# IV: Looking ahead: modeling both the spatial location choices and the spatial behavior of economic agents

## Firm demography and survival analysis

### Introduction

Part II of this book was devoted to methods and techniques for analyzing the spatial behavior of individual economic agents taking their locations as exogenously given. Part III was devoted to the methodologies used to study the locational choice of economic agents and their joint locations with respect to other agents. The scope of the growing field of spatial microeconometrics makes use of both streams of literature to build up a new modeling strategy which treats location as endogenous and takes into account simultaneously both individuals’ locational choices and their economic decisions in the chosen location. The literature in this area is still relatively in its infancy (Dube and Legros, 2014; Arbia et al., 2016) and rather scattered in a few articles. The aim of this chapter is to show through case studies how it is possible to join together within a unified framework the lessons learnt in the first chapters of this book and produce models in this direction.

A first example of a spatial microeconometric model can be found in the literature related to firm demography and firm survival. The current state-of-the-art in this area includes a vast variety of contributions and empirical methodologies mainly for data aggregated at macro- or meso-territorial levels, in which the typical observations consist of administrative units such as regions, counties or municipalities. Comparatively less attention has been devoted to the development of a systematic approach to the analysis of individual micro-data where the observations are represented by the locations of each individual firm. This approach strongly limits the possibility of obtaining robust evidences about economic dynamics for two main reasons. The first is related to the modifiable areal unit problem (Arbia, 1989) mentioned in Chapter 1: with regional data we do not observe the dynamics of the single individual but only the dynamics of variables within arbitrary partitions of the territory. The second reason is that theoretical models of firm demography are based on behavioral models of single individual economic agents (Hopenhayn, 1992; Krueger, 2003; Lazear, 2005 among others), so that if we base our conclusions on regional aggregates we support the theoretical model only if we are ready to admit the restrictive and unrealistic assumption of the homogeneity of each firm’s behavior within the region. In the few remarkable cases where a genuine micro-approach was adopted, the results confirm the relevance of neighborhood effects that reveal interesting scenarios for future researches. For instance, Igami (2011) shows that the introduction of a new large supermarket in one area increases the chance of failure for larger stores in the neighborhood, but increases the probability of survival of smaller incumbents. Analyzing a set of data collected in the food retailing sector, Borraz et al. (2014) show that the establishment of a supermarket in the neighborhood of a small store significantly increases the probability of the small store going out of business in the same year. A good way of overcoming these limitations is to simply remove the boundaries and analyze the economy of a continuous space. Economists often see that economic activities are located in a continuous space and that “there is no particular reason to think that national boundaries define a relevant region” (Krugman 1991a; 1991b). So why should a regional boundary define a relevant region? Obviously we are not saying that boundaries should be ignored altogether but only that we need to distinguish between the meanings of boundaries in different situations. In some instances boundaries can be classified as significant borders, that is, places where the economic conditions change abruptly because of some change, for example, in the tax system or transport costs. In other instances borders are irrelevant, where nothing actually happens from an economic standpoint. Starting from these considerations, we think that the shift of emphasis from a meso- to a micro-level is likely to bear interesting fruit. Krugman (1991a) has remarked that “if we want to understand differences in national growth rate, a good place to start is by examining differences in regional growth”. Here we assert that a good way to understand regional economics is to begin by examining the micro-behavior of economic agents in the economic space, and so explore the micro-foundations of regional economics. After a model has been identified at the micro spatial level, we can always superimpose an administrative grid and examine the implied meso-scenario.

In fact, phenomena in nature are encountered in continuous space and are developed over continuous time; it is only due to our limitations that we discretize phenomena in some way (and subsequently distort it by reducing the quantity of information). Apart from the motivations given in the previous sections, a more remote incentive to study the continuous properties of economic phenomena dates back to Leibniz and his famous quote: “natura non facit saltus”.^{1} The same general idea has been adopted in time-series analysis with the development of continuous time econometrics and is providing significant contributions to many branches of economics (see Gandolfo 1990; Bergstrom 1990). The idea of continuous space modeling is not new in economic geography and spatial economics: it was present in Weber’s studies of industrial location at the beginning of the twentieth century (Weber, 1909). More recently Beckmann (1970) and Beckmann and Puu (1985) analyzed equilibrium conditions of models defined in a continuous space. Griffith (1986) discusses a spatial demand curve based on a central place economic landscape defined on a continuous surface. Kaashoek and Paelinck (1994; 1996; 1998) derive the properties of a non-equilibrium dynamic path of continuous space economic variables based on partial differential equation theory (John 1978; Toda 1989). However, these studies are all concerned with the theoretical properties of models, whereas we are interested in identifying models susceptible to statistical estimation and testing on the basis of existing data.

There are many reasons why such an approach has not been adopted thus far. The most obvious are lack of an appropriate statistical methodology, lack of accurate data (often not available for confidentiality reasons) and lack of appropriate computer technologies. However, the methods for analyzing spatial data on a continuous space now form a well-consolidated methodological body as it was extensively discussed in this book. The availability of statistical data at the individual agent level has also increased considerably in recent times, due to the diffusion of spatially referenced administrative records, new Big Data sources, as discussed at length in Chapter 1.3, and the development of methods to conceal confidential data without seriously distorting the statistical information (see Cox 1980; Duncan and Lambert 1986; De Waal and Willenborg 1998; Willenborg and De Waal 1996; Arbia et al., 2016; Chapter 3.5). As a consequence, there no longer appear to be any technical obstacles in a microeconomic approach to regional problems. We will formalize such an approach in the next section.