Sparse demand systems: corners and complements

Résumé

We propose a demand model where consumers simultaneously choose a few different goods from a large menu of available goods, and choose how much to consume of each good. The model nests multinomial discrete choice and continuous demand systems as special cases. Goods can be substitutes or complements. Random coefficients are employed to capture the wide variation in the composition of consumption baskets. Non-negativity constraints produce corners that account for different consumers purchasing different numbers of types of goods. We show semiparametric identification of the model. We apply our model to the demand for fruit in the United Kingdom, analyzing a range of tax and policy change scenarios.