Simulation-based estimation of Tobit model with random effects

The estimation of limited dependent variable panel data models usually involves objective functions in which integrals appear without a closed form solution: this is the case of the panel data Tobit model with random effects. Recently, simulation methods have shown to be useful in the inference process, as they offer methods to approximate such integrals (Laroque, Salanie, 1989; Gouri´eroux, Monfort, 1991, 1993; Hajivassiliou, McFadden, 1998; Mealli, Rampichini, 1999; Inkmann, 2000). Although the asymptotic performances of such methods are known and their application has been successfully undertaken, more precise ideas on their finite sample performance and computational efficiency is still needed. In this paper we propose to use the method of indirect inference, using different auxiliary models, and the simulated maximum likelihood to estimate these models. We use a panel data Tobit model with a simple correlation structure in the unobservables (i.e. a one-factor structure), but the model could be easily extended. Using both simulated and real data, we show the perfomances of the proposed methods in finite samples. The application on real data is concerned with a model of female labour supply.