9729430 Kyriazidou This project develops estimation methods for models of discrete choice and sample selection using longitudinal (panel) data. The models studied are used in a variety of economic, medical and social studies. A large amount of research has focused on developing methods for estimating panel data models, especially in the case of short fixed-length models, that rely heavily on the parametric specification of the statistical distribution of unobservable variables, both of the permanent individual ones as well as the time-varying idiosyncratic shocks or disturbances. This project addresses the limitations inherent in this approach: biased and inconsistent estimation of the parameters of interest and incorrect inference due to mis-specifications of the distribution of unobservables and their statistical relationship with observed explanatory variables, restrictions on parameter values that can not be justified by economic theory, and very demanding computational requirements. More specifically, the project constructs a class of M-estimators, that includes Least-Absolute-Deviations-type (LAD) estimators, and examines their asymptotic properties. The project examines how these estimators, which rely on the assumption of strictly exogenous explanatory variables, can be modified to allow for dynamic feedback from the lagged choice and outcome variables on the current choice and outcome. The second part considers estimation of panel data discrete choice models where the explanatory variable set includes strictly exogenous as well as lagged endogenous variables and unobservable individual-specific ('fixed") effects that can be correlated with the other explanatory variables in an arbitrary way. It is currently not known how to estimate this type of models or whether estimation is even possible. The contribution of the project will be to give conditions under which such models can be estimated, propose estimators and derive their asymptotic properties. ??
