Is Newey–West optimal among first-order kernels?

Thomas Kolokotrones, James H. Stock and Christopher D. Walker

Journal of Econometrics, 2024, vol. 240, issue 2

Abstract: Newey–West (1987) standard errors are the dominant standard errors used for heteroskedasticity and autocorrelation robust (HAR) inference in time series regression. The Newey–West estimator uses the Bartlett kernel, which is a first-order kernel, meaning that its characteristic exponent, q, is equal to 1, where q is defined as the largest value of r for which the quantity k[r](0)=limt→0|t|−r(k(0)−k(t)) is defined and finite. This raises the apparently uninvestigated question of whether the Bartlett kernel is optimal among first-order kernels. We demonstrate that, for q<2, there is no optimal qth-order kernel for HAR testing in the Gaussian location model or for minimizing the MSE in spectral density estimation. In fact, for any q<2, the space of qth-order positive-semidefinite kernels is not closed and, moreover, all continuous qth-order kernels can be decomposed into a weighted sum of qth and second-order kernels, which suggests that there is no meaningful notion of ‘pure’ qth-order kernels for q<2. Nevertheless, it is possible to rank any given collection of qth-order kernels using the functional Iq[k]=k[q](0)1/q∫k2(t)dt with smaller values corresponding to better asymptotic performance. We examine the value of Iq[k] for a wide variety of first-order estimators and find that none improve upon the Bartlett kernel. These comparisons provide additional justification for the continued use of the Newey–West estimator with testing-optimal smoothing parameters and fixed-b critical values despite the lack of optimality of Bartlett among first-order kernels.

Keywords: Heteroskedasticity- and autocorrelation-robust estimation; HAR; Long-run variance estimator; Kernel (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407623000301
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:240:y:2024:i:2:s0304407623000301

DOI: 10.1016/j.jeconom.2022.12.013

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().