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Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects

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  • Isaac Meza
  • Rahul Singh

Abstract

Several causal parameters in short panel data models are scalar summaries of a function called a nested nonparametric instrumental variable regression (nested NPIV). Examples include long term, mediated, and time varying treatment effects identified using proxy variables. However, it appears that no prior estimators or guarantees for nested NPIV exist, preventing flexible estimation and inference for these causal parameters. A major challenge is compounding ill posedness due to the nested inverse problems. We analyze adversarial estimators of nested NPIV, and provide sufficient conditions for efficient inference on the causal parameter. Our nonasymptotic analysis has three salient features: (i) introducing techniques that limit how ill posedness compounds; (ii) accommodating neural networks, random forests, and reproducing kernel Hilbert spaces; and (iii) extending to causal functions, e.g. long term heterogeneous treatment effects. We measure long term heterogeneous treatment effects of Project STAR and mediated proximal treatment effects of the Job Corps.

Suggested Citation

  • Isaac Meza & Rahul Singh, 2021. "Nested Nonparametric Instrumental Variable Regression: Long Term, Mediated, and Time Varying Treatment Effects," Papers 2112.14249, arXiv.org, revised Mar 2024.
  • Handle: RePEc:arx:papers:2112.14249
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    Cited by:

    1. Guido Imbens & Nathan Kallus & Xiaojie Mao & Yuhao Wang, 2022. "Long-term Causal Inference Under Persistent Confounding via Data Combination," Papers 2202.07234, arXiv.org, revised Aug 2024.
    2. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2022. "Automatic Debiased Machine Learning for Dynamic Treatment Effects and General Nested Functionals," Papers 2203.13887, arXiv.org, revised Jun 2023.
    3. Rahul Singh, 2022. "Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions," Papers 2201.05139, arXiv.org.

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