Endogeneity and non-response bias in treatment evaluation - nonparametric identification of causal effects by instruments

This paper proposes a nonparametric method for evaluating treatment effects in the presence of both treatment endogeneity and attrition/non-response bias, based on two instrumental variables. Using a discrete instrument for the treatment and an instrument with rich (in general continuous) support for non-response/attrition, we identify the average treatment effect on compliers as well as the total population under the assumption of additive separability of observed and unobserved variables affecting the outcome. We suggest non- and semiparametric estimators and apply the latter to assess the treatment effect of gym training, which is instrumented by a randomized cash incentive paid out conditional on visiting the gym, on self-assessed health among students at a Swiss university. The measurement of health is prone to non-response, which is instrumented by a cash lottery for participating in the follow-up survey.