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

Yuehao Bai, Shunzhuang Huang, Sarah Moon, Andres Santos, Azeem Shaikh and Edward J. Vytlacil

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Abstract: We propose a general approach to inference for a broad class of models that arise in the analysis of treatment effects with discrete-valued treatments and instruments and a general-valued outcome. In addition to instrument exogeneity, the main substantive assumption in our class of models rules out certain response types by assuming that they occur with probability zero. Here, the response type refers to the vector of potential outcomes and potential treatments, and we refer to a set of possible values for the response type as a generalized principal stratum. Through a series of examples, we show that this framework encompasses a wide variety of assumptions that have been considered in the previous literature. Our framework allows inference on any treatment effect parameter that can be expressed as the expectation of a function of the response type conditional on a generalized principal stratum. We develop methods for inference on such parameters under these assumptions, as well as methods for testing the validity of the assumptions themselves. A key result of our analysis is a characterization of the identified set for such parameters under these assumptions and the testable restrictions for the assumptions themselves in terms of existence of a nonnegative 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).

Date: 2024-11, Revised 2026-09
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