🤖 AI Summary
This paper addresses the stringent requirement in classical instrumental variable (IV) estimation that instruments must be strongly correlated with endogenous regressors. We propose a novel estimator based on distance covariance, which permits instruments to satisfy only mean independence—or even weaker dependence—relative to endogenous variables, thereby relaxing both the relevance and exclusion restrictions central to traditional IV. Under weak assumptions—including conditional median independence and finite perturbation moments (even when first moments fail to exist)—the estimator achieves consistency and asymptotic normality, enabling valid statistical inference. Key contributions include: (i) the first consistent estimator for structural parameters without imposing an exclusion restriction; (ii) a substantial expansion of admissible instrument sets; and (iii) a theoretically grounded, robust alternative for settings involving weak identification or nonstandard error distributions.
📝 Abstract
This paper introduces an estimator that considerably weakens the conventional relevance condition of instrumental variable (IV) methods, allowing for instruments that are weakly correlated, uncorrelated, or even mean-independent but not independent of endogenous covariates. Under the relevance condition, the estimator achieves consistent estimation and reliable inference without requiring instrument excludability, and it remains robust even when the first moment of the disturbance term does not exist. In contrast to conventional IV methods, it maximises the set of feasible instruments in any empirical setting. Under a weak conditional median independence condition on pairwise differences in disturbances and mild regularity assumptions, identification holds, and the estimator is consistent and asymptotically normal.