Francis J. DiTraglia, Laura Liu
arXiv 18 Aug 2025 · Econometrics
arXiv:2508.12688 · PDF · DOI · OpenAlex · Extracted main text
This paper proposes a simple, novel, and fully-Bayesian approach for causal inference in partially linear models with high-dimensional control variables. Off-the-shelf machine learning methods can introduce biases in the causal parameter known as regularization-induced confounding. To address this, we propose a Bayesian Double Machine Learning (BDML) method, which modifies a standard Bayesian multivariate regression model and recovers the causal effect of interest from the reduced-form covariance matrix. Our BDML is related to the burgeoning frequentist literature on DML while addressing its limitations in finite-sample inference. Moreover, the BDML is based on a fully generative probability model in the DML context, adhering to the likelihood principle. We show that in high dimensional setups the naive estimator implicitly assumes no selection on observables--unlike our BDML. The BDML exhibits lower asymptotic bias and achieves asymptotic normality and semiparametric efficiency as established by a Bernstein-von Mises theorem, thereby ensuring robustness to misspecification. In simulations, our BDML achieves lower RMSE, better frequentist coverage, and shorter confidence interval width than alternatives from the literature, both Bayesian and frequentist.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Hahn, P.R., Carvalho, C.M., Puelz, D., He, J (2018) Regularization and Confounding in Linear Regression for Treatment Effect Estimation | 1.000 | 10 | 4 | 100% |
| 2 | Belloni, A., Chernozhukov, V., Hansen, C (2014) Inference on Treatment Effects after Selection among High-Dimensional Controls | 1.000 | 5 | 3 | 100% |
| 3 | Linero, A.R (2023) In Nonparametric and High-Dimensional Models, Bayesian Ignorability is an Informative Prior | 0.965 | 20 | 6 | 90% |
| 4 | Hahn, P.R., Murray, J.S., Carvalho, C.M (2020) Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects (with Discussion) | 0.874 | 5 | 2 | 100% |
| 5 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters | 0.737 | 3 | 2 | 100% |
| 6 | Ahrens, A., Chernozhukov, V., Hansen, C., Kozbur, D., Schaffer, M.,… (2025) An Introduction to Double/Debiased Machine Learning | 0.511 | 2 | 1 | 100% |
| 7 | Breunig, C., Liu, R., Yu, Z (2024) Semiparametric Bayesian Difference-in-Differences | 0.511 | 2 | 1 | 100% |
| 8 | Luo, Y., Graham, D.J., McCoy, E.J (2023) Semiparametric Bayesian doubly robust causal estimation | 0.511 | 2 | 1 | 100% |
| 9 | Walker, C.D (2025) Parametrization, Prior Independence, and the Semiparametric Bernstein-von Mises Theorem for the Partially Linear Model | 0.511 | 2 | 1 | 100% |
| 10 | Angrist, J.D., Frandsen, B (2022) Machine Labor | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 35 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Debiased Bayesian Inference for High-dimensional Regression Models | 0.405 | 1 | 1 |