arXiv 27 Jun 2026 · Statistics — Methodology
arXiv:2606.29009 · PDF · DOI · OpenAlex · Extracted main text
Time-varying treatment effects, surrogate-identified treatment effects, and mediation effects can all be written as recursive regressions, in which each regression's predicted values become generated outcomes for the next regression. We study how standard causal estimators behave in this setting. Formally, we compare the recursive plug-in, recursive balancing weight, and recursive doubly robust estimators. When every stage is fitted by ordinary least squares (OLS), the three recursive estimators coincide in any finite sample, whether or not the models are correctly specified. As such, estimation by recursively regressing generated outcomes is numerically equivalent to estimation by recursively balancing generated regressors. Under ridge penalisation for the balancing weights, the doubly robust estimator is a backward recursion of stage-wise blends of penalised and OLS regressions. The weight on the recursive OLS regression decays geometrically in the number of time periods. Therefore, the intuition from the cross-sectional setting, where the bias correction moves the estimator towards OLS, applies less and less as the number of time periods increases. For general convex penalties, we derive an identity at each stage.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chernozhukov, Victor and Newey, Whitney and Singh, Rahul and Syrgkan… (2022) Automatic debiased machine learning for dynamic treatment effects and general nested functionals self | 1.000 | 10 | 3 | 100% |
| 2 | Bruns-Smith, David and Dukes, Oliver and Feller, Avi and Ogburn, Eli… (2025) Augmented balancing weights as linear regression | 0.886 | 23 | 8 | 70% |
| 3 | Chernozhukov, Victor and Newey, Whitney K and Singh, Rahul (2022) Automatic debiased machine learning of causal and structural effects self | 0.737 | 3 | 2 | 100% |
| 4 | Robins, James M (1986) A new approach to causal inference in mortality studies with a sustained exposure period–-application to control of the healthy… | 0.737 | 3 | 2 | 100% |
| 5 | Pearl, Judea (2001) Direct and indirect effects | 0.644 | 2 | 2 | 100% |
| 6 | Robins, James M and Greenland, Sander (1992) Identifiability and exchangeability for direct and indirect effects | 0.644 | 2 | 2 | 100% |
| 7 | Rotnitzky, Andrea and Robins, James M and Babino, Lucia (2017) On the multiply robust estimation of the mean of the g-functional | 0.644 | 2 | 2 | 100% |
| 8 | Rotnitzky, Andrea and Smucler, Ezequiel and Robins, James M (2021) Characterization of parameters with a mixed bias property | 0.644 | 2 | 2 | 100% |
| 9 | Viviano, Davide and Bradic, Jelena (2021) Dynamic covariate balancing: estimating treatment effects over time with potential local projections | 0.644 | 2 | 2 | 100% |
| 10 | Bang, Heejung and Robins, James M (2005) Doubly robust estimation in missing data and causal inference models | 0.511 | 2 | 1 | 100% |
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