Before revision:  Based on the characterization of this treatment parameter as a weighted average derivative (Heckman and Vytlacil, 2001, 2005, 2007), we apply the methods and theory of average derivative estimation to the framework of the policy-relevant treatment effects. Our proposed method yields point estimates with valid standard errors. Simulation studies confirm our theoretical results .
After revision:  These preliminary estimators can affect the asymptotic distribution of the PRTE estimator in complicated and intractable manners. In this light, we propose an orthogonal score for double debiased estimation of the PRTE, whereby the asymptotic distribution of the PRTE estimator is obtained without any influence of preliminary parameter estimators as far as they satisfy mild requirements of convergence rates. To our knowledge, our work is the first to develop limit distribution theories for inference about the PRTE .