Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model

Abstract

The maximum likelihood estimator (MLE) in nonlinear panel data models with fixed effects is widely understood (with a few exceptions) to be biased and inconsistent when T, the length of the panel, is small and fixed. However, there is surprisingly little theoretical or empirical evidence on the behavior of the estimator on which to base this conclusion. The received studies have focused almost exclusively on coefficient estimation in two binary choice models, the probit and logit models. In this note, we use Monte Carlo methods to examine the behavior of the MLE of the fixed effects tobit model. We find that the estimator's behavior is quite unlike that of the estimators of the binary choice models. Among our findings are that the location coefficients in the tobit model, unlike those in the probit and logit models, are unaffected by the “incidental parameters problem.” But, a surprising result related to the disturbance variance emerges instead – the finite sample bias appears here rather than in the slopes. This has implications for estimation of marginal effects and asymptotic standard errors, which are also examined in this paper. The effects are also examined for the probit and truncated regression models, extending the range of received results in the first of these beyond the widely cited biases in the coefficient estimators.