Shrinkage priors for high-dimensional demand estimation

Adam N. Smith () and Jim E. Griffin ()
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Adam N. Smith: University College London
Jim E. Griffin: University College London

Quantitative Marketing and Economics (QME), 2023, vol. 21, issue 1, No 3, 95-146

Abstract: Abstract 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 (search for similar items in EconPapers)
JEL-codes: C11 C13 D12 M31 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11129-022-09260-7

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