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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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    1. S. Vansteelandt & E. Goetghebeur, 2003. "Causal inference with generalized structural mean models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 817-835, November.
    2. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. Zheng Wenjing & van der Laan Mark J., 2012. "Targeted Maximum Likelihood Estimation of Natural Direct Effects," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-40, January.
    7. Martin Huber & Yu‐Chin Hsu & Ying‐Ying Lee & Layal Lettry, 2020. "Direct and indirect effects of continuous treatments based on generalized propensity score weighting," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(7), pages 814-840, November.
    8. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    9. Severini, Thomas A. & Tripathi, Gautam, 2012. "Efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 491-498.
    10. Raj Chetty & John N. Friedman & Nathaniel Hilger & Emmanuel Saez & Diane Whitmore Schanzenbach & Danny Yagan, 2011. "How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project Star," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1593-1660.
    11. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    12. Cai Weixin & van der Laan Mark, 2020. "Nonparametric bootstrap inference for the targeted highly adaptive least absolute shrinkage and selection operator (LASSO) estimator," The International Journal of Biostatistics, De Gruyter, vol. 16(2), pages 1-36, November.
    13. Jason Abrevaya & Yu-Chin Hsu & Robert P. Lieli, 2015. "Estimating Conditional Average Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 485-505, October.
    14. Victor Chernozhukov & Juan Carlos Escanciano & Hidehiko Ichimura & Whitney K. Newey & James M. Robins, 2022. "Locally Robust Semiparametric Estimation," Econometrica, Econometric Society, vol. 90(4), pages 1501-1535, July.
    15. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, May.
    16. V Chernozhukov & W K Newey & R Singh, 2023. "A simple and general debiased machine learning theorem with finite-sample guarantees," Biometrika, Biometrika Trust, vol. 110(1), pages 257-264.
    17. A Rotnitzky & E Smucler & J M Robins, 2021. "Characterization of parameters with a mixed bias property," Biometrika, Biometrika Trust, vol. 108(1), pages 231-238.
    18. Cai Weixin & van der Laan Mark, 2020. "Nonparametric bootstrap inference for the targeted highly adaptive least absolute shrinkage and selection operator (LASSO) estimator," The International Journal of Biostatistics, De Gruyter, vol. 16(2), pages 1-36, November.
    19. Yizhen Xu & Numair Sani & AmirEmad Ghassami & Ilya Shpitser, 2021. "Multiply Robust Causal Mediation Analysis with Continuous Treatments," Papers 2105.09254, arXiv.org, revised Oct 2024.
    20. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    21. Susan Athey & Raj Chetty & Guido Imbens & Hyunseung Kang, 2016. "Estimating Treatment Effects using Multiple Surrogates: The Role of the Surrogate Score and the Surrogate Index," Papers 1603.09326, arXiv.org, revised Aug 2024.
    22. Peter Z. Schochet & John Burghardt & Sheena McConnell, 2008. "Does Job Corps Work? Impact Findings from the National Job Corps Study," American Economic Review, American Economic Association, vol. 98(5), pages 1864-1886, December.
    23. repec:mpr:mprres:6097 is not listed on IDEAS
    24. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2020. "Adversarial Estimation of Riesz Representers," Papers 2101.00009, arXiv.org, revised Apr 2024.
    25. C. B. Begg & D. H. Y. Leung, 2000. "On the use of surrogate end points in randomized trials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(1), pages 15-28.
    26. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    27. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part II: Proofs of Results," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-19, March.
    28. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    29. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
    30. Rahul Singh, 2021. "Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection," Papers 2111.05277, arXiv.org.
    31. Orellana Liliana & Rotnitzky Andrea & Robins James M., 2010. "Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-49, March.
    32. Gruber, Susan & Laan, Mark van der, 2012. "tmle: An R Package for Targeted Maximum Likelihood Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i13).
    33. Heejung Bang & James M. Robins, 2005. "Doubly Robust Estimation in Missing Data and Causal Inference Models," Biometrics, The International Biometric Society, vol. 61(4), pages 962-973, December.
    34. Rahul Singh & Liyuan Xu & Arthur Gretton, 2021. "Sequential Kernel Embedding for Mediated and Time-Varying Dose Response Curves," Papers 2111.03950, arXiv.org, revised Jul 2023.
    35. Wang Miao & Zhi Geng & Eric J Tchetgen Tchetgen, 2018. "Identifying causal effects with proxy variables of an unmeasured confounder," Biometrika, Biometrika Trust, vol. 105(4), pages 987-993.
    36. van der Laan Mark J. & Petersen Maya L & Joffe Marshall M, 2005. "History-Adjusted Marginal Structural Models and Statically-Optimal Dynamic Treatment Regimens," The International Journal of Biostatistics, De Gruyter, vol. 1(1), pages 1-41, November.
    37. Anish Agarwal & Rahul Singh, 2021. "Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy," Papers 2107.02780, arXiv.org, revised Feb 2024.
    38. Ben Deaner, 2018. "Proxy Controls and Panel Data," Papers 1810.00283, arXiv.org, revised Nov 2023.
    39. Keith Battocchi & Eleanor Dillon & Maggie Hei & Greg Lewis & Miruna Oprescu & Vasilis Syrgkanis, 2021. "Estimating the Long-Term Effects of Novel Treatments," Papers 2103.08390, arXiv.org, revised Feb 2022.
    40. Jelena Bradic & Weijie Ji & Yuqian Zhang, 2021. "High-dimensional Inference for Dynamic Treatment Effects," Papers 2110.04924, arXiv.org, revised May 2023.
    41. Edward H. Kennedy & Zongming Ma & Matthew D. McHugh & Dylan S. Small, 2017. "Non-parametric methods for doubly robust estimation of continuous treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1229-1245, September.
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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. Rahul Singh, 2022. "Generalized Kernel Ridge Regression for Long Term Causal Inference: Treatment Effects, Dose Responses, and Counterfactual Distributions," Papers 2201.05139, arXiv.org.
    3. 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.

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