HAR Inference: Recommendations for Practice

Eben Lazarus, Daniel J. Lewis, James H. Stock, Mark W. Watson

Research output: Contribution to journalComment/debate

7 Scopus citations

Abstract

The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time series regression. This literature finds that using a larger-than-usual truncation parameter to estimate the long-run variance, combined with Kiefer-Vogelsang (2002, 2005) fixed-b critical values, can substantially reduce size distortions, at only a modest cost in (size-adjusted) power. Empirical practice, however, has not kept up. This article therefore draws on the post-Newey West/Andrews literature to make concrete recommendations for HAR inference. We derive truncation parameter rules that choose a point on the size-power tradeoff to minimize a loss function. If Newey-West tests are used, we recommend the truncation parameter rule S = 1.3T1/2 and (nonstandard) fixed-b critical values. For tests of a single restriction, we find advantages to using the equal-weighted cosine (EWC) test, where the long run variance is estimated by projections onto Type II cosines, using ν = 0.4T2/3 cosine terms; for this test, fixed-b critical values are, conveniently, tν or F. We assess these rules using first an ARMA/GARCH Monte Carlo design, then a dynamic factor model design estimated using a 207 quarterly U.S. macroeconomic time series.

Original languageEnglish (US)
Pages (from-to)541-559
Number of pages19
JournalJournal of Business and Economic Statistics
Volume36
Issue number4
DOIs
StatePublished - Oct 2 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics
  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Statistics, Probability and Uncertainty

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