Median treatment effect in randomized trials

For two response variables y _t and y _c corresponding to two treatments for two policies) T and C , we wish to learn about quantiles of y _t− y _c from the marginal quantiles of y _t and y _c; only one of y _t and y _c is observed for an individual. We find that, in general, this is difficult for quantiles other than the median unless strong assumptions are imposed on how y _t is related to y _c. For the median, we present conditions under which the sign of the median treatment effect is identified.