Modeling charity donations: target selection, response time and gift size

Charitable organizations often consider direct mailings to raise donations. Obviously, it is important for a charity to make a profitable selection from available mailing lists, which can be its own list or a list obtained elsewhere. For this purpose, a charitable organization usually has to address the following four questions: 1. Who should we send a mailing? 2. Who is likely to respond to that mailing? 3. How much time will it take for such an individual to respond? 4. How much money will this individual donate? Several techniques for addressing one or more of these questions have been suggested in the literature. For example, Bult and Wansbeek (1995) develop a model that addresses question 2. Otter et al. (1997) develop a model that jointly considers questions 2 and 4. In practice one often relies on techniques such as RFM-based decision rules (Bauer 1988) in order to answer question 1. In this paper we develop a model which enables a charitable organization to make an optimal selection from its own mailing list, while simultaneously considering the four questions above. Hence, our model consists of four components with a possible non-zero correlation structure. The explanatory variables in each of these components are RFM-type variables, where these are allowed to have different effects on the various variables to be explained. In particular, we show that the first component is essential when a target selection model is applied on a database. Neglecting this component can generate a substantial bias in the results of subsequent analysis. The various model parameters are estimated by maximum likelihood. We illustrate our model using a random drawing of about 5,300 individuals from the database of a large Dutch charitable organization. Our empirical results indicate the relevance of the non-zero correlation across the model components, and the relevance of taking account of the target selection part. We find some RFM variables to have effects with opposite signs on the probability to respond, the time for response and the donation. It is found that the most profitable individuals are not the ones who have maximum scores on the RFM variables. We conclude with a discussion of various further research topics.