It is also perhaps worth considering the case in which the alternative model y Zy + co contains the same regressors as the true model (i.e., Z X). Then the above proof shows that the probability limit of the estimated error variance is smaller when the true value of p is used to perform the Orcutt transformation than when any other value po is used. (This, in fact, constitutes a relatively simple proof of the consistency of the maximum likelihood estimate of p, for a correctly specified model.)

George C. Bitros, Harry H. Kelejian, On the Variability of the Replacement Investment Capital Stock Ratio: Some Evidence from Capital Scrappage, The Review of Economics and Statistics, Vol. 56, No. 3 (Aug., 1974), pp. 270-278

Gordon C. Rausser, J. W. Freebairn, Estimation of Policy Preference Functions: An Application to U.S. Beef Import Quotas, The Review of Economics and Statistics, Vol. 56, No. 4 (Nov., 1974), pp. 437-449