Dummy Endogenous Treatment Effect Estimation Using High-Dimensional Instrumental Variables

Dummy endogenous variables are commonly encountered in program evaluations using observational data. Motivated by the increasing availability of rich micro data, we develop a two-stage approach to estimate the dummy endogenous treatment effect using high-dimensional instrumental variables (IV). In the first stage, instead of using a conventional linear reduced form regression to approximate the optimal instrument, we propose a penalized logistic reduced form model to accommodate both the binary nature of the endogenous treatment and the high-dimensionality of instrumental variables. In the second stage, we replace the original treatment variable by its estimated propensity score and run a least squares regression to obtain a penalized Logistic-regression Instrumental Variables Estimator (LIVE). Moreover, to deal with the structural equation model uncertainty, we further propose a double selection (DS) estimator, called DS-LIVE, for selecting both control variables and IVs. We theoretically show that the proposed LIVE and DS-LIVE are both root-n consistent to the true treatment effect and asymptotically normal. The LIVE also achieves the semiparametric efficiency bound under the homoscedasticity condition. Monte Carlo simulations demonstrate that the LIVE and DS-LIVE perform more efficiently than the existing IV estimators for the endogenous treatment effects. We also demonstrate the usefulness of the proposed methods using two empirical case studies. We investigate whether the Olympic Games could facilitate the host nation's economic growth and whether teachers' home visits could enhance students' academic performances