Han’s maximum rank correlation (MRC) estimator is shown to be√ n-consistent and asymptotically normal. The proof rests on a general method for determining the asymptotic distribution of a maximization estimator, a simple U-statistic decomposition, and a uniform bound for degenerate U-processes. A consistent estimator of the asymptotic covari-ance matrix is provided, along with a result giving the explicit form of this matrix for any model within the scope of the MRC estimator. The latter result is applied to the binary choice model, and it is found that the MRC estimator does not achieve the semiparametric efficiency bound.

We develop a √n-consistent and asymptotically normal estimator of the parameters (regression coefficients and threshold points) of a semiparametric ordered response model under the assumption of independence of errors and regressors. The independence assumption implies shift restrictions allowing identification of threshold points up to location and scale. The estimator is useful in various applications, particularly in new product demand forecasting from survey data subject to systematic misreporting. We apply the estimator to assess exaggeration bias in survey data on demand for a new telecommunications service.

We consider the identification of counterfactual distributions and treatment effects when the outcome variables and conditioning covariates are observed in separate datasets. Under the standard selection on observables assumption, the counterfactual distributions and treatment effect parameters are no longer point identified. However, applying the classical monotone re-arrangement inequality, we derive sharp bounds on the counterfactual distributions and policy parameters of interest.