The Size-Power Tradeoff in HAR Inference
Eben Lazarus, Daniel J. Lewis, James H. Stock
Econometrica · 2021 · Volume 89 · Issue 5
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-bdistribution istorF. 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 withtandFcritical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.
Keywords
Heteroskedasticity- and autocorrelation-robust estimation, HAR, long-run variance estimator
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