A Mathematical Reformulation of the Reference Price

TL;DR

This paper introduces a new mathematical formulation for reference prices that overcomes computational and heterogeneity limitations of previous models, providing more accurate managerial insights.

Contribution

It develops a closed-form expansion for reference prices, addressing computational, heterogeneity, and misspecification issues in prior iterative models.

Findings

Model estimated successfully on real data

Improved accuracy over traditional iterative models

Provides meaningful managerial recommendations

Abstract

Reference prices have long been studied in applied economics and business research. One of the classic formulations of the reference price is in terms of an iterative function of past prices. There are a number of limitations of such a formulation, however. Such limitations include burdensome computational time to estimate parameters, an inability to truly account for customer heterogeneity, and an estimation procedure that implies a misspecified model. Managerial recommendations based on inferences from such a model can be quite misleading. We mathematically reformulate the reference price by developing a closed-form expansion that addresses the aforementioned issues, enabling one to elicit truly meaningful managerial advice from the model. We estimate our model on a real world data set to illustrate the efficacy of our approach. Our work is not only useful from a modeling perspective, but also has important behavioral and managerial implications, which modelers and non-modelers alike would find useful.