Multi-stage purchase decision models: Accommodating response heterogeneity, common demand shocks, and endogeneity using disaggregate data

The most comprehensive models of purchase behavior for frequently purchased supermarket items explain households' purchase incidence decisions (whether to buy), brand choice decisions (what to buy), and purchase quantity decisions (how much to buy). In this study, we develop a three-stage purchase incidence/brand choice/purchase quantity model for household-level data in which all three stages are specified with (i) random coefficient distributions for model covariates and (ii) random effect distributions to account for unobserved factors affecting demand (known as common demand shocks), while also (iii) controlling for the effects of endogeneity on prices. Compared to current state-of-the-art models for multi-stage purchase decisions, the results show improvements in fit and forecasting accuracy when purchase behaviors are modeled with all of these components in combination. Perhaps more importantly, when common demand shocks are ignored, substantial differences in parameter estimates and diagnostic information about consumer behavior are likely (median differences in parameter estimates are 10% and 20% in two product categories), which impact managerial deliberations about price and promotion policies. Further, failure to account for common demand shocks affects the mean and variance of random coefficient distributions in unpredictable directions, which could produce results that encourage managers to pursue inappropriate and costly micro-level product marketing strategies.