Instrumental Variable Estimation Based on Mean

We propose a general estimation principle based on the assumption that instrumental variables (IV) do not explain the error term in a structural equation. The estimators based on this principle is independent of the normalization constraint, unlike the standard IV estimators such as the two-stage least squares estimator. Using the new principle, we propose the L1 IV estimator, which is an IV estimation counterpart of the least absolute deviation estimator. We investigate the asymptotic properties of this estimator, and propose a consistent estimator of its asymptotic covariance matrix and a consistent speciication test based the L1 IV estimator. We also discuss the identiiability in L1 IV estimation. The author is grateful to Professor Curt T. McMullen, who kindly provided a sketch of the proof of Lemma 4.1 in personal communications.