Individual and time effects in nonlinear panel models with large N, T

Fixed e ffects estimators of nonlinear panel data models can be severely biased because of the well-known incidental parameter problem. We develop analytical and jackknife bias corrections for nonlinear models with both individual and time e ffects. Under asymptotic sequences where the time-dimension (T) grows with the cross-sectional dimension (N), the time eff ects introduce additional incidental parameter bias. As the existing bias corrections apply to models with only individual e ffects, we derive the appropriate corrections for the case when both e ffects are present. The basis for the corrections are general asymptotic expansions of fixed eff ects estimators with incidental parameters in multiple dimensions. We apply the expansions to conditional maximum likelihood estimators with concave objective functions in parameters for panel models with additive individual and time eff ects. These estimators cover fi xed e ects estimators of the most popular limited dependent variable models such as logit, probit, ordered probit, Tobit and Poisson models. Our analysis therefore extends the use of large-T bias adjustments to an important class of models. We also analyze the properties of fixed eff ects estimators of functions of the data, parameters and individual and time eff ects including average partial effects. Here, we uncover that the incidental parameter bias is asymptotically of second order, because the rate of the convergence of the fixed e ffects estimators is slower for average partial eff ects than for model parameters. The bias corrections are still useful to improve fi nite-sample properties.