  Treatment effect heterogeneity is of major interest in economics, but its
assessment is often hindered by the fundamental lack of identification of the
individual treatment effects. For example, we may want to assess the effect of
insurance on the health of otherwise unhealthy individuals, but it is
infeasible to insure only the unhealthy, and thus the causal effects for those
are not identified. Or, we may be interested in the shares of winners from a
minimum wage increase, while without observing the counterfactual, the winners
are not identified. Such heterogeneity is often assessed by quantile treatment
effects, which do not come with clear interpretation and the takeaway can
sometimes be equivocal. We show that, with the quantiles of the treated and
control outcomes, the ranges of these quantities are identified and can be
informative even when the average treatment effects are not significant. Two
applications illustrate how these ranges can inform us about heterogeneity of
the treatment effects.
