Identification and estimation of semi-parametric censored dynamic panel data models of short time periods

In this paper, we present a semi-parametric identification and estimation method for censored dynamic panel data models of short time periods and their average partial effects with only two periods of data. The proposed method transforms the semi-parametric specification of censored dynamic panel data models into a parametric family of distribution functions of observables without specifying the distribution of the initial condition. Then the censored dynamic panel data models are globally identified under a standard maximum likelihood estimation framework. The identifying assumptions are related to the completeness of the families of known parametric distribution functions corresponding to censored dynamic panel data models. Dynamic tobit models and two-part dynamic regression models satisfy the key assumptions. We propose a sieve maximum likelihood estimator and we investigate the finite sample properties of these sieve-based estimators using Monte Carlo analysis. Our empirical application using the Medical Expenditure Panel Survey shows that individuals consume more health care when their incomes increase, after controlling for past health expenditures.