Demand Models With Random Partitions

Abstract

Many economic models of consumer demand require researchers to partition sets of products or attributes prior to the analysis. These models are common in applied problems when the product space is large or spans multiple categories. While the partition is traditionally fixed a priori, we let the partition be a model parameter and propose a Bayesian method for inference. The challenge is that demand systems are commonly multivariate models that are not conditionally conjugate with respect to partition indices, precluding the use of Gibbs sampling. We solve this problem by constructing a new location-scale partition distribution that can generate random-walk Metropolis-Hastings proposals and also serve as a prior. Our method is illustrated in the context of a store-level category demand model where we find that allowing for partition uncertainty is important for preserving model flexibility, improving demand forecasts, and learning about the structure of demand.

Keywords: Bayesian inference, location-scale family, Polya urn, Markov chain Monte Carlo, price elasticity