Spatial statistics and econometrics

Objectives

The use of spatial data is undergoing significant development as a result of its application in many fields: earth sciences, environment and climatology, epidemiology, econometrics, image analysis, etc…. Taken in its broadest methodological sense, spatial statistics refers to any analysis using the statistical tool and having a spatial dimension, whether this dimension concerns the tool itself, the object analyzed or the variables used as descriptors of this object. As with time series, spatial statistics differs from classical statistics in that the observations are dependent. Its originality lies in the fact that, in space, interactions can be multidirectional. Specific statistical tools are available to analyze localized objects. One of the most classic is the measurement of spatial autocorrelation, which gives an overall account of the tendency of nearby locations to resemble each other (positive autocorrelation) or, on the contrary, to oppose each other (negative autocorrelation). Spatial econometrics methods make it possible to take this spatial dependence into account in conventional statistical analyses, and to prevent it from introducing biases into parameter estimates.

After reviewing the different types of spatial data, the course introduces the basic tools of spatial statistics, which can be used to measure the degree of statistical significance of the spatial configurations and relationships of georeferenced data, thus complementing and enriching the strictly cartographic approach.

The course then focuses more specifically on the study of economic data. Spatial econometric methods are increasingly used in many fields (growth, regional and urban economics, marketing, real estate market studies, etc.). Favored by the development of geographic information systems, which provide simultaneous access to the values taken by the variables of interest and their geographical location, these methods enable spatial interaction phenomena to be taken into account in modeling in a variety of ways.

The aim is to extend standard econometric methods by considering the main problems encountered when using these data (heterogeneity of observations, spatial interaction). After presenting the different ways of formalizing spatial effects (spillover and spatial dependence effects, heterogeneity), we will outline the various spatial econometric specifications and their estimation by different methods (maximum likelihood and generalized method of moments). The most common specification tests will also be presented. The presentations will be illustrated by examples drawn from recent literature in this field.

Numerous examples using R or STATA illustrate the topics covered. The course will be complemented by 3 WORKSHOPS, one on data mapping and exploratory methods, the other 2 on econometrics.

Course outline

General introduction: the need to take the spatial dimension into account
Spatial statistics and time series
The importance of taking the spatial dimension into account
Stages in a spatial study
Various types of spatial data
Specificity of spatial data: heterogeneity and autocorrelation

PART 1: Spatial statistics
The spatial data analysis toolbox
Neighborhood matrices
Spatial weighting matrices
Other specific spatial statistics tools
Exploratory spatial data analysis and testing
Representation tools
Spatial autocorrelation tests
Local spatial autocorrelation indices
Homogeneity tests

PART 2: Spatial econometrics on cross-sectional data
The study of spatial autocorrelation in econometrics
A typology of spatial models
The multiplier effect and the spatial diffusion effect 
The spatially autoregressive model
The spatially autocorrelated error model
The spatial Durbin model
Specification tests
Models in the presence of missing spatial data
Does the choice of weighting matrix affect the interpretation of results? Rationalizing your choice
Criticisms of identification in spatial autoregressive models
The quasi-experimental approach to estimating spatial models
The study of spatial heterogeneity in econometrics
Parameter instability and statistical inference
Weighted geographic regression
Spatial regime models
Spatial quantile regression
Interactions between autocorrelation and spatial heterogeneity

PART 3: Introduction to spatial econometrics on panel data
Spatial econometrics on panel data
Typology of models
Static panels with spatial effects
Dynamic panels with spatial effects
Specification tests 

Prerequisites

Econometrics 2A, R, Multivariate exploratory statistics