Fig. 1.

Histograms of the unadjusted estimator and the Lasso-adjusted estimator when the moment conditions do not hold. We select the tuning parameters for Lasso using 10-fold CV. The potential outcomes are simulated from linear regression model and then kept fixed (see more details in SI Appendix). For the upper two subplots, the error terms are generated from t distribution with one degree of freedom and therefore do not satisfy second moment condition; whereas for the lower two subplots, the covariates are generated from t distribution with three degrees of freedom and thus violate fourth moment condition.