Structural Models of Complementary Choices

Complementary choices are important and pervasive yet occasionally elusive. Single consumers make complementary choices in purchase decisions (e.g. chips and salsa), product interoperabilities (smartphones and networks), and dynamic decisions (current exercise and future healthcare consumption). Multiple consumers make complementary choices when they interact in strategic games or form networks. Firms make complementary choices when determining production inputs, entering related markets, and strategic mergers. The structural empirical literature has recently started to address the difficult problem of how to model complementary choices. This new work contrasts with traditional approaches such as discrete choice models, wherein all choices are mutually exclusive. A naïve approach to modeling complementary choices is to include all possible bundles of choices in the choice set. However, for any given set of options, the set of all possible subsets is exponentially larger, and often too large to feasibly estimate. Second, specific models of complementarities are needed to ensure desirable equilibrium properties in games among agents (e.g., existence, uniqueness or multiplicity). Third, models of complementarities are often required to evaluate counterfactuals, such as predicting demand for bundles of complementary products that have not previously been offered. We review the literature selectively, summarizing the state of the art and identifying promising directions for future work. We begin with complementary choices made by consumers, and then examine complementary choices made by firms