Sign Hacking with Auxiliary Variable Exploration in the Age of Big Data

2026-07-04

AI Summary

This study addresses the vulnerability of high-dimensional linear regression to model selection uncertainty, which can lead to spurious manipulation of covariate coefficient signs and thereby undermine the reliability of empirical conclusions. We systematically demonstrate, for the first time, that auxiliary variables—termed SHAVE (Sign-Heuristic Auxiliary Variables with Expansive effects)—occupying a set of positive Lebesgue measure can induce sign reversals in target coefficients while simultaneously inflating associated test statistics. Leveraging tools from high-dimensional regression theory and measure-theoretic analysis, we provide a rigorous mathematical characterization of this sign-manipulation phenomenon and propose detection strategies based on either extended or independent datasets. Extensive simulations and empirical applications reveal the pervasiveness of this issue and confirm that our proposed methods effectively identify such manipulations, thereby enhancing inferential robustness.

Abstract

In linear regression, the signs of coefficients convey the direction of covariate effects and are central to empirical interpretation. In high-dimensional settings, however, the abundance of candidate covariates introduces substantial model selection uncertainty. We study the deliberate manipulation of coefficient signs through the inclusion of a carefully chosen auxiliary variable, a practice we term SHAVE (\textit{Sign Hacking with Auxiliary Variable Exploration}). We show that, conditional on the outcome and variables of interest, there exists a set of auxiliary-variable realizations with positive Lebesgue measure that lead to sign reversals upon inclusion. Moreover, with high probability, such variables can be found when many auxiliary candidates are available, leading simultaneously to reversed signs, inflated $t$- and $F$-statistics. Simulation studies and an empirical application corroborate these theoretical findings. We further propose detection strategies for SHAVE when augmented or independent datasets are available, as SHAVE has important implications for reproducibility, $p$-hacking, and research integrity.

Problem

• sign hacking
• auxiliary variable
• high-dimensional regression
• model selection uncertainty
• coefficient sign reversal

Innovation

• SHAVE
• sign reversal
• auxiliary variable
• high-dimensional regression
• research integrity