Robustness against incidental parameters

Neyman and Scott (1948) define the incidental parameter problem. In panel data with T observations per individual and unobservable individual-specific effects, the maximum likelihood estimator of the common parameters is in general inconsistent. This paper develops the integrated moment estimator. It shows that the inconsistency of the integrated moment estimator is of a low order, O(T^{-2}), and thereby offers an approximate solution for the incidental parameter problem. The integrated moment estimator allows for exogenous regressors, time dummies and lagged dependent variables and is efficient for an asymptotics in which T increases faster than N^1/3. We adjust the integrated likelihood estimator to allow for general predetermined regressors. The paper also shows that methods that rely on differencing away the individual-specific effects can be viewed as special cases of the integrated moment estimator.