An application of the two-stage, semi-parametric approach with double bootstrap to analyze technical efficiency of Critical Access Hospitals

This study examines technical efficiency of Critical Access Hospitals (CAH) using a two-stage approach and bootstrap procedures for making valid inference about the impact of environmental variables on CAH efficiency. In the first stage, a data envelopment analysis (DEA) efficiency estimator is used to estimate technical efficiency of each hospital in the sample. In the second stage, efficiency scores are regressed on environmental variables using a truncated regression with bootstrap. Alternatively, a double bootstrap procedure is used, where bias-corrected DEA efficiency scores, obtained by means of bootstrap in the first stage, are used in the second stage bootstrapped truncated regression. While both procedures provide valid inference in the second stage analysis, the double bootstrap procedure has also been shown to improve statistical efficiency in the second stage truncated regression. Our results indicate that, while the two procedures yield in general similar and consistent results, only the double bootstrap procedure unveiled the direct association between Medicare cost-based reimbursement and CAH inefficiency.