Evaluating the E ffects of Having Friends on Sales with Observational Data

Abstract

We use a two-phase approach to examine the causal sales impact of having friends with observational data. The first phase uses propensity score matching to address sample selection endogeneity. The second phase leverages principal stratification to address the issue that sales are zero to both inactive customers and active customers with no value, and that customer value is only well de ned for active customers. We apply our approach to data from a massive multiplayer online game, where the sale is measured by cash spending and customer value equals to the sale if a customer logs in. Our causal estimands are: (1) the average causal effects on the probability of logging in, and the probability and amount of cash spending over all customers; (2) the average causal effects on the probability and amount of cash spending for customers who would log in regardless of whether having friends or not. We conduct a likelihood-based analysis using mixtures of two-part models, discuss identification issue, investigate the plausibility of meaningful restrictions, and conduct some sensitivity analyses. Our results demonstrate that the two-phase approach can make more detailed causal inference and have better predictive performance than the one-phase approach that uses propensity score matching only.