How to model consumer heterogeneity? Lessons from three case studies on SP and RP data

The structure of consumer taste heterogeneity in discrete choice demand models is important, as it drives the structure of own and cross-price elasticities of demand, and the pattern of competition between products. Here we compare performance of three leading discrete choice models, using three datasets with very different properties. The models are the mixed logit with normal heterogeneity (N-MIXL), the generalized multinomial logit (G-MNL) and the mixture-of-normals logit (MM-MNL). Which model is preferred depends on the context: G-MNL does an excellent job of capturing the sort of departures from normality that are prevalent in stated preference (SP) data. But MM-MNL can capture more general departures from normality that are prevalent in revealed preference (RP) data. The finding that the structure of consumer taste heterogeneity is very different in SP vs. RP data suggests that caution should be applied before using SP to answer questions about the distribution of taste heterogeneity in actual markets. In an application to RP data on demand for frozen pizza, we obtain the interesting result that when a variety of a brand raises its price, most of the lost market share goes to other brands (rather than alternative varieties of the same brand). This suggests modeling heterogeneity in tastes for varieties is quite important for understanding brand switching.