PARAMETERS OF INTEREST, NUISANCE PARAMETERS AND ORTHOGONALITY CONDITIONS - AN APPLICATION TO AUTOREGRESSIVE ERROR COMPONENT MODELS

In general, when one considers a set of orthogonality conditions, the parameters can be divided into parameters of interest that the econome trician wants to estimate - the coefficient of the lagged endogenous v ariable in the case of an autoregressive error component (AREC) model, for instance, - and nuisance parameters - most of the second-order te rms in an AREC model. We demonstrate that the elimination of such nuis ance parameters using their empirical counterpart does not entail an e fficiency loss when only the parameters of interest are estimated. App lications of our results to both autoregressive error component models and time-varying individual fixed effects models are discussed at len gth. They show the nature of the efficiency losses when some orthogona lity conditions are left aside. (C) 1997 Elsevier Science S.A.