Controlling for Retailer Synergies when Evaluating Coalition Loyalty Programs: A Bayesian Additive Regression Tree Approach

Abstract

Spatial models in retailing allow for correlations among purchase decisions from consumers within predefined geographic areas. The purpose of these models is to control for unobserved demand side effects at the regional-level (e.g., a neighborhood), but they typically ignore synergies among individual retailers within a region. To capture the synergies on both the supply side (e.g., store density) and the demand side (e.g., socioeconomic differences across regions), we augment a traditional spatial model with a Bayesian Additive Regression Tree (BART). This allows us to account for unobserved regional differences and observed but potentially complex interactions among individual customers and retailers. We apply this model to a credit card coalition loyalty program (CLP). In our empirical setting, we are interested in analyzing the impact of the loyalty program earnings structure on monthly spend. We do this while controlling for the evolving coalition network, which contains hundreds of geographically dispersed partner retailers. Our data has two key features that permit this. First, the retail partner network evolves over time; this variation in retailer participation allows us to observe card spending patterns when individual retailers are both in and out of the coalition network. Second, the data contains a natural experiment where the loyalty program changed its earning structure, which allows us to estimate the impact of the rewards rate of the loyalty program on customer spend. Our findings show that failure to control for the dynamics of the coalition network results in severely biased estimates of CLP rewards effectiveness. We discuss the implications of BART in our empirical setting and highlight its potential in other marketing situations which contain numerous, interacting control variables.

Keywords: Spatial modeling, machine learning, bayesian estimation