Open AccessThe identification power of smoothness assumptions in models with counterfactual outcomes
Author(s) -
Kim Wooyoung,
Kwon Koohyun,
Kwon Soonwoo,
Lee Sokbae
Publication year - 2018
Publication title -
quantitative economics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.062
H-Index - 27
eISSN - 1759-7331
pISSN - 1759-7323
DOI - 10.3982/qe545
Subject(s) - counterfactual thinking , smoothness , identification (biology) , econometrics , mathematics , computer science , psychology , mathematical analysis , social psychology , biology , botany
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.