The bias of OLS, GLS, and ZEF estimators in dynamic seemingly unrelated regression models
type: Item
instance of: scholarly article
title: The bias of OLS, GLS, and ZEF estimators in dynamic seemingly unrelated regression models
zbMATH Open document ID: 0852.62097
DOI: 10.1016/0304-4076(94)01670-U
author: Jan F. Kiviet
author: Bernhard Schipp
author: G. D. A. Phillips
published in: Journal of Econometrics
publication date: 1996-11-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 803357
zbMATH Keywords: asymptotic approximations
zbMATH Keywords: bias correction
zbMATH Keywords: seemingly unrelated regression equations model
zbMATH Keywords: two-stage Aitken estimator
zbMATH Keywords: Monte Carlo experiments
zbMATH Keywords: two-equation dynamic model
zbMATH Keywords: small-sample estimation bias
zbMATH Keywords: bias reduction
zbMATH Keywords: mean squared error
zbMATH Keywords: bias approximations
MaRDI profile type: Publication
cites work: The Unbiasedness of Zellner's Seemingly Unrelated Regression Equations Estimators
cites work: The Bias of the Two-Stage Least Squares Estimator
cites work: Q4040694
cites work: Estimation of seemingly unrelated regression with lagged dependent variables and autocorrelated errors
cites work: An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias
full work available at URL: 0304-4076(94)01670-u
OpenAlex ID: W2149262808
description: scientific article; zbMATH DE number 803357