• Nonparametric methods;
  • partial identification;
  • sharp bounds;
  • treatment response;
  • returns to schooling
  • C14;
  • J24

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.