  This paper proposes a framework to analyze the effects of counterfactual
policies on the unconditional quantiles of an outcome variable. For a given
counterfactual policy, we obtain identified sets for the effect of both
marginal and global changes in the proportion of treated individuals. To
conduct a sensitivity analysis, we introduce the quantile breakdown frontier, a
curve that (i) indicates whether a sensitivity analysis is possible or not, and
(ii) when a sensitivity analysis is possible, quantifies the amount of
selection bias consistent with a given conclusion of interest across different
quantiles. To illustrate our method, we perform a sensitivity analysis on the
effect of unionizing low income workers on the quantiles of the distribution of
(log) wages.
