A sequential choice model for multiple discrete demand

Abstract

Consumer demand in a marketplace is often characterized to be multiple discrete in that discrete units of multiple products are chosen together. This paper develops a sequential choice model for such demand and its estimation technique. Given an inherently high-dimensional problem to solve, a consumer is assumed to simplify it to a sequence of one-unit choices, which eventually leads to a shopping basket of multiple discreteness. Our model and its estimation method are flexible enough to be extended to various contexts such as complementary demand, non-linear pricing, and multiple constraints. The sequential choice process generally finds an optimal solution of a convex problem (e.g., maximizing a concave utility function over a convex feasible set), while it might result in a sub-optimal solution for a non-convex problem. Therefore, in case of a convex optimization problem, the proposed model can be viewed as an econometrician's means for establishing the optimality of observed demand, offering a practical estimation algorithm for discrete optimization models of consumer demand. We demonstrate the strengths of our model in a variety of simulation studies and an empirical application to consumer panel data of yogurt purchase.