Latent complementarity in bundles models

This paper studies partial identification of latent complementarity in an optimizing model with two goods and binary quantities of each good (buy/do not buy). We provide bounds on the fraction of individuals for whom goods are complements, or substitutes. When utility indices are unknown, we present simple bounds that require only the average structural function (“mean demands”). We show these simple bounds are sharp with only a binary demand shifter. Next, we characterize sharp bounds with richer variation in covariates when utility indices are known, using either the average structural function or structural choice probabilities. In simulations with binary variation in regressors for both goods, we find that the latter bounds coincide. Together, these results indicate that mean demands contain rich information for measuring complementarity without observing whether goods are chosen together.