Zipf Law and the Firm Size Distribution: a critical discussion of popular estimators

The upper tail of the firm size distribution is often assumed to follow a Power Law behavior. Recently, using different estimators and on different data sets, several papers conclude that this distribution follows the Zipf Law, meaning that the fraction of firms whose size is above a given value is inversely proportional to the value itself. We compare the different methods through which this conclusion has been reached. We find that the family of estimators most widely adopted, based on an OLS regression, is in fact unreliable and basically useless for appropriate inference. This finding rises some doubts about previously identified Zipf Laws. In general, when individual observations are available, we recommend the adoption of the Hill estimator over any other method.