive specific "urban" characteristics like anonymity etc. to be intrinsically attractive. These individuals would thus not perceive "costs" of congestion, but rather benefits from it. b) Status-quo inertia Apart from centrifugal forces that directly oppose spatial agglomeration, there are other factors that in general produce a status-quo bias with respect to the spatial economic structure. Mobility costs are a good example. Neither relocation of firms, nor of workers is costless. Not only physical relocation costs (moving production facilities or furniture) have to be considered. Also more subtle, psychological mobility costs arise: the costs for adapting to new environments, the costs for gathering information about suitable housing etc. Mobility costs do not specifically favour or prevent agglomeration. They rather invoke a bias for any spatial economic structure that exists initially. Mobility costs can be seen as a inertial force that prevents the instantaneous adjustment of the actual spatial structure to the equilibrium structure that is determined by the balance of centripetal and centrifugal forces. Related to mobility costs is the concept of a "regional preferences". Workers might intrinsically prefer to live in a specific area (e.g. the area of birth, in which case we would speak of a "home bias"). The reasons might be that they are accustomed to the local culture and language, they can draw on intact social networks etc. The presence of these biases leads workers not to respond instantaneously to interregional differences in observable economic variables with migration. Since living elsewhere is subject to a discount factor in the individuals' utility function, the difference in economic prospects must be sufficiently large in order to invoke a relocation of workers. c) Other location factors One should note that technological centripetal and centrifugal forces are always overlapped with unchangeable regional characteristics like the natural environment, the fertility of land, the climate etc. that might be summarized by the term "regional comparative advantages". These underlying features are at the root of 100 New economic geography neoclassical trade and location models ( as well as of the wage curve models discussed in the last chapter). We have argued that comparative advantages alone are insufficient to explain the spatial economic structure (and the pattern of sectoral specialization) in the real world, as they leave no room for cumulative processes. This, however, does not mean that comparative advantages are irrelevant. The interplay between exogenous comparative advantages and endogenous location forces has been discussed e.g. by Krugman (1999) and should always be kept in mind. The enumerative list of various centripetal, centrifugal and other influence factors provided in sections D3 and D4 is supposedly still incomplete and subject to further expansion. The core-model of NEG, however, has essentially singled out one centrifugal and one centripetal force, and abstracted from all other location or inertial forces. We not turn to the discussion of this seminal model of Krugman (1991a). D5) The core-periphery model of 'new economic geography' Krugman ( 1991 a) considers what he calls a "2 x 2 x 2"-model, i.e. he analyses an economy consisting of two regions r= 1,2, two sectors (labelled agriculture A, and manufacturing M,) and two types of workers, farmers and manufacturing workers, who are specific inputs to the respective sector. Both regions are identical with respect to technology, preferences and endowments. There are no inherent comparative advantages or intrinsic regional differences. Agricultural production is assumed to operate under perfect competition and constant returns to scale. The products from the agricultural sector can be freely shipped across space. The manufacturing sector on the other hand is characterised by monopolistic competition and internal increasing returns to scale a la Dixit-Stiglitz ( 1977). Interregional transportation of manufacturing products imposes so called 'iceberg' - transportation costs that were introduced first by Samuelson ( 1952). Furthermore, farmers are assumed to be regionally immobile and equally split across the two regions. Manufacturing workers on the other hands are mobile, but initially also split across the two regions. We have already pointed out above that the centrifugal force in this model will be the manufacturing demand of the regionally tied farmers. Let us thus shortly consider this critical assumption on the differential mobility behaviour of farmers and manufacturing workers, as this will drive the results in the Krugman-model. One can more generally think of the agricultural sector as a basic services sector in which increasing returns does not play any role. The farmers who are employed in this sector are low skilled workers. The manufacturing, or "modern" sector however exhibits scale economies and employs mobile, high-skilled workers. There seems to be the implicit assumption that skilled workers from the modern sectors are in principle mobile, whereas low skilled workers are not. In chapter F New economic geography 101 of this book, where we take up the issue of selective labour mobility more explicitly, we show that this assumption is in principle not unreasonable. D5.1.) Consumer behaviour The representative consumer in each region r= { 1,2} respectively maximizes a Cobb-Douglas utility function U, = M/ A,1-µ (D. l) where Ar are units of the agricultural good that can be freely shipped across regions, and the aggregate M, is a symmetric CES function over a continuum of (n, + ns) single consumption varieties m(i) from the manufacturing sector. The parameter µ reflects the manufacturing share. I M, =[n,(mrr(i)t +ns(m,,(i)t]P (D.2) n, indicates the number of varieties that are produced and consumed in the respective region itself (mrr), and n5 is the number of varieties imported from the other region (m5 ,). The parameter O< p <l measures how close substitutes the single varieties are. The lower is p, the more differentiated are the single consumption goods, and the lower is the elasticity of substitution cr = 1 / (1-p ). Consumers maximize (D. l) subject to the budget constraint P, A A,+ ( n,p,mrr (i) + n,T Psms, (i)) = ~ (D.3) where Y, is total regional income, and p/ is the price of the agricultural commodity. The 'iceberg' -costs that are involved in the transportation of manufactured goods across regions are captured by the parameter T. For one unit of m,5(i) to arrive, T > 1 units need to shipped and the rest "melts away" during the transportation. Since the manufacturing aggregate M, consists of symmetrical commodities, the mill prices p,(i) within each region are the same for all varieties, i.e. p,(i) = p, and Ps(i) = Ps for all i, j. Prices for the good A, are equalized across regions due to the free tradability. Therefore p/ can serve as the numeraire and is normalized to one. Since the utility function is Cobb-Douglas, expenditure on each of the three aggregates is a constant share of income. The demand for the agricultural good is simply A,= (1-µ)Y,, and the demand for the consumption aggregate M, can be written as M, = µ Y, /G,. The variable G, is the composite price index for manufactured goods in region r. It can be understood as an expenditure function dual to the 102 New economic geography quasi-utility function M,, i.e. it describes the minimum costs of purchasing one unit of the manufacturing aggregate M,. The function G, can be computed as9 I G, =[n,(p,t" +n,(T P,t"] 1 -". (D.4) The manufacturing price index G, is decreasing in n, and n,, with the partial effect of an increase in n, being stronger. These negative partial derivatives represent a "love for variety" effect and can be seen as a pecuniary external scale effect. If the number of available consumption varieties increases, the costs for purchasing one unit of an aggregate M,, and thus the costs for attaining a given utility level, decline. This effect is stronger if the increase in varieties is local, because no transportation costs apply to the new varieties. The demand functions for single local consumption commodities and for imported varieties are respectively given by mrr(i) = µ Y, P,-" G, -<0--1) , (T p,f" m,,(i) = µ Y, G -<0--1) r (D.5) The parameter cr not only gives the elasticity of substitution between varieties, but is also equal to the price elasticity of any single manufacturing good. This construction is an artefact of the Dixit-Stiglitz-model frequently criticised in the literature.10 It is also important to note that it is assumed that each single producer neglects the influence of price change for his specific commodity on the price index G,. Let qi,r be the total sales of a manufacturing firm i in region r. Using (D.5), and taking into account the fraction of the product that melts away during interregional transportation, sales per firm amount to qi,r = mrr + Tm,,, or 9 For details about the derivation of a composite manufacturing price index dual to a CES-function see FIKN (1999:46f.) 10 See e.g. Ottaviano/Tabuchi/Thisse (2002): "Though convenient from an analytical point of view, such a result conflicts with research in spatial competition which shows that demand elasticity varies with distance while prices change with the level of demand and the intensity of competition. Moreover, the iceberg assumption also implies that any increase in the price of the transported good is accompanied by a proportional increase in its trade cost, which is unrealistic." New economic geography 109 trade, the location of production does not matter any longer and there is perfect wage equalization across regions. The two other parameters affecting the equilibrium are µ and p (i.e. cr). Ceteris paribus, sustainability is more likely the lower is p, i.e. the more important are increasing returns in manufacturing, and the higher is µ, i.e. the more important is the manufacturing sector (F !KN, 1999: ch. 5). D5.5.) Stability Sustainability only means that an initially existing core-periphery-structure can be maintained for given parameter values. This, however, does not address the process of agglomeration, i.e. whether a c-p-structure can emerge endogenously in the model. To deal with this issue, one has to assume that a symmetric equilibrium with A = ½ exists initially. Around this steady state, all endogenous variables, including ro 1 and ro2, are identical in both regions. FIKN then check whether this steady state is stable or unstable for given parameters. For the emergence of agglomeration, instability is necessary: one single worker must be better off when migrating from region 2 to region I. If he is, a circular and cumulative process develops, at the end of which the whole manufacturing labour force will be located in region l. Formally this condition can be written as dro 1 /dl > 0 and dro 2 /dl < 0 around A = ½. Since under initial symmetry small changes of endogenous variables in one region are exactly mirrored by changes in the opposite direction in the other region (dro 1 = -dro2), we can write the condition for instability simply as dro/dA > 0. The analytical expression for dro/dl as a function of exogenous variables can be obtained by computing the values of all endogenous variables (D.11) -(D.13) for 'A.= ½ , substitute those into the real wage equation (D.14) and then differentiate this expression with respect to A. It yields the following expression 13 dw = 2ZG-µ(lp)[µ(l + p)-Z(µ2 + ~)] d)., p 1 - µZ (1p) - pZ- (D.17) where z = (1 - rl-'7) = (1 - rl-'7). (1 + r1 -(7) 2G 1 -(7 This condition (D.17) is graphically represented in figure D2 as a function of T, with exogenous parameters µ and cr as in fig. D 1. The symmetrical equilibrium is unstable if (D.17) is positive, i.e. if the curve runs above the thick horizontal line. This is the case for low and intermediate transportation costs. At some critical value of T, the property of symmetry breaking will 13 Details of the derivation are given in F/KN (l 999:76f.) 110 New economic geography vanish. It can be shown that this critical level, the break point (T 8 ), is strictly lower than the critical level of T beyond which sustainability does not hold anymore, the sustain point (Ts). This is the so-called 'locking-in-effect' that gives rise to a tomahawk bifurcation and multiple equilibria. It can be seen best in the bifurcation diagram in figure D3). Figure D2) The stability of the symmetric equilibrium 0,1 0,05 0 1, 1 1,2 1,3 2 -0,05 -0, 1 -0,15 It describes the geographical structure of this economy (given by the spatial distribution of the manufacturing workforce) as a function of transportation costs T. Solid lines represent stable equilibria, whereas dotted lines represent unstable ones. Figure D3 summarizes the working of the Krugman-model. Various points should be noted. Firstly, for high trade impediments (T > Ts) there is a unique and stable geographical equilibrium that is characterised by complete regional symmetry. The manufacturing workforce is equally split across the two regions (A= ½ ), and all endogenous variables are identical in both areas. We have described the reason for this result above. For values of T below T 8, the whole manufacturing workforce is concentrated in only one region (which one is indeterminate), because the centripetal increasing returns in the M-sector are more pervasive. At intermediate levels of T (T 8 < T < Ts), the model exhibits multiple equilibria and local hysteresis. In this range, a symmetrical equilibrium would not break, but a pre-existing core-periphery equilibrium would be sustainable. The actual equilibrium configuration thus depends on the initial conditions and is "pathdependent". New economic -geography 111 It has been central to the NEG-literature to analyse the effects of secularly declining transportation costs. The term is broadly defined and captures all sorts of spatial transaction costs, including information costs, trade impediments etc. Falling transport costs can either represent regional integration (for example in the EU), or it can be used as a proxy for "globalisation", or it might reflect the decline of spatial transaction costs brought about by road infrastructure investments or innovations in the telecommunication sector. The important implication of the Krugman-approach is that declining trade impediments can result in regional divergence. When trade costs decline from a level that is initially very high, they first pass the level TsThis has at first no consequences, as the symmetrical equilibrium is still stable. Once they cross the critical level T 8, however, the symmetrical configuration breaks and a core-periphery structure develops endogenously. A circular spiral of cumulative causation sets in: one manufacturing worker is better off when changing locations from region 2 to region 1. Through this initial move, the incentives for manufacturers to leave region 2 as well increase. Eventually all manufacturers will have emigrated from region 2. In the theoretical model, this cumulative causation mechanism does not unravel gradually, but the emergence of the core-periphery structure happens spontaneously. The model implies a "catastrophic" agglomeration. Figure D3) The bifurcation diagram of the Krugman-model I I I ;' , ½ ------------------------- ~ ;, . ' ' .. 0------------------- T Another important feature, that can not be seen directly in figure D3, is that the agglomeration rents for the centre are hump-shaped with respect to T. We have commented on this fact when discussing figure D 1: the real wage premium of the centre fades away as trade costs T approach the free trade case with T= 1. The disparity between core and periphery is highest for intermediate transportation costs. 112 New economic geography In the original Krugman-model, this u-shape is immaterial, as region 2 will never regain manufacturing. The substance of the hump-shaped agglomeration rents, however, has shown up much clearer in other NEG-models in the aftermath of Krugman (1991a) which will be discussed below. D5.6.) 'New economic geography' and the new trade theory We have argued above that the basic model of NEG is a direct follower of the core model of the NTT developed by Krugman (1980). Since the connection between the two is actually very close, and since we will also rely on insights from NTT later, we will briefly discuss this approach here. In short, what distinguishes NEG from NTT is the assumption that high-skilled manufacturing workers are mobile across regions. In the two-country model of Krugman (1980), all agents are assumed to be immobile. Moreover, there is only one consumption good sector in the economy that is identical to the manufacturing sector in the above NEG model: there is a large number of monopolistically competitive firms, each producing a distinct consumption commodity under increasing returns to scale by employing labour only. The maximum number of varieties that a country can potentially produce is, as above, restricted by labour supply. Consumers "value variety", i.e. they have symmetric CES-preferences where utility increases in the number of consumption varieties N. I U; = [ N(c)P ]-;; 0<p<l In such a model, the increasing returns become an independent source of (intraindustrial) trade, apart from the traditional arguments known from neoclassical trade theory ( comparative advantage, preference heterogeneity etc.). Allowing for international trade enlarges the number of available consumption varieties. Since consumers value variety, the introduction of trade increases welfare in both trading countries. If trade is costless, there will be no welfare differences between countries, since all consumption varieties are equally available everywhere. In a second step, Krugman (1980) then assumes the presence of 'iceberg'- transportation costs. If this is the case, large regions have an advantage over small regions, since they will produce a larger number of varieties locally and hence save on transportation costs .. Via a zero profit condition similar to (D.18), this scale advantage of large nations is absorbed by a higher equilibrium wage rate of the larger country. Since labour is assumed to be immobile in Krugman (1980), this wage differential does not lead to migration. The step from the NTT towards NEG is taken if one allows for labour mobility, which is an endogenous agglomeration channel. Viewed at it in this light, the introduction of the constant-returns sector ("agricul- New economic geography 113 ture") in the core model of NEG, which has not been introduced in the core model of NTT, was simply needed in order to have a centrifugal force in the model. Without the agricultural sector, theoretically all labour would flow from the small to the large country and there would be no break on the spatial concentration process. All in all, one can see from this section that the core models of NEG and NTT are structurally very similar, if not identical. 14 D6) Other 'new economic geography' -models In this section, we will briefly describe the main ideas and results of some other NEG-models. The models that will be discussed in this section were all motivated in one way or the other by the seminal Krugman (1991 a )-model and extended and changed it in various directions. 15 D6.1.) Venables (1996) and KrugmanNenables (1995) One important approach that is actually by now considered the second "standard" model of NEG has been developed by Venables (1996). His main motivation to depart from the Krugman-model has been the insight that labour mobility is low in the European Union, across regions but particularly across countries (see Decressin/Fatas, 1995; Puhani, 1999). The agglomeration channel in the Krugmanmodel, however, critically hinges on the mobility of manufacturing workers. Venables (1996) formulated a model, where labour is immobile and still coreperiphery structures can develop endogenously (contrarily to Krugman, 1980). In his model, the agglomeration channel does not occur through labour mobility, but rather through the sectoral specialization pattern of regions. Venables (1996) argues that firms like to be close to each other because of direct input-output linkages amongst themselves. In the model set-up, Venables introduces an explicit input-output-structure of the manufacturing sector, where upstream industries produce intermediate inputs for downstream industries. Both vertically linked industrial sectors are operating under imperfect competition and exhibit internal increasing returns to scale. Additionally, there is again a competitive sector (agriculture) in the two-region economy. Labour is now assumed to be immobile across regions, but mobile across sectors. Interregional transportation of commodities imposes the usual 'iceberg' transaction costs. A similar model set-up as in Venables (1996) has already been proposed in KrugmanN enables (1995), 14 For a very intuitive discussion of the common elements and the differences between NTT and NEG see Krugman ( 1999). 15 There are by now various surveys of the NEG, as well as textbooks that cover the contents of the original contributions. For surveys see Ottaviano/Puga (1998), or Puga (2002). The standard models are furthermore covered in the textbook of Brakrnan/Garretsen/Marrewijk (200 I) on an introductory level. The most recent contribution of Baldwin et.al. (2003) presents a very comprehensive overview of different NEG-models in great technical detail. A broader survey that also discusses NEG in relation to other approaches in urban and regional economics is Fujita/Thisse (1996). 114 New economic geography only with the difference that there has been no explicit input-output-structure between upstream and downstream firms. The (monopolistically competitive) manufacturing sector in that model is rather assumed to produce differentiated commodities under increasing returns that are used both as final consumption goods and as intermediate inputs for other manufacturing firms. The results and the underlying logic of the two approaches of Venables ( 1996) and Krugman/Venables (1995) are, however, qualitatively quite similar to each other. It is important to note that there are 'forward' and 'backward' linkages between vertically linked firms from the manufacturing sector. Again, these linkages show up in the form of pecuniary externalities. The basic intuition can be described as follows: with high transportation costs each region will be essentially self-sufficient and produce both manufacturing and agricultural goods locally to satisfy the regional consumption demand. As trade costs fall, there will be increasing two-way or intra-industrial trade of manufacturing intermediates and final goods. But there will at first be no change in the relative sectoral specialization of either region. However, at some point when trade costs have fallen further, the involved agglomeration economies make it profitable to spatially concentrate manufacturing production and satisfy peripheral consumption demand through (costly) exports. This leads both to backward linkages, as manufacturing firms located in the agglomeration area have easier access to intermediate inputs. And there is a forward linkage, as more intermediates also imply declining costs for producing the goods destined to final consumption. These linkage effects together dominate over the centrifugal force, which again stems from the fact that final goods need to be shipped also to the de-industrialized region. There is thus also a critical level of transportation costs below which there will be industrial concentration in one region. Since this process can not be triggered through migration of workers from the other region, the industrial core must draw on workers formerly employed in the agricultural sector. This increase in labour demand will put incipient upward pressure on real wages in the industrial core. Similarly, real wages in the de-industrialized periphery tend to drop, since manufactured goods must now be imported and transportation costs need to be paid. A real wage ( or: real income) gap opens up between the two regions as the industrial sector concentrates in only one location. But if transportation costs continue to fall, the market access considerations, the importance for firms to be close to each other, gradually vanishes. Eventually factor price consideration will again come to dominate the location decision of industrial firms, which have an incentive to relocate their plants to the low-wage peripheral area. Krugman/Venables (1995) see as the main appeal of this model that initial spatial divergence and subsequent convergence between the two regions are attributed to the same cause, the long-term decline in transportation costs. The exact shape of the bifurcation diagram depends on several details that shall not be discussed New economic geography 115 here. 16 The essence of the Krugman/Venables-model can, however, be highlighted in figure D4). Figure D4) Location of the industrial sector in the KrugmanNenables-model N, N max I I I ,, " '/2 N max N1=N2 ----------~------------------- \ \ 0 ' ' ... Ts T The figure depicts the number of manufacturing firms in region r as a function of transportation costs. As argued above, there is complete regional symmetry if trade costs are very high. Once trade costs fall short of the critical level T 8, there is a catastrophic tomahawk bifurcation and a multiple equilibrium range between T 8 and T 5. This time, however, the "catastrophic" event refers to the complete deindustrialization of region 2, and the complete specialization of region 1 to manufacturing production. What is new compared to the Krugman-model is that below some other critical transport cost level TL, there is a re-emergence of symmetry. Below TL, factor price consideration outweigh market access considerations. The core-periphery structure, that gives rise to an interregional real wage gap, is only stable for intermediate levels of transportation costs. The regional real wage levels as functions of T can also be highlighted in a stylised manner. This is done in figure D5). 17 As long as the location of industries is symmetrical, there is no interregional real wage gap. With the catastrophic transition at T 8, there is a spontaneous rise in the real wage of region 1, and a spontaneous drop in w2• The agglomeration rents, however, eventually fade away as the trade cost decline evolves. Finally, when symmetry re-emerges, there is again regional wage equalization. 16 See F /KN, ch.16 ff. and Venables ( 1996) for an extensive discussion. 17 Again, figure D4b) is only meant as a stylised representation of the main ideas of the class of models introduced by Krugman/Venables (1995) and Venables (1996). It must not be understood as the bifurcation diagram of one particular model version. 116 New economic geography All in all, one can look at the Venables-model as a way to explain the emergence of core-periphery patterns also for environments in which geographical labour mobility plays a minor role. It has been shown that agglomeration forces can also arise because of inherent linkages only between vertically linked firms. The dispersion force that has been used was exactly identical to that in Krugman (1991 a). Another main theoretical contribution in our view is the possibility to account for the existence of a lower bound of transportation costs, where regional disparities do no longer prevail. It is a representation of a plausible economic consideration, namely that factor price differentials will become an increasingly important factor for firms when market access considerations loose importance. Figure D5) Real wages in the KrugmanN enables-model T Ts This "0-shaped" relationship between transport costs and real wage disparities highlighted in figure D5) is studied further by Puga (1999). He uses an unified framework in which both interregional migration and input-output linkages may drive agglomeration. Essentially, the framework proposed by Puga combines the approaches of Krugman (1991a) and KrugmanNenables (1995). In Puga's model, either both agglomeration forces can be at work, or only one of them. He confirms that the Krugman-type of agglomeration (as described in section D5) is going to prevail when labour is regionally mobile, and he shows that the centripetal forces are even magnified if one additionally allows for input/output-linkages between firms. If labour is immobile, however, industrial agglomeration can only be expected for intermediate levels of transportation costs. Since spatial concentration New economic geography 117 raises local wages, symmetrical equilibria will reconvene as trade costs approach low levels. This logic is essentially identical to the model of Venables ( 1996). The Puga-model has some attractive features. This concerns the fact that it allows for agglomeration patterns that seem more realistic than the results of Krugman (1991a), Krugman/Venables (1995) or Venables (1996). His model is able to replicate the emergence of stable equilibria in which the manufacturing sector is neither completely agglomerated in one region, nor symmetrically distributed across space. It rather exists the possibility of an intermediate equilibrium in which one of the two regions has a larger manufacturing share than the other, but the "periphery" is not completely deserted from all industrial activity. And secondly, the Puga-model can go beyond the logic of "catastrophic" or discontinuous agglomeration. It leaves the possibility of gradual and continuous changes in the economic landscape. 18 The bifurcation results are surely fascinating from a theoretical point of view. Whether this logic is applicable to real world scenarios, is, however, disputable. It is worth noting that the type of NEG-models in spirit of Krugman/Venables (1995), Venables (1996) and Puga (1999), which rely on input/output-linkages within the production sector, again have an important precursor in the NTT. This is the trade model of Ethier (1982). That model must be seen in direct relation to the NTT approach of Krugman (1980). Ethier's point was to construct a model where the welfare gains of international trade do not develop because of a "love for variety"-effect for the consumers. He rather saw an increase in the variety of intermediate industrial inputs as the main effect of international trade. The positive welfare effects of trade in the Ethier-model are caused by the greater differentiability of the production process. However, he did not develop a "spatial" model. He assumed free tradability of industrial intermediates. His model was thus not equipped to study the possibility of endogenous agglomeration, even though he also worked with internal increasing returns to scale, since location questions do not matter if there are no transportation costs involved. But there is a fundamental similarity between Ethier (1982) and the NEG-models discussed in this section insofar, as both focus on linkage effects and increasing returns that occur solely within the production sector of an economy. D6.2.) Housing scarcity: Helpman (1998) The NEG-model of Helpman departs in a more fundamental way from Krugman ( 1991 a). It has been argued that the seminal model of NEG uses one particular dispersion force, namely the immobility of demand in combination with transpor18 The analytical conditions that need to hold in order for these "attractive" results to prevail in the Puga-model are quite complicated and can not easily be phrased in an intuitive form. We therefore leave out the discussion of the respective conditions at this point. 118 New economic geography tation costs. But it was also argued that there are other, maybe more relevant centrifugal mechanisms in the real world. Helpman therefore uses housing prices as the dispersion force opposing the technologically given tendency to agglomerate. He replaces the traditional constant returns sector ("agriculture") from the Krugman-model with an immobile housing stock that is assumed to be equally owned by all individuals in the economy. The manufacturing sector in the Helpman-model is identical to the standard NEGmodel, including the 'iceberg' -costs for interregional transportation. Labour is again assumed to mobile across regions. With this model, it is quite straightforward to see the competing impacts on real wages that drive the location decision of workers. Given the increasing returns to scale technology alone, workers like to concentrate in only one region. But the higher housing prices oppose this tendency. The critical parameter that determines the relative strength of agglomeration and dispersion forces is again the level of transportation costs. If transportation costs are quite low, the location of industrial production does not matter very much. The workers location decision is not driven by agglomeration wage differentials, but rather by housing cost considerations. The workforce will split evenly across regions, since there is little to be gained from the concentration in one region. The balance, however, shifts with higher transportation costs. Since interregional trade becomes more costly, workers have an incentive to concentrate. This is so for two reasons. Firstly, in order to enjoy lower goods prices, and secondly to exploit the localised agglomeration economies. Thus, the higher are transport costs, the smaller is the impact of housing prices on the workers' location decision. The fundamental diagram that shows the population fraction living in either region as a function of transportation costs looks like figure D6: Below some critical level TL, the two-region economy is characterised by complete symmetry, as considerations on housing prices drive the location decisions. The higher are transportation costs, the higher is the degree of population concentration in one of the two regions (which one is again indeterminate). Note that there is no catastrophic bifurcation in this model, but rather a smooth transition from symmetry to a core-periphery structure. There is the possibility of intermediate equilibria beyond full concentration and complete symmetry. 19 These are surely attractive features that improve on the realism of NEG. However, one should note that the final results of the Helpman-model completely reverse the logic of the Krugman-approach. Helpman finds that agglomeration is more likely the higher are transportation costs. This fundamentally contradicts the notion that is central to much of the NEG-literature, namely that secularly falling transportation costs result at least initially in regional divergence and the emer19 This property is the reason why the Helpman-model is often used for empirical research on NEG, see e.g. Brakman/Garretsen/Schramm (2001) New economic geography 125 Table D1: Income, size and cost-of-living in US metropolitan areas Jobs average wage rel. pers. population Area (n=208) (thousands) per job( $) New York, NY (PMSA) 4500,156 56,434 Honolu lu , HT (MSA) 476,349 31,682 San Francisco, CA (PMSA) 1185,2 13 59,077 San Jose, CA (PMSA) 1099,966 74,374 Boston, MA 3410,183 44,395 Philadelohi a, PA-NJ (PMSA) 2534,87 38,648 Newar k, NJ (PMSA) 1048,783 47 ,651 Hartford, CT <NECMA) 655 624 4 1,673 Santa Rosa, CA (PMSA) 205,975 35,1 48 Washington, DC-MD-VAWV (PMSA) 3009,72 45 ,129 [ ... l Lincoln, NE (MSA l 158,191 28,389 Amari ll o, TX (MSA) 10 3, 147 26,357 Hattiesburg, MS (MSA) 54,465 23,366 Little RockNorth Little Rock, AR/MSA) 338,296 29,541 Anniston AL (MSA) 52,462 24,764 Danville, VA (MSA) 49, 441 24,65 Montgomery, AL (MSA) 178,367 28,245 Joolin, MO /MSA) 82,3 14 24,76 Clarksville-Hopkinsville, TNKY/MSA) 99,761 26,296 Jonesboro, AR (MSA) 43,647 24,44 United States, total 139552 34,652 MSA = metropolitan statistical area. PMSA NECMA= New England metropolitan statistical area. income (thousands) rel. COLI 1 33 932 1,82 199 ,000 102 875,67 155,700 195 1 73 1, 7 16 151,400 187 1683,908 139,700 132 6067,5 1 127,400 114 5104,291 124,500 136 2035, 127 124 ,3 00 1 23 I 150,619 123,000 11 8 460,268 120 ,700 136 4948,2 13 120,300 98 25 1,008 90,800 83 218,321 90,30 72 112 ,105 90,000 93 585,228 89,600 72 11 1,35 89,50 71 I 10,05 89,500 87 333,479 89,400 75 157,667 89,300 76 207,6 13 88,900 74 82,436 88,700 100 1282124,6311 100 Primary metropolitan statistical area. This descriptive evidence supports the view outlined in the introduction that large agglomeration areas with high nominal wage and income levels tend to have higher costs-of-living than corresponding rural places. The model implication of Krugman (1991a) and F/K/V (1999) that core regions have lower COLI-levels is strongly rejected by the data. A plausible hypothesis seems to be that the higher central COLI-levels are due to housing costs differentials. A casual empirical finding that supports this belief is that New York City reveals housing prices 325% above the US average, even 126 New economic geography though the overall COLI is only 99% above average (American Chamber of Commerce). Table D2: Correlation matrix (all 208 observations) COLI POPULATION JOBS WAGE INCOME COLI 1 0.53. 0.52 •• 0.66 •• 0.57 " POPULATION I 0.99 .. 0.61 •• 0.46 .. JOBS I 0.65 •• 0 .5 2 •• WAGE I 0.89 •. INCOME I ** = s1gmficant at the I % level. Note: For information about the definitions of MSAs and a full list of all areas used in this classification scheme consult http://www.bea.gov/bea/regional/docs/msalist.htm. For detailed information about the regional accounts data see http://www.bea.gov/bea/regional/reis/. More information about the COLI-data can be found under www.datamasters.com. The full list of all 208 metropoli• tan areas for which both COLIand BEA-data exist is available upon request from the author. All in all, we feel that the empirical relation described in this section is robust, plausible, and supposedly quite similar for the European Union, although we can not show this because of data limitations. Starting from this empirical motivation we now come to the model that aims to explain the endogenous emergence of c-pstructures in spirit of the traditional NEG-literature, but with the important difference that the core region in our model can reveal the higher regional COLI in the long-run equilibrium. D7.2) The basic structure of the extended model The economy under consideration is structurally very similar to the standard NEG-model, and we closely follow the notation of section D5). The representative consumer in each region still maximizes a Cobb-Douglas utility function U, = M/ H/ A,1-µ-r (D.19) where Hr are the units and y is the expenditure share of the "new" non-tradable home good. The budget constraint now reads as AA HH +( (')+ T ("))-Y Pr r + P, r n,p,mrr l n, p,m,, l -r ' (D.20) where PrH is the price of the home good in region r. The demand for the home good is simply H, = yY, Ip, H. The price for the agricultural good A is still the numeraire and in equal to unity in both regions. Demand for the agricultural good is New economic geography 127 simply Ar= (1-µ-y)Yr, and for the consumption aggregate Mr= µYr/Gr. The composite manufacturing price index Gr , as well as the demand and supply functions for the single manufacturing commodities are completely identical to the standard model, i.e. the respective equations are given by (D.4)-(D.10). We can directly tum to the equilibrium conditions, analogously to section D5.3). Most equilibrium condition also remain unchanged with respect to section D5.3). The market for the agricultural good still clears automatically at the numeraire price pA=l. The regional supplies of home goods are fixed at H1 = H2 = y/2. In equilibrium, home goods prices must adjust such that supply equals demand for home goods, H, = yY, / p/. For market clearing, home goods prices and wages must thus be directly proportional to the respective regional income. P,H = w,H = 2Y,. (D.21) The equilibrium prices and wages in the manufacturing sector are still given by (D.22) But regional income Yr is now (D.23) The composite manufacturing price index remains unchanged. It is given by I G, = [l,(wf" + (1-1,) (w,T)'-"] I-a (D.24) Substituting (D.23) and (D.24) into (D.21) and (D.22), we can find the set of nominal wages Wr, WrH at which there is market clearing in all sectors and regions. These equilibrium values only depend on the parameters T, µ, y, cr and on the endogenous variable ArOf course an analytical solution is "even less" feasible in this three-sector case. But one can still single out some effects and provide the respective economic intuition. As Ar increases, more individuals compete for a given supply of home goods. Formally, we know from (D.21) that WrH increases with regional income Yr. Yr is clearly an increasing function of 'Ar, since nominal wages Wr can never drop so sharply to overcompensate the effect stemming from the entry of more manufacturing workers. Thus, we find the plausible result that WrH CPrH) rises with Ar- 128 New economic geography The effects of an entry of workers on regional manufacturing wages have been extensively discussed above. To briefly repeat the intuition: an immigration of new manufacturing workers increases competition on the regional goods markets, which puts incipient downward pressure on nominal manufacturing wages. At the same time, there are linkage effects operating in the other direction. The only effect that is new compared to the standard model in section D5) is a demand linkage effect that applies to the home goods producers: since their income rises with Ar, they will demand more manufacturing commodities and thus also perpetuate the upward tendency of nominal manufacturing wages. Let us tum to real manufacturing wages COr, Contrary to the above model, the regional cost-of-living index is no longer identical with the composite manufacturing price index Gr, since now also the regional price level of home goods must be included. Let 'l'r denote the regional CPL Real wages are then given by (D.25) Similar to the nominal wage, also the real wage COr endogenously only depends on A,. Considering real wages, there are two additional effects to consider. The first is the well known backward linkage from above. Since Gr is decreasing in Ar, the establishment of new firms in the region implies an increase in real wages by lowering the living expenses for manufacturing commodities. However, this is not the end of the story here. As more manufacturing workers pool in one location, home goods prices are driven up and put real wages under strain. Thus, the overall impact of an increase in Ar on real wages COr is ambiguous and heavily depends on the exogenous parameters. In this extended model there are also only two possible structures that can prevail in the long run. The economy will either be characterised by a complete agglomeration of all manufacturing labour in one region, or the two regions are completely symmetrical. The analysis will proceed completely analogous to the standard model above. First we check sustainability of an initially existing coreperiphery-structure. Afterwards we determine if symmetry breaking can occur around the steady state with A= ½ . Note that Krugman-model is entailed in our analysis as a special case where y= 0. Therefore we will consider this benchmark case repeatedly. D7.3) Sustainability and stability When all manufacturing labour is pooled in region 1 (A= 1 ), the regional income levels in the core (Y1) and in the periphery (Y2) are New economic geography 129 Lw H + 1-µ-y 2 2 2 (D.26) Since the expenditure on home goods yY, in each region must in equilibrium equal the income from home goods ( r /2) w, H, we find that H H 2µ 1-µ-r P1 =w1 =--w1+--- l-y 1-y H H 1-µ-y 1 P2 =W2 =--'-----'-< · 1-y (D.27) Note that the equation(s) (D.27) can only be derived ify is strictly positive, since otherwise there is no home goods sector and hence no home goods prices. To determine the manufacturing wage w1 we look at total national income for the case with )..=I: r; + f2 = µwl + !_ ( wt + w/) + (1µ - r) = WI (_!!_) + l - µ -y 2 1-r 1-r Since a fraction µ of total income is spent on manufacturing, and this expenditure needs to equal manufacturing earnings µw 1, it is still the case that WJ = I (D.28) Using (D.28) in (D.24), we can see that regional manufacturing price indices in this situation are still given by G1 =1 and G2 = T > l respectively. Thus, the manufacturing price index is indeed lower in the core than in the periphery, unlike the prices for home goods. Using (D.28) in (D.27), the closed form solution for home goods prices in the core is given by Pt = wt = (1 + µ - r) / (1r) > 1 . This implies that the aggregate costs-of living in the two regions are =(1+ µ-r)r 1/11 1 -r and ( I-µ-r)r 1/12 = Tµ 1-y (D.29) 130 New economic geography From (D.29) one can easily see that it is possible that the periphery has a lower CPI than the core in this completely agglomerated situation. Proposition D2. The overall CPI is lower in the periphery (lf/2 < lf/1) if transportation costs are below with Ten =(O+µ-r)/(I-µ-r)tµ. a critical level: T < r:PI, Figure D7) plots the relative CPI of region 2 as a function of T and y. Overall living expenses in the periphery are lower if the curve \j/2/\j/1 runs below the thick horizontal line. The critical level TCPI is at the crossing point. Figure D7) Relative CPI \Jfil\Jf 1 as a function of T and y p=0,7; µ=0.5 1.3 1,2 1, 1 0,9 0,8 L-- - "---------- - ------' ;; N _ "' - "'- "'- "'- N o_ T y= O 11 ~--~ y = OI I ,= O.~ I Obviously, the relative CPI of the periphery is monotonously increasing with T, since it needs to pay more and more for its manufacturing imports. TCPI is shifted to the right the higher is y. The range of T for which living expenses are cheaper in the periphery is larger, the more important is the home goods sector in which it has a price advantage. Moreover, TCPI is also increasing in µ. For a given level of y, nominal manufacturing wages and home goods demand in the core rise rapidly in the core if the manufacturing share µ is increased. Home goods prices are driven up, and the periphery is the cheaper area for a larger parameter range of T. The parameter p on the other hand does not affect the relative CPI. Note that the critical level TCP! is equal to one with y=O. The condition T < TCPI can by definition not hold in this case, and therefore the core can never have higher costs-ofliving than the periphery in the basic Krugman-model. Using (D.28) and (D.29), the real manufacturing wage in the core region 1 can be computed as New economic geography 131 1-y ( ) r cu,= l + µ-y (D.30) We can furthermore derive, in a similar way as above, the theoretical value of the nominal wage w2 from equation (D.22), and deflate this expression with the regional CPI \j/ 2 from (D.29) to obtain the theoretical real wage CO2 that one single manufacturing worker could earn if he decides to move from region l to region 2. The nominal wage w2 is given by ¼ w2 = [1 + µr r'-" + 1µr r"-'] , 2(1-y) 2(1-y) (D.31) and the corresponding real wage is CO2= w2 / \j/2. Using (D.29), (D.30), and (D.31) the relative real wage in the initial situation is given by I CO2 =(I+µ-y)r r-µ[l+µ-y rl-cr + 1-µ-y T"-']-;; (D.32) cu, 1-µ-y 2(1-y) 2(1-y) The existing core-periphery-structure is sustainable if co 2 /co 1 < 1. Figures D8) plots the real wage quotient (D.32) as a function of T for different constellations of exogenous parametersµ, y and cr. Figure D8) Real wage quotient co 2 /co 1 as a function ofy p=O. 7 ; µ=0.5 , .. ,-------------------, 1.3 \ 1.2 \. y=0.2 1.1 \ 8_ .- N r"') ~ ~ ~ ~ m m N .- N M • ~ ~ ~ m ~ M ~ ~ ~ ~ ~ ~ N N N N N N N N N T 132 New economic geography As can be seen, the function ffi2/ffi 1 has a "u-shape" with respect to T. For the case with y = 0 in figure D8), the Krugman-model, sustainability is warranted for low and intermediate values of T. In cases with a home goods sector, the coreperiphery-structure is sustainable only for intermediate levels of T. The reason why an asymmetric geographical structure can not be maintained with high transportation costs is well known from the standard model: it is too costly to satisfy the manufacturing demand of the immobile workers in the periphery through exports from the core. But in our extended approach, sustainability in our model also fades away for low values of T. The reason is that nominal manufacturing wages do not differ markedly in core and periphery if T is close to one, nor do manufacturing price indices. But home goods are significantly cheaper in region 2, leading to higher real wages CO2 that make it worthwhile for a worker to leave the core. However, in our model there can also be sustainable core-periphery-equilibria if transportation costs are on an intermediate level. The core can exploit the increasing returns in production and consequently pay higher nominal wages. Moreover, individuals in the core face a lower manufacturing price index G1• In opposite to these forward and backward linkages there are the higher home goods prices in region 1. The greater is y, i.e. the more value people put on home goods, the more pronounced is this centrifugal force. The u-shaped curve is shifted upwards in figure D8) as y increases, and beyond some critical point y8 the home goods sector is so important that a core-periphery-structure can never be sustainable. But if the home goods share is not too large, i.e. if y < y8, sustainability of the c-pequilibrium is possible. The two other parameters affecting the equilibrium are µ and p (i.e. cr). Ceteris paribus, sustainability is more likely the lower is p, i.e. the more important are increasing returns in manufacturing, and the higher is µ, i.e. the more important is the manufacturing sector. The important question is now, whether there can be sustainable c-p-structures in which the core reveals a higher overall price index 'l'l than the periphery. In proposition D2 we have shown that '!' 2 is lower than lj/ 1 ifT is below some critical level TCPI_ Therefore, a c-p-structure must be sustainable for values ofT < TCPI in order to match both desired properties ffi 2/ffi 1 < 1 and 1j12/'!' 1 < 1. Proposition D3. c-p-equilibria can be sustainable with 1/,'2 < 1/-'I, if: i) the home goods share y is on intermediate levels, but below /; ii) transportation costs Tare on an intermediate level, but below yCPI_ Such an equilibrium is more likely iii) the larger isµ, and iv) the smaller is p. Sustainability of the pre-existing c-p-structure requires intermediate levels of T and is more likely the lower is y. On the other hand, the property '!'2 < '!'1 requires that T is low enough to fall short of TCPI, which is more likely to hold the higher is y. For the parameters Tandy there is thus a trade-off: Transportation costs have to New economic geography 133 be substantial enough in order for the core to pay sufficiently higher wages, but they must not be higher than Teri. The home goods sector must be important enough, so that the periphery is in total the cheaper place. On the other hand, real wages in the core must not be put under too much strain from home goods prices, so that individuals are better off moving to the periphery. Such a trade-off does not exist for the parameters µ and p. A large value of µ contributes both to sustainability and lower overall prices in the periphery for reasons discussed above. In the same vein, p leaves the relative CPis unchanged, but sustainability is strengthened the lower is p. Taken together, these comparative statics imply proposition D3. The final thing to do is to show that a core-periphery structure with lower central CPI is consistent with the property of symmetry breaking. The analytical expression for dco/d)., as a function of exogenous variables can be obtained in an identical way as in section D5.5). Details of the complicated derivation are given in the appendix of this chapter. [ ~ l (1-µZ--)(µ-Z(l-y)) dm =2G-µZ 1-y _µ ~+-yd}., a(l -y) - µZ -Z 2 ( a -1 )(1 -y) Z (i _ a I - r) . (D.33) Figure D9) graphs (D.33) as a function of T and y, for given values of p and µ. The symmetrical equilibrium is unstable if (D.33) is positive, i.e. if the curve runs above the thick horizontal line. This is the case for low and intermediate transportation costs if y = 0, as known from above. If y is positive but not too high, symmetry breaking occurs for intermediate values of T. 22 Analogously to sustainability, symmetry breaking is less likely the higher is y. 23 In fact, if y becomes too large, it turns out that a c-p-equilibrium can never emerge endogenously. However, the existence of a home goods sector per se does not rule out that a symmetrical equilibrium breaks up and a c-p-equilibrium occurs.24 22 At some critical value of T, the property of symmetry breaking will vanish. It can be shown that this critical level, the break point, is strictly lower than the sustain point, i.e. the level ofT at which sustainability would vanish. This 'Jocking-in-effect' that gives rise to a tomahawk bifurcation and multiple equilibria is extensively discussed at other places in context with the seminal Krugmanmodel. 23 Changes in p and µ produce qualitatively similar results as for sustainability: symmetry breaking is more likely the lower is p and the higher is µ. 24 This is different from a model where agricultural transportation costs are added (see F/KN, ch. 7). It can be shown that under such a model it is also possible to establish sustainable c-pequilibria with a lower CPI in the periphery. However, F/KN:103 show (albeit without any refer- 134 New economic geography Figure D9) Stability of the symmetric equilibrium p=0.7;µ=0.5 0.25 1 0,2 0 ,1 5 0,1 0,05 -0 ,05 ·0 ,1 -0,15 l y= O y = 0.1 -0 ,2 -N N N N N N N N N ~ ~ N ~ • ~ m ~ m I I ::: w i=I =y===0.=2 ===l Importantly, there is no contradiction between the property of symmetry breaking and the condition that the CPI is higher in the centre in the resulting c-pequilibrium. In figures D10a)-D10c) we show for some examples that there are parameter constellations where the condition of symmetry breaking is satisfied for values of T below TCPI_ Therefore, the parameter ranges T1 -TCPI indicate those levels of transportation costs where for given values of y, µ and p an asymmetric c-p-structure with a lower CPI in the periphery emerges and persists. Figure 10) Different scenarios of symmetry breaking a) p = 0.75; µ = 0.5; y = 0.15 I real wage r at io - - pri ce indicex ratio 1, -;. r-- ~ -- , -· I I T, : : T, ,,,,,,. 1.1 I I ,,,,,,. : : ,,,,,,. : : ,,,,,,. I I I I .,,.,,,, I I 0,9 I I I I I I I I \ "· · I I - 1I 1,2 1,3 I•• 1,~ 1,6 1 .7 1,8 1,9 - _ -stab ~ . 7 - - ,,,,,,. 2 ,1 2, 2 2,3 2,• ence to the issue of regional CPis) that with homogenous agricultural products symmetry will never break. Regional agglomeration and regional unemployment 141 duction process of manufacturing goods. Firstly, there are so called "unfinished" goods that are produced by unskilled labour only. To these raw goods, producer services of high skilled workers must be added in order to make the goods marketable. Both unfinished goods and services exhibit scale economies in the production, and both are tradable across regions subject to transportation costs. The standard agricultural sector with constant returns that employs low skilled labour only is also part of their model. In principle, they derive standard NEGimplications with respect to the impact of globalisation: the effect of falling transportation costs on the labour market position of low-skilled workers is ambiguous and depends on the range of transportation costs. They are able to make some further qualifications, as they can distinguish what type of transportation costs declines (for raw goods, for producer services, both). But we want to focus on their implications with respect to unskilled unemployment. They consider different minimum wage regimes for the low-skilled workers in the manufacturing sector of the home country. All other labour markets, including that for low-skilled manufacturing workers in the foreign country, must clear for the analysis to be internally consistent. The prevalence of a minimum wage induces unemployment for the unskilled in the manufacturing sector of the home country. In view of falling transportation costs, parts of the globalisation impacts on low skilled workers do not occur through changes in the relative skilled/unskilled wage, but rather through changes in the unemployment exposure of the low skilled workers. Of course these conclusions can not be obtained as closed-form analytical solutions, but Peeters/Garretsen (2000) have to rely on numerical solution techniques. For the purpose to analyse regional unemployment disparities within the EUI 5, the approach of Peeters/Garretsen (2000) is hardly applicable. Recall that there will be unemployment only in the home country, whereas all foreign labour markets clear. For an analysis of spatial disparities, there should be unemployment in both regions. Furthermore, Peeters/Garretsen rely on institutional differences, since the minimum wage legislation can exist only in one country, but not in the other. For our purposes, however, we would like to see regions with identical labour market institutions in order to analyse if disparities in unemployment rates can still arise. Furthermore, Peeters/Garretsen do not incorporate a wage curve, or a labour market equilibrium relation between wages and unemployment, but rather impose a specific minimum wage. Hence, the model of Peeters/Garretsen, that should really be seen as pioneering work, can serve for us as a related piece of literature. But it is designed to address a totally different economic problem, not to analyse regional unemployment disparities. There is thus still enough room for us to formulate an own theoretical approach. 142 Regional agglomeration and regional unemployment E3) Regional agglomeration and the wage curve: The model The exposition of our model goes in three steps: first we present a closedeconomy setting where there is neither trade in intermediate inputs, nor factor mobility. This setting is identical to the autarky model of Matusz (1996). We then allow for trade in intermediate inputs. But we generalize the Matusz-model to account explicitly for geographical factors by assuming the presence of iceberg costs for interregional transportation of intermediate inputs. Yet, we keep at first the assumption of immobile workers. The last step is to relax also this assumption and analyse the impacts of (imperfect) labour mobility. E3.l.) The closed economy setting Consider an economy that produces (without using labour) a final consumption good Y under the use of a large variety of N single intermediate inputs Xi. The production function of the final product Y is given by the symmetrical CES function ( N )¼ Y= ~Xf 0<0<1. (E.l) The parameter 0 is a measure of the differentiability of single intermediate inputs. If 0 is close to one, inputs are nearly perfect substitutes. The elasticity of substitution between the single intermediates is given by er = 1/( 1-0). The minimum cost function of producing Y can be obtained by minimizing total consumption expenditure subject to (E. l ). This yields 0-1 C (pl,•••,PN,YJ = GY where G = ( t P;'1/r 0-1 J 0 (E.2) The term G in (E.2) can be understood as a minimum unit cost function for the final good Y. We apply the standard assumption ofNTT that all intermediate inputs enter symmetrically into the productioni/function. This implies that the production function simplifies to Y = ( N ( X; )°) , and furthermore implies that the minimum unit cost function becomes G = ( N(p)°/<0-1) r-1)/0 (E.3) where p is simply the price of one of the symmetrical intermediates produced in that economy. As can be seen, the minimum unit costs decrease with N. Accord- Regional agglomeration and regional unemployment 143 ing to Ethier (1982) and Matusz (1996), this intends to capture the famous "pin factory"-idea of Adam Smith. It is an advancement for an economy to have a deeper division of labour, i.e. more narrowly defined sub-steps in which a specific production task (Y) is partitioned. An important assumption made by Matusz ( 1996), that will also be used here, is perfect competition in the Y sector, which ensures that profits must always be equal to zero. We furthermore use the price of the final good p Y as the numeraire and normalize it to one. By the condition re Y = 1. Y - G. Y = 0, we can easily derive the first product market equilibrium condition of the model. It is given by the requirement that minimum unit costs need to equal the product price G=(N(p)9f<0-l)t-1)/0 =l. Since Y is the only commodity in this economy that is directly consumed, also the consumer price index is given by the value p Y = 1 at any time. This assumption is thus simplifying in another respect, as it allows us to abstract from the distinction between nominal and real wages. In equilibrium, prices of the intermediates will have to adjust such that this condition is satisfied. Each of the N single intermediates Xi is produced by using labour only. The production function in the X-sector is virtually identical to that described for the manufacturing sector in section D5.2.). There are N single firms, each producing one distinct (but symmetrical) intermediate under increasing returns to scale and within a monopolistically competitive market. The labour requirement £ i necessary to produce the quantity Xi is given by f;=a+/JX; with a>O, /J>O Each firm sets prices as a constant mark-up over marginal costs 1• (E.4) Despite of the assumption of monopolistic competition, profits for every single intermediate good are driven down to zero by the entry of potential competitors. This again implies that all X-firms operate at a unique scale of output, and employ a well defined number of workers, respectively given by 1 In the formulation with cr, which is also the perceived elasticity of demand, the pricing rule takes the form p(l-1/cr) = J3w. This form might look more familiar. 144 Regional agglomeration and regional unemployment X -(~J(_!!_) /3 I-0 and f_ = __!!_ 1-0 (E.5) a) The model with full employment The determination of the equilibrium price and the equilibrium number of intermediate inputs can most easily been done for the case with full employment. We know that the equilibrium number of workers that each firm employs is given by (E.5). Let the size of the total labour force be given by L. The equilibrium number of firms N is then simply given by N =!::_ = L(I-0). f a (E.6) This condition states that the equilibrium number of firms is higher, the larger is the local labour force L. But recall that the number of firms N will also affect the production costs in the Y-sector. We have already established the equilibrium condition to be G = .w 0·1 J 10 p =1. Using (E.4) and (E.6) in this equilibrium condition, we can derive the equilibrium wage per worker (w) as a function ofN: (E.7) The individual wage is higher, the larger is the local labour force and the higher is the equilibrium number of firms N. What is the intuition of this result? We have seen that production costs for the final product decrease in the number of available intermediate inputs. But the price p Y is the numeraire and always equal to one. Suppose N increases. On instance, there will be positive profits in the Y sector, because costs have decreased at constant sales prices. With perfect competition, new entrepreneurs will enter the market for Y production and compete profits down to zero. This must be done by paying more for intermediate products. By (E.4) and the assumption of zero profits in the X sector, these price increases will be absorbed by higher wages. In other words: If more intermediates can be produced, the increasing returns to scale can better be exploited. This will lead to higher wages. Regional agglomeration and regional unemployment 145 b) The model with unemployment Matusz ( 1996) now adds unemployment to the closed-economy model through a standard efficiency wage approach in the vein of Shapiro/Stiglitz (l 984). His setup is in principal the same as described in section C3.la). We shall therefore present the essence of this model here only very briefly. We stick to the notation of chapter C and apply our version of a shirking model rather than the set-up of Matusz ( 1996). Workers living in the closed economy are risk-neutral and derive utility from wage income w, but disutility from work-effort e, which is simply a technologically fixed number. The work utility is Y=w-e. (E.8) "Shirking" individuals spend zero effort ( e=0), but run a risk ( 1-y,) of being detected and then fired. By using the unemployment rate U = lN £ /L , we can derive the utility levels of an unemployed individual (Yu), a non-shirking employed worker (Yen) and a shirker (Yes) respectively. Vu= a(w-e) Ven= w-e Ves = yw + (1-y)( a(we)), where a is again the outflow probability from unemployment that negatively depends on the unemployment rate U (see section C3.5.). The firms pay efficiency wages such that the "non-shirking condition" Yes =Yen holds. The regional wage curve, or aggregate non-shirking condition, is given by the following expression w=e+ ye (1-y)(l-a(U)) (E.9) Of course the required efficiency wage is again lower the higher is the regional unemployment rate U. Equation (E.9) is the labour market equilibrium curve, and can be viewed at as the "first half' of full general equilibrium. The product market equilibrium condition has also been derived above. It only needs to be slightly modified if we allow for unemployment. The maximum number of varieties N that can be produced in this economy is no longer given by labour supply. Since labour supply and employment can now differ, it is by definition now given by the latter. The equilibrium condition (E. 7) becomes 146 Regional agglomeration and regional unemployment 0(1-0 )1 ~ 8 w = /3 --;;- (1U)L (E.10) The two equilibrium relations (E.9) and (E.10) can be illustrated within the same graph, given in figure El. Figure El: Equilibrium in the closed economy w w V B 7 L V B --1---------------------•u U* The locus VV represents the familiar wage curve locus. It is the graphical illustration of all combinations of wages and unemployment rates where shirking is just prevented for workers in the intermediate good sector. For all points to the right of VV, unemployment is too high for any given wage. Consequently firms can hire new workers and trust that they do not shirk. Hence, equilibrium unemployment must fall. This determines the phase arrows in the horizontal direction. The locus BB represents all combinations of w and U where all goods markets (Y and all X) are in equilibrium: there are no profits for either firm, there is cost minimization in the Y-sector and profit maximization for the X-sector. The curve is downwardsloping and convex, because of the involved increasing returns in the technology. Regional agglomeration and regional unemployment 147 For all points below BB, wages are too low for a given unemployment rate. Profits arise in the Y-sector than attract new producers. Labour demand rises and consequently wages have to go up. Full equilibrium in this closed economy is given at an intersection of VY and BB. The phase arrows indicate that only one equilibrium is stable. This one is at point A, with equilibrium unemployment U* and equilibrium wages w*. Note that the equilibrium unemployment is strictly involuntary. Workers would in principle be willing to work at going wages w. But employers know that further recruiting would lead the incumbent workers to shirk at going wages. Therefore they do not hire additional workers. Put differently, the combination with full employment (U=O) and wages equal tow might be desirable, but it is not feasible, since rational individuals would respond to this constellation with shirking behaviour. Let us briefly look at some comparative statics. No parameter change affects both curves. The wage curve VY shifts with the disutility of effort e, or the shirking detection rate y. As argued in chapter C, these parameters might reflect structural characteristics of the respective labour market and could (through appropriate model extensions) be explicitly modelled as contingent on public policy, like e.g. the welfare state regime or employment laws. The goods market curve BB shifts out to the right top as a, 13, or 0 decrease. Lower values of a or 13 reflect lower production costs at given output prices, i.e. an increase in profits. Due to perfect competition, this must lead to higher real wages stemming from the product market equilibrium condition. A decrease in 0 reflects a higher degree of increasing returns to scale. By a similar reasoning this advantage for the production sector must be absorbed by higher equilibrium wages. c) The introduction of perfect trade The final reason why the BB-locus could shift out to the top right is an increase in the exogenously given size of the labour force L. Since the VY-curve is not affected by this parameter change, the resulting new equilibrium would be one with higher equilibrium wages w and a lower equilibrium unemployment rate U. The intuition is straightforward. An increase in L implies that it becomes feasible for the economy to produce a larger number of intermediate goods, which leads to a decline in production costs for one unit of Y. This intuition is also at the core of the analysis of Matusz ( 1996), who moves from a closed-economy setting to a two-country case with perfect (=costless) trade in final goods and intermediate products. Suppose that the closed economy described in this section now starts to trade with a structurally identical foreign country. The final good Y as well as all intermediates X can be freely shipped across space, and all intermediates will be used symmetrically in the Y-production of either country. In such a setting, the home country can draw on imported inputs from the foreign country as if the intermedi- 148 Regional agglomeration and regional unemployment ates were produces locally. In other words, there is no substantial difference between the introduction of trade and an increase in the size of the domestic labour force in the Matusz-model. The unit costs for the home country now read as G = ( N(p )8fl0-1J + N * (p*)°f(0-1J ye-1)/0 = 1 ' (E.11) where an asterisk denotes variables of the foreign country. An analogous equation like (E.11) applies to the foreign country. Since there is free tradability and perfect competition in the Y-sector, the equilibrium condition is still given by the requirement that unit costs G (and G*) need to equal the numeraire price py=l. Due to free trade in the intermediates sector, there must also be price equalization for the symmetrical industrial inputs (p = p*). The equilibrium condition for the product market in both countries is thus given by W = w* = !!....(N + N*t0> 10 /3 (E.12) If both countries face structurally identical labour markets, i.e. the same wage curve locus, (E.12) inevitably implies that there must be equalization of real wages and unemployment rates across the two countries. The real wage is higher and the unemployment rate is lower in either country than it has been the case in autarky. The basic implication of the model is thus that the introduction of free trade per see has positive welfare effects by increasing wages and lowering unemployment. E3.2.) The two-region case with imperfect trade As argued above, this basic version of the Matusz-model is ill-equipped to study regional disparities and agglomeration We will therefore extend and generalize the model of Matusz ( 1996) in this section. In chapter D we have shown that there are basically three core elements of the regional agglomeration theories in the vein of NEG. The first, increasing returns to scale, is already a feature of the model approach by Matusz. The second, transportation costs, will now be introduced. It will open up the possibility of regional disparities, since now one can explicitly discriminate the economic variables of the different spatial units. The third core element, the presence of an endogenous mechanism that pushes for spatial concentration, will be introduced in the next section through (imperfect) labour mobility. Regional agglomeration and regional unemployment 149 a) The product market We now consider a nation consisting of two regions r and s with identical technology and preferences (if preferred, one can use the original terminology of Matusz with a home and a foreign country). Both regions produce the final consumption good Y under the use of symmetrical intermediate inputs which are partly manufactured in the respective region itself (Xrr), and partly imported from the other region (X,,). Transportation of intermediates across regions now imposes ·iceberg· costs ,> 1. For each unit Xsr dispatched, only I /'t units arrive. The standard CES production function for region r is now given by y =[N X 8 +N [X,,] 0 )¼ r r rr s r (E.13) The minimum unit cost function G, becomes ( O 0 J 0 ; 1 G, = N,(p,)0-1 +N,(rp,)0-1 , (E.14) and the demand functions for intermediates Xrr and X,r can be written as I 0 I 0 - - X" = P, 0-1 G, i-0 };_ and X,, = ( r P, )0-1 G, i-0 };_ . (E. l 5) where Pr is the mill price of an symmetrical intermediate from region r. G, is decreasing in both N, and N.: A larger array of intermediate inputs reduces costs in the Y-sector in both regions. But due to the transportation costs, the decline is larger in the region where the increase in the number of varieties has occurred. Put differently, an increase in N, has a stronger negative effect on G, than on G,. With respect to the final goods sector, we maintain the assumptions from the last section. The Y-sector is perfectly competitive, and the final consumption good can be freely traded across space. This implies that there is price equalization on the market for the final consumption good. Y-producers in both regions have to take the price p Y as given, potentially as determined on world markets outside the nation. Without loss of generality we keep p Y = I as the numeraire. At first sight the assumption of perfect tradability in the consumption goods sector, but imperfect tradability in the sector of industrial inputs might seem peculiar. But apart from offering analytical convenience, its use can be justified on intuitive grounds. Production in the Y-sector is just the assembly of intermediates without use of labour. 150 Regional agglomeration and regional unemployment Therefore, the function Yr simply reflects with what level of technological sophistication the region r can produce a given final output bundle. The advantage of sophisticated (large) regions is the high availability of locally produced intermediates, whereas small peripheral regions have higher costs of producing the same level of output. Zero profits and efficient production in the Y-sector imply that unit costs need to equal one in both regions. Using (E.14), the respective equilibrium condition is 0 0 - - l = N,(p,)0-1 + Ns('• Ps)0-I for region r 0 0 - - and l=N,(rp,)0-1 +N,(p,)0-1 for region s. (E.16) The production of the single intermediates is unchanged compared to the closedeconomy case. Therefore, the number of locally produced intermediates is restricted by regional employment: N =(1-U )L' r r f, and N =(1-U )L, s s f_ (E.17) where Lr and Ls denote the exogenously given sizes of the regional labour forces. The regional wage levels Wr and Ws are determined in the same way as in (E.4), i.e. prices are constant mark-ups j3/9 over marginal costs. Contrary to the case with free tradability of intermediates, there is no longer price and wage equalization in the X-sector if the two regions differ in size and 't > 1. If one region is larger than the other one, it has an advantage since it can produce more intermediates locally. We substitute (E.17) into (E.16) and set ~=9 for notational simplicity. We obtain [ (1-U,/' ] 1 ~ 0 w = f_ r 1- (1U,) ] ( rw,)8~1 (E.18) The nominal (=real) regional wage Wr derived from the condition for product market equilibrium is increasing in employment in both regions, but decreases