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On Causal Inference with Model-Based Outcomes

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  • Dmitry Arkhangelsky
  • Kazuharu Yanagimoto
  • Tom Zohar

Abstract

This paper investigates causal inference for policies affecting group-level outcomes derived from microdata models. We formalize these outcomes using population moment conditions and show that standard one-step GMM estimators are generally inconsistent due to an endogenous weighting problem: policy-induced changes in the microdata distribution alter implicit GMM weights. In contrast, two-stage Minimum Distance (MD) estimators perform well when group sizes are sufficiently large, a statement we formalize. While MD estimators can become inconsistent in very small groups due to a policy-induced sample selection problem, we demonstrate this can be addressed by incorporating auxiliary population information.

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  • Dmitry Arkhangelsky & Kazuharu Yanagimoto & Tom Zohar, 2024. "On Causal Inference with Model-Based Outcomes," Papers 2403.19563, arXiv.org, revised May 2025.
    • Handle: RePEc:arx:papers:2403.19563
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    References listed on IDEAS

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    1. Victor Chernozhukov & Mert Demirer & Esther Duflo & Iván Fernández-Val, 2018. "Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments, with an Application to Immunization in India," NBER Working Papers 24678, National Bureau of Economic Research, Inc.
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    3. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    4. Martin Eckhoff Andresen & Emily Nix, 2022. "Can the child penalty be reduced?. Evaluating multiple policy interventions," Discussion Papers 983, Statistics Norway, Research Department.
    5. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    6. Vira Semenova & Victor Chernozhukov, 2021. "Debiased machine learning of conditional average treatment effects and other causal functions," The Econometrics Journal, Royal Economic Society, vol. 24(2), pages 264-289.
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