Adaptive Econometric Inference under Unknown Dependence: Contrast-Local Validity

Abstract

Empirical conclusions can depend on how researchers model dependence when constructing standard errors. We develop contrast-local validity, which asks whether a covariance restriction is accurate for the particular coefficient or weighted contrast being reported, even when the restriction is globally misspecified. The method tests target-specific covariance contamination, compares numerically certified structured corrections with an unrestricted benchmark, and adapts inference to the economic target. In a separate growing-block benchmark, valid structure achieves an optimal faster rate for estimating the target variance, while any globally misspecified covariance approximation must fail for some contrast. In a Fama--French calibration where validity is imposed, the feasible selector preserves nominal coverage and reduces variance-estimation root mean squared error by 39 percent. A publicly available FHFA house-price application illustrates target-specific verdicts across regional exposures. Detectability and coverage-risk analyses show when non-rejection is informative and when unrestricted inference should remain primary.