The Size‐Power Tradeoff in HAR Inference. Issue 5 (27th September 2021)

• Record Type: Journal Article
• Authors: Lazarus, Eben; Lewis, Daniel J.; Stock, James H.
• Is Part Of: Econometrica. Volume 89:Issue 5(2021)
• Page Start: 2497
• Page End: 2516
• Publication Date: 2021-09-27
• Subjects: Heteroskedasticity‐ and autocorrelation‐robust estimation -- HAR -- long‐run variance estimator; Econometrics -- Periodicals; Economics, Mathematical -- Periodicals; Economics -- Periodicals; Économétrie -- Périodiques; Mathématiques économiques -- Périodiques; Économie politique -- Périodiques; 330.05
• DOI: 10.3982/ECTA15404
• Languages: English
• ISSNs: 0012-9682

Abstract

Abstract : Heteroskedasticity‐ and autocorrelation‐robust (HAR) inference in time series regression typically involves kernel estimation of the long‐run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test's null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher‐order expansions, we provide a unified size‐power frontier for both kernel and weighted orthonormal series tests using nonstandard "fixed‐ b " critical values. We also provide a frontier for the subset of these tests for which the fixed‐ b distribution is t or F . These frontiers are respectively achieved by the QS kernel and equal‐weighted periodogram. The frontiers have simple closed‐form expressions, which show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.