Considering endogeneity for optimal catalog allocation in direct marketing

The majority of catalog allocation models using historical data ignore endogeneity of past catalog decisions. We investigate two alternative approaches which either impose a relationship between the number of catalogs allocated to a customer and customer-specific coefficients of the sales response function or use instrumental variables. Heterogeneity across customers is modeled by cluster effects following a nonparametric distribution derived from a Dirichlet process prior. Models are estimated by Markov chain Monte Carlo simulation methods and evaluated by cross-validation predictive densities. Models which consider endogeneity imply much lower effects for sending a higher number of catalogs. These models also lead to optimal allocations which differ strongly from optimal allocations obtained for models which ignore endogeneity. Higher values of both posterior model probabilities and model average profits suggest to allocate catalogs based on the instrumental variables approach.