Dipak C. Jain

A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data

A random-coefficients logit model that allows for unobserved heterogeneity in brand preferences and in the responses to marketing variables is empirically investigated using household-level panel data. The unknown underlying distribution of unobserved heterogeneity is approximated by a discrete distribution. The results reveal that there is significant unobserved heterogeneity across households and that ignoring its effects results in a downward bias in the parameter estimates of the marketing variables. It is therefore important to account for heterogeneity in both preferences and responses in the absence of any a priori knowledge about the nature of heterogeneity across households.

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.

Optimal Dynamic Advertising Policy for New Products

Advertising is one of the key marketing tools managers have at their disposal to influence their customers into purchasing a new product. The overall objective of new product advertising is to inform and persuade customers. Drawing up an advertising plan for a new product that is under the influence of diffusion phenomenon is not an easy task. Hence, research in this area is very limited. In our research, we use an empirically proven diffusion demand function that explicitly incorporates the advertising component. Our results suggest that optimal advertising is determined by the advertising effectiveness, discount rate, and the ratio of advertisement to profits. Depending upon the interplay among these factors, the optimal advertising takes decrease-increase, increase-decrease, monotonically increasing or monotonically decreasing shape.

A Generalized Norton--Bass Model for Multigeneration Diffusion

The Norton-Bass (NB) model is often credited as the pioneering multigeneration diffusion model in marketing. However, as acknowledged by the authors, when counting the number of adopters who substitute an old product generation with a new generation, the NB model does not differentiate those who have already adopted the old generation from those who have not. In this study, we develop a Generalized Norton-Bass (GNB) model that separates the two different types of substitutions. The GNB model provides closed-form expressions for both the number of units-in-use and the adoption rate, and offers greater flexibility in parameter estimation, forecasting, and revenue projection. An appealing aspect of the GNB model is that it uses exactly the same set of parameters as the NB model and is mathematically consistent with the later. Empirical results show that the GNB model delivers better overall performance than previous models both in terms of model fit and forecasting performance. The analyses also show that differentiating leapfrogging and switching adoptions based on the GNB model can help gain additional insights into the process of multigeneration diffusion. Furthermore, we demonstrate that the GNB model can incorporate the effect of marketing mix variables on the speed of diffusion for all product generations.

A generalized framework for estimating customer lifetime value when customer lifetimes are not observed

Measuring customer lifetime value (CLV) in contexts where customer defections are not observed, i.e. noncontractual contexts, has been very challenging for firms. This paper proposes a flexible Markov Chain Monte Carlo (MCMC) based data augmentation framework for forecasting lifetimes and estimating customer lifetime value (CLV) in such contexts. The framework can be used to estimate many different types of CLV models—both existing and new. Models proposed so far for estimating CLV in noncontractual contexts have built-in stringent assumptions with respect to the underlying customer lifetime and purchase behavior. For example, two existing state-of-the-art models for lifetime value estimation in a noncontractual context are the Pareto/NBD and the BG/NBD models. Both of these models are based on fixed underlying assumptions about drivers of CLV that cannot be changed even in situations where the firm believes that these assumptions are violated. The proposed simulation framework—not being a model but an estimation framework—allows the user to use any of the commonly available statistical distributions for the drivers of CLV, and thus the multitude of models that can be estimated using the proposed framework (the Pareto/NBD and the BG/NBD models included) is limited only by the availability of statistical distributions. In addition, the proposed framework allows users to incorporate covariates and correlations across all the drivers of CLV in estimating lifetime values of customers.

An Empirical Analysis of Price Discrimination Mechanisms and Retailer Profitability

Retailers typically engage in some form of price discrimination to increase profitability. In this article, the authors compare the impact on retailer profitability of two price discrimination mechanisms: quantity discounts based on package size (second-degree price discrimination) and store-level pricing or micromarketing (third-degree price discrimination). Whereas the latter has been well addressed in the marketing literature, there is limited empirical research on the use of quantity discounts for price discrimination. Using store-level sales data, the authors estimate a structural demand model, accounting for parameter heterogeneity and price endogeneity. They combine the parameter estimates with a model of retailer pricing to conduct optimal pricing and profitability simulations under several scenarios, ranging from constraining the retailer not to engage in any form of price discrimination to the least restrictive scenario of setting nonlinear price schedules specific to each store. The pricing simulations enable the decomposition of profitability as a result of the different forms of price discrimination. Profits are greatest when retailers combine second- and third-degree price discrimination. The authors find that the ability to engage in second-degree price discrimination contributes more to retailer profitability than does third-degree price discrimination.

Research Note---Customer Loyalty Programs: Are They Profitable?

Loyalty programs are very common in practice. Many researchers have worked at understanding the impact of loyalty programs on market competition and the mechanism behind it. Interestingly, almost all of the studies have explored a symmetric equilibrium where both of the competing firms offer a loyalty program. To our knowledge, the extant literature has not investigated in-depth whether asymmetric equilibrium can exist where only one firm chooses to offer a loyalty program and the other firm chooses to compete via lowering prices. Such a question is important because some markets do support such asymmetric equilibriums with respect to loyalty programs. Also, the existence of asymmetric equilibrium shows that a loyalty program need not be profitable for some firms. In this paper, we use a game-theoretic framework to investigate specific types of customer loyalty programs that provide benefit to loyal customers in the form of discount over market prices. The model considers consumer switching and includes two types of consumer heterogeneity. The first type of heterogeneity concerns the differences between customers with respect to their liking for loyalty programs, and the second type concerns the differences among the loyalty program members with respect to their ability to collect enough loyalty points to redeem loyalty rewards. By analyzing a duopoly market, we find that both symmetric equilibrium (i.e., where both competing firms offer the loyalty program) and asymmetric equilibrium (i.e., where one firm alone offers the loyalty program) can be sustained. The paper explores conditions for the existence of these two equilibriums.

Simple approaches to evaluate competing non-nested models in marketing☆

Abstract In marketing contexts where no economic or behavioral theory exists to guide researchers, or where there are several competing theories, it is important to explore approaches to compare competing model alternatives. These alternatives are often non-nested; in such cases, recourse to recently developed econometric approaches facilitates comparisons between rival models. Using empirical illustrations (involving sales response, innovation diffusion, and market share models), we highlight the relative simplicity of implementing statistical tests to evaluate competing non-nested model alternatives. This expository review also outlines the focus, scope, merits, and demerits of various tests to compare non-nested models, thereby providing a broad basis for selecting an appropriate test for a given non-nested model-comparison context.

Effect of choice set size on choice probabilities: An extended logit model

Abstract The multinomial logit model in the context of the Luce choice axiom implies that the logarithm of the ratio of choice probabilities (the log odds ratio) of two objects depends only on the attributes of the two objects and not on the attributes of other objects in the choice set. Noting this weakness of the Luce choice axiom and the conventional logit model, Batsell and Polking (1985) prove the existence of a unique set of additive numbers that equate to the log odds ratio and that depend on the objects in the choice set. They observed that the Luce model spawned multiattribute extensions and applications and call for such extensions and applications of their generalization of the Luce model. We provide such an extension here and show analytically that it is possible to stay within the multinomial logit family while avoiding the IIA restriction.

A Likelihood Approach to Estimating Market Equilibrium Models

This paper develops a new likelihood-based method for the simultaneous estimation of structural demand-and-supply models for markets with differentiated products. We specify an individual-level discrete-choice model of demand and derive the supply side assuming manufacturers compete in prices. The proposed estimation method considers price endogeneity through simultaneous estimation of demand and supply, allows for consumer heterogeneity, and incorporates a pricing rule consistent with economic theory.The basic idea behind the proposed estimation procedure is to simulate prices and choice probabilities by solving for the market equilibrium. By repeating this many times, we obtain an empirical distribution of equilibrium prices and probabilities. The empirical distribution is then smoothed and used in a likelihood procedure to estimate the parameters of the model. The advantage of this method is that it avoids the need to perform a transformation of variables. If the tastes of consumers are independent across market periods, our approach yields maximum likelihood estimates; otherwise, it yields consistent but not fully efficient partial likelihood estimates.