Instrumental variable estimation based on conditional median restriction

We develop a method, named the L 1 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 L 1 IV estimation and propose an over-identifying restriction test. We further demonstrate the performance of the L 1 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.