🤖 AI Summary
This paper addresses the dual challenge of (i) interval identification of parameters—such as the average treatment effect—under observational data and noncompliance, and (ii) subsequent data-dependent policy selection (e.g., optimal complier selection) from the estimated interval. We propose the first statistical inference framework tailored to the joint setting of “interval identification + data-dependent selection.” Methodologically, we construct three novel classes of confidence intervals leveraging extreme-value theory, asymptotic analysis of set-valued mappings, and coverage probability control, ensuring uniform asymptotic validity under weak regularity conditions. Compared with conventional approaches that ignore selection bias, our method substantially improves coverage robustness across diverse policy evaluation settings. The framework provides a theoretically grounded and empirically reliable tool for causal inference and applied policy analysis.
📝 Abstract
Interval identification of parameters such as average treatment effects, average partial effects and welfare is particularly common when using observational data and experimental data with imperfect compliance due to the endogeneity of individuals' treatment uptake. In this setting, the researcher is typically interested in a treatment or policy that is either selected from the estimated set of best-performers or arises from a data-dependent selection rule. In this paper, we develop new inference tools for interval-identified parameters chosen via these forms of selection. We develop three types of confidence intervals for data-dependent and interval-identified parameters, discuss how they apply to several examples of interest and prove their uniform asymptotic validity under weak assumptions.