Identification and Estimation of Categorical Random Coefficient Models

Abstract: This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments of the random coefficients. A Generalized Method of Moments estimation procedure is proposed also employed by Peter Schmidt and his coauthors to address heterogeneity in time effects in panel data models. Using Monte Carlo simulations, we find that moments of the random coefficients can be estimated reasonably accurately, but large samples are required for estimation of the parameters of the underlying categorical distribution. The utility of the proposed estimator is illustrated by estimating the distribution of returns to education in the U.S. by gender and educational levels. We find that rising heterogeneity between educational groups is mainly due to the increasing returns to education for those with postsecondary education, whereas within group heterogeneity has been rising mostly in the case of individuals with high school or less education.