A Unified Parsimonious Model for Structural Demand Estimation Accounting for Stockout and Substitution

33 Pages Posted: 17 Jun 2022

See all articles by Yiting Deng

Yiting Deng

University College London

Yuexing Li

Duke University, Fuqua School of Business, Students

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business

Date Written: June 12, 2022

Abstract

By analyzing a large-scale transactions data set from a grocery chain, we observe that customers arrive randomly at a non-stationary rate, they usually purchase multiple products together and in continuous quantity, and products are often out of stock. However, extant demand estimation methods do not consider these features simultaneously, which can result in biased demand estimation and lead to supply and demand mismatch. In this study, we develop a unified parsimonious model for structural demand estimation to fill this gap. First, we incorporate stockout into the model framework and estimate the parameters governing the demand of multiple products for any continuous quantity within a shopping trip based on consumers' direct utility maximization. Second, to facilitate store-level demand estimation, we estimate the non-stationary customer arrivals following a Markov-modulated Poisson process with a novel implementation procedure. Through synthetic experiments, we show that our approach effectively recovers the ground-truth demand parameters and yields accurate predictions on demand. We then apply our method to the real-life data set to estimate demand parameters and customer arrivals. Based on these estimates, we conduct counterfactual experiments to quantify how consumptions change in response to pricing and inventory decisions and illustrate how the grocery retailer can leverage our method to jointly optimize pricing and inventory. We find that, for any given price level, consumption increases in the inventory level at a decreasing rate, while for any inventory level, consumption decreases in the price level at a decreasing rate. We also show that, compared with the optimal decisions based on demand estimation that ignores stockout and the company's actual decisions, the optimal decisions based on our approach yield much higher profits and consumer surplus.

Keywords: Structural estimation, direct utility, stockout, substitution, non-stationary demand

Suggested Citation

Deng, Yiting and Li, Yuexing and Song, Jing-Sheng Jeannette, A Unified Parsimonious Model for Structural Demand Estimation Accounting for Stockout and Substitution (June 12, 2022). Available at SSRN: https://ssrn.com/abstract=4134738 or http://dx.doi.org/10.2139/ssrn.4134738

Yiting Deng

University College London ( email )

Level 38, 1 Canada Square
London, Please Select E14 5AA
United Kingdom
2031086081 (Phone)

Yuexing Li (Contact Author)

Duke University, Fuqua School of Business, Students ( email )

Durham, NC
United States

Jing-Sheng Jeannette Song

Duke University - Fuqua School of Business ( email )

100 Fuqua Drive
Duke University
Durham, NC 27708
United States

HOME PAGE: http://people.duke.edu/~jssong/

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