Instrumental variable estimation based on conditional median restriction

We develop a method, named the L1 IV estimator, to estimate structural equations based on the conditional median restriction imposed on the error terms. We study its asymptotic behavior and show how to estimate its asymptotic covariance matrix. We also discuss the point identification in the L1 IV estimation and propose an over-identifying restriction test. We further demonstrate the performance of the L1 IV estimator in comparison with the familiar two-stage least squares estimator. The proposed method is applied to estimate the labor supply and wage offer functions for working, married women.