Latent Complementarity in Bundles Models

This paper studies partial identi cation of latent complementarity in an optimizing model with two goods and binary quantities of each good (buy / don't buy). We provide simple bounds on the fraction of individuals for whom goods are complements/substitutes. Despite using only involve marginal choice probabilities, these bounds are sharp with a binary demand shifter. With rich variation in demand shifters, we show how to identify the distribution of latent complementarity using only marginal choice probabilities. Together, these results indicate that mean demands are su cient for measuring complementarity without observing whether goods are chosen together.