Spatial Dependence in Regressors and its Effect on Estimator Performance

34 Pages Posted: 3 Apr 2011 Last revised: 9 Apr 2011

See all articles by R. Kelley Pace

R. Kelley Pace

Louisiana State University - E.J. Ourso College of Business Administration

James P. LeSage

Texas State University - McCoy College of Business Administration

Shuang Zhu

Kansas State University - Department of Finance

Date Written: April 2, 2011

Abstract

Most spatial econometrics work focuses on spatial dependence in the regressand or disturbances. However, LeSage and Pace (2009) show that the bias from applying OLS to a regressand generated from a spatial autoregressive process was exacerbated by spatial dependence in the regressor. Also, the marginal likelihood function or restricted maximum likelihood (REML) function includes a determinant of a function of the regressors. Therefore, high dependence in the regressor may affect the likelihood through this term. Finally, the notion of effective sample size for dependent data suggests that the loss of information from dependence may have implications for the information content of various variables. Empirically, many common economic regressors such as income, race, and employment show high levels of spatial autocorrelation. Based on these empirical results, we conduct a Monte Carlo study using maximum likelihood, restricted maximum likelihood, and two instrumental variable specifications for the lag y model (SAR) and spatial Durbin model (SDM) in the presence of correlated regressors while varying signal-to-noise, spatial dependence, and weight matrix specifications. We find that REML outperforms ML in the presence of correlated regressors and that instrumental variable performance is affected by such dependence. The combination of correlated regressors and the SDM provides a challenging environment for instrumental variable techniques. In addition, we examine the estimation of marginal effects and show that this can behave better than estimation of component parameters. We also make suggestions for improving Monte Carlo experiments.

Keywords: regressor autocorrelation, spatial Durbin model, REML, spatial autoregression, maximum likelihood, spatial econometrics

JEL Classification: C11, O31, R11

Suggested Citation

Pace, R. Kelley and LeSage, James P. and Zhu, Shuang, Spatial Dependence in Regressors and its Effect on Estimator Performance (April 2, 2011). Available at SSRN: https://ssrn.com/abstract=1801241 or http://dx.doi.org/10.2139/ssrn.1801241

R. Kelley Pace

Louisiana State University - E.J. Ourso College of Business Administration ( email )

Department of Finance
2164 B Patrick F. Taylor Hall
Baton Rouge, LA 70803-6308
United States
(225)-578-6256 (Phone)
(225)-578-9065 (Fax)

HOME PAGE: http://www.spatial-statistics.com

James P. LeSage (Contact Author)

Texas State University - McCoy College of Business Administration ( email )

Finanace and Economics Department
601 University Drive
San Marcos, TX 78666
United States
512-245-0256 (Phone)
512-245-3089 (Fax)

HOME PAGE: http://www.spatial-econometrics.com

Shuang Zhu

Kansas State University - Department of Finance ( email )

Manhattan, KS 66506
United States

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