Long Story Short: Omitted Variable Bias in Causal Machine Learning (2112.13398v5)

Abstract: We develop a general theory of omitted variable bias for a wide range of common causal parameters, including (but not limited to) averages of potential outcomes, average treatment effects, average causal derivatives, and policy effects from covariate shifts. Our theory applies to nonparametric models, while naturally allowing for (semi-)parametric restrictions (such as partial linearity) when such assumptions are made. We show how simple plausibility judgments on the maximum explanatory power of omitted variables are sufficient to bound the magnitude of the bias, thus facilitating sensitivity analysis in otherwise complex, nonlinear models. Finally, we provide flexible and efficient statistical inference methods for the bounds, which can leverage modern machine learning algorithms for estimation. These results allow empirical researchers to perform sensitivity analyses in a flexible class of machine-learned causal models using very simple, and interpretable, tools. We demonstrate the utility of our approach with two empirical examples.

• The paper presents a framework that derives bounds on omitted variable bias for various causal parameters using the Riesz-Frechet representation.
• It employs sensitivity analysis with interpretable measures like R² to assess the impact of unobserved confounders in semiparametric and nonparametric models.
• Real-world examples, including 401(k) eligibility and gasoline demand elasticity, demonstrate the practical applicability of the proposed method.

Overview of "Long Story Short: Omitted Variable Bias in Causal Machine Learning"

The paper "Long Story Short: Omitted Variable Bias in Causal Machine Learning" by Victor Chernozhukov et al. addresses the critical issue of omitted variable bias (OVB) in the context of causal inference with machine learning models. The authors present a framework for deriving bounds on OVB for a broad class of causal parameters, including average treatment effects (ATE), average causal derivatives, and policy effects. This work aims to aid empirical researchers in performing sensitivity analyses to assess the robustness of their causal findings against potential violations of conditional ignorability.

Methodological Contributions

The paper's central contribution is the derivation of general bounds on the size of OVB for semiparametric and fully nonparametric regression models. This is achieved by leveraging the Riesz-Frechet representation of the target parameter, which allows the authors to express the bounds in terms of the additional variation that latent variables create in both the outcome regression and the Riesz representer of the causal parameter of interest.

The paper provides a significant methodological advancement by introducing a sensitivity analysis framework applicable to broad causal estimands. This framework allows researchers to reason about the possible impact of unobserved confounders using interpretable measures of explanatory power, such as $R^2$. This approach bypasses the need for observing the latent variables directly, making it tractable to use in real-world scenarios where complete data is rarely available.

Empirical Examples

To demonstrate the practicality of their approach, the authors present empirical examples involving real-world data sets. These examples include assessing the impact of 401(k) eligibility on financial assets and estimating the price elasticity of gasoline demand. By illustrating how their methods can be applied to flexibly account for potential confounders, the authors showcase the robustness and adaptability of their model in performing causal inferences across different applications.

Implications and Future Developments

The paper's results have significant implications for both theoretical and practical aspects of causal inference. The theoretical advancement in representing OVB via the Riesz-Frechet representation provides a solid foundation for further research into more complex models of causal inference. Practically, the introduction of tools for sensitivity analysis in machine learning-augmented causal research allows for more reliable and interpretable conclusions regarding causal relationships. The paper's method enables practitioners to quantify how unmeasured confounders could potentially bias results, thus offering a more nuanced assessment of empirical findings.

Future developments could extend these methods to broader contexts, such as dynamic treatment regimes or structural equation models, where omitted variables might play a crucial role. Additionally, further exploration of the auto-DML and its implications on empirical causal inference could be insightful, particularly in refining the estimation processes for causal parameters.

Conclusion

The research by Chernozhukov et al. presents a comprehensive approach to addressing omitted variable bias in causal machine learning, providing both theoretical rigor and practical tools for empirical researchers. By focusing on generalizable and interpretable bounds for various causal estimands, the paper lays important groundwork for advancing causal inference methodologies in data-rich environments. As researchers and practitioners seek to uncover causal relationships within increasingly complex data sets, the methods outlined in this paper will likely play a critical role in ensuring robust and credible conclusions.