Estimation of Treatment Effects based on Kernel Matching

Kernel matching is a widely used technique for estimating treatment effects, particularly valuable in observational studies where randomized controlled trials are not feasible. While kernel-matching approaches have demonstrated practical advantages in exploiting similarities between treated and control units, their theoretical properties have remained only partially explored. In this paper, we make a key contribution by establishing the asymptotic normality and consistency of kernel-matching estimators for both the average treatment effect (ATE) and the average treatment effect on the treated (ATT) through influence function techniques, thereby providing a rigorous theoretical foundation for their use in causal inference. Furthermore, we derive the asymptotic distributions of the ATE and ATT estimators when the propensity score is estimated rather than known, extending the theoretical guarantees to the practically relevant cases. Through extensive Monte Carlo simulations, the estimators exhibit consistently improved performance over standard treatment-effect estimators. We further illustrate the method by analyzing the National Supported Work Demonstration job-training data with the kernel-matching estimator.