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Prof. Geert Dhaene

KU Leuven, Belgium

Authors: Geert Dhaene, Koen Jochmans, Martin Weidner

Abstract: In many panel data models, fixed effects typically lead to an incidental parameter problem: maximum likelihood estimation of the model’s common parameters (e.g., common slope or variance parameters) is often biased/inconsistent as the number of cross-sectional units grows large while the number of time periods is fixed (Neyman and Scott 1948). I will discuss two methods to correct for incidental parameter bias. Their power lies in the fact that they can be iterated. (1) The first method, called approximate functional differencing, has a Bayesian flavor. It uses the posterior predictive density to construct a q-th order bias corrected score function, starting from an initially chosen (biased) score function. In the limit as q goes to infinity, the method is equivalent to Bonhomme’s (2012) method of functional differencing in point-identified models. When point identification fails, the limit remains well defined and yields estimates with very small bias. (2) The second method is entirely frequentist. Starting from the (biased) profile score function, it constructs a bias corrected score function by calculating the bias as a function of the incidental parameters and using maximum likelihood estimates thereof as plug-in estimates, and it iterates these steps. In several models, it is found that the first-order bias corrected profile score function is already exactly unbiased, hence resolving the incidental parameter problem. In other models, the infinitely iterated bias correction leads to estimates with very small bias.

The talk combines two related papers:  Profile-Score Adjustments For Incidental-Parameter Problems
                                                               Approximate functional differencing