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

Abstract

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.