Estimating CLV using aggregated data: The Tuscan Lifestyles case revisited

Abstract

The Tuscan Lifestyles case (Mason, 2003) offers a simple twist on the standard view of how to value a newly acquired customer, highlighting how standard retention-based approaches to the calculation of expected customer lifetime value (CLV) are not applicable in a noncontractual setting. Using the data presented in the case (a series of annual histograms showing the aggregate distribution of purchases for two different cohorts of customers newly “acquired” by a catalog marketer), it is a simple exercise to compute an estimate of “expected 5 year CLV.” If we wish to arrive at an estimate of CLV that includes the customer's “life” beyond five years or are interested in, say, sorting out the purchasing process (while “alive”) from the attrition process, we need to use a formal model of buying behavior that can be applied on such coarse data. To tackle this problem, we utilize the Pareto/NBD model developed by Schmittlein, Morrison, and Colombo (1987). However, existing analytical results do not allow us to estimate the model parameters using the data summaries presented in the case. We therefore derive an expression that enables us to do this. The resulting parameter estimates and subsequent calculations offer useful insights that could not have been obtained without the formal model. For instance, we were able to decompose the lifetime value into four factors, namely purchasing while active, dropout, surge in sales in the first year and monetary value of the average purchase. We observed a kind of “triple jeopardy” in that the more valuable cohort proved to be better on the three most critical factors.