The sensitivity of OLS when the variance matrix is (partially) unknown.

Banerjee, A.N.; Magnus, J.R.

Abstract

We consider the standard linear regression model y=Xβ+u with all standard assumptions, except that the variance matrix is assumed to be σ2Ω(θ), where Ω depends on m unknown parameters Full-size image (<1 K). Our interest lies exclusively in the mean parameters β or Xβ. We introduce a new sensitivity statistic (B1) which is designed to decide whether ŷ (or Full-size image (<1 K)) is sensitive to covariance misspecification. We show that the Durbin–Watson test is inappropriate in this context, because it measures the sensitivity of Full-size image (<1 K) to covariance misspecification. Our results demonstrate that the estimator Full-size image (<1 K) and the predictor ŷ are not very sensitive to covariance misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable.

Citation

Banerjee, A., & Magnus, J. (1999). The sensitivity of OLS when the variance matrix is (partially) unknown. Journal of Econometrics, 92(2), 295-323. https://doi.org/10.1016/s0304-4076%2898%2900093-1

• Journal Article Type: Article
• Publication Date: 1999-10
• Deposit Date: Nov 18, 2014
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 92
• Issue: 2
• Pages: 295-323
• DOI: https://doi.org/10.1016/s0304-4076%2898%2900093-1
• Keywords: Linear regression, Least squares, Autocorrelation, Durbin–Watson test, Sensitivity.
• Public URL: https://durham-repository.worktribe.com/output/1417410