Multivariate nonparametric estimation on censored panel data

Heckman and Singer (1984) argued that in typical longitudinal analyses, standard treatments of heterogeneity components result in incorrect parameterization of the duration model. As a consequence, estimation bias is not limited to duration dependence, but extends to the structural parameters as well. They show that a nonparametric mass point approach to marginal likelihood estimation is possible due to Lindsay's characterization of the mixture density. However, their method makes the strong assumption that observed variables are uncorrelated with unobserved heterogeneity and that a small number of mass points can represent the sample distribution of unobservables. In their Monte Carlo study, the mass point method failed to estimate the underlying heterogeneity distribution even though a simple unimodal distribution was used for contamination.I propose two competing methods to deal with this issue. Maximum Penalized Likelihood Estimation (MPLE) and Simulation Based Estimation (SIMEST). MPLE is an estimator which is based on likelihood inference conditional on unobserved heterogeneity. In order to estimate conditional densities from the mixture joint density, heterogeneity is smoothed out while maximizing goodness of fit. MPLE is an application of spline function. On the other hand, SIMEST is based on axioms which presumably govern the stochastic process. Therefore noises which could not be explained by the axioms are regarded as heterogeneity. SIMEST is computationally efficient for the large panel data analysis because it can avoid closed-form expressions for the density function. Monte Carlo experimental results indicate that these methods are quite attractive vis-a-vis the Heckman and Singer estimator.