Incidental Parameters Problem: The Case of Gompertz Model

The order of bias of the fixed effects gompertz model is studied, using Monte Carlo approach. Performance criteria are bias and root mean squared errors. For fixed N, bias is found to decrease steadily between T=5 and T=20 but exhibits a mixture of increase and decline afterwards. At each value of T involved, bias steadily decreases with increased value of N. Bias is found to be at most 123%, due to the combination of minimum of each of N and T involved. Decrease in order of bias is found to be more definite with increased N at fixed T than with increased T at fixed N.

BOOTSTRAP AND k-STEP BOOTSTRAP BIAS CORRECTIONS FOR THE FIXED EFFECTS ESTIMATOR IN NONLINEAR PANEL DATA MODELS

Because of the incidental parameters problem, the fixed effects maximum likelihood estimator in a nonlinear panel data model is in general inconsistent when the time series length T is short and fixed. Even if T approaches infinity but at a rate not faster than the cross sectional sample size n, the fixed effects estimator is still asymptotically biased. This paper proposes using the standard bootstrap and k-step bootstrap to correct the bias. We establish the asymptotic validity of the bootstrap bias corrections for both model parameters and average marginal effects. Our results apply to static models as well as some dynamic Markov models. Monte Carlo simulations show that our procedures are effective in reducing the bias of the fixed effects estimator and improving the coverage accuracy of the associated confidence interval.