A Distance Covariance-based Estimator

Abstract: This paper introduces an estimator that significantly weakens the relevance condition of conventional instrumental variable (IV) methods, allowing endogenous covariates to be weakly correlated, uncorrelated, or even mean-independent, though not independent of instruments. As a result, the estimator can exploit the maximum number of relevant instruments in any given empirical setting. Identification is feasible without excludability, and the disturbance term does not need to possess finite moments. Identification is achieved under a weak conditional median independence condition on pairwise differences in disturbances, along with mild regularity conditions. Furthermore, the estimator is shown to be consistent and asymptotically normal. The relevance condition required for identification is shown to be testable.