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Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects

Author

Listed:
  • Wenlong Ji
  • Lihua Lei
  • Asher Spector
Abstract
Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper bounds; however, unless the covariates are discrete with relatively small support, this approach typically requires binning covariates or estimating the conditional distributions of the potential outcomes given the covariates. Binning can result in substantial efficiency loss and become challenging to implement, even with a moderate number of covariates. Estimating conditional distributions, on the other hand, may yield invalid inference if the distributions are inaccurately estimated, such as when a misspecified model is used or when the covariates are high-dimensional. In this paper, we propose a unified and model-agnostic inferential approach for a wide class of partially identified estimands. Our method, based on duality theory for optimal transport problems, has four key properties. First, in randomized experiments, our approach can wrap around any estimates of the conditional distributions and provide uniformly valid inference, even if the initial estimates are arbitrarily inaccurate. A simple extension of our method to observational studies is doubly robust in the usual sense. Second, if nuisance parameters are estimated at semiparametric rates, our estimator is asymptotically unbiased for the sharp partial identification bound. Third, we can apply the multiplier bootstrap to select covariates and models without sacrificing validity, even if the true model is not selected. Finally, our method is computationally efficient. Overall, in three empirical applications, our method consistently reduces the width of estimated identified sets and confidence intervals without making additional structural assumptions.

Suggested Citation

  • Wenlong Ji & Lihua Lei & Asher Spector, 2023. "Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects," Papers 2310.08115, arXiv.org, revised Nov 2024.
    • Handle: RePEc:arx:papers:2310.08115
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    References listed on IDEAS

    as
    1. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    3. Zheng Fang & Andres Santos & Azeem M. Shaikh & Alexander Torgovitsky, 2023. "Inference for Large‐Scale Linear Systems With Known Coefficients," Econometrica, Econometric Society, vol. 91(1), pages 299-327, January.
    4. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    5. Sung Jae Jun & Sokbae Lee, 2023. "Identifying the Effect of Persuasion," Journal of Political Economy, University of Chicago Press, vol. 131(8), pages 2032-2058.
    6. Brigham R. Frandsen & Lars J. Lefgren, 2021. "Partial identification of the distribution of treatment effects with an application to the Knowledge is Power Program (KIPP)," Quantitative Economics, Econometric Society, vol. 12(1), pages 143-171, January.
    7. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    8. Tetsuya Kaji & Jianfei Cao, 2023. "Assessing Heterogeneity of Treatment Effects," Papers 2306.15048, arXiv.org.
    9. Victor Chernozhukov & Iv·n Fern·ndez-Val & Alfred Galichon, 2010. "Quantile and Probability Curves Without Crossing," Econometrica, Econometric Society, vol. 78(3), pages 1093-1125, May.
    10. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    11. David S. Lee, 2009. "Training, Wages, and Sample Selection: Estimating Sharp Bounds on Treatment Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 1071-1102.
    12. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. Chiburis, Richard C., 2010. "Semiparametric bounds on treatment effects," Journal of Econometrics, Elsevier, vol. 159(2), pages 267-275, December.
    14. repec:cwl:cwldpp:1840rr is not listed on IDEAS
    15. Arun Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2012. "Inference for best linear approximations to set identified functions," CeMMAP working papers CWP43/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Peng Ding & Jiannan Lu, 2017. "Principal stratification analysis using principal scores," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 757-777, June.
    17. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    18. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, July.
    19. Victor Chernozhukov & Denis Chetverikov & Kengo Kato & Aureo de Paula, 2019. "Inference on Causal and Structural Parameters using Many Moment Inequalities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1867-1900.
    20. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    21. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4b6ga2g is not listed on IDEAS
    22. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    23. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    24. Pietro Tebaldi & Alexander Torgovitsky & Hanbin Yang, 2023. "Nonparametric Estimates of Demand in the California Health Insurance Exchange," Econometrica, Econometric Society, vol. 91(1), pages 107-146, January.
    25. Fan, Yanqin & Guerre, Emmanuel & Zhu, Dongming, 2017. "Partial identification of functionals of the joint distribution of “potential outcomes”," Journal of Econometrics, Elsevier, vol. 197(1), pages 42-59.
    26. Jacob Dorn & Kevin Guo & Nathan Kallus, 2021. "Doubly-Valid/Doubly-Sharp Sensitivity Analysis for Causal Inference with Unmeasured Confounding," Papers 2112.11449, arXiv.org, revised Jul 2022.
    27. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    28. Constantine E. Frangakis & Donald B. Rubin, 2002. "Principal Stratification in Causal Inference," Biometrics, The International Biometric Society, vol. 58(1), pages 21-29, March.
    29. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
    30. Vira Semenova, 2023. "Aggregated Intersection Bounds and Aggregated Minimax Values," Papers 2303.00982, arXiv.org, revised Jun 2024.
    31. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    32. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    33. Fan, Yanqin & Park, Sang Soo, 2010. "Sharp Bounds On The Distribution Of Treatment Effects And Their Statistical Inference," Econometric Theory, Cambridge University Press, vol. 26(3), pages 931-951, June.
    34. Aviv Nevo & John L. Turner & Jonathan W. Williams, 2016. "Usage‐Based Pricing and Demand for Residential Broadband," Econometrica, Econometric Society, vol. 84, pages 411-443, March.
    35. Sungwon Lee, 2021. "Partial Identification and Inference for Conditional Distributions of Treatment Effects," Papers 2108.00723, arXiv.org, revised Nov 2023.
    36. Hsieh, Yu-Wei & Shi, Xiaoxia & Shum, Matthew, 2022. "Inference on estimators defined by mathematical programming," Journal of Econometrics, Elsevier, vol. 226(2), pages 248-268.
    37. Fan, Yanqin & Park, Sang Soo, 2012. "Confidence intervals for the quantile of treatment effects in randomized experiments," Journal of Econometrics, Elsevier, vol. 167(2), pages 330-344.
    38. Victor Chernozhukov & Whitney Newey & Rahul Singh & Vasilis Syrgkanis, 2020. "Adversarial Estimation of Riesz Representers," Papers 2101.00009, arXiv.org, revised Apr 2024.
    39. Thomas M. Russell, 2021. "Sharp Bounds on Functionals of the Joint Distribution in the Analysis of Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 532-546, March.
    40. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    41. Victor Chernozhukov & Ivan Fernandez-Val & Alfred Galichon, 2007. "Quantile and probability curves without crossing," CeMMAP working papers CWP10/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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