The Tobit model with feedback and random effects: A Monte-Carlo study

We study a random effects censored regression model in the context of repeated games. Introducing a feedback variable into the model leads to violation of the strict exogeneity assumption, thus rendering the random effects estimator inconsistent. Using the example of contributions to a public good, we investigate the size of this bias in a Monte-Carlo study. We find that the magnitude of the bias is around one per cent when initial values and individual effects are correlated. The rate of censoring, as well as the size of the groups in which subjects interact, both have an effect on the magnitude of the bias. The coefficients of strictly exogenous, continuous regressors remain unaffected by the endogeneity bias. The size of the endogeneity bias in our model is very small compared to the size of the heterogeneity bias, which occurs when individual heterogeneity is not accounted for in estimation of nonlinear models.