Estimating Conditional Average Treatment Effects with Heteroscedasticity by Model Averaging and Matching

Causal inference is indispensable in many fields of empirical research, such as marketing, economic policy, medicine and so on. The estimation of treatment effects is the most important in causal inference. In this paper, we propose a model averaging approach, combined with a partition and matching method to estimate the conditional average treatment effect under heteroskedastic error settings. In our methods, we use the partition and matching method to approximate the true treatment effects and choose the weights by minimizing a leave-one-out cross validation criterion, which is also known as jackknife method. We prove that the model averaging estimator with weights determined by our criterion has asymptotic optimality, which achieves the lowest possible squared error. When there exist correct models in the candidate model set, we have proved that the sum of weights of the correct models converge to 1 as the sample size increases but with a finite number of baseline covariates. A Monte Carlo simulation study shows that our method has good performance in finite sample cases. We apply this approach to a National Supported Work Demonstration data set.