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Proxy Controls and Panel Data

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  • Ben Deaner

Abstract

We provide new results for nonparametric identification, estimation, and inference of causal effects using `proxy controls': observables that are noisy but informative proxies for unobserved confounding factors. Our analysis applies to cross-sectional settings but is particularly well-suited to panel models. Our identification results motivate a simple and `well-posed' nonparametric estimator. We derive convergence rates for the estimator and construct uniform confidence bands with asymptotically correct size. In panel settings, our methods provide a novel approach to the difficult problem of identification with non-separable, general heterogeneity and fixed $T$. In panels, observations from different periods serve as proxies for unobserved heterogeneity and our key identifying assumptions follow from restrictions on the serial dependence structure. We apply our methods to two empirical settings. We estimate consumer demand counterfactuals using panel data and we estimate causal effects of grade retention on cognitive performance.

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  • Ben Deaner, 2018. "Proxy Controls and Panel Data," Papers 1810.00283, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:1810.00283
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    References listed on IDEAS

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    1. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    2. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    3. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    4. 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.
    5. Hu, Yingyao & Shiu, Ji-Liang, 2018. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Econometric Theory, Cambridge University Press, vol. 34(3), pages 659-693, June.
    6. Joachim Freyberger, 2018. "Non-parametric Panel Data Models with Interactive Fixed Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1824-1851.
    7. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-1395, November.
    8. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    9. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    10. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    11. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
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    Citations

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    Cited by:

    1. Ziyu Wang & Yucen Luo & Yueru Li & Jun Zhu & Bernhard Scholkopf, 2022. "Spectral Representation Learning for Conditional Moment Models," Papers 2210.16525, arXiv.org, revised Dec 2022.
    2. 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.
    3. AmirEmad Ghassami & Andrew Ying & Ilya Shpitser & Eric Tchetgen Tchetgen, 2021. "Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference," Papers 2104.02929, arXiv.org, revised Mar 2022.
    4. Rahul Singh, 2020. "Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments," Papers 2012.10315, arXiv.org, revised Mar 2023.
    5. Guido Imbens & Nathan Kallus & Xiaojie Mao, 2021. "Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models," Papers 2108.03849, arXiv.org.
    6. Ben Deaner, 2022. "Controlling for Latent Confounding with Triple Proxies," Papers 2204.13815, arXiv.org, revised May 2023.
    7. Ben Deaner, 2021. "Many Proxy Controls," Papers 2110.03973, arXiv.org.
    8. 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.
    9. Zhang, Jeffrey & Li, Wei & Miao, Wang & Tchetgen Tchetgen, Eric, 2023. "Proximal causal inference without uniqueness assumptions," Statistics & Probability Letters, Elsevier, vol. 198(C).

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