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Concave‐monotone treatment response and monotone treatment selection: With an application to the returns to schooling

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  • Tsunao Okumura
  • Emiko Usui

Abstract

This paper identifies sharp bounds on the mean treatment response and average treatment effect under the assumptions of both the concave‐monotone treatment response (concave‐MTR) and the monotone treatment selection (MTS). We use our bounds and the U.S. National Longitudinal Survey of Youth 1979 to estimate mean returns to schooling. Our upper‐bound estimates are substantially smaller than (i) estimates using only the concave‐MTR assumption of Manski (1997), and (ii) estimates using only the MTR and MTS assumptions of Manski and Pepper (2000). Our upper‐bound estimates fall in the range of the point estimates given in previous studies that assume linear wage functions.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:quante:v:5:y:2014:i::p:175-194
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    2. Sung Jae Jun & Sokbae Lee, 2020. "Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions," Papers 2004.08318, arXiv.org, revised Oct 2023.
    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. Das, Tirthatanmoy & Polachek, Solomon, 2017. "Micro Foundations of Earnings Differences," IZA Discussion Papers 10922, Institute of Labor Economics (IZA).
    6. Stefan Boes, 2009. "Bounds on Counterfactual Distributions Under Semi-Monotonicity Constraints," SOI - Working Papers 0920, Socioeconomic Institute - University of Zurich.
    7. 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, Osaka University.
    8. Stefan Boes, 2010. "Convex Treatment Response and Treatment Selection," SOI - Working Papers 1001, Socioeconomic Institute - University of Zurich.
    9. 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.

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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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