Identification of Causal Effects Within Principal Strata Using Auxiliary Variables

TL;DR

This paper develops a comprehensive theoretical framework for identifying and estimating principal causal effects in causal inference using auxiliary variables, enhancing empirical research methods.

Contribution

It provides general identification and estimation results for principal causal effects with auxiliary variables, extending existing models and accommodating various outcomes and variables.

Findings

Established non-parametric and semi-parametric identification results.

Generalized models used in empirical studies to broader settings.

Proposed flexible parametric models for unidentifiable cases.

Abstract

In causal inference, principal stratification is a framework for dealing with a posttreatment intermediate variable between a treatment and an outcome, in which the principal strata are defined by the joint potential values of the intermediate variable. Because the principal strata are not fully observable, the causal effects within them, also known as the principal causal effects, are not identifiable without additional assumptions. Several previous empirical studies leveraged auxiliary variables to improve the inference of principal causal effects. We establish a general theory for identification and estimation of the principal causal effects with auxiliary variables, which provides a solid foundation for statistical inference and more insights for model building in empirical research. In particular, we consider two commonly-used strategies for principal stratification problems: principal ignorability, and the conditional independence between the auxiliary variable and the outcome given principal strata and covariates. For these two strategies, we give non-parametric and semi-parametric identification results without modeling assumptions on the outcome. When the assumptions for neither strategies are plausible, we propose a large class of flexible parametric and semi-parametric models for identifying principal causal effects. Our theory not only establishes formal identification results of several models that have been used in previous empirical studies but also generalizes them to allow for different types of outcomes and intermediate variables.