A Distance Covariance-based Estimator

Abstract

This paper proposes an estimator that relaxes the conventional relevance condition in instrumental variable (IV) analyses. The method allows endogenous covariates to be weakly correlated, uncorrelated, or even mean-independent -- though not independent -- of the instruments, enabling the use of the maximal set of relevant instruments in a given application. Identification is attainable without exclusion restrictions and without finite-moment assumptions on the disturbance term. Under either of two non-nested exogeneity conditions, combined with mild regularity conditions, the parameter of interest is identified. The estimator is shown to be consistent and asymptotically normal, and the relaxed relevance condition required for identification is testable.