A Penalty Function Approach to Bias Reduction in Non-linear Panel Models with Fixed Effects

In this paper, we consider estimation of nonlinear panel data models that include individual specific fixed effects. Estimation of these models is complicated by the incidental parameters problem; that is, noise in the estimation of the fixed effects when the time dimension is short generally results in inconsistent estimates of the common parameters due to the nonlinearity of the problem. We present a penalty for the objective function that reduces the bias in the resulting point estimates. The penalty function involves only cross-products of scores and the hessian matrix and so is simple to construct in practice and requires no modification for models with multiple individual specific parameters. We present simulation results that suggest that the penalized optimization approach may substantially reduce the bias in nonlinear fixed effects models. We illustrate our approach in an empirical study of insider trading activity, where we estimate a dynamic ordered probit model with multiple firm specific effects.