Statistical Inference in Random Coefficient Regression Models

This short monograph which presents a unified treatment of the theory of estimating an economic relationship from a time series of cross-sections, is based on my Ph. D. dissertation submitted to the University of Wisconsin, Madison. To the material developed for that purpose, I have added the substance of two subsequent papers: "e;Efficient methods of estimating a regression equation with equi-correlated disturbances"e;, and "e;The exact finite sample properties of estimators of coefficients in error components regression models"e; (with Arora) which form the basis for Chapters 11 and III respectively. One way of increasing the amount of statistical information is to assemble the cross-sections of successive years. To analyze such a body of data the traditional linear regression model is not appropriate and we have to introduce some additional complications and assumptions due to the hetero- geneity of behavior among individuals. These complications have been discussed in this monograph. Limitations of economic data, particularly their non-experimental nature, do not permit us to know a priori the correct specification of a model. I have considered several different sets of assumptionR about the stability of coeffi- cients and error variances across individuals and developed appropriate inference procedures. I have considered only those sets of assumptions which lead to opera- tional procedures. Following the suggestions of Kuh, Klein and Zellner, I have adopted the linear regression models with some or all of their coefficients varying randomly across individuals.