Modified maximum likelihood estimation of Tobit models with fixed effects: theory and an application to earnings equations

This paper starts from the orthogonalization method proposed by Cox and Reid which is aplied to the Tobit model panel for data with fixed effects. Neyman and Scott showed that, generally, the maximum likelihood estimator is inconsistent (the incidental parameter problem). The methodology explained here recovers the use of the log-likelihood function to solve this problem taking advantage of the time-series dimension of panel data. For the Tobit model we show when is it possible to recover the orthogonal parameters, and study the characteristics of the estimators obtained with simulation methods. Also, an illustration for earnings equations has been performed.