FIML estimation of dynamic econometric systems from inconsistent data - PLOEG, F. VAN DER (International journal of systems science, 1985)
Economic data are typically inconsistent, contain measurement errors and are sometimes unavailable. The paper therefore proposes a bayesian and a generalized least-squares procedure for adjusting the data to satisfy accounting identities, to incorporate subjective views and to recover unobserved data. The resulting posterior observations may be used to estimate the parameters of a multivariate ARMAX model of the economy by maximizing the appropriate log-likelihood criterion subject to the constraints of the Kalman-Bucy filter (generating the optimal estimates of the states of the economy). The paper proposes a generalized reduced-gradient algorithm, based on a state space realization of the ARMAX model, for the estimation procedure, and discusses a number of special cases where the filter need not be implemented. Extensions to the estimation of continuous-time or non-linear models from noisy data are also provided. When the original data contain systematic errors time-decomposition is not valid, hence the paper develops a final form estimation procedure for the general case. The paper reports applications of the proposed techniques to U.K. data.