  This paper provides a set of methods for quantifying the robustness of
treatment effects estimated using the unconfoundedness assumption (also known
as selection on observables or conditional independence). Specifically, we
estimate and do inference on bounds on various treatment effect parameters,
like the average treatment effect (ATE) and the average effect of treatment on
the treated (ATT), under nonparametric relaxations of the unconfoundedness
assumption indexed by a scalar sensitivity parameter c. These relaxations allow
for limited selection on unobservables, depending on the value of c. For large
enough c, these bounds equal the no assumptions bounds. Using a non-standard
bootstrap method, we show how to construct confidence bands for these bound
functions which are uniform over all values of c. We illustrate these methods
with an empirical application to effects of the National Supported Work
Demonstration program. We implement these methods in a companion Stata module
for easy use in practice.
