They are as inevitable as death and taxes: public radio fund drives. For weeks they cast their lures of silk-screened travel mugs, embroidered fleece jackets, and logo-embossed tote bags out over the airwaves, hoping to hook listeners who might not otherwise write a check.

Such rewards often do increase nonprofits’ take, says Roland Bénabou, a professor in Princeton University’s department of economics and Woodrow Wilson School of Public and International Affairs. But if radio stations...

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