A Monte Carlo Study of EC-estimation in Panel Data Models with Limited Dependent Variables and Heterogeneity

The EC (Estimation-Classiication) estimator, and its companion EC-algorithm, were introduced in El-Gamal and Grether (1995), and their properties further analyzed in El-Gamal and Grether (1996). The purpose of EC estimation is to uncover heterogeneity in panel data models in a manner which is more parsimonious and computationally less costly than some of the standard methods (e.g. xed eeects). The latter concern is particularly evident in limited dependent variable models where no simple method of estimating xed eeects is available (e.g. probits). One of the applications of El-Gamal and Grether (1996) employed the EC algorithm to estimate multiple probits in a population of 257 individuals, each being observed for 14 to 19 periods, providing very satisfactory results. Since the asymptotic theory behind EC estimation relies on \Large T " approximation (i.e. we require T " 1, then n " 1 in proving consistency of the estimator), we provided a diagnostic statistic (called the Average Normalized Entropy (ANE) for diagnosing the adequacy of the large T approximation. In this paper, we provide a Monte Carlo analysis of the EC estimator in comparison to pooling, and xed eeects (pooled slopes) estimators. The results show that for T as small as 3, the EC-estimator does signiicantly better than xed eeects estimators in unpoolable slope environments, and almost as well in the poolable slopes case. As T gets larger the EC estimator's performance becomes progressively superior, with T = 20 providing virtually perfect estimation of the number of types, what the types are, and the classiication of individuals to types. The ANE statistic is found to provide a very useful indicator of the proportion of possible misclassiications.