Fixed effects estimates of structural parameters in nonlinear panel models can be severely bi-ased due to the incidental parameters problem. In this paper I show that the first term in a large-T expansion of the incidental parameters bias for probit fixed effects estimators of index coefficients is proportional to the true parameter value for general distributions of regressors and individual effects. This result allows me to derive a lower bound for the bias that depends only on the number of time periods of the panel. Proportionality is also used to show that the biases of ratios of coefficients and average marginal effects are identically zero in the absence of heterogeneity. Moreover, for a wide range of distributions of regressors and individual effects, numerical examples show that these biases are also very small. These results help explain pre-vious Monte Carlo evidence for probit fixed effects estimates of index coefficients and marginal effects. Additional Monte Carlo examples suggest that the small bias property for fixed effects estimators of marginal effects holds for logit and linear probability models, and for the effects of exogenous variables in dynamic discrete choice models. The properties of logit and probit fixed effects estimates of model parameters and marginal effects are illustrated through an analysis of female labor force participation using data from the PSID. The results suggest that the sig-nificant biases in fixed effects estimates of model parameters do not contaminate the estimates of marginal effects in static models
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