We present a new model of charitable giving where individuals regard out-of-pocket donations and the matches they induce as different. We show that match-price elasticities combine conventional price effects with the strength of warm glow, so that a match-price elasticity alone is insufficient to characterize preferences for giving. Match- and rebate-price elasticities will be different, but together they lead to new tests of underlying giving preferences. We estimate, for the first time, a match-price elasticity in a high-stakes setting together with a rebate elasticity induced by tax policy. The estimates reject extant models of giving but are consistent with the new theory.

Researchers measure crowd-out around one level of charity output to identify whether giving is motivated by altruism and/or warm-glow. However, crowd-out depends on output, implying first that the power to reject pure altruism varies, and second that a single measurement of incomplete crowd-out can be rationalized by many different preferences. By instead measuring crowd-out at different output levels, we allow both for identification and for a novel and direct test of impure altruism. Using a new experimental design, we present the first empirical evidence that, consistent with impure altruism, crowd-out decreases with output. (JEL D64, L31)