The paper shows that conventional HAC estimators are conservative for design-based GMM in finite-history time series and that projection adjustments using predetermined covariates can yield tighter conservative bounds under long-run orthogonality.
Proposition 9.Consider the fixed-weight estimator obtained by settingbAN ≡A in the sample criterion
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Design-Based Inference for Time-Series GMM
The paper shows that conventional HAC estimators are conservative for design-based GMM in finite-history time series and that projection adjustments using predetermined covariates can yield tighter conservative bounds under long-run orthogonality.