How to Assess Power Law Behavior Using Stochastic Process Methods: A Note of Caution

Abstract

Power law distributions have a certain appeal to researchers, not least because they often insinuate a general empirical law. Hence, searching for them in data generated by social and political processes has become popular. In the political science literature, however, power law behavior has rarely been assessed rigorously. Relying mainly on qualitative appraisals of log-log plots, merely a necessary, but no sufficient, condition of power law behavior is tested. This letter therefore seconds the note of caution expressed recently. Moreover, it showcases the use of a principled statistical framework to test power law behavior in a quantitative manner. Applying this method to a seminal case in political science, the results of the analysis invite an empirical as well as theoretical refinement of the claim that changes in public budgets follow a power law. In a more general sense, the letter wishes to contribute to a more thorough practice of stochastic process methods in political science.