2024 | Buch

# A Primer for Spatial Econometrics

## With Applications in R, STATA and Python

verfasst von: Giuseppe Arbia

Verlag: Springer International Publishing

Buchreihe : Palgrave Texts in Econometrics

2024 | Buch

verfasst von: Giuseppe Arbia

Verlag: Springer International Publishing

Buchreihe : Palgrave Texts in Econometrics

This textbook offers a practical and engaging introduction to spatial econometric modelling, detailing the key models, methodologies and tools required to successfully apply a spatial approach.

The second edition contains new methodological developments, new references and new software routines in R that have emerged since the first edition published in 2014. It also extends practical applications with the use of the software STATA and of the programming language Python. The first software is used increasingly by many economists, applied econometricians and social scientists while the software Python is becoming the elective choice in many scientific applications. With new statistical appendices in R, STATA and Python, as well as worked examples, learning questions, exercises and technical definitions, this is a significantly expanded second edition that will be a valuable resource for advanced students of econometrics.

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Abstract

This introductory chapter provides the necessary background to understand the rest of the book and introduces the symbolism used elsewhere. The chapter covers the topics typically treated in a first course in econometrics at an undergraduate level; as such it can be omitted by the readers who are already knowledgeable on this subject. We present a summary of the basic multivariate linear regression model, and of the three most popular estimation methods (Ordinary Least Squares, Maximum Likelihood and Method of Moments). We then present the basic hypothesis testing procedures. We also discuss the model's assumptions, we briefly analyse the consequences of their violations and we present the alternative estimators that are necessary in these situations. Finally, the chapter contains a presentation of the codes necessary for the practical implementation of the procedures discussed in the chapter, by using the softwares R, STATA and Python.

Abstract

The major difference between standard econometrics and spatial econometrics lies in the fact that, in order to treat spatial data, we need two different sets of information. The first is related to the observed values of the economic variables, whereas the second relates to the particular locations where those variables are observed and to the links of proximity between them. This chapter is devoted to a presentation of the basic tools that are necessary to conduct a spatial econometric analysis. First of all, we introduce the spatial weight matrix, a tool that incorporates the information about the links of proximity between the spatial observations; we then use such a definition to introduce the notion of the “spatial lag”, which constitutes an extension of the popular definition of time lag. Based on thee definitions, we then present a test of the spatial autocorrelation among the regression residuals. The chapter ends with the computer codes needed to implement the procedure discussed in the computer language R, STATA and Python.

Abstract

This chapter discusses different specifications of linear spatial econometrics models that can be considered once the hypothesis of no spatial autocorrelation in the disturbances is violated. In particular, we present models where the idea of the spatial lag is applied to the dependent variable, to the independent variables, to the residuals or to any of their combinations. For each model, we provide the mathematical specification, we derive the appropriate estimators and we discuss their statistical properties, their relative advantages and their drawbacks. For the various models, we also introduce the tools necessary to measure the impact of changes in the independent variables on the dependent variable which are necessary in policy evaluations and scenario analyses. The chapter concludes with all the computer codes which are necessary to implement the procedures presented in the R, STATA and Python environments.

Abstract

This chapter discusses some advanced special topics in spatial econometrics that have been recently introduced in the literature. The primary purpose is to make the reader knowledgeable about a set of techniques that represent the evolution of those presented in Chapter 3 and that constitute an essential part of the skills currently required to spatial econometricians. These methods have the potential for tremendous impact in analyzing real problems in many scientific fields. In particular, the chapter presents the spatial peculiarities associated with the treatment of heteroscedastic disturbances, discrete choices, panel data, non-stationarity and prior information incorporated into a Bayesian framework. A section is also devoted to discuss the implications of treating non-deterministic weight matrices. Finally, consistently with the rest of the book, the chapter offers a detailed presentation of the computer codes in R, STATA and Python, needed for the practical implementation of all the models presented.

Abstract

Spatial econometrics is currently experiencing the Big Data revolution in terms of V: the Volume, the Velocity and the Variety with which spatial data are collected. Indeed, spatial data employed traditionally in the spatial econometric modeling, can be very large, the information being more and more available at a very fine resolution at the level of census tracts, local markets, town blocks, regular grids (or any other small partition of the territory) or even at the level of the single, spatially located, individual. As a consequence, the procedures discussed in this book can become in some cases computational prohibitive because of the vast quantity of data to be analysed. To overcome the computational problems raised by the treatment of large volumes of data, several procedures have been introduced in the literature. However, some of the most recent studies have followed a different route and concentrated, instead, on the definition of some alternative specifications that depart from the paradigms presented in the previous chapters of this book. These contributions have some common characteristics: they are theoretically very simple, they produce closed-form solutions and they improve dramatically the numerical performances. In this chapter we will review some of these alternative specifications presenting, in particular, the matrix exponential spatial specification, the unilateral approximation and the bivariate coding technique. While the bulk of the chapter is focused on the problems raised by the treatment of large volumes of data, the concluding Sect. 5.5 is devoted, instead, to consider the problems connected with the velocity with which, in many applications, spatial data can be acquired. Finally the chapter presents the computer codes in the languages R, STATA and Python needed for the implementation of the techniques presented.

Abstract

This monography text has the purpose of bridging the gap between the unspecialized econometric textbook literature and the more advanced spatial econometrics textbooks. This final chapter aims at providing the interested reader with some indications in this direction. In particular, indications are given to the reader interested in the probabilistic roots of the models treated here, to those willing to widening their knowledge on the possible modeling alternatives, to those interested in deepening their knowledge and practice on the available software, and to those that want to have an overview of the ongoing cutting-edge research in the subject under both the theoretical and the applied point of view.