Deriving the Information Bounds for Nonlinear Panel Data Models with Fixed Effects

This paper studies the asymptotic efficiency of estimates in nonlinear panel data models with fixed effects when both the cross-sectional sample size and the length of time series tend to infinity. The efficiency bounds for regular estimators are derived using the infinite-dimensional convolution theorem by van der Varrt and Wellner (1996). It should be noted that the number of fixed effects increases with the sample size, so they constitute an infinite-dimensional nuisance parameter. The presence of fixed effects makes our derivation of the efficiency bounds non-trivial, and the techniques to overcome the difficulties caused by fixed effects will be discussed in detail. Our results include the efficiency bounds for models containing unknown functions (for instance, a distribution function of error terms). We apply our results to show that the bias-corrected fixed effects estimator of Hahn and Newey (2004) is asymptotically efficient.