Semiparametric Estimation of Regression Models for Panel Data

Abstract

Linear models with error components are widely used to analyse panel data. Some applications of these models require knowledge of the probability densities of the error components. Existing methods handle this requirement by assuming that the densities belong to known parametric families of distributions (typically the normal distribution). This paper shows how to carry out nonparametric estimation of the densities of the error components, thereby avoiding the assumption that the densities belong to known parametric families. The nonparametric estimators are applied to an earnings model using data from the Current Population Survey. The model's transitory error component is not normally distributed. Use of the nonparametric density estimators yields estimates of the probability that individuals with low earnings will become high earners in the future that are much lower than the estimates obtained under the assumption of normally distributed error components.