A correction function approach to solve the incidental parameter problem

Following Lancaster (2002), we propose a strategy to solve the incidental parameter problem. The method is demonstrated under a simple panel Poisson count model. We also extend the strategy to accomodate cases when information orthogonality is unavailable, such as the linear AR(p) panel model. For the AR(p) model, there exists a correction function to fix the incidental parameter problem when the model is stationary with strictly exogenous regressors. MCMC algorithms are developed for parameter estimation and model comparison. The results based on the simulated data sets suggest that our method could achieve consistency in both parameter estimation and model selection