"Maximum Likelihood Estimation of Linear Equation Systems with Auto-regressive Residuals," (with G. C.Chow), Annals of Economic and Social Measurement, 1973.Paper: pdf file
This paper applies Newton's method to solve a set of normal equations when the residuals follow an autoregressive scheme. It is shown that this technique for computing maximum likelihood estimates can be applied to the "seemingly unrelated regression" model. An eight equation quarterly forecasting model of the U.S. economy is then used to illustrate the method described in the paper.
This paper shows for the seemingly unrelated regression case that iterating Zellner's method to convergence produces maximum likelihood estimates. Similarly, in the case in which the error terms are serially correlated, iterating Parks' procedure to convergence produces maximum likelihood estimates. The computational procedure presented in the paper to obtain FIML estimates handles the case of a linear simultaneous equations model with serially correlated errors and linear restrictions on the coefficients. The procedure is used to estimate the money GNP sector in my forecasting model--1971#5. At the time this paper was written a program was available for distribution that used the procedure to compute FIML estimates. See footnote 10 on page 28.