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.
Concave-monotone treatment response and monotone treatment selection: With an application to the returns to schooling
Article first published online: 31 MAR 2014
Copyright © 2014 Tsunao Okumura and Emiko Usui
Volume 5, Issue 1, pages 175–194, March 2014
How to Cite
Okumura, T. and Usui, E. (2014), Concave-monotone treatment response and monotone treatment selection: With an application to the returns to schooling. Quantitative Economics, 5: 175–194. doi: 10.3982/QE268
- Issue published online: 31 MAR 2014
- Article first published online: 31 MAR 2014
- Submitted April, 2012. Final version accepted June, 2013.
- Nonparametric methods;
- partial identification;
- sharp bounds;
- treatment response;
- returns to schooling
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.