Linear econometric models in a limited information framework

Abstract

A simultaneous econometric model is named as incomplete when the number of the structural equations is less than the number of the endogenous variables. One usual way to make this type of model statistically tractable is that of adding an adequate number of equations in unconstrained reduced form in such a way to "complete" it. In this paper the statistical bases of this type of models are analysed. In particular the hypotheses, implicit to their text-book formulation, are carefully examined. Following Engle, Hendry and Richard (1983), the structural equations are defined as a set of linear constraints on the vector of the means of a given multivariate conditional distribution. As in Florens, Mouchart and Richard (1979), three forms of the model are considered the abstract one, the implicit one and the explicit one. By emphasizing the choice of the model parametrization, the treatment of the incidental parameters present in the model is studied. In particular the use either of the erogeneity assumptions for their elimination or of the instrumental variables for their modelisation is carefully examined.