Adam N. Smith

Assistant Professor of Marketing, UCL School of Management

Contact InformationUCL School of Management University College London One Canada Square London E14 5AA, United Kingdom Office: Level 38, Rm NE2 Email: a.smith@ucl.ac.uk |

**Working Papers**

with Peter Rossi and Greg AllenbyThis 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 an identification condition for different product groups, 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. This paper relaxes this assumption and allows the partition to be an estimated model parameter. We focus on estimating partitions within a log-linear demand system where 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 markedly different than predefined category labels, which has implications for optimal category marketing strategies.

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 Satiationwith Nobuhiko Terui, Shohei Hasegawa, and Greg AllenbyWe 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.

**Notes**