Zipf law and the firm size distribution: a critical discussion of popular estimators

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractThe 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, that is 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.JEL codes: L11; C15; C46; D20

Measuring firm size distribution with semi-nonparametric densities

“…However, there is evidence that, on some occasions, a poor approximation of the empirical distributions of the firm size in the upper tail, which typically exhibit greater asymmetry as a small number of large firms exist alongside a large number of smaller firms [1] [12] [16], is obtained.…”

“…Meanwhile, the common point of departure under the hypothesis of Zipf's law is to assume that the firm size distribution is well described by a Pareto or power-law distribution above a certain minimum threshold [21] [15] [16] [22]. In this manner, if we seek to study the growth of smaller firms compared to that of larger firms, then we cannot use a Pareto or power-law distribution because the small firms are found in the upper tail, below the threshold value [2] [23].…”

A model for scaling in firms’ size and growth rate distribution

“…of receiving a worker. This attribution on its own would yield a binomial constraint, depending on a firm's size, as stated in equation (9). The growth rate has a cutoff at the upper value (1 + µ), but firms can shrink to any size ≥ 0.…”

“…It can be seen as growth of entirely independent subunits, where subunits are jobs (see appendix A). For both the alternative method and for equation (9), the Gaussian approximation of the probability for a firm of size n i,t to reach size n i,t+1 is written as…”

“…The topic has since then attracted much interest [41]. Recent empirical studies suggest that the firm size distribution follows a Zipf (power law) distribution [9,3,31]. Various different models exist for the formation of such distributions with power-law tails.…”