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Long Story Short: Omitted Variable Bias in Causal Machine Learning

Author

Listed:
  • Victor Chernozhukov
  • Carlos Cinelli
  • Whitney Newey
  • Amit Sharma
  • Vasilis Syrgkanis

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.

Suggested Citation

  • Victor Chernozhukov & Carlos Cinelli & Whitney Newey & Amit Sharma & Vasilis Syrgkanis, 2021. "Long Story Short: Omitted Variable Bias in Causal Machine Learning," Papers 2112.13398, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2112.13398
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Joseph G. Altonji & Todd E. Elder & Christopher R. Taber, 2005. "Selection on Observed and Unobserved Variables: Assessing the Effectiveness of Catholic Schools," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 151-184, February.
    3. Guildo W. Imbens, 2003. "Sensitivity to Exogeneity Assumptions in Program Evaluation," American Economic Review, American Economic Association, vol. 93(2), pages 126-132, May.
    4. Middleton, Joel A. & Scott, Marc A. & Diakow, Ronli & Hill, Jennifer L., 2016. "Bias Amplification and Bias Unmasking," Political Analysis, Cambridge University Press, vol. 24(3), pages 307-323, July.
    5. Pfanzagl, J. & Wefelmeyer, W., 1978. "A third-order optimum property of the maximum likelihood estimator," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 1-29, March.
    6. AlexanderM. Franks & Alexander D’Amour & Avi Feller, 2020. "Flexible Sensitivity Analysis for Observational Studies Without Observable Implications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1730-1746, December.
    7. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    8. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    9. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    10. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey, 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects," American Economic Review, American Economic Association, vol. 107(5), pages 261-265, May.
    11. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2016. "Double/Debiased Machine Learning for Treatment and Causal Parameters," Papers 1608.00060, arXiv.org, revised Nov 2024.
    12. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    13. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    14. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    15. Vira Semenova & Victor Chernozhukov, 2021. "Debiased machine learning of conditional average treatment effects and other causal functions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 264-289.
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    Cited by:

    1. Hünermund Paul & Louw Beyers & Caspi Itamar, 2023. "Double machine learning and automated confounder selection: A cautionary tale," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-12, January.
    2. Keyon Vafa & Susan Athey & David M. Blei, 2024. "Estimating Wage Disparities Using Foundation Models," Papers 2409.09894, arXiv.org.
    3. Geonwoo Kim & Suyong Song, 2024. "Double/Debiased CoCoLASSO of Treatment Effects with Mismeasured High-Dimensional Control Variables," Papers 2408.14671, arXiv.org.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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