Customer Lifetime Value Measurement

The measurement of customer lifetime value is important because it is used as a metric in evaluating decisions in the context of customer relationship management. For a firm, it is important to form some expectations as to the lifetime value of each customer at the time a customer starts doing business with the firm, and at each purchase by the customer. In this paper, we use a hierarchical Bayes approach to estimate the lifetime value of each customer at each purchase occasion by jointly modeling the purchase timing, purchase amount, and risk of defection from the firm for each customer. The data come from a membership-based direct marketing company where the times of each customer joining the membership and terminating it are known once these events happen. In addition, there is an uncertain relationship between customer lifetime and purchase behavior. Therefore, longer customer lifetime does not necessarily imply higher customer lifetime value. We compare the performance of our model with other models on a separate validation data set. The models compared are the extended NBD-Pareto model, the recency, frequency, and monetary value model, two models nested in our proposed model, and a heuristic model that takes the average customer lifetime, the average interpurchase time, and the average dollar purchase amount observed in our estimation sample and uses them to predict the present value of future customer revenues at each purchase occasion in our hold-out sample. The results show that our model performs better than all the other models compared both at predicting customer lifetime value and in targeting valuable customers. The results also show that longer interpurchase times are associated with larger purchase amounts and a greater risk of leaving the firm. Both male and female customers seem to have similar interpurchase time intervals and risk of leaving; however, female customers spend less compared with male customers.