Shrinkage Priors for High-Dimensional Demand Estimation

39 Pages Posted: 26 Apr 2021

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: April 24, 2021

Abstract

Estimating demand for wide 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 price elasticity parameters within a log-linear demand system where the number of price elasticity parameters 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 effects 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 (April 24, 2021). Available at SSRN: https://ssrn.com/abstract=3833417 or http://dx.doi.org/10.2139/ssrn.3833417

Adam N. Smith (Contact Author)

University College London - UCL School of Management

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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