Bruce G. S. Hardie

Modeling Customer Lifetime Value

As modern economies become predominantly service-based, companies increasingly derive revenue from the creation and sustenance of long-term relationships with their customers. In such an environment, marketing serves the purpose of maximizing customer lifetime value (CLV) and customer equity, which is the sum of the lifetime values of the company’s customers. This article reviews a number of implementable CLV models that are useful for market segmentation and the allocation of marketing resources for acquisition, retention, and cross-selling. The authors review several empirical insights that were obtained from these models and conclude with an agenda of areas that are in need of further research.

RFM and CLV: Using Iso-Value Curves for Customer Base Analysis

The authors present a new model that links the well-known RFM (recency, frequency, and monetary value) paradigm with customer lifetime value (CLV). Although previous researchers have made a conceptual link, none has presented a formal model with a well-grounded behavioral ”story.” Key to this analysis is the notion of ”iso-value” curves, which enable the grouping of individual customers who have different purchasing histories but similar future valuations. Iso-value curves make it easy to visualize the interactions and trade-offs among the RFM measures and CLV. The stochastic model is based on the Pareto/NBD framework to capture the flow of transactions over time and a gamma-gamma submodel for spend per transaction. The authors conduct several holdout tests to demonstrate the validity of the models underlying components and then use it to estimate the total CLV for a cohort of new customers of the online music site CDNOW. Finally, the authors discuss broader issues and opportunities in the application of this model in actual practice.

Analytics for Customer Engagement

In this article, we discuss the state of the art of models for customer engagement and the problems that are inherent to calibrating and implementing these models. The authors first provide an overview of the data available for customer analytics and discuss recent developments. Next, the authors discuss the models used for studying customer engagement, where they distinguish the following stages: customer acquisition, customer development, and customer retention. Finally, they discuss several organizational issues of analytics for customer engagement, which constitute barriers for introducing analytics for customer engagement.

Marketing-Mix Variables and the Diffusion of Successive Generations of a Technological Innovation

Research addressing the diffusion of successive generations of technological innovations has generally ignored the impact of marketing-mix variables. As a result, there have been several calls for the development of multiple-generation models that incorporate marketing-mix variables. The authors develop a model of first-time sales and subscriptions for successive generations of a technological innovation, which explicitly captures the effects of marketing-mix variables through a proportional hazards framework. The empirical analysis estimates the impact of price for two generations of cellular telephones in a European country. The results suggest that there are important substantive insights to be gained from the parameter estimates for this marketing-mix variable when intergenerational interdependencies are considered. For example, although the time path of the estimated price elasticities in a multiple-generation setting closely follows those reported previously for single generations, the authors find evidence of an important interaction in price response across generations. Therefore, empirical estimates in single-generation models may be missing an important part of the pricing equation.

An Empirical Comparison of New Product Trial Forecasting Models

While numerous researchers have proposed diAerent models to forecast trial sales for new products, there is little systematic understanding about which of these models works best, and under what circumstances these findings change. In this paper, we provide a comprehensive investigation of eight leading published models and three diAerent parameter estimation methods. Across 19 diAerent datasets encompassing a variety of consumer packaged goods, we observe several systematic patterns that link diAerences in model specification and estimation to forecasting accuracy. Major findings include the following observations: (1) when dealing with consumer packaged goods, simple models that allow for relatively limited flexibility (e.g. no S-shaped curves) in the calibration period provide significantly better forecasts than more complex specifications; (2) models that explicitly accommodate heterogeneity in purchasing rates across consumers tend to oAer better forecasts than those that do not; and (3) maximum likelihood estimation appears to oAer more accurate and stable forecasts than nonlinear least squares. We elaborate on these and other findings, and oAer suggested directions for future research in this area. #1998 John Wiley & Sons, Ltd. Almost every textbook discussion of the new product development process includes a call to conduct some form of market test before actually launching the new product. Such an exercise serves several objectives, including the desire to produce an accurate forecast of the new product’s sales performance over time. These forecasts can help lead to a final go/no-go decision and can also assist in the marketing and production planning activities associated with the product launch. In the case of consumer packaged goods, conducting a market test historically saw the company’s sales force selling the product into retail distribution in one or more markets for one to two years, after which a decision of whether or not to go national with the new product was

Customer-Base Valuation in a Contractual Setting: The Perils of Ignoring Heterogeneity

The past few years have seen increasing interest in taking the notion of customer lifetime value (CLV) and extending it to value a customer base (with subsequent links to corporate valuation). The application of standard textbook discussions of CLV leads to calculations based on a single retention rate. However, at the cohort level, retention rates typically increase over time. It has been suggested that these observed dynamics are due, in large part, to a sorting effect in a heterogeneous population. We show that failing to recognize these dynamics yields a downward-biased estimate of the residual value of the customer base (compared to an aggregate analysis that ignores these dynamics). We also explore the implications of failing to account for retention dynamics when computing retention elasticities and find that the frequently reported values underestimate the true effect of increases in underlying retention rates in a heterogeneous world.

New Perspectives on Customer “Death” Using a Generalization of the Pareto/NBD Model

Several researchers have proposed models of buyer behavior in noncontractual settings that assume that customers are “alive” for some period of time and then become permanently inactive. The best-known such model is the Pareto/NBD, which assumes that customer attrition (dropout or “death”) can occur at any point in calendar time. A recent alternative model, the BG/NBD, assumes that customer attrition follows a Bernoulli “coin-flipping” process that occurs in “transaction time” (i.e., after every purchase occasion). Although the modification results in a model that is much easier to implement, it means that heavy buyers have more opportunities to “die.” In this paper, we develop a model with a discrete-time dropout process tied to calendar time. Specifically, we assume that every customer periodically “flips a coin” to determine whether she “drops out” or continues as a customer. For the component of purchasing while alive, we maintain the assumptions of the Pareto/NBD and BG/NBD models. This periodic death opportunity (PDO) model allows us to take a closer look at how assumptions about customer death influence model fit and various metrics typically used by managers to characterize a cohort of customers. When the time period after which each customer makes her dropout decision (which we call period length) is very small, we show analytically that the PDO model reduces to the Pareto/NBD. When the period length is longer than the calibration period, the dropout process is “shut off,” and the PDO model collapses to the negative binomial distribution (NBD) model. By systematically varying the period length between these limits, we can explore the full spectrum of models between the “continuous-time-death” Pareto/NBD and the naive “no-death” NBD. In covering this spectrum, the PDO model performs at least as well as either of these models; our empirical analysis demonstrates the superior performance of the PDO model on two data sets. We also show that the different models provide significantly different estimates of both purchasing-related and death-related metrics for both data sets, and these differences can be quite dramatic for the death-related metrics. As more researchers and managers make managerial judgments that directly relate to the death process, we assert that the model employed to generate these metrics should be chosen carefully.

Bacon With Your Eggs? Applications of a New Bivariate Beta-Binomial Distribution

We present two everyday applications of a new bivariate beta-binomial distribution. Although the applications are familiar, they share unique characteristics that cannot be handled adequately by existing bivariate discrete distributions. These features are high levels of between- and within-trial correlation for the bivariate random variables. Our model is derived from a broad class of bivariate models based on a versatile, but little-known, family of distributions due to Sarmanov. For the applications presented, we show that our model fits observed data very well. In addition, for the bacon and eggs application, the model can be used to help improve the management of inventory in grocery stores.

A Joint Model of Usage and Churn in Contractual Settings

As firms become more customer-centric, concepts such as customer equity come to the fore. Any serious attempt to quantify customer equity requires modeling techniques that can provide accurate multiperiod forecasts of customer behavior. Although a number of researchers have explored the problem of modeling customer churn in contractual settings, there is surprisingly limited research on the modeling of usage while under contract. The present work contributes to the existing literature by developing an integrated model of usage and retention in contractual settings. The proposed method fully leverages the interdependencies between these two behaviors even when they occur on different time scales or “clocks”, as is typically the case in most contractual/subscription-based business settings. We propose a model in which usage and renewal are modeled simultaneously by assuming that both behaviors reflect a common latent variable that evolves over time. We capture the dynamics in the latent variable using a hidden Markov model with a heterogeneous transition matrix and allow for unobserved heterogeneity in the associated usage process to capture time-invariant differences across customers. The model is validated using data from an organization in which an annual membership is required to gain the right to buy its products and services. We show that the proposed model outperforms a set of benchmark models on several important dimensions. Furthermore, the model provides several insights that can be useful for managers. For example, we show how our model can be used to dynamically segment the customer base and identify the most common “paths to death” i.e., stages that customers go through before churn.

Bayesian Inference for the Negative Binomial Distribution via Polynomial Expansions

To date, Bayesian inferences for the negative binomial distribution (NBD) have relied on computationally intensive numerical methods (e.g., Markov chain Monte Carlo) as it is thought that the posterior densities of interest are not amenable to closed-form integration. In this article, we present a “closed-form” solution to the Bayesian inference problem for the NBD that can be written as a sum of polynomial terms. The key insight is to approximate the ratio of two gamma functions using a polynomial expansion, which then allows for the use of a conjugate prior. Given this approximation, we arrive at closed-form expressions for the moments of both the marginal posterior densities and the predictive distribution by integrating the terms of the polynomial expansion in turn (now feasible due to conjugacy). We demonstrate via a large-scale simulation that this approach is very accurate and that the corresponding gains in computing time are quite substantial. Furthermore, even in cases where the computing gains are more modest our approach provides a method for obtaining starting values for other algorithms, and a method for data exploration.