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Testing identification in mediation and dynamic treatment models

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  • Martin Huber
  • Kevin Kloiber
  • Lukas Laffers

Abstract

We propose a test for the identification of causal effects in mediation and dynamic treatment models that is based on two sets of observed variables, namely covariates to be controlled for and suspected instruments, building on the test by Huber and Kueck (2022) for single treatment models. We consider models with a sequential assignment of a treatment and a mediator to assess the direct treatment effect (net of the mediator), the indirect treatment effect (via the mediator), or the joint effect of both treatment and mediator. We establish testable conditions for identifying such effects in observational data. These conditions jointly imply (1) the exogeneity of the treatment and the mediator conditional on covariates and (2) the validity of distinct instruments for the treatment and the mediator, meaning that the instruments do not directly affect the outcome (other than through the treatment or mediator) and are unconfounded given the covariates. Our framework extends to post-treatment sample selection or attrition problems when replacing the mediator by a selection indicator for observing the outcome, enabling joint testing of the selectivity of treatment and attrition. We propose a machine learning-based test to control for covariates in a data-driven manner and analyze its finite sample performance in a simulation study. Additionally, we apply our method to Slovak labor market data and find that our testable implications are not rejected for a sequence of training programs typically considered in dynamic treatment evaluations.

Suggested Citation

  • Martin Huber & Kevin Kloiber & Lukas Laffers, 2024. "Testing identification in mediation and dynamic treatment models," Papers 2406.13826, arXiv.org.
  • Handle: RePEc:arx:papers:2406.13826
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    References listed on IDEAS

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    1. Lechner, Michael & Scioch, Patrycja & Wunsch, Conny, 2013. "Do Firms Benefit from Active Labour Market Policies?," Working papers 2013/11, Faculty of Business and Economics - University of Basel.
    2. Martin Huber, 2014. "Identifying Causal Mechanisms (Primarily) Based On Inverse Probability Weighting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(6), pages 920-943, September.
    3. Imai, Kosuke & Yamamoto, Teppei, 2013. "Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence from Framing Experiments," Political Analysis, Cambridge University Press, vol. 21(2), pages 141-171, April.
    4. Hugo Bodory & Martin Huber & Lukáš Lafférs, 2022. "Evaluating (weighted) dynamic treatment effects by double machine learning [Identification of causal effects using instrumental variables]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 628-648.
    5. Joshua D. Angrist & Miikka Rokkanen, 2015. "Wanna Get Away? Regression Discontinuity Estimation of Exam School Effects Away From the Cutoff," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1331-1344, December.
    6. Markus Frölich & Michael Lechner, 2015. "Combining Matching and Nonparametric Instrumental Variable Estimation: Theory and An Application to the Evaluation of Active Labour Market Policies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(5), pages 718-738, August.
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