Estimation of Structural Parameters and Marginal Effects in Binary Choice Panel Data Models with Fixed Effects

Fixed e®ects estimates of structural parameters in nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper I show that the most important com- ponent of this incidental parameters bias for probit ¯xed e®ects estimators of index coe±cients is proportional to the true parameter value, using a large-T expansion of the bias. This result allows me to derive a lower bound for this bias, and to show that ¯xed e®ects estimates of ratios of coe±cients and average marginal e®ects have zero bias in the absence of heterogeneity and have negligible bias relative to their true values for a wide range of distributions of regressors and individual e®ects. Numerical examples suggest that this small bias property also holds for logit and linear probability models, and for exogenous variables in dynamic binary choice models. An empirical analysis of female labor force participation using data from the PSID shows that whereas the signi¯cant biases in ¯xed e®ects estimates of model parameters do not contami- nate the estimates of marginal e®ects in static models, estimates of both index coe±cients and marginal e®ects can be severely biased in dynamic models. Improved bias corrected estimators for index coe±cients and marginal e®ects are also proposed for both static and dynamic models.