Econometrics Seminar - Xueyan Zhao (Monash)

Title: Bootstrap Hausdorff Confidence Regions for Average Treatment Effect Identified Sets

Authors: Don Poskitts and Xueyan Zhao

Abstract:  Empirical causal analyses often rely on restrictive and unrealistic model assumptions to achieve point identification. More general model assumptions can result in set identified treatment effects that are informative. But the complexity in estimating a set identified treatment effect and conducting inference hinders the application of such models. This paper introduces a simple bootstrap approach to the construction of confidence regions for Average Treatment Effect (ATE) identified sets. Minimum Hausdorff distance bootstrap confidence regions are developed and shown to be valid under suitable regularity. A novel measure of the discrepancy between a confidence region and the target identified set is advanced that contains two components analogous to conventional hypothesis test Type I and Type II errors. Monte Carlo experimentation is employed to compare the behaviour of the new confidence regions with an existing state of the art approach by Chernozhukov, Lee and Rosen (2013), using the proposed discrepancy measures. The performance of our approach compared favourably. Properties arising from the application of quasi-maximum likelihood estimation as a tool for conducting inference on ATEs are also examined. The approach is applied to an empirical study of causal effect of private health insurance on health service utilisation in Australia.