Before revision:  When dealing with very large data sets, we can run the MILP algorithm on only a small subsample and our theoretical results guarantee that the resulting estimator from the k-step correction is equivalent to computing GMM on the full sample . As a result, we can handle massive datasets of millions of observations within seconds. As an empirical illustration, we examine the heterogeneous treatment effect of Job Training Partnership Act (JTPA) using a regression with 13 interaction terms of the treatment variable .
After revision:  When dealing with very large data sets, we can run the MILP algorithm on only a small subsample and our theoretical results guarantee that the resulting estimator from the k-step correction is equivalent to computing GMM on the full sample can be implemented efficiently. Another contribution that is of independent interest is to propose a tuning-free estimation for the Jacobian matrix, whose definition nvolves conditional densities. This Jacobian estimator generalizes bootstrap quantile standard errors and can be efficiently computed via closed-end solutions. We evaluate the performance of the proposal in simulations and an empirical example on the heterogeneous treatment effect of Job Training Partnership Act (JTPA) using a regression with 13 interaction terms of the treatment variable .