The Challenges of Using Ranks to Estimate Sales

32 Pages Posted: 11 Mar 2020 Last revised: 12 Mar 2020

See all articles by Stan J. Liebowitz

Stan J. Liebowitz

University of Texas at Dallas - School of Management - Department of Finance & Managerial Economics

Alejandro Zentner

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: March 1, 2020

Abstract

Researchers have often used publicly available data on product ranks to estimate nonpublic sales quantities by assuming that the distribution of sales follows a power law. Using population sales data for a product frequently thought to follow a power law—books—we find the (double logged) rank-sales relationship, contrary to assumption, is not linear but is instead concave. We demonstrate that this nonlinearity is sufficiently strong to potentially disqualify hundreds of results from analyses that had assumed linearity, explain why the estimates of the rank-sales slope have been much too flat, and overturn an influential finding that the larger variety of titles held by Internet retailers leads to important changes in consumer purchase patterns and substantial improvements in social welfare. However, the concavity is sufficiently similar across time and book categories to allow the use of nonlinear specifications of this rank-sales relationship that provide reasonable predictions of sales from ranks while using samples with only a modest number of observations.

Keywords: power laws, zipf, pareto, ranks, sales, internet

Suggested Citation

Liebowitz, Stan J. and Zentner, Alejandro, The Challenges of Using Ranks to Estimate Sales (March 1, 2020). Available at SSRN: https://ssrn.com/abstract=3543827 or http://dx.doi.org/10.2139/ssrn.3543827

Stan J. Liebowitz (Contact Author)

University of Texas at Dallas - School of Management - Department of Finance & Managerial Economics ( email )

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HOME PAGE: http://www.utdallas.edu/~liebowit/

Alejandro Zentner

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

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