Sparse demand systems : corners and complements

We propose a demand model where consumers simultaneously choose a few different goodsfrom a large menu of available goods, and choose how much to consume of each good. Themodel nests multinomial discrete choice and continuous demand systems as special cases.Goods can be substitutes or complements. Random coefficients are employed to capturethe wide variation in the composition of consumption baskets. Non-negativity constraintsproduce corners that account for different consumers purchasing different numbers of typesof goods. We show semiparametric identification of the model. We apply the model to thedemand for fruit in the United Kingdom. We estimate the model's parameters using UKscanner data for 2008 from the Kantar World Panel. Using our parameter estimates, weestimate a matrix of demand elasticities for 27 categories of fruit and analyze a range of taxand policy change scenarios.