Econometrica Vol. 89 No. 5 2021
The Size‐Power Tradeoff in HAR Inference
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.
- DOI
- 10.3982/ecta15404
- Volume
- 89
- Issue
- 5
- Pages
- 2497-2516
- Language
- en
- Sources
- bibtex:phds-export.bib openalex crossref