Introduction to Spatial Econometrics, Study notes of Statistics

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Spatial Statistics and Econometrics

Roberto Patuelli Department of Economics University of Bologna EAERE-ETH European Winter School on “Spatial Environmental and Resource Economics”

Structure

• Basic concepts, definitions, indicators of spatial autocorrelation, exploratory statial data analysis
• Standard spatial econometric models, nonlinear spatial models?
• Panel spatial econometric models, further (alternative?) specifications Caveat : I’m not an econometrician… I’m a “user” of spatial methods. For those interested in going into spatial econometrics in-depth, there are several summer schools around (e.g., SEA’s summer school in Rome) with the top spatial econometricians teaching for up to three full weeks

Where?

• Spatial (georeferenced) data come in several forms

(Cressie 1993)

• Geostatistical data – continuous surface in the

bidimensional domain R

2

• Lattice/area (regional) data – finite (ir)regular set of points

in R

2

or areas that partition R

2

• Point pattern data – point process that can distinguish

between locations having or not having a certain attribute

• ( Objects – again point process, like point-pattern data, the

set D of points is result of a random process)

• Similar classification by Fischer and Wang (2011)

(see next slide)

• Methods often depend on type of data, although they

can sometimes be borrowed between classes of data

Where? (2)

Why?

• Spatial data are often non independent
  • Violation of assumption of observations coming from independent random variables given in classical statistical theory (sphericity of errors: homoskedasticity and no autocorrelation)
  • Spatial data tend to be positively correlated, with the degree of correlation decreasing over distance
  • In this conditions, OLS is not appropriate anymore
    • F and t tests on regression parameters may lead to wrong conclusions
    • Additionally, the assumption of homoskedasticity may be violated, if, for example, rates from areal data of widely different base population are analysed
• Data support
  • Incompatible data. How to combine data collected on different supports (e.g., different levels of spatial aggregation)?
  • Change of support
    • Combining data towards creating a new variable
    • Modifiable areal units problem (MAUP, Openshaw and Taylor 1979): often data are collected for purely administrative areas which don’t have intrinsic geographical meaning. But regression results often depend on the scale of the units (scale problem) and their configuration (aggregation problem)
    • Ecological fallacy (Robinson 1950): making statistical inference on individuals on the basis of aggregate data is flawed

How?

• 1) Exploratory Spatial Data Analysis (ESDA)

• Extension of Tukey-type data exploration
• Preliminary data analysis, based in particular on mapping
• GIS may help summarizing geographic information,

finding outliers, manipulating point data, etc

• Used mostly prior to model building, also to make

hypotheses about the data, but new ESDA techniques go

directly into the model building phase, showing how

variables relate to each other in space

How? (3)

• 3. Spatial Econometrics
  • Paelinck and Klaassen (1979), Anselin (1988)
  • Anselin: spatial lag model; spatial error model
  • Need for spatial statistical tests to check assumptions of spatial randomness in regression residuals - Moran’s I - Specification search: Lagrange multiplier tests…
  • Geographically weighted regression (GWR; Fotheringham, Brunsdon, Charlton) to allow regression parameters to vary over space
  • … and many more recently developed methods accounting for spatial autocorrelation in econometric techniques (e.g. instrumental variables, GMM methods, nonlinear (GLM) models…)
• 4. Geostatistics (not discussed here)
  • Geostatistical methods most often start from observations at points of single or multiple attributes, and are concerned with their statistical interpolation to a field or continuous surface (e.g. kriging ) assumed to extend across the whole study area

Spatial Autocorrelation

• Definitions

– ‘It represents the relationship between nearby

spatial units, as seen on maps, where each unit is

coded with a realization of a single variable’ (Getis

2009, p. 256)

– ‘Given a set S containing n geographical units, it

refers to the relationship between some variable

observed in each of the n localities and a measure

of geographical proximity defined for all n ( n – 1)

pairs chosen from S ’ (Hubert et al. 1981, p. 224)

What Is Spatial Dependence?

• Revelli (2003) asks whether the spatial patterns observed in model residuals are a reaction to model misspecification, or if they signal the presence of substantive interaction between observations in space? A similar point is raised by McMillen (2003) - “two adjacent supermarkets will compete for trade, and yet their turnover will be a function of general factors such as the distribution of population and accessibility.” - “the presence of spatial autocorrelation may be attributable either to trends in the data or to interactions; … [t]he choice of model must involve the scientific judgement of the investigator and careful testing of the assumptions” (Cliff and Ord, 1981, pp. 141-142)
• One way of testing the assumptions is through changes in the policy context over time, where a behavioural model predicts changes in spatial autocorrelation. If the policy changes, the level of spatial interaction should change too (borrowed from Roger Bivand)

Spatial Dependence vs Spatial

Heterogeneity

• Dependence → Interaction, interdependence
• Heterogeneity → Intrinsic characteristics unevenly distributed over space
• With a cross-section, hard (impossible) to tell whether outcomes arise from interaction or from intrinsic individual characteristics
• Spatial dependence vs spatial heterogeneity
  • Positive spatial autocorrelation → spatial diffusion/spillovers
  • Negative spatial autocorrelation → spatial competition
• Same problem as in social networks: intrinsic individual characteristics or personal interaction? (borrowed from Daniel Arribas-Bel)