A new method for measuring tail exponents of firm size distributions

We propose a new method for estimating the power-law exponent of a firm size variable, such as annual sales. Our focus is on how to empirically identify a range in which a firm size variable follows a power-law distribution. As is well known, a firm size variable follows a power-law distribution only beyond some threshold. On the other hand, in almost all empirical exercises, the right end part of a distribution deviates from a power-law due to finite size effect. We modify the method proposed by Malevergne et al. (2011) so that we can identify both of the lower and the upper thresholds and then estimate the power-law exponent using observations only in the range defined by the two thresholds. We apply this new method to various firm size variables, including annual sales, the number of workers, and tangible fixed assets for firms in more than thirty countries.