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The identification power of smoothness assumptions in models with counterfactual outcomes

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  • Wooyoung Kim
  • Koohyun Kwon
  • Soonwoo Kwon
  • Sokbae Lee

Abstract

In this paper, we investigate what can be learned about average counterfactual outcomes as well as average treatment effects when it is assumed that treatment response functions are smooth. We obtain a set of new partial identification results for both the average treatment response and the average treatment effect. In particular, we find that the monotone treatment response and monotone treatment selection bound of Manski and Pepper, 2000 can be further tightened if we impose the smoothness conditions on the treatment response. Since it is unknown in practice whether the imposed smoothness restriction is met, it is desirable to conduct a sensitivity analysis with respect to the smoothness assumption. We demonstrate how one can carry out a sensitivity analysis for the average treatment effect by varying the degrees of smoothness assumption. We illustrate our findings by reanalyzing the return to schooling example of Manski and Pepper, 2000 and also by measuring the effect of the length of job training on the labor market outcomes.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:quante:v:9:y:2018:i:2:p:617-642
    DOI: 10.3982/QE545
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    Cited by:

    1. Kevin P. Josey & Priyanka deSouza & Xiao Wu & Danielle Braun & Rachel Nethery, 2023. "Estimating a Causal Exposure Response Function with a Continuous Error-Prone Exposure: A Study of Fine Particulate Matter and All-Cause Mortality," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 20-41, March.
    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. Lixiong Li & Désiré Kédagni & Ismaël Mourifié, 2024. "Discordant relaxations of misspecified models," Quantitative Economics, Econometric Society, vol. 15(2), pages 331-379, May.
    4. 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.
    5. Shosei Sakaguchi, 2025. "The Identification Power of Combining Experimental and Observational Data for Distributional Treatment Effect Parameters," Papers 2508.12206, arXiv.org, revised Jan 2026.
    6. Bertanha, Marinho & McCallum, Andrew H. & Seegert, Nathan, 2023. "Better bunching, nicer notching," Journal of Econometrics, Elsevier, vol. 237(2).
    7. Yiwei Sun, 2023. "Extrapolating Away from the Cutoff in Regression Discontinuity Designs," Papers 2311.18136, arXiv.org.
    8. Santiago Acerenza, 2024. "Partial Identification of Marginal Treatment Effects with Discrete Instruments and Misreported Treatment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 74-100, February.

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