• Open Access

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


  • Tsunao Okumura,

    1. Yokohama National University; okumura@ynu.ac.jp
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  • Emiko Usui

    1. Nagoya University and IZA; usui@soec.nagoya-u.ac.jp
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    • The authors thank the anonymous referees, Hidehiko Ichimura, Brendan Kline, Sokbae Lee, Adam Rosen, Elie Tamer, Edward Vytlacil, and especially Charles Manski for their helpful comments. The authors also thank participants at the annual meetings of the Econometric Society, the European Association of Labour Economists, the Midwest Econometrics Group, the Symposium on Econometric Theory and Applications (SETA), and the Western Economic Association, and those in seminars at Hitotsubashi University, Kyoto University, Northwestern University, and the University of Tokyo. This research is supported by JSPS Grant 21530167, the Kikawada Foundation, JCER, and TCER.


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.