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Concave-Monotone Treatment Response and Monotone Treatment Selection: With an Application to the Returns to Schooling

Author

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  • Okumura, Tsunao
  • 奥村, 綱雄
  • オクムラ, ツナオ
  • Usui, Emiko
  • 臼井, 恵美子
  • ウスイ, エミコ

Abstract

This paper identifies sharp bounds on the mean treatment response and average treatment effect under the assumptions of both concave monotone treatment response (concave-MTR) and monotone treatment selection (MTS). We use our bounds and the US National Longitudinal Survey of Youth to estimate mean returns to schooling. Our upperbound estimates are substantially smaller than (1) estimates using only the concave-MTR assumption of Manski (1997) and (2) estimates using only the MTR and MTS assumptions of Manski and Pepper (2000). They fall in the lower range of the point estimates given in previous studies that assume linear wage functions. This is because ability bias is corrected by assuming MTS when the functions are close to linear. Our results therefore imply that higher returns reported in previous studies are likely to be overestimated.

Suggested Citation

  • Okumura, Tsunao & 奥村, 綱雄 & オクムラ, ツナオ & Usui, Emiko & 臼井, 恵美子 & ウスイ, エミコ, 2010. "Concave-Monotone Treatment Response and Monotone Treatment Selection: With an Application to the Returns to Schooling," PIE/CIS Discussion Paper 475, Center for Intergenerational Studies, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:piecis:475
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    1. is not listed on IDEAS
    2. Sung Jae Jun & Sokbae Lee, 2024. "Causal Inference Under Outcome-Based Sampling with Monotonicity Assumptions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(3), pages 998-1009, July.
    3. Sung Jae Jun & Sokbae (Simon) Lee, 2020. "Causal inference in case-control studies," CeMMAP working papers CWP19/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Demuynck, Thomas, 2015. "Bounding average treatment effects: A linear programming approach," Economics Letters, Elsevier, vol. 137(C), pages 75-77.
    5. Sung Jae Jun & Sokbae Lee, 2025. "Bounding the Effect of Persuasion with Monotonicity Assumptions: Reassessing the Impact of TV Debates," Papers 2503.06046, arXiv.org, revised Apr 2025.
    6. Das, Tirthatanmoy & Polachek, Solomon, 2017. "Micro Foundations of Earnings Differences," IZA Discussion Papers 10922, Institute of Labor Economics (IZA).
    7. Stefan Boes, 2009. "Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints," SOI - Working Papers 0920, Socioeconomic Institute - University of Zurich.
    8. Nobuyoshi Kikuchi, 2017. "Intergenerational Transmission of Education in Japan: Nonparametric Bounds Analysis with Multiple Treatments," ISER Discussion Paper 1011, Institute of Social and Economic Research, The University of Osaka.
    9. Stefan Boes, 2010. "Convex Treatment Response and Treatment Selection," SOI - Working Papers 1001, Socioeconomic Institute - University of Zurich.
    10. 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.
    11. Sungwon Lee, 2024. "Partial identification and inference for conditional distributions of treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 107-127, January.

    More about this item

    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

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