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"Maximum Likelihood Estimation of Linear Equation Systems with
Auto-regressive Residuals," (with G. C.Chow), Annals of Economic
and Social Measurement, January 1973, 17-28.
pdf file (733KB).
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
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.