Research using observational data and natural experiments relies on statistical analysis to provide reliable results. This project develops new methods to help data analysts test hypotheses about the causes of observed outcomes. The team improves statistical methods in a practical way that can be widely adopted by researchers, business analysts, policy analysts, and others who want to isolate the effects of changes in business and/or government methods, policies, and regulations. This award funds development of (a) computationally simple methods for sharp identification of causal parameters, (b) good estimators for the bounds on partially identified parameters, (c) computationally reliable methods to derive identifying restrictions, and (d) translational research through a publicly available code library that implements the methods and makes these advances available to the broad community that uses statistical tools to conduct program evaluation. The research advances knowledge by developing a unified framework for identification, counterfactual prediction, and specification analyses for potential outcome models through two subprojects. The first subproject uses a new approach, based on random set theory, to bound counterfactuals of interest in a class of potential outcome models. Crucially, this approach avoids computing the sharp identified set for the joint distribution of potential quantities, which is often intractable. The team obtains simple closed-form solutions in