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Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions

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  • Sung Jae Jun
  • Sokbae Lee

Abstract

We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the potential outcome framework. It is shown that strong ignorability is not always as powerful as it is under random sampling and that certain monotonicity assumptions yield comparable results in terms of sharp identified intervals. Specifically, the usual odds ratio is shown to be a sharp identified upper bound on causal relative risk under the monotone treatment response and monotone treatment selection assumptions. We offer algorithms for inference on the causal parameters that are aggregated over the true population distribution of the covariates. We show the usefulness of our approach by studying three empirical examples: the benefit of attending private school for entering a prestigious university in Pakistan; the relationship between staying in school and getting involved with drug-trafficking gangs in Brazil; and the link between physicians' hours and size of the group practice in the United States.

Suggested Citation

  • Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions," Papers 2004.08318, arXiv.org, revised Oct 2023.
  • Handle: RePEc:arx:papers:2004.08318
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    1. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn & Zhipeng Liao, 2014. "Asymptotic Efficiency of Semiparametric Two-step GMM," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 919-943.
    2. Imbens, Guido W, 1992. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Econometrica, Econometric Society, vol. 60(5), pages 1187-1214, September.
    3. James J. Heckman & Petra E. Todd, 2009. "A note on adapting propensity score matching and selection models to choice based samples," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 230-234, January.
    4. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    5. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    6. 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.
    7. Wooyoung Kim & Koohyun Kwon & Soonwoo Kwon & Sokbae Lee, 2018. "The identification power of smoothness assumptions in models with counterfactual outcomes," Quantitative Economics, Econometric Society, vol. 9(2), pages 617-642, July.
    8. Alexandre Belloni & Victor Chernozhukov & Ying Wei, 2016. "Post-Selection Inference for Generalized Linear Models With Many Controls," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 606-619, October.
    9. Tamer, Elie, 2010. "Partial Identification in Econometrics," Scholarly Articles 34728615, Harvard University Department of Economics.
    10. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    11. Carvalho, Leandro S. & Soares, Rodrigo R., 2016. "Living on the edge: Youth entry, career and exit in drug-selling gangs," Journal of Economic Behavior & Organization, Elsevier, vol. 121(C), pages 77-98.
    12. 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.
    13. Kani Chen, 2001. "Parametric models for response‐biased sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 775-789.
    14. Hua Yun Chen, 2007. "A Semiparametric Odds Ratio Model for Measuring Association," Biometrics, The International Biometric Society, vol. 63(2), pages 413-421, June.
    15. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
    16. Janet Currie & Matthew Neidell, 2005. "Air Pollution and Infant Health: What Can We Learn from California's Recent Experience?," The Quarterly Journal of Economics, Oxford University Press, vol. 120(3), pages 1003-1030.
    17. Machado, Cecilia & Shaikh, Azeem M. & Vytlacil, Edward J., 2019. "Instrumental variables and the sign of the average treatment effect," Journal of Econometrics, Elsevier, vol. 212(2), pages 522-555.
    18. Brent Kreider & John V. Pepper & Craig Gundersen & Dean Jolliffe, 2012. "Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 958-975, September.
    19. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    20. Yu Xie & Charles F. Manski, 1989. "The Logit Model and Response-Based Samples," Sociological Methods & Research, , vol. 17(3), pages 283-302, February.
    21. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    22. Imbens, Guido W. & Lancaster, Tony, 1996. "Efficient estimation and stratified sampling," Journal of Econometrics, Elsevier, vol. 74(2), pages 289-318, October.
    23. Jay Bhattacharya & Azeem M. Shaikh & Edward Vytlacil, 2008. "Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization," American Economic Review, American Economic Association, vol. 98(2), pages 351-356, May.
    24. Lancaster, Tony & Imbens, Guido, 1996. "Case-control studies with contaminated controls," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 145-160.
    25. Eric J. Tchetgen Tchetgen & James M. Robins & Andrea Rotnitzky, 2010. "On doubly robust estimation in a semiparametric odds ratio model," Biometrika, Biometrika Trust, vol. 97(1), pages 171-180.
    26. Heckman, James J. & Robb, Richard Jr., 1985. "Alternative methods for evaluating the impact of interventions : An overview," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 239-267.
    27. Tsunao Okumura & Emiko Usui, 2014. "Concave‐monotone treatment response and monotone treatment selection: With an application to the returns to schooling," Quantitative Economics, Econometric Society, vol. 5, pages 175-194, March.
    28. E. H. Kennedy & A. Sjölander & D. S. Small, 2015. "Semiparametric causal inference in matched cohort studies," Biometrika, Biometrika Trust, vol. 102(3), pages 739-746.
    29. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    30. Bhattacharya, Jay & Shaikh, Azeem M. & Vytlacil, Edward, 2012. "Treatment effect bounds: An application to Swan–Ganz catheterization," Journal of Econometrics, Elsevier, vol. 168(2), pages 223-243.
    31. Daniel Ackerberg & Xiaohong Chen & Jinyong Hahn, 2012. "A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 481-498, May.
    32. Ian Domowitz & Robert L. Sartain, 1999. "Determinants of the Consumer Bankruptcy Decision," Journal of Finance, American Finance Association, vol. 54(1), pages 403-420, February.
    33. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    34. 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.
    35. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    36. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, October.
    37. Jing Zhou & Amy H. Herring & Anirban Bhattacharya & Andrew F. Olshan & David B. Dunson, 2016. "Nonparametric Bayes modeling for case control studies with many predictors," Biometrics, The International Biometric Society, vol. 72(1), pages 184-192, March.
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    Cited by:

    1. Sung Jae Jun & Sokbae Lee, 2022. "Average Adjusted Association: Efficient Estimation with High Dimensional Confounders," Papers 2205.14048, arXiv.org, revised Apr 2023.

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