Bootstrap Hausdorff Confidence Regions for Average Treatment Effect Identified Sets

This paper introduces a new 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 and the impact of different features on the properties of the alternative techniques are investigated. Properties arising from the application of quasi-maximum likelihood estimation as a tool for conducting inference on ATEs