Semi-parametric estimation of non-separable models: a minimum distance from independence approach

This paper studies non-separable structural models that are of the form Y = m(alpha)(X,U) with U uniform on (0, 1) in which m(alpha) is a known real function parametrized by a structural parameter alpha. We study the case in which alpha contains a finite dimensional component theta and an infinite dimensional component h. We assume that the true value alpha(0) is identified by the restriction U perpendicular to X. Our proposal is to estimate alpha(0) by a minimum distance from independence (MDI) criterion. We show that: (a) our estimator for h(0) is consistent and we obtain rates of convergence and (b) the estimator for theta(0) is root n consistent and asymptotically normally distributed.