The Challenges of Using Ranks to Estimate Sales
32 Pages Posted: 11 Mar 2020 Last revised: 12 Mar 2020
Date Written: March 1, 2020
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
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