Spatial Microeconometrics

Giuseppe Arbia, Giuseppe Espa, Diego Giuliani

• Éditeur: Routledge
• Année: 2021
• ISBN:
  9781317563471
• Édition: 1
• Sujet: Economia
• Sous-sujet: Econometria

Spatial Microeconometrics introduces the reader to the basic concepts of spatial statistics, spatial econometrics and the spatial behavior of economic agents at the microeconomic level. Incorporating useful examples and presenting real data and datasets on real firms, the book takes the reader through the key topics in a systematic way.

The book outlines the specificities of data that represent a set of interacting individuals with respect to traditional econometrics that treat their locational choices as exogenous and their economic behavior as independent. In particular, the authors address the consequences of neglecting such important sources of information on statistical inference and how to improve the model predictive performances. The book presents the theory, clarifies the concepts and instructs the readers on how to perform their own analyses, describing in detail the codes which are necessary when using the statistical language R.

The book is written by leading figures in the field and is completely up to date with the very latest research. It will be invaluable for graduate students and researchers in economic geography, regional science, spatial econometrics, spatial statistics and urban economics.

Part I

Introduction

1 Foundations of spatial microeconometrics modeling

1.1 A micro-level approach to spatial econometrics

This book is devoted to the spatial econometric analysis of individual micro-data observed as points in the economic space (Dubé and Legros, 2014), sometimes referred to as “spatial microeconometrics” (Arbia et al., 2016). This branch is rapidly emerging onto the stage of spatial econometrics, building upon results from various branches of spatial statistics (Diggle, 2003) and on the earlier contributions of Arbia and Espa (1996), Duranton and Overman (2005), Marcon and Puech (2003; 2009; 2010) and Arbia et al. (2008; 2010; 2014a; 2014b; 2015b). In a relatively recent paper Pinkse and Slade (2010) heavily criticized the current developments of spatial econometrics, observing:

The theory is in many ways in its infancy relative to the complexity of many applications (in sharp contrast to time-series econometrics, where the theory is well developed) … due to the fact that it is almost invariably directed by what appears to be the most obvious extension of what is currently available rather than being inspired by actual empirical applications.

and:

Many generic large sample results treat locations as both exogenous and fixed and assume that they are observations at particular locations of an underlying spatial process. … Economists have studied the locational choices of individuals … and of firms … but generally treat the characteristics of locales as given. The purpose of much spatial work, however, is to uncover the interaction among (authorities of) geographic units, who choose, e.g., tax rates to attract firms or social services to attract households. … An ideal model would marry the two; it would provide a model explaining both individuals’ location decisions and the action of, say, local authorities. (Pinkse and Slade, 2010)

This new modelling strategy, which treats location as endogenous by taking into account simultaneously both individuals’ locational choices and their economic decisions in their chosen location, represents the scope of the growing field of spatial microeconometrics.

As a matter of fact, a spatial microeconometric approach (unconceivable until only a few decades ago) is now more and more feasible due to the increasing availability of very large geo-referenced databases in all fields of economic analysis. For instance, the US Census Bureau’s Longitudinal Business Database provides annual observations for every private-sector establishment with a payroll and includes approximately 4 million establishments and 70 million employees each year. Sourced from US tax records and Census Bureau surveys, the micro-records document the universe of establishments and firms characterized by their latitude–longitude spatial coordinates (Glaeser and Kerr, 2009). Examples of this kind can be increasingly found in all branches of economics including education, health economics, agricultural economics, labor economics, industrial economics, house prices, technological diffusion and many others. We will discuss them in the next section.

The availability of these detailed geographical databases now makes it possible to model individuals’ economic behavior in space to gain information about economic trends at a regional or macro-level. A spatial microeconometric approach had already been suggested some 30 years ago by Durlauf (1989), at a time when data allowing this kind of approach were not yet available, appropriate models had not been developed and computing power was limited. Durlauf criticized the mainstream macroeconomy, pointing out that “macroeconomic modeling currently relies upon the representative agent paradigm to describe the evolution of time series. There is a folk wisdom that heterogeneity of agents renders these models unsatisfactory approximations of the macroeconomy”. He then proceeded to describe a “lattice economy” where a “collection of agents are distributed across space and time” and “macroeconomy consists of many simple agents simultaneously interacting”. Durlauf (1989; 1999) suggested a parallel between physics and economic analysis. In particular he concentrated on the links existing between formal individual choice models and the formalism of statistical mechanics, which suggested that there are many useful tools that applied economists could borrow from physics. Just as in statistical mechanics models explain how a collection of atoms can exhibit the correlated behavior necessary to produce a magnet, in economics one may devise models aimed at explaining spatially interdependent behaviors. The basic idea in statistical mechanics, that the behavior of one atom is influenced by the behavior of other atoms located nearby, is indeed very similar to the hypothesis that forms the basis of all spatial econometric studies that individual or collective decisions depend upon the decisions taken in other neighboring regions or by neighboring economic agents.

According to Kirman (1992) the traditional approach considers “the aggregate behavior of the economy as though it were the behavior of a single representative agent”. However there is strong evidence that “heterogeneity and dispersion of agents’ characteristics may lead to regularity in aggregate behavior” and that “once we allow for interdependence … consistency between microeconomic characteristics and macroeconomic characteristics may be lost” and, finally, “strong local random interacting agents who are a priori identical may produce macroeconomic irregularities”. Kirman concludes his work by stating that we must change our attitude and start thinking “of the economy as a self-organizing system, rather than a glorified individual”.

Perhaps the most radical criticism in this respect is, however, presented by Danny Quah (1993), who states:

Modern macroeconomics concerns itself, almost by definition with substitution of consumption and production across time. The macroeconomist wishes to understand the dynamic of inflation and asset prices, output and employment, growth and business cycles. Whether in doing so, one uses ideas of search and nonconvexities, intertemporal substitution and real business cycles, sticky prices and wages, or dynamic externalities, one implicitly assumes that it is the variation in economic activity across time that is the most useful to analyse. But why must that variation be the most important?

In doing so the macroeconomist “almost exclusively focuses on aggregate (rather than disaggregate) shocks as the source of economic fluctuations” ignoring “rich cross-sectional evidence on economic behaviour” and losing “the ability to say anything about the rich heterogeneous observations on economic activity across space, industries, firms and agents”. These criticisms should be distinguished from those implying the

failure of aggregation to a representative agent (e.g. Forni and Lippi, 1997; Kirman, 1992). There, the researcher points out the inability to represent aggregate behaviour because of individual heterogeneity. Here I assert instead that it is individual heterogeneity that is more interesting even from the perspective of wishing to understand macroeconomic behaviour.

However in introducing such concepts into the discussion and ignoring the empirical tools, “researchers have used empirical ideas that are altogether uninformative. Those econometricians who model dynamic adjustment have done so not because adjustment occurs only in time and not in space, but because time series methods are already readily available for the former and not the latter” (Quah, 1993). The quoted sentences can be considered in some sense the manifesto of spatial microeconometrics.

1.2 Advantages of spatial microeconometric analysis

The biggest advantage of a spatial microeconometric approach over orthodox spatial econometrics is the possibility of treating location and distances as endogenous thus allowing the modeling of both economic variables and locational choices within the same methodological framework (Pinkse and Slade, 2010). Spatial microeconometrics present many distinctive features with respect to orthodox spatial econometrics based on regional data and with respect to standard microeconometrics. Concerning the general field of microeconometrics, Cameron and Trivedi report six distinctive features: (i) discreteness and nonlinearity, (ii) greater realism, (iii) greater information content, (iv) microeconomic foundations, (v) disaggregation and heterogeneity and (vi) dynamics (Cameron and Trivedi, 2005). The lack of theories to support regional econometric modelling (Pinkse and Slade, 2010; Corrado and Fingleton, 2012) is one of the deeper criticisms against spatial econometrics restrictively conceived, which can, at most, lead to the identification of technical relationships with little or no possibility of drawing causal inferences. On the contrary, a spatial microeconometric approach provides the possibility of identifying more realistic models because hypotheses about economic behavior are usually elicited from theories related to the individual choices of economic agents. The inconsistency between microeconomic theories and macro-relationships has long been discussed in the economic literature (Pesaran et al., 1987; Klein, 1946). As a matter of fact, a relationship estimated at an individual level, such as a production function, may be regarded as a behavioral relationship that, for the single firm, embodies a particular interpretation of the causal mechanism linking inputs to outputs. However, the same relationship at an aggregate level does not depend on profit maximization but purely on technological factors (Klein, 1946). The relatively cavalier fashion with which most empirical studies shift from one unit to the other has seldom been criticized in the literature (Green, 1964; Hannan, 1970; Haitovsky, 1973). Traditionally economists have been faced with this problem in the analysis of family budgets: if we estimate a linear consumption function on aggregate data the impact of income on consumption has nothing in common with the individual marginal propensity to consume (Modigliani and Brunberg, 1955; Stocker, 1982).

The aggregation problem is a particularly relevant feature of the spatial econometrics of regional data that can be tackled by estimating models at a micro-geographical level. In fact, geographically aggregated data within discrete portions of space are based on arbitrary definitions of the spatial observational units, and, in this way, they introduce a statistical bias arising from the discretional characterization of space. This issue is very well known in the statistical literature, where it is referred to as the “modifiable areal unit problem” or MAUP (Arbia, 1989). The modifiable areal unit problem is more severe than the traditional modifiable unit problem (Yule and Kendall, 1950), because regional data are usually very irregular aggregations of individual characterized by large differences in terms of the size and the shape of the various spatial units. The MAUP manifests itself in two ways: (i) the scale problem, dealing with the indeterminacy of any statistical measure to changes in the level of aggregation of data, and (ii) the aggregation problem, having to do with the indeterminacy of any statistical measures due to changes in the aggregation criterion at a given spatial scale. The effects of aggregation on standard econometric models are well known, dating back to the early contributions of Prais and Aitchinson (1954), Theil (1954), Zellner (1962), Cramer (1964), Haitovsky (1973). More contributions were made by Barker and Pesaran (1989), Okabe and Tagashira (1996), Tagashira and Okabe (2002) and Griffith et al. (2003). The main results found in the literature are that the estimators of regression’s parameters have a larger variance when using aggregated rather than individual data, leading to false inferential conclusions and to the acceptance of models that should be discarded. Orcutt et al. (1968), through a microsimulation study, pointed out that “detailed study of the individual regression indicates a tendency to reject the null hypothesis more frequently than the usual sampling theory suggests. … Perhaps this is why economic theories are almost never rejected on the basis of empirical evidences.” Similar conclusions were reached by Arbia (1989), who considered a spatial random economy constituted by many interacting agents. He noticed that “even a small amount of autocorrelation between the individuals can produce the ecological fallacy effect”.¹ The loss in efficiency due to aggregation depends on the grouping criterion and it is minimized when individuals are grouped so as to maximize the within-group variability. The effects of MAUP on different statistical measures, pioneered by Gehlke and Biehl (1934), Yule and Kendall (1950), Robinson (1950) and Openshaw and Taylor (1979), have been studied at length by Arbia (1989) who derived the formal relationship between the Pearson’s correlation coefficient at the individual level and the same coefficient at the aggregate level when data are spatially correlated. Arbia and Petrarca (2011) presented a general framework for analyzing the effects of MAUP on spatial econometric models showing that the efficiency loss, connatural to any aggregation process, is mitigated by the presence of a positive spatial correlation parameter and conversely exacerbated by the presence of a negative spatial correlation. This result is intuitive: positive spatial correlation implies aggregation between similar values thus preserving variability, while negative spatial correlation implies aggregation between very different values thus implying a more dramatic increase of variability.

1.3 Sources of spatial micro-data

The large availability of...

Table des matières

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Foreword
• Preface and acknowledgements
• Part I Introduction
• Part II Modeling the spatial behavior of economic agents in a given set of locations
• Part III Modeling the spatial locational choices of economic agents
• Part IV Looking ahead: modeling both the spatial location choices and the spatial behavior of economic agents
• Appendices
• Bibliography
• Index