Adam N. Smith
Assistant Professor of Marketing
University College London

Working Papers

This paper presents a methodology for identifying groups of products that exhibit similar patterns in demand and responsiveness to changes in price using store-level sales data. We use the concept of economic separability as the basis for establishing similarity between products, and build a weakly separable model of aggregate demand. A common issue with separable demand models is that the partition of products into separable groups must be known a priori, which severely shrinks the set of admissible substitution patterns. We develop a methodology which allows the partition to be an estimated model parameter. In particular, we specify a log-linear demand system in which weak separability induces equality restrictions on a subset of cross-price elasticity parameters. An advantage of our approach is that we are able to find groups of separable products rather than just test whether a given set of groups is separable. Our method is applied to two aggregate, store-level data sets. We find evidence that the separable structure of demand can be inconsistent with category labels, which has implications for optimal category marketing strategies.

Demand Models with Random Partitions
with Greg Allenby

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 in modeling partitions is that they are defined on a high-dimensional, discrete, and non-Euclidean domain. We build on previous nonparametric Bayesian models for random partitions to construct a new partition distribution characterized by a location partition and scale parameter. This location-scale partition distribution is useful in two ways: (1) as a proposal distribution within the context of a Markov chain Monte Carlo routine; and (2) as a prior or random-effects distribution of partition heterogeneity. Our method is illustrated in the context of both store-level and household-level demand models. We find that allowing for uncertainty in the partition is important for preserving model flexibility, improving demand forecasts, learning about the structure of demand, and informing targeted marketing strategies.

An Integrated Model for Discontinuous Preference Change and Satiation
with Nobuhiko Terui, Shohei Hasegawa, and Greg Allenby

We develop a structural model of horizontal and temporal variety seeking using a dynamic factor model that relates attribute satiation to brand preferences. The factor model employs a threshold specification that triggers preference changes when customer satiation exceeds an admissible level but does not change otherwise. The factor model is developed for high dimensional switching data encountered when multiple brands are purchased across multiple time periods. The model is applied to two scanner-panel datasets where we find distinct shifts in consumer preferences over time where consumers are found to value variety much more than indicated by traditional models. Insights into brand preference are provided by a dynamic joint space map that displays brand positions and temporal changes in consumer preferences over time.


Bayesian Linear Regression
Cholesky Decomposition
Gibbs Sampling
Monte Carlo Integration and Importance Sampling