Growing locations: Industry location in a model of endogenous growth
Introduction
Until recently, the theoretical research on endogenous growth and on new `economic geography' have mostly been kept separate. In most economic geography models, location dynamics are based on the redistribution of a given amount of resources and in most new growth models, the geographical dimension is absent. An exception is Bertola (1993) who develops a model of growth driven by capital accumulation to analyse how the move from autarky to capital and labour mobility affects the location of activity. The result – with increasing returns and mobile factors, one of the two regions will `disappear' – does not however tell us what is the relation between location and growth in less dramatic scenarios. Walz (1996) constructs a R&D model of growth and location based on aggregate returns to scale at the local level and migration. Trade liberalisation is shown to lead to agglomeration and faster growth. However, his focus on aggregate rather than firm-level increasing returns to scale makes the model distant from one of the main themes of the “new economic geography”. The separation between the two fields is unfortunate because they ask related questions. Endogenous growth theory, especially in its most recent direction (Romer, 1990; Grossman and Helpman, 1991) asks the question of how new firms or new goods are created through technological change. The new economic geography asks where firms are located and why they tend to concentrate in a few regions. The absence of a geographical dimension in growth models also contradicts a point stressed by Lucas (1988), that is that the economic mechanism at the origin of endogenous growth requires social interactions or external effects which, precisely, are mostly local in nature.
The separation between the two fields is also surprising. First, from a methodological point of view some of the models used in the two literatures often share a common assumption on the structure of the industry, namely monopolistic competition. This implies that technically the models are not very far apart. Second, the link between growth and location has been studied extensively at the empirical level. A large literature using industrial data at the level of cities and regions has shown the essential role of economic concentration and geography in explaining growth, innovation and the level of productivity.1
Hence, we believe that the process of creation of new firms and the process of location should be thought as joint processes. When the external effects which are at the source of endogenous growth are local in nature because they involve localized interactions between economic agents, then the location of firms and of R&D activities will affect the process of technological change. Technological change, when it materializes in the creation of new goods and new firms, will in turn have an impact on the extent and the direction of foreign direct investment and, more generally, capital flows.
This paper presents a model that integrates the features of endogenous growth and endogenous industry location. We analyse how the dynamics of growth (the creation of new firms) and the dynamics of industrial location interact and show that the introduction of explicit dynamics in a location model changes some of the results of the “new geography” literature. We examine how growth affects the location decisions of firms and hence how it affects geography and the dynamics of spatial distribution of economic activities. We also analyse how the rate of technological progress, at the origin of growth, is determined by the location decision of firms and economic geography.
To answer these questions we construct a model where firms can choose to locate between two trading locations, that we call North and South. New firms, each requiring a new “idea”, are continuously created through R&D so that growth comes into the form of an expansion in the variety of products consumed. Hence, our model puts together a growth framework à la Romer (1990) and Grossman and Helpman (1991) and a location framework based on Martin and Rogers (1995) itself a variant of Helpman and Krugman (1985) and Krugman (1991). This location framework is different from the “new economic geography” because cumulative causation mechanisms such as migration or vertical linkages are excluded so that we do not model a catastrophic agglomeration phenomenon.
We analyse the relation between location and growth in two different contexts. In the first one, the spillovers in R&D are global: the invention of a new good affects negatively the future cost of R&D in both locations. In this equilibrium, economic geography has no influence on the growth rate. However, determinants of growth such as the cost of R&D and the discount rate have an impact on income differentials between North and South and therefore on the location of firms. We show that in this case high growth rates and high transaction costs are associated with foreign direct investment from North to South. In the second specification, R&D spillovers between industries are local, that is the R&D cost is lowest in the location with the highest number of firms producing differentiated products. In this case, all R&D activities agglomerate in the North where firms are more numerous and the growth rate is higher the more concentrated the industry. This induces an interesting link between trade costs, location and growth. A decrease of transaction costs, for example through trade integration, leads firms to concentrate, but not always entirely, in the location with the R&D activity, and because of local spillovers, it also induces an increase in the growth rate. This positive link between trade integration and growth is different from the ones identified by Rivera-Batiz and Romer (1991), Baldwin (1992), Baldwin and Seghezza (1995) and Baldwin and Forslid (1995). Also, in contrast to the literature in new geography, and due to the introduction of endogenous growth we show that welfare in the South can improve when industrial concentration in the North increases if transaction costs are low enough. This is because the increase in the rate of innovation which comes from spatial concentration also benefits the South.
The next section presents the general framework of the model. Section 3describes the location decision of firms. Section 4analyses the related dynamics of growth and location when spillovers are global. Section 5does the same exercise when the spillovers are local. Section 6analyses the welfare impact of industrial concentration.
Section snippets
The general framework
We study two locations which trade with each other and which we will call North and South. The two are identical except for their initial level of non-labour wealth, K0 in the North and K0* in the South. We assume that the North is initially richer than the South so that K0>K0*. We therefore describe the economy only in the North as the South is almost symmetric. An asterisk refers to variables of the South. Both locations are inhabited by representative households who perform the tasks of
The equilibrium location of firms
The location of firms is free and we assume no relocation costs. For example, if a firm owned by an agent of the North locates in the South, then the operating profits of this firm are repatriated to the North.
Four equilibrium conditions determine firms' size (x, x*) and location (n, n*). First, when differentiated goods are produced in both locations, demands (inclusive of transport costs) must equal supplies at home and abroad:Next, when
The case of global spillovers
We now want to analyse how the stock of patents is growing. We introduce the R&D sector which works as in Grossman and Helpman (1991): to invent a new variety, a researcher must employ η/N units of labor. This is also the cost of R&D as the wage rate is 1. This specification says that the invention of a new good in one country decreases the future R&D cost in both countries so that the spillovers are global and the cost of R&D is the same in the North and in the South.
The case of local spillovers
We now look at the case of localized spillovers in R&D. These spillovers, between different industries at the level of a city or a region, have been documented by Glaeser et al. (1992), Henderson et al. (1995) and also Jacobs (1969). In line with these studies, we assume that the cost of R&D in a certain location depends negatively on the number of firms located in that location such that: η/n in the North and η/n* in the South. These are different spillovers from the ones assumed by Grossman
Welfare analysis
We now want to ask whether the concentration of firms in the market equilibrium described above is too low or too high from a welfare point of view when spillovers are local. In particular, starting from the market equilibrium, we ask whether a Pareto improvement can be obtained by a marginal change in economic geography as described by γ. The model exhibits several externalities which, in general, will make the market equilibrium different from the one chosen by a planner.
First of all, there
Conclusion
The model we have presented is an attempt to merge the theory of endogenous growth and the theory of endogenous location. Through this exercise, we have been able to learn both on growth and on location:
(1) When spillovers are global, economic geography does not influence the growth rate. However, high growth rates are associated with capital flows to the South because the factors that increase the growth rate (such as a decrease in the R&D cost) also decrease the differential in income between
Acknowledgements
We thank Richard Baldwin, Vincenzo Denicolo, Elhanan Helpman, Diego Puga, Jacques Thisse, Tony Venables and two anonymous referees for their comments on a previous version. We are also grateful for comments from participants at the CEPR/CUSO conference on “Trade, Location and Technology” in Champéry, the CEP/CEPR workshop in London, the CEPR/NBER conference International Seminar in International Trade in Royaumont and at seminars at Universities of Bologna, Lausanne, Ancona, Base and CORE
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