The Challenges of Using Ranks to Estimate Sales
Abstract
Researchers have frequently used publicly available data on product ranks to estimate nonpublic sales quantities, believing that there is a linear relationship between logged rank and logged sales values due to the assumption that sales follow a power law. However, using data on book sales, which are commonly thought to follow a power law, we find that the (double logged) relationship between ranking and sales is not linear, but actually concave. We demonstrate that this concavity is likely to cause poor predictions of sales in many instances. We also explore the use of nonlinear specifications as an alternative method to predict sales from ranks and find a simple specification that ameliorates many of these poor sales estimates. We illustrate some of the problems of applying a linear technique to this nonlinear relationship by examining the claim that the greater product variety made available to shoppers on the Internet has a large positive impact on social welfare, and also a claim about sales levels in top 20 and top 50 “charts.”