Estimating Endogenous Treatment Effect Using High-Dimensional Instruments with an Application to the Olympic Effect

Endogenous treatments are commonly encountered in program evaluations using observational data where the selection-on-observables assumption does not hold. In this paper, we develop a two-stage approach to estimate endogenous treatment effects using high-dimensional instrumental variables. In the first stage, instead of using a linear reduced form regression in the conventional two-stage least squares approach, we propose a new high-dimensional logistic reduced form model with the SCAD penalty to approximate the optimal instrument. In the second stage, we replace the original treatment variable by its estimated propensity score and run a least squares regression to obtain the penalized Logistic-regression Instrumental Variables Estimator (LIVE). We show that the proposed LIVE is root-n consistent to the true average treatment effect, asymptotically normal and achieves the semiparametric efficiency bound. Monte Carlo simulations demonstrate that the LIVE outperforms the traditional TSLS estimator and the post-Lasso estimator for the endogenous treatment effects. Moreover, in the empirical study, we investigate whether the Olympic Games could facilitate the host nation's economic growth using data from 163 countries. The proposed LIVE estimator shows a strong Olympic effect on the host nation's economic growth.