Adam N. Smith
Assistant Professor of Marketing
University College London


Inference for Product Competition and Separable Demand
with Peter Rossi and Greg Allenby, Marketing Science, 38(4), 690-710, 2019.

Demand Models with Random Partitions
with Greg Allenby, Journal of the American Statistical Association, forthcoming


Learned Complementarity
with Daniel Ershov

Product substitution patterns are often treated as static concepts in the analysis of consumer purchase behavior. In this paper, we examine the temporal dynamics in complementarity that arise in the do-it-yourself (DIY) market. We argue that the complexity of a DIY project can shape substitution patterns through the amount and type of materials required. Using data from a specialty retailer, we first document temporal changes in consumer purchases which support complementarity dynamics. We then develop a formal demand model that allows the nature of complementarity to change over time and based on past purchases. Targeting and segmentation strategies based on a consumer's evolution of learned complementarity are discussed.

Shrinkage Priors for High-Dimensional Demand Estimation
with Jim Griffin

We propose a new class of shrinkage priors for the price elasticity parameters of a high-dimensional log-linear demand model. Log-linear models suffer from a dimensionality problem as the number of price elasticity parameters grows quadratically in the number of goods. Traditional regularization techniques can be used to overcome this problem, but the assumption of fixed shrinkage points set to zero is often at odds with economic properties of cross-price effects. We develop a hierarchical horseshoe prior which allows the direction and rate of shrinkage to depend on a product classification tree. This allows the cross-price effects to be shrunk towards higher-level cross-category effects rather than zero. Our model is fit to store-level price and movement data. The effects on demand predictions and inference for elasticity parameters are discussed.

Constrained Heterogeneity
with Tetyana Kosyakova, Thomas Otter, and Max Pachali

Adding sign and order constraints to consumer preference parameters helps to preserve many theoretical properties of demand and thus validates market counterfactuals. We review current practices for implementing these constraints based on the lognormal and truncated normal distributions. While the lognormal model remains widely used in practice, its tail behavior can have undesirable consequences on the shape and curvature of demand functionsTruncated normal models can be more robust, but are challenging to implement in practice because of a lack of conjugacy at the upper level. We propose a new computational strategy for estimating hierarchical models with a truncated normal distribution of heterogeneity. Our approach is based on recent advances in MCMC methods for intractable likelihoods. We apply our model to data from a discrete choice experiment and discuss the economic implications of the distinct prior functional form assumptions.

An Integrated Model for Discontinuous Preference Change and Satiation

with Nobuhiko Terui, Shohei Hasegawa, and Greg Allenby

We develop a model of horizontal and temporal variety seeking using a dynamic factor model that relates attribute satiation to brand attributes. 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.