Gaussian estimation of a second order continuous time macroeconometric model of the UK

Abstract

This paper describes the first application to an economy-wide macroeconometric model of recently developed methods for the exact Gaussian estimation of higher order continuous time dynamic models. The new model is formulated as a system of second order differential equations, thus providing a much richer dynamic specification than the predominantly first order continuous time macroeconometric models developed during the last 15 years. It also makes intensive use of economic theory to obtain a parsimonious parametrization, is designed in such a way as to permit a rigorous mathematical investigation of its steady state and asymptotic stability properties, and makes systematic use of the assumption of long-run rational expectations. In addition to the exact Gaussian estimates of the structural parameters, the paper includes the first set of continuous lag distributions derived from estimates that take account of the exact restrictions on the distribution of the discrete data implied by a continuous time model. It also includes the first estimates of the coefficient matrices of the exact discrete model, in its VARMAX form, satisfied by the discrete stock and flow data generated by a higher order continuous time dynamic model.