Shrinkage Priors for High-Dimensional Demand Estimation

51 Pages Posted: 26 Apr 2021 Last revised: 23 Sep 2022

See all articles by Adam N. Smith

Adam N. Smith

University College London - UCL School of Management

Jim E. Griffin

University College London

Date Written: September 22, 2022


Estimating demand for large assortments of differentiated goods requires the specification of a demand system that is sufficiently flexible. However, flexible models are highly parameterized so estimation requires appropriate forms of regularization to avoid overfitting. In this paper, we study the specification of Bayesian shrinkage priors for pairwise product substitution parameters. We use a log-linear demand system as a leading example. Log-linear models are parameterized by own and cross-price elasticities, and the total number of elasticities grows quadratically in the number of goods. Traditional regularized estimators shrink regression coefficients towards zero which can be at odds with many economic properties of price effects. We propose a hierarchical extension of the class of global-local priors commonly used in regression modeling to allow the direction and rate of shrinkage to depend on a product classification tree. We use both simulated data and retail scanner data to show that, in the absence of a strong signal in the data, estimates of price elasticities and demand predictions can be improved by imposing shrinkage to higher-level group elasticities rather than zero.

Keywords: Hierarchical Priors, Global-Local Priors, Non-Sparse Shrinkage, Horseshoe, Seemingly Unrelated Regression, Price Elasticities

JEL Classification: C10, C11, L11, L81, M31

Suggested Citation

Smith, Adam N. and Griffin, Jim E., Shrinkage Priors for High-Dimensional Demand Estimation (September 22, 2022). Available at SSRN: or

Adam N. Smith (Contact Author)

University College London - UCL School of Management ( email )

1 Canada Square
London, E14 5AA
United Kingdom

Jim E. Griffin

University College London ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

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