Econometrica: Sep 2021, Volume 89, Issue 5

The Size-Power Tradeoff in HAR Inference

https://doi.org/10.3982/ECTA15404
p. 2497-2516

Eben Lazarus, Daniel J. Lewis, James H. Stock

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.



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