Semi-Nonparametric Estimation of Binary Choice Models Using Panel Data: An Application to the Innovative Activity of German Firms

Abstract

In the last few years panel data have become an increasingly popular data source among microeconometricians. Panel data sets allow the estimation and testing of more realistic behavioral models. Which could not be identified using a single cross section or a time series data set alone. More applied econometricians would agree that for linear models the grains from using panel data by far linear outweigh the additional complexity involved by coping with heteroscedasticity and autocorrelation problems simultaneously. For models with qualitative or limmited dependent variables the use of panel data introduces a nimber of additional theoretical and computational problems. In the most usual situation of a short time series of cross sections with a large number of individuals observatuion, convensional maximum likelihood estimation of models with individual effects leads to inconssitent parameter estimates if the individual effects are assumed to be fixed, becauseof the corrresponding incidental parameter problem: The Number of parameters to be estimated increases with the number of individual observations⁽¹⁾. On the other hand, for random effects additional distributional assumptions are required, as well as the evaluation of multivariate distribution, since the observations for a single individual over time are no longer independent.

Support from the Deutsche Forschungsgemeinschaft is gratefully acknowledged. We also wish to thank our colleagues in Mannheim, as well as three anonymous referees, for helpful comments.