Before revision:  At the second stage, I construct the estimator of the expected value function as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .
After revision:  At the second stage, I plug the first-stage estimates into a moment inequality and solve for the structural parameter. The moment function is presented as the sum of the naive plug-in estimator expected value function of ? and the bias correction term which removes the bias of the naive estimator .