TRADE: Consumer Demand with Price Aggregators; Professor Thibault Fally (University of California-Berkeley)

Abstract

Estimating consumer demands is a bread-and-butter undertaking in applied economics. In general, demand for each good depends on the prices of all goods and services, but for most applications it is impractical to estimate models of such high dimension. In this paper, we simplify cross-price effects through the introduction of functions we call ``aggregators'', where each aggregator maps information from an arbitrarily large vector of prices (and perhaps income) into a scalar. The rank of the matrix of cross-price effects is then bounded by the number of aggregators. We provide a complete characterization of the preferences which rationalize a demand system having such aggregators. These results have applications in a broad range of fields in economics. Most commonly-used demand systems (including directly-additive, indirectly-additive, non-homothetic CES and Kimball preferences) can be described with one or two of such aggregators where the price index may coincide with one of the aggregators. Nested and mixed logit can also be expressed as having as many aggregators as nests or consumer types. Aggregators can also be naturally expressed as a function of observed product attributes. Using barcode data on yogurt purchases, we illustrate how to estimate a simple yet flexible specification of such a demand system with K aggregators, with or without using information on product attributes.