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 econometrician wants to estimate — the coefficient of the lagged endogenous variable in the case of an autoregressive error component (AREC) model, for instance, — and nuisance parameters — most of the second-order terms in an AREC model. We demonstrate that the elimination of such nuisance parameters using their empirical counterpart does not entail an efficiency loss when only the parameters of interest are estimated. Applications of our results to both autoregressive error component models and time-varying individual fixed effects models are discussed at length. They show the nature of the efficiency losses when some orthogonality conditions are left aside.