Causal Inference for Qualitative Outcomes (2502.11691v2)

Abstract: Causal inference methods such as instrumental variables, regression discontinuity, and difference-in-differences are widely used to identify and estimate treatment effects. However, when outcomes are qualitative, their application poses fundamental challenges. This paper highlights these challenges and proposes an alternative framework that focuses on well-defined and interpretable estimands. We show that conventional identification assumptions suffice for identifying the new estimands and outline simple, intuitive estimation strategies that remain fully compatible with conventional econometric methods. We provide an accompanying open-source R package, $\texttt{causalQual}$, which is publicly available on CRAN.

• The paper advances methodological innovation by proposing Probability Shifts as causal estimands for qualitative outcomes.
• It adapts standard econometric methods like IV, RD, and DiD with modified assumptions to identify treatment effects in categorical data.
• The approach enhances causal inference rigor in empirical studies, with practical applications in political science, health economics, and beyond.

Causal Inference for Qualitative Outcomes: A Methodological Exploration

The paper "Causal Inference for Qualitative Outcomes" by Riccardo Di Francesco and Giovanni Mellace addresses a critical gap in the application of causal inference methodologies to qualitative outcomes in econometrics. It identifies the inherent limitations of traditional causal estimands, such as the Average Treatment Effect (ATE), when applied to qualitative or categorical data. These estimands become ill-defined in contexts where outcomes are not numerical, thereby necessitating a robust framework centered on probability distributions over outcome categories.

Analytical Framework and Methodological Innovations

This paper introduces an innovative causal framework that pivots from conventional approaches by focusing on well-defined Probability Shifts (PS) as causal estimands for qualitative outcomes. The distinction is crucial because traditional estimands, which rely on arithmetic operations, do not hold valid interpretations in the field of qualitative outcomes. Instead, the PS quantifies how a treatment influences the probability distribution across different outcome categories, providing a meaningful alternative to standard causal parameters.

The authors assert that conventional identification assumptions, such as those employed in instrumental variables (IV), regression discontinuity (RD), and difference-in-differences (DiD) designs, can be adapted to facilitate PS identification. The paper substantiates that minor modifications to these assumptions ensure their applicability to qualitative contexts. This innovative approach enables researchers to harness familiar econometric tools while maintaining the integrity of causal inferences with categorical data.

Methodological Applications

1. Selection-on-Observables Designs: The paper suggests that conventional assumptions in these designs are sufficient for identifying the Conditional Probability of Shift (CPS) and, thus, the PS. The shift from the ill-defined ATE to PS offers a pertinent solution for qualitative outcomes.
2. Instrumental Variables (IV): The authors extend the IV framework, traditionally employed with quantitative outcomes, by defining a Local Probability Shift (LPS). The LPS estimates how treatment impacts traduce into probability shifts within compliers, circumventing the arbitrary coding issue prevalent with qualitative outcomes.
3. Regression Discontinuity (RD): For RD designs, the introduction of continuity assumptions on probability mass functions, as opposed to mean outcomes, provides a method to identify the Probability Shift at the Cutoff (PSC). This adaptation allows for meaningful interpretations of treatment effects at arbitrary thresholds.
4. Difference-in-Differences (DiD): By implementing a parallel trend assumption over probability mass functions, the paper proposes a framework to identify Probability of Shift on the Treated (PST) in a setting where conventional DiD would otherwise fall short.

Implications and Future Developments

The implications of this research are significant, both theoretically and practically. The pivot from arithmetic-based estimands to those defined over probability distributions allows researchers to engage rigorously with qualitative data, thus enhancing the robustness of causal conclusions in empirical studies. From a practical standpoint, these methods apply to a wide array of fields that deal with ordinal data, including political science, health economics, and consumer research, among others.

Future research avenues may focus on expanding this framework to accommodate more nuanced scenarios such as multiple instruments in IV designs or staggered adoption in DiD frameworks. The authors' provision of an R package, causalQual, signals ongoing development and adaptation to contemporary research challenges, inviting contributions and extensions from the research community.

Conclusion

This paper makes a substantive contribution to the econometrics literature by addressing a clear methodological gap with innovative solutions for qualitative outcomes. It harmonizes qualitative data analysis with robust causal inferential paradigms, paving the way for enhanced analytical precision in applied econometrics.