Flexible estimation of time-varying effects for frequently purchased retail goods: a modeling approach based on household panel data

In most previous applications of brand choice models, possible time-varying effects in consumer behavior are ignored by merely imposing constant parameters. However, it is very likely that trends or short-term variations in consumers’ intrinsic brand utilities or sensitivities to marketing instruments occur. For example, preferences for specific brands or price elasticities in product categories such as coffee or chocolate may vary in the run-up to festive occasions like Easter or Christmas. In this paper, we employ flexible multinomial logit models for estimating time-varying effects in brand choice behavior. Time-varying brand intercepts and time-varying effects of covariates are modeled using penalized splines, a flexible, yet parsimonious, nonparametric smoothing technique. The estimation is data driven; the flexible functions, as well as the corresponding degrees of smoothness, are determined simultaneously in a unified approach. Our model further allows for alternative-specific time-varying effects of covariates and can mimic state-space approaches with random walk parameter dynamics. In an empirical application for ground coffee, we compare the performance of the proposed approach to a number of benchmark models regarding in-sample fit, information criteria, and in particular out-of-sample fit. Interestingly, the most complex P-spline model with time-varying brand intercepts and brand-specific time-varying covariate effects outperforms all other specifications both in- and out-of-sample. We further present results from a sensitivity analysis on how the number of knots and other P-spline settings affect the model performance, and we provide guidelines for the model building process about the many options for model specification using P-splines. Finally, the resulting parameter paths provide valuable insights for marketing managers.