Modeling Scale Attraction Effects : An Application to Charitable Donations and Optimal Laddering

Charities seeking donations usually employ an "appeals scale," a set of specific suggested amounts presented directly to potential donors. Choosing them well is crucial: if charities select overly high scale points, they risk their being ignored or even alienating donors and receiving nothing, while overly low scale points may encourage donors to give less than they'd have otherwise. Despite their widespread use, little is known about the degree to which the points on such scales affect both whether a donation is made and, if so, its size. Using panel data from a 3.5 year quasiexperiment, we develop a joint model accounting for both donation incidence and amount. The model incorporates heterogeneity across donors in both scale attraction effects and in donation patterns (e.g., seasonality), and allows tests of distinct operationalizations of internal and external reference price theories. Results suggest that scale points do exert substantial attraction effects; that these vary markedly across donors; that donors are more easily persuaded to give less than more; and that there are strong seasonal donation patterns in giving. A significantly negative correlation between error terms in (latent) donation propensity and (observed) donation amount highlights the importance of accounting for selectivity effects. We illustrate the framework with a speculative application to "laddering": how much charities should increase amounts subsequently requested of individual donors, based on their donation histories