We propose the use of instrumental variables and pairwise matching to identify the average treatment effect on variance in potential outcomes. We show that identifying and estimating program impact on dispersion of potential outcomes in an endogenous-switching model is possible, without using the identification-at-infinity argument, if we impose semi-parametric conditions or shape restrictions on the error structure. In the presence of a multi-valued or continuously distributed instrument, we recommend the pairwise-matching method under a set of symmetry conditions. Simulations and an empirical example show that the matching method is much more precise than the instrumental-variable approach. Copyright © 2013 John Wiley & Sons, Ltd.