Evaluating Eigenvector Spatial Filter Corrections for Omitted Georeferenced Variables

Daniel Griffith,Yongwan Chun

doi:10.3390/econometrics4020029

Abstract

The Ramsey regression equation specification error test (RESET) furnishes a diagnostic for omitted variables in a linear regression model specification (i.e., the null hypothesis is no omitted variables). Integer powers of fitted values from a regression analysis are introduced as additional covariates in a second regression analysis. The former regression model can be considered restricted, whereas the latter model can be considered unrestricted; this first model is nested within this second model. A RESET significance test is conducted with an F-test using the error sums of squares and the degrees of freedom for the two models. For georeferenced data, eigenvectors can be extracted from a modified spatial weights matrix, and included in a linear regression model specification to account for the presence of nonzero spatial autocorrelation. The intuition underlying this methodology is that these synthetic variates function as surrogates for omitted variables. Accordingly, a restricted regression model without eigenvectors should indicate an omitted variables problem, whereas an unrestricted regression model with eigenvectors should result in a failure to reject the RESET null hypothesis. This paper furnishes eleven empirical examples, covering a wide range of spatial attribute data types, that illustrate the effectiveness of eigenvector spatial filtering in addressing the omitted variables problem for georeferenced data as measured by the RESET.

Highlights

A practitioner spends considerable time contemplating which covariates to include in a descriptive regression equation, as well as the functional forms they should have
A serious problem in regression analysis is misspecification of a descriptive equation by failing to include all relevant covariates in it: the omitted variables problem. One result of such omissions is omitted-variable bias (OVB), which arises when parameter estimates for the covariates included in a descriptive equation are over- or under-estimated because estimation attempts to compensate for the omitted variables
The regression equation specification error test (RESET) for an eigenvector spatial filtering (ESF) model was conducted with the selected eigenvectors as additional independent variables

Summary

Introduction

A practitioner spends considerable time contemplating which covariates to include in a descriptive regression equation, as well as the functional forms they should have. A serious problem in regression analysis is misspecification of a descriptive equation by failing to include all relevant covariates in it: the omitted variables problem. One result of such omissions is omitted-variable bias (OVB), which arises when parameter estimates for the covariates included in a descriptive equation are over- or under-estimated because estimation attempts to compensate for the omitted variables. In part, this outcome arises from multicollinearity; in part, this outcome arises from a biased error variance estimate (i.e., covariates being removed from a specification because they are deemed insignificant when they are significant).

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