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Article Excerpt
We propose a utility-theoretic brand-choice model that accounts for four different sources of state dependence: 1. effects of lagged choices (structural state dependence), 2. effects of serially correlated error terms in the random utility function (habit persistence type 1), 3. effects of serial correlations between utility-maximizing alternatives on successive purchase occasions of a household (habit persistence type 2), and 4. effects of lagged marketing variables (carryover effects). Our proposed model also allows habit persistence to be a function of lagged marketing variables, while accommodating the effects of unobserved heterogeneity in household choice parameters. This model is more flexible than existing state-dependence models in marketing and labor econometrics. Using scanner panel data, we find structural state dependence to be the most important source of state dependence. Marketing-mix elasticities are systematically understated if state-dependence effects are incompletely accounted for. The Seetharaman and Chintagunta (1998) model is shown to recover spurious variety-seeking effects while overstating habit-persistence effects. Ignoring habit persistence type 1 leads to an underestimation, while ignoring habit persistence type 2 leads to an overestimation of structural state-dependence effects. We find lagged promotions to have carryover effects on habit persistence. Ignoring one or more sources of state dependence underestimates the total incremental impact of a sales promotion. We draw implications for manufacturer pricing.
Key words: brand choice; state dependence; habit persistence; lagged choices; lagged utilities; serial correlation; distributed lags; marketing carryover; random utility
History: This paper was received April 24, 2002, and was with the authors 1 month for 2 revisions; processed by Pradeep Chintagunta.
1. Introduction
A household's prior purchase experiences with specific brands typically influence the household's purchase propensities for the same brands in the future. In such cases, there is said to be structural state dependence in the household's brand choices over time. Structural state dependence can be positive or negative, in which cases they are called inertia (Jeuland 1979) and variety seeking (McAlister 1982), respectively. The existence of inertia motivates marketers' employment of promotional schemes such as free sampling in the hope that the current-period costs of distributing free samples will be more than offset by the benefits of "hooking" households to the brand for the long term. The existence of variety seeking motivates the lengthening of product lines by manufacturers, in the hope that households' variety-driven brand switching benefits their franchise. There has been a lot of empirical work in marketing over the past 20 years on the estimation of structural state-dependence effects using scanner panel data. The consensus that has emerged in this literature is that there is substantial evidence of structural state dependence in households' brand choices even after adequately controlling for unobserved heterogeneity across households (Keane 1997, Abramson et al. 2000, Moshkin and Shachar 2002). In this literature, structural state dependence is modeled using an exponentially smoothed loyalty variable constructed on the basis of all previous choices of the household as a covariate in the household's random utility for a brand (Guadagni and Little 1983).
In addition to the abovementioned structural state-dependence effects (i.e., the effects of lagged choices), there is a second source of state dependence in a household's brand choices over time, namely, the effects of the household's lagged utilities for brands. This source of state dependence is called habit persistence (Heckman 1981b). For example, if a household's relative evaluation of brand j is high during a shopping trip at time t, the household's favorable evaluation of brand j is likely to persist during the household's next shopping trip at time t + 1 even if the household does not actually purchase brand j at time t. Such lagged utility effects imply that even if a brand's current promotions do not stimulate households to purchase the brand in the current period, they may induce them to purchase the brand in the future (through the persistence in favorable brand evaluations). In this study, we propose a distributed lag model of brand choices that accounts for not only structural state dependence, using a loyalty variable, but also three distinct sources of habit persistence. The first, called carryover effects, arises on account of marketing-mix effects on households' brand choices "spilling over" into future periods, for example, due to decaying effects of advertising and reference price effects. The second, called habit persistence type 1, arises on account of temporal persistence in households' utilities for brands for reasons unknown to the researcher, for example, due to the effects of guests staying over at home, which necessitates purchases of similar brands to suit their needs over time. The third, called habit persistence type 2, measures temporal dependencies between a household's successive brand choices that arise on account of multiple (unobserved) information signals that households keep receiving over time between purchases (from such sources as billboard signs, television advertisements, etc., that are not recorded in the data). In other words, our proposed model accounts for state dependence (1) in as complete a manner as possible, and generalizes previously proposed state-dependence models such as Allenby and Lenk (1994), Roy et al. (1996), Keane (1997), etc. that have accounted for only a subset of the effects captured in our model. We derive implications for marketing strategy.
2. Model Formulation
Heckman's (1981b) model allows an individual's current utility for an alternative [U.sub.jt] to be related both to the individual's lagged choice outcome for the alternative and the individual's lagged utility for the same alternative [U.sub.jt-1]. One specific parametric form of Heckman's (1981b) model is given below.
(1)[U.sub.jt] = [[alpha].sub.j] + [X.sub.jt] * [beta] + [gamma] * [I.sub.jt-1] + [lambda] * [U.sub.jt-1] + [[epsilon].sub.jt],
where [U.sub.jt] and [U.sub.jt-1] stand for the household's random utility for brand j at time t and t - 1, respectively; [X.sub.jt] is a vector of explanatory variables (marketing variables such as price, display, and feature in the context of brand choices) characterizing alternative j at time t; [I.sub.jt-1] is an indicator variable that takes the value 1 if alternative j was purchased at time t - 1 and otherwise; and [[epsilon].sub.jt] is a random error term that captures the effects of unobserved variables. In this model, [[alpha].sub.j] and [beta] are the alternative-specific intercept and the vector of marketing-mix response parameters, respectively, while parameter [gamma] estimates the effect of structural state dependence, while parameter [lambda] estimates the effect of habit persistence.
Consider the following distributed lag model.
(2) [U.sub.jt] = [[alpha].sub.j] + ([X.sub.jt] + [X.sub.jt-1] * [lambda] + [X.sub.jt-2] * [[lambda].sup.2]
+ [X.sub.jt-3] * [[lambda].sup.3] + ...) * [beta] + [gamma]
* ([I.sub.jt-1] + [I.sub.jt-2] * [lambda] + [I.sub.jt-3] * [[lambda].sup.2] + [I.sub.jt-4] * [[lambda].sup.3]...
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