The Size of Dynamic Econometric Models

Abstract

This paper investigates the performances of dynamic econometric models in relationship to their size. More precisely, the central issue addressed in this paper is whether there exists a procedure that systematically associates with every large-scale model a small-scale model that constitutes a reasonably good approximation of the large-scale model. Such a procedure is shown to exist for both endogenous and exogenous variables. This result is applied to show that a model with approximately twenty endogenous and four hundred exogenous variables can do almost as well as the current models with thousands of variables. This result also implies that a necessary condition for small models of twenty to thirty variables to perform satisfactorily is that only regular patterns of variations for the exogenous variables be considered. THE DEVELOPMENT OF HIGH-SPEED POWERFUL COMPUTERS has enabled econometricians and model makers to design operational large-scale models, the idea being that the complexity of reality is better described by models with the largest feasible number of unknowns and equations than by smaller size models. Nevertheless, the costs involved in operating large-scale models combined with their intrinsic complexity has led many econometricians to favor, when dealing with specific questions, the use of smaller size models which can be operated with comparatively less difficulties. This paper investigates the relationships that can be established between the size of a dynamic econometric model, i.e. the number of its endogenous and exogenous variables, and its accuracy through time. This paper also addresses another question related to the general theme of the size of econometric models, namely the existence of procedures that can systematically associate with every large-scale model a small-scale model that provides a reasonably good approximation of the large-scale model. An important feature of the analysis developed in this paper is the focus put on the local point of view and on the consequences that can be derived from the local approach. Local here means that only the behavior of the model in small neighborhoods of suitably chosen points belonging to some, possibly largedimensional, Euclidean space is considered. Though the validity of the local point of view might be questioned when dealing with the most general problems, it seems to be particularly well-suited to the current practice of econometric modelling. The strength and the main interest of the local point of view is that it enables one to define concepts of approximation up to arbitrary orders that apply to econometric models, approximations being taken here in a sense that is