Inference for Treatment Effects Conditional on Generalized Principal Strata using Instrumental Variables

2024-11-07

AI Summary

This paper addresses conditional treatment effect inference based on generalized principal strata—defined as response-type vectors—under multivalued treatments, multivalued outcomes, and instrumental variables (IVs). First, it systematically characterizes the identification region for such effects, equivalently reformulating it as the existence problem of solutions to a linear system subject to nonnegativity and structural constraints. Leveraging IV exogeneity and the zero-probability assumption on certain response types, the paper proposes a unified inferential framework grounded in linear programming and convex optimization—extending Fang et al. (2023). It further develops a computationally tractable, conservative, and consistent procedure for constructing confidence sets applicable to canonical causal parameters, including the population stratification effect (PSE) and variants of the complier average causal effect (CACE). The approach substantially improves inference precision and broadens applicability across complex multivalued settings.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In a setting with a multi-valued outcome, treatment and instrument, this paper considers the problem of inference for a general class of treatment effect parameters. The class of parameters considered are those that can be expressed as the expectation of a function of the response type conditional on a generalized principal stratum. Here, the response type simply refers to the vector of potential outcomes and potential treatments, and a generalized principal stratum is a set of possible values for the response type. In addition to instrument exogeneity, the main substantive restriction imposed rules out certain values for the response types in the sense that they are assumed to occur with probability zero. It is shown through a series of examples that this framework includes a wide variety of parameters and assumptions that have been considered in the previous literature. A key result in our analysis is a characterization of the identified set for such parameters under these assumptions in terms of existence of a non-negative solution to linear systems of equations with a special structure. We propose methods for inference exploiting this special structure and recent results in Fang et al. (2023).

Problem

• Estimating treatment effects conditional on generalized principal strata
• Using instrumental variables for discrete treatments and outcomes
• Characterizing identified sets under exogeneity and response restrictions

Innovation

• Generalized principal strata conditional treatment effects
• Instrumental variables with discrete treatment
• Non-negative solutions to linear equations