Individual-level Carryover-Parameters in Reference-Price Models

Reference-price models applied to real purchase data have a long history in marketing and consumer research (Winer 2014). Here, the researcher assumes that product choice is driven by deviations between current prices and consumers’ reference-price. There is the consensus that ignoring unobserved consumer heterogeneity in reference-price models will overestimate consumer response to gains and losses (Mazumdar et al. 2005, Kopalle et al. 2012, Neumann and Böckenholt 2014). However, previous research has neglected heterogeneity for the carryover-parameters that explain the short- vs. long-term memory of consumers in reference-price formation. Consumer research acknowledges individual differences in consumer’s ability to remember prices (Monroe and Lee 1999, Vanhuele and Drèze 2002). Hence, the current practice in reference-price modeling may disregard realistic choice behavior. To the best of our knowledge, only two previous studies have made attempts to partly account for heterogeneity in the carryover-parameters. Erdem et al. (2010) used a Maximum Simulated Likelihood approach to estimate the mean and standard deviation of a Normal mixing distribution to account for heterogeneity. To obtain individual-level estimates, this approach would require an additional Bayesian updating step (see, Revelt and Train 2000). In addition, the authors assumed no correlation in the heterogeneity distribution which simplifies identification but impairs capturing realistic choice behavior. A second study by Dayaratna and Kannan (2012) provides a mathematical reformulation of reference-price models. The authors estimate a finite-mixture heterogeneity distribution with three segments (and therefore only three segment-specific carryover-parameters). In this context, Dayaratna and Kannan (2012) discuss hierarchical Bayesian (HB) approaches as an avenue for future research to obtain individual-level carryover-parameters.