Power Laws

I've been interested in "power laws" for literally years. Now, saying I've been interested is a bit of a fiction, too, though, because I wasn't so interested that I worked on it actively. But, my research on sex and STD constantly put me into contact with statisticians and epidemiologists writing about statistical properties of epidemics, and that led me to constantly having to figure out just what a power law even was. Plus, I'm a big fan of de Vany's book on "Hollywood Economics," which is basically a treatise on the power law when it comes down to it, so that also is a reason. The power law is, as far as I can tell, equivalent to that old adage you hear in church circles - that 80% of all the work done in church (giving, volunteering, etc.) is by 20% of the people. It is, in other words, a kind of superstar regularity - the idea that "most" of the revenues are accrued by the top 1% of all films made in a year, or some such. Still, the exact statistical properties is something I don't quite understand, so I always wished I could have found some paper written to someone to explain all that I needed to know about power laws and their relevance for economics. Xavier Gabaix may have done so with his new NBER working paper entitled appropriately "Power Laws in Economics and Finance." Here's the abstract.

A power law is the form taken by a large number of surprising empirical regularities in economics and finance. This article surveys well-documented empirical power laws concerning income and wealth, the size of cities and firms, stock market returns, trading volume, international trade, and executive pay. It reviews detail-independent theoretical motivations that make sharp predictions concerning the existence and coefficients of power laws, without requiring delicate tuning of model parameters. These theoretical mechanisms include random growth, optimization, and the economics of superstars coupled with extreme value theory. Some of the empirical regularities currently lack an appropriate explanation. This article highlights these open areas for future research.

It's 62 pages and gated, so for those two reasons, you likely won't be reading it. But I might, and so just printed it out. Enjoy (or not)!