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The estimated causal effect on the variance based on the front-door criterion in Gaussian linear structural equation models: an unbiased estimator with the exact variance

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  • Manabu Kuroki

    (Yokohama National University)

  • Taiki Tezuka

    (Yokohama National University)

Abstract

In this paper, we assume that cause–effect relationships between random variables can be represented by a Gaussian linear structural equation model and the corresponding directed acyclic graph. Then, we consider a situation where a set of random variables that satisfies the front-door criterion is observed to estimate a total effect. In this situation, when the ordinary least squares method is utilized to estimate the total effect, we formulate the unbiased estimator of the causal effect on the variance of the outcome variable. In addition, we provide the exact variance formula of the proposed unbiased estimator.

Suggested Citation

  • Manabu Kuroki & Taiki Tezuka, 2024. "The estimated causal effect on the variance based on the front-door criterion in Gaussian linear structural equation models: an unbiased estimator with the exact variance," Statistical Papers, Springer, vol. 65(3), pages 1285-1308, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01401-8
    DOI: 10.1007/s00362-023-01401-8
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    References listed on IDEAS

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    1. Imai, Kosuke & Keele, Luke & Tingley, Dustin & Yamamoto, Teppei, 2011. "Unpacking the Black Box of Causality: Learning about Causal Mechanisms from Experimental and Observational Studies," American Political Science Review, Cambridge University Press, vol. 105(4), pages 765-789, November.
    2. Manabu Kuroki & Takahiro Hayashi, 2016. "On the Estimation Accuracy of Causal Effects using Supplementary Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 505-519, June.
    3. Manabu Kuroki & Judea Pearl, 2014. "Measurement bias and effect restoration in causal inference," Biometrika, Biometrika Trust, vol. 101(2), pages 423-437.
    4. Jacob M. Montgomery & Brendan Nyhan & Michelle Torres, 2018. "How Conditioning on Posttreatment Variables Can Ruin Your Experiment and What to Do about It," American Journal of Political Science, John Wiley & Sons, vol. 62(3), pages 760-775, July.
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    Cited by:

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