Local Industrial Clusters: Existence, Emergence & Evolution (Studies in Global Competition, V. 20)

Local Industrial Clusters

Local industrial clusters, such as Silicon Valley in the United States, have become an important subject of scholarly inquiry in recent years. This book offers a unifying view by capturing the general characteristics and prerequisites of local industrial clusters both on a theoretical as well as an empirical level. The book establishes a mathematical model to analyse the dynamics of clustering and the conditions that are to be satisfied if a local industrial cluster is to evolve. This model allows predictions about the spatial distribution of firms to be deducted, which are empirically tested in the book. This thorough methodology allows the author to study the existence of local industrial clusters in Germany, their stability and the industrial characteristics that are responsible for their existence. An impressive scholarly exercise, this book also contains important policy lessons. As such, Local Industrial Clusters will be a valuable read for policy-makers as well as academics. Thomas Brenner is Research Associate at the Max Planck Institute for Research into Economic Systems and lecturer at the University of Jena, Germany.

Studies in Global Competition

A series of books edited by John Cantwell, The University of Reading, UK and David Mowery, University of California, Berkeley, USA Volume 1 Japanese Firms in Europe Edited by Frdrique Sachwald Volume 2 Technological Innovation, Multinational Corporations and New International Competitiveness The Case of Intermediate Countries Edited by Jos Molero Volume 3 Global Competition and the Labour Market By Nigel Driffield Volume 4 The Source of Capital Goods Innovation The Role of User Firms in Japan and Korea By Kong-Rae Lee Volume 5 Climates of Global Competition By Maria Bengtsson Volume 6 Multinational Enterprises and Technological Spillovers By Tommaso Perez Volume 7 Governance of International Strategic Alliances Technology and Transaction Costs By Joanne E.Oxley Volume 8

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Regional Systems of Innovation By John Cantwell and Simona Iammarino Volume 19 Knowledge and Innovation in Regional Industry An Entrepreneurial Coalition By Roel Rutten Volume 20 Local Industrial Clusters Existence, Emergence and Evolution By Thomas Brenner Volume 21 The Emerging Industrial Structure of the Wider Europe Edited by Francis McGowen, Slavo Radosevic and Nick Von Tunzelmann Volume 22 Entrepreneurship A New Perspective By Thomas Grebel

Local Industrial Cluster Existence, Emergence and Evolution

T.Brenner

LONDON AND NEW YORK

First published 2004 by Routledge 11 New Fetter Lane, London EC4P 4EE This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/.” Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 © 2004 T.Brenner All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloging in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalog record for this book has been requested ISBN 0-203-41724-0 Master e-book ISBN

ISBN 0-203-68045-6 (Adobe e-Reader Format) ISBN 0415334691 (Print Edition)

To Ulrich

Contents

List of figures

x

List of tables

xi

List of symbols

xiii

Acknowledgements

xvii

1 Introduction

1

2 Theoretical approach

8

3 Empirical study of Germany

68

4 Simulating local mechanisms

126

5 Conclusions and policy implications

164

Appendix

186

Bibliography

206

Index

214

Figures

2.1 Structure of the interactions between the variables of the model.

21

2.2 Stable and unstable stationary states of local systems

30

2.3 Dynamics of local systems

33

2.4 Distribution of inhabitants among regions

61

2.5 Distribution of the number of students among regions

62

2.6 Distribution of the relative numbers of firms among regions

63

3.1 Empirical firm distribution for the office machines industry

73

3.2 Theoretical firm distribution for office machines

74

3.3 Schematic representation of theoretical change in the number of firms

89

3.4 Local clusters in Germany

103

4.1 Ranking of regions with clusters after two years

159

4.2 Ranking of regions with clusters after three years

161

Tables

3.1

Frequencies of different dynamics of types of firm distributions 86

3.2

Classification of the dynamics in all industries

90

3.3

Dynamic and static features of manufacturing industries

92

3.4

Dynamic and static features of service industries

93

3.5

Dynamics and changes of clustering in the manufacturing and service sectors

94

3.6

Clustering in the optical industry

107

3.7

Descriptive statistics for the independent variables of clustering 116 in Germany

3.8

Descriptive statistics for the dependent variables of clustering in 117 Germany

3.9

Results for the logistic regressions for the variable CLUSTEXIST

118

3.10 Results for the logistic regressions for the variable CLUSTDYN 119 3.11 Results for the logistic regressions for the variable EQUALDYN

120

4.1

List of parameters and their ranges

147

4.2

Clustering in five repetitions of the same parameter set

152

4.3

Distribution of the number of clusters

154

4.4

Differences in the cumulative distribution between parameter sets

155

4.5

Dependence of the number of local clusters on the size of the regions containing a cluster

156

4.6

Time of the emergence of clustering

158

4.7

Year of stabilisation

158

4.8

Number of simulation runs in which the location of the highest relative numbers of firms change after four years

162

5.1

Potential causes of the existence of local industrial clusters

167

A.1 List of 3-digit industries and their clustering characteristics

193

A.2 Correlations between variables in Section 3.5

203

Symbols

aƒƒ, aƒc,…

strengths of the impacts of the variables ƒ(t), c(t) and s(t) on each other

CL(ƒ)

part of the spatial firm distribution that describes clustering

c, c(t)

advantage of the local conditions (Ch. 2)

č

stationary state of c(t)

c

index denoting consumers (Ch. 3)

D(t)

total demand at time t maximal and final demand

d(n, t)

demand for the products of firm n at time t

d(i)

distance between the theoretical and the empirical distribution for industry i for to the Kolmogorov-Smirnov test

e, e(t)

exogenous conditions

e1, e2

critical values of the exogenous conditions

Ft(i, ƒ)

theoretical frequency of regions that contain ƒ firms of industry i

Fe(i, ƒ)

empirical frequency of regions that contain ƒ firms of industry i

ƒ, ƒ(t)

size of firm population in a region and industry stationary state of ƒ(t) carrying capacity of a region with respect to the exogenous conditions

ƒ(i, r), ƒ(i, r, t)

number of firms in industry i and region r at time t total number of firms in industry i

g(n)

kind of good produced by firm n

g(c)

kind of good preferred by consumer c

i

index denoting industries

in

industry to which firm n belongs

Kk(r, t)

human capital in the form of knowledge available in region

r at time t Ks(r, t)

human capital in the form of skills available in region r at time t

kk(r, t)

creation of human capital in the form of knowledge in region r at time t

kl(r, t)

creation of human capital in local schools in region r at time t

ks (r, t)

creation of human capital in the form of skills in region r at time t

ku(t)

total education in universities at time t

L(n, t)

labour force of firm n at time t total number of people employed in region r at time t

Lc(i) Lm(i)

likelihood value for the cluster distribution in industry i likelihood value for the mixed distribution in industry i maximum likelihood value for the cluster distribution in industry i maximum likelihood value for the mixed distribution in industry i

m(i, r, t)

number of employees in industry i and region r at time t

N(t)

number of firms at time t

Nr(t)

number of regions at time t

n

index denoting firms

n(c, t)

firms from which consumer c buys one piece of the good at time t

ncl(i)

number of local clusters that are described by the cluster term CL(ƒ) in industry i

N(t)

set of all indices of firms at time t

p(n, t)

price of the goods produced by firm n in the market at time t

P(i, ƒ)

probability that a randomly chosen region contains ƒ firms of industry i

Pm(i, r, ƒ)

probability according to the mixed distribution that a randomly chosen region contains ƒ firms of industry i

Pc(i, r, ƒ)

probability according to the cluster distribution that a randomly chosen region contains ƒ firms of industry i

P(n, t)

probability of firm n innovating at time t

R

number of regions

r

index denoting regions

rn

region in which firm n is located

s, s(t)

size of the population of service firms and suppliers in a region

š

stationary state of s(t)

s(r), s(r, t)

size of region r at time t in terms of its share of total employment

T(n, t)

technological advancement of firm n at time t

Tmax(t)

most advanced technology used by any firm in industry i at time t

Tmin(t)

least advanced technology used by any firm in industry i at time t

t

index denoting time

u(r)

share of universities that is located in region r

w(r, t)

labour costs in region r at time t

wg(r, t)

wages for general workers in region r at time t

wk(r, t)

wages for human capital in the form of knowledge in region r at time t

ws(r, t)

wages for human capital in the form of skills in region r at time t

x(r)

coordinate denoting the location of region r in east-west direction

y(r)

coordinate denoting the location of region r in north-south direction geographic distance between the regions

and r

αff, αfc,…

exponents of the impacts of the variables ƒ(t), c(t) and s(t) on each other

α0 to α3

regression parameters

β↑, β↓

parameters determining the economies of scale

∆(n, t) 0

production capacity of firm n at time t basic probability of the occurrence of start-ups

η

share of firms about which consumers gather information each day

κa

speed of the adaptation of skill creation in firms to the requirements

κb

basic share of workers who are skilled/have knowledge

κd

share of human capital that deteriorates in each time step

κe

number of people that are educated in firms in relation to the number of skilled people that are required

κmobil, k

maximal share of people with knowledge who move to other regions

κmobil, s

maximal share of people with skills who move to other

regions κs

speed of the adaptation of the education system to the demand for qualified labour

κu

share of education that takes place in universities

κ+

number of people that obtain public education in relation to the number of people with the respective knowledge that are required

Λ

maximal size of new firms

λ

maximal possible increase of the size of firms

λ(i)

likelihood ratio for industry i

µ0

basic constant rate of innovation per day in each firm

µL

factor for innovation rate per day proportional to the size of the firm strength of the negative feedback of ƒ(t), c(t) and s(t) on itself

π

strength of the preference of consumers for the preferred kind of good

Φ(r)

number of potential employees in region r share of general workers that are employed in other industries

ρƒ, ρc, ρs

exponent of the negative feedback of ƒ(t), c(t) and s(t) on itself

σ

amount of spillovers within an industry proportional decrease of production costs due to one innovation dependence of the innovation step on the distance to the technology frontier

ωk

number of workers with the respective knowledge necessary for the production of one good

ωs

number of skilled workers necessary for the production of one good

ωe

unemployment elasticity of wages

ξ1 to ξ6

parameters of the industrial size-distribution of regions

ζmobil

parameter that determines the decrease of labour movements with geographic distance

ζspill

parameter that determines the decrease of spillover between firms with their geographic distance

ζspin

parameter that determines the decrease of the likelihood for the location of spin-offs with the geographic distance from the incubator firm

Acknowledgements

My research into local industrial clusters was triggered by a contract with the German Ministry for Education and Research on advising them in running the InnoRegio programme from 1999 until 2001. Although the research continued after this contract, the work for the German ministry set a great deal of the agenda of my whole research. It helped me focusing on topics that are relevant for giving policy advice and kept me from being lost in purely academic questions. Therefore, I would like to thank the German Ministry for Education and Research not only for financial support and access to data but also for a guiding line and fruitful interaction. The work on this book was completely done at the Max Planck Institute for Research into Economic Systems in Jena which offered me great opportunities for research. During this time I profited much from the huge knowledge and experience of Ulrich Witt and from his critical comments. I also profited strongly from the freedom of research I have experienced at the Max Planck Institute and from the financial support for all kinds of scientific activities. Furthermore, I wish to thank my colleagues at the Max Planck Institute for the good atmosphere within the Evolutionary Economics Group which was helpful as much for my personal well-being as for the productivity in my research. The joint work with other researchers, especially Dirk Fornahl, Deborah Tappi and Paolo Seri, on the same topic of local industrial clusters was very helpful in developing my own approach. I also received many good comments during my presentations at the institute and from the colleagues who read the first manuscript and helped me to improve the book, especially Dirk Fornahl, Peter Murmann, Guido Bünstorf, and Deborah Tappi. The book also profited from the comments on its first version by Ulrich Witt, Uwe Cantner, Hariolf Grupp and an anonymous referee. Besides the German Ministry for Education and Research, I wish to thank Bart Verspagen and the ZEW for the provision of data. Furthermore, I want to thank Sandra Gottschalk for the help in using data from the Mannheimer Innovationspanel. Various research assistants at the Max Planck Institutes have also been helpful in using different sources of data. These are Kristin Joel, Peter Stangner and Heiko Bubholz. Finally, I wish to thank my family, my friends and Sabine. In my opinion, recreation is an important factor for scientific work. However the people around me have not only provided me with the opportunity for recreation, they have also supported me with a lot of understanding, they have offered me the chance to discuss my ideas with people outside science, and they have prevented me from getting lost in science and divorced from reality.

1 Introduction

In recent years local processes have attracted much attention within economic research. Despite the fact of globalisation, local conditions still play an important role in the economic development of firms, industries and states. The simultaneous occurrence of the delocalisation of some economic activities and the sustained importance of the local environment for other economic activities seems to be a contradiction. The costs of transferring goods and money from one place to another have decreased tremendously in terms of direct costs for transportation as well as in terms of indirect costs caused by taxes, laws and different institutional systems. This has made it more easy for firms to act globally. This development has not caused location to play a less important role. Plenty of studies have found that the specialisation of regions and nations has remained fairly constant in the past twenty or thirty years (see, for example, Dalum & Villumsen 1996, Fagerberg & Verspagen 1996, and Amiti 1999). Hence, the spatial distribution of industry-specific economic activities seems to be quite stable. Despite all the discussion of a relocation of factory sites to countries with much smaller labour costs in the 1980s, many labour-intensive industries have remained within countries with high labour costs. Examples are the automobile industry in Germany and, on a more local level, the very labour-intensive porcelain manufacturing in Meissen. Some emerging industries have also become concentrated in a few, high-labour-cost locations. The location of the telecommunications industry in Scandinavia is a prominent example. These examples and many others in the literature show that firms in the same industry tend to locate in the same few places and that this geographic concentration is quite stable despite all the changes in global and local conditions. Such regularity points to a fundamental cause common to all, or at least a specific kind of geographic industrial concentration. Here the geographic concentration in the form of industrial districts is studied. Indeed, it can be shown (see Chapter 3) that about half of the manufacturing industries, on a 3-digit level, in Germany show a type of geographic concentration in line with the definition of industrial districts by Marshall (1920, Book IV, Ch. X). Hence, industrial districts or local industrial clusters, as they are called here, are not isolated cases but a general phenomenon of industrial organisation. Nevertheless, it is not a universal phenomenon. This implies that there have to be underlying causes that are common for quite a number of industries and situations but not for all of them.

Local industrial cluster

2

OPEN QUESTIONS AND AIMS OF THE BOOK The observations described above imply three kinds of questions: the question of why local industrial clusters exist, the question of when and where they emerge, and the question of how they develop and how they can be characterised. The latter question is extensively discussed in the literature because the successful development of local industrial clusters has made them especially attractive for academic research (see, e.g., Becattini 1990, Camagni 1991b, Paniccia 1998, Braunerhjelm & Carlsson 1999, Keeble & Wilkinson 1999 and Maggioni 2002). Many scientists have studied the causes for this success. Through this they have identified the specific characteristics of local industrial clusters. Various definitions and characterisations have been given. This book focuses on the questions of why local industrial clusters exist and when and where they emerge. This also requires at some points some discussion of their characteristics and development. These discussions, however, are means and not ends of this book. It is helpful to start with such a discussion. The identification of characteristics of local industrial clusters in the literature makes one thing clear: local industrial clusters differ in many aspects and have little in common. The differences of local systems studied under the labels of industrial districts, innovative milieux, local clusters is explicated in several studies (explicit statements about the differences can, e.g., be found in Scott 1992, Paniccia 1998 and Longhi & Keeble 2000). These differences imply that it is difficult to answer the questions put forward above on a general level. This is probably the reason why much of the literature has focused on the understanding of specific cases. Some authors have attempted to generalise part of the findings on local industrial clusters. Consequently, a large number of different definitions can be found in the literature (see, e.g., Aydalot 1988, Becattini 1990, Camagni 1995, Cooke 1998, Braunerhjelm & Carlsson 1999 and Keeble & Wilkinson 1999 for a good overview of some of these developments). However, a similar number of works can be found that argue that these definitions are inadequate. A general definition is difficult to obtain. Nevertheless, these local systems seem to have something in common. One of the topics that is taken up repeatedly throughout this book is the distinction between general and specific features in the context of local industrial clusters. The book aims to increase the understanding of what kind of features are general and what kind of features are specific in local clusters. Hence, the content of this book can be characterised on two levels. First, there are the research questions of why local industrial clusters exist and when and where they emerge that are to be answered. These questions are rarely addressed on a general level in the literature. There are a huge number of case studies that provide answers to these questions for specific cases. A few attempts are made to generalise these findings (such studies can be found in Porter 1990, Paniccia 1998, Pietrobelli 1998 and Maggioni 2002). Second, the book takes a novel approach to answering the research questions. It approaches these questions on a general level, but it does not start from the empirical findings in case studies in an attempt to generalise them. Instead, it starts from a general theoretical approach, which is, of course, informed by the huge empirical knowledge in the literature. It studies how far we might progress on the basis of such a general approach in theoretically understanding the phenomenon of local industrial clusters, in

Introduction

3

analysing the phenomenon empirically and in deducing policy advice. It examines what can be understood on a general level and what has to be classified as historical, industrial or local specificity. RESEARCH QUESTIONS The question of why local industrial clusters exist is motivated from an academic perspective. It results from the desire to understand why we repeatedly observe the phenomenon of local industrial clusters in different places, at different times and in industries with different characteristics. However, before an explanation for the phenomenon of local industrial clusters can be found, it has to be clarified whether and where this phenomenon exists. Hence, answering the question of why local industrial clusters exist involves more than finding some causes. First, it has to be proved that local industrial clusters can be differentiated from the populations of firms and the situation in other regions. A clear distinction must be possible if local industrial clusters are a ‘real’ phenomenon. This problem has not previously been addressed in the literature and is taken up in this book. Second, whether this phenomenon is restricted to certain countries, times or industries has to be studied. Case studies suggest that local industrial clusters emerge in all industrialised countries and have existed for at least the last 100 to 150 years. However, they seem not to exist in all industries. This anomaly has not been further analysed in the literature. An empirical study is conducted here to classify industries into the class of those in which local clusters exist and the class of those in which no such clusters are found. In this context, the question of which mechanisms cause the existence of local industrial clusters can be addressed. The question about the mechanisms that cause the existence of local industrial clusters should not be mixed up with the question of why such clusters are economically successful. They are, to some extent, intertwined but not identical. Of course, if local industrial clusters implied an economic disaster for the region, they would not exist or they would disappear quickly. Thus, being not economically disadvantageous is a necessary condition for the existence of local industrial clusters. Beyond this, however, no general statement is possible on a theoretical level. This means that the mechanisms that cause the emergence of local industrial clusters and the mechanisms that stabilise them have to be studied independently of the question of why they are successful. New Economic Geography (an overview of this research can be found in Fornahl & Jasper 2002) has contributed to answering this question by showing that local positive externalities may lead to geographical clustering. This is a first answer at an abstract level. Case studies, however, show that different mechanisms underlie the positive externalities that are assumed in New Economic Geography models. Although each existing local industrial cluster has its own specific history, clustering is a phenomenon common for many industries and for different times in the history of industrialised production. Therefore, there has to be a common underlying basic mechanism. This book aims to dispense with the apparent contradiction between the specificity and the generality of the phenomenon of local industrial clusters. A theoretical framework is developed on the basis of the general underlying mechanisms in this book. Within this framework it can be shown that different processes have the same implications for the

Local industrial cluster

4

development of local systems. This allows the complementarity and substitutability among the aspects and processes identified in the literature to be analysed. Subsequently, it will be studied in this book how and to what extent the question of why local industrial clusters exist can be answered in a general approach. One aim of the book is to provide a theory that allows us to structure the findings obtained in case studies. The question of where and when local industrial clusters emerge has a political connotation. In recent years policy makers have repeatedly designed programmes to trigger the emergence of local industrial clusters. The design of such programmes requires a detailed knowledge about how the timing and location of the emergence of such clusters is determined and how this can be influenced. There is a huge literature that offers insights. Within the last 20 years an enormous number of case studies have been conducted, many of them offering a detailed analysis of the specific mechanisms and the circumstances that caused the developments in the regions under consideration. A general approach that allows the findings to be structured and the complementary and substitutable causes to be identified is, however, missing. The theoretical framework that is developed here represents such a structuring device. It allows not only the question of why local industrial clusters exist to be separated from the questions of where and when they emerge, but also the latter two questions to be separated. This book examines the extent to which these three questions can be separated and answered on a general level. The basic aim is to obtain a classification of different kinds of mechanisms and characteristics that influence the timing and location of the emergence of local industrial clusters. Several kinds of influences are distinguished, such as global developments, local prerequisites and local historical developments. These influences do not depend much on each other. This implies that they can be studied separately and that for each of them, independent conditions for the emergence of local industrial clusters can be formulated. This is done on an abstract level. The aim is to state general conditions and the relations between these. This leads to a framework in which every combination of circumstances can be tested with respect to the satisfaction of the general conditions. In this context, one question is studied in more detail. This is the question about the comparative impact of the different conditions. In some recent case studies doubt has been cast over the superior conditions said to exist in the regions in which the industrial clusters have emerged. This raises questions about the stochasticity of the processes and the rigidity of certain conditions. These questions are addressed with the help of simulations here. METHODS AND CONTENT Thus far the content of this book has been characterised according to the research questions it addresses. Alternatively, it might be characterised methodologically. Three ends can be distinguished according to such a characterisation. First, a general framework is developed that allows the specific findings in the literature to be structured and it allows what is general and what is specific in context of the phenomenon of local industrial clusters to be understood. This will have implications for science and policy. It

Introduction

5

informs science about the aspects that can be approached on a general level (some of which will be examined here) and the aspects that can only be understood separately in each specific context. It also informs policy makers about what a general approach might offer and to what extent specific knowledge has to be taken into account. Second, the general theory is applied to Germany in an empirical study to test the general theory and to show how far a general approach can take us. The empirical study also provides some results about the actual clustering and the causes for clustering in Germany. Third, the stochastic characteristics of the emergence of local industrial clusters are studied with the help of simulations. The aim is to understand what impact stochastic events have and to what extent history matters. As a consequence, the book consists of three main parts in which three different methods are used to study the emergence and evolution of local industrial clusters. In Chapter 2, a theoretical approach is taken. This approach consists of three steps. It starts with a definition of the concept of local industrial clusters. In the next step an abstract model of the evolution of such clusters is developed. The modelling is based on the definition and allows some fundamental characteristics of local industrial clusters and their evolution to be deduced. In particular, it allows for the separation of the questions of why, when and where local industrial clusters emerge. However, these characteristics and dynamics are formulated in an abstract manner. Therefore, the last step is to identify the real processes that underly these abstract dynamics. The candidates for this identification are taken from the literature. The results of the abstract modelling can be used to select among these candidates and classify them according to the question or questions they help to answer. A distinction is made between those aspects that lead to the emergence of a cluster in a particular region and at a particular time and those aspects that cause the existence of clusters and their relative stability. A first theoretical structuring of local characteristic and mechanisms is obtained. Further analyses of the local characteristics and mechanisms are conducted in Chapter 3 on the basis of empirical data. An empirical approach is taken in Chapter 3 to test the theoretical findings in Chapter 2 and to obtain further insights into the mechanisms and conditions relevant for the emergence of local industrial clusters. Two sources of empirical data are used: data on the spatial distribution of the industry-specific numbers of firms in Germany and data on certain industry-specific characteristics, such as the relevance of innovations, spillovers, the importance of human capital and cooperation. The spatial distribution of firms in Germany is used to test the stationary and dynamic predictions of the abstract model that has been set up in Chapter 2. Furthermore, it is used to study the differences between industries with respect to clustering. Some industries tend to cluster spatially while others do not cluster. Those industries that show clustering are identified. Subsequently, the conditions for the identification of local clusters are deduced empirically for each of these industries. As a consequence, all local clusters in these industries in Germany can be identified. The resulting list is discussed in the light of existing case studies. Finally, the reasons for the differences between industries are examined with the help of further empirical data about industries. This provides some test of the mechanisms that are claimed to be important in case studies on a general level. In Chapter 4, a simulation approach is taken. All local mechanisms that are identified in the theoretical approach are implemented in a spatial simulation model. This model is used to study the characteristics of clustering on a general level. To this end, specific

Local industrial cluster

6

features of the clustering process and the resulting spatial distribution of economic activity are studied. The analysis focuses on the path-dependence of the processes. Chapter 4 analyses whether industrial characteristics determine the existence, number and location of industrial clusters and at which time the development in regions in which a local cluster emerges differs from the development in other regions. Chapter 5, which has three sections, concludes the book. The first section sums up the findings made within this book and reported in the literature with respect to the main questions addressed here: the questions of why local industrial clusters exist and when and where they emerge. The second section discusses the political implications of these findings. It focuses on the question of when and where policy should and could influence local processes. The final section discusses the questions that are still open and gives suggestions for research that could follow.

2 Theoretical approach

2.1 CONCEPTS AND DEFINITIONS Before a theoretical model for the evolution of local industrial clusters can be developed, the economic phenomenon that is called local industrial cluster has to be defined. Only when a clear definition of the research subject is given can a well-structured theory be developed. Most of the concepts in the literature, such as industrial districts, innovative milieux and clusters, have arisen from empirical studies. In the case of industrial districts and clusters, various different definitions can be found (the original discussion of industrial districts is given in Marshall 1920, Book IV, Ch. X, an overview of the concept is given in Rabellotti 1997 for industrial districts and in Braunerhjelm & Carlsson 1999 for clusters), while in the case of innovative milieux, the definitions are more homogenous (the most prominent definition can be found in Camagni 1995). In the industrial districts literature there is quite a dispute over the definition with some authors claiming that the concept of industrial districts has been defined too narrowly (see e.g. Schmitz 1992), while others claim that it has been defined too broadly (see e.g. Dijk 1995). The concept that is defined here differs from those in the literature. The approach in this book starts from a general theoretical perspective and analyses what insights this general perspective can offer. It aims to give some answers to the questions of why industrial districts, clusters and the like exist and when and where they emerge, and it approaches these questions on a general level. This implies that the aspects that are common to all these phenomena need to be examined. This requires a general concept for most of the variously named clusters of industries. This concept is called ‘local industrial clusters’ here. Its definition is entirely based on a few very fundamental assumptions. Whether the definition fits into the concepts that are common in the literature will be discussed at the end of this section. Therefore, the most common concepts are reported first.

Theoretical approach

9

2.1.1 Concepts in the literature Industrial districts Of all such concepts in the literature, the concept of industrial districts was the first. It was established by A.Marshall (1920) who describes ways in which firms might benefit from co-location. He argues that large corpora-tions are not the only way of benefiting from economies of scale. External economies might cause small firms that are located in the same district to experience something similar. He gives several examples of such external economies: information spillovers, local non-traded inputs, and a local skilled labour pool. These external economies are seen by Marshall as a counterbalance to the economies of scale of large firms. Marshall’s basic ideas were taken up in the Italian literature in the late 1970s. However, the concept has been modified in this literature so that some authors now talk about ‘Marshallian industrial districts’ and ‘Italian industrial districts’. The concept of Italian industrial districts focuses more on the social aspects that are involved in districts. The importance of the socio-economic structure and interaction was first discussed by Becattini (his first works on this subject were published in the late 1970s, but Becattini 1990 provides a good overview of his view). Becattini influenced most of the early Italian literature on industrial districts. Another strong influence resulted from case studies of districts in the north and east of Italy (especially the collection of studies in Pyke, Becattini & Sengenberger 1990 and Pyke & Sengenberger 1992). As a consequence, aspects such as “a network of small and medium-sized urban centres with strong craft and trading traditions”, “the spread of family-based agricultural smallholdings” and “the presence of local political traditions and institutions linked in with a Catholic tradition and a socialist and communist movement” have been identified as the prerequisites for the emergence of Italian industrial districts (see Trigilia 1992). With time and a quickly increasing number of approaches on this topic, the concept of industrial districts became more diverse. An intensive debate appeared in the 1990s about the most important preconditions for and mechanisms within industrial districts. This debate was triggered by new developments within the Italian districts, an increased scientific interest in the topic and the problems that arose when some scientists tried to transfer the concept to regions outside Italy (see, e.g., Schmitz 1992). Therefore, a welldefined common definition of an Italian industrial district cannot be identified in the literature any more. Nevertheless, there are some common features on which at least most of the authors would agree and which are somehow seen as the basic characteristics of an industrial district within the scientific society. These are the co-location of a large number of small and specialised firms, the strong division of labour among these firms and the social network of the relevant local economic actors favoured by a shared cultural background (see, e.g., Dijk 1995). Empirical studies, mainly case studies, had a strong influence on the definition of industrial districts. However, in recent years some approaches have appeared that try to find a definition of industrial districts that allows for their empirical identification. Again the main impulses come from the Italian literature, where the government has implemented a programme for the identification of industrial districts (see Tappi 2003 for

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an overview and discussion of these developments). In these approaches, industrial districts are defined as local labour market areas in which the employment in an industry is significantly higher than its proportion on a national level would predict. Furthermore, the firm population in the region has to be dominated by small and medium-sized firms and some other conditions have to be satisfied (see, e.g., Sforzi 1990). The social aspects of industrial districts are usually neglected in these approaches since these aspects are difficult to measure. Nevertheless, all these definitions go far beyond the concept that Marshall had in mind when he discussed industrial districts. He focused on external economies that cause small firms to profit from their co-location. The aim was to show that there are external causes for their success although they lack the internal economies of scale. The different causes of external economies that he discussed should be seen as examples for such external effects. Innovative milieux The concept of ‘innovative milieux’ was developed by a French research project, the socalled GREMI-study (the main results are presented in Camagni 1995). In this research project French regions outside the big cities are analysed according to their innovativeness and the local synergies among firms. This research presents the first attempt to rank the state of regions with respect to their development towards a ‘successful region’. The ranking is based on a two-dimensional scale consisting of the innovativeness and the synergies within regions. The potential developments in regions are also discussed in this literature. By studying all regions this concept also allows a highlighting of the differences between the more successful and the less successful regions. Furthermore, the concept of innovative milieux is based on the theoretical proposition that the success of a region depends on the existence of ‘district economies’ and ‘proximity economies’. These are caused by the human capital that is created in the region by educational and training activities, informal contacts between firms and the flow of information within the region, and a common cultural, psychological and often political background. Therefore, the theoretical assumptions behind the concept of innovative milieux are very similar to the assumptions on industrial districts. However, the concept of innovative milieux is not restricted to one or a few industries and it focuses more on information exchange and less on business contacts between firms. Furthermore, this strand of the literature has identified two factors that are seen as being most important for the advantage of a region: the human capital accumulated and the local synergies between firms. Regions can be ranked according to these two factors and these two factors should be supported by policy makers in order to help the region flourish (see Camagni 1995). This clear restriction to a few, in this case two, measurable aspects is missing in the rest of the literature.

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Clusters The concept of ‘clusters’ is neither restricted with respect to the number of industries nor spatially. However, there are related concepts of ‘regional clusters’ and ‘industrial clusters’ that add these restrictions to the original concept of clusters. The concept of clusters focuses on the linkages between firms, mainly demand and supply linkages, and the spillovers caused by these linkages (an overview is given in Braunerhjelm & Carlsson 1999). Other criteria that are mentioned in the descriptions of industrial districts and innovative milieux are not considered. The concept of clusters focuses on the profits that firms accrue because of the connections to other firms or their proximity. These profits result from cooperation, market relations, spillovers, and in some cases the fact that more start-ups occur. Most of these processes, especially those of spillovers and the increased frequency of start-ups, are much more effective locally. Thus, clusters often have a local connotation. However, whether they are restricted to local systems differs between the approaches. Similar to the concept of industrial districts, the concept of clusters has been used in recent years by many researchers in different ways. Several factors that have been identified as common to industrial districts or innovative milieux have been included in some definitions of clusters. However, the centre of the concept is still the linkages between firms and the effects of these linkages. Again, in recent years some definitions have been developed that allow for the empirical identification of clusters. The conditions formulated are a comparably high employment rate, a share of some industries on local employment that is significantly above the national average, and strong linkages between the industries that dominate in the region according to input-output tables (such an approach can be found in Braunerhjelm & Carlsson 1999). Further concepts Further definitions of different kinds of local systems have appeared in recent years and because many of the concepts discussed in the previous sections are often too restrictive for more general treatments, especially if different countries and industries are studied, some authors have modified the definitions of existing concepts, so that many different definitions appear with the same name. Others have reacted by creating new terms. Therefore, a large number of further concepts now exist that will not all be discussed here. These are, for example, the concepts of ‘regional innovation systems’, ‘flexibly specialised regional economies’, ‘sectoral agglomeration’ and ‘local systems’. The existence of many different concepts is also due to the existence of different schools of thought within economics and geography. Each of these schools concentrates on different aspects and mechanisms that play a role for the existence of clusters and districts. At the same time there are always attempts to establish more general concepts or to integrate aspects of one concept into another concept. Others argue that real clusters and districts are very different and that a unifying theory is not feasible. Some attempts have been made to classify the observed phenomenon into some general types (examples are given in Scott 1992, Markusen 1996 and Dijk 1999).

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There does not seem to be an end to this discussion in sight. This is partly caused by the fact that different scientific studies aim at different goals. These different goals require different definitions. The same holds for the approach taken here, which focuses on the understanding of why local industrial clusters exist and when and where they emerge. In particular, examining why local industrial clusters exist and the fact that an empirical study is conducted requires at least a modification of the concepts offered in the literature. Therefore, a new notation was chosen: ‘local industrial cluster’. 2.1.2 Local industrial clusters Phenomena to be studied Below a general theory for a certain kinds of local systems is developed. To this end, the kinds of systems under consideration have to be defined clearly. Furthermore, the definition has to be chosen such that all systems included in the definition have some features in common, on which the theory can be based. A general finding in nearly all case studies is that there are regions in which large numbers of firms that belong to the same or some related industries are located. These regions seem to be specialised in two ways. First, a large share of all the firms or employees in the country or in the world that belong to the industry under consideration, are located in the region. Second, a large share of all firms or employees located in the region belong to the industry under consideration. Isaksen (1996) has called this sectoral agglomeration and has developed an empirically measurable definition. This definition is based on the relative share of the employment in one industry. If this share exceeds 3 times the national average, a sectoral agglomeration is assumed to exist. Since this requirement is a common feature of all ‘local system’ concepts in the literature, it seems to be an adequate starting point for a general approach. However, a few concerns have to be put forward. A random location of firms does not lead to a uniform distribution in space. Ellison and Glaeser (1997) have comprehensively discussed this fact. In particular if very large firms exist, high concentrations of employment in a few regions have to exist but their existence does not necessarily imply the existence of any specific local mechanism. Therefore, the number of firms and not employees should be considered as is done by Ellison and Glaeser. In addition, a more adequate definition of a minimal amount of economic activity that is necessary to call it an agglomeration is needed. It should be defined in comparison to a ‘natural’ spatial distribution of firms. A vague definition is chosen here but the theoretical model that is developed below will allow more precision in Section 2.5. Finally, for empirical reasons the study conducted here is restricted to the separate analysis of single industries. Therefore, the term ‘industrial agglomeration’ is used here and defined as follows. DEFINITION 1: An industrial agglomeration exists if and only if, in one region the number of firms in one industry is significantly higher than the number that would represent an average share in comparison to other regions.

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All approaches that aim to identify local clusters and the like require a condition that is similar to the one above (see Sforzi 1990, Isaksen 1996, Paniccia 1998 and Braunerhjelm & Carlsson 1999). In addition, the definitions in this literature require further conditions. The authors do not aim to explain all kinds of industrial agglomeration, but focus on certain kinds of such agglomeration. The same holds for the approach proposed here. However, while the additional conditions in the literature are mainly inspired by the results of case studies, the additional conditions that will be set up here are inspired by theoretical considerations and the aim is to include those industrial agglomerations whose existence can be explained by the same general causes. Several causes might be put forward for the existence of industrial agglomerations. First, the traditional argument is that industrial agglomerations appear where the necessary natural resources are available, or are available more cheaply than in other places. This argument explained a lot of industrial agglomeration at the time of industrialisation and shortly after that period. However, with decreasing transportation costs and globalisation, the explanatory power of this traditional argument decreases, although it does not vanish. Second, industrial agglomeration might be caused by the necessity to be located near to customers. However, this implies that there has either to be a population with specific preferences or an industrial agglomeration with respect to another industry, the industry that buys the products of the industry under consideration. In the latter case, one agglomeration is explained by another and the task remains to explain the first of these industrial agglomerations. Third, it might be argued that some industrial agglomerations appear for statistical reasons. If all firms locate randomly, a certain number of regions will be populated by more firms than the average. Empirically, these regions will be identified as industrial agglomerations, although no specific circumstance exists that causes their emergence. Fourth, there might be forces that make the location of a firm in a certain region more likely once there are already other firms in the same industry located in this region. Such forces make the location of firms pathdependent. Although none of the regions might be advantageous at the beginning, the location of the first few firms favours some regions, which consequentially become more attractive for further firms. A self-augmenting process results. There are many different mechanisms that might cause such a self-augmenting process. These will be discussed in detail in Section 2.3.1. All four causes explain some of the existing industrial agglomerations and some of them are even explained by a combination of two or three causes. However, it is assumed here that the existence of most industrial districts or clusters that are studied in the literature is caused by the fourth explanation. This has two implications. First, the study of industrial agglomerations can be restricted to those industrial agglomerations that are caused by this mechanism, namely the self-augmenting process of firm location. Second, a general approach that deals with all industrial agglomeration that is caused by this mechanism includes nearly all cases that have been studied in the recent literature on industrial districts, clusters and innovative milieux. The approach taken here is based on these theoretical considerations.

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Definition Since the subject that is to be studied here does not match the concepts in the literature exactly, a new label is used: ‘local industrial clusters’ (LICs). Like industrial districts and clusters, local industrial clusters are restricted to one industry or a few related ones. In the empirical analysis conducted in Chapter 3 it is even restricted to one industry. However, choosing the adequate aggregation level and classification of industries allows the study of agglomerations that include several industries. Furthermore, this approach is restricted to a certain geographic space, called a region here. Both the restriction to an industry or a few industries and the restriction to a locality in the form of a region, require further discussion which is provided below. For the moment let us assume that regions and industries are somehow adequately defined. Then, a local industrial cluster is defined as follows. DEFINITION 2: A local industrial cluster is an industrial agglomeration that is caused by local self-augmenting processes. This means that, according to the definition of industrial agglomeration (see Definition 1), there have to be significantly more firms in a region with respect to an industry than there are on average in other comparable regions. However, such an agglomeration is only called a local indus-trial cluster if the high number of firms is caused by local selfaugmenting processes, and not by natural resources, the proximity of customers, or by chance. These other possible causes might have an additional influence, but a significant part of the above-average number of firms has to be caused by self-augmenting processes. Such a definition has some drawbacks. It is difficult to identify the exact causes for each industrial agglomeration empirically. This issue is taken up in Chapter 3 again. Nevertheless, Definition 2 is the guiding line for the theoretical approach that is conducted in this chapter. The local self-augmenting processes might be caused by different mechanisms. Two basic categories of such mechanisms can be distinguished. First, existing firms in a region might cause a higher start-up rate in this region because, for example, there are spin-offs, there is venture capital available or there is an increased attractiveness of the region through the existence of firms. Second, economies of location might help firms within industrial agglomeration to be more successful, so that they grow faster and fail less frequently than in other regions. There are many different mechanisms that cause such economies of location, for example, spillovers, cooperation between firms, and the development of a skilled labour pool (see also McCann 2001 for a discussion of economies of location and related concepts). All this will be discussed in more detail below. The general theory that is developed in Section 2.2 is based only on the abstract notion of local self-augmenting processes and the fact that these lead to an industrial agglomeration. Thus, the discussion is restricted to those local systems that satisfy Definition 2. This definition embraces most of the concepts in the literature because these mainly differ with respect to the causes of the self-augmenting processes they assume to be most important.

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Industries and regions If industrial agglomerations are studied empirically, the results depend very much on the classification of industries and the division of space into regions. Hence, some discussion about how industries and regions should be defined seems to be necessary here. The definition of regions has attracted quite some attention in the recent literature on industrial districts (for a discussion see Tappi 2003). The classification of industries is also repeatedly discussed in the literature. However, this discussion takes place mainly among researchers who classify industries in different countries. Within the literature on local industrial clusters it plays a very minor role. Empirical studies of industrial agglomeration are usually based on the existing classifications of industries in national statistics. This tends to be done for practical reasons as using other industry classifications would require additional collection of data, which is usually not feasible. In case studies of local clusters, however, the researchers are free to include all firms and economic activities that are found to be relevant for the cluster. This does not usually result in the analysis of just one industry. There are even several examples of local clusters in which the combination of relevant industries changes with time (such examples are described in Lissoni & Pagani 2003 and Tappi 2002). Definition 2 characterises local industrial clusters by the fact that they emerge as a result of local self-augmenting processes. Such processes do not occur among all kinds of firms. Only firms with a specific relationship might interact in a self-augmenting manner, such that local industrial clusters might emerge. Examples of such a relationship are the use of the same technologies, spillovers or buyer-supplier relations. Therefore, an adequate classification of industries with respect to local industrial clusters would be one according to which all firms that show a sufficient number of these interactions among one another would belong to the same industry. This implies that an adequate classification of industries can only be found if the self-augmenting processes that lead to local industrial clusters are comprehensively understood. These interactions are studied in detail in Section 2.3.1. Similar arguments hold for a definition of regions. If local self-augmenting processes cause the co-location of firms and the emergence of local clusters, the effects of these processes have to be somehow spatially bounded. Spillovers, for example, have been found to be significantly effective only within a range of 50 km (see Anselin, Varga & Acs 1997). Many other interactions between firms are similarly bounded. An adequate definition of regions in the context of local industrial clusters has to be based on these ranges of the local self-augmenting processes. Each type of mechanism behind these processes might have a different range and a different spatial structure. Thus, a final definition of regions is only feasible if the respective mechanisms have been studied in more detail, which is done in Section 2.3.1. Relationship to other concepts of local systems Although most regions that are identified in the literature as industrial districts or clusters satisfy the above definition of local industrial clusters, a fundamental difference exists between these concepts and the concept used here. The definition of industrial districts and clusters is based on the characteristics of local systems. However, Definition 2 is

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based on the causes for the existence of the respective local systems. It is assumed here that these mechanisms are, on an abstract level, the unifying aspect of those local systems that are called, for example, industrial districts or clusters. The characteristics of various existing local industrial clusters have been found to be very different. Besides this fundamental difference, the concept of local industrial clusters is more general than the concepts of industrial districts and regional clusters. Industrial districts and regional clusters, both also require the prevalence of a sectoral or industrial agglomeration. However, they are more demanding with respect to the local selfaugmenting processes. In this sense, they are subclasses of local industrial clusters. Innovative milieux, in contrast, do not require the prevalence of a industrial agglomeration. Instead of a relative high number of firms or employees, this concept focuses on the high number of innovations. Usually, but not necessarily, a high number of innovations implies a high number of firms and employees. Furthermore, the definition of innovative milieux requires strong synergies between firms. This is quite similar to the argument that there must be local self-augmenting processes that might be caused by economies of location. In this respect, the concepts of innovative milieux and local industrial clusters match quite well. However, there are local industrial clusters that are not based on a high innovativeness and there might be innovative regions without an industrial agglomeration. The latter implies that the concept of innovative milieux is not a subclass of local industrial clusters. Nevertheless, the relationship between these two concepts seems to be quite strong. To sum up, the concept of local industrial clusters mixes some of the conditions defined for other concepts in the literature. It is more general than these concepts and mainly subsumes them. It deviates from other concepts by focusing more on the causes for the existence of these local systems than on their characteristics once they exist. Local industrial clusters are furthermore defined on an abstract level, avoiding a definition of the underlying mechanisms. This book will show that, from such a general approach, predictions can be deduced that can be tested on a general level empirically. Without specifying the underlying mechanisms it is possible to identify the local industrial clusters that exist in Germany. This means that it is possible to develop a unifying theory of local clustering and apply this empirically, which is one of the major aims of this book. Excluded local systems It has been argued above that most of the local systems that are discussed in the recent literature are included in the concept of local industrial clusters. Nevertheless, not all local systems are local industrial clusters. It might sharpen the understanding of the concept proposed here to discuss those local systems that are excluded by Definition 2. Regions where not much economic activity is observed are usually neglected in the literature. They are also excluded by the definition of local industrial clusters. Nevertheless, an analysis of these systems could contribute significantly to the understanding of local industrial clusters. Studies on such backward regions can rarely be found in the literature (see Seri 2003 for an exception). The theoretical approach that is developed here will include these regions. According to this theoretical approach, there will emerge regions with a high economic activity as well as regions with no significant economic activity in the considered industry whenever the local self-augmenting

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processes are sufficiently strong. Hence, the theory that is developed here explains the different developments in different regions, instead of only focusing on the characteristics and developments in successful regions. Many of the science or technology parks that have been frequently discussed in the recent literature (see, for example, Garnsey 1998 and Quéré 2002) are excluded. These parks are usually supported by the government to attract firms to a certain area. Some of them focus on a certain industry, but many are not restricted to particular industries. If they develop only because they are supported by policy makers, they are excluded by the above definition. However, often the governmental action works as a trigger for further development in which the parks become more focused on a few industries and location economies occur (an example of this is described in Quéré 2002). In such a case they become a local industrial cluster. Hence, science parks might sometimes function as a breeding ground for local industrial clusters, but they are not a subclass of them. Local networks have been increasingly discussed in the literature in recent years (see, e.g., Camagni 1991b, Storper 1992, Camagni 1993, Malmberg 1996 and Walker, Kogut & Shan 1997). They are discussed in this literature as a phenomenon on their own. Under the definition of a local industrial cluster developed here, they are neither explicitly excluded nor explicitly included. Whether they play a role in the context of local industrial clusters depends on the answer to the question of whether they are able to cause local self-augmenting processes. This answer has not been given in the literature so far. Therefore, it is not possible to state whether all local networks constitute a local industrial cluster. At least, it can be stated that there is no obvious reason for a dependence in the opposite direction. In case studies no evidence is found that networks automatically develop in all local industrial clusters. Hence, the relation between local networks and local industrial clusters is somewhat unclear. The case of hub-and-spoke districts (see Markusen 1996 for a definition of this kind of local system) is somewhat more complicated. These districts are dominated by one or a few large firms. Other firms are attracted to the region mainly because they supply these large firms. Let us assume that there is only one large firm, which was located in the region first. The fact that this firm is located in this region is, therefore, a random event, influenced by the circumstances in the region, but not by other firms. If all other smaller firms move there because they are suppliers to this firm, the industrial agglomeration emerges as a result of the advantages of being located near one’s own customers. Hence, such a local system is not a local industrial cluster. However, there might be several large firms that interact with each other in the region or the large firm might have located there because some smaller firms were already there. Furthermore, the situation described above with one large firm and plenty of suppliers might trigger further developments that attract other firms to the region which do not supply the large firm. In all these cases the conditions for a local industrial cluster are satisfied if the respective effects are sufficiently strong. This indicates how difficult it might be to distinguish local industrial clusters from other similar local systems. The situation is further complicated by the fact that Definition 2 contains requirements that apply to the causes of the existence of local industrial clusters. As a consequence, they cannot be identified according to their actual characteristics only. It is possible to deduce some predictions about the characteristics of existing local industrial clusters. These predictions contain necessary conditions that can be used to identify existing local

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industrial clusters. However, all sufficient conditions refer to the causes of the emergence of industrial agglomeration. Therefore, historical knowledge is necessary for a final identification of local industrial clusters. This will be discussed in detail in Chapter 3. 2.2 ABSTRACT THEORY The definition of local industrial clusters is based on the mechanisms that cause their emergence and existence. Specific requirements for these mechanisms are defined and based upon these, a mathematical model is formulated. The modelling is restricted to these basic mechanisms in order to obtain a general model. Such a model offers several opportunities. First, it describes the evolution of all local systems that satisfy Definition 2. Thus, on an abstract level a description of such systems and their dynamics can be found. On the basis of the model the common features of these systems can be identified. These features can be used in an empirical approach (Chapter 3) to identify the industries that show clustering and the existing local industrial clusters. Second, different phases of the evolution of local industrial clusters and their characteristics can be identified. Statements about the dynamics and the kinds of mechanisms that occur at different times can be deduced. Third, for each phase, characteristics of the mechanisms that are active can be identified. This allows the different mechanisms discussed in the literature to be assigned to different phases and different developments in the context of the evolution of local industrial clusters. As a consequence, the findings in the literature can be structured and the mechanisms can be discussed with respect to their complementarity and substitutability. Hence, the theoretical model and its analysis has two main aims: it provides the basis for a general empirical approach on Germany, which is conducted in Chapter 3, and it provides a tool to structure the findings in the literature, which is also the basis for the simulation model developed in Chapter 4. To this end, the mechanisms and processes involved in the evolution of local industrial clusters will be modelled on an abstract level, similar to the approaches in the New Economic Geography (see, e.g., Krugman 1991 and Allen 1997). Besides its restriction to the fundamental characteristics of the mechanisms involved, the approach proposed here is clearly distinguished from the approaches in the New Economic Geography. These approaches model the spatial distribution of economic activity. Here only one region is explicitly considered (a similar approach is taken in Maggioni 2002, Ch. 4). All other regions are implicitly considered in the form of external circumstances. The aim is to understand the evolution of one local industrial cluster and the abstract characteristics that are necessary for the existence and emergence of such a local system. 2.2.1 Basic considerations Implications of the definition of LICs The definition of local industrial clusters contains two aspects. First, the existence of a local industrial cluster implies the existence of an industrial agglomeration. In Definition 1, an industrial agglomeration was defined as having a relatively high number of firms in

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a specific industry. Therefore, the first variable in the theoretical model is defined as the number of firms belonging to one industry in the region under consideration, and is denoted by ƒ and called the firm population. Second, the existence of industrial agglomeration might be caused by different factors. Definition 2 restricts the name ‘local industrial clusters’ to those industrial agglomerations that are caused by one specific kind of factor: it requires the involvement of local self-augmenting processes. Above, four different causes for industrial agglomerations are listed: natural resources, necessity to locate near to customers, statistical reasons and local self-augmenting processes. These four causes can be classified into two groups. The first three causes are exogenous to the firm population ƒ, meaning that the firms that constitute the industrial agglomeration do not influence the causes of this agglomeration. The fourth cause originates within the local dynamics, meaning that the firms that constitute the industrial agglomeration also cause directly or indirectly its existence. This distinction is crucial for the model that is developed here. Therefore, it is important to clarify which circumstances are exogenous and which circumstances are endogenous. The firm population, meaning the firms in the region under consideration belonging to the studied industry, is at the centre of the perspective taken here. Anything that is not systematically and significantly influenced by this firm population is called exogenous. ‘Systematically’ means that an increase or decrease in the firm population has to have, on average, a specific effect on the circumstances. If there is one or a few historical cases in which a firm influences a specific circumstance but in all other cases not, this circumstance is called exogenous. There has to be a general link between the firm population and a circumstance to call the circumstance endogenous. ‘Significantly’ means that the impact of the firm population has to be clearly identifiable, usually by a statistical approach. There are two kinds of exogenous factors: those which refer to the local conditions and those which refer to the global conditions. Examples of the former are the availability of natural resources or the proximity to customers. The most important factor of the latter kind is the size of the demand market. Marketing and other influences on the demand that firms might have are excluded here for simplicity. Other global or national exogenous factors are, for example, the legal system and global institutions. Summing up, for all conditions that are exogenous to a firm population ƒ, a variable e can be defined that characterises the state of these conditions. Although these conditions are not influenced by the state of the firm population, they have an impact on the firms. Hence, the firm population changes according to two processes: the dynamics within the firm population and the reaction to changes in the exogenous conditions. Most of the exogenous conditions, such as the availability of natural resources and the legal system, change slowly. Therefore, it is assumed in the following that the exogenous conditions change more slowly than the endogenous conditions and the firm population itself. As a consequence, the analysis of the endogenous processes and the dynamics caused by exogenous change can be separated. First, the exogenous conditions are assumed to be constant and the endogenous dynamics are studied. Then, the impact of exogenous changes is examined (see Section 2.3.1). The endogenous dynamics are examined in this section. Hence, the exogenous conditions, e, are assumed to be constant here. They are assumed to be measured on a

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scale that increases if the exogenous conditions are more favourable for the firms under consideration. This means that the higher the value of e, the higher is the number of firms that is expected to exist. As noted above, the exogenous conditions result from the local circumstances that are not influenced by the firm population—which will be called attractiveness of the location here—and the global situation. Let us neglect for a moment all endogenous influences and dynamics. Then, the exogenous conditions would determine the size of the firm population ƒ. The resulting firm population is denoted by . It is called the ‘natural’ firm population because it represents the firm population that is expected to exist without any local self-augmenting processes. It differs between regions. Now, the local dynamics have to be modelled. The basic assumption is that there are local self-augmenting processes. These might result from various processes. First, there might exist direct contacts between firms. These might take the form of cooperation between firms, local information flows, joint use of facilities or the provision of venture capital by established firms. In addition, there might be local externalities from which firms benefit. Two kinds of such externalities are distinguished here: local externalities in the form of industry-specific local conditions and local externalities in the form of the existence of other firms that provide certain services for the industry. Therefore, the second form of self-augmenting process within the firm population, ƒ, is the creation of advantageous local conditions, for example, in the form of the accumulation of human capital in the region, the development of an industry-specific infrastructure or supportive public opinion. The third form is the stimulation of the establishment of other firms in the region that provide the firm population, ƒ, with industry-specific services, products or demand. This last self-augmenting process leads to a co-evolution of two populations of firms. Variables and interaction These three different forms of self-augmenting processes within the firm population, ƒ, require different variables to be included in the model. Each process might be modelled separately. However, in reality they might appear simultaneously, hence, a general model is developed here that contains all three forms. For this purpose, the effects of each of them has to be formulated in the form of an increase or decrease in ƒ. Direct contacts, such as cooperation, information flows and joint activities, between firms in the same location become more likely the more firms are co-located. Firms benefit from such direct contacts and are more likely to grow and less likely to fail if there are more firms in the same industry located in the same region. In addition, firms often provide venture capital or advise on start-ups in the same region and industry. There are also negative effects of a high concentration of firms of one industry in a region: If the firms serve a local market, competition becomes more fierce if more firms co-locate. These negative effects might outweigh the benefits of co-location. In such a case, there are no local self-augmenting processes. In the model that is set up below large populations, ƒ, are assumed to have a positive effect on the further development of ƒ. A negative impact can be easily modelled by turning the respective parameters negative. The second form of local self-augmenting processes is based on the assumption that firms create local externalities in their locality. The size of the firm population, ƒ, in a

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region influences the development of specific conditions in this region, such as industryspecific human capital, infrastructure or public support. These local conditions, in turn, have a positive impact on the firm population. A second local variable is necessary to capture these conditions. This variable is denoted by c here and describes, in an abstract way, all local conditions that have an influence on the firm population. The higher c is, the more support there is for ƒ to increase, while at the same time the value of ƒ determines the dynamics of c. Finally, firms demand certain services and products. The suppliers of such services and products often appear in the same location once one or several firms that demand these things are located there. Thus, firms

Figure 2.1 Structure of the interactions between the variables of the model. induce positive dynamics on the populations of service and supplier firms. To keep the model simple, service and supplier firms are not separated here and only one further population of firms, the service and supplier firms, is introduced. The size of the second firm population is denoted by s. The dynamics of this population, s, are positively influenced by the size of the firm population, ƒ, while the size of population, s, also positively influences ƒ. Two situations have to be distinguished with respect to the firm population, s. First, the firms of this population might only provide goods or services for the firm population, ƒ. In this case the size of s is mainly determined by the size of ƒ (a depiction of this situation is given in Figure 2.1). Second, the firm population, s, might supply a global market that is independent of firm population ƒ. This implies that for the firm population, s, dynamics similar to those modelled for the firm population, ƒ, have to be considered. Such a co-evolution of two firm populations is omitted here in order to keep the model tractable.

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22

The three mechanisms that have been discussed above differ between industries with respect to their relevance and impact. Nevertheless, in a general model all three have to be included. Parameters will determine their strength in the model below, so that the implications can be studied conditional upon the respective strengths. 2.2.2 Mathematical modelling The model depicted in Figure 2.1 contains four variables: ƒ IR+, e IR+, s IR+ and c IR+. However, these four variables are not treated identically. It has been argued above that e changes slowly. Therefore, e is assumed to be constant here and represents a parameter in the first analysis. Later the impact of changing exogenous conditions is discussed. The structural relations between the variables ƒ, e, s and c are described above. Figure 2.1 reveals that the interactions between the variables ƒ and c and between the variables ƒ and s can be characterised as being mutually supportive. In biology, such a process is well known and is called symbiosis, which describes the interaction between two species that rely on the coexistence of each other and which mutually benefit from populating the same habitat. Mathematical models for such symbiotic interactions between species can be found in the biological literature (see, e.g. Murray 1993, p. 83–84). These models could be used as a basis for a model of the local interactions of firms (a discussion of similarities and differences can be found in Brenner 2001a). However, the model applied here is set up on the basis of economic considerations only. To this end, the dynamics of the variables ƒ, c and s are discussed successively. Dynamics of the firm population Excluding the direct and indirect interactions between the firms in a region, the size of the firm population, ƒ, would be determined by the exogenous conditions, e, such as the market situation, the natural resources and the proximity of customers. The natural firm population, , which characterises the expected state of the firm population determined by the exogenous conditions, has been defined above. Excluding all endogenous dynamics, it is assumed that the firm population, ƒ, converges towards from any starting point. However, even if no endogenous dynamics exist, such a convergence is not necessarily given. The assumption of such a convergence is far from natural. Nevertheless, this assumption is used throughout this chapter and therefore deserves some discussion. In reality, path dependence occurs. Several factors reduce the ability of the system to react to changes in exogenous conditions. Examples are the immobility of factory sites, the resistance of people to changes and entry barriers. Thus, if the exogenous conditions, e, change, the firm population, ƒ, might not be able to adapt to the new value of . This argument will be taken up again in Section 2.3. In the model used here, however, these conditions are excluded in order to keep the model as simple as possible. This section aims only to show the most fundamental processes involved in the

Theoretical approach

23

emergence and existence of local industrial clusters. Hence, a dynamic trend towards the natural firm population is assumed to be always given. Mathematically these dynamics are formulated by (2.1) where aeƒ determines the speed of the convergence process. A linear dependency is chosen here for simplicity, without restricting generality, because the mathematical form of one interrelation between the variables can be chosen quite arbitrarily. Nevertheless, a linear dependency can be supported by the following argument. If the number of firms adapts according to exit and entry processes, assuming that the success of firms is proportional to , a linear dependency results. The other interrelations have to and will be formulated in a more general way. In a next step, all variables that have a positive impact on the development of the firm population, ƒ(t), are added to the right-hand side of Equation (2.1) in the form of a general exponential function with two parameters, one defining the strength of the impact and one defining the exponent and therefore the shape of the impact. The variables that have such a positive impact are, according to Figure 2.1, the size of the firm population, ƒ(t), itself, the local conditions, c(t), and the population of service firms and suppliers, s(t). The respective parameters for the strengths of these impacts are aƒƒ, acƒ and asƒ and the respective exponents are aƒƒ, αcƒ and αsƒ. In addition, the firm population, ƒ(t), cannot increase unboundedly. The more firms that there are located within a region the more competition there is for space and employees. This will have a negative impact on the further development of the firm population, ƒ(t). Thus, a negative term has to be added on the right-hand side of Equation (2.1). This negative impact is modelled in the same way the positive impacts have been modelled, except with the negative sign. Hence, again a parameter is defined that characterises the strength of this impact and a parameter ρƒ is defined that determines the shape of the impact. It is obvious that this negative impact is only relevant for a large firm population, ƒ(t). For smaller populations the above impacts should dominate. Mathematically, this implies that the exponent, ρƒ, is larger than the exponents, Ⴣ, αcƒ and αsƒ. Including all these impacts, the dynamics of the firm population, ƒ(t), are described as (2.2)

Dynamics of the local conditions The modelling of the dynamics of the local conditions c(t) is done in analogy to the modelling of the dynamics of ƒ(t). The only variable that has a positive impact on the dynamics of c(t) is the size of the firm population, ƒ(t). The respective parameters are denoted by aƒc and αƒc. Furthermore, it is assumed that the development of favourable local conditions is also restricted by negative feedback. There are different causes of such

Local industrial cluster

24

a restriction for the different factors included in the local conditions. Let us consider, for example, the available human capital in a region. The limited number of people in a region restricts the increase in human capital. In the case of local policy, support for the firm population is restricted by the potential measures that can be applied and by budget restrictions. Similar arguments hold for the other aspects of the local conditions. The resulting negative feedback is modelled in the same way as it was done for the firm population, ƒ(t), and the respective parameters are denoted by and ρc. According to the same arguments that have been put forward above ρc>αƒc holds. The dynamics of the local conditions are then given by (2.3)

Dynamics of the population of service firms and suppliers Again the same kind of modelling is chosen. The population, s(t), is influenced by the firm population, ƒ(t), in the same way as ƒ(t) influences c(t). Therefore, the same mathematical formulation can be used, denoting the parameters by aƒs and αƒs. The development of s(t) is restricted in the same way as the development of ƒ(t). The respective parameters are denoted by and ρs. Again ρs>αƒs holds. The dynamics of the population of service firms and suppliers s(t) are given by (2.4)

2.2.3 Analysis of the model Equations (2.2), (2.3) and (2.4) describe the dynamics of the local system on an abstract level. They will be analysed mathematically in the following. The aim of this analysis is to deduce some general statements about the dynamics of local systems that are influenced by local self-augmenting processes. The model allows the following issues that arise in the context of the emergence and evolution of local industrial clusters to be addressed: • the basic characteristics of local systems that are described by the above model, • the influence of the different local mechanisms, such as the interaction among firms, the interaction with local conditions and the interaction with service and supplier firms, • the conditions that have to be satisfied by the local interactions between firms with respect to the existence of local industrial cluster, and • the possible developments of the kinds of local systems described above, including the evolution of local industrial clusters. The results of this analysis are used in the following sections to structure the findings in the literature about local industrial clusters. Furthermore, predictions of the model are tested empirically and used for the identification of local industrial clusters in Germany in Chapter 3.

Theoretical approach

25

Basic characteristics Before the analysis turns to the factors that are of specific interest in the context of this book, some general issues are examined that turn out to be helpful in the analysis below. For a first characterisation of the dynamics given by mathematical equations it is adequate to calculate the stationary states of the system and their stability. These are given for the above model by LEMMA 1: Let ρƒ>aƒƒ, ρƒ·ρc>αƒc·αcƒ and ρƒ·ρs>αƒs·αsƒ. Then, the local system, described by Equations (2.2), (2.3) and (2.4) has either one or three stationary states within the range given by ƒ(t)>0, c(t)>0 and s(t)>0. In the first case this stationary state is stable, while if there are three stationary states, two of them are stable and one is unstable and located between the other two states with respect to each variable. The system converges to one of the stable states. The proof of Lemma 1 is given in the appendix. According to Lemma 1, the local system shows a bifurcation, a typical characteristic of self-organisation. Due to changes in the parameters or the exogenous conditions, the system may switch between two structural states: one that is characterised by only one stable stationary state and one that is characterised by two stable states. These two structural states deserve further discussion. It should be remembered that the mathematical model describes the dynamics within a region. The parameters of the model vary between regions. If there is only one stable state, the local system converges to this state. If the regions only vary to a small extent and the parameters are such that for all of them only one stable state exists, then every local system converges into a clearly defined stable state. There might be slight differences in the values of , č and š that characterise the stable state in each of the regions. Nevertheless, the resulting global situation is characterised by a more or less uniform spatial distribution of firms in the industry being considered. No local industrial clusters occur in this case. If, instead, the dynamics of a local system are characterised by two stable states, the system might converge into a state that is characterised by a large population of firms or into a state that is characterised by a small population of firms (see Figure 2.2 for a visualisation of such a situation). Again it might be assumed that all regions are similar with respect to their parameters. However, in the case of two stable states, regions with the same characteristics might contain different sizes of firm populations. Each local system converges to one of the two stable states. The local systems that converge to the stable state with a large population of firms are called local industrial clusters (see Definition 2). Furthermore, a situation might occur in which two stable states exist for some local systems while only one stable state exists for others. While the latter local systems converge to the only stable state with an average firm population, the former local systems converge either to a state with a large firm population or to a state with a small firm population. The local systems with a large population of firms are again called local industrial clusters.

Local industrial cluster

26

It has been stated above that the parameters of the model also depend on the industry and the region under consideration. Differences between regions are included in the above discussion. Hence, which of the three possible situations occurs depends on the industry. This means that there are industries in which no local clusters exist, industries in which local clusters might emerge in a particular set of regions, and industries in which local clusters might emerge in any region. In the latter two cases, regions exist in which clusters might emerge. Whether they emerge is determined by the history of the region. The development in these regions is path-dependent and not completely determined by the exogenous conditions. History matters for these regions and the respective industries. Influence of different local mechanisms To understand the factors that influence the existence of local industrial clusters further, the implications of the local mechanisms are studied. Three different mechanisms are included in the model. All three mechanisms describe symbiotic interactions. However, one describes symbiotic interactions within the population of firms, one between the population of firms and the local conditions, and one between two firm populations. Nevertheless, it can be shown that they have the same impact on the dynamics of the local system. LEMMA 2: Let us call the number, stability, and location of the stationary states of the dynamics given by Equations (2.2), (2.3) and (2.4) the structure of the local system. Then, the structure of the local system is influenced by the symbiotic interaction within the firm population, by the symbiotic interaction between firms and the local conditions and by the symbiotic interaction between firms of the populations ƒ(t) and s(t) in an identical way. This means that for each combination of aƒƒ and aƒƒ, values for the parameters acƒ, aƒc, αcƒ and αƒc and for the parameters asƒ, aƒs, αsƒ and αƒs, respectively, can be found such that all three mechanisms have exactly the same implications for the structure of the local system. The proof of Lemma 2 is given in the appendix. Lemma 2 implies that the modelling might be restricted to the inclusion of only one of the three symbiotic mechanisms without neglecting any possible structural characteristic of the stationary states of the system. Thus, the local conditions, c(t), and the firm population, s(t), will be ignored mathematically in the following analysis. All statements about the symbiotic interaction within the firm population, ƒ(t), that are deduced from this analysis can be transferred to the symbiotic interaction between firms and the local conditions or to the symbiotic interaction between the two firm populations, ƒ(t) and s(t). This implies that quite different local mechanisms might lead to the emergence of local industrial clusters. The three fundamental kinds of self-augmenting processes that are considered here are not simultaneously necessary for the existence of local industrial clusters. They represent substitutes and not complementarity. This holds if the local system converges to its stable state and stochastic processes play a minor role.

Theoretical approach

27

Conditions for the existence of local industrial clusters Now the analysis will turn to the impact of the local self-augmenting processes on the existence of local industrial clusters. This analysis will be restricted to the symbiotic interactions within the firm population, ƒ(t). The dynamics are given by Equation (2.2) without the terms depending on c(t) and s(t): (2.5) According to Lemma 2 the results can then be transferred to the other mechanisms. The analysis is based on the identification of the parameter sets for which the local system has two stable states. The parameters can be classified into two groups. The parameters aƒƒ and ρƒ describe the structural characteristics of the mechanisms. aƒƒ and describe their strengths. It seems adequate to assume that the structure of the mechanisms is much more stable than their strength. Therefore, the influence of the parameters, aƒƒ and ρƒ, on the number of stable states of the system is studied first. LEMMA 3: Let ρƒ>aƒƒ and ρƒ>1. Then, the local system has only one stable state if Ⴣ ≤ 1. The proof of Lemma 3 is given in the appendix. The stable state of ƒ does not, in general, equal zero but is small compared to the higher stable state in the case of two such states (see, e.g., Figure 2.2). Remark: Lemma 3 states that the power, Ⴣ, of the symbiotic interactions within the firm population, ƒ(t), has to be greater than one in order for two stable states to exist. A power greater than one means that the impact of the particular mechanism is comparably small as long as the conditions for this mechanism are less favourable but becomes comparably large if the mechanism becomes more active. An example of such a mechanism is the symbiotic relation between the population of firms and local public opinion. People tend not to recognise industries in which only a small number of people are employed. Thus, if the population of firms in an industry is small, these firms are barely recognised by local people. Even if the population of these firms increases, recognition does not change much as long as the firm population is below a certain level. However, once the firm population has exceeded a certain level, recognition increases rapidly. This causes increased pressure on politicians to support the industry, a higher willingness of the people to invest in industry-specific skills, and probably also a higher number of start-ups in this industry. Hence, this mechanism is quite sluggish in its reaction to small increases in ƒ(t) but reacts relatively more strongly to large increases in ƒ(t). Its effect does not depend linearly on ƒ(t) but in a way that can be represented mathematically by with Ⴣ>1. According to Lemma 3, such a symbiotic mechanism is necessary for the local system to have two stable states. Symbiotic interactions that do not have such a structure do not support the existence of local industrial clusters.

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According to Lemma 2, a result similar to the one described in Lemma 3 can be obtained for the other two symbiotic interactions. In the case of symbiotic interactions between the firm population, ƒ(t), and the local conditions, c(t), ≤1 implies the existence of only one stable state. In the case of symbiotic interactions between the firm populations, ƒ(t) and s(t), ≤1. However, if all three mechanisms are active at the same time, the existence of local industrial clusters can only be excluded if all three conditions, namely Ⴣ≤1, argument results in Theorem 1.

≤1 and

≤1 are satisfied. Reformulating the

THEOREM 1: Let ρƒ>aƒƒ, ρƒ·ρc>αƒc·αcƒ and ρƒ·ρs>αƒs·αsƒ. Then, two stable states can only exist if at least one of the three local mechanisms is selfaugmenting, meaning that either aƒƒ>1, satisfied.

>1 or

>1 is

Theorem 1 follows from Lemmas 2 and 3. It states a first condition for the existence of local industrial clusters: at least one local symbiotic interaction has to exist that is more sluggish in its effect at the beginning but stronger for higher values of ƒ(t) than a linear effect. It can be provided either by the symbiotic interactions within the firm population, by the interactions between the firms and the local conditions or the interactions between firms of the populations, ƒ(t) and s(t). Now the analysis can be focused on the second group of parameters: the strengths of the mechanisms, which are given by aƒƒ, aeƒ, acƒ, aƒc, asƒ, aƒs, and . Again, the aim is to identify those parameters for which two stable states exist. A rigorous mathematical analysis is not feasible in this context. However, some structural results can be obtained. To this end, it is assumed that each of the three kinds of symbiotic interactions—the interactions within the firm population, ƒ(t), the interactions between the firms and the local conditions, and the interactions between the two firm populations, ƒ(t) and s(t)—either satisfies the conditions in Theorem 1 or has no impact on the local dynamics. In the latter case the respective parameter, aƒƒ, acƒ or asƒ equals zero. The following result is obtained. < ρƒ and 1 < <ρƒ. THEOREM 2: Let 1<Ⴣ<ρƒ, 1< Then, a combined parameter, a, can be defined that monotonically increases with aƒƒ acƒ and asƒ If and only if this combined parameter, a, is sufficiently high, is there a range [e1, e2] for the exogenous conditions, e, for which the local system described by Equations (2.2), (2.3) and (2.4) has two stable and one unstable

Theoretical approach

stationary states for ij0. For all e state exists.

29

[e1, e2] only one stable stationary

The proof of Theorem 2 is given in the appendix and the implications are depicted in Figure 2.2. According to the discussion above, the structure of the system described by the parameters aƒƒ, αƒc, αƒs, αcƒ, asƒ, ρƒ, ρc and ρs is much more stable than the strengths of the different mechanisms described by the parameters aƒƒ, aƒc, aƒs, acƒ, asƒ, and . Therefore Theorem 2 starts with the assumption that the structure of the system allows for the existence of local industrial clusters. Given this condition, it implies conditions for the other parameters. First, it states the necessary condition for the existence of two stable states with respect to the strengths of the mechanisms. The result is that the combination of the selfaugmenting processes has to be sufficiently strong. This means that, adding up the strengths of the different symbiotic interactions, a critical strength exists such that, below that strength no clustering occurs while above this strength clustering might occur. More precise results can only be obtained if the structural parameters are fixed (see Brenner 2001a for such an analysis). In a second step, it is assumed that the strengths of the mechanisms are such that clustering is possible, which allows the impact of the most volatile parameter, the exogenous conditions, e, to be examined. Theorem 2 states that there is a certain range of e for which the dynamics (2.2), (2.3) and (2.4) possess two stable and one unstable stationary states. Let us denote the stable states by state by

. According to the proof of Theorem 2,

and and

and the unstable stationary can be defined such that

holds. Let the range be defined by [e1, e2]. Then, the proof of Theorem 2 implies that for e=e1 and for e=e2. This means that for values of e below the range [e1, e2] the stable state with the larger firm population disappears, while for values of e above this range the stable state with the smaller firm population disappears. For all cases in which the structure of the system and the strengths of the mechanisms are such that clustering might occur, the dependence of the stationary states on the exogenous conditions e has the form that is depicted in Figure 2.2. This implies that the local economic activity shows hysteresis if the exogenous conditions e vary with time. To analyse the impact of such a variation, we write e(t), to make clear that the exogenous conditions are now regarded as a time-dependent variable. For small values of e(t), the firm population, ƒ(t), converges to a low level. An increase in e(t) only slightly increases the firm population. Only if e(t) passes e2, does the state of the local system change tremendously. It converges to the stable state with the larger firm population. A later decrease in e(t) decreases the economic activity only gradually until another threshold, e1, is reached. If e(t) decreases below this threshold, the local system switches back to the original dependence on e.

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2.3 EVOLUTION OF LOCAL INDUSTRIAL CLUSTERS Although the evolution of local industrial clusters is not a main topic here, some understanding of the successive developments is necessary to address the main questions, especially the questions of when and where local indus-

Figure 2.2 Stable (solid lines) and unstable (dashed line) stationary states dependent on the exogenous conditions, e, for aƒƒ=1, aeƒ=132, acƒ=0, asƒ=0, Ⴣ=2, ρƒ=4.

=0.00001,

trial clusters emerge. In many case studies the evolution of the local system is comprehensively described. However, a general theoretical approach can rarely be found in the literature (exceptions can, e.g., be found in Maggioni 2002 and Wolter 2003). The model above provides a good basis for developing a theory of the evolution of local industrial clusters. In the context of this book there are three reasons for adopting such a model. First, different stages in the evolution of local industrial clusters can be identified. In each of these stages different mechanisms and processes matter. Knowledge about these mechanisms allows the various influences to be structured according to the time at which they are relevant and according to the processes they cause. As a consequence, the mechanisms that are discussed in the literature can be categorised as causing either the existence, the location, or the timing of the emergence of local industrial clusters. Such an understanding is important for designing adequate policy programs.

Theoretical approach

31

Second, the different stages are characterised by different dynamics within the regions. The respective dynamics are identified here. Knowledge about these dynamics allows the stage of a local industrial cluster to be identified empirically, which is done in Section 3.3. Third, knowledge about the emergence of local industrial clusters is of specific interest in this book. It relates to the questions of when and where such clusters emerge. Therefore, the conditions and circumstances that are necessary for or involved in the emergence of local industrial clusters have to be understood. The above theory provides a tool to classify conditions and to understand which of them are complementary and which of them are substitutable. Furthermore, the emergence of a local industrial cluster can be partitioned into several successive developments. This leads to a further understanding of the time structure of the processes involved. 2.3.1 Stages in the evolution of local industrial clusters In the analysis of the above model hysteresis has been identified. It has been shown that for certain values of the parameters two stable states exist and the situation in a region depends on its history. Furthermore, it has been shown that changes in the exogenous conditions can trigger switches between the two stable states. This can be used to explain the evolution of local industrial clusters and to identify several stages and the processes therein. The evolution of many of the local industrial clusters that are studied in the literature follows the developments of the respective industry. This does not hold for all cases. However, it seems to be a typical feature that is well captured by the theoretical model used here. Therefore, a situation in which the evolution of a local cluster is caused by the developments in the respective industry is studied here. Other possible causes for the emergence of local industrial clusters are discussed in Section 2.3.3. Industrial life cycle To study the evolution of a local industrial cluster that is purely determined by the developments in the respective industry, the developments in the industry have to be defined first. A usual industrial life cycle is assumed here. Such a life cycle is characterised by three phases (an overview about the industrial life cycle is given in Klepper 1997, a discussion in the context of local clusters can be found in Dybe & Kujath 2000). The initial phase is characterised by high uncertainty, a low market volume and a high number of entries. Competition is based mainly on product innovations in this phase. It is called the embryonic stage. The growth stage follows. In this phase the products become more stable. Process innovations become more important than product innovations. Demand increases quickly in this phase. Profits of firms are high. The number of entries is lower than in the first stage. Furthermore, shakeouts of firms occur. The third stage, the so-called mature stage, is characterised by a slow down of output growth. The situation stabilises. The numbers of entries and exits are low. Market shares stabilise and both product and process innovations become less important.

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From industrial development to cluster evolution With the help of the model developed in Section 2.2, the developments of the industry can now be transfered to the evolution of local industrial clusters. It is assumed that the parameters of the mathematical model are such that two stable states exist for a certain range [e1, e2], as depicted in Figure 2.2. This means that the conditions for the existence of local industrial clusters are given (these conditions will be discussed in detail in Section 2.4). For such a system, how the local system reacts to changes in the industry will now be discussed. One of the major factors included in the exogenous conditions, e(t), in the above model is the market situation. This contains mainly the total demand and the strength of competition on the global or, at least, interregional market. Therefore, the different stages of the industrial life cycle will be interpreted with respect to the developments in demand and competition. The implications of these developments for the local system are studied. At the beginning of the initial phase there is nearly no demand and the situation is quite unfavourable for firms. This implies a low value of the exogenous conditions, e(t): e(t)<e1. For such a situation only one stable state, exists, which is characterised by a small firm population (see Figure 2.2), hence, no cluster exists in the region and industry under consideration. This is the starting point of the evolution that we are concerned with. The growth stage of the industrial life cycle comes with a strong increase in the demand for the products of the industry. This implies an increase of the external conditions, e(t). As long as they remain below e2 (see Process 1 in Figure 2.3), their increase causes only small changes in the firm population, although a second stable state might exist. If the changes in the exogenous conditions are slow compared to the adaptation of the local system, the system develops along the lower solid line in Figure 2.3. Hence, a first critical point in the development of a local industrial cluster is identified. If the market situation does not increase sufficiently strongly, the exogenous conditions do not exceed the value e2 and no local industrial cluster emerges. The value e2 can be called a critical value or critical mass (for other uses of the critical mass in economics see, e.g., Witt 1997). The exceeding of the critical mass is called the first stage in the evolution of a local industrial cluster here. If the exogenous conditions exceed e2, the lower stable state disappears, so that only one stable state exists, which is characterised by a large firm population. The local system converges towards this state as long as the external conditions, e(t), remain above e2 local economic activity

Theoretical approach

33

Figure 2.3 Different changes in the exogenous conditions and the resulting dynamics of the local system (solid lines signify stable states of the system, dashed lines signify unstable states). (see Process 2 in Figure 2.3). The convergence is caused entirely by internal forces, the mechanisms that have been called self-augmenting processes above and are discussed in detail in Section 2.4. Since this convergence changes the situation within the region tremendously, it takes some time. Here, it is called the second stage in the evolution of a local industrial cluster. Within this stage the number of firms in the industry increases strongly in many regions. At some point in time the global firm population and therefore also the supply increases faster than the demand. As a consequence, competition becomes more fierce and finally leads to an increasing occurrence of shakeouts. Although the demand might still increase, the market situation becomes less favourable. The exogenous conditions, e(t), decrease. For the emergence of the local industrial cluster it is decisive how far the convergence process has taken the local system, meaning the speed of the adjustment matters. If the firm population is still quite small it might not be able to survive the increased competition. It might be below the unstable state (dotted line in Figure 2.3) so that a convergence towards the lower stable state results (see Process 3’ in Figure 2.3). If, instead, the firm population has become large enough, the convergence process towards the higher stable state is continued (see Process 3 in Figure 2.3). Hence, again a critical mass, this time in the form of a large firm population, has to be exceeded. Only if this critical mass is exceeded, will a local industrial cluster emerge.

Local industrial cluster

34

The third stage is characterised by a more or less stable firm population on a high level. This stage is entered once the convergence process towards the higher stable state (given e(t)>e2) has increased the firm population above the critical level. Then, the exogenous conditions, e(t), might decrease below e2 without hindering the further convergence towards the stable state with a large firm population. As long as e(t)>e1, all changes in the exogenous conditions cause only small changes in the firm population. Furthermore, all these changes are reversible. This corresponds to the phase of maturity in the industrial life cycle. The end of an industrial life cycle is characterised by a decrease in demand. There are two possible developments with respect to the local cluster: either the firms are able to enter new markets or they lose, at least, part of their market shares. The latter implies that e(t) decreases tremendously for these firm. If the exogenous conditions decrease below e1, the higher stable state disappears. This causes a convergence towards the lower stable state (see Process 4 in Figure 2.3). The local industrial cluster disappears (see, for example, the development reported in Isaksen 2003). 2.3.2 Dynamics within local industrial clusters In Section 3.3 the dynamics within regions are studied empirically. To analyse the results, we have to know how different dynamics can be interpreted. The above theory can be used to make predictions for the dynamics that should be expected in the different stages of the evolution of local industrial clusters. In the empirical study many different regions are analysed. Above it has been argued that the parameters of the model might differ between regions. This causes different values of the stable sizes of the firm population. However, Theorem 2 states that for a situation, in which two stable states exist, the dependence of the stationary states on the exogenous conditions always has the form depicted in Figure 2.2. Nevertheless, the location of the critical values, e1 and e2, as well as the size of the firm population that corresponds to the stationary states might differ between regions. Furthermore, the actual state of the firm population differs between regions because their histories differ. In order to make predictions for the dynamics within regions, the difference between regions is mainly ignored. It is assumed that most regions are at least similar to such an extent that the actual exogenous conditions fall within the same range, where the possible ranges are defined as e(t)<e1, e1<e(t)<e2 and e(t)>e2. In contrast, the actual size of the firm population is allowed to differ between regions without restriction. Given these assumptions, the dynamics expected in a region can be studied conditional upon the actual situation in the region. To this end, the four stages of the evolution of local industrial clusters are examined separately. First stage It has been argued above that in the first stage the critical value, e2, is exceeded. According to the assumption that the exogenous conditions fall into the same range for nearly all regions, e>e2 holds almost everywhere. e>e2 implies that the number of firms increases if it has not already reached or exceeded the value at the high stable state. It is

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unlikely that at the beginning of the first stage any region contains a large number of firms. Thus, the number of firms can be expected to increase in nearly all regions. Second stage In the second stage the exogenous conditions decrease so that e1<e(t)<e2 is satisfied. Again this is assumed to hold for nearly all regions. Figure 2.3 shows that the dynamics in such a case depend crucially on the actual situation in the region (see the Processes 3 and 3’). In regions where the number of firms is below the unstable stationary state, this number converges towards the lower stable state. If the number of firms is, instead, above the unstable state, it converges towards the higher stable state. Hence, there are two ranges of the number of firms for which this number increases. These are the range below the lower stable state and the range between the unstable and the higher stable state. If the number of firms is between the lower stable state and the unstable state or above the higher stable state, it can be expected to decrease. Third stage In the third stage the regions are assumed to have approximately reached the stable states. Small fluctuations might occur. After each disturbance the local systems can be expected to converge towards the stable states again. However, the location of the stable states differs between regions. Hence, it is not possible to predict the direction of development in a region on the basis of its actual state. All that can be said about the third stage is that only minor dynamics should occur. Fourth stage According to the discussion above, the exogenous conditions fall below e1 in the fourth stage. This implies that the size of the firm population converges to the lower, and only, stable state. Since the exogenous conditions had earlier been more favourable, the firm population can be expected to be above the stable state in most regions. Hence, the number of firms will decrease in most regions, except a few regions in which there are actually almost no firms belonging to the industry under consideration. 2.3.3 Inertia of clustering The theoretical model developed above is based, among others, on the assumption that the dynamics always converge to the stable state. This requires continual exit and entry of firms or continual movement of firms between regions. Movements of firms are rare, but exits and entries of firms occur in some industries continually. In many industries, however, they mainly occur at certain points in time. Considering the life cycle that is discussed above, entries mainly occur in the first two phases, while exits mainly occur in the second and the fourth phase (a discussion of entry and exit rates in different phases of the industrial life cycle is given in Fritsch 1996 for Germany). In the third phase, when an industry is called mature, little fluctuation occurs in the firm population. Hence, the

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assumptions used above are not given at all times and how the implications change if more realistic assumptions are made has to be discussed. Implications of inertia Let us consider an industry in a phase in which no exits and entries occur and no firms move between regions. This implies that the firm population stays the same. If any of the parameters of the model change in such a situation, the firm population does not adapt to this change. This might even hold for changes in the market conditions, although usually such changes cause either exits or entries of firms. It holds, however, for all changes of those parameters that determine the shape of the curve presented in Figure 2.2. For example, the strength and structure of the local self-augmenting processes might change without having an impact on the firm population. The self-augmenting processes might even disappear without influencing the firm population. The same holds for the attractiveness of the region. Hence, a situation might be reached in which, according to the above model, the local industrial cluster is no longer stable. Nevertheless, the cluster will be sustained as long as no exits or movements of firms occur. This holds especially if the industry under consideration is in its mature stage. The characteristics of an industry might have changed in such a stage compared to its initial stage. It might even be the case that clustering in the form described by the above model is not stable any more. Nevertheless, if no exits and entries occur, the local industrial clusters that have developed in earlier stages will remain. This means that local clusters might be very stable even if the conditions for their existence are not given any more. The conditions for the emergence of local industrial clusters have only to be satisfied at the beginning of the industrial life cycle. Eventually, a few entries and exits might occur. If their location is randomly chosen, the local industrial cluster will disappear very slowly. Implications for the conditions of clustering The arguments above imply that for some industries, only the characteristics at the beginning of the life cycle are decisive for the existence of local industrial clusters. This means that the conditions formulated for the local self-augmenting processes have to be satisfied only at the time at which the local clusters emerge. Hence, the existence of local industrial clusters does not imply that self-augmenting processes exist. It is sufficient that they have existed once. If they do not continue to exist, the local industrial clusters might nevertheless be sustained for a very long time and decay only very slowly. Thus, the theory above describes the situation at a time at which local industrial clusters emerge. It does not necessarily describe the situation during their existence equally well. 2.4 CONDITIONS FOR THE EXISTENCE OF LICS The major aim of this book is to answer the questions of why local industrial clusters exist and when and where they emerge. To what extent these questions can be answered

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on a general level is examined. Here, complementary and substitutable conditions for the existence and emergence of local industrial clusters are identified. The analysis above shows that different kinds of conditions have to be satisfied for the emergence of a local industrial cluster. Two kinds of conditions can be separated very clearly. On the one hand, two stable states have to exist. This means that the conditions formulated in Theorem 1 and Theorem 2 have to be satisfied. Only in such a case do the stable states of local systems have the form depicted in Figure 2.2. This is a necessary condition. On the other hand, there have to be processes that move the local system from the lower stable state to the higher stable state. This is a second necessary condition that has to be satisfied independently of the first one. The first condition determines whether local industrial clusters might emerge and is discussed in this section. The second condition determines when and where local industrial clusters emerge and is discussed in the next section. The first condition is formulated mathematically in Theorem 1 and Theorem 2. It is formulated in the form of requirements for the parameters of the model. It has been stated in Section 2.2 that the parameters of the model depend on the industry and on the region concerned. This means that for each industry the parameters vary between regions within certain ranges. As a consequence, there are three kinds of industries, those in which all regions satisfy the conditions, those in which some regions satisfy the conditions, and those in which no region satisfies the conditions. Hence, the discussion of industrial characteristics might be separated from the discussion of regional characteristics. However, before the industrial and regional characteristics are discussed, the processes and mechanisms that determine the parameters have to be identified. Thus, the real processes that are modelled in an abstract way in Section 2.2 have to be examined. This is done first. Then, the industrial, and finally the regional, characteristics are discussed. 2.4.1 Local mechanisms and processes The aim of this section is to identify those local mechanisms and local processes that might be responsible for the existence of local industrial clusters. The theoretical approach above has shown that local symbiotic mechanisms might cause the existence of local industrial clusters. However, these mechanisms have to satisfy the conditions formulated in Theorem 1 and Theorem 2. Including the assumptions that have been used to set up the model, three conditions result that have to be satisfied by those mechanisms. First, they have to imply a positive feedback loop either within the firm population under consideration or between this firm population and either another firm population or local conditions (this is assumed in the development of the model). Second, they have to be self-augmenting, meaning that the positive feedback increases more than linearly with the size of the firm population (Theorem 1). Third, they have to be sufficiently strong (Theorem 2). The first and the second conditions are necessary conditions that each mechanism has to satisfy separately (see Theorem 1). Hence, only mechanisms that satisfy these conditions have to be included in the following discussion. The third condition has to be satisfied by the combination of all mechanisms (see Theorem 2). Therefore, the mechanisms that satisfy the first and the second condition might substitute each other. The third condition only requires that the sum of these mechanisms has a sufficiently

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large impact on the economic development in a region. As a consequence, two separate questions have to be answered here. On the one hand, those local mechanisms that satisfy the first and the second condition have to be iden-tified. On the other hand, whether the combination of these mechanisms is sufficiently strong has to be examined. The first question is addressed here, while the second question is addressed in Section 2.4.2. To identify the local mechanisms that satisfy the first and the second condition, processes must exist that are related to the entry of firms in a region and industry or to the profitability of existing firms, so that their likelihood of exit decreases. All factors that positively influence the firm population and all local factors that profit from an increasing firm population have to be studied. An increase in the number of firms occurs through start-ups, the establishment of branches in the region and by the movements of firms from other regions into the region under consideration. Firms are more likely to survive if they have competitive advantages over other firms. The competitive advantage of a firm increases either because of successful innovations or because of a decrease in costs. Hence, the following analysis concentrates on four processes, namely; 1) start-ups, 2) movement of firms and the establishment of branches, 3) the increase in the competitive advantages as a result of innovations conducted by a firm, and 4) the decrease of costs. To obtain a self-augmenting process, there has to be a local factor that simultaneously causes one of these four processes and benefits from the increase in the local firm population. This mutual support has to increase with the size of both factors. In addition, these interactions have to have a clear local connotation, meaning that they either only occur locally or are much more intensive within a region than between regions. Finally, the local factor has to be one that changes on a time scale similar to the one on which the firm populations change. These three conditions will be checked here for all local factors that are repeatedly discussed in the literature on industrial districts and clusters. The result will be an identification of those mechanisms that satisfy the conditions formulated above and therefore might contribute to the existence of local industrial clusters. Interaction within the firm population In the theoretical model three kinds of local self-augmenting processes have been distinguished: the interaction within the firm population, the interaction between the firm population and another firm population, and the interaction between the firm population and local circumstances. The interactions within the firm population are discussed first. It is necessary to identify interactions between firms that increase the number of startups in the region, cause the movement of firms to the region, increase the innovativeness of existing firms or reduce their costs of production. With respect to start-ups two kinds of interactions play a role. First, existing firms in the region can act as incubators. In this case the spin-off firm is a direct result of the existence of the incubator firm. The number of start-ups can be assumed to increase linearly with the number of firms existing. Furthermore, there is empirical evidence for the fact that most spin-off firms are founded in the region in which the incubator firm is located (in Bramanti & Senn 1990 it is found that 56% of the firm locations can be explained by personal or historical causes, while in Pleschak 1995 it is found that 58% of the founders chose the location for personal reasons). Second, existing firms often assist

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start-up firms (for a detailed study of the help that existing firms provide for start-ups see Rickne 2000). This assistance is mainly given by local firms. Therefore, it might be claimed that the amount of assistance that start-ups can build upon increases with the number of respective firms already in the area, although there is no empirical evidence for this. There is no study of the shape of these dependencies given in the literature. Hence, it can only be stated here that the processes described constitute a positive feedback loop. Whether it is self-augmenting is an open question. In the literature four kinds of interactions among firms are put forward that increase the innovativeness of firms: information flows caused by informal contacts between employees of different firms, information flows implied by formal cooperation, information flows caused by the movement of employees from one firm to another and joint research projects. These processes are also often subsumed under the term, ‘spillover’, in the literature (for a theoretical discussion of the different explanations of spillovers see Camagni 1991b, Branstetter 1998 and Dalum, Holmen, Jacobsson, Praest, Rickne & Villumsen 1999). The movement of employees from one firm to another will be studied in detail under the heading of human capital. The other three kinds of interactions have a similar structure: Firms benefit from interaction with other firms. It seems to be adequate to assume that such mutually beneficial interactions are more likely the more other firms that there are in the locality. In empirical studies the different kinds of spillovers are difficult to separate. However, all different approaches show a clear and locally bounded impact on the existence of firms and/or the amount of research conducted by firms on the innovativeness of other firms (see Jaffe, Trajtenberg & Henderson 1993, Grupp 1996, Anselin, Varga & Acs 1997, Audretsch 1998 and Maurseth & Verspagen 1998). Furthermore, it has been shown that the impact of firms on the number of innovations increases more than linearly with the number of firms in a region, at least, for some industries (see Brenner & Greif 2003). There is also some evidence for some of the underlying processes (the importance of informal contacts is shown in Kozul-Wright 1994 and Brown & Hendry 1998, while the impact of the amount of cooperation on the innovativeness is confirmed in MacPherson 1997). Thus, spillovers, in whatever form they are created, constitute a self-augmenting process. Which of the underlying mechanisms is most important cannot be answered on the basis of empirical findings in the literature. Finally, firms profit from each other in terms of reducing their costs if they either cooperate in using certain resources or as a result of supplierbuyer relations between them. Again, in both cases it seems to be plausible that the existence of a large number of firms in a region increases the potential to form such mutually profitable relations. However, the empirical literature on cooperation and supplier-buyer relations is somewhat ambiguous. There is some evidence that a large share of cooperation occurs between firms that are located in the same region (evidence can be found in Koschatzky 1998, Oerlemans, Meeus & Boekema 1998, Sternberg 1998 and Fritsch 1999), but it is difficult to track down a causal relationship between the intensity of cooperation and the success of a firm in terms of cost reductions or innovations (in Koschatzky 1999, at least, a positive impact of regional cooperations with research institutes on the innovativeness of firms is shown). There are claims in the literature that cooperation is an important aspect in industrial districts (see, for example, Sengenberger & Pyke 1992, Dei Ottati

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1994, Vou & Wilkinson 1994 and Vipraio 1996), but there are also findings that point in the opposite direction (see Staber 1996 and Paniccia 1998). However, besides the spillovers discussed above, there is no empirical evidence for the significance of such a mechanism. This causes Staber (2001) to state that, “it has never been demonstrated empirically that district success is a function of primarily local business networking” (p. 330). Other authors are similarly sceptical with respect to the importance of inter-firm relationships (see, e.g., Grotz & Braun 1997a). With respect to supplier-buyer relations it is well-known that, in many industries, intensive contacts between suppliers and customers are necessary for the joint development of products. At the same time, there is, however, also evidence for the fact that contacts between suppliers and customers are of approximately the same intensity, independent of the distance between the locations of the respective firms (Hahn & Gaiser 1994 and Oerlemans, Meeus & Boekema 1998 find similar intensities, while Fritsch 1999 finds a slightly higher intensity for nearby firms). Thus, the location of suppliers and customers seems not to influence the intensity of cooperation. The claim that more firms of the same industry in the region increases cooperation between them and subsequently decreases the costs of production in the respective firms cannot be supported by empirical evidence. However, there is empirical evidence for the fact that the choice of location is influenced by the location of suppliers and customer firms (see Patel & Pavitt 1991 and Maskell 1999). This is discussed in the next subsection. There is one case identified in the literature that differs from what has been discussed above. In the film industry products can rarely be developed without cooperating with other firms (see Enright 1995). This cooperation is significantly easier to coordinate if the partners are located in the same region. Thus, productivity hinges very much on the availability of potential partners, for example other firms of the industry, in the region. This constitutes a self-augmenting process. However, except for the film industry, such a situation has not been reported for any other industry. Symbiosis with other industries There are many pairs of industries that depend on each other. This is mainly the result of supplier-buyer relations between the respective firms. If one industry is the main supplier or main customer of another industry, it depends strongly on the developments in the other industry. Such a dependence exists without doubt. Whether this dependence is significantly stronger on a regional level than on a national or global level is less obvious. Such a difference, however, is required if the symbiosis between industries constitutes a self-augmenting process of the kind described above. Again, the four kinds of impacts that interactions with firms of other industries might have are discussed separately. If start-ups mainly supply or buy from one specific industry, they might indeed consider the location of this industry during their choice of location. There is empirical evidence for such a dependence (see, e.g., Keeble, Lawson, Moore & Wilkinson 1999), so it is adequate to assume that positive local feedback exists between some industries due to the interdependence of location decisions. However, there is no detailed empirical study. As a consequence, it is unclear whether the attractiveness of a region increases more than linearly with the number of supplier or customer firms located there. One might argue that it does not matter much whether there

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are no or very few supplier or customer firms in a region, but that once their number becomes significant, the region becomes attractive. This would imply a self-augmenting process. However, we have no detailed empirical information about such a process. The same holds for the establishment of branches and the movement of firms. With respect to the innovativeness of firms, two factors are relevant. First, intensive contacts between suppliers and buyers are necessary in some industries. However, the discussion above has shown that this interaction does not depend, or at least not very much, on the location of the firms involved. Second, spillovers have repeatedly been found between certain pairs of industries (see Scherer 1984, Grupp 1996, Verspagen 1997 and Verspagen & Schoenmakers 2000). Verspagen and Schoenmakers show that spillovers between technologically related fields appear more often if the firms are located near to each other. This implies that the conditions for a positive feedback loop are satisfied for spillovers between certain industries. Whether these spillovers constitute a local self-augmenting process is less clear. Finally, if customers and/or suppliers of a firm are located nearby, the costs of transportation and communication are lower. Nowadays, because of improvements in transportation and telecommunication, this factor might be less important (this decrease in importance is shown in, for example, Hahn & Gaiser 1994 and Grotz & Braun 1997b). However, since the theory that is established here aims to explain the emergence of local industrial clusters on a general level and is not intended to be restricted to particular situations, this factor has to be included. The structure of this factor, however, might not satisfy the condition of a self-augmenting process since the benefits from proximity can be assumed to increase linearly with the number of firms that are located nearby. Human capital Human capital is frequently argued in the literature to be a crucial ingredient for the success of regions. It is usually classified as one of the most important criteria for the choice of the location of factory sites and firms (see, for example, Porter 1994). Employees are, in general, not willing to move, so that firms mainly rely on the local labour market. In the literature on industrial districts and innovative milieux, similar arguments are put forward. There, the existence of an adequate labour force is seen as a crucial factor for the success of such regional systems (see, for example, Marshall 1920, Maillat & Lecoq 1992, Zeitlin 1992 and Pietrobelli 1998). According to the approach taken here, it is necessary to check whether the firm population has an influence on the local human capital and whether the human capital influences one of the following processes: the occurrence of start-ups, the movement of firms, their innovativeness and the costs of production. To address the first question two kinds of human capital have to be distinguished: transferable and non-transferable or specific human capital (for a similar distinction see Huiban & Bouhsina 1998 or Becker 1993). Transferable human capital is based on academic knowledge and can be obtained in schools and universities, while nontransferable human capital mainly contains skills and can be obtained, to a large extent, only through practical experience. Although firms also use seminars to train their employees theoretically, the main impact of firms on the stock of human capital relates to non-transferable human capital. While actually doing their jobs, employees gain a lot of

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experience. This is usually referred to as ‘learning by doing’. If they leave a firm, they take this experience and related skills with them and enrich the labour market (a detailed study of such a process is given in Tomlinson 1999). Obviously, the existence of many firms in a region increases the amount of non-transferable human capital that is accumulated in this region. The respective effect is much smaller in the case of transferable human capital. In addition, a large firm population is able to attract workers to the region. This holds for both transferable and non-transferable human capital. The larger the firm population in a region, the more will the region be able to attract adequate workers. Furthermore, a high number of firms that require employees with a certain training might also influence the local education system. This point will be dealt with in the next section. However, there are several mechanisms that cause a positive feedback loop in the context of human capital. Whether it is self-augmenting is less clear. The literature on start-ups reveals that most start-ups in the manufacturing sector are founded either by researchers who have previously worked in universities or research institutes or by employees of firms that operate on a similar product market or with similar technologies (see, e.g., Keeble, Lawson, Moore & Wilkinson 1999). The knowledge that these people bring with them is important for the new firm. Furthermore, most start-ups are located in the region or near the region where its founder is already living or working (see, for example, Bramanti & Senn 1990 and Dalum, Holmen, Jacobsson, Praest, Rickne & Villumsen 1999). Thus, the number of start-ups in a region depends strongly on the human capital accumulated there (see Audretsch & Fritsch 1999 for some empirical evidence). This constitutes a positive feedback loop. Again it is not clear whether it is self-augmenting. Similar arguments hold in principle for the impact of human capital on innovations. However, empirical evidence is not available since most empirical studies examine the impact of education on the number of innovations, while according to the arguments above, some knowledge about the impact of non-transferable human capital is required here. This means that the movement of experienced employees between firms has to increase the innovativeness of these firms. Experts support this view in private discussions, but empirical evidence is lacking. There seems to be no doubt that better education increases productivity. However, again the knowledge and experience obtained by employees in other firms has to be relevant in order to create a self-augmenting process between the firm population and the human capital in the region. Empirical studies on this point are not yet available. Local education system and public research The analysis now turns to the other aspect of human capital: human capital created outside firms. Since human capital is also created in public research institutes, universities and schools, it seems to be useful to approach the education system and public research simultaneously. In the literature both are repeatedly mentioned as important factors for the emergence of industrial districts or clusters (see, e.g., MitchellWeaver 1992, Saxenian 1994 and Dalum 1995). To check whether this might constitute a self-augmenting process, the first question that is to be answered is the question of whether the firm population in a region has an impact on the local education system and the public research in the region. Two aspects

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are contained in this question. On the one hand, there might be local spillovers from firms to public research, so that public research becomes more productive if more firms are around. On the other hand, firms might influence the creation, orientation and location of research and/or education institutions. The former aspect is disproved (see Anselin, Varga & Acs 1997). The latter aspect is rarely addressed in the literature. However, there are some hints to such an impact. Some research institutes are founded by firms or at least supported by firms. For example, the Kaiser Wilhelm foundation, the ancestor of the Max Planck Society, was originally financed to a large extent by private firms. Similarly public vocational training is usually adapted to the needs of firms in a process of local coordination between the respective actors. Universities are usually more independent. Nevertheless, research projects financed by private firms influence the focus of research done at universities as well. Hence, there seems to be an influence by firms on the local education system and public research. This influence clearly increases with the number and size of the respective firms. Some of this influence is national, some of it is local. The influence of the education system and public research on the performance of firms is studied in a large number of empirical works (examples are given below). These indicate that they influence all four processes, the foundation of start-ups, the relocation of firms, their innovativeness and the production costs. Quite a number of start-ups are founded by people who previously worked in research institutes or universities (see Keeble, Lawson, Moore & Wilkinson 1999 where a share of 25% is reported). These startups are usually located in the neighbourhood of the research institute or university where the founder came from (see, e.g., Keeble, Lawson, Moore & Wilkinson 1999). Thus, a regional aspect is clearly given. In addition to this impact, the local education system and the existence of research institutes is an important criterion for the choice of location by firms (see, e.g., Pleschak 1995). There is also strong evidence for the fact that public research increases the innovativeness of nearby firms (see, for example, Jaffe & Trajtenberg 1996, Anselin, Varga & Acs 1997 and Audretsch 1998). Such research offers to firms the possibility of joint research projects, an easy access to new technological knowledge and the availability of experienced employees. Again, the spatial limitation of this effect has been clearly demonstrated in the literature (Anselin, Varga & Acs 1997 have shown that spillovers from public research to firms are significant within a range of 50 miles and become insignificant outside this range). In addition, a good and well-adapted local educational system increases the innovativeness of the firms in the region (see Audretsch 1998). A similar argument seems to hold for an increase of the productivity of firms due to better educated employees. Some evidence for this argument can be taken from the fact that firms are concerned about the education system in a region when they choose their location. The impact of the employees’ education on their productivity is, however, quite difficult to measure. Furthermore, education is much more important for research, development and management than for production. Hence, the local creation of human capital by schools, university and public research has a clear impact on the firm population, especially in the form of increasing the number of start-ups and the innovativeness of firms. A positive feedback loop exists if, in addition, there is a positive influence of the firm population on the public education in the

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region. As discussed above, such an influence is not empirically detected in the literature and it is unclear whether it exists. Local capital market The existence of venture capitalists has been repeatedly put forward in the literature as one of the preconditions for the successful development of a region (see Miller & Coté 1985, Maillat & Lecoq 1992, Rabellotti 1997 and Garnsey 1998). It is argued that the firm population needs adequate access to venture capital if it is to grow. However, investment flows have become increasingly global. The local capital market is rarely important for those firms that have access to the global capital market, for example, the larger and well-established firms. Start-ups and small firms lack access to the global capital market and they rely heavily on local capital supplies. Start-ups profit a lot from local venture capitalists, not only in terms of the provision of necessary capital but often also in terms of the business experience that venture capitalists have accumulated (see Maillat & Lecoq 1992 and Rickne 2000). Thus, there is clear empirical evidence that local availability of venture capital and experienced venture capitalists increases the number of start-ups and the likelihood of their success. Research and development is also costly. Small firms, in particular, finance such endeavours through the capital market. However, the regional context plays a much smaller role for financing research and development compared to the founding of a firm (in Rickne 2000 financial resources have been found to originate from local sources in 96% of the cases in initial financing of start-ups and only in 57% and 45% of the cases in financing continued technological development). Thus, the innovativeness of firms is restricted by the local capital market only to some extent. In the case of production costs, there does not seem to be any reason why these should depend on the local capital market. Hence, the local capital market has been found to mainly impact on the number of start-ups in a region. However, to constitute a self-augmenting process, there also has to be an impact in the opposite direction. Local firms of the same industry often provide the capital for start-ups, especially for start-ups that operate in related areas or are even suppliers (Rickne 2000 finds that local firms are involved in 22% of the initial financing and 67% of development financing). This implies that a higher number of firms in a region might improve the local availability of venture capital. In addition, local banks play an important role in the supply of capital to small firms. Local banks are more willing to lend money to firms that operate in industrial or technological fields where these banks have already had experience. Therefore, the existence of a number of firms in a region should imply that the local banks are experienced in the respective industrial or technological field and should be more willing to provide capital for similar ventures. This line of argument has not been tested empirically, but experts have repeatedly supported it in private talks. This implies the existence of a positive feedback loop between the provision of venture capital and the number of firms in the region. Whether it constitutes a selfaugmenting process is unclear.

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Culture and local historical specificities In the literature, especially on the Italian industrial districts, it is repeatedly claimed that the culture and certain specificities in the history of the studied regions have caused the emergence of the observed industrial clusters (see, for example, Sengenberger & Pyke 1992 and Trigilia 1992). Whether these factors contribute to the existence of local industrial clusters is examined here. According to the discussion above, there has to be an impact of the firm population on the culture and the local historical specificities in order to create a positive feedback loop. Furthermore, such an impact has to occur in a time span that is similar to the time span that the local industrial cluster takes to emerge. This is not given in the case of culture because culture changes comparatively slowly. The historical specificities discussed in the literature are not influenced by the firm population in the region, but are seen as prerequisites for the emergence of local industrial clusters. Thus, culture and local historical specificities do not constitute a positive feedback loop. However, that does not mean that they might not influence the emergence of local industrial clusters in certain locations. Their impact is discussed in Section 2.5.2 in the context of the conditions for exceeding the critical masses. Local attitudes It is sometimes claimed in the literature that public attitudes play an important role in industrial districts and innovative milieux (see, for example, Miller & Coté 1985 and Camagni 1995). In particular, the literature on innovative milieux talks of a so-called ‘innovative atmosphere’. This means a positive attitude towards innovations, a large number of people who are capable of and willing to conduct and use innovations, and the availability and flow of information in the region. Some of these factors have already been discussed above under the labels of spillovers and human capital. What remains might be subsumed under the following two factors: the attitude towards starting an enterprise and the willingness of people in the region to work in a certain industry. Again, whether there are positive feedbacks between these two aspects and the firm population in the region has to be examined. The attitude towards starting an enterprise is influenced by existing firms in two ways: the success of existing firms may act as a role model, and the development of other startups might be a source of information about the market situation and might focus attention on certain fields of economic activity (a detailed discussion of these topics is given, e.g., in Fornahl 2003a). A related empirical study shows that there is some evidence for the claim that successful start-ups increase the awareness and positive attitude towards founding an enterprise (see Fornahl 2003b). This can be assumed to increase the number of start-ups in a region so that positive feedback loops result. Whether it leads to a selfaugmenting process cannot be answered because empirical work is lacking in the literature. Brenner (2002) studies the second factor, the willingness of people to work in certain industries, using a survey conducted in German schools. The results showed that the career plans of pupils are influenced with respect to their industrial orientation by the actual employment numbers in the region. However, the willingness to work in a certain

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industry increases less than linearly with the number of employees in this industry in the region. This implies that no self-augmenting process results. Further empirical evidence is not available. It is concluded here that it is rather unlikely that a self-augmenting process results from the interaction between the willingness of people to work in a certain industry and the local number of firms in this industry. Local policy In the literature on Italian industrial districts, specific support by local policy makers is repeatedly mentioned as an important cause for the emergence of these districts (see, for example, Rabellotti 1997). It is obvious that local policy makers have a strong influence on local economic devel-opment. Examples for such influences are the founding and orientation of universities and public research institutes, the provision of good infrastructure, the support for start-ups and the direct support of firms in the form of tax reductions or subvention. There is significant empirical evidence for all these factors (see the reference below). For the radiocommunication cluster in Northern Denmark, Dalum (1995) finds that the creation and location of university institutes was decisive for its emergence. In many regions startups are now heavily supported by local and national government programs (see Miller & Coté 1985, Dohse 2000 and Koschatzky 2003). Finally, tax reductions and cheap land prices are typical methods used by local policy makers to attract firms to a region. Universities and public research institutes have already been discussed above in this section, so no further discussion is included here. The other factors show that local policy makers have a large impact on the number of firms and branches that are set up in the region and some impact on the innovativeness and performance of local firms. However, to constitute a positive feedback loop, the local firms have to influence local policy makers as well. Usually, there is a great deal of contact between local governments (mainly on the community level) and firms. It might be argued that the larger the firm population in a region, the more influence they have on the local policy. Unfortunately, comprehensive empirical studies of this issue are lacking. In all case studies in which a crucial impact of local policy on the development of local industrial clusters is identified, the respective policy has not been triggered by the firm population in the region. It is unclear whether a positive feedback loop is constituted by the mechanisms discussed which exceeds the processes that have already been described under the label of local education systems and public research. Potential self-augmenting mechanisms The intention of the above discussion was to identify those mechanisms that might, according to the empirical findings in the literature, constitute a local self-augmenting process that is necessary for the existence of local industrial clusters. All factors that are usually discussed in the context of industrial districts and clusters have been considered. Each of these factors has been investigated according to the requirements of the theoretical approach in Section 2.2. Two such requirements exist. First, the mechanisms have to constitute a positive feedback loop. Second, this feedback loop has to be self-augmenting. The former

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requirement can be examined for most mechanisms on the basis of the available empirical literature. For the latter requirement very few empirical studies are available. Hence, it is not possible to determine which of the mechanisms cause a self-augmenting process. All that can be done here is to identify those mechanisms that at least constitute a positive feedback loop. This is done in the following list. For each of the factors distinguished above, the respective mechanisms are listed. In those cases in which no clear evidence for the constitution of a positive feedback loop exists, the mechanisms are in italics. In the case of the interaction between firm populations only one mechanism of positive influence has to be given, because this mechanism might function in both directions: • spin-offs • assistance for start-ups • spillovers • choice of location • cooperation • buyer-supplier relationship In the case of the interaction between the firm population and local circumstances mechanisms for a positive impact in both directions have to be given. This is done for each kind of local circumstance separately: Human capital: →

source of founders and R&D staff necessary for expansion

←

learning by doing within firms

Local education and public research: →

source for human capital, technological knowledge and founders

←

firm population influences education system and public research

Local capital market: → influences the number of start-ups and the innovativeness of small firms ← providers of venture capital are influenced by the local history and the local number of firms in the industry

Local attitudes: →

entrepreneurial attitude influences the number of start-ups

←

successful models improve attitude towards founding a firm

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Local policy: →

gives specific support to start-ups and existing firms

←

policy makers are influenced by the local firm population

Furthermore, there is no empirical evidence of the strength of these mechanisms. Although they might constitute a self-augmenting process, they might be too weak to cause the existence of local industrial clusters. The strength of the mechanisms can be expected to vary between industries and regions. This is discussed in detail below. In Section 3.5 an attempt is made to empirically study the impact of some of the mechanisms on the existence of local industrial clusters. The list of mechanisms that is given above might not be complete. It contains the factors that are frequently discussed in the literature. Mechanisms might exist that have not been identified so far. However, the processes have been studied in such a large number of case studies that a neglect of relevant mechanisms is not very likely. It is more likely that more complex feedback loops exist. Above, only feedback loops that contain not more than two positive causations are discussed. This means that only the interaction between one factor and the firm population is considered at a time. The different factors might, however, also influence each other. This causes feedback loops that consist of more than two causations. To keep the discussion simple it has been restricted to the most simple feedback loops. There are several other reasons to restrict the analysis in such a way. First, the more complex mechanisms are also based on the above factors. Second, it is even more difficult to obtain empirical evidence for more complex mechanisms. This does not mean that influences between the factors and more complex mechanisms do not exist. On the basis of the theoretical model it is only possible to state the following. The mechanisms that are listed above at least satisfy one of the requirements obtained for selfaugmenting processes. The theoretical analysis has shown that such self-augmenting processes are necessary for the existence of local industrial clusters. Furthermore, they have to be strong enough to cause the existence of local clusters. In this context, the above mechanisms are substitutes. All those that are self-augmenting processes add up. Their sum has to be sufficiently effective. Hence, the local industrial clusters identified in the literature might, indeed, be caused by different mechanisms. A general theory is only able to elaborate the characteristics that potential mechanisms must satisfy. This can be used to identify all mechanisms that might play a role. This is done above. Which of the mechanisms is responsible for the existence of a particular local industrial cluster is an empirical question that has to be answered in a case study. It should be remembered here, that the existence of self-augmenting processes is not a sufficient condition for the existence of local industrial clusters. It is only a necessary condition. Further conditions exist that refer to the global and local situation. These are discussed in Section 2.4.2. They are complementary to the conditions discussed here.

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2.4.2 Industrial and regional characteristics Most of the mechanisms that have been identified above differ significantly between industries. The theoretical analysis has shown that the structure and the strength of the mechanisms should be treated separately. It seems to be plausible that the structure of the mechanisms is approximately the same for different industries, although there is no empirical evidence for this. However, the strength of the mechanisms seems to vary greatly between industries. For example the start-up rate varies tremendously between industries (see Audretsch & Fritsch 1999). The same holds for the innovation rate (see Acs & Audretsch 1990) and the number of spillovers (see Scherer 1984, Grupp 1996 or Verspagen 1997). Similar arguments and evidence can be put forward for most of the other mechanisms. The importance of human capital or venture capital varies between industries, and buyersupplier relations differ with respect to the role they play. A difference in the importance of these mechanisms implies a difference in their strength. This has two consequences: not all industries show clustering and not all clustering is caused by the same mechanisms. Industrial characteristics and clustering It has been shown above that the sum of all self-augmenting processes has to be sufficiently strong if local industrial clusters emerge. Since the strengths of the above mechanisms vary between industries, this condition might be satisfied for some industries and not for others. As a consequence, clustering does not occur in all industries. In Section 3.2 the industries in which local clusters exist in Germany are identified empirically. The weakness of the self-augmenting processes is one possible explanation for the lack of local clusters in some industries. A lack of regions that are sufficiently attractive so that the critical mass of the firm population is exceeded is another possible explanation. However, developments differ between regions and it is unlikely that if clustering is possible in an industry, all regions fail to exceed the critical mass. Therefore, whether local clusters exist in an industry seems to be mainly determined by the characteristics of the industry, namely the strength of the sum of all self-augmenting processes that are active. It has to be restated that the self-augmenting processes do not have to be present at all times. It is sufficient that they are strong enough during a certain period of time in which the local clusters emerge. This is especially important in the context of start-up and spinoffs. Usually there are many firm entries while a new industry develops. Hence, the selfaugmenting processes that are related to firm entries are strong at that time. If, in combination with all other self-augmenting processes, they are sufficiently strong, local industrial clusters emerge. Once the industry has become mature, firm entries become rare and the related self-augmenting processes become weak. Although this might cause the self-augmenting processes to fall below the required level, the existing local clusters are sustained for a long time. It can be concluded that the strength of the sum of all local self-augmenting processes in an industry at the time when local clusters might emerge determines whether local

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clusters will exist in this industry. Hence, the local self-augmenting processes can be seen as the answer to the question of why local industrial clusters exist. They also give some answer to the question of when they emerge. An emergence of local industrial clusters is not possible before the self-augmenting processes become strong enough. However, the other conditions, which are discussed in the next section, also play a role in this context. The industry-specific self-augmenting processes give no answer to the question of where local clusters emerge. The industrial characteristics that might be responsible for the existence of clusters are studied empirically in Section 3.5. However, different characteristics might be decisive in different industries. Industry-specific causes of clustering The different mechanisms that constitute local self-augmenting processes are found to be substitutes with respect to the conditions for the emergence of local industrial clusters. Hence, the characteristics of industries might differ significantly and nevertheless they might all show clustering. An identification of one mechanism that is responsible for the existence of local industrial clusters cannot be expected. What we might aim for is to identify those mechanisms that are involved in the emergence of local industrial clusters and to classify industries according to the active mechanisms. The former is done in the literature and in Section 2.4.1, which has led to the list of potential mechanisms that is given above. A further approach is given in Section 3.5. The classification of industries according to the relevance of the different mechanisms is difficult to reach. It has been found above that different mechanisms might add up. Hence, not every existing local industrial cluster can be assigned to one responsible mechanism. However, more comparative case studies might allow the crucial mechanisms to be identified at least for some industries. Regional differences in the self-augmenting processes The local self-augmenting processes might also differ between regions. Again it is not plausible that the structure of these processes should differ between regions. Their strength, however, might differ. For example, in some regions it might be easier to start a firm because the local government provides space, unbureaucratic rules or financial support (the availability of venture capital is included in another mechanism). There might be more spillovers in a region because the local culture causes more cooperation and exchange of information. The mechanism that is based on the influence of firms on the public research that is done in the region requires the existence of public research institutes. This is not given in all regions. There might also be different degrees of coordination between firms and local policy makers in different regions. As a consequence, the adaption of the education system or the legal system to the needs of the firms might be different. These examples can be classified into three categories. First, different cultures cause different strengths of some self-augmenting processes. Second, differences in regional policies strengthen or weaken different mechanisms. Third, the existence of universities

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and public research institutes is necessary for some mechanisms or for their strengths to be sufficient. The first two categories contain aspects that differ much more between countries than within a country. In the study of Germany conducted in Chapter 3, they can be expected to play a minor role. However, they might offer explanations for the fact that certain industrial clusters emerge only in a few countries. With respect to the latter category, regions differ enormously. Whenever the respective self-augmenting processes are decisive for the existence of local industrial clusters, all regions that do not contain a university or public research institute are excluded from the set of potential locations of the cluster. As a consequence, regional differences in the self-augmenting processes provide some answers to the question of where local industrial clusters emerge. However, they are not able to explain the location of such clusters. The above discussion allows the regions in which the self-augmenting processes are sufficiently strong to be differentiated from those regions in which they are too weak. Sufficiently strong self-augmenting processes are a necessary condition for the emergence of local industrial clusters. Hence, the above differences between regions explain why in certain regions no industrial clusters can emerge. It does not, however, provide a sufficient condition, so that this discussion does not allow prediction of where the industrial clusters will emerge. 2.5 CONDITIONS FOR THE EMERGENCE OF LICS Besides the question of why local industrial clusters exist, this book focuses on the questions of when and where they emerge. The first stage of the evolution of local industrial clusters is of most interest here. The usual developments that are triggered by the industrial life cycle were discussed above. For these developments to occur necessary conditions have been formulated. However, the developments triggered by the industrial life cycle represent only one possible causation for the emergence of local industrial clusters. There are other possibilities that are discussed here. Nevertheless, the distinction of different necessary conditions, as done above, is also helpful if the dynamics take another form. All together, there are three independent necessary conditions for the emergence of local industrial clusters. First, there have to be local self-augmenting processes. Second, the attractiveness of the region in combination with the market situation has to be high enough to exceed the critical value, e2, of the exogenous conditions for some time. Third, the local firm population has to exceed a critical value during the initial phase. Stochastic fluctuations might also cause the firm population to exceed the latter critical value. In this case the second condition of e(t)>e2 for some period of time is not strictly necessary. However, stochastic fluctuations might cause an exceeding of the critical mass of firms only if the exogenous conditions, e(t), are, at least, not far below the critical value e2. Only if all three conditions are satisfied, will a local industrial cluster emerge. These three conditions are complementary. Nevertheless, a clear temporal hierarchy exists between these three conditions. As long as the first condition is not satisfied, the other two are not decisive. If the first condition is satisfied, the second condition determines

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whether the third becomes relevant. Hence, these three conditions are satisfied successively. They will be discussed separately in this order in the following. 2.5.1 Emergence of self-augmenting processes The local self-augmenting processes have been extensively discussed above. It has been found that they do not appear in all industries or in all regions. Many different mechanisms that might constitute such self-augmenting processes have been put forward. This section focuses on the question of when and where local industrial clusters emerge. The latter question can be partly answered on the basis of self-augmenting processes, which has already been done above. To answer the question of when local industrial clusters emerge, it is important to know when the respective self-augmenting processes emerge. Hence, the temporal aspects of the self-augmenting processes are discussed here. Two developments have to be considered. First, the self-augmenting processes might require certain circumstances in order to work. These circumstances might change over time. Second, self-augmenting processes might change in time. The two developments are discussed separately. Necessary circumstances for self-augmenting processes That local self-augmenting processes depend on the characteristics of industries was extensively discussed above. For example, in some industries spin-offs are frequent while in other industries they are rare. The extent to which spin-offs are supported by their incubator or the technical opportunities of workers to start their own firms seems to depend, first of all, on the characteristics of the industry. These characteristics seem to be quite constant over time. Nevertheless, spin-offs will rarely occur while the market for the products is very small. Spin-offs are also rare if the market is mature and there are high entry barriers. This means that, although the mechanism of spinoffs remains the same, its selfaugmenting character changes according to the circumstances. The same holds for several of the other potentially self-augmenting processes. For example, the provision of venture capital is only important if start-ups have a chance to survive in the market, or spillovers are only crucial for firms if there is significant technological development. This means that the circumstances allow or disallow the unfolding of the self-augmenting processes. The relevant circumstances in this context are mainly the market situation and the technological development, both of which influence some of the potential selfaugmenting processes. This implies that there are times in which the self-augmenting processes in an industry are stronger and times in which they are weaker. Only if they are sufficiently strong, do local industrial clusters emerge. Many of the self-augmenting processes are stronger when there is technological change or the demand increases, which causes the founding of many new firms. Both developments are present particularly during the first phase of the industry life cycle. However, other developments exist that cause similar circumstances. An example is an increase in demand that is not caused by the industry life cycle, but by changes in the preferences of the consumers, legal changes, or cheaper production.

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To sum up, the market situation and technological change influence the strength of some of the local self-augmenting processes. They might, and often do, cause this strength to exceed the critical level. In such a case changes in the market or technology trigger the emergence of local industrial clusters. In addition, the market situation is part of the exogenous conditions. Therefore, changes in the market situation are often decisive for the timing of the emergence of local industrial clusters. Often such clusters emerge when the markets for the respective products grow (see, e.g., Porter 1990 and Dalum 1995). Change in the local self-augmenting processes The same impact would also be caused by a change of the self-augmenting processes themselves. If the characteristics of an industry change in such a way that the selfaugmenting processes become stronger, local industrial clusters might emerge. However, no evidence for such a development can be found in the case studies that are reported in the literature. Alternatively, the social, cultural, political, or legal conditions might change in such a way that self-augmenting processes become stronger or weaker. For example, the attitude towards cooperation might change in a region or a country (see Lundvall 1992 for a discussion of the influence of culture on cooperation and information flows). This might trigger the emergence of local industrial clusters. Theoretically such a causal relationship is plausible and in line with the model developed above. Empirically the relationship between the local attitudes and economic development has not been sufficiently studied. Most of the cases studied in the literature are related to changes in demand and technology. Most of them occur at the beginning of the industry life cycle or after tremendous technological changes. However, there are also other cases in which different historical events are claimed to have caused the development of local industrial clusters. Most of these relate somehow to an increase in start-ups in the region (see, e.g., MitchellWeaver 1992). Such a change might increase the effect of all self-augmenting processes that are related to the founding of new firms. This might explain the emergence of the Italian industrial districts at this time. However, the empirical evidence reported in the literature is too weak to prove this supposition. It can be concluded that there might be changes in local self-augmenting processes that trigger the emergence of local industrial clusters. However, the knowledge about self-augmenting processes is not sufficient to make a final statement. More research on this is needed. 2.5.2 Attractiveness of regions The analysis of the theoretical model has shown that the exogenous conditions have to exceed a certain level, e2, to trigger a development towards a local industrial cluster. The local dynamics have been modelled in a deterministic manner above. In reality the dynamics are stochastic. Hence, the local system might cross the line of unstable states and converge towards an industrial cluster because of random events. Exogenous conditions above e2 might not be necessary for such an event. Thus, the condition e(t)>e2 is not a strict condition. However, the larger e(t) is, the more likely is the crossing of the

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unstable state. This links the two conditions—the one with respect to the exogenous conditions and the one with respect to the firm population—to each other. Positive developments in the firm population might compensate for less favourable exogenous conditions and vice versa. Nevertheless, the two conditions will be treated separately. The former one is treated in this subsection and the latter one is treated in the next subsection. The exogenous conditions contain two aspects: the market situation and the attractiveness of the region. Changes in the market situation influence many different regions at the same time. Hence, the market dynamics mainly determine the timing of the emergence of local industrial clusters. This has already been discussed in Section 2.5.1. It will be less decisive for the location of the emerging clusters. In some cases market dynamics might affect only certain regions. In general, however, local industrial clusters supply global markets. If they only supplied local markets, their economic activity would be restricted by the local demand and no clustering could appear. Thus, changes in the global market matter and these usually affect different regions in similar ways. Nevertheless, the critical mass, e2, will not be exceeded in all regions at the same time. The shape of the function depicted in Figure 2.2 and the attractiveness of regions vary. Hence, the critical point, e2, and the exogenous conditions differ. Differences in the critical point are caused by differences in the local self-augmenting processes. These have been discussed above. Here the differences in the attractiveness of regions are discussed. Determinants of the attractiveness of regions The attractiveness of regions, as it is defined in the theoretical model above, is part of the variable that represents the exogenous conditions. This variable has been introduced to reflect all aspects that are not included via the firm population and the local conditions in the model. The attractiveness of regions is the local part of this variable. This means that the attractiveness refers to all local aspects that are sufficiently constant, so that it makes no sense to include them as variables in a dynamic model. These are the size of the population in the region, the population density, the geographic location, the education system, culture, institutional settings, the political system, the long-term public research conducted in the region, specific characteristics of the local market and other similar aspects. Everything that makes the region more likely to be the location of firms and is not influenced by the firm population in the region might be considered here. Such a long and open list is not very helpful as the attractiveness of regions is quite decisive for the location of industrial clusters. Therefore, it is desirable to obtain more information about the factors that matter most. The general theoretical approach that is taken here cannot offer more information. It can only be deduced that the local conditions add up. Thus, none of the local circumstances is necessary and none of them is sufficient. Case studies might help to obtain some knowledge about the most important local factors. However, the literature is quite heterogeneous with respect to the local factors it claims to be responsible for the emergence of industrial districts or clusters. Factors that are repeatedly highlighted are the geographic location, the education system including the existence of universities, public research, culture, institutional density, regional and national policy, specific characteristics of the local market, and the history of the region.

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For all of these factors plausible reasons for their importance in the present context can be found. However, for each factor a counter-example can also be given, in which either the respective condition is present and no local industrial cluster emerged or the condition is not present and, nevertheless, such a cluster emerged. This confirms the theoretical finding that none of the factors is decisive and their sum is the variable that really matters. However, some of local circumstance are of specific interest and therefore briefly discussed here. The existence of a university is repeatedly highlighted in the literature. This is in line with the arguments above. In Section 2.4.2 it was stated that, for some industries, universities are necessary for sufficiently strong local self-augmenting processes. Hence, they not only increase the attractiveness of a region but they are also decisive for the satisfaction of another necessary condition for the emergence of local industrial clusters: the existence of local self-augmenting processes. Therefore, the existence of a university is often crucial for the emergence of local industrial clusters. However, this does not hold for all industries. Culture, which has many facets, is often mentioned in the case studies of local industrial clusters. It has various influences on local development (an overview is given in Pilon & De Bresson 2003). Similar to the existence of a university, cultural factors influence the impact of local self-augmenting processes and the attractiveness of the region. Different factors might matter, such as the attitude towards entrepreneurship, the attitude towards cooperation, the governance structure in a region, and the attitude of the population towards technological development. Many more factors could be listed here and many of them are highlighted in some case studies. A general approach, like the one taken here, is only able to state that culture differs between regions and that if this causes an advantage for some regions, it increases the likelihood of the emergence of a local industrial cluster in these regions. Finally, the influence of the history of a region is discussed here. Many of the factors mentioned above depend on the history of the region. These are, for example, the local culture, the existence of universities and research institutes and local policy. A factor that is less explicitly mentioned in the literature but is often found in case studies is the existence of related industries. Regions show some path dependence in their development with respect to the industries in which they specialise (such a path dependence is explicitly reported in Tappi 2002). If new industries or technologies emerge, those regions that are already specialised in related fields have an advantage and are more likely to become the location of local industrial clusters. Competition between regions The literature extensively discusses the prerequisites for the emergence of local industrial clusters. It is implicitly assumed that there are certain conditions that cause the emergence of such clusters. However, the theory discussed above implies that the local conditions add up to the attractiveness of a region. Regions compete on the basis of their attractiveness for the location of emerging industrial clusters. Hence, there are no specific prerequisites that determine the development but a bundle of local conditions. Furthermore, local processes are assumed to be stochastic in this book. The competition between regions proceeds as follows according to the theory developed

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above. Changes in the exogenous conditions, usually market or technological changes, cause them to exceed or reach a critical level (denoted by e2 above). This holds for many regions at the same time. In all these regions the firm population might increase. This increase is stochastic, so that it cannot be predicted (a similar argument can be found, for example, in Pouder & St. John 1996). However, the more attractive regions benefit earlier and more strongly from the change in the market or the technology, at least on average. Nevertheless, it is not guaranteed that the most attractive region develops most quickly because the underlying processes are stochastic. The increase in the firm population in many regions increases competition in the market. As a consequence, the exogenous conditions become less favourable. According to the argument in Section 2.3.1, in those regions in which the firm population has exceeded the critical value (unstable state), the firm population will continue to grow and an industrial cluster emerges. This implies that the location of industrial clusters is stochastically determined. However, some regions are excluded from the set of potential locations (this is discussed in Section 2.4.2) and the attractiveness of the remaining regions determines their likelihood to be the location. This means that all factors that influence the attractiveness of regions also influence the likelihood of different locations of emerging industrial clusters. However, the probability of a certain location is never a value of 1. No factor that influences the attractiveness of regions is sufficient for the emergence of a local industrial cluster. Therefore, the question about the prerequisites for the emergence of local industrial clusters has to be re-stated. How much the factors discussed above influence the probability of the emergence of such a cluster in a certain location has to be examined. An answer to that question cannot be given on the basis of the above theoretical approach nor on the basis of the literature. Some answers will be provided with the help of simulations in Chapter 4. Further empirical studies of this question would be helpful. The emergence of local industrial clusters has been characterised above as a competition between regions. It might be argued that a certain region exceeds the critical value independently of any global developments and independently of the processes in other regions. This is, indeed, possible. However, all local clusters in an industry usually develop at approximately the same time (see, e.g., Rosegrant & Lampe 1992, Saxenian 1994 and Dalum 1995). Hence, the developments in the different regions mutually influence each other, so that an independent development in one region is unlikely in the first phase of the evolution of local industrial clusters. 2.5.3 Forces that support local self-augmenting processes It has been stated above that changes in the market or technology trigger the development towards local industrial clusters and the attractiveness of regions determines the chances of each region to become the location of industrial clusters. The development of the firm population in the regions, however, has been said to be stochastic. In modelling, stochastic elements are used for two reasons. The first reason is that there are processes that are stochastic in reality. The second reason is that there are causes of processes that cannot be captured by the modelling and are included as stochastic elements.

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Here the second reason dominates. The growth of a local firm population is mainly caused by the founding of firms. Whether firms are founded depends not only on the local and global circumstances but also on the personal characteristics and history of potential founders. It is not possible to include these factors in a general abstract model like the one above. The literature on start-ups reveals that, besides the local circumstance that are included in the above modelling, the entrepreneurial attitude of the population plays an important role (see Saxenian 1994 and Fornahl 2003b). A few actors might be decisive in this context. Furthermore, it is argued in the literature that the local coordination plays an important role for the emergence of local industrial clusters (see, e.g., Lorenzen & Foss 2003). Again a few actors play an important role and again this aspect cannot be included in the above modelling. In the literature there has been some discussion of the importance of local actors which is briefly discussed here. Two factors seem to be important: entrepreneurs and local coordination. Entrepreneurs Many case studies have highlighted the importance of entrepreneurs for economic development and local learning in a region (see, e.g., Keeble, Lawson, Moore & Wilkinson 1999). In some cases one or a few entrepreneurs or regional actors have even been decisive for the development in the region (see, e.g., Maarten de Vet & Scott 1992, Saxenian 1994 and Paniccia 1998). These people are typically characterised by an ability to imagine future development and their promotion of activities in the region. For example, in the case of Jena, Carl Zeiss realised the opportunity of combining glass production, optical manufacturing and allied research in one place and developed strong ties with Otto Schott and Ernst Abbe. This can be seen as the origin of the local cluster in glass and optics that still exists in Jena (the history of the Zeiss firm is described in Hellmuth & Mühlfriedel 1996 and Walter 2000). In general the theory above predicts that regions in which the firms are founded earlier have a higher chance of developing into a local cluster. Hence, entrepreneurs who sieze opportunities early are decisive for the emergence of local industrial clusters. Such entrepreneurs are rare. Their occurrence in certain places might be influenced by local conditions but is not determined by these conditions. Hence, it is by chance that some regions can benefit from the existence of such entrepreneurial regional actors. Local coordination Another factor from which regions can benefit is the local coordination of activities. Some case studies show that the coordination of certain actions within the region has given the region a crucial advantage (examples can be found in Dalum 1995 and Murmann 2003, a discussion of the importance of this aspect is given in Lorenzen & Foss 2003). This coordination can be provided by very different persons or groups. It sometimes occurs for specific historical reasons, sometimes because of the vision of one or some actors, and sometimes because of good connections among the relevant actors in the region.

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Again it is not possible to gain further insights about these processes from the general approach taken here. More empirical studies should be conducted to obtain a better understanding of the local coordination. Experience with policy programs might help in this context. In recent years a number of programs have been developed that attempt to trigger the emergence of local industrial clusters by, among other things, the initiation and support of local coordination and networking (examples are the BioRegio- and the InnoRegio-Programme in Germany). First results are reported in the recent literature (see Dohse 2000). 2.6 SPATIAL DISTRIBUTION OF LIC The model that is developed above describes the processes and situation within one region. In Chapter 3 the spatial distribution of economic activity in Germany is analysed empirically. Therefore, in this section the theoretical analysis (conducted in Section 2.2) is used to predict the spatial distribution of industries. These predictions are tested empirically in Chapter 3. In Section 2.2.3 it has been shown that depending on the strength of the local selfaugmenting processes, two different situations might occur: • a monotonously increasing dependence of the firm population on the regional attractiveness and the market situation and • the existence of two stable states, which indicates the existence of local industrial clusters For both situations predictions of the industrial firm distribution among regions are deduced in the following. This is done in three steps. First, the findings about a single region in Section 2.2.3 are transferred to a spatial situation. Second, the distribution of the attractiveness of regions is studied. Finally, a mathematical model is developed for the spatial distribution of firms in an industry. 2.6.1 From local systems to spatial distributions The model in Section 2.2 is set up to describe the dynamics within one region. It is assumed that an adequate partition of space into a number of regions can be done. In the empirical study the partition for which data is available has to be used. Let the regions be denoted by r (r {1, 2,…, R}). The industries are studied separately. They are denoted by i (i {1, 2,…, I}). The number of firms in each region, r, and industry, i, is denoted by ƒ(i, r). The aim of this section is to predict the industrial firm distribution among regions. The industrial firm distribution assigns to each number of firms, ƒ, the expected number of regions that contain exactly ƒ firms. It does not distinguish between the regions. It only matters how often a certain number of firms, ƒ, appears in a region. The respective probability of finding a region that contains ƒ firms of industry i is denoted by P(i, ƒ). Function P(i, ƒ) is called industrial firm distribution among regions here. Mathematically, it can be written as

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(2.6)

where (2.7)

To obtain predictions for the function P(i, ƒ) it is assumed that the firm population in each region has approximately reached a stable state. This requires that the market situation is approximately constant. Furthermore, it requires that no inertia occurs. In Section 2.3.3 it was noted that some inertia can be expected in most industries. Nevertheless, the theoretical approach taken here is based on the assumption that the local systems converge to the stable states. The effects of inertia are assumed to cause some random disturbance of the function P(i, ƒ). According to the theoretical model, the number of firms depends on the external market conditions and the attractiveness of the region, meaning those advantages and disadvantages that are either natural or at least not influenced by the considered firm population in the region. This dependence is either monotonously increasing or shows hysteresis in the case of clustering. The influence of the global market conditions on the firm population in a region is assumed to be the same for all regions. Let the attractiveness of region r with respect to industry i be denoted by e(i, r). Theorem 2 states that there is a certain range of the exogenous conditions for which two stable states exist. If the market conditions are constant and the same for every region, the attractiveness of regions determines into which range the exogenous conditions fall in comparison to the critical values e1 and e2. Thus, considering an industry in which local clusters exist—assuming that the other conditions with respect to the self-augmenting processes are given—three kinds of regions can be distinguished: e(i, r)≤e1: These regions are characterised by one stable state with a small number of firms. Thus, they contain no cluster with respect to the industry under consideration. e1<e(i, r)<e2: These regions are characterised by two stable states. Their history determines whether they have a large or a small number of firms. Thus, they might, but do not have to, contain a cluster with respect to the industry under consideration. e(i, r)≥e2: These regions are characterised by one stable state with a large number of firms. Thus, they contain a cluster with respect to the industry under consideration. These results for one region are now transformed to a situation with several regions. Each of the regions might be characterised by one of the above situations. From the findings in the literature it can be deduced that the number of regions containing a cluster in a certain industry should be small. Otherwise we would not talk about the phenomenon of

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clustering. For the regions that are characterised by two stable states those with a higher attractiveness are more likely to, but do not necessarily, contain a cluster (see Section 2.5.2). 2.6.2 Distribution of regional attractiveness Above it has been argued that the spatial distribution of firms is mainly determined by the attractiveness of regions. The attractiveness of regions is determined by several local aspects. These are, for example, the size of the population in the region, the geographic location, the local education system, public research, the availability of suppliers or customers in the region, culture, local policy and specific characteristics of the local market. These aspects differ from region to region. The way in which they differ depends on the industry under consideration and on the kinds of regions that are compared. The attractiveness of a region is the sum of all these aspects. Therefore, the way in which these factors are distributed among regions has to be discussed in order to make some statements about the distribution of attractiveness. Germany serves as a reference point, because the empirical study in Chapter 3 is conducted for the distribution of firms in Germany. The empirical study is conducted on the basis of the 441 German administrative districts (‘Kreise’). They differ significantly with respect to the number of their inhabitants. The number of regions with a particular size of the population is presented in Figure 2.4. This distribution has some similarities with a type of Boltzmann distribution that is given by N·E·exp[−ξ·E].1 The geographic location of regions plays a role for certain industries. Some industries depend on natural resources, while other firms have to be near the market that they supply. The importance of geographic location usually implies that a few regions are advantageously located. The regions next to these might still profit somewhat. Because of the transportation costs, the attractiveness of regions decreases with their distance from the resources or respective causes of advantage. Assuming a continuous two-dimensional space the number of regions with a certain distance to the most advantage place increases exponentially with distance. Thus, the distribution of attractiveness with respect to the geographic location of regions can be expected to be described by an exponentially decreasing function. 1

The Boltzmann distribution is used in physics and describes the distribution of energy states. If Maxwell’s assumption about the state space of velocities is used, a distribution is obtained that is given by N·E·exp[−ξ·E], where N is a normalising factor, ξ is a parameter and E is the variable ‘energy’.

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Figure 2.4 For each number of inhabitants (horizontal axis) the number of administrative districts in Germany (vertical axis) that contain approximately this number of inhabitants is depicted. The education system in Germany shows some differences between regions. However, in an international comparison, education varies only slightly among German regions. If universities and public research institutes matter for an industry, large difference between regions exist. Universities and public research institutes are usually located in a few regions. These regions have an advantage compared to other regions. The distribution of the number of students per inhabitant is depicted in Figure 2.5. It is approximately exponentially decreasing. The impact of specific characteristics of local markets differs very much between industries. In many industries they are of nearly no importance for the attractiveness of regions. In some industries the early or elaborated demand for new products in some locations (see, for example the case of the telecommunication cluster in Denmark reported in Dalum 1995) causes these places to be advantageous locations for firms (a discussion of this aspect is found in Porter 1990). Within Germany such differences are less apparent. In the literature no case is studied in which such a difference is important. Culture has so many facets and its influence on economic development can be so varied that it is difficult to predict the distribution of attrac-

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Figure 2.5 For each number of students per 1000 inhabitants (horizontal axis) the number of administrative districts in Germany (vertical axis) that contain approximately this number of students is depicted. tiveness among regions with respect to culture. It might be argued that if many different, statistically independent sources of fluctuations add up, the resulting variation is Gaussian distributed. However, it might be doubted whether the different aspects of culture are independent. The availability of supplier and customer firms is unequally distributed among regions. For each industry other supplier and customer industries are important. These industries might be distributed differently. Below it is found that the industrial firm distribution among regions is adequately described for most industries either by a Boltzmann distribution, by an exponential distribution or by a mixture of the two. If all industrial firm distributions among regions are added up, a distribution that is shown in Figure 2.6 is obtained. This distribution also looks like a mixture of an exponential and a Boltzmann distribution. Therefore, as a first approximation, supplier and customer industries might be assumed to be distributed according to such a mixture. The above list of factors that determine the attractiveness of regions might not be complete. Further factors can be found in the literature, such as the quality of life, local policy or the unemployment rate. However, the list and discussion above give a sufficient impression of how the

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Figure 2.6 The frequency with which different relative numbers of firms occur for all 3-digit industries and all administrative districts in Germany. attractiveness is distributed among regions. The result is that most of the factors discussed are either Boltzmann or exponentially distributed among regions. Of course, other distributions exist that are similar to these distributions and might describe the distribution of the attractiveness adequately as well. Since no empirical test for different distributions is conducted here, the relevance of other distributions cannot be excluded. Distributions with a completely different shape can, however, be excluded according to the discussion above and the empirical data shown. Among those distributions with a similar shape, a definitive choice would require a detailed empirical study which goes beyond the scope of this book (some further discussion is given in Brenner (forthcoming)). The Boltzmann and the exponential distributions seem to be natural choices and the findings in Chapter 3 confirm this choice. 2.6.3 Prediction for the industrial firm distribution To make predictions about the industrial firm distribution among regions, the distribution of the attractiveness of regions is combined with the findings about clustering. The theoretical study above has shown that two situations might appear: one in which clustering takes place and one in which no clustering occurs. Whether one or the other of these two situations appears is mainly determined by the characteristics of the respective industry, which determine the strength of the local self-augmenting processes. For both

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situations testable predictions are made here. Let us start with the situation without clustering. In the case of no clustering there is one stable state. The firm population in this stable state increases monotonically with the exogenous condition. Hence, the attractiveness of a region transforms monotonically into the size of the firm population in that region. Therefore, the industrial firm distribution P(i, ƒ) can be expected to be of the same shape as the distribution of the attractiveness of regions. The latter was found above to be a mixture of a Boltzmann and an exponential distribution. Thus, it is predicted here that the industrial firm distribution, P(i, ƒ), is a similar mixture in the case of no clustering. This prediction is tested mathematically. It is assumed that both the Boltzmann and the exponential distributions explain a part of the industrial firm distribution. Hence, the distribution is given by (2.8) if there are no local industrial clusters. The first term on the right-hand side of Equation (2.8) is an exponential distribution. The second term on the right-hand side of Equation (2.8) is a Boltzmann distribution. ξ1(i), ξ2(i) and ξ3(i) are the parameters that determine the shape of the distribution. They all depend on the industry. ξ1(i) determines the slope of the exponential distribution, ξ2(i) determines the shape of the Boltzmann distribution, and ξ3(i) determines the share of the total distribution that is explained by the Boltzmann part. This industrial firm distribution is called the ‘natural distribution’ because it is based on the assumption that no local self-augmenting processes are at work. For an industry in which the local self-augmenting processes are sufficiently strong, three kinds of regions can be distinguished according to their attractiveness. Regions that have a low attractiveness, (e(i, r)≤emin), converge to a small firm population. If the attractiveness of a region satisfies emin<e(i, r)<emax, two stable states exist. Depending on the history of the region it might be found in the lower or the higher stable state. A region that satisfies e(i, r)≥emax, converges to a large firm population. Let us consider only those regions that converge to the stable state with a small firm population. This stable state increases monotonically with the attractiveness of the regions (see Figure 2.2). There are only a few regions that do not belong to this group. Therefore, the distribution of the attractiveness among the regions concerned here is similar to the distribution of the attractiveness among all regions. As a consequence, the mathematical formulation in Equation (2.8) can be used to describe the industrial firm distribution among the regions that contain no industrial cluster. Hence, even if local clusters exist in an industry, the firm distribution among regions should be described by the natural distribution for most of the regions. This means that the above distribution (2.8) can be used as a basis for modelling the firm distribution in the case of clustering. In addition to the regions that contain no cluster in the industry under consideration, a few regions exist that contain such an industrial cluster. These are mainly those regions with a level of high attractiveness. The distribution of the attractiveness is exponentially decreasing for high values of the attractiveness, independent of the mixture between the Boltzmann and the exponential distribution that is adequate (see, e.g., Figure 2.6). The probability that a region contains an industrial cluster is decreasing for an increasing attractiveness of the region. Hence, we obtain the following statements for the firm

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distribution among those regions that contain a cluster: first, all these regions have at least an attractiveness that leads to exogenous condition e>e1, so that they contain at least firms; second, the probability of a region to contain a cluster increases with e. Therefore, there should be nearly no regions with e≈e1 that contain a cluster and more regions with e≈e2 that contain a cluster. The same holds for the number of firms. Thus, the firm distribution should increase for values of ƒ slightly below . Finally, the number of regions that have a high attractiveness decreases exponentially with e. Thus, the firm distribution should also decrease exponentially for high values of ƒ. To model such a shape of the industrial firm distribution among the regions with a local cluster, a function has to be found that is zero for low values of ƒ, increases for value slightly above a certain value and decreases exponentially for high values of ƒ. The Boltzmann distribution has the latter two characteristics. If the Boltzmann distribution is shifted so that it assigns positive probabilities only to high values of ƒ, it satisfies all the above requirements. Therefore, a shifted Boltzmann distribution is used here which is mathematically given by (2.9)

Of course, other functions could be found that have similar characteristics. However, since the Boltzmann distribution has already been used in the natural distribution, it will be

seems to be adequate to use it again here. In the following the value

replaced by a parameter, ξ4(i) because we are not able to calculate theoretically and its value will be fixed in the next chapter on the basis of empirical data. According to the above discussion, the industrial firm distribution among regions should be given by a sum of the natural distribution and a shifted Boltzmann distribution. Mathematically, such a distribution is given by (2.10)

where (2.11)

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ξ1(i), ξ2(i), ξ3(i), ξ4(i), ξ5(i) and ξ6(i) are again the parameters that determine the shape of the distribution. ξ1(i), ξ2(i) and ξ3(i) have the same meaning as in Equation (2.8). ξ4(i) determines the minimal number of firms that occur in a local industrial cluster. The Boltzmann distribution that describes the regions containing a cluster is shifted by this value. ξ5(i) determines the shape of this Boltzmann distribution. ξ6(i) determines the share of the industrial firm distribution that is described by the additional cluster term, CL(ƒ). This means that ξ6(i) describes the share of regions that contain an industrial cluster. The distribution given by Equation (2.10) is called a cluster distribution here. The natural distribution is more general than the mixed distribution. It contains the natural distribution as special cases. If ξ6(i)=0 is inserted into the cluster distribution (2.10) the natural distribution results. In addition to the natural distribution, the cluster distribution assumes that there are quite a few regions with a very large number of firms. Whenever significant clustering takes place, the cluster distribution should be the only one that is able to describe the empirical data adequately. This is tested in Section 3.2.

3 Empirical study of Germany

In the previous chapter a theoretical analysis of the phenomenon of local industrial clusters has been conducted. This analysis provides some useful insights. It separates several questions, such as the questions of why local industrial clusters exist, and when and where they emerge. Furthermore, several conclusions about the features and characteristics involved in the evolution of local industrial clusters have been identified from the theoretical modelling. However, a theoretical analysis is only able to make logical arguments. It is able to identify necessary or sufficient conditions for certain phenomena, such as local industrial clusters. It is, however, not able to state whether and to what extent these phenomena really do exist. These are empirical questions. In addition, the conditions that are identified in the theoretical approach might be satisfied by different developments or situations. In the present context, this holds especially for the local mechanisms that are responsible for the existence of local industrial clusters. There are many different mechanisms that satisfy the conditions identified in the theoretical analysis. It is not possible to determine the strength or the impact of these mechanisms theoretically. The case studies available in the literature even suggest that different mechanisms are relevant in different industries. Therefore, an empirical approach needs to address industries separately. Such an empirical study is done here for Germany. It is conducted in several steps. In the next section the data set is described and discussed. The following sections address different questions. In Section 3.2, the existence of local industrial clusters is studied. To this end, the spatial distribution of firms in each industry is compared to the predictions that have been obtained in the theoretical analysis. This provides a test for the theoretical analysis in Chapter 2. It is shown that the theory developed in Chapter 2 describes the situation in almost all industries adequately. This confirms the theoretical approach taken above and shows that, indeed, there is a general level on which clustering in different industries can be treated jointly. Furthermore, those industries in which local clusters exist are identified. A list of all industries in which local clusters can be identified is presented. It shows that about half of the manufacturing industries and a few service industries show clustering. In Section 3.3 the same is done with respect to the dynamics of the spa-tial firm distribution in each industry. Again the theoretical predictions are compared with the empirical data. Again there is quite a correspondence. The results are used to identify those industries in which local clusters disappear or clustering is weakened and those

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industries in which local clusters emerge or clustering is strengthened. Several results are obtained. First, it is found that there are many industries in which clustering is weakened, while there are only a few industries in which clustering is strengthened. This confirms the suggestion that clustering forces are only active for a short time in each industry. At this time local clusters emerge. The fact that most of them do not later disappear is a result of path-dependence rather than of clustering forces. Second, it is shown that the static analysis in Section 3.2 matches quite well with the dynamic analysis in Section 3.3. Finally, some industries in which clustering emerged or disappeared between 1995 and 2000 are identified. In Section 3.4, all local industrial clusters in Germany are identified. This results in a map of all local industrial clusters in Germany. The results are compared with the case studies available in the literature. The findings here match quite well with the literature which confirms the approach taken in this book. Some industries are discussed exemplarily. It can be shown that the analysis that is used in Section 3.2 and Section 3.3 is helpful for understanding the specific developments in certain industries, although it is not sufficient. The map of Germany’s local clusters is also used to discuss the relationship between economic development and the existence of local clusters. It is found that the existence of local industrial clusters is more long-lasting than their effect on local economic prosperity. The question of which mechanisms are responsible for the existence of local industrial clusters is addressed Section 3.5. The industries are assigned either to the class of industries that show clustering or to the class of industries that do not show clustering. Then, the characteristics of both classes of industries are studied in order to identify those characteristics that have an impact on the existence of local industrial clusters. It can be shown that the mechanisms based on spillover, process innovations and local cooperation have an impact on whether an industry shows clustering. For the mechanisms of product innovation and human capital accumulation no such impact is found. 3.1 EMPIRICAL DATA 3.1.1 Available data Two kinds of data are used in the empirical analysis that is conducted here. The main source for the empirical approach is data on the spatial distribution of firms in Germany. In addition, the Mannheimer Innovation Panel and literature on spillovers is used as a source for data about several characteristics of industries. In this section only the data on the spatial firm distribution in Germany are described and discussed. These data are used throughout the whole of Chapter 3. The other data are only used in Section 3.5 and are described there. The data set on the spatial firm distribution, which is used here, has been collected by the Bundesanstalt für Arbeit. It contains the number of firms1 for each 3-digit industry (according to the WZ73-classification2) and each of the 440/4413 administrative districts (Landkreise and kreisfreie Städte) in Germany. The data are recorded for the 30th of June 1995, the 30th of June 1997, and the 12th of April 2000.

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According to the WZ73-classification, there are 293 3-digit industries, of which 150 are manufacturing industries, 129 are service industries and 14 belong to mining and agriculture. The industries are denoted by i ( {1, 2,…, Ni}, Ni=293). The regional units are the 440/441 administrative districts, which are denoted by r ( {1, 2,…, Nr(t)}, Nr(t)=440,441). They are constructed according to administrative and historical aspects. The administrative districts contain two types of regions. On the one hand there are larger cities, called kreisfreie Städte. Most large cities, but also some smaller cities, for example Zweibrücken with 35,800 inhabitants, belong to this type. On the other hand there are districts that contain many municipalities, called Landkreise. Most of these are rural areas containing only smaller cities, and are defined such that they contain approximately the same number of inhabitants (between 60,000 and 200,000). However, some middle-sized cities and some agglomeration of cities, which have up to 500,000 inhabitants, are also assigned to this type of district. The number of firms in each industry, i, and each district, r, is denoted by ƒ(i, r, t) at each time, t(t=1995, 1997, 2000). The assignment of firms to industries is done by the firms. The assignment of firms to regions is done on the level of localities. Hence, a firm that has several branches is counted several times in the data used here. Each branch is counted at its location. In the approaches that identify local clusters in the literature, the number of firms or employment is usually compared to the ‘natural’ share of the region (see, e.g., Sforzi 1990, Isaksen 1996, Paniccia 1998 and Braunerhjelm & Carlsson 1999). This implies that the number of firms has to be studied in relation to the size of the respective region. This seems to be plausible for the approaches taken in the literature. In the context of the theory developed in Chapter 2 the situation is less clear. Arguments can be put forward for the use of both the absolute number of firms and the relative number of firms in the context of this theory. On the one hand, it is assumed here that the existence of local industrial clusters is caused by local selfaugmenting processes. These result from the symbiotic interaction among firms and between firms and local circumstances. The effects of these interactions depend on the number of firms but not on the total size of regions in terms of population or employees. Therefore, the self-augmenting processes should occur whenever the absolute number of firms exceeds a certain value. On the other hand, the total number of employees in a region might well determine the number of firms that might be established in a region, once a cluster emerges. The relative number of firms takes this into account. 1

As a unit of firm the classification Betrieb by the Bundesanstalt für Arbeit is used here. The Bundesanstalt für Arbeit assigns a number to each Betrieb. They define Betrieb according to economic considerations and location. Each Betrieb is assigned to an industry. If a firm has several branches in different municipalities, the branches are defined as separate Betriebe, while production sites in the same municipality are counted only once. 2 ‘WZ73’ stands for the classification of industries (Wirtschaftszweige) that was established in Germany in 1973 and used by the Bundesanstalt für Arbeit until 1996. 3 One administrative district was split between 1997 and 2000 so that the number of districts changed during the time of observation.

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Therefore, both the relative and the absolute number of firms are used below. To calculate the relative number of firms, a variable has to be defined that represents the size of regions. To be in line with the literature, the size of a region is defined here as the share of all employees in Germany that are employed within the region: (3.1)

where m(i, r, t) denotes the number of employees in industry, i, and region, r, at time, t. Whenever the relative numbers of firms are concerned, they are defined by (3.2)

for all regions. If the absolute number of firms is used, the shares, s(r, t), are set to This allows the same mathematical formulations for both numbers of firms to be used. 3.1.2 Limitations of the data The approach that is used here has some shortcomings that are mainly caused by the restrictions of the empirical data available and should not be ignored. First, the number of values that are available for each test of distributions is small. 440 or 441 regions, respectively, are studied, so that 440/441 values are used to test whether a certain distribution can be rejected. This means that, for example, the Kolmogoroff-Smirnov test, which is used below, requires a deviation of 26 regions to reject a distribution at a significance level of 0.1. Other statistical methods are similarly constrained by the small number of observations. A solution to this problem would be the use of more data. However, more data would only be available if either, additional countries are included in the analysis, which would imply other problems, or the size of the analysed regions is decreased. The size of regions, however, also has other implications. According to the theoretical discussion in Section 2.1.2, clusters should emerge in regions that are determined by the spatial ranges of the respective self-augmenting processes. These processes, for example spin-offs, tacit knowledge and the accumulation of human capital, are spatially bounded by the range within which people interact. The spatial sphere in which people act is mainly defined by their daily commuting. The respective spatial units are the so-called local labour market areas (a detailed discussion is given in Tappi 2003). A division of Germany into local labour market areas does not exist. All available divisions of Germany are based on administrative and historical factors. There are the so-called Raumordnungsregionen which are intended to reflect labour markets most closely. However, they have another disadvantage: there are only 97 Raumordnungsregionen. Therefore, the administrative districts are used. Of all available divisions above the community level, this division offers the highest number of regions. Nevertheless, this division of Germany might be too detailed and might divide single clusters so that they

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become less visible in the analysis. The study in Section 3.3 shows that this is the case for some industries, but that in general, the use of administrative districts is adequate. Furthermore, if using administrative districts causes a failure, it is in not identifying existing clusters and not the other way round. Hence, it makes the approach more conservative. Finally the WZ73 classification of 3-digit industries is used (2-digit industries are used in Brenner (forthcoming) where it is shown that the level of 2-digit industries is less adequate). Again an adequate classification of industries would be one which assigns all firms that benefit from each other in the form of self-augmenting processes to the same class. Such a classification of industries is not available. The WZ73 classification might assign firms to the same industry that should belong to different industries or might assign firms to different industries although they benefit from each other. The latter case might be studied on the basis of the data available here (such a study is conducted in Brenner 2000). The former problem cannot be cured with the available data. Let us assume that firms that should be assigned to two different industries are assigned to the same industry. If both industries show clustering and the clusters are of different sizes, the clustering will be less visible in the analysis below. If only one of the two industries clusters, the clustering will be less strong in the empirical analysis conducted here. If neither industry clusters, the empirical test should correctly identify the absence of clusters. Thus, the inadequate definition of industries should lead to an identification of less clustering in the analysis below. Again the restrictions of the data make the identification of local industrial clusters more conservative. The results above and their correspondence to the findings in the literature show that the limitations of the data have no crucial impact on the results. There are only a few specific industries for which the general approach that is taken here fails to identify the situation correctly. 3.2 EXISTENCE OF LOCAL INDUSTRIAL CLUSTERS The question that is to be answered in this section is the one of whether local industrial clusters exist and in which industries they exist. In the theoretical chapter (especially in Section 2.6) predictions about the industrial firm distribution were made. Two distributions have been set up: the ‘natural distribution’ that describes a situation without local clusters and the ‘cluster distribution’ that describes a situation with local clusters. The following analysis is based on statistical tests of these distributions. It is tested whether the cluster distribution, which includes local clusters, represents the empirical data significantly better than the natural distribution and whether these distributions are able to describe reality significantly well. These tests are done for each industry separately. The major results are as follows. A statistical method is developed that allows identification of industries that show clustering, and the location of these clusters (Section 3.2.1). This method is in contrast to those used in the literature because of the fact that it does not assume a certain size of clusters. Instead, the size of clusters is a result of the empirical approach. The application of the method to Germany shows that the model is able to describe the situation in nearly all industries (Section 3.2.2). Furthermore, those industries that show clustering are identified (Section 3.2.2). The

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results show that around half of the manufacturing industries show clustering. The respective findings are listed in the appendix. In addition, it shows that industries differ with respect to the number and size of local clusters. The empirical approach used here allows both aspects to be identified empirically, so that the difference between industries can be discussed (Section 3.2.3). It is found that the minimal size of clusters is often larger than is usually assumed in the literature.

Figure 3.1 Empirical industrial firm distribution among regions for the office machines industry. 3.2.1 Statistical methods Fitting the two theoretical distributions to the empirical data In Section 2.6 the industrial firm distribution among regions was denoted by P(i, ƒ). P(i, ƒ) denotes, for each industry, i, and each number of firms, ƒ, (relative or absolute numbers of firms might be used) the probability of finding the respective number of firms in a randomly chosen region. If many regions are considered and the number of regions that contain a certain number of firms are counted, a frequency distribution should result that is similar to P(i, ƒ). For example, let us consider the industry producing office machines. There are 119 administrative districts that contain one firm in this industry. There are 53 districts that contain two firms and so on. This can be displayed in a figure, as in Figure 3.1. The frequency is depicted on a log-arithmic scale because it usually decreases exponentially (a linear function seems to fit the graph quite well for small firm numbers). The theoretical distributions that are discussed in Section 2.6 should be able to describe this distribution if the theory developed in Chapter 2 is adequate. Two theoretical distributions have been proposed. One is a combination of an exponentially decreasing distribution and a Boltzmann distribution. It is called a ‘natural’ distribution, and is denoted by Pn(i, ƒ) and it assumes that no local clusters exist. An example is depicted in Figure 3.2. The other theoretical distribution is a natural distribution to which a shifted Boltzmann distribution is added which describes clusters. This added distribution only assigns probabilities greater than zero to high numbers of firms. It

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causes the distribution to increase for a certain number of firms, so that it is bimodal. The difference between the two distributions can be seen in Figure 3.2. To study the two theoretical distributions, they are first fitted to the empirical data. They contain 3 and 6 parameters, respectively. The fit-

Figure 3.2 Theoretical industrial firm distributions among regions that result from fitting the natural distribution (circles) and the cluster distribution (crosses) to the empirical distribution of firms producing office machines. ting of the parameters is done on the basis of maximising the likelihood of predicting the empirical data (Figure 3.2 shows such a fitting to the data depicted in Figure 3.1). Powell’s method is used to maximise the likelihood function4. This fitting is done for each year separately. Therefore, the dependence of the variables and parameters on the time, t, is omitted in the following for convenience. In the distributions that are defined in Section 2.6, general parameters, ξ1(i), ξ2(i), ξ3(i), ξ4(i), ξ5(i) and ξ6(i), are used. The theoretical firm distributions are deduced for one region, while 440/441 regions are studied here. These regions differ in size. As long as the absolute numbers of firms are studied, this does not matter. For the relative numbers of firms, the size of a region matters. There are two possibilities for dealing with this fact. First, the theoretical distributions might be defined dependent on the relative number of firms instead of the absolute numbers ƒ. This is not possible because the functional forms that are used are defined for natural numbers and because it would make a comparison with the empirical data, in which only certain values can appear, very difficult. Second, the theoretical distributions have to be stretched according to the size of the region. The natural distribution consists of two terms. The parameters are chosen in such a way that the average value of each term increases linearly with the size of the region s(r). This is obtained by defining the natural distribution as the probability of finding ƒ firms of industry i in region r, which is given by (compare Equation (2.8)) 4

A description of Powell’s method and the implementation on the computer can be found in Press, Teukolsky, Vetterling & Flannery 1988. It is based on the gradient method of finding the minimum of a function.

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(3.3)

with (3.4)

and (3.5)

is the total number of firms in the industry under consideration, which is defined by . The specification of the distribution is chosen such that is the average number of firms predicted by the first term and is the average number of firms predicted by the second term (this is shown in the appendix). Hence, the average number of firms that is predicted for each region increases linearly with the share, s(r), of the region. In the same way the theoretical cluster distribution (2.10) is adapted. It is defined as the probability of finding ƒ firms of industry i in region r and is given by (3.6)

where (3.7)

and (3.8)

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The first two terms are identical to the natural distribution (3.3), except for the factor (1−ξ3(i)−ξ6(i)) in front of the exponential part. The last term of the cluster distribution (3.6) is defined in a similar way to the second term with the form of a Boltzmann distribution. It is a shifted Boltzmann distribution which is zero for all numbers of firms below

and has the shape of a Boltzmann distribution for all numbers

. Hence, this term represents the clusters that are of firms above existing. The mean value again increases linearly with the share, s(r), of a region (this is shown in the appendix). The parameters, and ξ6(i), are restricted in the analysis below. The function CL(ƒ) is designed to describe the local clusters existing in an industry. This implies several characteristics of this function. First, function CL(ƒ) should only describe a few regions. Local clusters have to be the exception. We would not talk about ‘local industrial clusters’ if they occurred in most of the regions. Hence, the share of the regions that contain a cluster has to be small. The above theory does not inform us about how many regions might contain a cluster. Therefore, the maximal number of clusters has to be arbitrarily chosen. It has to be chosen in order to avoid the possibility that the cluster term CL(ƒ) shifts in the empirical fitting downwards and becomes similar to the second term on the righthand side of Equation (3.7). Hence, 10% is assumed to be the maximal share of regions that contain a cluster. This implies that ξ6(i)≤0−1 has to be satisfied. Second, only those regions with a high number of firms should be classified as local industrial clusters. Nevertheless, the line between clusters and other regions should be empirically determined. It is represented by the parameter

. A value of

would imply that all regions containing a number of firms above average would be called clusters. This seems to be inadequate. In the literature a value of is used (see Isaksen 1996). Here, a more complicated restriction is chosen for the parameter . According to the analysis in Section 2.6, every region that includes a cluster of the industry under consideration should contain more firms than any region that does not contain such a cluster. This implies that the part of the distribution described by the last term CL(ƒ) in Equation (3.6) should be separated from the rest of the distribution. In reality such a separation cannot be expected because regions differ with respect to factors other than their attractiveness (see the discussion in Section 2.4.2). Nevertheless, the overlapping of the two parts of the distribution should be small. The amount of overlap is given by the number of regions that contain a number of firms higher than according to the first and second part of the cluster distribution. This number is denoted by ncl, n(i) here. It should be small compared to the number of regions that contain industrial clusters. Otherwise, most of the regions containing many firms could be explained without considering the phenomenon of clustering. Again, how small this overlap should be cannot be obtained from the theory. Therefore, arbitrarily to those values for which at least

is restricted

of the regions that contain a number of

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firms higher than are explained by the cluster part CL(ƒ) of distribution (3.6). This is reached by the condition (3.9)

is, of course, determined empirically by fitting the parameters. The exact value of For all industries the two distributions, the natural and the cluster distribution, are fitted to the empirical data. For each parameter set, the likelihood value can be calculated for the data on each industry, i. The likelihood value is the probability that the empirical situation occurs according to the theoretical distribution. It is given by (3.10)

and the analogous equation for the cluster distribution (replacing ‘n’ by ‘c’). The maximum likelihood is the maximal value of Ln(i) and Lc(i), respectively, that can be reached for any parameter set. It is denoted by and , respectively. The respective parameter sets determine those distributions that describe reality best. An example of a fitted natural and cluster distribution is given in Figure 3.2. Comparison of the two theoretical distributions The cluster distribution contains 6 parameters, while the natural distribution contains only 3 parameters. Furthermore, the natural distribution is a special case of the cluster distribution. Therefore, the cluster distribution will always fit reality better, so that is satisfied for all industries. The aim of the study that is conducted here is to find out whether and in which industries local clusters appear. The additional term in the cluster distribution should describe such clusters. Thus, the cluster distribution should describe the empirical data significantly better than the natural distribution if clusters exist. The likelihood ratio test is used to check this for each industry. The value (3.11) is calculated for each industry. Above it was stated that the cluster distribution always describes reality better than the natural distribution because it is more general due to the additional parameters. However, the extent to which it describes reality better might vary. λ(i) measures this difference in the fitting of the data. Statistical theories tell us that λ(i) can be expected to follow a X2-distribution if the additional term in the cluster distribution does not really make the model more adequate (see Mittelhammer 1996). Whether λ(i) falls into this distribution can be tested. Hence, the hypothesis that the cluster distribution is not more adequate than the natural distribution can be tested. If it is

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rejected, the industry is said to be clustering. The results for each industry, each year studied and both the absolute and relative numbers of firms are given in Table A.1 in the appendix. Testing the adequacy of the resulting distribution The likelihood ratio test answers the question of which distribution describes the empirical data better. However, it does not answer the question of whether they describe the empirical data adequately. To test the adequacy of the distributions, the distribution that is more adequate in each industry is compared to the empirical distribution. To test whether the theoretical distribution and the empirical distribution deviate from each other significantly, the Kolmogorov-Smirnov test is used. The KolmogorovSmirnov test compares the cumulative distribution function of a theoretical and an empirical distribution. It makes a statement about the maximal distance of these two functions that should occur with a certain probability if the two distributions are identical. Hence, if the distance is too large, the hypothesis that the theoretical and the empirical distribution are identical can be rejected. To use the Kolmogorov-Smirnov test, the cumulative distribution function has to be calculated for the theoretical and the empirical data. Thus, for each number of firms, ƒ, the expected frequency of regions that contain at most such a number of firms has to be calculated. The probability of each region containing at most ƒ firms is given by and respectively. Thus, the cumulative distribution function is given by

, (3.12)

and (3.13)

respectively. The empirical cumulative distribution function is calculated according to (3.14)

where (3.15)

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The maximal distance between the two cumulative distribution functions is calculated according to (3.16) If this test leads to the rejection of the hypothesis that both distributions are identical, none of the two distributions is able to describe the empirical data. These cases are marked by an entry ‘none’ in Table A.1. 3.2.2 Existence of clusters in industries The above analyses are conducted for each of the 293 3-digit industries and for the years 1995, 1997 and 2000 separately. The results are given in Table A.1 in the appendix. Each industry is classified at each time into one of three categories: none of the distributions (‘none’): industries for which the comparison between the theoretical and the empirical distribution leads to a rejection of the theoretical distribution natural distribution (‘nat’): industries for which the natural distribution is not rejected (significance level: 0.1) and the cluster distribution does not describe the empirical data significantly better than the natural distribution cluster distribution (‘cl’): industries for which the cluster distribution describes reality significantly better than the natural distribution and is not rejected (significance level: 0.1) Adequacy of the modelling First of all the statistical analysis that is conducted here can be seen as a test of the predictions that have been made in Section 2.6. Hence, it is a test of the theoretical analysis in Section 2.6 and the whole of Chapter 2. If an adequate model has been found, the two theoretical distributions should describe reality for almost all industries. Although the cluster distribution seems to be quite general with its six parameters, it restricts the shape of the distribution tremendously. For example, a uniform distribution of firms in space cannot be adequately described by this theoretical distribution. Furthermore, all parts of the theoretical distribution (3.6) decrease exponentially for larger numbers of firms. If this does not hold in reality, the distribution should be rejected. Hence, a correspondence with reality is not an automatic result and should be seen as a confirmation of the modelling. The correspondence is tested with the Kolmogorov-Smirnov test, as described above. Only for 17 industries is the theoretical distribution rejected on a significance level of 0.01 for both the relative and the absolute numbers of firms. These are the wine industry, air conditioners, repair of motor vehicles, electricians, other shops, German post, transportation of people, insurance, restaurants, chimney sweeps, hairdressers, private educational institutions, physicians in private practice, chartered accountants, architects, other public administration, and social security. This confirms the approach that is taken here. First, the number of industries for which the theoretical distribution is rejected is small. Second, 15 of these 17 industries are service industries, although service industries

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do only account for 130 of the 293 industries. The theoretical distribution that is used here ignores forces that may cause firms to be uniformly distributed among regions. These forces have been ignored because they oppose the forces that are responsible for the existence of clusters. Uniform spatial firm distributions should be expected if firms have to be at the place at which their goods are demanded and demand is proportional to the number of people at a location. This is the case for quite a number of service industries, such as shops and physicians. Many of these industries fail to be explained by the theoretical distribution that is tested here. The theoretical distribution used might be expanded to include these industries. However, since the phenomenon of local industrial clustering is studied here, such an expansion does not seem to be necessary. The theoretical distribution used seems to describe adequately all industries that might cluster. All industries for which the theoretical distribution is rejected are excluded from the analysis below. In principle, this means that some industries that are clustering might be omitted. Most of the industries that are omitted, however, are industries in which the firms are approximately uniformly distributed among regions. It does not seem to be the case that potentially clustering industries are omitted by the exclusion of the 17 industries that are rejected by the Kolmogorov-Smirnov test. Existence of clusters Since many case studies of local clusters have been reported in the recent literature, proving their existence seems to be an unnecessary endeavour. However, the literature only shows that there are regions containing more firms, employment or economic activity in a certain industry than other regions. This might be a stochastic phenomenon caused by a random spatial distribution of firms. Ellison and Glaeser (1997) have shown that the concentration of firms in certain regions is more than the result of a random distribution. However, they have not particularly focused on the existence of local clusters. Their result might still be explained by assuming forces that favour regions already containing many firms. Ellison and Glaeser (1997) do not require the existence of a critical mass that separates two types of regions. The approach that is taken here shows that in 148 industries such a separation can be found empirically. Whether this result is caused by ‘natural’ conditions or local mechanisms as it is assumed in the theoretical approach in Chapter 2 is not proved so far. This will be discussed in more detail below. Let us now consider the 276 3-digit industries for which the theoretical spatial firm distribution is not rejected for the relative and the absolute number of firms at the same time. Do clusters exist in these industries? This question is answered here through a comparison of the natural and the cluster distribution. The cluster distribution is assumed to be adequate if it describes reality sufficiently better than the natural distribution (details are given above). The results are given in Table A.1. For many industries the results differ between the years that are analysed. In Section 3.3 these differences are analysed. The results show that a number of these differences is caused by the statistical method that is used here. Although the likelihood values for the fitting of the distributions to the data from different years do not vary much, these variations are large enough to change the results of the statistical test. The statistical test that is used here is very sensitive to changes in the empirical spatial firm distribution. Considering the parameters that are fitted, the major differences between the years appear

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in the cluster part CL(ƒ). In particular, the parameter, tremendously between the years.

, varies for some industries

defines the minimal number of firms that a region has to contain to be called a local cluster. Often there are different values of that describe reality similarly well. This means that there exist different points of separation between local clusters and other regions that explain the em-pirical data. This might be caused by the fact that the industries studied here contain sub-industries with independent cluster formations. Another possible cause is the different strength of local self-augmenting mechanisms that cause different points of separation in different regions. On the basis of the approach used here only speculation about the causes is possible. The variations between different years are further examined in Section 3.3. Here the results for different years are pooled. In the following, each industry is characterised by the distribution that is found to be adequate for most of the years studied. As a consequence, the cluster distribution is found to describe the empirical data significantly better for 148 of the 293 industries for at least either the relative or the absolute number of firms. This proves empirically that local agglomeration of industries exists, at least in the form predicted by the theory developed in Chapter 2. Alternative causes for clustering The analysis conducted here identifies 148 industries for which the spatial distribution of firms is adequately described by the cluster distribution. This means that the empirical situation in these industries is in line with the predictions for an industry that shows clustering. However, it does not prove that local industrial clusters exist. There are other reasons that might cause the same industrial firm distribution among regions. Three such alternative reasons can be distinguished. First, agglomeration might be caused by industry-specific characteristics. It might be very advantageous for the firms in an industry to be located in a certain region or a few regions. As a consequence, agglomeration will appear in these regions. For example, the packaging industry agglomerates in only one region: Hamburg. The fact that Hamburg dominates overseas trading in Germany is an obvious explanation for this agglomeration. Second, agglomeration might be caused by the fact that the firms of the industries benefit from being located in large cities in such a way that agglomeration occurs in these places. In such a situation the agglomeration can be expected to have certain characteristics. On the one hand, the cluster distribution should describe the spatial distribution of the absolute numbers of firms adequately, while the same does not necessarily hold for the relative numbers of firms. On the other hand, the clusters that are identified by the approach used here should be located in the largest German cities, meaning Berlin, Hamburg, Munich, and so on. These characteristics are found for 46 of the 72 service industries that are adequately described by the cluster distribution. This means that for most of the service industries, the cause that is outlined here holds. Examples are department stores, chemical cleaning, libraries, betting offices and lotteries, and unions.

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Third, agglomeration might be caused by natural circumstances, such as the availability of certain resources in a few regions. Examples are the fishing industry or potash salt mining. In both cases, as well as in other industries, certain natural circumstances are necessary for the activity of firms. If these circumstances are only present in a few regions, the respective firms will agglomerate in these regions. Industries that show clustering For 148 industries the cluster distribution is confirmed (see Table A.1 in the appendix). Above it has been suggested that this result can be caused by different factors. In the context of local industrial clusters, we are only interested in those agglomerations that are caused by local self-augmenting processes. In principle it is possible to discuss all 148 industries with respect to the causes for the existence of agglomeration. They could be classified respectively. However such a classification would be subjective and requires an examination of the history of each of the industries. For some industries a further discussion is provide in Section 3.4.3. There it is shown that a combination of a general approach, as is taken here, and some industryspecific, often case study-based, knowledge is very fruitful for the understanding of industrial dynamics. However, such a study is not possible for all 148 industries given the aim of this book. Therefore, the study conducted here proceeds on a general level. Nevertheless, we restrict further analysis to certain industries. 71 of the 148 industries for which the cluster distribution is confirmed are manufacturing industries, 4 are agricultural industries, 1 is a mining industry, and 72 are service industries. It has been argued above that many of the service industries agglomerate in large cities. Furthermore, agriculture and mining require natural resources. Therefore, within these sectors there are many industries in which agglomeration appears that is not caused by local selfaugmenting processes. As a consequence, further analysis is restricted to the 71 manufacturing industries and the 26 service industries that do not cluster in the largest cities only. A list of these is given in Section 3.4.2 together with the locations at which these industries cluster. For some of these industries natural reasons seem to cause the agglomeration, for example, the quarry stones industry and fish processing. However, this is speculation. Let us consider for example the shipbuilding industry. Natural circumstances are important in this industry. Hence, the agglomerations that are found seem to be caused by natural circumstances. However, in Section 3.3 it is shown that clustering increased in this industry between 1995 and 2000. Such a development cannot be explained by natural circumstances because these circumstances do not change. It can be concluded that two forces are active that cause the existence of clusters: natural circumstances and local selfaugmenting processes. This shows that each case has to be carefully examined to make a final statement. This is not possible here, so that we have to accept that some clusters that are identified here occur for other reasons. In the manufacturing sector there are not many industries for which obvious other causes can be put forward. The situation is somewhat different in the service sector. Except for the concern about other causes for the existing agglomeration, the clustering for the industries listed in Section 3.3 is proven statistically. The same does not hold in the opposite direction. This means that an existence of local clusters in some of

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the industries for which the cluster distribution has not been confirmed is possible. The likelihood ratio test only allows rejection of the hypothesis that no clustering takes place. Hence, there might be industries that are not identified by the approach taken here but nevertheless show clustering. 3.2.3 Number and size of local industrial clusters The empirical study conducted here not only allows identification of those industries in which local clusters exist, it also provides information about the number and size of these clusters. This information is contained in the parameters that are fitted to the empirical data. determines the minimal number of firms that form a cluster, while ξ6(i) determines the number of regions that contain such a cluster. These parameters differ significantly between industries. Hence, the phenomenon of clustering differs between industries in a way that is worth discussing. Size of local industrial clusters Above it has been assumed and confirmed that regions containing a local cluster can be described by a shifted Boltzmann distribution with a minimal number of (see the cluster term CL(ƒ) in Equation (3.6)). Hence, can be seen as the critical number of firms that constitute a cluster. It is formulated either in relative or absolute terms. In the case of relative numbers of firms, this critical value differs between regions, while it is the same for all regions in the case of absolute numbers of firms. In the literature, similar critical numbers of firms or employment are used to identify local industrial clusters. There the critical number is usually defined in relative terms. Isaksen (1996), for example, identifies clusters according to the condition that there are at least three times as many employees in an industry and region as there should be according to the total number of employees in the region. This relates to a value of . In the approach that is taken here, this critical value is obtained as a result of fitting the theoretical model to the empirical data. Thus, information is obtained about how large clusters are. The cluster distribution that is fitted to the data is bimodal with two parts: one that is described by the natural distribution (3.3) and one that is described by function CL(ƒ). Ideally, these two parts of the distribution would rarely overlap. Such a situation is depicted in Figure 3.2. In such a case, represents the critical value that separates the numbers of firms in a region that we call a local industrial cluster from the other numbers of firms. The parameter, , defines this critical number of firms in relation to the average number that should be located in a region either according to the size of the region (in terms of total employment) or according to the number of regions. The values of

range from

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3 to 330. However, values between 3 and 20 are found most frequently. Values larger than 20 only appear in those cases in which one region contains a very large agglomeration of firms and is identified as the only local cluster. Hence, for a few industries the value that is found here fits the value assumed in the literature quite well. However, for many industries, is much higher than it is assumed to be in the literature. Hence, the number of local industrial clusters that exists is overestimated in the literature. Furthermore, such a critical value for the identification of local clusters is applied equally to all industries in the literature (see, e.g., Sforzi 1990, Isaksen 1996, Paniccia 1998 and Braunerhjelm & Carlsson 1999). It was shown above that not all industries contain local clusters. This reduces the total number of clusters further. In the next section all clusters that exist in Germany are identified according to the approach taken here. The quite large values of make the phenomenon of local industrial clusters even more significant. It shows that in some industries there is a large difference between the economic activity in a few regions and the economic activity in all other regions. The represents the ratio between the average number of value firms in local clusters and the average number of firms in any region. It shows that local clusters contain, on average, between 3 and 30 times more firms in the industry under consideration than the average regions. In a few cases the difference is even larger. The differences in the size of clusters between industries might be caused by different market sizes, different strengths of local self-augmenting processes, and different histories. In addition, the study is restricted to Germany although many industries face global markets. On a global level the results might differ significantly. Furthermore, the results for the size of clusters are quite sensitive to changes in the firm population. Therefore, they are an inadequate tool for making any conclusions about the characteristics of industries. The interpretation of the results that are obtained here is restricted to the statement that the size of clusters varies significantly between industries and is, in general, above the size used in the literature to identify local clusters. Number of local industrial clusters Besides the size of clusters, the empirical approach used above also predicts the number of clusters in each industry. ξ6(i) represents the probability measure of the distribution (3.6) that falls on the cluster part, CL(ƒ), of the distribution. Hence, ξ6(i) represents the probability of a region containing an industrial cluster. Multiplying ξ6(i) by the total number of regions we obtain the number of clusters that should be expected according to the theoretical distribution (3.6) that is fitted to the empirical data. This number does not have to correspond to the numbers of clusters that are found according to the condition (3.17) that is used below to identify local industrial clusters in Germany. A deviation between the two values might have two causes. First, the theoretical spatial firm distribution consists of two parts: an exponentially decreasing ‘natural’ part and a part that represents

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clusters. According to the exponentially decreasing part, there should be a few regions that contain many firms. Using Condition (3.17), some of these regions might be classified as clusters, although they are not caused by local mechanisms but by local advantages, exogenous influences and chance. Second, the procedure of fitting the theoretical distribution to the empirical data does not guarantee that in each part of the distribution the number of observations fits the number of predicted observations. If the difference is too large, the Komolgorov-Smirnov test will reject the theoretical distribution. Smaller deviations, however, occur. As a consequence, the number of clusters identified according to Condition (3.17) might deviate and is often higher than the number of clusters that is explained by the theoretical model. This leads to a distinction between the number of regions that contain a cluster and the number of regions that satisfy Condition (3.17). There are regions that contain a large number of firms because of the phenomenon of clustering and there are regions that contain a large number of firms because of local advantages. Condition (3.17) which is used below for the identification of local industrial clusters in Germany is not able to make this distinction. As a consequence, the general empirical approach that is applied here might misclassify some regions. Additional information should be taken into account if the correct regions are to be identified. This will be further discussed below. 3.3 DYNAMICS OF LOCAL INDUSTRIAL CLUSTERS The data available here allow only partly for an analysis of the emergence and life cycle of local industrial clusters. Local industrial clusters usually emerge in new industries. It takes some time before new industries are adequately reflected in the official classifications of industries. Hence, data on new industries is not available. Furthermore, the time span of 5 years is quite short. Nevertheless, a few aspects can be studied. The analysis conducted here will focus on two aspects: First, whether the spatial distribution of firms switches between the natural and the cluster distribution and how this can be interpreted will be examined. Second, whether the changes in the number of firms in each region are in line with the predictions of the theoretical approach in Section 2.6 will be investigated. The major results are as follows. Again the predictions that were made in Chapter 2 are confirmed (Section 3.3.2). This increases the support for the model that was developed. It is furthermore found that there are more industries with a tendency towards the disappearance of local clusters than industries in which local clusters emerge or strengthen (Section 3.3.1 and 3.3.2). This is interpreted as evidence for the claim that local industrial clusters emerge during a short period of time while they might face dissolving forces for a long time. A comparison of the dynamic analysis in this section with the static analysis in the last section leads to the following result (Section 3.3.3). There are many industries in which local clusters exist and are strengthened over time and there are many industries in which no clusters exist and the dynamics are such that no clusters emerge. Hence, in most industries the situation with respect to the existence of clusters is found to be very stable. Only in a few industries does the situation change at any point in time. In addition, it is found that all industries that show a disappearance of

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local clusters are characterised by a decreasing total number of firms (one exception can be explained by industry-specific developments). Hence, a decrease in the number of firms seems to be a necessary condition for the disappearance of local clusters. 3.3.1 Switches in the spatial firm distribution Table A.1 shows that in many industries switches between the two theoretical distributions, the natural and the cluster distribution, occur. These switches might have different reasons that lead to different interpretations. On the one hand, the characteristics of the industries might change in such a way that clustering emerges or disappears. On the other hand, the switches might be statistical artefacts. Switches are observed for approximately one sixth of the firm distributions studied. This number is too high to be caused by changes in industrial characteristics. Therefore, whether the switches might be a statistical artefact is first studied here.

Table 3.1 Specific sequences of spatial firm distributions and the frequency with which they are found in the empirical analysis. distribution in

number of cases in

1995

1997

2000

manufacturing

all industries

natural

natural

cluster

9

18

natural

cluster

natural

8

12

natural

cluster

cluster

10

14

cluster

natural

natural

15

24

cluster

natural

cluster

5

7

cluster

cluster

natural

14

26

Statistical analysis of switches To understand how a statistical artefact might occur, let us consider a case in which the cluster distribution fits the empirical data better than the natural distribution. Let us furthermore assume that the likelihood ratio is just greater than the value necessary for a statistically significant result. Small changes in the firm population might easily move the likelihood ratio across the significant value in such a case. In the following analysis, each industry is considered as a separate case. Furthermore, the analyses of the relative and the absolute numbers of firms are seen as separate results. Hence, there are 586 observations: 293 industries that are studied with respect to the relative and the absolute number of firms. All cases in which the theoretical distribution is rejected in at least one year are excluded. Furthermore, the statistical analysis is restricted to those cases in which not the same distribution results in all three years. This restriction is done in order to concentrate on the reasons for changing distributions. 101

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cases remain. These might show 6 different sequences of results. The possible sequences are listed in Table 3.1 together with the number of cases in which they are observed. If the switches between the two distributions are a statistical artefact, all six sequences should appear with the same frequency. Alternatively, the switches might be caused by changes in industry-specific characteristics. It is unlikely that an industry changes between the existence of clusters and no existence of clusters twice within 5 years. Therefore, the spatial firm distribution should change in one direction within a period of 5 years more frequently than changing to and fro if changes in the characteristics of the industry cause the changes in the distribution. Therefore, industry-specific changes imply that mainly the sequences ‘natural-cluster-cluster’, ‘naturalnatural-cluster’, ‘clusternatural-natural’ and ‘cluster-cluster-natural’ appear. The two possible causes for the changes that are observed can be examined statistically. To this end, the frequency of the sequences ‘naturalcluster-natural’ and ‘cluster-natural-cluster’ is compared to the total frequency of switches. The assumption of a statistical artefact predicts a share of one third. The assumption of changes in industry-specific characteristics predicts a very small share. 19 of the 101 switches are reported to be of the kind ‘natural-cluster-natural’ or ‘cluster-natural-cluster’ in Table 3.1. This corresponds to a share of 18.9%. In the case of the manufacturing industries the share is 21.3%. These values are neither around 33.3% nor very small. Reality seems to fall between the two predictions. The latter prediction cannot be tested statistically because it is not clearly formulated. The former prediction can be tested by comparing the number of switches of the kind ‘natural-cluster-natural’ or ‘cluster-natural-cluster’ with the number of other switches. The latter should occur twice as often as the former if the switches are a statistical artefact. This can be rejected (X2 test, significance level: 0.05) if all industries are considered, while it cannot be rejected for the manufacturing industries. Thus, it can be concluded that in the manufacturing industries, only a few ‘real’ switches are observed. Most of the 61 switches that appear in these industries are statistical artefacts. This makes it impossible to identify the industries that change their characteristics in such a way that clustering emerges or disappears by simply looking at changes in the form of the spatial firm distribution. ‘Real’ switches However, there might be a few cases of ‘real’ switches. This view is supported by the fact that the share of 21.3%, which is calculated above, is below, although not significantly, the 33.3% predicted by a statistical artefact. This is further confirmed by a comparison of the number of industries in which clustering emerges and the number of industries in which clustering disappears. According to Table 3.1 the former is observed in 19 manufacturing industries, while the latter is observed in 29 manufacturing industries. The difference between the two values is statistically only slightly significant (X2 test, significance level: 0.1). The number of cases in which the form of the fitted distribution switches twice between the natural and the cluster distribution is 13. These cases are likely to be caused by a statistical artefact, assuming that the characteristics of industries do rarely change twice in different directions within 5 years.

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It might be concluded that the relevance of clustering is decreasing. However, the empirical analysis that is conducted here only shows that the phenomenon of local industrial clusters disappears in some industries. In other industries local clusters appear to be stable, as the analysis that is conducted in the next subsection confirms. 3.3.2 Dynamics within regions In Section 2.3.2 some predictions about the dynamics of the number of firms within regions have been made based on the theoretical modelling of local industrial clusters. To this end, four stages in the evolution of local industrial clusters have been distinguished. In the first stage the only possible prediction was the increase of the number of firms in nearly all regions. Above it has been argued that it is difficult to study the emergence of local clusters on the basis of the data available here. New industries are not reflected in the industrial classification that has to be used here. Hence, the following analysis will be restricted to the predictions for the other three stages of the evolution of local industrial clusters. In the second stage, the self-augmenting processes lead to the separation of regions into those in which an industrial cluster evolves and those in which no such clusters appear. During this phase the theory predicts a change in the number of firms, which depends on the number of firms existing in a region as depicted in Figure 3.3. In regions with a small number of firms this number will increase. Regions that have a somewhat higher number of firms that is nevertheless below a critical value will experience a decreasing number of firms. Above the critical value the number of firms will increase again, while regions with a very high number of firms should experience decreasing numbers of firms. The latter regions should be rare. The third phase is characterised by a quite stable situation. Only minor fluctuations should occur in this phase. These should be randomly distributed. No structural dependence of changes in the firm population on the number of firms in a region should be observed. The fourth phase has been defined as the disappearance of clusters. This is usually caused by a diminishing of the market for the respective goods. In this case, regions with a large firm population will experience a strong decrease in the number of firms, simply because they contain more firms. Empirical method To test these predictions the dependence of the empirical changes on the number of firms is compared with the predictions. The most complex predictions result for the second phase. They are depicted in Figure 3.3. The simplest mathematical formulation of a function that has the form depicted in Figure 3.3 is a polynomial of third order. Therefore, a regression analysis is conducted for such a function. The independent variable is the number of firms, ƒ(r, i, t0), at time, t0 (t0=1995, 1997). The dependent variable is the change of the number of firms from time t0 to time t1 (t1=1997, 2000), given by ƒ(r, i, t1)−ƒ(r, i, t0). The regression function is given by

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Figure 3.3 Schematic representation of the theoretically expected change of the number of firms in regions in the second phase of the evolution of local industrial clusters. (3.18) α0, α1, α2 and α3 are the regression parameters. The regression is conducted for each industry i and each pair of times (t0, t1) {(1995, 1997), (1995, 2000), (1997, 2000)} separately. The regression is furthermore done for the relative and the absolute numbers of firms. Hence, altogether there are 1758 regressions. It is impossible to discuss each regression and its results. Therefore, the results have to be structured in some way. To this end, the theoretical predictions are transformed into predictions about the regression parameters. Parameter α0 reflects the average development in the whole industry. If the number of firms in an industry increases (decreases), the value of α0 will be positive (negative). Hence, α0 is unimportant for the test of the theoretical predictions about clustering. In industries that show no clustering and in which no other forces influencing the spatial firm distribution are at work, only random fluctuations should be observed. This means that the changes in the number of firms should not depend on the size of the firm population in a region. It implies that α1, α2 and α3 should equal zero. However, in many industries a lot of regions contain no firm. In these regions a decrease of the number of firms is impossible. The average change in these regions has to be positive even if the total number of firms is decreasing. This fact causes α1 to be negative in some industries. Hence, α2 and α3 are expected to be zero and α1 is expected to be either zero or negative for all industries that show no clustering or similar other forces. According to the

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argument above, the same holds for the third phase of the evolution of local industrial clusters. In the second phase of this evolution, dynamics similar to those depicted in Figure 3.3 can be expected. These are described by negative values of α1 and α3 and a positive value of α2. It has been argued above that there might be no region containing a number of firms high enough to be described by the last term in Equation (3.18). In such a case the last term is not necessary to describe the data and α3 will not significantly differ from zero. Hence, the prediction for the second phase reads as follows: α1 should be significantly negative, α2 should be significantly positive, and α3 should at least not be significantly positive. The same holds if clustering is for some reason strengthened. In the fourth phase of the evolution of local industrial clusters the number of firms will decrease in all regions, except in some regions that contain very low numbers of firms. Therefore, we expect that at least one of the parameters, α1, α2 and α3, is significantly negative while none of them is significantly positive. Above it has been discussed that there are also industries in which the firms tend to be uniformly distributed in space. This means that there are forces that tend to equalise the numbers of firms in regions. Consequently, the number of firms will decrease in regions with large firm populations and increase in regions with small firm populations. This is reflected by a decreasing function. Hence, one of the regression parameters, α1, α2 and α3, should be significantly negative while all others should at least not be significantly positive if the firms tend to be uniformly distributed in space. As a consequence, three empirical situations can be distinguished: fluctuations: If the dynamics are driven by fluctuations only, α2 and α3 should not be significantly different from zero, while α1 should not be significantly positive. clustering: If clustering emerges or is strengthened, α1 should be significantly negative, α2 should be significantly positive, and α3 should not be significantly positive. equalising: If the spatial firm distribution is driven towards a uniform distribution, none of the parameters, α1, α2, or α3, should be significantly positive, while at least one of them should be significantly negative.

Table 3.2 Classification of all dynamics in the 293 industries between the years 1995, 1997 and 2000 with respect to the relative and absolute number of firms. classification of the dynamics

number of cases relative firm numbers

absolute firm numbers

95−97

97−00

95−00

95−97

97−00

95−00

fluctuations

210

215

212

197

167

185

clustering

35

34

30

37

38

41

equalising

56

30

64

90

51

76

unclear

31

29

29

30

60

44

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It is important to recognise that the two situations labelled as ‘fluctuations’ and ‘equalising’ cannot be clearly separated. There is some overlap between these classes, meaning that some situations fall into both categories. Furthermore, situations exist that do not fall in any of the classes listed above. Below these situations will be called ‘unclear’. Regression results Above it has been stated that this empirical approach is applied to the relative and the absolute numbers of firms separately. It could be expected that they lead to similar results. This is not the case. Dynamics that fall into the category ‘clustering’ are mainly observed for relative numbers in manufacturing industries and for absolute numbers in service industries. The total of dynamics that are classified into each of the above classes are given in Table 3.2. Table 3.2 clearly shows that most dynamics that are observed fall into the category ‘fluctuations’. In most industries the spatial firm distribution is quite stable. This might be caused by the short period of time that is studied. However, the results do not differ significantly between the time spans from 1995 to 1997 and from 1997 to 2000 and the longer time span from 1995 to 2000. This finding contradicts the proposition that the high number of stable spatial firm distributions is caused by the quite short time span that is analysed. Equalising forces might be caused by fluctuations, by the disappearance of local clusters, or by a tendency of an industry to be uniformly distributed in space. It is not possible to distinguish between these three mechanisms on the basis of the above analysis. However, independent of their causes, dynamics that are classified as ‘equalising’ tend to destroy the phenomenon of clustering. More such dynamics are found than dynamics that are classified as ‘clustering’. This confirms the above finding that on an overall level, the phenomenon of clustering seems to be weakened. However, quite a number of cases exist that are classified as ‘clustering’ in Table 3.2. This proves that clustering forces still exist in some industries and that the above finding of a decreasing number of industries for which the existence of local clusters can be proved should not be generalised. Industries seem to differ significantly in this respect. 3.3.3 Comparison of the static and the dynamic analysis Several cases have been identified in which the dynamics are classified as ‘clustering’. According to the theoretical analysis such dynamics should appear in the second phase and maybe in the third phase of the evolution of local industrial clusters. Therefore, the industries that are characterised by ‘clustering’ dynamics should match those that either show the emergence of local clusters or already contain such clusters. This is tested in the following analysis. The test is restricted to the manufacturing and service sectors because these sectors dominated in the literature on clustering and therefore seem to be most relevant for the discussion here.

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Matching of the classifications The approach that is used here results in 6 classifications of the dynamics in each industry, namely for each period of time and for the relative and the absolute number of firms. The test of the correspondence between the dynamic and the static approach might be conducted for each of these 6 classifications separately. The results are very similar, so that they are presented on an aggregated level here. To this end, the 6 classifications are aggregated as follows. For each industry the following steps are taken until a classification is reached: 1. If the dynamics of the relative and the absolute numbers of firms between 1995 and 2000 are both classified identically into one of the categories ‘clustering’ and ‘equalising’, the industry is classified into the same category. 2. If one of these two dynamics is classified as ‘fluctuations’ or ‘unclear’ and the other is classified as ‘clustering’ or ‘equalising’, the industry is classified according to the latter dynamic. 3. If one of these two dynamics is classified as ‘clustering’ and the other as ‘equalising’, the industry is classified as ‘other’. 4. The dynamics are classified according the above procedure with respect to the time spans from 1995 to 1997 and from 1997 to 2000.

Table 3.3 Number of industries that fall into each combination of categories according to their dynamic and static features (the results that are based only on the relative number of firms are given in brackets). classification of dynamics

manufacturing industries with clusters

with no clusters

with no fitting

‘clustering’

23 (15)

11 (17)

−(2)

‘equalising’

30 (23)

41 (47)

−(1)

‘other’

18 (12)

26 (26)

1 (7)

This aggregation leads to 34 manufacturing and 25 service industries being classified as ‘clustering’. The dynamics of another 71 manufacturing and 45 service industries are observed to be ‘equalising’. The remaining 45 manufacturing and 59 service industries are classified as ‘other’. The results for all industries are given in Table A.1 in the appendix. This classification can be matched with the identification of those industries that contain local clusters according to the analysis in Section 3.2. The results are given in Tables 3.3 and 3.4. For the manufacturing sector the results confirm the prediction that industries in which local clusters exist are more likely to show ‘clustering’ dynamics than industries in which no local clusters exist. There are significantly more manufacturing industries that either

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contain local clusters and show ‘clustering’ dynamics or contain no clusters and show ‘equalising’ dynamics than there are manufacturing industries that are characterised by the opposite combinations (Fisher test: X2=5.93 (X2=1.82), p-value: 0.01 (0.1)), although the results are not very significant if only the results for the relative numbers of firms are considered. The same does not hold for the service sector. Significant correlations between the results of the dynamic and the static approach only appear if the study is restricted to the relative numbers of firms (Fisher test: X2=0−49 (X2=2.63)). The percentage of service industries in which the dynamics are classified as ‘other’ is very large: 46%. Hence, the picture in the case of the service sector is rather vague. This is related to the fact that the approach fails to describe the firm distribution in quite a number of service industries and that for many service industries clustering is only identified because more firms are found in the very large cities. The picture changes if only the results for the relative numbers of firms are considered. If only relative numbers of firms are used, even more industries fail to be adequately described by the above models (51 out of 129 industries). However, among the remaining industries there are also significantly more service industries that either contain local clusters and show ‘clustering’ dynamics or contain no clusters and show ‘equalising’ dynamics than there are service industries that are characterised by the opposite

Table 3.4 Number of industries that fall into each combination of categories according to their dynamic and static features (the results that are based only on the relative number of firms are given in brackets). classification of dynamics

service industries with clusters

with no clusters

with no fitting

‘clustering’

15 (7)

8 (7)

2 (11)

‘equalising’

23 (7)

18 (21)

4 (17)

‘other’

31 (8)

19 (28)

9 (23)

combinations (Pearson test: X2=2.63, p-value: 0.05). Hence, the analysis again shows that the relative numbers of firms should be used if service industries are studied while in the case of manufacturing industries the results are slightly better if both numbers of firms are used. As a consequence, in the following analysis the results of the relative and absolute numbers of firms are used for all manufacturing industries while only the results for the relative numbers of firms are used for all service industries. Although there is a clear correlation between the results of the static and the dynamic studies, there is quite a number of industries in which different results are found. This means that there are industries in which local clusters can be proved to exist but ‘equalising’ dynamics are found and that there are industries in which no local clusters have been found but ‘clustering’ dynamics exist. These results might be interpreted as the disappearance or emergence of clustering.

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There are 29 manufacturing and 7 service industries containing local clusters that show ‘equalising’ dynamics. In these industries local clusters are disappearing or at least the significance of clustering is decreasing. At the same time, 12 manufacturing and 7 service industries that do not contain local clusters show ‘clustering’ dynamics. In these industries some clustering seems to be emerging. Comparing the two numbers, the above finding of a decreasing number of industries that are clustering is confirmed, especially for the manufacturing sector. However, again it is shown that industries differ and that there are industries that show the opposite development. The manufacturing industries in which clustering is weakening are natural stones, cement, pottery, tiles, cold-rolling mills, boiler making, agricultural machinery, office machines, electronic user goods, telecommunication, optics, clocks, weapons, other metal goods, toys, sawmills, chipboard, wooden furniture, paper products, leather goods, shoes, silk processing, rope making, knitting, other textiles, men’s clothes, working clothes, dairy products, fish processing, and breweries. The service industries in which clustering is weakening are other railways, inland navigation, non-profit in-

Table 3.5 Number of manufacturing and service industries that fall into each combination of categories according to their dynamics and the changes in their spatial firm distribution between 1995 and 2000. classification of dynamics

Spatial firm distribution switches from natural to cluster

cluster to natural

manufacturing sector

service sector

manufacturing sector

service sector

‘clustering’

9

1

4

0

‘equalising’

5

3

9

4

‘other’

3

2

7

5

stitutions, social securities institutions, non-profit libraries, reform schools of local authorities, and public libraries of local authorities. The manufacturing industries in which clustering is emerging are synthetic textiles, hot-rolling mills, textile machinery, washing machines, electronics, steel furniture, wool twisting, cotton spinning and weaving, linen processing, sugar, and tobacco. The service industries in which clustering is emerging are non-profit institutions for education, theatres of local authorities, television & radio producers, publishers, private fairgrounds, fairgrounds of local authorities, and translators. The industries of each list seem not to share any obvious characteristics. It seems to be difficult to explain why certain industries appear in the above lists while others do not. This is likely to be caused by the sensitivity of the dynamic approach. The regression analysis that is conducted here might easily misclassify an industry. Therefore, the dynamic and the static approach will be combined below in a different way. If clusters

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really emerge or disappear during the 5 years that are studied, this should show up in the dynamic and the static approach. Emergence and disappearance of clusters Above several industries have been identified that switch from being described by the natural distribution in 1995 to being described by the cluster distribution in 2000 or the other way round (see Table 3.1). It has been argued that these findings cannot be interpreted as the emergence or disappearance of clusters because the underlying approach is very sensitive and change in the shape of the distribution might be statistical artefacts. The study of the dynamics of the spatial firm distribution provides additional evidence, so that the two studies can be merged. The results are given in Table 3.5. In Section 3.3.1, it has been concluded that many of the switches between the natural and the cluster distribution within the 5 years that are studied are statistical artefacts. Table 3.5 confirms this conclusion. Indeed, quite a number of the switches are not confirmed by the dynamic approach. Especially in the case of the service sector there are nearly as many industries for which the switch in the shape of the firm distribution is contradicted as there are industries for which the switch is confirmed by the dynamic analysis. However, in the manufacturing sector there are significantly more cases in which the switches and the dynamics observed match each other than cases in which they contradict each other (Pearson test: X2=3.03, significance level: 0.1). Not all changes in the spatial firm distribution seem to be statistical artefacts. It seems to be adequate to assume that all changes in the spatial firm distribution that are confirmed by the dynamics in the regions represent the emergence or disappearance of local clusters. Hence, we observe 9 manufacturing industries in which local clusters emerge and 9 manufacturing industries in which local clusters disappear. Furthermore, there is one service industry in which local clusters emerge and 4 service industries in which local clusters disappear. The industries in which clusters emerge are basic chemicals, synthetic textiles, porcelain, sheet-metal industry, precision tools, instruments, cotton spinning and weaving, linen processing, distilleries and homes. The industries in which clusters disappear are cement, boiler making, train building, heating and cooking equipment, package utilities, paper products, cotton twisting, silk processing, dairy products, social security homes, nonprofit libraries and stationed forces. The detailed study of the dynamics in the industry of paper products that is conducted in Section 3.4.3 shows that the number of firms in this industry is decreasing. The same holds for all the other industries listed here. Thus, a decreasing number of firms seems to be a requirement for the disappearance of local clusters. The same does not hold for the industries in which local clusters seem to emerge. There seems not to be a common characteristic of these industries. The number of firms in the industries cotton spinning and weaving, linen processing and distilleries are very small, so that the results for these industries are not very reliable. Many of the remaining industries that show an emergence of clustering are technology based while most of the industries that show a disappearance of clustering are traditional industries. Hence, there seems to be some confirmation of the life-cycle arguments in the last chapter, although the results are rather vague.

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3.4 CLUSTERS IN GERMANY After the general discussion of the phenomenon of local industrial clusters in the last section, this section is dedicated to the identification of clusters in Germany. The identification of local industrial clusters is done on the basis of a general condition. Similar approaches have been applied to other countries in the literature (see Sforzi 1990, Isaksen 1996, Paniccia 1998, and Braunerhjelm & Carlsson 1999). The major results are as follows. For the first time a general approach is applied to Germany that results in a complete list of local industrial clusters. A few misspecifications might be included in this list (the reasons are discussed below). However, a comparison with case studies shows that many cases are identified correctly. The obtained list provides some information about where industrial clusters are located in Germany. It shows that they are not only located in the regions which are economically successful at the moment. Clear evidence is obtained for the fact that history matters. Many of the local industrial clusters that exist today in Germany have emerged many decades ago. Local industrial clusters emerge at certain times and their spatial distribution reflects the economic situation at that time. Their ongoing existence does not lead to economic prosperity in the region. Local industrial clusters seem to have an effect on the economic development in a region only for a short time although their existence is often more permanent. Finally, the discussion of some industries shows that the general analysis that is taken here is also very helpful for the understanding of the dynamics and situation in specific industries. 3.4.1 Empirical method In the literature several approaches can be found that are used to identify local industrial clusters on a general basis (see Sforzi 1990, Isaksen 1996, Paniccia 1998, and Braunerhjelm & Carlsson 1999). The approaches taken differ with respect to the additional conditions they require and with respect to the measure of economic activity. Some researchers argue on the basis of employment numbers (such approaches can be found in, for example, Sforzi 1990, Isaksen 1996, Paniccia 1998 and Braunerhjelm & Carlsson 1999) while others argue on the basis of firm numbers (such an approach is found in Ellison & Glaeser 1997). Approaches that are based on employment numbers are much more common. However, many clusters that are identified by such approaches are dominated by large firms (a discussion of this fact is found in Isaksen 1996). Therefore, some of the approaches add another condition which requires a large share of small firms within the region (this is done in the approaches in Sforzi 1990 and Paniccia 1998). Such a concentration on small firms does not fit the definition of local industrial clusters that is used here. However, regions that contain only one large firm do not fit into the definition used here either because there is no beneficial local interaction between firms. Therefore, the approach that is taken here uses the industrial firm distribution among regions as the basis for the analysis. Similar to the approach of Ellison and Glaeser (1997), it has been argued above that there is a ‘natural’ distribution of firms. However, the approach taken here differs from their approach in two ways. First, a more general distribution is called ‘natural’ here. Second, the approach taken here does not rank industries according to their geographic

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concentration but aims to identify those industries in which clusters exist. As a consequence, the approach taken here also allows for the identification of local industrial clusters. None of the approaches in the literature have so far been applied to Germany. The literature provides, instead, a large number of case studies in which the local industrial cluster that is examined is chosen according to the knowledge and experience of the individual researcher. This provides considerable information about existing clusters. However, there is no guarantee that all existing local clusters are reported in some case study. Therefore, only some of the local clusters can be expected to be represented in the case study literature. The aim of this section is to provide a complete list of local industrial clusters in Germany and discuss it. An obvious means to identifying the local industrial clusters in Germany would be the application of one of the approaches in the literature. A different approach is taken here for two reasons. First, the most elaborated approach—the one used by Sforzi (1990)— cannot be applied to Germany because of the lack of data. This approach requires employment and commuting data on the level of municipalities, which I have not been able to obtain for Germany. Second, the analysis conducted above allows the use of different conditions for different industries and the exclusion of those industries that have not been found to show clustering. Identification of local industrial clusters The identification of local industrial clusters is based on the fitted theoretical cluster distribution (3.6). As has been discussed above, the parameter of this distribution determines the minimal number of firms in a cluster. Accordingly, all regions that contain a higher number, meaning all regions that satisfy Condition (3.17), are said to contain a local industrial cluster. This is the only condition that has to be satisfied by a local industrial cluster, except for the condition that local clusters have to be found to exist in the respective industry. Hence, no specific characteristics of the firms or their interaction is required in the approach used here. Neither is it required that most firms are small (this is required, for example, in the approach in Sforzi 1990) nor is it required that firms of different industries interact in a certain way (this is required, for example, in the approach in Isaksen 1996). All these features are connected to specific concepts such as those of industrial districts or economic clusters. This does not match the more general approach taken in this book. By contrast, the approach taken here is more elaborated with respect to industrial differences. First, industries in which no agglomeration has been found are excluded from the analysis. Second, the condition with respect to the number of firms is set up differently for different industries. 3.4.2 List of local industrial clusters For 71 manufacturing industries and 22 service industries (only relative firm numbers are considered in the case of service industries), the existence of local clusters has been confirmed above. In these industries altogether more than 500 local industrial clusters are

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identified according to Condition (3.17). It is impossible to discuss or even describe all of them. However, a complete list of them is given here. The industry of distilleries is excluded because the number of firms is low so that all small regions that contain at least one firm show up in the list of local clusters. Furthermore, the industries for repair of agricultural machinery, plasterers and stove fitters are excluded because there are more than 30 regions in which clusters are identified. The film industry is added to this list, although it is a service industry and shows clustering only for the absolute number of firms, because it is repeatedly discussed in the literature. The list contains, for each industry that is studied, a list of the names of all administrative districts that satisfy Condition (3.17). Neighbouring districts are included in brackets. Regions that satisfy Condition (3.17) only with respect to either the relative or the absolute number of firms are presented in italics. The identification of local industrial clusters is conducted for each year separately. As a consequence, the results might differ between the years. Two kinds of changes are distinguished: changes in a particular direction or changes that look like fluctuations. In the former case the findings for the year 2000 are listed below. If, instead, the number of local clusters fluctuates around a particular value, all local clusters that are identified in all the years are listed below. In the case of optics, the listing below deviates from the results of this procedure. The details of this deviation are explained in Section 3.4.3. basic chemicals: Bitterfeld paints & varnishes: Hamburg, Wuppertal, Cologne, Herford, Frankfurt a. Main, (Stuttgart, Ludwigsburg), Karlsruhe, Berlin (West) pharmaceuticals: Berlin (West), Dresden petroleum processing: Hamburg natural stones: Hamburg, Mayen-Koblenz, Eichstätt, Weiβenburg-Gunzhausen, Berlin (West) cement: (Warendorf, Soest), Donnersbergkreis, Forchheirn, Bernburg other stones: Westerwaldkreis concrete: Mayen-Koblenz porcelain: Wuppertal, Coesfeld, Tirschenreuth, (Hof, Kronach, Lichtenfels), Wunsiedel i. Fichtelgebirge, Mittlerer Erzgebirgskreis, (Dessau, Anhalt-Zerbst, Bernburg, Köthen), Quedlinburg, (Sonneberg, Saalfeld-Rudolstadt, Saale-Holzland-Kreis) pottery: Westerwaldkreis tiles: Westerwaldkreis, Wunsiedel i. Fichtelgebirge hollow glass: Holzminden, Main-Tauber-Kreis, Freyung-Grafenau, Regen, Neustadt a.d. Waldnaab, Kronach, Jena, Hildburghausen, (Sonneberg, Saalfeld-Rudolstadt) glass fabrics: Westerwaldkreis, Main-Tauber-Kreis, Regen, (Neustadt a.d. Waldnaab, Bayreuth,) Kaufbeuren, (Ilm-Kreis, Sonneberg) hammer mills: Remscheid, Euskirchen, Ennepe-Ruhr-Kreis, Märkischer Kreis, Odenwaldkreis, Rottal-Inn non-ferrous intermediates: Märkischer Kreis iron foundry: Osterode am Harz, Solingen, Mettmann, Donnersbergkreis, Fürth (city) non-ferrous foundry: Solingen, (Mettmann, Hochsauerlandkreis, Märkischer Kreis, Olpe), Westerwaldkreis, (Pforzheim, Enzkreis) cold-rolling mills: (Hagen, Märkischer Kreis)

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sheet-metal industry: Solingen, (Hagen, Ennepe-Ruhr-Kreis, Märkischer Kreis, Olpe), Enzkreis, (Rottweil, Schwarzwald-Baar-Kreis, Tuttlingen) surface refinement: Solingen, (Märkischer Kreis, Enzkreis) locksmithing: Hamburg, (Mettmann, Märkischer Kreis), Ludwigsburg, (Berlin (West), Berlin (Ost)) boiler making: Siegen-Wittgenstein precision tools: Enzkreis agricultural machinery: Gifhorn, Südliche Weinstraβe, Neustadt a. d. Aisch—Bad Windsheim horse-drawn carriages: Mittweida ships: Hamburg, Bremen boots: (Hamburg, Ostholstein, Schleswig-Flensburg) office machines: Hamburg, Hannover (city), Bremen, (Düsseldorf, Cologne), Frankfurt a. Main, Munich (city), (Berlin (West), Berlin (Ost)), Leipzig electric cables: Altenkirchen (Westerwald), Rottweil, Schwarzwald-Baar-Kreis, Landshut, Wartburgkreis electronic user goods: Hamburg, Munich (city), Berlin (West) lights: Hochsauerlandkreis television & radio: Munich (city), Berlin (West) telecommunication: Munich (city), Berlin (West) instruments: Hamburg, Tuttlingen, Munich (city), Berlin (West) optics: Lahn-Dill-Kreis, Havelland, Jena clocks: (Pforzheim, Enzkreis, Schwarzwald-Baar-Kreis) tools: Remscheid, (Solingen, Wuppertal), (Birkenfeld, Pirmasens (city)), (SchmalkaldenMeiningen, Sonneberg locks & mountings: Mettmann cutting tools: Solingen weapons: (Rhön-Grabfeld, Suhl) other metal goods: (Solingen, Hochsauerlandkreis, Märkischer Kreis, Olpe), Enzkreis, (Schwabach, Roth), Schmalkalden-Meiningen musical instruments: Erlangen-Höchstadt, Vogtlandkreis toys: (Coburg, Sonneberg,) Mittlerer Erzgebirgskreis jewellery: Birkenfeld, (Pforzheim, Enzkreis), Kaufbeuren sawmills: Hochsauerlandkreis, Ortenaukreis chipboards: Gütersloh, Herford, Höxter, Lippe wooden furniture: (Herford, Lippe, Minden-Lübeck), Coburg wickerwork & brooms: Gütersloh, Garmisch-Partenkirchen, Freyung-Grafenau, Regen, (Coburg, Kronach, Lichtenfels, Haβberge), Ansbach, Berlin (West), Freiberg, (Annaberg, Mittlerer Erzgebirgskreis, Aue-Schwarzenberg), Saale-Holzland-Kreis paper products: Düren, Bad Dürkheim, Mittlerer Erzgebirgskreis printing: Hamburg, Munich (city) chemigraphics: Hamburg, Munich (city), Berlin (West) leather goods: (Offenbach (city), Offenbach) shoes: (Pirmasens (city), Pirmasens) wool weaving: (Mönchengladbach, Aachen), (Hof (city), Hof) cotton weaving: (Grafschaft Bentheim, Borken, Steinfurt), (Hof, Kulmbach)

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silk processing: Krefeld, Wuppertal, Viersen, Heinsberg, Waldshut rope making: Wittmund, Steinfurt, Emmendingen, Rottal-Inn, Schwabach, TorgauOschatz, Unstrut-Hainich-Kreis, Greiz knitting: (Reutlingen, Zollernalbkreis) other textiles: Wuppertal, Zollernalbkreis, (Hof, Kulmbach), (Annaberg, Vogtlandkreis) men’s clothes: (Aschaffenburg, Miltenberg) working clothes: Zollernalbkreis, (Freyung-Grafenau, Cham), (Bayreuth, Kronach), Aschaffenburg corsetry: Zollernalbkreis, Stollberg, Niederschlesischer Oberlausitzkreis other bed products: Hamburg, Zollernalbkreis, Berlin (West) dairy products: Rotenburg (Wümme), Emsland, Ravensburg, Lindau (Bodensee), Oberallgäu fish processing: (Cuxhaven, Bremerhaven) food production: Hamburg sweets: Berlin (West) abattoir: Hamburg, Cloppenburg, Osnabrück, Vechta, Gütersloh, Berlin (West) breweries: Bamberg mineral water: Wetteraukreis, Limburg- Weilburg, Ahrweiler, Daun, Kusel, NeuburgSchrobenhausen, Pfaffenhofen a. d. Ilm, Traunstein, Straubing, Passau, Regen, RottalInn, Tirschenreut, Neustadt a. d. Aisch—Bad Windsheim other railways: Soltau-Fallingbostel, Grafschaft Bentheim, Ahrweiler, Ortenaukreis, Zollernalbkreis, Regen, Rügen inland navigation: Emsland, Leer, Wesermarsch, Duisburg, Miltenberg, Main-Spessart sea shipping: Flensburg, Lübeck, Dithmarschen, Nordfreisland, Ostholstein, Plön, Rendsburg-Eckernförde, Schleswig-Flensburg, Steinburg, Hamburg, Cuxhaven, Stade, Emden, Aurich, Emsland, Friesland, Leer, Wesermarsch, Wittmund, Bremen, Bremerhaven, Rostock, Stralsund, Wismar, Ostvorpommern, Rügen shipping brokerage: Hamburg, Stade, Wesermarsch, Bremen non-profit institutions: Nordfreisland, Goslar, Aurich, Friesland, Wittmund social security institutions: Nordfreisland, Goslar, Cuxhaven, Aurich, Wittmund, Oberbergischer Kreis, Breisgau-Hochschwarzwald, Miesbach am Lech, Schweinfurt, Ohrekreis, Altmarkkreis Salzwedel homes: Dithmarschen, Herzogtum Lauenburg, Nordfreisland, Rendsburg-Eckernförde, Schleswig-Flensburg, Segeberg, Steinburg, Osterode am Harz, Schaumburg, Celle, Cuxhaven, Lüchow-Dannenberg, Osterholz, Rotenburg (Wümme), Uelzen, Verden, Odenwaldkreis non-profit libraries: Bonn, Heidelberg, Freiburg im Breisgau, Tübingen, Bad TölzWolfratshausen, Garmisch-Partenkirchen, Berlin (East), Barnim, Potsdam-Mittelmark, Greifswald, Bad Doberan, Jena private schools: Neumarkt i. a. Opf, Regensburg non-profit schools: Schleswig-Flensburg, Kassel, Schwalm-Eder-Kreis technical colleges: Havelland, Ostprignitz-Ruppin, Prignitz, Greifswald, Rostock, Stralsund, Wismar, Güstrow, Zwickau, Freiberg, Leipzig, Halberstadt, Quedlinburg, Wernigerode, Erfurt, Gera, Suhl, Eichsfeld, Hildburghausen reform schools of local authorities: Nienburg (Weser), Cochem-Zell, Rhein-HunsrückKreis, Kusel, Eichstätt, Neumarkt i. a. Opf, Regensburg, Demmin, Mecklenburg-Strelitz

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sports grounds of local authorities: Nienburg (Weser) public libraries of local authorities: Uecker-Randow, Vogtlandkreis, Sächsische Schweiz, Weiβeritzkreis clinics of social securities: Höxter, Bad Kissingen undertakers of local authorities: Dithmarschen, Plön, Rendsburg-Eckernförde, Schleswig-Flensburg, Wunsiedel i. Fichtelgebirge packaging: Mainz-Bingen, Fürth professional associations: Bonn foreign embassies & consulates: Bonn film industry: Hamburg, Hannover (city), Bremen, (Düsseldorf, Bonn, (Cologne, Erftkreis, Dortmund), (Frankfurt a. Main, Wiesbaden), Stuttgart, (Munich (city), Munich), (Berlin (West), Berlin (East), Potsdam). Comparison with case studies In the literature quite a number of case studies of local industrial clusters in Germany can be found. Most case studies that are cited and discussed in the context of industrial districts, local clusters and the like describe the historical development of a specific industry in a certain region. In contrast, many studies of German regions are conducted in order to evaluate advantages and disadvantages and to identify possible ways to improving the prosperity of a region. Factors that influence specialisation and clusters are sometimes discussed in this context. Therefore, it is not claimed here that the following list of case studies conducted in Germany is complete. However, it has to be stated that the list is restricted to those local systems that fit into the concept used here, meaning those systems that satisfy Definition 2. iron and steel: Ruhr area (Grabher 1993) biotechnology: Munich, upper Rhine, Heidelberg and Mannheim, Frankfurt, middle Rhine, and Berlin (Zeller 2001 and for Munich see, in addition, Lechner & Dowling 1999) machinery: Baden-Württemberg (Cooke 1994) printing machinery: several places around Offenbach, Frankenthal, Heidelberg, Leipzig, Würzburg and Augsburg (Porter 1990) automobiles: Bergisches Land, Bochum, Zwickau, Regensburg, Cologne, Frankfurt, Hannover, Wolfsburg, Munich and Mittlerer Neckar (Rehfeld 1992) train building: mainly Berlin, but also Ruhr area, Braunschweig, Nürnberg and Saxony (Dybe & Kujath 2000) textiles: Zollernalbkreis (Grotz & Braun 1997b), Reutlingen (Staber 1997) media: Berlin/Babelsberg and Cologne/Düsseldorf (Lutz, Sydow & Staber 2003) In addition, Munich is regarded as an innovative milieu in the literature because it is strong in the motor vehicles, aerospace, electronic engineering, precision instruments/optics, and office machinery/data processing industries (see Sternberg & Tamásy 1999). The comparison leads to very different results. In some cases quite a good correspondence is found, although industries or regions are not always defined in exactly

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the same way. For example, the industrial districts in textiles show up in the analysis conducted here as a local cluster in knitting, working clothes, other textiles and corsetry. Similarly, metal processing is subdivided into many different industries here. Many of them show clustering, namely hammer mills, non-ferrous intermediates, iron foundry, non-ferrous foundry and cold-rolling mills. Most of these local clusters are found in the Ruhr area. In some of these cases more local clusters are found in the analysis above than are described in the literature. This holds for textiles and media. There are also many industries for which local clusters are discussed in the literature but no significant clustering is observed in the above analysis. These are the industries of machinery, automobiles (some clustering is found here for automobile parts, which is discussed in detail below) and train building. This discrepancy might have different causes. First, the statistical approach used here is only able to reject the assumption that no local clusters exist in an industry. It might fail to identify all industries that show clustering. Second, the approach taken here is based on the distribution of firms, while case studies usually refer to the number of employees in an industry and region. For example, in the case of automobiles the clusters described in the literature are characterised by a very large factory site or company. The above approach does not identify the locations of large firms, but only agglomerations of many firms. Therefore, it might lead to very different results. Finally, in the literature regions are often discussed that are much larger than administrative districts. Examples are the industries of machinery and printing machinery. If clustering occurs in such large spatial units, it is not identified by the approach taken here. However, it might be doubted whether in such large regions the local self-augmenting processes that are discussed in the theoretical analysis have a significant impact on the developments. The case of biotechnology differs from the other cases discussed. Many of the biotechnology firms are assigned to the industry of precision instruments in the WZ73 classification. Hence, the analysis is not able to capture the developments in this subindustry adequately. Nevertheless, it seems to be able to catch some of these developments. A detailed discussion is given in Section 3.4.3. Regional perspective The local industrial clusters that have been identified are listed above according to the industry to which they belong. Alternatively, their spatial distribution might be given. This is done in Figure 3.4 for the manufacturing sector. The spatial distribution has several characteristics that are worth discussing here. First, 158 of the 441 administrative districts contain at least one industrial cluster. Above it has been stated that the approach taken here might underestimate the number of industries that show clustering and therefore might underestimate the total number of clusters. Hence, a sizeable share of all districts contain industrial clusters. In other words, the existing local industrial clusters are well scattered across space. Nevertheless, local industrial clusters are not everywhere. They are not uniformly distributed across Germany. There are some areas in which they are concentrated. In Figure 3.4 three such areas can be easily identified: the Ruhr area, an area in the north of Bavaria and the south of Thuringia and Saxony, and an area in the south of BadenWürttemberg. In addition there are many smaller spots, many of them around large cities

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Figure 3.4 Clustering in Germany (strongly shaded districts contain more than one industrial cluster, weakly shaded districts contain exactly one industrial cluster, light districts contain no industrial clusters in the manufacturing sector).

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like Berlin, Hamburg, Hannover, Leipzig, Frankfurt a. Main, Stuttgart and Munich. Some areas are completely empty. This is especially the case in the northeast, where, for example, no cluster is found in the state of MecklenburgWest Pomerania. The large empty spots match quite well with those regions in which there is little industrial employment and development. These regions seem to be unable to exceed the critical mass for the emergence of local industrial clusters. Although random processes are involved in the determination of the location of clusters and although these clusters are quite scattered within Germany, certain regions seem not to offer sufficient circumstances. This can be seen as evidence for the existence of a critical mass with respect to the attractiveness of regions as one necessary condition for the emergence of local industrial clusters. It does, however, not help us to exactly specify this critical mass. We can only speculate. There is little discussion in the literature about what is lacking in those regions that are lagging behind (an exception is found in Seri 2003). Research in this direction would be helpful to understand the local conditions necessary for the emergence of industrial clusters. While the empty spots in Figure 3.4 match quite well the distribution of economic activity in Germany, the same does not hold for the place in which many local clusters exist. In Baden-Württemberg (south-west of Germany) there should be many more districts containing one or several clusters, for example in the east of Stuttgart and at the Rhine from Karlsruhe to Mannheim. At the same time, the strong concentration of clusters in the north of Bavaria and the south of Thuringia does not match the lack of economic prosperity of this area. This shows that the existence of local industrial clusters should not be mixed up with economic prosperity. They might differ tremendously. Two factors are responsible for this. On the one hand, the spatial distribution of local clusters reflects the history of places rather than their actual situations. Many clusters remain stable over decades or even centuries. For example the area in the north of Bavaria and the south of Thuringia and Saxony was strong in handcrafts many decades ago. Textiles, porcelain, toys, musical instruments and other similar things have been produced there. This is still the case today. Although employment has decreased strongly in many of these industries, the respective districts are still strong in these industries compared to other regions in Germany. The same holds for metal processing and metal goods production in the Ruhr area. Most of the clusters identified above can be assigned to a particular time in which they emerged. Many case studies in the literature confirm this. At this time they cause economic prosperity for the region. Later on they remain stable in many cases but without a further impulse for economic development and sometimes even causing problems for the region if the respective industry declines (see Grabher 1993 and Pouder & St. John 1996). On the other hand, the identification of local industrial clusters identifies neither regions that prosper because of a heterogeneous mix of industries nor those that are characterised by a large, successful firm. BadenWürttemberg is usually claimed to be one of the major locations of the automobile, machinery and chemical industries (see Cooke 1994 for a detailed discussion of the economic situation in Baden-Württemberg). However, most of these industries are characterised by a few very large firms, so that most of them are not identified as clustering industries above and are not included in the search for local clusters in this section. Furthermore, these industries are quite scattered

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within Baden-Württemberg, so that they seldom fall into the same administrative district. Baden-Württemberg is a very decentralised state with respect to its economic activity (this becomes, for example, very obvious in the patent distribution shown in Greif 1998). It is furthermore characterised by a heterogeneous mix of industries. This, among other aspects, causes Schmitz (1992) to argue that the concept of industrial districts does not fit the situation there. These discussions show that we should not confuse local industrial clusters and economic development. Their existence in a region does not necessarily imply economic development there, although their emergence might well do. It seems that their economic impact appears in a particular period of time around their emergence. Later the success of the region depends on other factors, but not purely on the existence of clusters. Some concerns In Section 3.1.2 the restrictions of the data that are used here were extensively discussed. These restrictions have some impact on the identification of local industrial clusters. There is the restriction with respect to the definition of regions. Administrative districts are used as the unit of analysis here. Considering the case studies that exist for Germany, the administrative districts are units that are either adequate or too small. Thus, all existing local clusters should be identified by Condition (3.17). It might be that the number of clusters is overestimated since clusters might spread across several administrative districts and, therefore, might be counted several times. Describing the spatial location of the identified clusters helps in such a situation. Furthermore, the data only allow an analysis of the 3-digit industries according to the WZ73 classification. This classification might be inadequate. There might be local clusters in industries that are not analysed here. For example, industries such as biotechnology are not identified in the list of 3-digit industries according to the WZ73 classification. Hence, we cannot expect to identify local clusters in biotechnology. The analysis is restricted to those industries that can be identified in the WZ73 classification. Thus, the resulting list of local industrial clusters will be incomplete. Finally, some industries might have been excluded from the analysis because no clustering has been found by the analysis in Section 3.2. The statistical test used in Section 3.2 has been applied in a conservative way. Industries have only been said to be clustering if it has been proven that the cluster distribution describes reality significantly better than the natural distribution. There might be further industries in which clusters exist but which are not identified by this examination. Therefore, it cannot be guaranteed that all local industrial clusters are identified by the approach applied here. 3.4.3 Discussion of some cases A general approach has been taken above to identify local industrial clusters and the dynamics within industries. This has the advantage that subjective impressions do not interfere with the scholarly results. Furthermore, a general approach applied in the same way to all industries and regions is the only way to obtain a somewhat complete list of local industrial clusters. However, such an approach also has an important shortcoming: it is not able to consider industrial specificities. It only classifies industries into two

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categories: those in which local clusters exist and those in which no such clusters are identified. The study of the dynamics in regions adds to this. However, the causes, forms and evolution of clusters might differ significantly between industries. In this respect, case studies are superior to the approach taken here. In case studies the industry-specific characteristics of local clusters are usually comprehensively analysed. Unfortunately, case studies typically collect data about one cluster only. A few compare different clusters within the same industry. A comparison between industries is missing. The approach used here offers a good starting point for such a comparison. To this end, the findings above have to be enriched with some case-based information. Limitations on time and space make a discussion of all 293 industries impossible. Therefore, a few typical cases are chosen. They are chosen such that they represent typical examples of different situations that might occur. Furthermore, some industries which show specific developments or are of special interest are discussed. Basic chemical industry In the case of basic chemical industry no cluster was found in 1995. For the years 1997 and 2000 one cluster was found, which is located in Bitterfeld. The changes in the findings result from an increase of the number of firms in this district from 10 in the 1995 to 17 in the 1997. No change in the number of firms in this region is observed between 1997 and 2000. The observed change is a late result of the recent reunification of Germany. Before the reunification Bitterfeld was a major location for the chemical industry in East Germany but the industry in this area lost most of its importance and employment after the reunification. In the mid-1990s it regained some of its importance and became the district with by far the largest relative number of basic chemicals producing firms. In other industries similar recent consequences of the reunification of Germany can be observed. The findings here suggest that the situation was somewhat more stable between 1997 and 2000 than between 1995 and 1997. In the mid-1990s a number of local industrial clusters reappeared in East Germany. However, this process seems to have ended in most industries now. Optics In the optics industry the general approach that is used above identifies the following locations of clusters: Hamburg, Bremen, Düsseldorf, Essen, Frankfurt (Main), Lahn-DillKreis, Stuttgart, Munich (city), Berlin (West), Berlin (East), and Leipzig. This result contradicts the findings about this industry in the literature (see, for example, the analysis of Jena in OECD 2000). This is caused by a specific characteristic of the WZ73 classification. According to the WZ73 classification, all firms that repair goods are classified as manufacturing firms. While in the case of automobiles and clocks, firms that repair these products are classified in a separate 3-digit industry, the firms that repair optical goods are classified in the optics industry. There are more firms that repair optical goods than firms that produce them. Therefore, the optical repair firms dominate the industry and determine the spatial firm distribution.

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Table 3.6 Results for the optical industry excluding all firms with less than 10 employees. number of firms relative

absolute

year

distribution

critical number of firms

number of clusters

1995

cluster

8.7

4

1997

cluster

10.3

3

2000

cluster

10.5

3

1995

natural

−

−

1997

natural

−

−

2000

natural

−

−

Firms that repair optical goods should be classified in the service sector. This has been done in later classifications of industries in Germany that are used nowadays. However, in the WZ73 classification this is not the case. Therefore, the results that are found above for the optical industry are similar to those that are found for many other service industries: it clusters in some of the very large cities. Almost all of the firms that repair optical goods are small, so all small firms are eliminated from the data, and thus excluded from the analysis. Such an elimination also excludes some firms that manufacture optical goods. However, many manufacturing firms remain. Therefore, the analysis is conducted again for all firms that have at least 10 employees. The results are given in Table 3.6. Clustering is found for the relative number of firms, while no clustering is found for the absolute number of firms. Hence, local clusters exist in the optical industry, but they occur outside of large cities. Three local clusters are observed in all years studied. They are located in the following districts: Lahn-Dill-Kreis (containing Wetzlar), Havelland (east of Berlin containing Rathenow), and Jena. This is in line with the results found in the literature on the optical industry. Hence, the different results obtained in the general analysis are caused by the inadequate aggregation of the optical industry data, which includes firms that repair optical goods. This is an example of the problems that can be caused by an inadequate classification of industries. Similar problems might occur in other industries. Automobile parts The automobile parts industry shows very large fluctuations in the number of firms in each region. This holds especially in East Germany. As a result, the shape of the spatial firm distribution is not robust. Two findings confirm this. First, clustering is only found for the year 1997, and not for the years 1995 and 2000. Second, the approach used in Section 3.3 classifies the dynamics in the automobile parts industry as ‘fluctuation’. These results make an interpretation difficult. The dynamics in East Germany still seem to be unsettled, so that it is unclear what the spatial firm distribution will finally look like. The maximum likelihood value that is obtained for the cluster distribution is, in

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all three years, much higher than the one for the natural distribution. However, the likelihood ratio is around the value that is necessary to make this result significant. Hence, there seems to be some clustering taking place in this industry. However, the result might also be a statistical artefact. Further data would be necessary to get a clearer picture. Similar results are obtained for the industries of vulcanisation, non-ferrous metal mills, and agricultural machinery. Biotechnology and instruments There is a huge literature on local clusters in biotechnology (see Ernst & Young 2000, Braunerhjelm & Carlsson 1999, Lechner & Dowling 1999 and Zeller 2001). Hence, there seems to be no doubt about the fact that biotechnology is clustering. Unfortunately, the data that are used here do not classify biotechnology as an independent industry. Many firms that belong to biotechnology are classified into the industry of instruments and some into other industries according to the WZ73 classification. Therefore, clusters in biotechnology cannot be identified here. However, we might expect that even the larger class of instruments shows clustering. Indeed, the empirical analysis that is conducted above identifies local clusters in the instruments industry. Furthermore, it identifies ‘clustering’ dynamics, meaning that the phenomenon of clustering intensifies between 1995 and 2000. In addition, the phenomenon of clustering is not significant in 1995, while it is significant in 1997 and 2000. This shows that there was a clear development towards clustering in the instruments industry between 1995 and 2000. The 3-digit industry of instruments contains several 4-digit industries, such as different kinds of measuring instruments, controlling instruments and medical instruments. Altogether the number of firms in these industries increased by 603 between 1995 and 2000. For biotechnology an increase from 129 to 279 is reported for Germany for the period from 1996 to 2000 (see Zeller 2001). Hence, it seems plausible to assume that the development within the industry of instruments is strongly influenced by the developments in biotechnology, although the total share of biotechnology firms is small because the industry of instruments contained a total number of 11,384 firms in the year 2000. The districts that are found above to contain local clusters in instruments differ from those that are identified in the literature as the biotechnology centres (a detailed study of the German biotechnology industry is given in Zeller 2001). Hamburg, Tuttlingen, Munich and West Berlin are identified as the locations of these clusters. A more detailed examination of the data shows that these are the locations that already contained the highest number of firms in the year 1995. Munich and West Berlin then benefited from biotechnology, increasing the gap between these four districts and all others (Tuttlingen and Hamburg had the highest numbers of firms in instruments in 1995). This made clustering more obvious so that it became identifiable by the statistical approach used here. However, the large number of instruments firms outside biotechnology still dominates the spatial distribution of the whole industry. The picture would look somehow different if only biotechnology firms were considered. The approach used here is not able to reflect the developments in biotechnology because the classification of industries is determined by the available data.

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Nevertheless, the discussion of biotechnology has shown two things. First, some development was observable although the classification of industries was inadequate. This shows that developments in a sub-industry might influence the industry under consideration to such an extent that they are identifiable on the higher level of aggregation. In addition, it shows that a general approach, as is taken here, is indeed able to catch even minor developments. However, it might not always be able to identify developments that do not match the structure of the data used. Second, the developments in biotechnology are only identified in the approach used here because a significant share of these developments took place in regions that had already been strong in instruments. This suggests the the development of biotechnology firms is somehow related to the existence of firms in instruments. Such a spatial correlation between related fields seems not to be an exception but rather a general feature (a detailed study of these relations is conducted in Brenner 2000). Paper products The case of the paper products industry seems to be typical of a disappearing cluster that is caused by the decline of a particular industry. The total number of firms in the industry decreased from 444 in 1995 to 404 in 2000. This decrease mainly took place in the regions that contained a cluster in 1995. All of them experienced a decrease in the number of firms between 1995 and 2000. On average these regions lost 32% of the firms manufacturing paper products, which is well above the average decrease in the industry. According to the table in the appendix the dynamics in this industry are classified as ‘equalising’. This confirms the weakening of the phenomenon of clustering in this industry. It results in a disappearance of significant clustering between the years 1997 and 2000. Similar processes are observed in the industries of cement, boiler making, railway carriages, heating and cooking equipment, package utilities, cotton twisting, silk processing, and dairy products, meaning for all the industries for which a disappearance of clusters has been found above. Hence, a decrease of the number of firms in an industry seems to be a necessary condition for the disappearance of local clusters. Data processing According to the analysis conducted above, the local clusters that existed in the data processing industry disappeared between 1995 and 2000. This result is obtained for the spatial firm distribution and is confirmed by the classification of the dynamics as ‘equalising’. At the same time, the number of firms in this industry increased tremendously from 971 in 1995 to 1379 in the year 2000. This increase in the number of firms can be assigned mainly to one sub-industry, namely that of software development and provision. As in the case of biotechnology, the dynamics take place in a subset of the industry for which data are not available. However, contrary to the developments in biotechnology, many firms in the software industry are founded outside the data processing clusters. No strong relationship to other data processing sub-industries seems to exist in the case of the software industry. As a consequence, the dynamics in the software industry destroy the empirical evidence for clustering in data processing. This, however, can be interpreted neither as a

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disappearance of clusters in data processing nor as a lack of clustering forces in the software industry. The aggregation of industries that seem to be located in different places and show different kinds of clustering, if at all, makes conclusions impossible. Separate data on the different sub-industries of data processing would be necessary to draw conclusions. Hence, the data processing industry is an example of misleading results that are obtained by a general approach which is based on the use of inadequately classified data. In most other industries that have been discussed explicitly in this section the results have matched quite well with the available information about the industries. Thus, such misleading results seem to be an exception rather than the rule. Nevertheless, it has to be kept in mind that they might occur. 3.5 DETERMINANTS OF CLUSTERING It has been found above that local industrial clusters exist in some but not in all industries. This raises the question of which industrial characteristics are responsible for the existence of local clusters. This question corresponds to the more general question of why local industrial clusters exist. In the literature many different answers are given. Most researchers agree on the fact that local industrial clusters differ and that different mechanisms are at work. This complicates the answering of the above question. However, the general approach that is taken here offers a unique opportunity to study the causes of clustering which should not be missed. All 3-digit industries have been classified above into two categories: industries that contain local clusters and industries that do not contain such clusters. Furthermore, the dynamics within each industry have been classified into three categories: ‘clustering’ dynamics, ‘equalising’ dynamics and ‘other’ dynamics. If some characteristics of industries cause the existence of local clusters, they should be observed in those industries that show clustering and not in the others. Thus, a comparison of the characteristics of the industries in the different classes should allow us to identify the causes of clustering. Of course, there might also be combinations of industrial characteristics responsible for the existence of local clusters. This could also be tested by a comparison of the different types of industries. However, only simple characteristics of industries are studied here for simplicity. Further analysis of this kind might turn to studying more complex combinations of characteristics and their influence on clustering. The situation is not as simple as it seems to be. Restrictions in the available data, the somewhat fuzzy identification of clustering and the industrial dynamics, and the relevance of many influences make the empirical analysis difficult. However, despite these problems, which should cause rather insignificant results, it is possible to detect some relationships between industrial characteristics and clustering. A logistic regression is used to study the relations between industrial characteristics and clustering. Data on the industrial characteristics is obtained from the Mannheimer Innovation Panel and from a study of spillovers by Verspagen (1997). This data is described in detail below in Section 3.5.1. Clustering is measured according to the static approach described in Section 3.2 and the dynamic approach described in Section 3.3. In

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these sections a classification of industries has resulted that is given in Table A.1. The statistical characteristics of these data and the method used for the analysis are described in Section 3.5.2. The results of the analysis are presented and discussed in Section 3.5.3. The major results are as follows. The relationship between the industrial characteristics and clustering is more significant for the classification of industries according to their dynamics than for their classification according to their firm distribution. This confirms the above finding that local clusters are sustained even if the conditions that caused their emergence are no longer present. The industrial characteristics that are found to be related significantly to clustering are: the number of intra-industry spillovers, cooperation, knowledge flows, and the number of process innovations. 3.5.1 Empirical data Statistical offices do not collect data on the characteristics of industries. Hence, there is no general source on which this approach can rely. However, different studies exist that analyse certain aspects for different industries separately. Sometimes the results of such studies are even published such that the characteristics are given for each industry separately. A common source of data for different characteristics on the level of 3-digit industries would, nevertheless, be more adequate. The Mannheimer Innovation Panel is such a source for at least a number of industrial characteristics. The Mannheimer Innovation Panel (MIP) is conducted by the ZEW (Zentrum für Europäische Wirtschaftsforschung) in Mannheim on behalf for the German ministry for economics. Around 2500 firms complete a questionnaire each year. The questionnaire mainly focuses on the innovation activities of firms but also addresses a number of related questions. The data that are used here originate from the questionnaires conducted in the years 1993 and 1999. Data from the year 1993 are used for three characteristics that are related to cooperation because this is the only year the firms have been asked about their cooperation activities. For all other industrial characteristics the most recent available data (1999) are used. The data from the Mannheimer Innovation Panel and Verspagen’s study are chosen because they satisfy two conditions. First, they are available on an industrial basis. Second, they are related to the emergence of local industrial clusters. In the literature and in Chapter 2 of this book several factors have been identified that are assumed to cause the existence of local industrial clusters. These are tested here. Therefore, data are needed which relate to these factors. Most of the causes suggested in the literature have a dynamic character. An example is the accumulation of human capital in regions. General empirical studies on such dynamics do not exist. Characteristics have to be found that somehow approximate the relevance of these processes. The theoretical analysis implies that industrial characteristics related to human capital, innovations, spillovers, cooperation among firms and startups should be studied. For all these factors except for start-ups, some characteristics are found that approximate their relevance in an industry. These characteristics are only studied for the manufacturing sector because in the above study it has been argued that local clusters exist mainly within manufacturing industries and that most of the service, mining and agricultural

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industries are less adequately described by the approach taken here. The data and the respective sources are described for the two sources separately. Mannheimer Innovation Panel The Mannheimer Innovation Panel classifies firms according to the WZ93 classification.5 The data that are used above are based on the WZ73 classification of industries. However, most of the 4-digit industries in the WZ93 classification can easily be assigned to an industry of the 3-digit level in the WZ73 classification. The few cases in which the classifications of industries cannot be matched have been excluded from the analysis below. Through this the firms surveyed in the Mannheimer Innovation Panel are assigned to the WZ73 classification. This results in different numbers of firms assigned to each industry. To measure industrial characteristics the average value of each characteristic of all firms assigned to the industry is calculated. If there is only one firm in an industry, the average values are determined by the characteristics of this firm. Such a value is not very reliable. Therefore, all industries in which fewer than 5 firms are surveyed in the Mannheimer Innovation Panel are excluded from the following analysis. This exclusion can be justified by the following argument. Those industries that are represented by a small number of firms in the Mannheimer Innovation Panel are also those industries that contain, in total, a small number of firms in Germany. This would cause the results of the analyses in Sections 3.2 and 3.3 to be unreliable. Hence, an exclusion of these industries seems to be justified. Sixty industries remain after excluding all service, mining and agricultural industries, all industries for which the match between the WZ93 and the WZ73 classification causes problems, and all industries that are represented by fewer than 5 firms in the Mannheimer Innovation Panel. All of the 22 2-digit manufacturing industries (according to the WZ93 classification) are represented by at least one 3-digit industry. The 60 industries seem to be an adequate representation of the manufacturing sector in Germany. They represent around 85% of the firms surveyed in the Mannheimer Innovation Panel. Thirteen different characteristics, which are identified in the Mannheimer Innovation Panel, are studied here. These are:6 PRODCYC: the average duration of the product cycle of the most important product of the firm PRODINNO: variable that equals 1 if the firm has conducted product innovations or activities to develop product innovations within the last 3 years and equals 0 otherwise PROCINNO: variable that equals 1 if the firm has conducted process innovations or activities to develop process innovations within the last 3 years and equals 0 otherwise 5

The WZ93 classification (Wirtschaftszweige 93) is the official German classification of industries that was developed in 1993 and is now used in all official statistics. 6

The abbreviations used here differ from those given in the data in order to make it more obvious what each of them describes.

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INNOEXP: share of turnover that is spent on innovation projects and investments related to innovation projects REVNEW: share of revenues that are obtained through new or significantly improved products INFOINNO: variable that characterises the importance of information from competitors and firms in the same industry for innovation activities (takes the value of 1 if such information is seen as important for at least either product or process innovations and takes the value of 0 if it is regarded as unimportant for innovation activities) SCIEINNO: variable that characterises the importance of scientific knowledge for innovation activities (values are defined in the same way as in the case of INFOINNO) EMPNAT: share of employees that hold a degree in natural sciences EMPSOC: share of employees that hold a degree in social sciences EMPTECH: share of employees that are trained at a technical college COOPCOM: share of cooperation with competitors that occurs locally COOPSUP: share of cooperation with suppliers that occurs locally COOPUNI: share of cooperation with universities that occurs locally The data for the last three characteristics are obtained from the Mannheimer Innovation Panel conducted in 1993. All other data come from the Panel conducted in 1999. Spillover tables from Verspagen There are several approaches in the literature that study spillovers between industries. These approaches differ with respect to the data they use. Usually patent data are used to analyse the connection between research fields. However, while some researchers use data on the industries that create and use patents (see, e.g., Scherer 1984), other researchers use the fact that patents are classified into several industries (see, e.g., Grupp 1996 and Verspagen 1997). The results obtained by Verspagen (1997) are used here. They fit best to the approach taken here, because the analysis is done for an industry classification that matches quite well with the classification used here (in Grupp 1996 a classification of technological fields is used instead) and the data refer to Europe and are quite recent (Scherer 1984 reports results for the U.S.A. from approximately 1980). Verspagen calculates spillover matrices, meaning rates of spillovers between industries. In the context of the study conducted here, it is only important to know how much knowledge spills over within an industry. To be more precise, it would be good to know how important spillovers within an industry are for firms. This cannot be measured by spillover matrices. Neither the importance nor the total number of spillovers within an industry can be calculated on the basis of the spillover matrices of Verspagen. Therefore, a measure has to be used that is somehow related to the importance of spillovers within industries. The ratio between spillovers within an industry and the total amount of spillovers that originate from the industry is used here. Below this ratio is called the intra-industry spillover ratio. This ratio can be directly taken from the spillover matrices. Verspagen (1997, pp. 52–53) provides three matrices. Two of them relate to Europe and are denoted ‘matrix A’ and ‘matrix B’. The values of the respective intraindustry spillover ratios are denoted by SPILLRATA and SPILLRATB here.

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The industry classification that is used by Verspagen is quite similar to the 2-digit level of the WZ93 classification. However, the spillover ratio is not available for all of the 60 industries that are chosen above. Each intraindustry spillover ratio in Verspagen’s matrix refers to one or several of the 60 industries. There are three possible ways to deal with this problem. First, the regression analysis can be conducted for the variables obtained from the Mannheimer Innovation Panel and the variables obtained from Verspagen’s study separately. Second, the findings about clustering and the observations in the Mannheimer Innovation Panel can be transformed to the industry classification used by Verspagen. Third, the results obtained by Verspagen can be assigned to the 60 industries chosen above. Each of these three procedures has some shortcomings. The latter procedure is used here because it seems to have the least problematic shortcomings, while it has several advantages. The advantages are the possibility of using 60, instead of 22, industries for the analysis, which makes the results more significant, the possibility of studying all independent variables within one analysis, and the fact that all 3-digit industries with a certain number of firms (in the Mannheimer Innovation Panel) are considered in the same way. The only shortcoming of the procedure chosen is the assignment of the industries studied by Verspagen to the 60 industries chosen above. Each of the 60 industries can be easily assigned to one of the industries studied by Verspagen but not the other way round. Therefore, the spillover ratios that are found in the analysis of Verspagen are transferred to all industries that are assigned to the respective industry in Verspagen’s study. This means that many values are used for several industries. This can be expected to lower the significance of any relationship between intra-industry spillovers and clustering. Hence, the procedure chosen here is rather conservative because it underestimates the influence of spillovers. 3.5.2 Method and descriptive statistics The aim of this analysis is to study the industrial characteristics that are responsible for the existence of local clusters. The theoretical literature and the literature on case studies suggest many different mechanisms that may be responsible for the emergence of local clusters. The empirical analysis conducted here tests whether these mechanisms are especially active in those industries that are found to be clustering in the above study. Hence, it detects relations between industrial characteristics and clustering. Fifteen variables are defined in the previous subsection that more or less reflect the mechanisms suggested in the literature. The task is to test which of these 15 variables are able to predict clustering in industries. Measuring clustering To this end, a variable has to be defined that reflects the above findings on clustering for each industry. The study conducted in Section 3.2.2 classifies each 3-digit industry into one of two categories: one containing all industries in which local clusters exist and one containing all industries in which no such clusters are found, at least not significantly. Hence, a variable can be defined that takes the value 1 for all industries that fall into the

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former category and 0 for all industries in the latter category. This variable is called CLUSTEXIST in the following. In Section 3.3 the dynamics within all 3-digit industries were studied. This resulted in the classification of all 3-digit manufacturing industries into one of three classes: ‘clustering’, ‘equalising’ and ‘other’. The results are given in Table A.1. Two variables are defined on the basis of these results. A variable called CLUSTDYN takes the value 1 if ‘clustering’ dynamics are observed and the value 0 if either ‘equalising’ or ‘other’ dynamics are observed. A variable called EQUALDYN takes the value 1 if ‘equalising’ dynamics are observed and the value 0 if either ‘clustering’ or ‘other’ dynamics are observed. All three variables are clearly specified for the 60 industries chosen above. Hence, there are 3 dependent variables, 15 independent variables and 60 observations. Statistical procedure The independent variables only take the value 1 or 0. Furthermore, it is shown in Section 4.3 that the emergence of local industrial clusters is a stochastic process in which, in general, industrial characteristics influence the probability of clustering but only in some cases does clustering actually take place. Therefore, a logistic regression is chosen here. A logistic regression means that it is assumed that it is possible to predict the likelihood of the dependent variables being 1 on the basis of the independent variables. Let us denote the independent variables by Xi (i {1, 2,…, 15}) and the dependent variables by Yj (j {1, 2, 3}). Then, the assumed dependence is given by (3.19)

where βi are the regression coefficients. The independent variables are chosen such that they reflect different processes that are suggested as causes of clustering in the literature, namely the accumulation of human capital, innovations, spillovers, knowledge flows and cooperation among firms. For each of these factors several variables are chosen that more or less measure the strength of these processes. Different measures are chosen for each of these processes because it is not clear how these processes can be measured precisely. However, this implies that there are groups of variables that measure approximately the same. As a consequence, these variables can be expected to be highly correlated. Therefore, the problem of multicollinearity has to be considered. The correlations between all independent variables are given in Table A.2 in the appendix. The variables that concern the same processes are found to be significantly correlated in most cases. However, very strong correlations (>0.65) are only obtained between the variable PRODINNO and the variables PROCINNO and REVNEW. Therefore, it is studied below whether the results of the regression analyses change significantly if only one of each group of very similar variables is used. The variables are grouped as follows.

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Innovations: PRODCYC, PRODINNO, PROCINNO, INNOEXP, REVNEW Information sources: INFOINNO, SCIEINNO Human capital: EMPNAT, EMPSOC, EMPTECH Cooperation: COOPCOM, COOPSUP, COOPUNI Spillovers: SPILLRATA, SPILLRATB The regression is conducted repeatedly, each time including all variables of four of the groups but only one variable of the remaining group. This test shows that multicollinearity is a problem for the three variables PRODINNO, PROCINNO and REVNEW, while it is not a problem for the other variables. The result changes significantly—which is defined here as a change in the variables with a significant influence—only if the inclusion of the variables PRODINNO, PROCINNO and REVNEW is changed. Therefore, the results of the regressions are presented below for the complete model containing all variables and for the three models that are restricted to one of the variables, PRODINNO, PROCINNO or REVNEW. Descriptive statistics Table 3.7 lists the average value and the variance of all independent variables. The dependent variables are binary variables. The frequency with which they take the two values ‘0’ and ‘1’ is given in Table 3.8. 3.5.3 Results and Discussion Results of the logistic regressions Three dependent variables are defined above. For each of them 4 logistic regressions are conducted: one that includes all independent variables and three that include each one of the independent variables, PRODINNO, PROCINNO and REVNEW, and all other independent variables. The regressions are conducted using the robust covariances according to Huber and White, so that problems caused by heteroscedasticity should not appear. The results are given in Table 3.9 for the variable CLUSTEXIST, in Table 3.10 for the variable CLUSTDYN, and in Table 3.11 for the variable EQUALDYN. In the case of the dependent variable CLUSTEXIST only for one independent variable, the variable SPILLRATA, is a significant result ob-

Table 3.7 Descriptive statistics for the independent variables. variable

average

std. deviation

PRODCYC

10.51

5.57

PRODINNO

0.702

0.179

PROCINNO

0.634

0.175

INNOEXP

0.0532

0.0395

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REVNEW

15.42

9.45

INFOINNO

0.120

0.109

SCIEINNO

0.246

0.128

EMPNAT

0.0890

0.0650

EMPSOC

0.0231

0.0132

EMPTECH

0.0968

0.0377

COOPCOM

0.040

0.069

COOPSUP

0.150

0.181

COOPUNI

0.020

0.054

SPILLRATA

0.398

0.142

SPILLRATB

0.284

0.163

Table 3.8 Descriptive statistics for the dependent variables. frequency of the value variable

‘0’

‘1’

CLUSTEXIST

27

33

CLUSTDYN

44

16

EQUALDYN

35

25

tained. This positive relationship disappears if two of the three variables, PRODINNO, PROCINNO and REVNEW, are excluded. In the case of the independent variable CLUSTDYN the inclusion of the variables PRODINNO, PROCINNO and REVNEW has only little influence on the results of the regression. The variables PROCINNO, COOPSUP and COOPUNI have a strongly significant positive impact on the probability of ‘clustering’ dynamics. The impacts of INFOINNO and SPILLRATA depend on the inclusion of the variables PRODINNO, PROCINNO and REVNEW. In the study of the variable EQUALDYN the inclusion of the variables PRODINNO, PROCINNO and REVNEW matters. PROCINNO has a positive impact if all independent variables are considered. If only one of them

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Table 3.9 Results for the logistic regressions for the variable CLUSTEXIST (the p-values are given in brackets, significant results (significance level 0.05) are given in bold letters). independent variable complete model reduced model reduced model reduced model const.

−2.80 (0.19)

−1.76 (0.35)

−3.49 (0.05)

−1.69 (0.28)

PRODCYC

−0.12 (0.09)

−0.07 (0.23)

−0.07 (0.20)

−0.09 (0.16)

PRODINNO

−1.45 (0.68)

−0.86 (0.74)

−

−

PROCINNO

4.46 (0.10)

−

3.11 (0.19)

−

INNOEXP

−19.3 (0.15)

−16.7 (0.17)

−19.0 (0.14)

−18.5 (0.15)

REVNEW

−0.06 (0.38)

−

−

−0.04 (0.41)

INFOINNO

0.97 (0.75)

−0.74 (0.84)

−3.01 (0.48)

−0.91 (0.82)

SCIEINNO

−3.37 (0.48)

0.36 (0.90)

−0.06 (0.98)

0.91 (0.76)

EMPNAT

−13.1 (0.19)

−12.8 (0.13)

−15.9 (0.08)

−10.4 (0.26)

EMPSOC

56.1 (0.11)

59.7 (0.07)

56.4 (0.09)

55.9 (0.09)

EMPTECH

19.0 (0.12)

16.7 (0.15)

19.4 (0.11)

16.3 (0.17)

COOPCOM

−4.00 (0.45)

−1.83 (0.71)

−3.97 (0.45)

−1.74 (0.73)

COOPSUP

−1.38 (0.44)

−0.74 (0.66)

−0.97 (0.57)

−0.92 (0.59)

COOPUNI

3.13 (0.64)

3.49 (0.57)

2.45 (0.72)

3.66 (0.55)

SPILLRATA

7.26 (0.05)

6.57 (0.07)

6.31 (0.07)

6.53 (0.06)

SPILLRATB

−0.06 (0.98)

−0.29 (0.91)

−0.20 (0.94)

0.03 (0.99)

0.242

0.196

0.219

0.204

2

R (Cox & Snell)

is considered, this influence vanishes. Furthermore, COOPCOM is found to have a significant negative impact for some model specifications. For all other variables no significant dependence is found. Summing up, in the case of EQUALDYN no robust significant dependencies are identified. The independent variables chosen seem to be less adequate for the explanation of ‘equalising’ dynamics than they are for the explanation of ‘clustering’ dynamics. Clustering and dynamics towards clustering The following discussion of the results described above starts with a comparison between the results for the variable CLUSTEXIST and the results for the variable CLUSTDYN. This is done for two reasons. First, the different quality of the fits confirms the findings in Section 3.4, as will be discussed below. Second, an analysis and comparison of both

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results gives additional insight into the impact of industrial characteristics (the independent variables) on clustering (the dependent variables). In Section 3.4 the spatial distribution of local industrial clusters in Germany is discussed. It has been stated that many clusters are located in

Table 3.10 Results for the logistic regressions for the variable CLUSTDYN (the p-values are given in brackets, significant results are given in bold letters). independent variable complete model reduced model reduced model reduced model const.

−17.9 (0.01)

−8.25 (0.05)

−17.1 (0.01)

−7.91 (0.02)

PRODCYC

0.03 (0.82)

0.13 (0.22)

0.22 (0.06)

0.03 (0.82)

PRODINNO

−10.3 (0.23)

−1.11 (0.78)

−

−

PROCINNO

18.4 (0.01)

−

9.16 (0.03)

−

INNOEXP

−71.1 (0.10)

−20.5 (0.41)

−49.2 (0.16)

−20.3 (0.41)

REVNEW

−0.26 (0.10)

−

−

−0.15 (0.10)

INFOINNO

16.1 (0.10)

15.6 (0.05)

17.0 (0.07)

14.6 (0.06)

SCIEINNO

8.03 (0.20)

1.11 (0.77)

−0.83 (0.84)

5.27 (0.26)

EMPNAT

6.15 (0.64)

−0.70 (0.94)

−5.60 (0.65)

4.58 (0.68)

EMPSOC

−5.11 (0.93)

12.8 (0.72)

−1.58 (0.97)

4.06 (0.91)

EMPTECH

17.6 (0.33)

−3.65 (0.78)

3.32 (0.81)

−1.47 (0.91)

COOPCOM

−0.53 (0.95)

3.87 (0.48)

2.05 (0.74)

4.21 (0.47)

COOPSUP

10.7 (0.03)

8.26 (0.01)

10.8 (0.01)

8.07 (0.02)

COOPUNI

42.0 (0.01)

21.9 (0.01)

27.7 (0.01)

25.6 (0.01)

SPILLRATA

21.6 (0.03)

7.47 (0.16)

12.5 (0.10)

7.89 (0.14)

SPILLRATB

−0.22 (0.97)

−0.32 (0.93)

−0.65 (0.89)

1.84 (0.63)

0.494

0.338

0.407

0.370

2

R

places where the conditions for the emergence of local clusters have been present in the past but are no longer present today. In the theoretical approach in Chapter 2 a similar argument is repeatedly put forward. It is argued there that only the situation and processes during the emergence of clusters matter. In general, clusters remain for quite some time after the causes for their emergence have disappeared. Here, actual industrial characteristics (from 1997 and 1999) are used to explain actual clustering (1995–2000). According to the arguments above, this should be possible for the dynamics towards clustering but not for the existence of clustering. The latter should only be possible if either the industrial characteristics have not changed or the clusters have emerged recently. Hence, an explanation of the variable CLUSTEXIST on the basis

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of actual industrial characteristics should be less fruitful than an explanation of the variable CLUSTDYN on the same basis. The findings recorded in the Tables 3.9 and 3.10 confirm this. The R2 is much higher for the latter regressions than for the former ones, and more independent variables are found to significantly explain the value of CLUSTDYN than the value of CLUSTEXIST. Hence, industrial characteristics seem to be indeed responsible for the emergence of local clusters,

Table 3.11 Results for the logistic regressions for the variable EQUALDYN (the p-values are given in brackets, significant results are given in bold letters). independent variable complete model reduced model reduced model reduced model const.

3.71 (0.11)

0.94 (0.63)

4.90 (0.03)

1.355 (0.38)

PRODCYC

0.03 (0.66)

−0.05 (0.45)

−0.08 (0.20)

0.000 (1.00)

PRODINNO

4.82 (0.20)

2.90 (0.31)

−

−

PROCINNO

−10.1 (0.01)

−

−4.96 (0.08)

−

INNOEXP

−10.1 (0.35)

−11.3 (0.25)

−11.1 (0.25)

−9.24 (0.30)

REVNEW

0.13 (0.08)

−

−

0.11 (0.07)

INFOINNO

−1.13 (0.82)

−6.23 (0.12)

−2.33 (0.58)

−5.74 (0.17)

SCIEINNO

1.22 (0.71)

2.52 (0.40)

3.20 (0.29)

1.31 (0.68)

EMPNAT

1.34 (0.89)

1.64 (0.85)

5.18 (0.56)

−3.24 (0.73)

EMPSOC

−9.07 (0.83)

8.04 (0.83)

14.9 (0.69)

15.2 (0.67)

EMPTECH

−0.66 (0.96)

−1.96 (0.88)

−2.46 (0.85)

−1.68 (0.90)

COOPCOM

−12.7 (0.08)

−16.2 (0.03)

−12.20 (0.07)

−15.6 (0.03)

COOPSUP

−2.13 (0.33)

−2.174 (0.23)

−2.91 (0.15)

−1.69 (0.36)

COOPUNI

−8.34 (0.22)

−7.83 (0.20)

−5.72 (0.37)

−9.21 (0.15)

SPILLRATA

−7.83 (0.07)

−4.75 (0.20)

−3.88 (0.28)

−5.00 (0.18)

SPILLRATB

3.83 (0.26)

2.14 (0.45)

2.58 (0.37)

1.56 (0.59)

0.386

0.267

0.296

0.300

R2

while they are less or even not at all involved in the persistence of clusters. This also has important implications for the causal relationship between the independent and the dependent variables. The regression analysis that is conducted here only leads to conclusions about the relations between variables. Hence, the argument might be put forward that the existence of clusters increases certain processes in the industry and therefore influences certain industrial characteristics. This is plausible for a number of independent variables that are used above. However, such a causation would

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imply that the variable CLUSTEXIST is more strongly related to the respective industrial characteristics than the variable CLUSTDYN. Hence, on a general basis, it can be stated that most of the relations between the independent and the dependent variables in this approach are caused by an impact of the independent variables on the dependent variables. For the different variables this is discussed separately below. Human capital The importance of human capital has been measured by the share of employees with particular educational specialities. The kinds of education that have been considered are studies of natural sciences at universities, studies of social sciences at universities and studies at technical colleges. The various types of education have not been found to have any significant impact on any of the variables CLUSTEXIST, CLUSTDYN and EQUALDYN. Hence, no evidence is found here for the claim that the accumulation of human capital is important for the emergence of local industrial clusters. However, this does not exclude the possibility that the accumulation of human capital matters. First, the results here only state that no empirical evidence is found for such a relationship. Second, the variables examined here relate only to human capital that is created outside of firms and is used by firms. Experience and tacit knowledge that are acquired on the job might play a role, but they are not included here. It has to be doubted whether the measures used here are good measures for the importance of human capital in industries. Other measures are, however, not available. Hence, all that can be stated is that industries in which employees that hold a university or college degree play a strong role are neither more likely to show clustering nor more likely to show clustering dynamics. Innovations The importance of innovations in an industry is measured by a number of different values. Four different kinds of measures that are used here can be distinguished. These are measures of the length of the product life cycle, of the number of innovations, of the expenditures on innovations, and of the share of innovative products within sales. Strongly significant results are only obtained for the number of process innovations. A high frequency of process innovations seems to be related to a high probability of ‘clustering’ dynamics and a low probability of ‘equalising’ dynamics. At the same time, it is not related to a high probability of the existence of clusters. According to the discussion above, this points to a causal relationship between the number of process innovations and the existence of local clusters. Hence, a high frequency of process innovations seems to be one factor involved in the emergence of local industrial clusters. The same seems not to hold for product innovations. No significant results are obtained for the frequency of product innovations, even if the variable related to process innovations is excluded from the analysis. Product and process innovations seem to have different impacts on the emergence of local clusters. For the total amount of innovation expenditures (INNOEXP), the length of the product life cycle (PRODCYC) and the share of new products among the sales of a firm (REVNEW) no significant results have been found.

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Spillovers The assumption that spillovers cause the existence of local industrial clusters is based on the argument that firms have to be located near to each other to profit from such spillovers. The relevance of spillovers is not measured directly by the variables INFOINNO, SCIEINNO, SPILLRATA and SPILLRATB. However, if spillovers cause the co-location of firms, firms should be located near those other firms from which they receive most spillovers. If they receive most spillovers from within the industry they should co-locate with other firms of the same industry. This should cause the existence of local clusters. If they receive most spillovers from other industries, co-location within the industry is less important. Hence, the intra-industry spillover ratio (SPILLRATA and SPILLRATB) and the flow of information among competitors (INFOINNO) should be a good predictor for the existence of local industrial clusters if the above argument is correct. The variable, SCIEINNO, measures the importance of knowledge flows from universities. The regressions for SCIEINNO and SPILLRATB show no significant relationship between these variables and the dependent variables, while the regressions for INFOINNO show a significant relationship with one dependent variable for one specification of the reduced model that is the least adequate one (considering the obtained R2). Only for the variable, SPILLRATA, are significant results obtained. Intra-industries spillovers in the form measured by SPILLRATA seem to explain the existence of local clusters and the occurrence of ‘clustering’ dynamics, although the significance of these findings is not robust with respect to changes in the model specification. Hence, it can be concluded that spillovers seem to be related to the existence of local industrial clusters. The causal relation might work in both directions. Spillovers might cause co-location and co-location might causes spillovers. The empirical approach taken here is not able to differentiate between the two possible directions of the causal relationship. The latter causal relationship is shown to exist in empirical studies (see, e.g., Anselin, Varga & Acs 1997). However, Verspagen and Schoenmakers (2000) have shown that spillovers in the form of patent citations are influenced by technological distance more robustly than by spatial distance. This provides some evidence for a causal relation that also leads in the opposite direction. This would imply that the importance of intra-industrial spillovers influences the existence and emergence of local industrial clusters. The different results for the variables INFOINNO, SPILLRATA and SPILLRATB suggest that spillovers of a certain type are important. INFOINNO measures spillovers in the form of knowledge flows about potential innovations. SPILLRATA measures to what extent patents are classified under several industries that belong to the same 2-digit industry. SPILL-RATB measures to what extent the supplementary patent classifications also belong to the same 2-digit industry as the main classification. Therefore, the variable INFOINNO measures the use of knowledge, while the other two variables measure the relatedness of knowledge in different industries. It seems to be important for the existence of local industrial cluster that the technology developed in an industry is relevant for other sub-industries of the same 2-digit industry. It seems to be less important whether innovations trigger innovations by other firms within the same industry or whether the technology used mainly relates to technology within the same 2-

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digit industry. Knowledge flows from universities do not seem to matter either (see the results for SCIEINNO). Regional cooperation Local cooperation is very often considered to be an important factor in the context of local industrial clusters in the literature. However, the empirical evidence provided is mixed and no proof of this influence is given (a discussion of this can be found, e.g., in Grotz & Braun 1997b). It has been found that cooperation with local partners is said to be important by firms and accounts for a large share of all cooperation of a firm (this is reported, for example, in Koschatzky 1998, Oerlemans, Meeus & Boekema 1998, Sternberg 1998, Fritsch 1999 and Keeble, Lawson, Moore & Wilkinson 1999). However, this does not prove that local cooperation causes the emergence of local industrial clusters. It rather suggests that the existence of local industrial clusters might increase the amount of cooperation. Here, evidence for the impact of local cooperation on the emergence of local industrial clusters is provided. The variables COOPSUP and COOPUNI measure the share of cooperation with suppliers and universities, respectively, that takes place locally. They both show a significant positive impact on CLUSTDYN, while they show no significant impact on CLUSTEXIST. According to the discussion above, this implies that a high rate of local cooperation appears together with the emergence but not with the existence of local industrial clusters. Hence, if cooperation mainly takes place locally in an industry, clustering is more likely to occur. This does not hold for all kinds of cooperation. A positive impact is only found for cooperation with suppliers (COOPSUP) and universities (COOPUNI). No impact is found for cooperation with competitors (COOPCOM). Hence, there is no evidence for the claim that local cooperation among competitors characterises local clusters or is important for their emergence. Such a claim has been repeatedly put forward in the context of the Italian industrial districts (see, e.g., Dei Ottati 1994). Summing up The coincidence between specific industrial characteristics and the emergence and existence of local industrial clusters is studied above. It is found that those industries with a high number of process innovations, with many intra-industry spillovers in the form of co-classifications of patents and with a high rate of local cooperation with suppliers and universities are more likely to show clustering dynamics. The simultaneous study of dependent variables that represent the existence (CLUSTEXIST) and emergence (CLUSTDYN) of local clusters allows conclusions to be drawn about the causal direction of these relations. It shows that many process innovations and the regional limitation of cooperation with suppliers and universities have a positive impact on the emergence of local clusters. In the case of intra-industry spillovers, the situation is less clear. In the case of all other industrial characteristics that are examined here, no conclusions can be drawn. The study finds no significant results for these characteristics. However, this might be caused by the fact that these characteristics are not related to the emergence and existence of local industrial clusters or by the restrictions of the data and the small

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number of observations (60). The R2 of around 0.4 that is obtained suggests that more determinants of the emergence of local clusters exist than are considered here. The approach presented here seems to be the first attempt to identify the determinants of clustering in a general approach. It can be hoped that more approaches of this kind follow and that evidence is collected that can be finally used to comprehensively answer the question of why local industrial clusters exist.

4 Simulating local mechanisms

4.1 AIMS AND METHODS In this chapter a simulation model will be developed on the basis of the theoretical discussion in Chapter 2. To this end all local mechanisms that have been identified in Section 2.4.1 as potential causes for the existence of localised industrial clusters will be included in the simulations. The resulting simulation model can be used to analyse the dynamic characteristics of local processes and the factors that influence these processes. The use of simulation models can easily lead to a situation where all possible developments can be created by a specific choice of the parameters. This often leads to strong criticism of simulation models. The present simulation model will contain a large number of parameters. Therefore, all these dangers are present and it is very important to define the aims of the approach carefully and to choose the method for the analysis of the results adequately. These factors will be discussed in detail below. 4.1.1 Aims and scope The previous chapters show that the emergence and evolution of localised industrial clusters is a complex process. Many mechanisms are relevant for this process and they all interact. Different questions can be raised in the context of localised industrial clusters. In this book, for example, the questions of why localised industrial clusters exist, when they emerge and where they appear are addressed. Simulations can add to the necessary analyses in several ways. Here the use of simulations is restricted to one factor that cannot be studied empirically: the stochastic characteristics of the emergence of local industrial clusters. In the previous two chapters, it was repeatedly noted that clustering differs between industries. In addition, each industry has different characteristics. Hence, for each set of characteristics the empirical data offer us one realisation of a time path. At the same time, it is obvious that many of the processes that are involved in the emergence of local industrial clusters are stochastic processes. Hence, the dynamics might look different if there was the chance to repeat time, even if the industrial characteristics were exactly the same. Reality does not offer us such a chance. As a conse-quence, no empirical data about the stochasticity of the emergence of local industrial clusters is available. Simulations offer such a possibility. They can be run repeatedly. However, the results of simulation models depend crucially on the choice of the parameters. Therefore, this

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choice has to be made carefully. In the present context the parameters cannot be fixed empirically for two reasons. On the one hand, not all of them can be studied using an empirical approach. On the other hand, they differ between industries. A fitting to a certain industry is not done here. In line with the overall concept of this book, the simulation study is conducted on a general level. However, ranges can be determined for the parameters in such a way that the characteristics of all industries are reflected by some values within these ranges. The ranges have to be chosen carefully. They restrict the possible outcomes of the simulations in such a way that not everything is possible. The range of possible outcomes can then be discussed. The simulation model is tested by checking whether the empirically observed developments fall into these ranges. Once this is done, all characteristics that are found to be general in the simulations and do not depend on the parameter set can be assumed to describe reality quite well. Hence, the simulation approach will allow the study of statistical characteristics that cannot be studied empirically. Three questions are addressed. First, whether the existence of local clusters is a deterministic or stochastic event is studied. Second, the question of whether the number of local clusters is predetermined is addressed. Third, when and how the location of clusters is determined is examined. 4.1.2 Possibilities and problems Simulations offer seemingly unlimited possibilities to model all kinds of complex systems. With the increasing speed of computers everything seems possible. This is not the case. Of course, in principle every mechanism can be included in the simulations and arbitrarily complex combinations of mechanisms can be modelled. However, all simulation modellers agree that a simulation model should be kept as simple as possible and that at least the modeller should be able to understand what is going on in the model. This limits the applicability of simulation models. This contradicts the fact that simulation models are, in general, used if the systems that are to be examined are too complex to be studied analytically. Sometimes it is very helpful to be able to analyse multi-dimensional processes and the only way to do this is to use simulations. Here such a situation is faced. In the literature many local mechanisms are claimed to play a role in localised industrial clusters. Most of them cannot be rejected on the basis of empirical studies. Therefore, it would be helpful to test the arguments underlying these claims in simulations. Since the different local mechanisms interact and mutually influence their impact, all mechanisms have to be included in one simulation model. As a consequence, it is difficult to follow the processes in the simulations. To make this task easier, the simulation model is set up in the form of a combination of modules. Each mechanism can easily be included or excluded. This allows the mechanisms to be studied separately and a notion of their impact to be developed. It is then also possible to keep track of the developments in the complete model with all mechanisms included.

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Testing intuition and lines of argument In general, simulations are a perfect tool for testing intuition. Theoretical economics, as well as other theoretical sciences, make arguments with the help of relations between causes and effects. This is often done on the basis of logical arguments and intuition. In addition to mathematical analyses and empirical studies, simulations can be used to test these relations. To this end, the causes are included in the simulations and whether they affect the outcome is tested. There are two major restrictions to such an approach. First, simulations are only able to deliver an answer to the question of whether a particular cause implies a particular effect. This should not be mixed up with the question of whether a particular effect is caused by a particular cause. The latter question cannot be answered by simulations. There is an infinite pool of different models and specifications and each effect can be obtained by many different models. Each of them might be the decisive cause in reality, and there are always possible causes remaining that are not tested. However, the same holds for all theories and also for all empirical approaches. Theoretical approaches, empirical studies and simulations are only able to eliminate those causes that are, for some reason, not able to cause the effect under consideration. Second, simulations require a clear specification of the cause that is to be tested. While verbal arguments might remain somewhat vague, in simulations the processes and factors have to be defined precisely. This is an advantage and a disadvantage at the same time. On the one hand, it forces researchers to formulate the line of argument exactly. On the other hand, it makes the test of verbal arguments difficult. If for an implemented cause the cause-effect relation is rejected by simulations, the verbal argument is not automatically rejected as well. It might always be argued that, for another specification, the cause-effect relation might hold. The more specifications are simulated with a negative result, the less likely is the correctness of the cause-effect relation, but it can never be completely rejected. However, specifications of arguments can be rejected with the consequence that the argument has to be formulated more precisely. Hence, simulations cannot prove that a cause is decisive for a particular effect. Furthermore, they cannot prove that a vaguely formulated cause is unable to produce a particular effect. This should be kept in mind while using simulations, so that they are not overdone. Nevertheless, simulation studies can be very helpful. They are able to show that some causes are able to produce certain effects, while other, precisely specified causes are unable to do so. Comparison of simulations and empirical data The argument above also holds and is even more relevant in the context of a comparison with empirical data. One might be tempted to adapt the simulation to reality by narrowing the difference between the simulation result and the empirical data. This is misleading. It has been stated above that many specifications of the model can be found that produce results similar to empirical findings. Identifying one of these specifications does not imply that a correct formulation of the processes has actually been found.

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What can be done, however, is the classification of specifications according to some characteristics of the simulation results. The real characteristics can be studied with the help of empirical data. Then, a comparison between empirical and simulation results can be used to distinguish between those specifications of the simulation model that lead to results in line with reality and those that are not in line with reality. If the characteristics under consideration differ for various real systems (in this analysis, for example, for different industries), the comparison will even allow classification of the studied specification of the simulation model according to the real systems that they might represent. A simulation model with many parameters, like the one used here, however, contains the problem that not all parameters can be specified with the help of empirical data. This implies that for each real system, only some of the parameters can be fixed and an infinite number of specifications remain that cannot be fixed according to empirical data. This infinite number of specifications can never be tested and one can never be sure to have found all specifications for which the simulation results match reality. 4.1.3 Methods of analysing the simulation results The problems that have been discussed above imply that the methods for analysing simulation results have to be chosen carefully. The most important problem identified above is the large set of possible specifications. This problem can, at least, be decreased to some extent by restricting the set of possible specifications as much as possible. Here empirical studies from the literature are used to define a range for each of the parameters. The range for each parameter should be such that it contains all cases occurring in reality but is as small as possible. The questions that are addressed with the help of simulations here differ significantly. Therefore, the methods that are applied also vary. Some questions are answered by descriptive statistics while others are approached with the help of regressions. However, all studies face the problem of a large set of possible specifications of the parameters. Experimental design In the literature a so-called experimental design is used to deal with the problem discussed above (see Winer 1971 for a comprehensive description of this method). This procedure defines several values for each parameter within its range. Usually, at least the two most extreme values are chosen. Depending on the number of values that are chosen for each parameter, the other values are fixed such that they separate the range into equal distances. Through this method several values are obtained for each parameter. For each combination of these values a simulation is run and the characteristics that are to be studied are reported. These characteristics are now treated as dependent variables while the parameters are treated as independent variables. Regression analysis can be used to study the impact of different parameters on the various aspects of the simulation results. This method is not adequate for the simulations that are run here. There are 31 parameters in the simulation model. Choosing only two values for each parameter already implies that 2147 million runs are necessary. Hence, a different approach has to be chosen here.

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Monte-Carlo simulation Instead of the well-structured experimental design described above, the parameter sets that are used can also be determined according to a specific Monte-Carlo approach. In this approach, for each simulation run, all parameters are determined stochastically within their range. This is repeated many times. Again, for each simulation run, the parameters used and the characteristics of the simulation results are reported. The resulting data can be treated like empirical data and studied with the help of regression analysis and other statistical methods. 4.2 SIMULATION MODEL 4.2.1 Concept The simulation model is based on the model that was developed in Chapter 2. It focuses on the firms in a particular industry and their development. In line with the theoretical modelling, it is assumed that these firms interact with local circumstances in such a way that self-augmenting processes appear. However, while the model in Chapter 2 was very abstract with respect to these self-augmenting processes, these processes are modelled in detail here. In Section 2.4.1 the possible mechanisms underlying the self-augmenting processes were identified. They were discussed intensively in that section and were studied empirically in Section 3.5. For some of the mechanisms evidence exists that they are involved in the emergence of local industrial clusters. These are, among others, the accumulation of human capital in regions, local spillovers and spin-offs. They are explicitly included in the simulation model. The dynamics of the respective local circumstances will be modelled and the interactions between these and the population of firms will be simulated and analysed. Furthermore, the simulation model is not restricted to one region. Instead, Germany, with its 4391 administrative districts, is studied. Besides the interactions within each region, interactions between regions and their spatial characteristics are considered in the model. Through this, it is aimed to depict a quite realistic picture of the development of a firm population in one industry in space, at least with respect to all factors that are important for the distribution of firms in space. Similar simulation models are studied elsewhere (see Camagni & Diappi 1991, Jonard & Yildizoglu 1998, Caniels & Verspagen 1999, Brenner 2001b, Brenner & Weigelt 2001 and Brenner 2003). These studies differ with respect to the local mechanisms that are included in the model and with respect to the questions they address. In the model that is used below only the mechanisms of the accumulation of human capital, spillovers and spin-offs are included. The simulation models in the literature also contain the interaction of firms with public opinion and policy, local venture capital markets and cooperation 1

In contrast to the empirical study in Chapter 3, West Berlin and East Berlin are merged here because only joint data are available. Other than this, the regions are defined in accordance to the empirical data for the years 1995 and 1997.

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among firms (see Jonard & Yildizoglu 1998, Brenner 2001b and Brenner 2003), as well as synergies between firms (see Camagni & Diappi 1991 and Brenner & Weigelt 2001). In contrast, the model used here is much more elaborated with respect to the three mechanisms that are considered. In the literature the features of the dynamics (see Jonard & Yildizoglu 1998 and Brenner & Weigelt 2001), the spatial structure that develops (see Camagni & Diappi 1991 and Caniëls & Verspagen 1999), the influence of the parameters (see Brenner 2001b and Brenner & Weigelt 2001) and the influence of policy measures (see Brenner 2003) are studied. Here the path dependence and stochastic characteristics of the developments are studied. 4.2.2 Simulation model Firms and their characteristics Due to the entry and exit processes the number of existing firms changes during the simulations. Nevertheless, a natural number, n ( N(t)), is assigned to each firm for identification purposes. The set N(t) changes with time and always contains only a part of the set of all natural numbers. t denotes time which is assumed to proceed in steps of one and therefore is also a natural number, (t IN). One time step characterises one day in the simulations. Periods of time smaller than one day seem not to matter for processes such as the exit or entry of firms, innovations, production and sales. Hence, the use of a discrete time and a basic unit of time of one day seems to be adequate. The state of a firm, n, at any time, t, is characterised by its labour force, L(n, t) ( IN), its technological advancement, T(n, t) ( IR+), the industry, in ( {1, 2,…, I}, to which it belongs and the region, rn ( {1, 2,…, R}), in which it is located. While the labour force and the technological advancement of a firm change with time according to the processes that are defined below, the location of a firm and the industry to which it belongs remains constant. Movements of firms are excluded in the simulation model. In the simulations conducted here, only one industry is considered. Therefore, the dependence on i is omitted in the following although most parameters depend on the industry. Geographic space In order to be able to compare the results of the simulations with the findings in the empirical analysis in Chapter 3, the same spatial structuring is used here. The administrative districts are used as regions here, hence, developments in 439 regions are simulated and the results analysed. Several characteristics of these regions are explicitly used in the simulations. From the spatial perspective, the geographical distance between each pair of regions is important. These distances are calculated here between the centre of gravity of the regions. The centres of gravity are calculated according to the real spatial shapes of the regions. They are denoted by x and y coordinates. This means that the geographic location of a region r is given by x(r) and y(r). Furthermore, data about the population and the number of students in the regions are used (see Section 4.2.3).

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Size of firms The employed labour force L(n, t) has been mentioned above as one of the variables defining the state of a firm. A fixed coefficient technology is assumed here. This means that for each amount of labour, the respective amount of capital is necessary. As a consequence, the amount of capital always increases and decreases proportionately to the amount of labour used by a firm. Therefore, it is possible to consider only labour explicitly. Firms are assumed to adapt their labour force, and their capital, to the demand they face. Hence, the amount of labour, L(n, t), that is employed by a firm adapts to the demand for its products. This means that firms are assumed to behave entirely adaptively with respect to the market situation. They do not actively decide to increase their sales, but offer their products on the market for a price that is determined by the production costs and react to demand. Forward-looking firm strategies are not considered here. It is assumed that labour and capital inputs can be reduced very quickly. The speed for increasing labour and capital inputs is assumed to be limited to a maximal increase of λ·L(n, t) within one time step, meaning one day. This implies that firms might face demand that is greater than they can serve. Demand To keep the model as simple as possible no demand function is used here. The total demand is assumed to be constant or changes exogenously. It is denoted by D. The prices at which the goods are offered by firms are assumed not to influence the total demand, D(t). The simulation model is constructed to contribute to the evolution of the spatial distribution of firms. Consumer behaviour has to be included only insofar as it has an impact on this evolution. Therefore, prices are assumed to influence the choice between products but not the total number of products that are consumed. All firms within one industry compete for the demand, D(t), in this industry. Demand is assumed to be global, so that the location of firms does not influence the demand for its products. However, the goods of different firms are assumed to be different and the consumers are assumed to be heterogeneous. The Hotelling model has become the common tool to describe such situations in the literature (examples are Norman & Thisse 1999 and Foros & Hansen 2001). The characteristics of the goods are defined in a onedimensional space and vary between 0 and 1. Each firm, n, produces one kind of good, which is characterised by g(n) (0
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total demand. Only the decision where they buy the good is modelled. p(n) is the price for which a firm, n, offers the good and π determines how important it is for the consumers that a good is similar to the one desired. Finally, it is assumed that consumers are reluctant to change the firm from which they buy the good. In the marketing literature the change between brands and brand loyalty are extensively studied (an overview of this huge literature is given in, e.g., Mellens, Dekimpe & Steenkamp 1996). Therefore, a variable, n(c, t), is introduced that characterises consumer, c, at each time t, where n(c, t) is the firm from which the consumer buys a piece of the good at time, t. The modelling of consumers’ behaviour is determined by the modelling of the change in n(c, t). This is constructed in the following way. Each consumer is assumed to check a share of η of all firms in the respective industry every day. Therefore, η determines how well consumers are informed about other firms’ offers and how quickly they will identify an existing offer that is better than the one they take currently. The number of firms that are checked is given by η·N(t), where N(t) is the number of firms in the industry under consideration at time t. If η·N(t) is not a natural number, it is randomly determined whether the next higher or next smaller natural number is used. The firms that are checked are randomly drawn out of the set of all firms. For each chosen firm, ñ, the consumer, c, compares the price and the type of good, g(c), that firm, ñ, offers with the same characteristics as firm, n(c, t). The consumer changes her choice of firm, n(c, t), to n(c, t)=ñ if the difference in the utilities exceeds a certain value of ρ. Mathematically this means that a change in the firm appears if (4.2) ρ denotes the reluctance of consumers to switch from one firm to another even if the good of the latter satisfies their wants better. If a consumer has not been able to buy a good, she switches to the first firm that she checks and which is still able to satisfy a higher demand. The production capacity of a firm, n, is denoted by ∆(n, t). At the end of each time step it is set to (4.3) d(n, t) denotes the number of goods that are sold by firm, n, at time, t. It has been assumed above that a firm adapts its size to the current demand. Furthermore, it has been stated that the size (labour force) of a firm cannot be increased faster than by a share of λ of the current size. Equation (4.3) reflects this fact. d(n, t) denotes the number of consumers who buy a good from firm, n, at time, t, which is determined by the process described above. A new customer at time t can only be accepted if the actual number of customers is smaller than ∆(n, t). This implies that the possible increase in the size (number of goods produced) of a firm is not exactly λ·d(n, t) but the next higher natural number. Thus, a firm is able to increase the number of goods produced by at least one each time step. If the maximal capacity is reached, (d(n, t)>∆(n, t)) consumers who want to switch to the firm are rejected and remain in their previous state.

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Price setting It is assumed that firms use mark-up pricing. This means that the price of goods is determined by the costs of their production. According to the above modelling of demand, only the relative prices matter. Hence, if the mark-up is the same for all firms in the same industry, which is assumed here, the mark-up has no influence on the model. It can be arbitrarily set and is assumed to be 1.1 in the simulations. Two factors are explicitly modelled to influence production costs here. These are labour costs and the technology used. It is assumed that the labour costs are the same for all firms in the same region and the same industry. The labour costs for firm n at time t are therefore denoted by w(rn, t). The way in which they are determined is discussed in detail below under the heading of ‘human capital’. All other costs (for capital, materials, energy and so on) are assumed to be either proportional to the labour costs or additive and constant per unit of production. This allows them to be omitted, again due to the fact that only the relationship between prices matters. Technological development can have different effects. It might increase the productivity of labour, increase the quality of products, decrease the amount of material inputs per unit of production and so on. For simplicity it is assumed that the technological advancement of firm, n, is denoted by the variable, T(n, t), at time, t. Below the average technology is set to a value of one. The more advanced is the technology, T(n, t), of a firm, the lower are the costs of production. This is accounted for in the model by the division of the costs by T(n, t) in Equation (4.4). The technological advancement of firms over time is described in detail below under the heading of ‘innovations’. Furthermore, economies of scale have to be considered. This is done by the last term in Equation (4.4). Costs are assumed to depend on the size of the labour force (which equals the size of production). The shape of the economies of scale is determined by two parameters which are assumed to be the same for all firms in an industry: β↑ ( IR+) and β↓ ( IR+). β↑≥1 is assumed, so that there are never diseconomies of scale for very small sizes of firms. However, if firms increase in size, diseconomies might develop (depending on the value of β↓). This reflects the fact that the dependence of the production costs on the size of a firm is usually s-shaped. The price of firm n’s products is given by (4.4)

Innovations The technology, T(n, t), of a firm is driven by innovations and catch-up processes. There is a basic rate of innovation for each firm which reflects successful research within the firm. It is assumed here that firms are not able to influence this basic rate of innovation. This means that the possibility of varying the amount of R&D expenditures is ignored. All firms are assumed to spend a certain amount on R&D which is proportional to their size, meaning the number of their employees. In the literature the number of innovations in firms is usually found to depend on the size of the firms (Audretsch & Acs 1991, Anselin, Varga & Acs 1997 and Blind & Grupp 1999), although this is not always the case (see for example Schulenburg & Wagner 1991). Some empirical studies found a u-

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shaped dependence of the innovation rate on the size of the firm (see Audretsch & Acs 1991 and Bertschek & Entorf 1996). Studies of the dependence of the innovation rate on the quadratic value of the firm size have found negative values (see Audretsch & Acs 1991 and Ray & Bhaduri 2001). This contradicts a u-shaped innovation rate. Therefore, the internal rate of innovations is assumed here to be the sum of two values: a constant, µ0 ( IR+), which is the same for all firms and a value, µL·L(n, t) (µL IR+), that is proportional to the number of employees in the firm. Besides this internal rate, µ0+µL·L(n, t), innovations are caused by technological spillovers. There is plenty of empirical evidence (cf. Anselin, Varga & Acs 1997, Audretsch 1998 and Blind & Grupp 1999) for the fact that the research conducted by other firms has an impact on the innovation output of a firm. Furthermore, there is also empirical evidence for the fact that technological spillovers decrease with the distance between firms (cf. Jaffe, Trajtenberg & Henderson 1993). Finally, it is assumed that firms create more spillovers, the larger they are. This means that the number of spillovers increases with the number of employees of the creating firm (in the literature—e.g. Anselin, Varga & Acs 1997—spillovers are found to increase with the research spending in the respective firms, which is assumed to be proportional to the size of the firms here). A parameter, σ ( IR+), is defined that determines the amount of spillovers that occur within the industry. It is defined in such a way that it represents the effect of a firm, n, on the innovation probability of another firm, ñ, at the same location compared to its own internal rate of innovation (see Equation (4.6)). The effect of spillovers decreases with the spatial distance between the firms. Firms located in another region have less impact on a firm than firms located in the same region. Nevertheless, they still have an impact that has to be considered here. Firms in another region, r≠rn, are assumed to create spillovers for firm n, which decrease with the distance between the regions r and rn. The geographic distance between two regions r and is given by (4.5) The decrease in spillovers with the distance between firms is reflected by a factor is a parameter which determines the strength of this effect. Including all these aspects leads to a probability, P(n, t), for firm n to innovate at time t that is given by (4.6)

Whether a firm n innovates at time t is a random event. The probability of such an event is given by Equation (4.6). All innovations are assumed to be incremental. Thus, an innovation increases the technology, T(n, t), that is used by firm n by a certain amount.

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In order to model catch-up processes the increase in technology from innovations depends on how far the technology of the firm is behind the technological frontier. The further behind a firm is, the larger is the innovation step if an innovation is made. The technology frontier is denoted by Tmax(t). It is assumed that there is a basic innovation step of ( IR+). This is the amount of technological improvement possible at the frontier. The innovation steps are assumed to increase linearly with the distance from the technology frontier. The respective factor is denoted by . Hence, the effect of an innovation at time t is given by (4.7) Assuming the amount of improvement is proportional to the current value of T(n, t) causes the impact of an innovation on the productivity of a firm to remain the same over time. Therefore, the values of T(n, t) can be reduced at each time step such that their average equals 1. This is done for normalisation and has no impact on the dynamics of the model since only the comparison between the prices of the firms matter. Exit and entry of firms It is assumed that firms exit if the demand for their goods, d(n, t), falls to 0. Two kinds of entries are considered: independent start-ups and spin-offs. Start-ups are assumed to appear with a particular probability that depends on the size of the population in the region. This probability is assumed to be given by where Φ(r) is the number of potential founders in the region, here approximated by the total labour force in the region. According to this probability, start-ups are created at each time step in each region randomly. The initial variables of these firms are defined as follows. The technology used by a start-up firm falls into the same range as the technologies currently used by all existing firms. To this end, the least and most advanced technologies that are used at time t by any firm in the industry are calculated: Tmin(t) and Tmax(t). The start-up firm might start with an initial innovation. Therefore, the technology of the start-up firm is randomly drawn from the range [Tmin(t), Tmax(t)·(1+ )]. The initial number of employed workers is also randomly determined. It ranges between 1 and Λ ( IN). The good, g(n), that a start-up firm n produces is randomly drawn from the set [0, 1]. Finally, before the new firm is created in the simulation programme, the algorithm checks whether the firm is able to attract the respective number of consumers. To this end the list of consumers is worked through. For each consumer the algorithm checks whether she would switch to the new firm. As soon as a number of consumers have been found that matches the initial number of employed workers in the new firm, these consumers switch and the firm is created. If the required number of consumers is not attracted, the firm is not created. Thus, not every founding process is successful. With a certain probability each firm n creates a spin-off firm ñ. The spin-off firm starts with the technology that firm n currently uses: T(ñ, t)= T(n, t). The initial number of employees is again drawn from a uniform distribution between 1 and Λ. The good that

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the spin-off firm produces, g(ñ), is drawn randomly from the set [0, 1]. Whether the founding process is successful in the case of spin-offs is tested in the same way as for start-ups. The probability of a spin-off depends on the number of workers in firm n. The more employees a firm has, the more likely one of them starts an own firm. The total frequency of spin-offs is given by the parameter, spin. Therefore, the probability of a spin-off from firm n is given by (48)

where (t) is the total employment in the industry under consideration. Spin-offs are often located near the firm in which the founder has worked before. In this approach it is assumed that the likelihood of the spin-off firm being located in a certain region decreases exponentially with the distance from the originating firm. The probability of the spin-off firm ñ being located in region r is given by (4.9)

where z(r, rn) is defined in Equation (4.5) and ζspin ( characterises the geographical stickiness of spin-offs.

IR+) is a parameter that

Human capital Two kinds of human capital have been distinguished in the previous chapter: transferable and non-transferable human capital. Although the matching is not exact, the terms knowledge and skills are used here and it is assumed that knowledge is only acquired in public education systems, while skills are only acquired on the job. This is a simplification that is used mainly to distinguish between factors that are admittedly more interlinked in reality. It allows the impact of the two factors to be examined separately in the simulations. It is assumed that the production of goods in an industry requires both kinds of human capital. The amount of these kinds of human capital that is necessary for the production of one good is assumed to be constant and industry-specific. The necessary number of workers with the respective knowledge is denoted by ωk ( [0, 1]). The number of skilled workers necessary for the production of one good is denoted by ωs ( [0, 1]). Furthermore, it is assumed that only a small share of workers move between regions at each time. This implies that local labour markets must be considered. The locally available labour force is characterised at each point in time by three factors: the total number of potential employees, Φ(r), the human capital in form of knowledge, Kk(r, t) and the human capital in form of skills, Ks(r, t). The number of potential employees, Φ(r), in a region is assumed to be constant. Changes in the population are omitted in this approach. Instead, the two kinds of human capital change over time due to endogenous processes which are modelled below.

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It has been assumed above that human capital in the form of knowledge is only created by the public education system. The number of new people that are educated with respect to the industry-specific knowledge in each time step is denoted by kk(r, t). This number is caused mainly by schools supplying vocation training and universities. How kk(r, t) changes over time is described below. Finally, it is assumed that a certain share of human capital deteriorates each time due to retirement, technological changes and moves of employees to other industries. This rate is denoted by κd ( [0, 1]). At the same time a basic amount of human capital is created by the move of people from other industries. This basic rate is denoted by κb·κd·Φ(r), so that at least a share of κb ( [0, 1]) of the workers in any region has industry-specific knowledge. Thus, the dynamics of the human capital in the form of knowledge are given by (4.10) The dynamics of human capital in the form of skills are modelled in a similar way. However, some differences exist. According to the above assumption, skills are only obtained on the job. With respect to the deterioration of human capital, the same processes are involved with respect to skills as with respect to knowledge. Therefore, the same modelling with the same parameter is chosen. Skills are created within firms. Therefore, the increase of skills depends on the number of firms and employees in the region. However, firms can be expected to adapt their education efforts to their needs. The required skilled labour force in a region is given by . It might be assumed that firms try to supply this amount of skills. However, firms might also educate some more employees because it is clear that some will move to other firms or other industries. This is reflected by a parameter κe ( IR+), which is larger than 1 if more skilled workers are educated and smaller than 1 if less skilled workers are educated than needed. As a consequence, the firms in a region r aim to educate workers at time t to fill the gap between the desired number of skilled workers and the real number. However, firms do not succeed in educating this number of workers immediately. It takes some time to educate workers. Hence, the creation of skills is determined by the decisions taken in the past. The actual number of skilled workers that are created in a region is denoted by ks (r, t). This number can only be changed slowly. The speed of the adaptation of this value towards the intended number is denoted by κa ( IR+). The dynamics of ks (r, t) are given by (4.11) If Equation (4.11) results in a value of ks(r, t)<0, ks(r, t)=0 is set. Again it is assumed that there is a basic rate of skill creation. For simplicity this basic rate is assumed to be identical for skills and knowledge. Again other industries might be seen as sources for such human capital. The dynamics of the human capital in the form of skills are given by

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(4.12) Migration of labour force It is assumed here that people migrate between the regions. In the case of the general labour force it is assumed that migration has no net impact. In the case of skills and knowledge, instead, some mobility of the respective employees is assumed. This mobility is restricted in three ways. First, people only move to regions in which their wage is higher than the wage in the region where they come from. Second, it is assumed that moves are more likely if the distance between the respective regions is small. The decrease in the likelihood of moving from one region to another is modelled as being exponential with a parameter ζmobil ( IR+). Third, there is a maximal number of employees that might move to other regions at any time. The maximal share of workers with industry-specific knowledge who might move is denoted by the parameter κmobil, k ( IR+). Hence, the share of knowledge that moves from region r to region at time t is given by (4.13)

The same holds for skilled workers, except that the maximal share of workers that might move might differ from those defined above. It is denoted by κmobil, s ( IR+). The share of skills that move from region r to region at time t is given by Pmobil, s(r→ ) where Pmobil, s(r→ ) is given analogously to Equation (4.13) by (4.14)

Wages The availability of human capital in a region influences the wages that have to be paid by firms there. In the literature usually an approach is used that assumes a wage curve depending on the share of unemployed workers. This is also used here. Three kinds of workers are distinguished but for each of them, the same unemployment elasticity of wages is assumed. This is denoted by ωe ( IR_). Thus, the wage for human capital in region r at time t is given by

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(4.15) and (4.16) respectively. In the case of general workers, the industry under consideration is assumed to compete with other industries. For simplicity the other industries are assumed to require the same share of workers in every region. This share is denoted by ( [0, 1]). Assuming the same kind of wage function as above, the wage for general labour results in (4.17) The total amount of wages that have to be paid per unit of production by a firm in region r is given by (4.18) Public education Above it has been argued that local public education influences the availability of human capital in a region. Public education is determined mainly by political decisions. In general it can be assumed that the number of people who are educated in public schools and universities is adapted to the demand in the job market, although this often happens with a time delay. However, the public education might fail to create exactly the number of educated people that are demanded by firms. The deviation is denoted by κ+. Thus, at any given time t, the education system aims to create in region r to close the gap between the amount of knowledge that is believed to be demanded and the available amount of knowledge. In the contrast to skills, knowledge is provided in two ways: by local schools and by universities. The share of education that takes place in universities is denoted by κu ( [0, 1]). Consequently, the share of education that takes place in local schools is (1−κu). It is assumed here that education in local schools adapts to demand within regions, while universities exist in certain places and adapt to national demands. Therefore, the shortfall in knowledge is divided respectively. , On the global level the shortfall is given by still assuming that the demand might not be adequately estimated. Let us denote the total amount of education in universities by ku(t). It should account for a share of κu of the global shortcoming in knowledge. However, again education cannot be adapted to the required level immediately because it takes time. The speed with which the education

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system adapts to changes in the demand for labour is denoted by κs ( [0, 1]). This parameter is assumed to hold for the adaptation of local schools and universities. As a consequence, the dynamics of education in all universities are given by (4.19)

Universities are located in particular regions. Thus, each region contains a particular share of universities which is defined by u(r) ( [0, 1]). This share is assumed to remain constant over time, meaning that universities only change in size simultaneously, so that their relative size remains the same within each discipline. Thus, the increase of knowledge in region r that is cause by education in universities is given by u(r) · ku(t). The education in local schools is assumed to adapt to the local short-coming of knowledge . The adaptation works according to the same laws as those described above and formulated in Equation (4.19). Hence, the education in local schools is given by (4.20) The total amount of knowledge creation in region r at time t is given by (4.21) 4.2.3 Parameters The simulation model that has been set up above contains 32 different parameters. In addition, some of them depend on the region. They all reflect some factors that could, in principle, be measured in reality. However, such a measurement goes beyond the research reported here, so that this approach has to rely on empirical studies conducted elsewhere. Some of the parameters can be fixed according to such empirical results reported in the literature, for others, no empirical studies exist. However, even for the parameters that can be fixed the results often differ between industries or regions. Therefore, ranges are defined for all parameters. These ranges are applied in all simulations conducted and are discussed in the following. Some of these ranges are taken from the empirical results in the literature, some of them are deduced from various arguments. The presentation of these ranges is again structured according to the local mechanisms they describe. Many of the parameters describe changes per unit of time, therefore, it should be kept in mind that the unit of time has been set to one day. Firm growth and price setting The parameter λ determines how much a firm is able to increase its labour force within one time step. In empirical studies in Germany it has been found that most start-up firms grow at a rate of between 0% and 25% per year (see Almus & Nerlinger 1999). Here,

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however, we are interested in the maximal growth rate of firms, meaning the growth rate that occurs if the demand does not limit growth. According to empirical findings (see again Almus & Nerlinger 1999), the maximal growth rates seem to be at least below 200% per year. This would be obtained by λ=0.003. Furthermore, the fact that many firms have growth rates of around 20% per year implies that the maximal growth rate is at least 20% per year. This induces 0.0005<λ<0.003. Many studies of economies of scale can be found in the literature (see, e.g., Schroeder 1992, Clark & Speaker 1994, Hardwick 1994, Rhine 2001, and Khaled, Adams & Pickford 2001). However, they all calculate the economies of scale for existing firms. Thus, they estimate the value β↑− β↓·L(n, t) of the above model for given values of L(n, t). Most studies find values between 0.8 and 1.6. In theoretical approaches it is usually assumed that economies of scale are above 1 for small firms and decrease with the size of firms. Taking this assumption and considering the empirical findings, the range for β↑ is set to 1<β↑<1.6 and β↓ is restricted to a range of 0<β↓< 0.01. This implies that the economies of scale will not increase above 1.6. They might become lower than 0.8, but firms with such values of the economies of scale will disappear from the market anyhow. Demand In Chapter 2 it was repeatedly argued that local industrial clusters emerge when the demand for the products of an industry increases. Therefore, the simulations are set up here in such a way that the demand increases for the first five years and remains constant after this period of time. The increase in the demand is assumed to be s-shaped. Thus, the demand is given by (4.22)

where denotes the maximal demand that is reached after approximately 5 years. The demand remains at that level for the rest of the simulations. To keep the model simple it was assumed that the labour force employed by a firm equals the demand for its goods. This implies that the total labour force in an industry equals D(t) if all demand is satisfied. The total employment ranges between 1000 and 500000 in the 2-digit industries in Germany. Thus, is used. The heterogeneity of goods is determined by the parameter π. The Hotelling model is frequently used in the literature but its parameter is not empirically studied. Therefore, π has to be fixed according to logical arguments. π=0 describes a situation with perfectly substitutable goods. The prices in the simulations are around one. Typical differences in the prices between firms are around 0.1. Hence, π=1 implies that there are around 10 different kinds of goods that are chosen according to their characteristics rather than according to their prices. There might even be more niches in reality so that 0.001≤π≤2 is assumed here. ρ determines the utility difference that motivates a consumer to change the good she purchases. A natural minimal value of ρ is zero, which implies that the consumers always

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buy the good that offers the highest utility for them. However, loyalty is a well-known fact in marketing. Experimental studies find that price reductions of up to 25% are necessary to induce a switch from the most preferred to the least preferred product (see, e.g., McConnell 1968). Hence, 0<ρ<0.25 is used here. The share of firms η that a consumer compares each time determines how fast a consumer recognises a better alternative. There are no empirical studies of the number of firms that customers compare each time. It seems to be plausible that consumers do not compare all possible alternatives each day. A producer that has been found to be suboptimal today will not be approached again tomorrow. Due to the lack of empirical evidence, it is assumed here that firms are reconsidered after between 1 month and 3 years on average. This implies 0.001≤η≤0.03. Innovations The number of innovations that a firm creates per year is intensively studied in the literature. These studies find different dependencies on the size of the firm. Here a linear dependence is assumed. Studies of the average number of innovations per firm find values between 0.1 and 10 per year (see Fritsch, Bröskamp & Schwirten 1996 and Evangelista 1999). Thus, µ0 is restricted to 0.0003<µ0<0.03. For the factor, µL, an average value between 0.001 and 0.002 is found in the literature (see Audretsch & Acs 1991 and Blind & Grupp 1999). It varies for different industries between 0.0005 and 0.01 per year (see Acs & Audretsch 1990). Therefore, 0.0000015<µL<0.00003 is used here. Spillovers have been frequently studied in the empirical literature. Henderson and Cockburn (1996) study the extent to which patents of a firm can be explained by the number of patents by competitors. They find values between 0.01 and 0.11. That means that between 1% and 11% of the effect of research is transfered to other firms. Thus, 0.01<σ<0.11. The empirical literature offers several approaches to the spatial range of spillovers (examples are given in Anselin, Varga & Acs 1997 and Orlando 2000). However, these approaches do not study an exponential dependence of spillovers on the geographic distance. Instead, they study the significance of the impact of spillovers for different distances. Orlando (2000) studies 6 different distances, so that a detailed knowledge about the decrease in spillovers with distance results. For spillovers within the same 4digit industry, no impact is found for firms further away than 25 miles. This means that the impact is reduced to less than 5% if the firms are more than 25 miles apart. This implies a value of ζspill≈0.06/km. In the case of spillovers between different 4-digit industries, the impact of spillovers decreases much more slowly. It seems to reach approximately 30% of the local value for a distance of 800 miles. This implies a value of ζspill≈0.0008/km. Therefore, 0.0008/km<ζspill<0.06/km is used here. denotes the amount by which the production costs are decreased or the value of the produced good is increased by one innovation. This is not directly measured in the empirical literature. However some measures can be found that approximate this value. Firms that innovate have been found to increase their turnover by 1% more than firms that do not innovate (see Smolny & Schneeweis 1999). Furthermore, improvements and innovations have been found to lead to a commercial gain of 1% to 2%, while new

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products and process breakthroughs lead to average gains between 5% and 7% (see Barlet, Duguet, Encaoua & Pradel 2000). Since the latter make up only for a fraction of all innovations, 0.01< <0.05 is used here. There are no studies available that examine the effect of catch-up processes in the form of an additional benefit from innovations. Again logical analysis has to be used to restrict the respective parameter. Values of =20 and =0.05 would imply that every innovation would cause the firm to reach the technology frontier. Thus, <20 has to be satisfied. =0 implies that there is no catch-up effect. Therefore, 1< <20 is assumed. Start-ups and spin-offs In the empirical literature the maximal number of start-ups in a 2-digit industry in Germany per year has been found to be 3600 (see Audretsch & Fritsch 1999). The present approach is based on 3-digit industries. Thus, the maximal number of start-ups should be lower. Furthermore, the number of start-ups varies greatly between industries. In some industries no startups occur. However, in the simulations conducted here the rate of start-ups defines the number of entrepreneurs who want to start a firm each year. Before the firm is started, the potential market situation is examined. Only if the firm can be expected to have customers is it actually started. Thus, the rate given by 0 is the maximal possible number. It is assumed here to range between 10 and 1000 in correspondence to the findings by Audretsch and Fritsch (1999). 0 denotes the number of start-ups that are not caused by the existence of other firms. In empirical studies it has been found that between 25% and 40% of start-ups are founded by people who have worked in private firms before (see, e.g., Christensen 1993 and Pleschak 1995). Most of the other start-ups are founded by people who come from universities or research institutes. This implies that most founders come from a location where economic activity in the respective industry is present. Therefore, it is assumed that between 50% and 95% of the start-ups are caused be the existence of firms in the region or nearby. These are called spin-offs here so that 0.01< spin<3 results. The remaining 5% to 50% of the start-ups are assumed to occur independently of the existing firm population, so that 0.001< 0<1 holds. For the location of start-ups it has been found that around 78% are located not further than 22 km away from the founders’ former place of residence (see Schmude 2001). Assuming that independent start-ups and spin-offs do not differ much in this respect, the same share of all spin-offs are founded not further away than 22 km from the incubator firm. This implies, for an exponential model, like the one chosen above, that ζspin has to be approximately 0.07/km. To increase the relationship between those who leave the area with a radius of 22 km and those who remain within this area to five times the empirical average value or decrease it to a fifth of this value, ζspin has to be increased or decreased by 0.05, respectively. Therefore, it is assumed here that 0.02/km<ζspin<0.12/km holds. The maximal initial labour force of start-ups and spin-offs is set to 5≤Λ≤30. Empirical studies on German start-ups have shown that a very small proportion have more than 30 employees at the beginning (for a distribution of the size of start-ups see Almus & Nerlinger 1999). Λ determines the maximal initial labour force, so that a value below 5 would mean that no newly founded firm in the industry has more than 5 employees.

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Human capital The Mannheimer Innovation Panel that is used in Section 3.5 provides information about the share of employees that hold a degree in natural sciences. This share is found to vary between 5% and 18%. This can be used as a proxy for the share of employees that have industry-specific knowledge. 0.03<ωk<0−2 is assumed here. There are no similar values that might be used as a proxy for the share of skilled employees. For simplicity the same range is used here. This means that 0.03<ωs<0.2 is assumed. The degeneration of human capital is characterised by κd. Human capital degenerates because of retirement of educated people, the technological development which makes old knowledge and skills obsolete and switches of people to other industries or jobs in which they cannot use their current knowledge and skills. The latter cause is rare and will be omitted here. People work between 30 and 50 years of their life. Thus, roughly 2.5% of the work force retires each year. This causes a deterioration rate for human capital of κd=0.00007 per time step (day). In addition, technological development makes human capital obsolete. Very fast technological development might devalue human capital every 5 years. This implies an additional deterioration rate of 0.00053, so that 0.00007<κd<0.0006 is assumed here. κa denotes the speed of the adaptation of firm-internal education. There is no empirical study of this in the literature. It is assumed here that people need at least one month to become skilled. Internal trainee programs usually run for one to three years. Therefore, it is assumed that it takes maximally 3 years for people to become skilled. Thus, 0.001<κa<0.03 is assumed. κb represents the basic share of skilled employees that is created in each region, by related industries, universities or research institutes or movements to the region for reasons not included in the model. This basis share of skilled employees enables start-ups to find their initial labour force. A value of Kb=0.00005 causes, in all regions, the existence of at least one skilled worker. Since the firm with only one employee requires between 0.03 and 0.2 skills, a value of 0.000002<κb<0.00001 is sufficient for the founding of a small firm. κe denotes the amount by which firms train more or fewer workers than they need. There is no respective empirical study. However, a similar parameter has been estimated by Brenner and Murmann (2003) on the basis of historical data for the synthetic dye industry. They find a range of 1 to 1.2. The same range is used here, so that 1<κe<1.2 is assumed. The same holds for κ+, so that 1<κ+<1.2 is used. In the literature about the mobility of employees it is found that around 5% change their employer within a period of 3 years (see, e.g., Hübler & König 1999). It is assumed here that the same mobility holds for skilled workers and for workers with industryspecific knowledge. Hence, the mobility is set to 0.00002<κmobil, k<0.0001 and 0.00002<κmobil, s<0.0001 which implies between 0.7% and 3.5% of the human capital moving each year. A parameter that is identical to ζmobil is measured in the literature on migration within Germany (see Haag, Munz, Reiner & Weidlich 1988). The result is a value of 0.00218/km. Therefore, 0.001/km<ζmobil<0.003/km is assumed here.

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Wages The total number of potential workers Φ(r) in each region is set to 50% of the population in each region. Data on the population is obtained from the Bundesamt für Bauwesen und Raumordnung2. The unemployment rate in Germany has varied in the last 20 years by between 5% and 10%. The demand and therefore the number of employees in the explicitly modelled industry is restricted above in such a way that it accounts for maximally 1% of the labour force. Therefore, it is assumed here that all industries that are not explicitly considered in the model take together between 90% and 95% of the labour force. Hence, 0.9≤ ≤0.95. Several empirical studies that estimate the unemployment elasticity of wages for Germany can be found in the literature (see, e.g., Buettner 1999 and Bellmann & Blien 2001). Values between −0.015 and −0.11 are obtained. For other countries values between −0.04 and −0.17 are observed (see, e.g., Blanchflower & Oswald 1994, Deller & Tsai 1998 and Pekkarinen 2001). The findings for Germany are used as a basis here. The range for e is set to −0.11< e<−0.015. Public education u(r) denotes the share of all education in universities that takes place in region r. The real numbers of students in each region are used to calculate these shares. The data is taken from Bundesamt für Bauwesen und Raumordnung. The share of the workers with higher education who received this education in universities varies very much with the industry under consideration. There are industries that employ almost no people with a university degree. Other industries employ almost only people with a university degree. Therefore, 0<κu<1 is assumed here. The speed κs with which the education system adapts to changes in the demand for qualified labour differs for different kinds of schools or universities. In some cases it is observed that the number of people who are allowed to enter higher public education is adapted when a mismatch between the number of people who finish this education and the number of qualified workers demanded by firms is observed. In such a case, the adaptation takes a period of time approximately equal to the duration of the education. This implies a delay of between 3 and 5 years. In some cases the responsible actors show some foresight and react to expected changes. If they have perfect foresight, the education system would adapt immediately to the demand for qualified labour. Perfect foresight seems to be unlikely, but it is assumed here that the delay might be as short as 1 month. This implies 0.0006<κs<0.03. 2

The data is provided in the Report ‘Aktuelle Daten zur Entwicklung der Städte, Kreise und Gemeinden, Ausgabe 2000

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Variation of parameters Below a Monte-Carlo approach is taken to study the results of the simulations. This means that the parameters are fixed for each simulation run randomly within their above defined range. The common approach would be to define a uniform probability distribution with the range of each parameter and draw one value from this distribution randomly for each simulation run. However, a uniform distribution is not adequate for all parameters. Some variables vary across several orders of magnitude. For example, the maximal demand varies between 1000 and 500000. The above method would imply that more than 80% of the simulations run with a value . Values between 1000 and 10000 would only occur in around 2% of the simulations. Therefore, whenever the maximal value of a parameter is at least 10 times as large as the minimal value, a different procedure is used. The range is transformed with the help of the natural logarithmic function. Then, a uniform distribution is used to select a value randomly. Finally, this value is transformed back using the natural exponential function. This causes values of each magnitude to be equally likely.

Table 4.1 The ranges for all parameters of the model and the way in which their values are determined (‘a’ stands for arithmetic, ‘g’ stands for geometric). parameter

lower limit

upper limit

type

β↑

1

1.6

a

β↓

0

0.01

a

1000

500000

g

0

0.001

1

g

e

−0.11

−0.015

a

spin

0.01

3

g

κa

0.001

0.03

g

κb

0.000002

0.00001

g

κd

0.00007

0.0006

a

κe

1

1.2

a

κmobil, k

0.00002

0.0001

a

κmobil, s

0.00002

0.0001

a

κs

0.0006

0.03

g

κu

0

1

a

κ+

1

1.2

a

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Λ

5

30

a

λ

0.0005

0.003

a

µ0

0.0003

0.03

g

µL

0.0000015

0.00003

g

η

0.001

0.03

g

π

0.001

2

g

0.9

0.95

a

ρ

0

0.25

a

σ

0.01

0.11

g

0.01

0.05

a

1

20

g

ωk

0.03

0.2

a

ωs

0.03

0.2

a

ζmobil

0.001/km

0.003/km

a

ζspill

0.0008/km

0.06/km

g

ζspin

0.02/km

0.12/km

a

Whether the geometric or the arithmetic approach is used for a parameter is given in Table 4.1 which also summarises the ranges of all parameters that are determined randomly in the simulations. 4.3 ANALYSIS OF THE SIMULATION DYNAMICS Many of the processes that are involved in the emergence of local industrial clusters are stochastic. This implies that the outcome of these processes cannot be predicted. They are not a deterministic result of the circumstances and all that can be done is to predict the probabilities of certain outcomes. Nevertheless, we observe one reality, meaning one realisation of the stochastic processes. It is difficult to induce from this realisation knowledge about the stochastic dynamics that lay behind it. Thus, in general, an empirical study does not allow the stochastic characteristics of processes to be analysed. Simulations are used here to study these characteristics. The following factors are addressed. The analysis starts with some general statements about the simulations. The extent to which the results of the simulations correspond with the empirical findings in Chapter 3 is discussed. Then, the different stochastic aspects of the emergence of local industrial clusters are studied. Three questions are addressed: first, whether the fact of clustering is determined by the characteristics of the industry or is the result of stochastic events is studied; second, the extent to which the number of clusters

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varies between realisations is examined; third, the question of how much the final state depends on early events is addressed. The major results are as follows. First, it is shown that the three local processes,— spin-offs, spillovers and the accumulation of human capital -that are included in the simulations are together able to cause the existence of local industrial clusters (Section 4.3.1). Second, the emergence of local industrial clusters is found to be a stochastic process. This does not only hold with respect to their location. The number of local clusters also varies greatly if the same situation is simulated again (Section 4.3.3). Even whether local clusters emerge is, for many situations, not determined by the industrial characteristics (Section 4.3.2). Finally, it is shown that early dynamics have a strong impact on the location of clusters. After a few years, before the demand stops increasing, the regions are segregated into those in which clusters emerge and those that lag behind (Section 4.3.4). 4.3.1 Simulation results and reality Simulations are often criticised using the argument that any result can be obtained using them. In my opinion this argument is false or at least holds only for certain procedures used in conducting simulations. How simulations are conducted is important for their results and the interpretation of these results. Hence, the procedure used here is discussed in detail. Procedure of simulating In Section 4.1 it is argued that simulations are a perfect tool to test whether certain mechanisms and processes cause certain effects. Such a test requires a two-step method. First, the simulation model has to be set up and the parameters fixed. The model has to be built up such that it represents the causes in the hypothesis that is to be tested. Then, the simulations have to be run and the results analysed. This is the way in which the simulations used here have been conducted. The first step was setting up the simulation model, which is given in Section 4.2.2. Then, empirical studies in the literature and logical arguments have been used to determine ranges for the parameters, which are given in Section 4.2.3. Some initial simulation runs have been conducted to identify some mistakes in the specification of the processes or their implementation. This led to some minor changes in the model. During these changes, the parameter ranges that have been specified earlier have not been changed. There were no tests of whether the results were favourable. After finalising the simulation model the simulations were run as described below. Interpretation of results In my opinion such a procedure of simulating is important because it guarantees that “not everything goes”. Different results might be obtained for different parameter sets. However, in reality industries have different characteristics and different industrial characteristics correspond to different parameter sets in the simulations.

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Defining ranges for each parameter also restricts the range of possible outcomes. Hence, not every result is possible. Furthermore, the likelihood of each result is determined by the ranges of the parameters in a Monte-Carlo simulation. As a consequence, the set of results that are observed in the simulations are those that the mechanisms implemented in the model are able to cause. The frequency of each of these results represents the probability with which the parameter ranges cause them. Thus, simulation studies that are conducted in the way described above allow analysis of what kind of effects the mechanisms implemented might cause. If there is knowledge about the ranges and distributions of parameters, it is also possible to obtain the probability of the occurrence of a certain feature according to the mechanisms implemented. A detailed discussion of the method that is used here is given in Brenner & Murmann 2003. Presented simulations and reality Information about the ranges and distribution of parameters is only available from the literature in a very few cases. This restricts the possibility of analysing the frequency with which certain features occur here. The parameter ranges have been chosen in such a way that no possible real situation is excluded. This means that the parameter ranges are likely to be too large rather than too small. Therefore, if the mechanisms that are simulated cause certain effects, these effects should show up in the simulations. If the effects do not show up in the simulations, the assumed causal relation between the simulated mechanisms and the effect is rejected (different mechanisms are studied in such a way in Brenner 2001b). The effect that is of interest here is industrial clustering. The analysis below, with results presented in Table 4.2, shows that the mechanisms implemented are able to cause clustering. In Section 2.4.1 many processes that might cause the existence of local industrial clusters were reported. Only some of them have been implemented in the simulation model, namely spinoffs, spillovers and the accumulation of human capital. The results of the simulations show that these three local self-augmenting processes are able to cause the existence of local industrial clusters. The results presented in Table 4.2, however, also show that only a few parameter sets cause the emergence of such clusters. Only in around 25% of all simulation runs is clustering observed. In contrast, around 40% of the industries have been found to show clustering in the empirical study in Chapter 3. In both cases the same spatial units and the same statistical method for the identification of clustering are used. There are three possible interpretations of this results. First, the three local self-augmenting processes that are included in the simulation model explain only some of the local industrial clusters in reality. Further processes are suggested in Section 2.4.1 that might strengthen clustering. Second, for some reasons the parameters might fall more frequently into those areas of the parameter ranges for which clustering occurs. Third, the three local selfaugmenting processes that are implemented in a particular way here might work differently and more effectively in reality. The simulation approach does not give any final answer to the question of which of these interpretations is correct. The first interpretation is supported by the simulation results reported in Brenner (2001b) where it is shown that other processes also have an

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impact on clustering. The other two interpretations can neither be rejected nor supported by the evidence available. 4.3.2 Existence of local industrial clusters In Section 3.2 the fact that local clusters exist in an industry is presented as a characteristic of the industry. This implies that the conditions in an industry determine whether local clusters emerge or not. An alternative viewpoint might be taken. It might be assumed that the emergence of lo cal industrial clusters is a stochastic process in such a way that under the same conditions local industrial clusters might emerge in one case and not in another. This means that if history were to be repeated with the same characteristics of the industries, local clusters might appear in different industries. If this holds, the characteristics of industries might still determine the likelihood of the emergence of local clusters but will not determine whether they emerge or not. Whether the assumption of such a path-dependence for the existence of local industrial clusters holds cannot be addressed empirically. Simulations, instead, can be repeated and whether the same results appear if the parameters are the same can be studied. Method To study whether the existence of local industrial clusters is a random event, the simulation is run several time with the same parameter set. The random processes of the founding of firms, the occurrence of innovations, and the search by customers for alternative firms cause the developments to differ between the simulation runs. Nevertheless, if the existence of local clusters is determined by the characteristics of the industry, local clusters should either appear in every simulation run with the same parameter set or in none of them. Therefore, each simulation is run for 2555 time steps (seven years).3 Then, the distribution of the firms among regions is analysed according to the method that is used in Section 3.2 (a detailed description and discussion of this method is given in Section 3.2.1). It is tested whether the ‘natural’—assuming no clustering—or the ‘cluster’— assuming the existence of clusters—distribution is more adequate for describing the simulation results. It is also tested whether these distributions describe the results adequately at all. They are rejected for none of the simulation runs that have been analysed in the context of this study. Hence, the use of the theoretical industrial firm distribution among regions is also confirmed to be adequate in the context of the simulations. Testing the two theoretical distributions results in one of two possible 3

The industry increases for the first five years according to the definition of the demand D(t) in Section 4.2.3. After this increase the situation stabilises very quickly in most simulation runs. It has been found that there is little change after seven years in most runs.

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Table 4.2 Result of the Monte-Carlo simulations with five repetition of the same parameter set. The number of parameter sets in which clustering is found in a specific number of the five repetitions for different level-α tests is reported. runs showing clustering

0

1

2

3

4

5

frequency (α=0.05)

22

6

3

2

2

2

frequency (α=0.1)

21

5

2

5

1

3

frequency (α=0.5)

16

3

5

3

4

6

statements for each simulation run: either local clusters have occurred or not. The parameters of the simulation mainly reflect industrial characteristics. Therefore, if the existence of local industrial clusters is determined by the characteristics of industries, rerunning a simulation with the same parameters should lead to the same result with respect to the existence of clusters. Therefore, the simulations are run five times with the same parameter set. The results might differ for different parameter sets. Therefore a Monte-Carlo approach is used, as described above. Results The method described above is applied to a total of 37 parameter sets4. For each parameter set five simulations are run and five results are obtained. Thus, local clusters appear in none, one, two, three, four or five of these simulation runs. The results are presented in Table 4.2. Discussion The results reported in Table 4.2 show that for many parameter sets no clustering is observed in any of the five simulation runs. This holds even if the significance level is reduced to α=0.5. For 5 of these cases 10 additional simulation runs have been conducted and only in one case was clustering observed. Hence, there are parameter sets for which no clustering occurs. This means that industrial characteristics exist that exclude the emergence of local clusters. At the same time, for two parameter sets significant (α=0.05) clustering has been obtained for all five simulation runs. These parameter sets are used for further analysis below (in addition to two others). For each of these parameter sets 30 simulation runs are conducted. For one of the two parameter sets local clusters emerged in all 30 runs, for the other parameter set local clusters emerged in 29 runs (significance level: 0.1). Hence, parameter sets exist that 4

The question that is to be answered by the simulation can be sufficiently answered on the basis of 37 parameter sets, so that no further simulations had been run.

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almost always cause the emergence of local clusters. This means that certain industrial characteristics determine the existence of local clusters. However, for around half of the parameter sets the situation is not that clear. In some runs clustering occurs while in other runs no clustering takes place. Hence, the emergence of local clusters depends on random events in these cases. This might be the result of the statistical test for clustering that is quite sensitive to changes in the firm population (a detailed discussion of this is given in Section 3.2.2). However, the finding that the emergence of local clusters is a stochastic feature of some parameter sets is very robust with respect to changes in the significance level (see Table 4.2). This implies that there are, indeed, parameter sets for which local clusters might or might not occur. Consequently, it can be expected that there are also industries in reality for which clustering might or might not occur. The existence of local industrial clusters is pathdependent in these cases. How many industries exist that show such characteristics cannot be deduced from the study conducted here since not all processes relevant for the emergence of local clusters are included in the simulation model and because there is not sufficient knowledge about the distribution of the parameters. Despite this stochastic character of the emergence of local industrial clusters, the existence of local clusters is not a completely random event. For some industrial characteristics it will never occur, for some industrial characteristics it will always occur, and for all other industrial characteristics it occurs with a certain probability that is determined by the industrial characteristics. 4.3.3 Number of local industrial clusters Above it has been shown that at least the likelihood of the existence of local clusters is determined by industrial characteristics. This means that the existence of local industrial clusters is, to some extent, predetermined and only partly depends on the specific developments in certain regions. Here the question is addressed whether the same holds for the number of local clusters in an industry. A process without any path-dependence should converge to the same situation independently of the initial developments. However, in Section 2.3.3 it was argued that history matters. Two aspects might cause a path-dependence of the number of local clusters. First, it was argued in Section 2.5 that once a region exceeds a critical mass, a local cluster emerges. The development of a region depends on stochastic events, such as the founding of firms and the occurrence of innovations. Hence, in each simulation run a different number of regions might exceed the critical mass. Second, if in each simulation run the clusters emerge in different regions, their size might differ because of the different sizes of the regions. Hence, more or less local clusters might be required to satisfy the demand. Method A procedure similar to the one used in Section 4.3.2 is applied here. This time 30 simulations are run for each parameter set. The results are again analysed according to the statistical method developed in Section 3.2. However, this time only four parameter

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sets are used. These are chosen from the parameter sets that are used above. Those parameter sets for which clustering occurs in at least four of the five runs above are used (α=0.1). Since the structure of clustering is to be studied, those parameter sets for which no clustering occurs are of no help. For three of these parameter sets clustering does not occur in all runs. Therefore, additional simulation runs are conducted until 30 runs are obtained in which local clusters emerge (in one case 1, in one case 6 and in one case 9 additional runs are necessary). For all simulation runs in which local clusters emerge these clusters are identified according to the method developed, used and described in Chapter 3. This analysis provides quite a lot of information. Two pieces of information are of interest here. First, the locations of the clusters are obtained. Second, the number of local clusters can be counted. Results First, it is studied whether the numbers of clusters that emerge for the same parameter set differ. For all four parameter sets that are analysed here they vary tremendously. For all four parameter sets simulation runs are obtained in which less than 5 local clusters emerge and for all four parameter sets, simulation runs are found in which more than 30 clusters exist after 7 years. Hence, the proposition that the number of local clusters might be determined by the industrial characteristics can be rejected, even for those industrial characteristics that cause the emergence of local clusters in every simulation run. The number of local clusters that emerge for the different parameter sets are presented in the form of classes in Table 4.3. To test whether industrial characteristics have at least some impact on the number of clusters, the results for the four parameter sets are compared. To compare the results of the four parameter sets, the number of clusters observed are assigned to nine ranges as shown in Table 4.3. Whether the numbers of runs that fall into each of these ranges differ between the

Table 4.3 Number of runs for which the respective number of clusters is observed. number of clusters 1−

6−

11−

16−

21−

26−

31−

36−

parameter specification

>40

5

10

15

20

25

30

35

40

1st set

7

5

2

1

12

1

2

0

0

2nd set

2

4

3

5

3

6

4

2

1

3rd set

8

10

4

3

4

0

0

1

0

4th set

3

4

2

1

2

3

6

7

2

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Table 4.4 Maximal difference Dij of the cumulative distribution functions for the number of clusters for different parameter sets. Significant differences are given in bold letters (*=significance level of 0.01). 1st set

2nd set

3rd set

4th set

1st set

−

0.33

0.33

0.50*

2nd set

0.33

−

0.47*

0.27

3rd set

0.33

0.47*

−

0.57*

4th set

0.50*

0.27

0.57*

−

parameter sets can now be tested with the help of the Kolmogorov-Smirnov test for the comparison of two empirical distributions. The results for the parameter sets are compared in pairs. This means that the resulting cumulative distribution functions Fi(n), defined as the share of runs for which equal or less than n local clusters emerged for the ith parameter set, are compared. The maximal difference is calculated according to (4.23) If this value is too large, the hypothesis that the distributions of the numbers of clusters are identical for different parameter sets can be rejected. The results are given in Table 4.4. For several comparisons a significant difference is found in Table 4.4. This provides evidence that industrial characteristics have an impact on the number of clusters. In some industries more clusters can be expected, on average, than in other industries. However, the number of clusters varies between simulation runs to such an extent that nearly every number of clusters might occur for every parameter set, given that the parameter set leads to clustering. It has be argued above that the number of clusters might be determined by the size of the regions in which they occur. This hypothesis is tested in the following. The 30 simulation runs for the four parameter sets are used again. For each of these 120 simulations, the average size of the regions in which clusters emerge is calculated. This value is denoted by (i, j) for the i-th parameter set and the j-th simulation run. The number of clusters that are observed for the i-th parameter set and the j-th simulation run is denoted by n(i, j). Then, it can be tested whether the value of n(i, j) can be explained by the value (i, j). A regression analysis is conducted. The dependence might be influenced by the characteristics of the industry, meaning the parameters chosen. Therefore the regression is conducted for each parameter set i separately. The regression equation is given by (4.24)

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The results of this regression are given for each of the four parameter sets in Table 4.5. The results contradict the assumption that the number of clusters increases if the respective regions are smaller in size. For one parameter set the opposite is actually found. For the other parameter sets no significant dependence is observed between the number of clusters and the size of the regions in which they are located.

Table 4.5 Regression results for the dependence of the number of local clusters on the size of the regions in which the clusters emerge. parameter set

α0(i)

α1(i)

p-value

adjusted R2

1

16.4

−0.000009

0.90

−0.035

2

−20.2

0.00074

0.003

0.24

3

8.72

0.000057

0.393

−0.009

4

44.9

−0.00034

0.151

0.039

Discussion The above study shows that the number of clusters that emerge is not determined by industrial characteristics. However, the industrial characteristics have some influence on the number of clusters. In some industries more local clusters can be expected to exist on average than in others. However, the variance within an industry is very high. If history were to be repeated, very different numbers of local industrial clusters might be observed under the same conditions. This implies that the emergence of local clusters is a strongly path-dependent process. If there are more regions that cross the critical mass by chance, more local clusters develop. The argument that if the clusters emerge in larger cities they might contain more firms so that fewer clusters are needed to supply the market, is rejected above. It seems to be a fundamental characteristic of clustering that the number of clusters is not predetermined by industrial characteristics. Random events in the regions play a role. This makes the competition between regions that has been discussed in Section 2.5.2 less exclusive. If for some reason one region develops differently so that a local cluster emerges, there is not necessarily another region in which no cluster emerges, although there is a certain probability that this happens. 4.3.4 Emergence of clustering and path-dependence The theoretical analysis in Chapter 2 shows that hysteresis might occur on the regional level. This means that a region that satisfies certain conditions (some of them have to be satisfied by the industry) converges to one of two stable states. The state into which it converges is not solely determined by its characteristics. The final state of the region also depends on the initial developments. History matters, or in other words, the development of the region is path-dependent.

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The history of a local system matters in many ways and for different reasons. The model and discussion in Chapter 2, however, identifies a point in time at which the further development of the region might take one of two directions. This focuses attention to that branching point. According to the discussion in Section 2.3.1, this branching point is reached when the demand in an industry increases and local clusters emerge. Some local systems exceed a critical mass and converge to an industrial clusters, while the other local systems remain below the critical mass and converge to the stable state with low activity in the industry. These processes could be examined in empirical studies. It would require an analysis of the spatial distribution of firms in one industry over time. To obtain a comprehensive picture, several such studies are necessary. Such studies are rare in the literature (an exception is found in Murmann 2003). Therefore, the respective processes are studied with the help of simulations here. Method Again the 120 simulation runs for the four parameter sets are used because clustering occurred in all of them. In this analysis, however, the development over time is of interest. Therefore, the firm distribution among regions is recorded for every 365th time step (every year). Since the simulations are run for 2555 time steps (seven years), seven firm distributions are obtained for each run. Three different methods are applied to analyse the timing of the emergence of local industrial clusters. First, the point at which in time it is determined which of the regions will become the locations of clusters is examined. The identification of clustering, which has been repeatedly used above, is applied to each of the seven firm distributions that are recorded for each simulation run. It can be expected that at the beginning no clustering is found, while at the end clustering is present because we only study here parameter sets that lead to the existence of local clusters. Thus, the year after which clustering occurs for the first time can be identified. This is done for all 120 simulation runs. The results are given in Table 4.6 for each parameter set separately. Second, the point in time from which local clusters remain the same is studied. Again, the local clusters are identified by the statistical method that is developed in Chapter 3. The locations of clusters after seven years are successively compared to those of the previous years, starting with the results after six years, then using the results after five years and so on. This is done until a difference in the results is found either with respect to the number of clusters or their location. The year in which this difference is observed is called the year in which clustering stabilises. Third, whether the regions that contain clusters in the end are originally those regions that contain most firms is examined. To this end, the regions are classified according to the situation after seven years. Two classes result, one with those regions that contain an industrial cluster and one with those regions that do not contain such a cluster after seven years. Then, it is studied how many regions of the latter group contain more firms after 1, 2, 3, 4, 5, or 6 years than at least one region of the former group.

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Time of the emergence of clustering The year in which clustering can be observed in a statistically significant way for the first time is recorded for the 120 simulation runs in Table 4.6. It can be observed that clustering appears in most cases either in the second or the third year. There are some differences between the parameter sets but these are of minor interest here. Taking into account that the demand increases for the first five years in the simulations, clustering occurs in the middle of this time or somewhat earlier. This means that local clusters already emerge while the industry is growing and not during the phase in which competition becomes fierce because the demand ceases to grow further.

Table 4.6 Frequency of the occurrence of clustering in a particular year for each of the four parameter sets studied. parameter specification

year of emergence 1

2

3

4

5

6

7

average

1st set

0

17

12

0

0

1

0

2.0

2nd set

5

21

3

1

0

0

0

1.5

3rd set

0

10

12

6

2

0

0

2.5

4th set

0

8

16

6

0

0

0

2.4

Table 4.7 Frequency of the stabilisation of the number and location of clusters in a certain year for each of the four parameter sets studied. parameter specification

year of the stabilisation 1

2

3

4

5

6

7

average

1st set

0

1

3

13

6

5

2

4.1

2nd set

0

1

2

13

10

1

3

4.1

3rd set

0

0

4

9

12

2

3

4.2

4th set

0

0

6

15

4

0

5

3.9

Stabilising of local industrial clusters The study of the changes in the location of clusters shows that it takes more time until the situation stabilises (see Table 4.7). In most simulations the situation stabilises in the third, fourth or fifth year. There are some simulation runs in which a stabilisation in the seventh year is observed. However, in these cases the situation has usually already been stable before, but some developments disturb the situation by chance. Hence, even if the

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number and location of the clusters remain stable for some time, changes might still occur. There is never a perfect stability of local clusters. Within the five years of growth in the demand for the products of the industry, the stabilisation of local clusters takes place in the second half of this period of time. Although, the phenomenon of clustering is visible quite early, the location and number of local clusters stabilises only later on. Therefore, it becomes crucial to know whether the location of clusters is already determined before it becomes visible or whether changes occur until the situation is stabilised.

Figure 4.1 Number of regions that contain at least as many firms (relative to their size) after two years as one of the regions that contain a cluster in the end (after seven years). The symbols , ×, and ∆ signify the results for the 1st, 2nd, 3rd and 4th parameter set.

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Path-dependence within regions To this end, the history of the regions that finally contain a local cluster is studied. In each year the regions are ranked according to the relative numbers of firms they contain. The region that is ranked lowest of all regions in which a local clusters exists after seven years is identified. Then, the number of regions that contain at least the same relative number of firms is counted. This is done for the end of each year. The resulting number is denoted by ň(t) for year t. Since all regions that finally contain a cluster satisfy the condition above, ň(t)≥nCL always holds where nCL denotes the number of clusters. In nearly all simulation runs after the first year at least one of the regions that contain a local cluster in the end still contains no firm. There is only one exception in the case of the first and second parameter set. Hence, after one year the development is far from determined. After the second year the regions are separated in a more decisive way. In some cases the regions in which the clusters are finally located each contain a higher relative number of firms than any of the other regions. However, this only holds for a few cases. In Figure 4.1 the pair of the numbers ň(2) and nCL is depicted for each simulation run. The results vary greatly between the simulation runs. In some cases the regions that finally contain clusters are already ahead after two years, while in other cases the region with the lowest number of firms (meaning no firm at this point in time) might still become a region containing a cluster. The processes involved in the emergence of local industrial clusters are stochastic. The fact that sometimes regions with no development after two years might contain a cluster in the end and sometimes this does not happen is a consequence of the stochastic processes. The results given in Figure 4.1 have to be interpreted such that after two years no determination has taken place in general. Regions that contain no firms are still able to become the location of clusters. This might be less likely than for regions with a large number of firms, but is still possible. This changes tremendously within the third year. Only three regions that do not contain any firm after three years have been observed in all simulation runs together to become the location of a cluster (two of these observations have been made for the 3rd parameter set, one for the 1st parameter set). There are still regions that are ranked up to 80th after three years and, nevertheless, they contain a cluster in the end (see Figure 4.2). However, the group of regions in which local clusters might emerge is restricted to at least one fifth of the regions, the fifth in which the relative number of firms is highest. After three years some branching has taken place. Some regions lag behind and will not catch up by chance. The situation becomes even more determined in the fourth year. In most simulation runs, those nCL regions that contain the highest relative number of firms after four years are those regions in which the industrial clusters are finally found. The number of exceptions is given in Table 4.8. There are only a few and the difference, ň(4)−nCL, is very small in these cases. It is always below 11 and in most cases smaller than 5. This means that only those regions with the highest relative numbers of firms after four years might contain an industrial cluster at the end. There might be a few regions for which the

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further development is unclear after four years. In these cases the situation is clarified in the fifth year. In none of the 120 simulation runs has a region been identified that contains a cluster after seven years but was not among the nCL regions that contained the highest relative number of firms after five years. Hence, the location of industrial clusters is determined finally after five years.

Figure 4.2 Number of regions that contain at least as many firms (relative to their size) after three years as one of the regions that contain a cluster in the end (after seven years). The straight line gives a situation in which only those regions that contain a cluster in the end satisfy this condition. Symbols as in Figure 4.1.

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Discussion The timing of the emergence of local industrial clusters is of political relevance. To support the emergence of local clusters in certain regions it is important to know at which times such support is likely to be successful. The study above shows that the emergence of clustering takes some time. Clustering already appears after two or three years (see Table 4.6). At the same time certain regions that lag behind can be excluded as candidates for the location of the final clusters. After two years the likelihood of the emergence of clusters in certain regions is reduced because other important developments are not occurring in these regions. However, it is still possible that local clusters emerge there. After three years such an emergence can be excluded for at least four fifths of the regions. Hence, in the third year

Table 4.8 Number of simulation runs for which those regions that become the locations of clusters in the end have not contained the highest relative numbers of firms after four years (in total 30 simulations are run for each parameter set). parameter specification

frequency of ň(4)>nCL

0 < ň(4)−nCL≤5

ň(4)>nCL+5

1st set

3

1

2

2nd set

4

4

0

3rd set

5

3

2

4th set

3

2

1

the first branching of regions occurs which excludes many regions from the list of potential locations of clusters. However, more regions contain a number of firms that is sufficient for the emergence of a local cluster than there are clusters at the end. Where the local industrial clusters are located is finally decided within the fourth or at most in the fifth year. This is also the period of time in which a stabilisation of the number and location of clusters is observed in most simulation runs (see Table 4.7). This shows that the emergence of local industrial clusters is a gradual process in which more and more regions fall behind until a few regions supersede and contain a local cluster in the end. The possibilities for policy to influence this process also decrease with time. Support of regions that lag behind becomes less likely to be successful with time.

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The exact time that the emergence of local industrial clusters takes might differ in reality from the observations in the simulation. It depends on the dynamics of the demand. However, all other parameters that concern the timing of processes are chosen in ranges that reflect reality. Thus, the dynamics that are found here can be expected to be similar to those in reality, at least if there are no further mechanisms that have a strong impact on these dynamics but are not considered in the simulation model.

5 Conclusions and policy implications

The topic that is addressed in this book is a quite complex one. Therefore, different approaches have been used to answer the questions of why local industrial clusters exist and when and where they emerge. It is impossible to give final answers to these questions within one book. However, some new insights have been added to those already existing in the literature. This chapter offers an overview of the knowledge about local industrial clusters that has been obtained in the literature and in this book, a discussion of the political implications and a list of some important questions that are still not answered. In Section 5.1, what we know about when, where and why local industrial clusters emerge is summarised. The political implications of the knowledge about local industrial clusters are discussed in Section 5.2. Finally, Section 5.3 puts forward some open questions that should be addressed in future research. 5.1 KNOWLEDGE ABOUT LOCAL CLUSTERS There is a huge and still quickly expanding literature on local industrial clusters. A complete summary of all this literature is not possible in one section of a book. Therefore, the summary that is provided here is restricted to the questions of whether and why local industrial clusters exist and when and where they emerge. 5.1.1 Existence of local industrial clusters Empirical evidence for the existence The existence of local industrial clusters is not disputed in the literature. Many cases of such local systems have been studied in various countries and industries. Thus, the question about the existence of local industrial clusters seems to be superfluous. However, the identification of the local industrial clusters that are studied in the literature is based on subjective evaluations and ad hoc conditions. It does not answer the question of whether local industrial clusters exist, it rather assumes that they do. To answer this question, rules for identifying clusters empirically have to be developed. The characteristics of the phenomenon, ‘local industrial cluster’, are comprehensively discussed in the literature. Many different concepts, such as industrial districts,

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innovative milieux, local clusters, regional innovations systems and so on, exist, which all highlight different characteristics (see, e.g., Camagni 1995, Rabellotti 1997 and Braunerhjelm & Carlsson 1999 for discussion of these concepts). This literature is based on the information obtained from the case studies. It successfully works out those characteristics that are common for several or many regions examined in case studies. On the basis of these characteristics conditions have been developed that have to be satisfied by the respective local systems. They have been applied to several countries so that the existing local industrial clusters have been identified (this is, e.g., reported for Italy in Sforzi 1990 and for Norway in Isaksen 1996). However, it is usually argued that none of the concepts captures all districts and clusters. There is a trade-off between clearly specifying the characteristics of these regions and formulating a concept that contains all of them. Furthermore, the conditions that are used in the literature to identify local industrial clusters are set up in correspondence with empirical observations. This means that local industrial clusters are recursively defined. The required conditions are deduced from the characteristics of those local systems that are to be identified. Therefore, proceeding in two steps is proposed here. First, local industrial clusters are modelled on an abstract level. Through this a unifying theory is established. From the theoretical approach certain predictions about the industrial firm distribution among regions are made. These predictions can be examined empirically. It is shown that the theoretical approach describes reality adequately. Then, all 3-digit industries are studied in Germany and the results show that theoretical predictions are confirmed for 70 of the 149 3-digit manufacturing industries. This proves that local industrial clusters exist. Furthermore, it shows that they do not exist in all industries. The industries that show clustering are listed in Section 3.2.2. Second, the industrial firm distribution is used to identify all local industrial clusters in Germany. This means that for each industry a different condition is deduced from the empirical approach. This makes the whole identification and study of local clusters less arbitrary and the results more sound. They are applied to Germany in Section 3.4. Reasons for the existence The emergence of local industrial clusters is usually explained in the literature by some local mechanisms that can be characterised as local self-augmenting processes and the existence of specific local prerequisites. In Chapter 2 of this book a clear separation between the causes of the existence of local industrial clusters and the determinants of their location is developed. It has been found that specific local circumstances are mainly relevant for answering the question of where local industrial clusters emerge, while the local self-augmenting processes are mainly relevant for answering the question of why they exist. Therefore, the search for reasons for the existence of local industrial clusters can be restricted to local self-augmenting processes. Different authors favour different combinations of such mechanisms. This implies that it is difficult to develop a unifying theory. In Chapter 2 it is shown that a theory able to capture the mechanism underlying the formation of local industrial clusters can be developed on an abstract level. The empirical

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analysis in Chapter 3 confirms that such a theory is able to describe reality. However, the empirical analysis also shows that the details and even the degree of clustering differ very much between industries. Comparing the case studies in the literature leads to the observation that clustering also differs between countries and varies with time. These difference not only occur in the shape of clustering but also in its causes. Furthermore, local industrial clusters do not occur in every industry. Hence, two questions have to be addressed. First, a list of mechanisms that might cause the existence of local industrial clusters should be developed. Second, some knowledge should be obtained that explains in which industries, at which times, and in which countries these mechanisms play a role. A list of mechanisms that might explain the existence of local industrial clusters can be set up by collecting all processes mentioned in the literature. This is done in Section 2.4.1. The local self-augmenting processes proposed in the literature are the local accumulation of tacit knowledge, the development of a local labour market for specific skills, the co-emergence of service industries, the increasing number of start-ups and spin-offs caused by a better provision of venture capital or an increasing entrepreneurial spirit, the co-evolution of local institutions, spillovers and locally increased innovativeness of the population, and the interdependencies between the economic and the political system. The literature is less comprehensive in answering the question of where, when and in which industries which of the above mechanisms matter. The case studies provide specific answers. Collecting all these answers might provide a more detailed picture. However, this has not been done so far. Simulations similar to the one conducted in Chapter 4 are also able to provide some answers (see Brenner 2001b). Here two kinds of studies are used to increase the respective knowledge. First, the processes listed above are studied comprehensively on a theoretical level. The abstract unifying theory of Section 2.2 is used to check whether each of the mechanisms mentioned above satisfies the conditions that have been identified on a general level. To this end, the empirical evidence available for each of the mechanisms is examined. Some statements about the relevance of the different mechanisms are made in Section 2.4.1. However, the major finding is that we know too little about most of the mechanisms. Second, the empirical analysis of clustering for different industries in Germany is used to study the causes for such clustering. In Section 3.2 those industries in which local clusters exist are identified. Subsequently, whether these industries differ from the other industries with respect to certain characteristics is studied in Section 3.5. It is shown that those industries with a high importance of local cooperations with public research institutions and suppliers, a strong relevance of process innovations, and a large number of intra-industry spillovers are more likely to show spatial clustering. The mechanism that seems to best explain the distinction between the industries that cluster and the industries in which no clusters exist is that of spillovers between firms. The mechanisms most present during the emergence of local clusters are those of local cooperation and process innovations.

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Summing up The analysis conducted here has shown that local industrial clusters are a phenomenon that can be clearly identified empirically. It has been shown that • local industrial clusters exist in Germany, • regions containing an industrial cluster can be clearly distinguished from other regions in an empirical approach, and • local clusters do not exist in all industries, but do exist in around half of the manufacturing industries. In the literature many processes that might cause the existence of local industrial clusters have been put forward. Here those processes have been taken up that satisfy the requirements identified from the theoretical approach. They are listed in Table 5.1. Whether there is empirical evidence for their effects has been discussed. Furthermore, whether they are stronger in those industries that show clustering has been examined.

Table 5.1 Potential causes of the existence of local industrial clusters and whether they are supported by empirical evidence in the literature and in the study conducted here (‘√’ denotes empirical support, ‘−’ denotes that no empirical evidence is available). evidence for effects

stronger in clustering industries

spin-offs

√

−

support for start-ups

√

−

spillovers

√

√

importance of innovations

−

√

cooperation

−

√

inter-industrial dependence

√

−

accumulation of human capital

√

−

firm-public research/education interaction

−

−

venture capital

−

−

local attitude towards entrepreneurship

√

−

firm-policy interaction

−

−

proposed processes

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5.1.2 Timing of the emergence of clusters The question of when local industrial clusters emerge is rarely discussed in the literature. Of course, in most case studies a comprehensive discussion of the situation under which the cluster emerged is given. This often includes a comprehensive description of the historical situation. However, a general approach that studies the reasons for the emergence of local industrial clusters at certain times is missing in the literature. The general theory that is developed in Section 2.2 is used to deduce some insights in this book. It shows that theoretically only four kinds of changes might trigger the emergence of local industrial clusters: increases in global or national demand, a technological change, an increase in the strength of local self-augmenting processes, and an increase in the attractiveness of a region. Most of the case studies confirm changes in demand or technology as being responsible for the timing of the emergence of clusters. Usually the industries in which local clusters emerge already satisfy the conditions necessary for clustering before clusters emerge. However, the local clusters will only emerge if the market exceeds a certain size. This can happen either by an increase of the global market, by the globalisation of markets, which allows the firms from particular regions to supply a larger share of the global demand, or by a shift in the market caused by technological changes. This means that local industrial clusters emerge in each industry only at certain times. The times at which they emerge are determined by the respective changes in the size and/or structure of the global market. Changes within a region might also trigger the emergence of a local industrial cluster. However, the analysis in Section 2.5.2 shows that such changes have to be very large in general. Only at certain times, usually when the size of the market increases, is the attractiveness of a region crucial. Hence, changes in the attractiveness of a region alone will rarely lead to the emergence of a local industrial cluster, while it might support such an emergence significantly if other processes, such as the increase of the size of the market, appear at the same time. Theoretically a change in the local self-augmenting processes might also trigger the emergence of a local industrial cluster. If the strength of these self-augmenting processes increases, an industry might change from one without clustering to one with clustering. However such a change is not described in any of the empirical studies related to local industrial clusters. 5.1.3 Location of industrial clusters The literature on local industrial clusters mainly aims to answer two questions: why are certain regions economically more successful than others, and what are the prerequisites for a region becoming successful? The latter is very similar to the one that is discussed here. Thus, a large literature exists that should not be ignored while attempting to answer the question of where local industrial clusters emerge. However, the approach that is taken here differs from the approaches taken in the literature. The analysis in this book is based on the abstract theory that is developed in Chapter 2. This theory provides the framework for all studies done here and structures the way in which the different

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questions are tackled. The theoretical approach distinguishes between three factors: the market situations, the local self-augmenting processes, and the attractiveness of regions. All three can be considered separately when answering the question of where local industrial clusters emerge. Several insights are gained in the theoretical analysis in Chapter 2 that are summed up in the following. Competition among regions Changes in the market situation usually cause the emergence of local clusters in the respective industry, as was stated above. This means that there are certain periods of time in which local clusters emerge with respect to one industry. The simulation study in Section 4.3 shows that the number of clusters is bound, although often to a wide range, by the characteristics of the industry. Hence, only a few regions will become the location of these clusters. As a consequence, it is not sufficient to examine regions separately if we want to understand why clusters emerge in some regions and not in others. Clusters emerge at particular times in particular industries and the regions compete to be the location of these clusters (see Maggioni 2002 for a similar argument). Competition is meant here in a metaphorical sense because the regions usually do not actively compete. However, an industrial cluster will only emerge in a few of them, meaning that a few of them supersede the others. This implies that it is not possible to explain the emergence of a local industrial cluster only on the basis of local prerequisites. On the one hand the development of the respective global or national markets have to be considered. On the other hand, the local prerequisites have to be compared to those of other regions. However, prerequisites that are superior to those in other regions and the necessary changes in the market do not automatically imply the emergence of a local cluster. Many of the events that get things started in a region are random events in the sense that they depend on decisions of single individuals and cannot be predicted on the basis of the general situation. These events are: the founding of firms, the coordination between a few crucial people, and the emergence of crucial innovations. Better prerequisites make these processes and the emergence of a local cluster more likely, but not certain. This means that differences between regions lead to different probabilities of the regions becoming the location of an industrial cluster. In the next paragraphs the differences that matter in this context are discussed. Differences in self-augmenting processes According to the discussion in Section 2.4 and 2.5, regions can differ with respect to the strength of the self-augmenting processes and with respect to their attractiveness. Here, the discussion of the differences in the strength of the self-augmenting processes from Section 2.4.2 will be summarised first. The self-augmenting processes have been listed above. Detailed studies about the strength of these processes are lacking. Thus, we can only make guesses about the differences between regions with respect to these processes. In some cases the differences between countries and regions can be assumed to be small. Other processes might differ

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significantly between countries, but little within countries. And some processes might even differ significantly between regions. In Section 2.4.2 three major factors that influence local self-augmenting processes were identified. These are different cultures, differences in regional policies and the existence of universities and public research institutes. The first two factors have an influence on the strength of the local self-augmenting processes. They increase or decrease the likelihood of the emergence of local industrial clusters in the regions. The latter factor represents a necessary condition for the occurrence of local self-augmenting processes in some industries. Thus, it excludes certain regions from the set of potential locations of industrial clusters. Attractiveness of regions The main determinants of the location of industrial clusters are the differences in attractiveness between regions. As mentioned above, regions compete with each other in order to be the location of emerging clusters. The outcome of this competition is partly determined by the attractiveness of the regions. This attractiveness is defined here as the sum of all advantages and disadvantages of a region with respect to the industry under consideration that are of a permanent character. This includes all those factors that do not develop during the emergence of a cluster or that are historical singularities. Factors that fall into this category are the geographic location, the size of the population, cultural specificities, the political system (if it is sufficiently stable), the location of universities and research institutes (if they are permanent), and the presence of other economic activity, such as other industries that are important for the industry under consideration. It is shown in Section 4.4 that these factors have a strong influence on the locations at which industrial clusters emerge. The influence of each of these factors depends on the industry under consideration. In some industries one of the factors might be crucial. For example, the existence of a university and research facilities is a necessary condition for the emergence of a cluster in quite a number of industries, for example, telecommunication and biotechnology (the importance of university and public research is reported in Rosegrant & Lampe 1992 and Dalum 1995). In these cases certain characteristics of the regions classify them into two groups: a group of regions in which industrial clusters might emerge and a group of regions in which such clusters cannot emerge. In other industries the above factors play a minor role or lead to a rather gradual difference between regions, making some regions more likely and other regions less likely to be the location of emerging clusters. The emergence of clusters in printing machine manufacturing (reported in Porter 1990) is an example of such a case. In such cases often a combination of factors determines the attractiveness and therefore the chances of regions becoming the location of clusters. Some disadvantages might be compensated by other advantages. Nevertheless, the attractiveness of regions does not unambiguously determine the location of industrial clusters. The discussion in Section 2.5 showed that random historical events have a strong influence on the location of clusters. This is also confirmed by many case studies. There are some developments that neither belong to the local self-augmenting processes nor are they part of the permanent characteristics of

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regions. These are the existence of local promoters or small groups of promoters, specific policy measures applied to a region, and historical singularities (for example, Trigilia 1992 suggested that the situation of peasants was an important factor for the development of the industrial districts in North Italy). From the perspective of a general model these factors have to be treated as stochastic influences. It is not possible to predict their occurrence on a general level. Often the emergence of local industrial clusters is triggered by the coordinated action of a few local people who have a vision about future products or about promising economic activity in the region. In particular, in the clusters that emerged at the end of the 19th and at the beginning of the 20th centuries this can be observed frequently (examples are the optical cluster in Jena and the automobile cluster in Stuttgart). Hence, individuals or small groups can promote certain developments in regions and through this they might give the region a decisive lead in the competition with other regions. The existence of such people cannot be predicted by a theory on the basis of the situation in the region. From the perspective of a general theory they are random events that occur in some regions and increase the likelihood of these regions containing an industrial cluster in the future. Similar events might happen on the level of local politics. Some policy makers might realise certain opportunities for the development of the region and might take respective actions. If these actions are appropriate and occur at the right time, they might trigger the emergence of an industrial cluster (examples are the founding of an institute conducting applied research in telecommunication technology in Aalborg reported in Dalum 1995). Whether such policy measures are taken depends again on one or a few people and their vision of future developments. From the perspective of a general theoretical model, these are random events that occur in some regions and give these regions an advantage. Finally, there are historical singularities that increase the attractiveness of certain regions. Examples are the high number of government orders (mainly from the defence department) for the products of firms in the Silicon Valley area (see Saxenian 1994) or the specific situation of the rural population in North Italy (see Trigilia 1992). These historical singularities are of relevance for the emergence of clusters only within a certain time period. If this time period is decisive for the emergence of a local cluster in an industry, the historical singularities have a strong impact on the location of the clusters. Historical singularities can, in general, be easily identified in an empirical approach, but not predicted or included in a general theoretical model. These three factors, especially the first one, make a prediction of where local industrial clusters will emerge impossible. Only statements about the approximate likelihood of certain locations are possible. The more that is known about a region and the relevant actors within it, the better will be the estimations of chances of the region. However, in addition to the above factors, the developments within a region depend on the success of the respective firms in the market. The innovations they make and the products they develop become decisive. At the time at which clusters emerge, there are usually only a few firms in the competing regions. The success of these firms becomes important. Thus, the developments at times in which clusters emerge depend on single events and are therefore quite unpredictable, while the situation becomes much more stable once the local industrial clusters have become established.

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Summing up The location of industrial clusters is decided in a competition of regions. This competition is usually not actively conducted by the regions. Nevertheless, some regions are able to supersede others in the economic developments in the industry under consideration. There are three factors that influence the success of regions. First, there are necessary local circumstances. They depend strongly on the industry under consideration. All regions that do not provide these circumstances have no chance of becoming the location of an industrial cluster. These circumstances are: • Existence of a university • Existence of research institutes • Natural circumstances (resources, geography) Second, there are factors that determine the attractiveness of regions and therefore the likelihood of the development of industrial clusters there. These factors are: • Cultural factors (entrepreneurship, innovativeness) • Political circumstances and laws • Geographic location • Type of region (city or rural area) • Universities and research institutes • Economic activities in related industries Third, there are developments that cannot be predicted on the basis of the local situation before they occur. These have to be taken as random influences that can only be understood after the emergence of local industrial clusters in the form of case studies, but cannot be predicted on a general level. These factors are: • Existence of local promoters • Specific policy measures • Historical singularities • Occurrence of path-breaking innovations • Founding of crucial firms

5.2 POLITICAL IMPLICATIONS The findings of this book, which are summarised above, can be used to advise policy makers. In recent years policy makers have become more and more interested in local industrial clusters. Since it is usually assumed in the literature that these clusters imply economic success in the regions in which they are located, at least for a certain period of time, regional policy makers are particularly eager to create local industrial clusters in their own backyards (a discussion of the increasing interest of policy makers in regions is given in Rehfeld 1999). Therefore, policy makers have an interest in receiving advice with respect to how such local industrial clusters can be created. However, the question of how such clusters can be created is not the only one that should be of interest in this context. Several other factors have to be taken into account as well. First, what might be gained by influencing the emergence of local industrial clusters

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should be discussed. Then, whether policy measures can have an impact and under what circumstances they might be successful needs to be examined. Finally, different policy measures should be discussed with respect to their effectiveness and adequacy. 5.2.1 Effects of influencing the emergence of clusters Before the measures that can be used to influence the emergence of local industrial clusters are discussed, the question of whether policy measures are able to create such clusters has to be answered. Two of the findings in this book are particularly important in this context. First, the emergence of local industrial clusters is not guaranteed even if certain prerequisites are given. Second, the location of clusters is determined in a competitive process among regions. Creation of local industrial clusters The first finding implies that local industrial clusters cannot be created at will by supplying some specific prerequisites. This is because of several factors. First, as is discussed in Section 2.5, local industrial clusters usually emerge when the industry and the market it supplies show certain dynamics, namely an increase in demand, a technological change or an increase of the importance of local self-augmenting processes. These aspects can not be much influenced by political measures, although such an influence is not completely excluded because laws and taxes might change markets. Thus, in general, the effect of policy measures depends on developments that are out of the reach of political influence. These developments can open windows of opportunity for policy making that are discussed in more detail in the next subsection. Even if the developments in the market and/or the local self-augmenting processes are favourable to the emergence of local industrial clusters, policy measures are not able to guarantee the creation of such a cluster in a particular region. Considering the factors of external conditions, self-augmenting processes, regional attractiveness and historical singularities, that are distinguished here, policy measures are mainly able to influence the attractiveness of certain regions. This can be done by changes in the education institutions, the infrastructure or by enabling firms to be founded or grow more easily. However, it has been stated above that an increase of the attractiveness of a region makes the emergence of an industrial cluster in this region more likely, but not a certain event. It is more difficult but possible for policy to change the strength of local selfaugmenting processes within an industry. This can be done on a global, national or regional level. If it is done on a global level, it does not influence the location of the emerging industrial clusters. On a local level there are only a few factors that can be influenced by policy measures, namely the development of an entrepreneurial spirit, the coevolution of some local institutions, and spillovers between firms. Again the result is an increase of the likelihood that an industrial cluster emerges in the respective region. Finally, policy makers might try to influence directly those aspects that have been called stochastic influences above. These are the existence of regional promoters, specific political circumstances, the coordination of local actors, and the market success of the firms in a region. The last factor cannot be much influenced by policy measures. It depends on the firm’s ability to undertake the correct innovations and produce the right

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goods. The existence of regional promoters can at least be partly influenced by local policy. Policy makers might actively support regional promoters or the interaction of these if they are available in the region. They might also increase the probability that such promoters appear, but it is not possible to create them. The political circumstances and coordination activities are, of course, within the scope of policy makers. As was argued in Section 2.5.3, this might trigger the emergence of local industrial clusters. Nevertheless, it does not exclude the dependence on random events, such as the success of the firms in the region. The different possibilities to support the emergence of local industrial clusters are discussed in detail below. Here it can be stated that none of these measures is able to create an industrial cluster in a particular region. All that can be achieved is either an increase of the likelihood that an industrial cluster emerges in a particular region or the occurrence of clustering in an industry that has not shown clustering before, however, without being able to determine where the clusters emerge. Whether these two possible results of policy measures are desirable has to be discussed next. Influencing clustering within an industry It was shown above that policy measures that influence the market or the local selfaugmenting processes might cause clustering in an industry that has not clustered before. Of course, the opposite might be true as well. In general, it is possible to increase or decrease the number of local clusters that exist in an industry. This causes the economic activity within the respective industry to be more or less concentrated geographically. The geographic concentration of economic activity has advantages and disadvantages. Advantages are caused by the mutual benefits that firms obtain from their co-location. These are generally related to the self-augmenting processes that cause the existence of local industrial clusters. Disadvantages emerge from the scarcity of space and people, which causes costs to increase. These effects become dominant if the size of clusters increases above a certain level and prevents clusters from increasing without limit and the industry from concentrating in only one region. Hence, there should be a natural number of clusters that is determined by the shape of these two opposing processes. The simulations in Section 4.3, however, show that the industrial firm distribution among regions shows path-dependence. The number of clusters that exist in an industry depends on the specific developments at the time when they emerge. There is a wide range of numbers of clusters that is stable. Only if the number of existing clusters does not fall into this range, do further processes take place. Otherwise the local clusters will be stable as long as the exogenous conditions, mainly the market situation, do not change. This implies that policy measures might change the number of clusters that emerge in an industry. However, it is impossible to judge whether such changes improve or worsen the situation on the basis of the current scientific knowledge about clustering. Thus, such policy measures cannot be recommended, given the current scientific knowledge. There might be exceptional cases in which the direction for improvement is obvious for some reasons. However, I have not seen any such case so far. Influencing the location of industrial clusters

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The situation is different if policy measures support the emergence of an industrial cluster in a specific region. If such a measure is successful two kinds of results might be obtained. Either an additional cluster is created or a cluster emerges in the supported region instead of in another region. If an additional cluster is created, we run into the problems discussed above. It is difficult to judge whether such an additional cluster is economically advantageous or not. Of course, there might be political reasons that favour an additional cluster. At the same time there are economic costs, the costs of the policy measures, and a change of the economic situation to a better or a worse one. A situation in which all regions or all countries support additional clusters is especially problematic. This might lead to the maximal number of clusters that can be stabilised or to even more clusters that have to be stabilised by permanent policy measures. Such a situation is definitely not optimal. Hence, only if policy measures are taken in a few regions, might the result be economically neutral on average and the political reasons have only to justify the costs of the measures. Similar arguments can be applied to a situation in which one region is supported such that the industrial cluster emerges there instead of in another region. On average the economic result is neutral. However, several additional factors have to be taken into account. The strength of the local self-augmenting processes might differ between regions. Therefore, firms might benefit more from their co-location in some regions than in other regions. Furthermore, some locations might be more beneficial than others, for example because of a specific geographic location, the presence of firms in other industries, or other factors of the attractiveness of regions that are extensively discussed in Section 2.5.2. With respect to the success of the firms, it would be best if the clusters emerged in the most beneficial regions. The analysis conducted in this book gives some hints about what aspects should be considered if the benefits of firms being co-located in a particular region are to be estimated. These are the geographic location of a region, cultural aspects, for example the innovativeness of the people, their opinion with respect to entrepreneurship, or their attitudes towards the goods under consideration, the presence of other relevant industries, and the presence of universities and research facilities. These will be discussed in more detail in the next subsection. In addition, it has to be taken into account that developments start in many regions before some clusters emerge in a few regions. This implies competition among regions in which some regions lose and the respective firms fail in the end. It seems to be preferable to have an earlier emergence of the clusters, so that no resources are wasted in the other regions. This might justify the support of a few regions, which have, of course, to be in ‘adequate’ locations. However, on the basis of the available knowledge about the processes involved, a final statement is not possible. Furthermore, political reasons might be given for the preference of an emergence of industrial clusters in certain regions. One reason is the existence of lagging regions. These are, however, often also inadequate locations for clusters. If these regions are underdeveloped because of their history and not because of disadvantages in their attractiveness or the strength of the local self-augmenting processes, a support of the emergence of industrial clusters might be an adequate measure to boost economic development.

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However, regional and national policy makers usually like to see industrial clusters emerge in their own regions. If many of them support their own regions, an ineffective race results in which many resources are wasted. Therefore, independent of the above arguments, there should never be many different regions supported at the same time with respect to the same industry, at least not if the effectiveness of the global economy is concerned. This implies that the support of the emergence of local industrial clusters can, if at all, only be coordinated on a supra-national, or at minimum national, level. Measures organised on the local level run the danger of leading to an ineffective competition among regions. 5.2.2 Likelihood of success of policy measures The previous discussion has shown that the economic desirability of local industrial clusters depends on where and when they are caused to emerge. This discussion has been based on the assumption that the respective policy measures are successful in creating a local industrial cluster. However, in this book it has been found that local industrial clusters cannot be created at will. There are no prerequisites or measures that guarantee the emergence of such clusters. All that can be achieved is an increase in the likelihood of their emergence. The effectiveness of policy measures depends very much on the region, time and industry to which they are applied. Therefore, these factors should be chosen carefully. Some hints how the region, time and industry should be chosen are given in the following. Choosing the right industry Local industrial clusters emerge in certain industries at certain times. Therefore, policy measures should only be applied to one or a few industries at any one time. The timing will be discussed below. It has been shown that not all industries show clustering. It is a waste of resources to support the emergence of local clusters in those industries that do not show any clustering. A detailed list of industries that currently show clustering in Germany is given in Section 3.4.2. However, this does, of course, not exclude the possibility of local clusters emerging in other industries in the future. Local clusters emerge mainly in new industries while the demand is increasing tremendously. Therefore, it is important to be able to predict whether new industries will show clustering. The causes of clustering have been discussed above and the list of potential causes is given in Table 5.1. However, the causes of the existence of local clusters are still not sufficiently studied. The above list offers only the possibility of making a guess about whether newly evolving industries might show clustering. For a concrete prediction further studies are necessary.

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Choosing the right region It has been argued above that, at most, only a few regions should be supported. Thus, the question of how to choose the right regions arises. According to the analysis in this book, regions differ with respect to their attractiveness and the strength of the local selfaugmenting processes. Above it has been argued, that those regions with a higher attractiveness and a higher strength of the self-augmenting processes should, in general, be preferred to contain clusters. The discussion in this section is based on the question of whether policy activities are or can be successful. In this context, success means that the policy measure causes the emergence of a local cluster which would not have emerged without the policy interference. Whether such an effect is desirable has been discussed above. If policy measures are taken in a particular region, three things might happen with respect to local industrial clusters: • A cluster might emerge that would also have emerged without the policy measures. • A cluster might emerge that would not have emerged without the policy measures. • No cluster will emerge. Assuming that policy measures do not worsen the situation, the emergence of a local industrial cluster cannot be hindered by policy measures. Therefore, the last of the above cases implies that no cluster would have emerged without the policy measures. Of the three possible outcomes only the second one is desirable. If the cluster would have emerged independently of the policy measure, these measures are superfluous and a waste of resources. If no cluster emerges, the policy measures did not have the desired effect. Hence, only regions that have a high probability of the second case occurring should be chosen. This implies that regions with a high likelihood that a cluster emerges independently of policy measures, and regions in which the emergence of a cluster is very unlikely should be avoided. It has been argued in Section 2.5.2 that the probability of the emergence of a local industrial cluster depends on the attractiveness of a region. The higher this attractiveness is, the more likely is the emergence of a cluster. Hence, policy measures are most successfully applied in those regions that are neither very attractive nor unattractive. Two situations have to be distinguished. First, the industry under consideration has just emerged, so that very few firms exist already. In this case the attractiveness of regions have to be estimated on the basis of factors, such as geographic location, cultural specificities, the political system, the location of universities and research institutes, and the presence of other economic activity, for example other industries. Regions that rank high according to this evaluation and that contain comparably little economic activity with respect to the industry under consideration should be chosen. Second, a situation has to be considered in which some clustering has already emerged. This means that in some regions the emergence of a cluster becomes visible. These regions are not the right choice. Policy measures are more effective in those regions that are attractive, but show, so far, only some development. Regions in which no development is found are also not adequate, because there is nothing on which the policy

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measures can be based. It is unlikely that in such regions the emergence of an industrial cluster can be triggered. Choosing the right time Only two situations have been discussed above. The situation in which local clusters have already emerged and stabilised in the industry under consideration has been ignored. There are good reasons for such an omission. The simulations in Section 4.3 have shown that local industrial clusters are quite stable. Furthermore, it has been found that the maximal number of clusters is limited in each industry. As a consequence, the support of the emergence of clusters in an industry in which the situation has stabilised is unlikely to be successful. If any policy measures are to be applied, they should be implemented at times in which clusters are emerging in the respective industry. This implies that there are certain windows of opportunity in each industry. According to the theoretical analysis in Section 2.5, these windows of opportunity usually appear when the demand for the goods produced by the industry increases significantly. Policy measures are likely to be successful only at such periods of time. Even within these periods of time the effectiveness of policy measures varies with time. In Brenner 2002 these variations are studied, and it is shown that measures that influence the number of start-ups should be implemented at a time when a new industry appears. Measures that influence the cooperation among firms, instead, are more effective at a time when the first clusters begin to take shape. Other measures, such as those that influence the accumulation of human capital in the region and the innovativeness of firms, are similarly effective during the whole period in which clusters emerge. None of the measures has been found to be significantly effective after the situation in the industry has stabilised. One problem should not be neglected in this context. It is much easier to detect windows of opportunity at a time once the first local industrial clusters take shape than to detect them at a time when the first firms appear. Therefore, measures that are effective at a later time might be more attractive. It is easier to focus efforts at such a time, because the situation can be better analysed. However, the findings also suggest that, in general, policy measures are more effective the earlier they are taken. 5.2.3 Adequate policy measures Defining adequate policies has two aspects: first, the economic processes that should be influenced have to be identified. Second, the ways in which they can be influenced have to be studied. There is an extensive literature on the ways in which different economic processes, for example innovations, education, start-ups and so on, can be influenced by policy measures. It is beyond the scope of this book to discuss this literature or even to present the results comprehensively. Hence, how economic processes can be influenced, is omitted here. Instead, the following discussion focuses on the question of which economic processes should be influenced in order to create local industrial clusters. This question is rarely addressed in the literature (exceptions can be found in Miller & Coté 1985, Maggioni 2002 and Barca 2003). The analysis conducted throughout this book offers several hints about how the emergence of local industrial clusters can be

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supported. Some of the above arguments should, however, be kept in mind in the following discussion. Policy measures can only be effective if they are applied to the right industry, at the right time and in the right region. Focusing on one or a few regions and on one or a few industries is strongly recommended. The following arguments are put forward under the assumption that industries, regions and time are adequately chosen and that there are good reasons for a political intervention. In addition, it has to be kept in mind that policy measures are, in general, not able to create local industrial clusters. All that can be achieved is an increase in the likelihood of the emergence of such clusters. Three different factors have been repeatedly highlighted in this book. These are the exogenous conditions, mainly the market situation, the local attractiveness, and the local self-augmenting processes. These three aspects will again be discussed separately here. Influencing the market situation Increases in demand are crucial for the emergence of local industrial clusters. However, it is difficult, rarely possible and somewhat risky to influence this factor by policy measures. The situation might be different if public institutions are the main source of the demand for a type of product (this was the case during the emergence of Silicon Valley). In such a case demand can be directly influenced by policy makers. They might favour certain firms or regions. However, only if private demand for similar goods develops will the situation become stable, independently of public demand. Such situations are rare. In addition, demand can be influenced by taxes, subvention and laws. These are sometimes used to favour new or environmentally desirable products and technologies. Two risks are involved in such measures. On the one hand, these measures only influence the demand side. Thus, they determine the timing of the emergence of clusters and probably also the number of clusters. Their location is only influenced if two conditions are present. First, the measure has to be applied to a region or nation in order to cause regional differences. Second, markets have to be such that local firms benefit more from an increase in local demand than firms outside the region. If the latter condition is not given, the policy measures might trigger the emergence of local industrial clusters, but are unable to determine where these clusters emerge. On the other hand, the support of certain technologies might prove to be disadvantageous in the medium and long run. If technologies and products change frequently, the flexibility of local industrial clusters is necessary for the durability of their success. Taxes, subvention and laws might encourage them to bind themselves to a certain product or technology too much. This might hinder the adaptation to new developments (examples of such developments are described in Grabher 1993 and Isaksen 2003). Increasing the attractiveness of regions It has been repeatedly found in this book that the attractiveness of regions determines the likelihood of the emergence of an industrial cluster within them. Hence, increasing the attractiveness of a region is an adequate way of supporting the emergence of a cluster there. The factors that determine the attractiveness of a region vary between industries. Potential candidates are listed in Section 2.5.2.

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Some hints about their importance are obtained from case studies. They show that, in particular, the existence of universities and research institutes, the entrepreneurial attitude of the population, the geographic location and accessibility of a region, the availability of venture capital, and the existence of firms in related or necessary industries in the regions are the main determinants. Their relative impact varies between industries. The attractiveness of regions plays an important role at a time when local clusters emerge and it is still undecided where they will be located. According to the theoretical discussion in Section 2.3, a high attractiveness causes a region to exceed the critical value of the exogenous conditions at a time when the market conditions are very advantageous. The market conditions are most advantageous when demand increases rapidly and supply is not able to keep pace with this increase. Policy measures that influence the attractiveness of regions have to be effective at this time if they are intended to influence the emergence of local industrial clusters. This points to a problem of the support of the attractiveness of regions. The respective policy measures have to be applied before clusters start to emerge or, at least, at the beginning of such processes. Policy makers have to identify these developments quite early. Hence, the approach discussed here is very demanding with respect to the capabilities of policy makers. They have to understand the developments within industries and have to recognise the emergence of local clusters early. Furthermore, they have to be able to compare regions with respect to their potential for being the location of the emerging clusters. Finally, the relative impact of different factors that might influence the attractiveness of the regions have to be estimated to focus policy measures adequately. Supporting local self-augmenting processes In Sections 2.4 and 2.5 it was found that the strength of the local self-augmenting processes not only determines whether local industrial clusters exist, but also influences the likelihood of their emergence in a certain region if this strength varies among regions. Hence, the strengthening of the self-augmenting processes in a region increases the likelihood of the emergence of an industrial cluster there. The local self-augmenting processes are responsible for the emergence of local clusters in the sense that they amplify initial positive developments. This implies that they only become active if some development has already taken place. Some firms have to be active in the respective industry and region in order to trigger the emergence of a cluster via these processes. As a consequence, all policy measures that focus on local self-augmenting processes require the existence of some initial activity in the region and industry under consideration. The strength of local self-augmenting processes is, in combination with the attractiveness of regions, decisive for the competition among those regions that show some initial development. In general the self-augmenting processes vary only slightly between regions. However, policy measures might increase their strength in certain regions. The processes that can be influenced by policy measures are interactions between firms and public research and educational institutions, spin-offs, spillovers among firms, and the coevolution of the local public opinion. The interactions between firms and public research

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and the content of public research and education can be directly influenced by policy makers. Spin-offs can be supported in the form of venture capital and advice for start-ups. The other two processes, spillovers and the changes in the public opinion, are much more difficult to influence. Experience shows that it is difficult to encourage sustainable cooperation and mutual exchange of information among firms. Furthermore, I am not aware of any case in which policy measures have successfully influenced the local public opinion. An alternative possibility is the support of those local agents who have caused the initial development. It has been stated above that regional promoters often play an important role in the emergence of clusters. This requires two things: their existence and a significant impact by them on the region. The latter aspect can be supported by policy measures. It might also be possible to bring together several local promoters, if they exist, in order to obtain a critical mass that has an impact on the development in the region. Focusing on local self-augmenting processes has the advantage that they have to be implemented at a time when initial developments are already visible. However, all other concerns put forward above still apply. Policy makers have to be able to estimate the attractiveness of regions and to evaluate the initial developments and the qualities of local promoters and actors. In any case, the effectiveness of the policy measures discussed here depends crucially on choosing the right industry, region and time. Once this is done, policy measures might be focused on the attractiveness of the region, the strength of local self-augmenting processes, or, perhaps preferably, a combination of both. 5.3 OPEN QUESTIONS The phenomenon of local industrial clusters has been analysed in the scientific literature for more than 20 years now and many insights have been obtained. However, especially if the question of how the emergence of such clusters can be adequately supported is posed, it becomes clear that further research is required. This is partly because of the various causes that underlie the emergence of different local industrial clusters. The heterogeneity of local conditions, historical developments, and relevant processes make a general understanding difficult. In addition, some questions have received much attention while others have been mainly neglected. Hence, quite a number of questions are still not sufficiently answered. Different opinions might be held with respect to the questions that are most important. Hence, any outlook on further research is subjective. Some topics will be proposed in the following without claiming that they are the only ones that might be taken up. The topics proposed are those where information was most missed during the work on this book, and they arose mainly within the development of a general theory, the identification of the relevant processes and the recommendations for policy implications. 5.3.1 General features and unifying approaches Most of the literature has either focused on certain local factors, such as knowledge, labour markets, innovativeness, institutions, and relationships among actors, or on specific developments within one region. Approaches that try to identify similarities or

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bring the various findings into a unifying system are rare (exceptions can be found in Porter 1990 and Paniccia 1998). This holds especially for empirical studies. Therefore, two kinds of empirical studies have to be conducted more often in the future: comparative studies between regions and studies in which whole countries are examined through a general approach. Recently, quite a lot of empirical work involving several regions in different countries has been conducted. Comparative studies seem to be becoming increasingly attractive to scientists. It is important that these studies define hypotheses about processes and causes that are tested in all regions in the same way. This could help to identify those processes and causes that are common to all local industrial clusters. It is also important to include regions in the study that contain no industrial clusters. Thus far, less successful regions have usually been neglected. However, only by including these regions can the necessary conditions for the emergence of local industrial clusters be identified. Another way of approaching the local circumstances that support the emergence of local industrial clusters is based on a separation of regions into those in which clusters are found and those in which no clusters exist. Then, the difference between these groups of regions can be studied with respect to local characteristics, initial states, and historical developments. Such an approach requires data on different factors at different points in time. This would allow some knowledge to be obtained about the factors that influence the likelihood of the emergence of local industrial clusters. These two types of research could add tremendously to our understanding of where and how local industrial clusters emerge. In particular, the question about the necessary or helpful local prerequisites might be answered more comprehensively than can be done at the moment. This would also help policy makers to focus their activities on the adequate regions and the adequate measures. 5.3.2 Detailed studies of local mechanisms Most of the literature and the study in this book highlights the importance of local selfaugmenting processes. Such processes are responsible for the existence of local industrial clusters and cause the economic success of these clusters. However, various mechanisms are put forward in the literature. The current knowledge about these mechanisms provides only little understanding of how much they contribute to the emergence and success of local industrial clusters under different circumstances. The research that is proposed above would provide some further knowledge. However, much more seems to be needed. Again some approaches in this directions have been undertaken in recent years. In particular, local spillovers, knowledge transfers through the movements of employees and personal contacts, and the development of an entrepreneurial spirit in a region have been studied (see Audretsch & Stephan 1999, Verspagen & Schoenmakers 2000, Zellner & Fornahl 2002, and Fornahl 2003a). However, many questions remain unanswered. To understand the emergence of local industrial clusters in different situations, the local mechanisms involved have to be understood comprehensively. Conducting simulations makes this very clear. Simulating processes require a detailed knowledge about their functioning. This is not available for all processes that are relevant for the emergence of local industrial clusters. In particular, the mechanisms of spin-offs, the accumulation of human capital in a region, the effects of cooperation among firms, the interdependence

Conclusions and policy implications

183

between industries, the interdependence between the availability of venture capital and the local firm population, the coevolution of public research and industrial firm population, and the interaction between firms and the public and political opinions are not sufficiently understood. Questions that should be answered are, for example: • What determines the number of spin-offs that a firm creates? • What kinds of human capital are important for firms, how do they accumulate and how important is the location in this context? • To what extent does the local availability of partners enhance cooperation and do firms benefit from this? • Which industries show local co-evolution and how does this co-evolution work? • To what extent do existing firms influence the availability of venture capital? • How does the public research conducted in a region react to the developments in the local firm population? • How and to what extent do firms influence public and political opinions? The questions listed here are those for which answers have been most missed during the approach taken in this book. There are of course other important, often related, questions. Many of the above questions are not addressed at all in the literature. I claim, however, that answering these questions is crucial for a comprehensive understanding of why local industrial clusters emerge, how this might vary with time, industry or region, and how it can be influenced by policy measures. As long as we do not fully understand the functioning of the different local mechanisms, it is not possible to judge their relevance. Therefore, the potential mechanisms should be studied more comprehensively in the future, especially with respect to their self-augmenting character. 5.3.3 Discussion of policy measures The empirical literature on local industrial clusters has so far mainly studied the local circumstances that might have caused their emergence and the reasons for their success. From this some policy implications have been deduced. However, these implications are mainly based on observations in the successful regions and are difficult to transfer to other regions with different preconditions. Another approach to understanding the influence that policy measures might have is proposed here. Many different policy measures have been applied in recent years because local clusters are enormously attractive to policy makers. Comparative studies of the effects of these measures might provide information about adequate policies. To this end, the dynamics that are caused by the policy measures have to be examined. Developments that have been triggered by these measures have to be distinguished from developments that are supported. This means that the states of the regions have to be considered in the analysis. According to the analysis above, the results of policy measures have to be expected to depend strongly on the region, the industry and the time at which they are applied. Hence, it is not possible to simply estimate the effects of different policy measures. Instead, the dependence of these effects on the facts of where, when and on what industries the measures have been applied has to be understood. Such results will only be obtained if comparative studies are conducted for cases in which similar policy measures are applied to different regions and industries at different

Local industrial cluster

184

points in time. Another possible approach is the study of the effects of different policy measures that are applied in similar situations. In any case, I see the comparative character of such studies as a crucial element. Otherwise we will not be able to judge the effects of policy measures objectively. One might hope that the huge number of policy programmes that have been set up in recent years will be used to achieve a better understanding of how effectively they work and under what circumstances they are adequate.

Appendix

A.1 MATHEMATICS A.1.1 Proofs for Chapter 2 Proof of Lemma 1 The stationary states ( , č, š) of the dynamic system (2.2), (2.3) and (2.4) have to satisfy and

simultaneously (‘st’ is used

as an abbreviation for the stationary state given by (ƒ(t), c(t), s(t))=( , č, š)). This implies the conditions (A.1)

(A.2)

and (A.3) Inserting Equations (A.1) and (A.2) into Equation (A.3) results in (A.4)

Appendix

187

Equation (A.4) determines the values of for all stationary states. For each value of , exactly one value of č and š is defined by Equations (A.1) and (A.2). Therefore, the dynamics given by (2.2), (2.3) and (2.4) have exactly the same number of stationary states as there are solutions to Equation (A.4). Let us assume that the parameters aƒƒ, αcƒ, asƒ, αƒc, αƒs, ρƒ, ρc and ρs are rational values which does not restrict the dynamics that can be modelled by the approach in any way that is crucial for depicting reality. Then, a natural number η can be found such that hƒ=aƒƒ·η, and hρ=ρƒ·η are natural numbers. A new variable x is defined by

. Equation (A.4) then reads (A.5)

The left-hand side of Equation (A.5) is a polynomial of order hρ. The hρ-th order derivative of this polynomial is a constant function (the hρ-th order derivative of the last term in the polynomial) that has no zero. Let us now consider each derivative in turn, from the hρ-th order derivative to the first-order derivative of the polynomial and consider all zero x0 with x0>0. The r-th order derivative of the polynomial is denoted by pr(x) in the following. Let us assume that pr(x) has nr zeros for x>0. Two situations are distinguished here: pr−1(x) has either the same number of terms or one term more than pr(x). In the first case, pr−1(0)=0. As a consequence, the number nr−1 is at most as high as nr, because pr(x) is the derivative of pr−1(x) which implies that pr−1(x) has exactly nr extreme points for x>0. In the second case, if pr−1(x) has one term more than pr(x), this term is a constant. Hence, pr−1(0)≠0. Nevertheless, pr−1(x) has nr extreme points for x>0. In addition, every polynomial pr−1(x) becomes negative for x→∞. Therefore, the number of zeros is either nr−1=nr, if either nr is even and pr−1(0)>0 or nr is odd and pr−1(0)<0, or nr−1=nr+1, if either nr is even and pr−1(0)<0 or nr is odd and Pr−1(0) > 0. There are two negative and four positive terms on the right hand side of Equation (A.5). The last term determines the polynomial Php(x) which we start with. Therefore, in one case pr−1(0)<0 holds and in four cases pr−1(0)>0 holds. As a consequence, there are at most three cases in which the number of zeros increases by one. Thus, this polynomial has at most three zeros with x>0. The fact that the dynamics given by (2.2), (2.3) and (2.4) never leave the range ƒ(t)>0, c(t)>0 and s(t)>0 can be easily verified:

becomes positive if ƒ(t) approaches zero,

and become positive if c(t) and s(t), respectively, approach zero, as while long as s(t) > 0. Furthermore, the conditions ρƒ>aƒƒ, ρƒ·ρc>αƒc·αcƒ and ρƒ·ρs >αƒs·αsƒ imply that the last term on the right-hand side of Equation (2.4) dominates the dynamics for sufficiently large values of ƒ(t). As a consequence, the variables are bounded from below and above.

Appendix

188

To examine the stability of the stationary states, the Jacobi-matrix is calculated. The zeros are ordered according to their value of and numbered by 1, 2, and 3. For the first and the third zero, the Equations (2.2), (2.3) and (2.4) imply (A.6)

(A.7)

and (A.8)

Furthermore, the following relations hold: (A.9)

and (A.10)

The Conditions (A.9) and (A.10) imply (A.11)

To prove that all eigenvalues are negative for the first and third zero, it will now be shown that condition (A.11) contradicts the assumption of a positive eigenvalue. Therefore, let us assume that a positive eigenvalue λ>0 exists. The corresponding eigenvalue is denoted by v=(1, υ2, υ3). The conditions (A.6), (A.7) and (A.8) imply that υ2>0 and υ3>0. Furthermore, Jv=λv has to hold, where J denotes the Jacobi-matrix. This condition leads to

Appendix

189

(A.12)

and (A.13)

The Conditions (A.12) and (A.13) imply (A.14)

which contradicts Condition (A.11). Thus, all eigenvalues of the first and last stationary states are negative and these states are stable. In the case of the second stationary state the condition (A.15)

does not necessarily hold. However, either the product of the eigenvalues or the sum of the eigenvalues is negative, so that at least one of the eigenvalues is negative. Due to the fact that both of the other stationary states are stable, at least one of the eigenvalues of the second stationary state is positive. Therefore, the second stationary state is a saddle-point. ■ Proof of Lemma 2 The location of the stationary states with respect to the variable ƒ(t) is determined by Equation (A.4). The number of stationary states equals the number of solutions for Equation (A.4) and their stability is determined by their number. Thus, these characteristics are identical for the two systems whenever Equation (A.4) is identical for the two systems. It is obvious that for every acƒ, aƒc, αcƒ, αƒc and ρc, and aƒƒ and aƒƒ can be chosen such that the two terms, and , in Equation (A.4) are identical. The same holds for the parameters asƒ, aƒs, αsƒ, αƒs and ρs and the respective terms in Equation (A.4) ■

Appendix

190

Proof of Lemma 3 Let us assume that aƒƒ≤1. Furthermore, aƒƒ>0 holds by definition. The stationary states for the reduced model have to satisfy (A.16) The second derivative on the left-hand side of Equation (A.16) reads (A.17) . Therefore, the left-hand side of Equation (A.4) has

which is negative for all values of at most one zero with

>0 (remember that this function is positive for

for sufficiently high values of

=0 and negative

). ■ Proof of Theorem 2

Again all stationary states are described by Equation (A.4) which can be written in the form (A.5). According to the prerequisites for Theorem 2, η1. This does not restrict the analysis since η can be doubled without changing its meaning. The first derivative on the left-hand side of Equation (A.5) is given by (A.18)

This function is zero for ƒ=0, decreases for small values of ƒ and is negative for ƒ→∞. It has a zero for ƒ>0 only if the first, third and fourth terms are large enough to outweigh the second and fifth terms for some values of x. Depending on aƒƒ, acƒ and asƒ, a value ƒmax can be calculated for which the function (A.18) becomes maximal. Then, a can be defined as the value of function (A.18) for ƒmax. α depends on aƒƒ, acƒ and asƒ and increases monotonically in each of these parameters. If a>0, the function (A.18) has two zeros for ƒ>0, which implies that the function on the left-hand side of Equation (A.5) has . For one maximum and one minimum for ƒ>0. For ƒ=0 this function equals small values of ƒ the function decreases until it reaches the minimum, then it increases until it reaches the maximum and then it decreases for all high values of ƒ. Changing the value

moves the function up and down without changing the characteristics just

mentioned. For

→−∞, the function on the right-hand side of Equation (A.5) is

negative for all ƒ. For

→∞ it is positive for all ƒ. In these cases the system

Appendix

191

described by the Equations (2.2), (2.3) and (2.4) has one stable stationary state if ƒ(t) is restricted to ƒ(t)>0. At the same time, values of can be found for which the minimum of the function on the left-hand side of Equation (A.5) is below zero and its maximum is above zero. This implies that the system described by the Equations (2.2), (2.3) and (2.4) has two stable and one unstable stationary states for ƒ≥0. ■ A.1.2 Mathematics for Chapter 3 Industrial firm distributions The cluster distribution defined by Equation (3.6) contains three terms. They contribute shares of (1−ξ3−ξ6), ξ3 and ξ6, respectively, to the distribution. The first part is an exponentially decreasing function given by (A.19)

The mean value of this function is given by (A.20)

The second part of the cluster distribution is a Boltzmann distribution given by (A.21)

The mean value of this distribution is

Appendix

192

(A.22)

The third part of the cluster distribution is again a Boltzmann distribution, which is transformed to higher values of ƒ and is given by (A.23)

and (A.24)

mod 1, the function Except for the transformation by CL(ƒ) is identical to the function (A.22). Thus, the mean value results in (A.25)

A.2 EMPIRICAL RESULTS AND DATA A.2.1 Results on clustering of industries In the following a list of all 3-digit industries and the results of the different analyses of their clustering is presented.

Appendix

193

Table A.1 List of the 3-digit industries and fact whether their spatial distribution is better explained by the theoretical natural distribution (‘nat’), the theoretical cluster distribution (‘cl’) or is described by none of them adequately (‘none’). The cluster distribution is taken if the likelihood-ratio test shows a better result on a significance level of 0.9, 0.95 (*) or 0.99 (**) and the theoretical distribution reported to be inadequate if it is rejected by the Kolmogorov-Smirnov test on a significance level of 0.99. relative number of firms

absolute number of firms

1995

1997

2000

1995

1997

2000

crop farming

none

nat

nat

nat

nat

nat

equalising

animal husbandry

cl**

cl**

cl*

cl**

cl*

cl*

other

landscape design

cl*

nat

nat

cl

nat

nat

other

market gardening

nat

none

nat

nat

nat

nat

other

grape growing

cl**

none

none

none

none

none

other

forestry

cl**

cl**

cl**

nat

nat

nat

equalising

fishery

cl**

cl**

cl**

cl**

cl**

cl**

clustering

fish-farming

cl**

cl**

cl**

nat

nat

nat

other

energy production

none

none

none

nat

nat

nat

other

black-coal mining

nat

nat

nat

nat

nat

nat

clustering

brown-coal mining

nat

nat

nat

nat

nat

nat

other

ore mining

nat

nat

nat

nat

nat

nat

equalising

oil & gas

nat

nat

nat

nat

cl*

nat

clustering

potash salt mining

cl**

cl**

cl**

cl**

cl**

cl

other

basic chemicals

nat

cl*

cl

nat

nat

nat

clustering

plastics & polymers

nat

nat

nat

nat

nat

nat

equalising

dye industry

nat

nat

nat

nat

nat

nat

equalising

fertilisers

nat

nat

nat

nat

nat

nat

equalising

paints & varnishes

nat

nat

nat

cl

cl**

nat

other

special chemicals

nat

nat

nat

nat

nat

nat

other

pharmaceutical

nat

nat

nat

cl

cl

nat

clustering

industry

dynamics

Appendix

194

cosmetics

nat

nat

nat

nat

nat

nat

equalising

wax & preservatives

nat

nat

nat

nat

nat

nat

other

petrochemical ind.

nat

nat

nat

nat

nat

nat

equalising

synthetic textiles

nat

nat

cl*

nat

nat

nat

clustering

petroleum processing

nat

nat

nat

cl**

cl**

cl*

clustering

plastic processing

nat

nat

nat

nat

nat

nat

other

rubber

nat

nat

nat

nat

nat

nat

equalising

tyres

nat

nat

nat

cl

nat

nat

equalising

vulcanisation

cl*

nat

nat

cl*

nat

nat

other

Industry

relative number of firms absolute number of firms

dynamics

1995

1997

2000

1995

1997

2000

nat

nat

nat

nat

nat

nat

equalising

none

none

none

cl

nat

cl

equalising

sand & quarry stones

nat

nat

nat

nat

nat

nat

other

cement

cl

cl*

nat

cl*

cl

nat

equalising

other stones

cl**

cl**

cl**

cl**

cl**

cl**

other

brickworks

cl

nat

nat

nat

nat

nat

other

earthenware

nat

nat

nat

nat

nat

nat

equalising

concrete

none

none

none

cl*

cl

cl*

other

porcelain

cl**

cl

cl*

nat

cl

cl

clustering

pottery

cl**

cl**

cl**

cl*

cl*

cl*

equalising

tiles

cl**

cl**

cl**

nat

cl

nat

equalising

plate glass

nat

nat

cl*

nat

nat

nat

equalising

hollow glass

nat

cl

cl**

nat

nat

nat

other

glass fabrics

cl**

cl**

cl**

cl*

cl**

cl**

clustering

hot-rolling mills

nat

nat

nat

nat

cl

nat

clustering

hammer mills

cl*

cl*

cl**

cl*

nat

nat

clustering

non-ferrous metal mills

nat

nat

nat

nat

cl*

nat

other

non-ferrous intermediates

nat

nat

nat

cl*

cl*

nat

clustering

iron foundry

cl*

nat

cl*

nat

nat

nat

clustering

non-ferrous foundry

cl*

nat

cl*

nat

cl

nat

other

cold-rolling mills

cl*

nat

cl*

cl*

cl**

cl**

equalising

asbestos natural stones

Appendix

195

sheet-metal ind.

cl**

cl**

cl**

nat

cl**

cl**

clustering

surface refinement

cl**

cl**

cl**

nat

nat

nat

other

locksmithing

none

none

none

cl*

cl

cl

other

cl*

nat

nat

nat

nat

nat

other

none

none

none

nat

nat

nat

other

boiler making

cl*

cl**

cl*

cl

cl*

nat

equalising

train building

nat

nat

nat

cl*

nat

nat

equalising

air conditioners

none

none

none

none

none

none

other

precision tools

nat

cl*

cl*

nat

cl

nat

clustering

construction mach.

nat

nat

nat

nat

nat

nat

other

agricultural mach.

cl*

cl

cl*

nat

nat

nat

equalising

repair of agr. mach.

cl**

cl**

cl**

nat

nat

nat

other

food processing mach.

nat

nat

nat

nat

nat

nat

equalising

textile machinery

nat

nat

nat

nat

cl*

nat

clustering

wood processing mach.

nat

nat

nat

nat

nat

nat

equalising

printing machinery

nat

nat

nat

nat

nat

cl

equalising

washing machines

nat

nat

nat

nat

nat

nat

clustering

cogwheels

nat

nat

nat

nat

nat

nat

other

smiths light metals

Industry

relative number of firms

absolute number of firms

dynamics

1995

1997

2000

1995

1997

2000

none

none

none

nat

nat

nat

other

motor vehicles & engines

nat

nat

nat

nat

nat

nat

equalising

automobile chassis

nat

nat

nat

nat

cl*

nat

other

automobile body & supporters

none

nat

nat

nat

nat

nat

equalising

motor cycles

nat

nat

nat

nat

nat

nat

equalising

bicycles & perambulators

nat

nat

nat

nat

nat

nat

equalising

horse-drawn carriages

cl*

cl

cl

nat

nat

nat

other

repair of motor veh.

none

none

none

none

none

none

other

painting of motor veh.

none

none

none

cl*

cl

cl

other

ships

nat

nat

nat

cl**

cl*

cl**

clustering

boats

nat

nat

cl*

cl*

cl*

nat

other

other machinery

Appendix

196

aircraft

nat

nat

nat

nat

nat

nat

equalising

office machines

nat

nat

nat

nat

cl**

cl*

equalising

data processing

nat

nat

nat

cl

cl

nat

other

electronic engineering

nat

nat

nat

nat

nat

cl

other

batteries

nat

nat

nat

nat

nat

nat

equalising

heavy power

nat

nat

nat

nat

nat

nat

other

large generators

nat

nat

nat

nat

nat

nat

other

electric cables

cl*

cl*

cl*

nat

nat

nat

clustering

electronic user goods

nat

nat

nat

cl

cl

cl

equalising

lights

cl*

cl*

cl*

cl

cl*

cl**

other

television & radio

nat

nat

nat

cl*

cl

cl*

clustering

telecommunication

nat

nat

nat

cl*

cl

cl

equalising

electronics

none

none

none

nat

nat

nat

clustering

instruments

none

none

none

nat

cl

cl*

clustering

optics

nat

nat

nat

cl*

cl**

cl**

equalising

clocks

cl**

cl**

cl**

cl**

cl**

cl**

equalising

clock repairs

nat

nat

cl**

nat

nat

nat

equalising

tools

cl*

cl**

cl**

cl**

cl**

cl**

other

locks & mountings

cl**

cl**

cl**

nat

nat

nat

other

cutting tools

cl*

cl**

cl**

cl**

cl**

cl**

clustering

weapons

cl*

cl**

cl*

nat

nat

nat

equalising

heating & cooking equipment

cl

nat

nat

nat

nat

nat

equalising

tinware

nat

nat

nat

nat

nat

nat

equalising

steel furniture

cl*

nat

nat

nat

nat

nat

clustering

Industry

relative number of firms absolute number of firms

dynamics

1995

1997

2000

1995

1997

2000

tinware packages

nat

nat

nat

nat

nat

nat

equalising

other metal goods

cl**

cl**

cl**

cl**

cl**

cl**

equalising

cycle parts

nat

nat

nat

nat

nat

nat

equalising

musical instruments

cl*

cl*

nat

nat

nat

cl*

other

toys

cl**

cl**

cl**

cl**

cl**

cl**

equalising

sports equipment

nat

cl

nat

nat

nat

nat

equalising

Appendix

197

jewellery

cl**

cl**

cl**

cl**

cl**

cl**

other

sawmills

cl**

cl**

cl**

cl

cl

cl

equalising

chipboard

cl**

cl**

cl*

cl

cl

cl

equalising

building joinery

none

none

none

nat

nat

nat

other

wooden furniture

nat

cl

nat

cl*

cl*

cl*

equalising

furniture joinery

nat

nat

nat

nat

nat

nat

other

packages

nat

nat

nat

cl*

nat

nat

equalising

wickerwork & brooms

cl**

cl**

cl**

cl**

cl**

cl**

clustering

paper products

cl*

cl*

nat

nat

nat

nat

equalising

paper processing

nat

nat

nat

nat

nat

nat

equalising

cartons

nat

nat

nat

nat

nat

nat

equalising

publishing

nat

nat

nat

nat

nat

nat

equalising

printing

nat

nat

nat

cl*

cl

cl

other

chemigraphics

nat

nat

nat

cl**

cl

cl*

clustering

tanning

nat

nat

nat

nat

nat

nat

equalising

leather goods

cl**

cl**

cl**

cl**

cl**

cl**

equalising

shoes

cl**

cl**

cl**

cl**

cl**

cl**

equalising

made-to-measure shoes

none

none

none

cl*

cl

nat

equalising

wool washing

nat

nat

nat

nat

nat

nat

equalising

wool spinning

cl

nat

nat

nat

nat

nat

other

wool twisting

nat

nat

nat

nat

nat

nat

clustering

wool weaving

cl**

cl*

nat

nat

cl*

cl*

clustering

wool spinning & weaving

nat

nat

nat

nat

nat

nat

equalising

cotton spinning

nat

nat

nat

nat

nat

nat

equalising

cotton twisting

cl

nat

nat

nat

nat

nat

equalising

cotton weaving

cl*

cl**

cl*

cl**

cl**

cl**

clustering

cotton spinning & weaving

nat

nat

cl

nat

nat

nat

clustering

silk processing

cl

cl*

nat

cl**

nat

nat

equalising

linen processing

nat

nat

cl

nat

nat

nat

clustering

rope making

cl*

cl**

cl

nat

nat

cl

equalising

knitting

cl**

cl**

cl**

cl**

cl**

cl**

equalising

textile refining

nat

nat

nat

nat

nat

nat

other

Appendix

Industry

198

relative number of firms absolute number of firms

dynamics

1995

1997

2000

1995

1997

2000

other textiles

cl**

cl**

cl**

nat

cl*

cl*

equalising

men’s clothes

cl*

cl*

cl*

cl**

cl**

cl**

equalising

men’s tailor-made clothes

nat

nat

nat

nat

nat

nat

equalising

women’s clothes

nat

nat

nat

nat

nat

nat

equalising

women’s tailor-made clothes

nat

nat

nat

cl**

cl**

cl**

equalising

working clothes

cl

cl

cl**

nat

nat

nat

equalising

corsetry

cl

cl*

nat

cl

nat

nat

other

bed linen

nat

nat

nat

cl*

nat

nat

other

hats

nat

nat

nat

nat

nat

nat

equalising

coats & furs

nat

nat

nat

nat

nat

nat

equalising

other bed products

cl**

cl**

cl**

cl*

cl**

cl*

clustering

upholsterers

nat

nat

nat

nat

nat

nat

other

sugar

nat

nat

nat

nat

nat

nat

clustering

fruit & vegetables

nat

nat

nat

nat

nat

nat

equalising

dairy products

cl**

cl**

cl**

cl*

cl

nat

equalising

fish processing

cl**

cl**

cl**

cl**

cl**

cl**

equalising

bread

nat

nat

nat

nat

nat

nat

equalising

none

none

none

none

nat

nat

other

edible oil

nat

nat

nat

nat

nat

nat

other

food production

nat

nat

nat

nat

cl

cl*

other

flour mills

nat

nat

nat

nat

nat

nat

other

sweets

nat

nat

nat

cl**

nat

cl*

equalising

cakes

nat

nat

nat

nat

nat

nat

other

abattoir

cl**

cl**

cl**

cl**

cl**

cl**

clustering

public abattoir

nat

nat

nat

nat

nat

nat

equalising

butcher shops

none

none

none

nat

nat

nat

clustering

breweries

cl**

cl**

cl**

cl*

cl

cl

equalising

distilleries

cl**

cl**

cl**

nat

nat

cl

clustering

mineral water

cl**

cl**

cl*

nat

nat

nat

other

cigarettes

nat

nat

nat

nat

nat

nat

equalising

confectionery

Appendix

tobacco

199

nat

nat

nat

nat

nat

nat

clustering

none

none

none

nat

nat

nat

other

nat

nat

nat

cl*

cl*

cl*

other

none

none

none

nat

nat

nat

other

insulating & fountains

nat

nat

nat

cl*

cl*

nat

other

plasterers

cl*

cl*

cl*

nat

nat

nat

clustering

carpentry

nat

nat

none

nat

nat

nat

other

roofers

none

none

nat

nat

nat

nat

equalising

plumbers

none

none

none

nat

nat

nat

other

construction surface engineering underground eng.

Industry

relative number of firms absolute number of firms

dynamics

1995

1997

2000

1995

1997

2000

none

none

none

none

none

none

other

glaziers

nat

nat

none

cl**

cl*

cl**

other

painters

none

none

none

nat

nat

nat

equalising

tile fixers

none

none

none

nat

nat

nat

equalising

stove fitters

cl**

cl**

cl**

cl

nat

nat

other

scaffolding

nat

nat

cl*

cl**

cl**

cl**

equalising

none

none

none

nat

nat

nat

equalising

merchant brokers

nat

none

none

cl*

cl*

nat

other

department stores

nat

nat

nat

nat

cl*

cl**

other

none

none

none

nat

nat

nat

equalising

nat

nat

nat

cl**

cl*

cl**

equalising

none

none

none

none

none

none

other

German railways

nat

nat

none

nat

nat

nat

equalising

other railways

cl

cl

cl*

nat

nat

cl**

equalising

German post

none

none

none

none

nat

none

other

transport. of people

none

none

none

nat

none

none

clustering

transport. of goods

none

none

none

nat

nat

nat

other

inland navigation

cl**

cl**

cl**

cl**

cl**

cl**

equalising

sea shipping

cl*

cl

cl*

cl**

cl**

cl**

clustering

none

none

none

nat

cl

nat

equalising

cl

nat

nat

cl**

cl**

cl*

other

electricians

wholesale business

supermarkets mail-order business other shops

forwarding business aviation

Appendix

pneumatic delivery system

200

nat

nat

nat

nat

nat

nat

equalising

none

none

none

cl*

cl

nat

other

cl*

cl*

cl**

cl**

cl**

cl**

other

banks

none

none

none

nat

nat

nat

clustering

insurance

none

none

none

nat

none

none

equalising

hotels

none

none

none

nat

cl

cl*

equalising

non-profit institutions

cl*

cl

cl*

nat

nat

nat

equalising

social security inst.

cl**

cl**

cl**

cl

nat

nat

equalising

restaurants

none

none

none

none

none

none

other

homes

nat

cl

cl*

nat

nat

nat

clustering

non-profit homes

nat

none

none

nat

cl*

nat

equalising

social sec. homes

cl

nat

nat

nat

nat

nat

equalising

chemical cleaning

none

none

none

cl*

cl*

cl*

clustering

cleaning of buildings

none

none

none

cl

cl

cl

other

chimney-sweepers

none

none

none

none

none

none

equalising

hairdressers

none

none

none

nat

none

none

equalising

cosmetic studios

nat

none

none

cl**

cl*

nat

equalising

libraries

cl

nat

nat

cl**

cl**

cl**

other

non-profit libraries

cl*

cl

nat

cl*

cl*

cl*

equalising

absolute number of firms

dynamics

travel agents shipping brokerage

Industry

relative number of firms 1995

1997

2000

1995

1997

2000

libraries of social sec.

nat

nat

nat

nat

nat

nat

equalising

private schools

cl

cl**

cl**

nat

nat

nat

clustering

non-profit schools

cl*

cl

cl*

nat

nat

nat

other

schools of local auth.

none

none

none

cl

none

cl*

equalising

technical colleges

cl**

cl**

cl**

cl**

cl**

cl**

other

non-profit technical colleges

nat

nat

nat

cl**

cl**

cl**

other

technical colleges of local authorities

none

none

none

nat

nat

nat

other

private institions for education

none

none

none

none

none

none

other

nat

nat

nat

cl

cl*

cl**

clustering

non-profit institions for education

Appendix

201

inst. for education of local authorities

nat

nat

nat

cl

cl*

cl**

other

priv. reform schools

nat

nat

cl

cl**

cl*

cl*

equalising

non-profit reform schools

nat

nat

nat

cl**

cl**

cl*

equalising

reform schools of local authorities

cl**

cl**

cl**

nat

nat

nat

equalising

private sports grounds

nat

none

none

cl*

cl

nat

equalising

non-profit sports gr.

nat

nat

nat

nat

nat

nat

other

sports grounds of local authorities

cl*

cl*

nat

nat

nat

nat

other

private theatres

nat

nat

nat

nat

nat

cl**

other

non-profit theatres

nat

nat

nat

nat

nat

nat

equalising

theatres of local auth.

nat

nat

nat

nat

nat

nat

clustering

film industry

nat

nat

nat

cl**

cl**

cl**

equalising

television & radio producers

nat

cl

nat

nat

nat

nat

clustering

independent artists

nat

nat

nat

nat

nat

nat

equalising

publishers

nat

nat

nat

cl**

cl**

cl**

clustering

public libraries

nat

nat

nat

nat

nat

nat

other

non-profit pub. libraries

nat

nat

nat

nat

nat

nat

equalising

pub. lib. of local auth.

cl*

cl

cl

cl**

cl**

cl**

equalising

newsagents

nat

nat

cl*

cl**

cl**

cl*

other

none

none

none

none

none

none

other

private clinics

nat

nat

nat

nat

nat

nat

other

non-profit clinics

nat

nat

nat

nat

nat

nat

other

clinics of local auth.

nat

nat

nat

nat

nat

cl*

other

Industry

relative number of firms

physicians in private practice

absolute number of firms

dynamics

1995

1997

2000

1995

1997

2000

clinics of social sec.

cl*

cl*

cl*

nat

nat

nat

clustering

veterinary surgeons in private practice

nat

nat

none

nat

nat

nat

other

legal advice

none

none

none

cl*

cl*

cl

other

chartered accountants

none

none

none

none

cl*

none

other

architects

none

none

none

none

none

none

clustering

Appendix

chemical laboratories

202

cl*

nat

nat

cl**

cl**

cl**

other

none

none

none

cl**

cl*

cl**

clustering

advertisement

nat

nat

nat

cl**

cl**

cl**

other

private fairgrounds

nat

nat

nat

nat

cl

cl**

clustering

fairgrounds of local authorities

nat

nat

nat

nat

nat

nat

clustering

none

none

none

cl**

cl**

cl**

clustering

private swimming pools

nat

nat

nat

nat

nat

nat

equalising

swimming pools of local authorities

nat

nat

nat

nat

nat

nat

equalising

private cleaning firms

nat

nat

nat

nat

nat

nat

other

cleaning firms of local authorities

nat

nat

nat

nat

nat

nat

other

private undertakers

none

none

none

cl*

cl

cl

equalising

undertakers of local authorities

cl**

cl**

cl*

cl*

cl

nat

clustering

auctioneers

nat

nat

nat

cl*

nat

cl

other

none

none

none

nat

nat

nat

other

show business

nat

nat

nat

cl*

cl*

cl**

equalising

security

nat

nat

nat

cl**

cl**

cl**

other

translators

nat

nat

nat

cl**

cl**

cl**

clustering

packaging

cl*

cl

nat

cl

nat

cl*

other

betting offices & lotteries

nat

nat

nat

cl**

cl*

cl**

equalising

contracting employment agencies

nat

nat

nat

nat

cl*

cl**

other

professional assoc.

cl*

cl*

cl*

cl**

cl**

cl**

other

unions

nat

nat

nat

cl**

cl**

cl**

equalising

trade associations

nat

nat

nat

cl**

cl**

cl**

other

none

none

none

nat

nat

nat

other

political parties

nat

nat

cl*

cl

cl*

cl*

other

cultural organisations

nat

nat

nat

cl**

cl**

cl**

other

sport organisations

none

nat

none

nat

nat

nat

clustering

churches

none

none

none

nat

nat

nat

clustering

private households

none

none

none

cl**

cl**

cl**

clustering

Industry

relative number of firms

trustees

photographers

leasing

charitable institutions

absolute number of firms

dynamics

Appendix

203

1995

1997

2000

1995

1997

2000

none

none

none

nat

nat

nat

other

nat

nat

nat

nat

nat

nat

other

other public admin.

none

none

none

none

none

none

other

national defence

none

none

none

nat

nat

nat

clustering

stationed forces

cl

nat

nat

cl**

cl**

cl

equalising

social security

none

none

none

none

none

none

equalising

foreign embassies & consulates

cl**

cl**

cl**

cl*

cl*

cl**

clustering

central administration legal system

A.2.2 Correlation table for Section 3.5

Table A.2 Pearson correlations between the variables in Section 3.5 (*= correlation is significant on a level of 0.05, **=correlation is significant on a level of 0.01). PRODCYC

PRODINNO

PROCINNO

INNOEXP

PRODCYC

1

−0.307*

−0.80

−0.145

PRODINNO

−0.307*

1

0.663**

0.338**

PROCINNO

−0.80

0.663**

1

0.285*

INNOEXP

−0.145

0.338**

0.285*

1

REVNEW

−0.450**

0.727**

0.464**

0.335

INFOINNO

−0.141

0.451**

0.365**

0.286*

SCIEINNO

−0.141

0.508**

0.539**

0.314*

EMPNAT

−0.109

0.567**

0.513**

0.394**

EMPSOC

0.084

0.390**

0.364**

0.222

EMPTECH

−0.045

0.421**

0.335**

0.262*

COOPCOM

−0.061

0.197

0.306*

−0.082

COOPSUP

−0.107

−0.099

−0.035

−0.215

COOPUNI

−0.042

0.103

0.071

0.012

SPILLRATA

−0.101

0.500**

0.305*

0.360**

SPILLRATB

0.031

0.202

0.130

0.270*

REVNEW

INFOINNO

SCIEINNO

EMPNAT

Appendix

204

PRODCYC

−0.450**

−0.141

−0.141

−0.109

PRODINNO

0.727**

0.508**

0.451**

0.567**

PROCINNO

0.464**

0.539**

0.365**

0.513**

INNOEXP

0.335**

0.314*

0.286*

0.394**

REVNEW

1

0.319*

0.458**

0.608**

INFOINNO

0.458**

1

0.404**

0.483**

SCIEINNO

0.319*

0.404**

1

0.432**

EMPNAT

0.608**

0.483**

0.432**

1

EMPSOC

0.317*

0.180

0.296*

0.543**

EMPTECH

0.382**

0.434**

0.489**

0.603**

COOPCOM

0.104

0.127

0.232

0.087

COOPSUP

−0.148

−0.144

−0.081

−0.083

COOPUNI

0.122

0.004

−0.108

0.069

SPILLRATA

0.485**

0.339**

0.348**

0.540**

SPILLRATB

0.254

0.080

0.107

0.182

EMPSOC

EMPTECH

COOPCOM

COOPSUP

PRODCYC

0.084

−0.045

−0.061

−0.107

PRODINNO

0.390**

0.421**

0.197

−0.099

PROCINNO

0.364**

0.335**

0.306*

−0.035

INNOEXP

0.222

0.262*

−0.082

−0.215

REVNEW

0.317*

0.382**

0.104

−0.148

INFOINNO

0.180

0.434**

0.127

−0.144

SCIEINNO

0.296*

0.489**

0.232

−0.081

EMPNAT

0.543**

0.603**

0.087

−0.083

EMPSOC

1

0.300*

0.194

−0.048

EMPTECH

0.300*

1

0.149

−0.010

COOPCOM

0.194

0.149

1

0.190

COOPSUP

−0.048

−0.010

0.190

1

COOPUNI

0.046

0.166

0.070

−0.132

SPILLRATA

0.249

0.456**

0.034

−0.086

SPILLRATB

0.322*

0.169

−0.045

−0.162

Appendix

205

COOPUNI

SPILLRATA

SPILLRATB

PRODCYC

−0.042

−0.101

0.031

PRODINNO

0.103

0.500**

0.202

PROCINNO

0.071

0.305*

0.130

INNOEXP

0.012

0.360**

0.270*

REVNEW

0.122

0.485**

0.254

INFOINNO

0.004

0.339**

0.080

SCIEINNO

−0.108

0.348**

0.107

EMPNAT

0.069

0.540**

0.182

EMPSOC

0.046

0.249

0.322*

EMPTECH

0.166

0.456**

0.169

COOPCOM

0.070

0.034

−0.045

COOPSUP

−0.132

−0.086

−0.162

COOPUNI

1

−0.009

0.037

SPILLRATA

−0.009

1

0.573**

SPILLRATB

0.037

0.573**

1

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Index

Acs, Z.J., 17, 44, 49, 56, 139, 153, 154, 163 Adams, M.B., 161 administrative district, 117 Allen, P.M., 21 Almus, M., 161, 165 Amiti, M., 1 Anselin, L., 17, 44, 49, 139, 153, 154, 163 applicability of simulation models, 144 attitudes, 52 attractiveness, 22, 192 attractiveness of regions, 61, 62, 68, 191 Audretsch, D.B., 44, 48, 49, 56, 153, 163, 164, 207 automobile parts, 123 Aydalot, P., 2 Baden-Württemberg, 119 Barca, F., 202 Barlet, C., 164 basic chemicals, 121 Bavaria, 119 Becattini, G., 2, 10 Becker, G.S., 47 Bellmann, L., 166 Bertschek, I., 153 Bhaduri, S., 153 bifurcation, 28 bimodal, 83 biotechnology, 123 Bitterfeld, 121 Blanchflower, D.G., 166 Blien, U., 166 Blind, K., 153, 163 Boekema, F.W.M., 45, 140 Boltzmann distribution, 69 Bouhsina, Z., 47

Index Bramanti, A., 44, 48 branch, 79 Branstetter, L.G., 44 Braun, B., 47, 116, 140 Braunerhjelm, P., 2, 9, 12, 14, 80, 95, 109, 123, 186 Bröskamp, A., 163 Brown, J.E., 44 Buettner, T., 166 Camagni, R.P., 2, 9, 11, 19, 44, 52, 148, 149, 186 Caniëls, M.C.J., 148, 149 capital market, 50 Carlsson, B., 2, 9, 12, 14, 80, 95, 109, 123, 186 case study, 4, 63, 115, 121 causal relationship, 137 causes for clustering, 92 change, 100 characteristic of industries, 126–128, 131, 136, 174 of local clusters, 186 Christensen, C.M., 164 city, 92 Clark, J.A., 161 classification of industries, 16, 79, 81 clustering, 105, 106, 135 clusters, 9, 12 co-evolution, 23 Cockburn, I., 163 competition, 23, 26, 36, 37, 64, 65, 191 competition among regions, 178, 190, 194, 199 competitor, 129 concepts, 9, 12, 13, 16, 18 condition, 35, 41, 42, 55, 58, 59, 110, 117, 186 condition for the existence of LICs, 41 Cooke, P., 2, 115, 119 cooperation, 45, 129, 140 coordination, 66 cost of policy measures, 198 Coté, M., 50, 52, 53, 202 country, 187 critical mass, 36, 37, 59, 117 critical number, 95 critical point, 36 critical value, 59, 100 crucial people, 191 cultural background, 10, 11

215

Index

216

culture, 51, 71, 191, 192 cumulative distribution function, 88 customer, 14, 22, 45, 71 Dalum, B., 1, 44, 48, 53, 60, 65, 66, 70, 192, 193 data, 97, 126–129 data fitting, 83, 95, 110 data processing, 125 De Bresson, C., 63 definition clusters, 12 industrial agglomeration, 14 industrial districts, 11 innovative milieux, 11 local industrial clusters, 15 regions, 17, 120 definitions, 9, 12 Dei Ottati, G., 45, 140 Dekimpe, M.G., 151 Deller, S.C., 166 demand, 22, 36, 150, 189 determinant of clustering, 126 Diappi, L., 148, 149 Dijk, M.P. van, 9, 10, 13 disappearance of local clusters, 99, 106–108, 125 district economies, 11 division of labour, 10 Dohse, D., 66 Dowling, M., 115, 123 Duguet, E., 164 Dybe, G., 35, 116 dynamics, 25–27, 38, 97, 100 economic development, 119 economic prosperity, 119 economies of location, 16 economies of scale, 10, 153 education, 157 education system, 49 effectiveness of policy measures, 199, 202 Ellison, G., 13, 91, 109, 110 emergence of local clusters, 34, 37, 41, 57–60, 99, 106–108, 117, 136, 138, 140, 172, 179, 183, 189 empirical approach, 6 empirical data, 78 empirical study, 77 employee, 80, 129 Encaoua, D., 164

Index

217

endogenous, 21, 22 endogenous dynamics, 22 Enright, M.J., 45 Entorf, H., 153 entrepreneur, 66 entrepreneurial attitude, 52, 65 entry, 40, 149, 155 entry barriers, 25 Evangelista, R., 163 evolution, 33 evolution of local clusters, 33, 35, 100 existence of local clusters, 28, 30–32, 41, 42, 55, 82, 89, 91, 126, 131, 139, 140, 174, 185, 187 exit, 40, 149, 155 exogenous, 21 exogenous conditions, 22, 33, 36, 68 experimental design, 147 external economies, 10 Fagerberg, J., 1 feedback loop, 54 firm distribution, 97 firm founding, 191 firm population, 21 fitting of parameters, 84 Flannery, B.P., 84 flexibly specialised regional economies, 13 fluctuations, 100–102 Fornahl, D., 4, 52, 65, 207 Foros, O., 150 Foss, N., 65, 66 founder, 65 framework, 5 Fritsch, M., 40, 45, 48, 56, 140, 163, 164 Gaiser, A., 45, 47 Garnsey, E., 19, 50 general approach, 3, 5, 13, 15, 120 general perspective, 9 general theory, 55 geographic concentration, 197 geographic location, 69, 192 geographic space, 149 Germany, 77, 109, 117 Glaeser, E.L., 14, 91, 109, 110 global situation, 22 globalisation, 1, 14, 189 Grabher, G., 115, 119, 203 Greif, S., 44, 119

Index

218

Grotz, R., 47, 116, 140 growth stage, 35 Grupp, H., 44, 46, 56, 130, 153, 163 Haag, G., 166 Hahn, R., 45, 47 Hansen, B., 150 Hardwick, P., 161 Hellmuth, E., 66 Henderson, R., 44, 154, 163 Hendry, C., 44 historical development, 4, 115 historical singularity, 192, 193 history, 5, 29, 51, 119, 174, 178 Holmen, M., 44, 48 Hotelling model, 150 hub-and-spoke districts, 19 Hübler, O., 166 Huiban, J.-P., 47 human capital, 11, 47, 48, 137, 156 hysteresis, 33, 35 identification of local clusters, 110, 186 immobility, 25 incubators, 43 industrial agglomeration, 14, 15, 21 industrial clusters, 12 industrial condition, 56, 57 industrial differences, 111 industrial districts, 9–11, 17 industrial firm distribution, 67, 72, 73, 75, 83 industrial life cycle, 35, 36 industry, 16, 17, 29, 79, 97, 120, 186, 187, 192, 199 industry-specific characteristics, 92, 121 inertia, 40 informal contacts, 11 information, 129 information flow, 11, 44, 139 inhabitants, 69 innovation, 18, 127, 129, 138, 153, 191 innovation expenditures, 138 innovation project, 129 innovative atmosphere, 52 innovative milieux, 9, 11, 18 innovativeness, 11, 44 instruments, 123 Isaksen, A., 13, 14, 38, 79, 86, 94, 95, 109, 111, 186, 203 Italian industrial districts, 10 Italian literature, 10

Index Jacobsson, S., 44, 48 Jaffe, A.B., 44, 49, 154 Jasper, J., 4 Jena, 66 Jonard, N., 148 Keeble, D., 2, 46, 48, 49, 66, 140 Khaled, M., 161 Klepper, S., 35 knowledge, 156 knowledge flow, 140 Kogut, B., 19 Kolmogorov-Smirnov test, 88, 176 König, A., 166 Koschatzky, K., 45, 53, 140 Kozul-Wright, Z., 44 Krugman, P., 21 Kujath, H.J., 35, 116 labour costs, 152 labour force, 149, 150 labour market, 156 lagging regions, 117 Lampe, D.R., 65, 192 Lawson, C., 46, 48, 49, 66, 140 learning by doing, 47 Lechner, C., 115, 123 Lecoq, B., 47, 50 life cycle, 97, 108 life cycle of local clusters, 97 likelihood ratio test, 87 linkages, 12 Lissoni, F., 17 list of industries, 77 of local clusters, 109, 110 local actor, 65 local circumstances, 187 local conditions, 23, 26 local dynamics, 22 local externalities, 22, 23 local factor, 63 local industrial cluster, 9, 13, 15, 29, 119 local labour market area, 81 local market, 70 local mechanism, 42, 43 local network, 19 local policy, 52 local prerequisite, 4 local process, 42 local synergies, 11

219

Index local system, 13, 27 location of local clusters, 187, 190, 192 logistic regression, 132 Longhi, C., 2 Lorenzen, M., 65, 66 Lundvall, B.-A., 61 Lutz, A., 116 Maarten de Vet, J., 66 MacPherson, A.D., 44 Maggioni, M., 2, 3, 21, 34, 191, 202 Maillat, D., 47, 50 Malmberg, A., 19 Mannheimer Innovation Panel, 126–128 mark-up pricing, 152 market, 189 market conditions, 68 market situation, 36, 60, 62 Markusen, A., 13, 19 Marshall, A., 1, 9, 47 Marshallian industrial districts, 10 Maskell, P., 45 mature stage, 35 Maurseth, P.B., 44 maximum likelihood, 87 McCann, P., 16 McConnell, J.D., 162 mechanism, 31, 32, 54, 187 Meeus, M.T.H., 45, 140 Mellens, M., 151 metal, 119 method, 131, 143 method of analysis, 143 methodology, 5 migration, 158 Miller, R., 50, 52, 53, 202 Mitchell-Weaver, C., 48, 61 Mittelhammer, R.C., 88 mobility, 166 model analysis, 27 modelling, 25–27 Monte-Carlo simulation, 147 Moore, B., 46, 48, 49, 66, 140 Mühlfriedel, W., 66 multicollinearity, 132 Munz, M., 166 Murmann, J.P., 66, 166, 170, 178 Murray, J.D., 25

220

Index natural circumstances, 93 natural resources, 14, 22 negative feedback, 27 Nerlinger, E., 161, 165 networking, 66 New Economic Geography, 4, 21 new product, 138 non-transferable human capital, 47 Norman, G., 150 number of employees, 80 of firms, 100, 149 of local clusters, 94, 96, 117, 120, 174 Oerlemans, L.A.G., 45, 140 optics, 121 Orlando, M.J., 163 Oswald, A.J., 166 Pagani, M., 17 Paniccia, I., 2, 3, 14, 45, 66, 79, 95, 109, 206 paper products, 125 parameter, 144, 161 Patel, P., 45 path-dependence, 15, 29, 172, 174, 177, 178, 181 Pavitt, K., 45 Pekkarinen, T., 166 persistence of local clusters, 137 personal characteristics, 65 Pickford, M., 161 Pietrobelli, C., 3, 47 Pilon, S., 63 Pleschak, F., 44, 49, 164 policy, 4, 52, 183 policy measure, 193, 202 political implications, 195 political influence, 196 political programmes, 4 political system, 192 polynomial, 100 Porter, M.E., 3, 47, 60, 70, 115, 192, 206 Pouder, R., 64, 119 Powell’s method, 84 Pradel, J., 164 Praest, M., 44, 48 prediction, 72 Press, W.H., 84 price setting, 152 process innovation, 129, 138 product cycle, 129, 138

221

Index product innovation, 129, 138 promoter, 193 proximity economies, 11 public attitudes, 52 public education, 159 public research, 48 public research institute, 191 Pyke, F., 10, 45, 51 Quéré, M., 19 questionnaire, 127 Rabellotti, R., 9, 50, 52, 186 random event, 61, 191, 192 Ray, A.S., 153 region, 15, 16, 120, 200 regional clusters, 12, 18 regional condition, 56, 57 regional differences, 57, 58 regional innovation systems, 13 regional policy, 191 regional unit, 79 regression, 101, 132 Rehfeld, D., 116, 195 Reiner, R., 166 research institute, 192 research projects, 44 resource, 93 restrictions of simulations, 145 reunification, 121 Rhine, R., 161 Rickne, A., 44, 48, 50, 51 Rosegrant, S., 65, 192 Ruhr area, 117, 119 Saxenian, A.-L., 48, 65, 66, 193 Saxony, 119 Scherer, F.M., 46, 56, 130 Schmitz, H., 9, 119 Schmude, J., 164 Schneeweis, T., 163 Schoenmakers, W., 46, 139, 207 school, 48 Schroeder, T.C., 161 Schulenburg, J.-M., 153 Schwirten, C., 163 science park, 19 scientific knowledge, 129 Scott, A.J., 2, 13, 66 sectoral agglomeration, 13

222

Index

223

self-augmenting process, 15, 16, 22, 23, 30, 32, 33, 41, 43, 53, 55, 57, 59, 148, 187, 191 self-organisation, 28 Sengenberger, W., 10, 45, 51 Senn, L., 44, 48 Seri, P., 18, 117 service firms, 24 service industries, 90 Sforzi, F., 11, 14, 79, 95, 109, 111, 186 shakeout, 37 Shan, W., 19 simulating, 170 simulation, 143, 144 simulation approach, 6 simulation model, 143, 148, 149, 170 simulation study, 146 single individual, 191 size of local clusters, 94 of regions, 80, 84 of the population, 192 skills, 156 small firm, 10, 109 Smolny, W., 163 social network, 10 socio-economic structure, 10 software, 125 space, 117 spatial distribution, 14, 67, 117 Speaker, P.J., 161 specialisation, 1, 13 specific human capital, 47 spillover, 44, 49, 130, 139, 153 spillover matrix, 130 spin-off, 43, 155 St. John, C., 64, 119 Staber, U., 45, 116 stabilisation, 184 stability, 28, 180 stage of evolution, 34–38 of industrial life cycle, 36 start-up, 43, 52, 155 start-up rate, 16 stationary states, 28 statistical analysis, 90, 98 statistical method, 82, 83, 91 statistical procedure, 132 Steenkamp, J.-B.E.M., 151 Stephan, P.E., 207 Sternberg, R., 45, 116, 140 stochastic characteristic, 143 stochastic dynamics, 61

Index

224

stochastic events, 5 stochastic process, 65, 169, 182 stochasticity, 144 Storper, M., 19 student, 70 success of policy measures, 199, 201 supplier, 24, 45, 71, 129 supplier-buyer relation, 45, 46 Sydow, J., 116 symbiosis, 25 symbiotic interactions, 25 Tamásy, C., 116 Tappi, D., 10, 16, 17, 64, 81 technological change, 60, 189 technology, 152, 153, 189 technology park, 19 temporal aspects, 59 test of intuition, 145 of predictions, 90, 100 of theory, 77 Teukolsky, S.A., 84 theoretical approach, 5 theoretical firm distribution, 84 theory, 9, 186 Thisse, J.-F., 150 Thuringia, 119 time, 184, 187, 190, 201 timing, 60, 179, 189 Tomlinson, M., 47 Trajtenberg, M., 44, 49, 154 transferable human capital, 47 Trigilia, C., 10, 51, 193 Tsai, T.-H.S., 166 uniform distribution, 29 unit of analysis, 120 university, 48, 70, 129, 140, 191, 192 Varga, A., 17, 44, 49, 139, 153, 154, 163 venture capital, 50 venture capitalist, 50 Verspagen, B., 1, 44, 46, 56, 127, 130, 139, 148, 149, 207 Vetterling, W.T., 84 Villumsen, G., 1, 44, 48 Vipraio, P.T., 45 Vou, J.-I., 45

Index wage, 159 Wagner, J., 153 Walker, G., 19 Walter, R., 66 Weidlich, W., 166 Weigelt, N., 148, 149 Wilkinson, F., 2, 45, 46, 48, 49, 66, 140 windows of opportunity, 201 Winer, B.J., 147 Witt, U., 36 Wolter, K., 34 Yildizoglu, M., 148 Zeitlin, J., 47 Zeller, C., 115, 123, 124 Zellner, C., 207

225