Valid inference for treatment effect parameters under irregular identification and many extreme propensity scores

This paper provides a framework for conducting valid inference for causal parameters without imposing strong variance or support restrictions on the propensity score. In particular, it covers the case of irregularly identified treatment effect parameters. We provide limit theorems for inverse probability weighting and doubly robust estimation of causal or counterfactual parameters that do not rely on trimming approaches. By construction the limiting distributions of these estimators belong to the alpha-stable class which implies that standard inference methods such as the nonparametric bootstrap are inconsistent. We propose an adaptive version of the m-out-of-n bootstrap that is robust to all types of identification and a bootstrap aggregation method for the optimal m choice. Monte Carlo simulations suggest that the modified resampling method compares favorably to conventional methods in finite samples. The method is applied to a re-analysis of the causal impact of right heart catheterization on survival rates.