The bias of OLS, GLS, and ZEF estimators in dynamic seemingly unrelated regression models
Since the seminal paper by \textit{A. Zellner} [J. Am. Stat. Assoc. 57, 348-368 (1962; Zbl 0113.34902)] on the efficient estimation of a seemingly unrelated regression equations model, a great many further contributions have been published in a wide variety of journals. One important strand of this literature employs asymptotic expansions to derive large-sample approximations to the moments of estimators, although in the case of only exogenous regressors and jointly normal disturbances it is possible to deduce straightforwardly that the Zellner efficient (ZEF) two-stage Aitken estimator is exactly unbiased. In this paper the properties of bias-corrected and uncorrected versions of the ordinary least squares (OLS) and ZEF estimators are examined and compared through the use of Monte Carlo experiments in a simple two-equations dynamic model with normally and serially independent disturbances. In contrast to the findings of \textit{J. Kmenta} and \textit{R. F. Gilbert} [ibid. 63, 1180-1200 (1968)] and \textit{G. H. K. Wang} et al. [J. Stat. Comput. Simulation 10, 133-146 (1980; Zbl 0424.62081)] our results show that small-sample estimation bias may be quite serious. We find that the methods of bias reduction explored here will usually lead to estimators with a smaller bias and often the mean squared error is reduced as well. The plan of the paper is as follows. In Section 2 the model and notation are introduced. In Section 3 bias approximations to \(O(T^{-1})\) are presented for the OLS, GLS, and, hence, ZEF estimators. In Section 4 the design of the Monte Carlo experiments is discussed, while Section 5 gives an analysis of the Monte Carlo results. Finally, some concluding remarks in Section 6 complete the paper.
seemingly unrelated regression equations model
scientific article; zbMATH DE number 803357