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 construct the estimator of the expected value function as the sum of two components, where the first one expresses the equilibrium assumption and the second one is a bias correction term which removes the bias of the naive estimator .