The Use of Multivariate Generated Regressors in the Presence of Heteroskedasticity

Abstract

This paper describes the estimation and testing of regression models that include multivariate generated or computed regressors in the presence of heteroskedasticity in the cross-section case. Hetero- skedasticity is often a problem in cross-section data and the usual tests for its presence cannot be applied when the heteroskedasticity is in some measure due to computed regressors. We investigate the case of multiple computed regressors that are generated from the results of a system of seemingly unrelated regressions and we propose a method to test and correct the covariance estimates for unknown heteroskedasticity in the errors of the model of interest. In contrast to most time-series applications, we allow for the observations in the first step regression to be different from those for the second stage regression. We present an application in which a hedonic model of home purchases is estimated with a set of computed regressors defined from a multivariate regression of school quality. We demonstrate that property values do reflect the characteristics of the neighborhood school. We find evidence that property values can reflect the peer effect of a public school in the Dallas Independent School District (DISD).

Keywords:

• School quality
• Two-step estimation methods
• Heteroskedasticity
• Hedonic price models
• Multivariate generated regressors

Acknowledgments

We would like to thank a referee, Rebecca Bergstrasser, Stephen P. A. Brown, Donna Ginther, Shawna Grosskopf, Jim Murdoch, Lori Taylor, and the participants at the Economics Department Workshop at the University of Melbourne for their helpful comments and suggestions; Kelly A. George for her research assistance; and the Dallas Independent School District for making its data available. The Faculty of Economics and Commerce at the University of Melbourne for financial support. Any remaining errors are our own.