Stochastic Models of Interpurchase Time with Time-Dependent Covariates

Abstract

Consumers’ purchase time decisions are important elements of their buying decision process. Stochastic models of interpurchase time, which have been used extensively in the marketing literature, are parsimonious, easy to estimate, and usually fit and predict the data well. However, there has been a striking omission of marketing variables in these models. Because empirical evidence suggests that marketing variables, such as promotions, can affect consumers’ purchase time decisions, the author presents a methodology for including such variables in these stochastic models. Four commonly used models are discussed: exponential, Erlang-2 (no heterogeneity), and these two models with gamma heterogeneity. Thus one can include duration dependence, heterogeneity, and nonstationarity in the model, and also account for right-censored data. Special care is shown to be needed when covariates, such as marketing variables, vary over time. The models are analytically tractable, which makes their estimation and validation simple and fast. An illustration of the methodology is provided with scanner panel data for coffee. Inclusion of duration dependence, heterogeneity, and marketing variables is shown to improve the model's diagnostics, fit, and predictions.