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

Fixed effects estimators of nonlinear panel models can be severely biased due to the incidental parameters problem. In this paper I find that the most important component of this incidental parameters bias for probit fixed effects estimators of index coefficients is proportional to the true value of these coefficients, using a large-T expansion of the bias. This result allows me to derive a lower bound for this bias, and to show that fixed effects estimates of ratios of coefficients and average marginal effects have zero bias in the absence of heterogeneity and have negligible bias relative to their true values for a wide variety of distributions of regressors and individual effects. 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 significant biases in fixed effects estimates of index coefficients do not contaminate the estimates of marginal effects in static models, estimates of both index coefficients and marginal effects can be severely biased in dynamic models. Improved bias corrected estimators for index coefficients and marginal effects are also proposed for both static and dynamic models