Fixed Effects Estimation in Panel Nonlinear Fractional Response Models

Estimations of nonlinear panel models that include individual specific fixed effects are complicated by the incidental parameters problem, that is, the asymptotic bias in the estimation of typical fixed effects panel models generally results in inconsistent estimates. In this paper, I characterize the leading term of a large-T expansion of the biases in the nonlinear least square estimator (NLSE) and estimators of the average partial effects in panel fractional response models. The resulting estimator after analytical bias correction is robust to the incidental parameters bias and reduces the bias order from O(T−1) to O(T−2). I also examine the finite sample performance of the proposed estimator using a new data generating process in which panel fractional response variables are collapsed from repeated, clustered cross-sectional binary probit choices. A proof showing the generated data satisfies the identification assumption at the cluster level has been given. Simulation results suggest that, in the static case, the bias corrected estimator performs comparably to the quasi-maximum likelihood estimator (QMLE), which is the standard approach in the literature, for 8 or more periods, while in the dynamic case, the bias corrected estimators are substantially superior to those QMLE’s.Fractional responses, Panel Data, Unobserved effects, Probit, Partial effects, Bias, Incidental parameters problem, Fixed effects, Bias Correction