On the Estimation of Structural Change: A Generalization of the Random Coefficients Regression Model

Abstract

IN THIS PAPER we extend the random regression coefficients model [20, 25, 36, 39], herein termed the constant mean response (CMR) model to a more general case in which the regression coefficients change systematically with calender time, herein termed the variable mean response (VMR) model. Two estimators are proposed for such a model. The first following Theil and Mennes [45], is a four step generalization of the Hildreth-Houck estimator [20], in view of the fact that the residuals in the second stage of the Hildreth-Houck (H-H) estimator are not homoscedastic. Second we derive a maximum likelihood estimator for the VMR model. The last section in this paper presents an empirical illustration of the comparative performance of the estimators under focus in this paper. The paper contains three appendices. Appendix A obtains the covariance matrix of the second stage H-H residuals for use in the four step estimator to which we allude above. In Appendix B we prove the consistency of the estimator proposed for the VMR model in view of the fact that as a consequence of the inclusion of calender time among the regressors the probability limit of the moments matrix of the regressors is no longer finite. Lastly, since the maximizing equations are highly non-linear, Appendix C outlines an algorithm for their solution.2