Bias-adjusted treatment effects under equal selection - Deepankar Basu (University of Massachusetts, Department of Economics, 2021)
In a recent contribution, Oster (2019) has proposed a method to generate bounds on treatment effects in the presence of unobservable confounders. The method can only be implemented if a crucial problem of non-uniqueness is addressed. In this paper I demonstrate that one of the proposed methods to address non-uniqueness that relies on computing bias-adjusted treatment effects under the assumption of equal selection on observables and unobservables, is problematic on several counts. First, additional assumptions, which cannot be justified on theoretical grounds, are needed to ensure a unique solution; second, the method will not work when estimate of the treatment effect declines with the addition of controls; and third, the solution, and therefore conclusions about bias, can change dramatically if we deviate from equal selection even by a small magnitude.
Keywords: C21; 330; treatment effect; omitted variable bias