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Conservative inference for counterfactuals

Author

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  • Balakrishnan Sivaraman

    (Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States)

  • Kennedy Edward

    (Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States)

  • Wasserman Larry

    (Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, Pennsylvania, United States)

Abstract

In causal inference, the joint law of a set of counterfactual random variables is generally not identified. But many interesting quantities are functions of the joint distribution. For example, the individual treatment effect is a difference of counterfactuals and any functional of this difference such as the variance, the quantiles and density, all depend on this joint distribution. For binary treatments, many researchers have found identifiable bounds on these quantities. We extend this idea to continuous treatments. We show that a conservative version of the joint law – corresponding to the smallest treatment effect – is identified. The notion of “conservative” depends on how we choose to measure the causal effect and we consider a few such measures. Finding this law uses recent results from optimal transport theory. Under this conservative law we can bound causal effects and we may construct inferences for each individual’s counterfactual dose-response curve. Intuitively, this is the flattest counterfactual curve for each subject that is consistent with the distribution of the observables. If the outcome is univariate then, under mild conditions, this curve is simply the quantile function of the counterfactual distribution that passes through the observed point. This curve corresponds to a nonparametric rank preserving structural model.

Suggested Citation

  • Balakrishnan Sivaraman & Kennedy Edward & Wasserman Larry, 2025. "Conservative inference for counterfactuals," Journal of Causal Inference, De Gruyter, vol. 13(1), pages 1-17.
  • Handle: RePEc:bpj:causin:v:13:y:2025:i:1:p:17:n:1001
    DOI: 10.1515/jci-2023-0071
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    References listed on IDEAS

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    1. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
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