A Direct Utility Model for Asymmetric Complements

Abstract

A symmetric complements refer to goods where one good is more dependent on the other, yet consumers receive enhanced utility from consuming both. Examples include garden hoses and sprinklers, chips and dip, and routine versus personalized services where the former has a broader base for utility generation and the latter is more dependent on the other's presence. Measuring asymmetric effects is difficult when all that is observed are the purchase quantities present in a consumer's market basket. We propose a direct utility model with a latent decision sequence for measuring asymmetric effects that allows us to capture differential responses to cross-category purchases and inventories. Scanner panel data of milk and cereal purchases are used to investigate the presence of asymmetric complementarity, and implications are explored through counterfactual analyses involving cross-price elasticities and spillover effects of merchandising variables.

Demand forecasting with high dimensional data: The case of SKU retail sales forecasting with intra- and inter-category promotional information

“…In Figure 3, a path diagram is presented to represent the Granger relationships among 15 selected product categories. (Wedel and Zhang, 2004;Walters, 1991;Lee et al, 2013;Hruschka, 2013), we also find that the interactions between pair of categories are asymmetric (as shown in Fig.3). For example, Carbonated beverage is affected by the promotion of Salty snack, but not vice versa.…”

Structural Models of Complementary Choices

“…Thus, we should model not only incidence but also purchase quantity (e.g., Kim et al 2002). For example, Lee and Allenby (2013) showed how to incorporate discrete package sizes into a direct utility model. Most consumer product categories admit only a few different package sizes; for example, in the US beer market, the most common options for beer are 40, 72 or 144 fluid ounces.…”

“…Furthermore, small-sample inference, coupled with discrete demand, lends itself to the use of Bayesian estimation methods (Rossi et al 2005). Data augmentation is particularly helpful in dealing with discontinuities in demand space (Lee and Allenby 2013). …”

“…A "summary statistic" approach is to capture the interaction by modeling the utility of one good, e.g., a salsa brand, as a function of the total inventory of goods from a complementary category, e.g., all brands of chips (Lee, Kim and Allenby, 2013). Thus, a consumer who has a large inventory of different brands of chips might feel compelled to buy more salsa.…”

Modeling marketplace behavior

“…Utility functions for demand models need to be developed that can cope with goods that are complements and goods that are tied, not just goods whose utility is of the additive separable form as in Eq. 17 (see for example Lee et al 2011). Additive separability is appropriate for goods that are substitutes, but not goods that are dependent on the consumption or presence of other goods.…”