Intertemporal Pricing via Nonparametric Estimation: Integrating Reference Effects and Consumer Heterogeneity

34 Pages Posted: 18 Nov 2020 Last revised: 24 Jan 2021

See all articles by Hansheng Jiang

Hansheng Jiang

University of California, Berkeley - Department of Industrial Engineering and Operations Research

Junyu Cao

University of Texas at Austin - Red McCombs School of Business

Zuo-Jun Max Shen

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR)

Date Written: September 30, 2020

Abstract

We consider intertemporal pricing in the presence of reference effects and consumer heterogeneity. Our research question encompasses how to estimate heterogeneous consumer reference effects from data and how to efficiently compute the optimal pricing policy. Understanding reference effects is essential for designing pricing policies in modern retailing. Our work contributes to this area by further incorporating consumer heterogeneity under arbitrary distributions. We propose a demand model that allows arbitrary joint distributions of valuations, responsiveness to prices, and responsiveness to reference prices among consumers. To learn consumer heterogeneity from transaction data, we use a nonparametric estimation method. We formulate the pricing optimization as an infinite horizon dynamic programming problem and solve it by applying a modified policy iteration algorithm. We investigate the structure of optimal pricing policies and prove the sub-optimality of constant pricing policies even when all consumers are loss-averse according to the classical definition. Our numerical studies further show that our estimation and optimization framework improves the expected revenue of retailers via accounting for heterogeneity. We validate our model using real data from JD.com, a large E-commerce retailer, and find empirical evidence of consumer heterogeneity. In practice, ignoring consumer heterogeneity may lead to a significant loss of revenue. Furthermore, the existence of heterogeneous reference effects offers a strong motive for promotions and price fluctuations.

Keywords: reference effect, consumer heterogeneity, data-driven, intertemporal pricing, nonparametric estimation, online retailing

Suggested Citation

Jiang, Hansheng and Cao, Junyu and Shen, Zuo-Jun Max, Intertemporal Pricing via Nonparametric Estimation: Integrating Reference Effects and Consumer Heterogeneity (September 30, 2020). Available at SSRN: https://ssrn.com/abstract=3702824 or http://dx.doi.org/10.2139/ssrn.3702824

Hansheng Jiang (Contact Author)

University of California, Berkeley - Department of Industrial Engineering and Operations Research ( email )

4141 Etcheverry Hall
Berkeley, CA 94720-1777
United States

Junyu Cao

University of Texas at Austin - Red McCombs School of Business ( email )

Austin, TX
United States

Zuo-Jun Max Shen

University of California, Berkeley - Department of Industrial Engineering & Operations Research (IEOR) ( email )

IEOR Department
4135 Etcheverry Hall
Berkeley, CA 94720
United States

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