Estimation of power laws for city size data : an optimal methodology

Power laws appear widely in many branches of economics, geography, demography and other social sciences. In particular, the upper tail of city size distributions appear to follow power laws, as many researchers have shown for different countries and different periods of times. A crucial point in the estimation of these laws is the correct choice of the truncation point. The aim of this paper is to investigate how to choice this truncation point from an optimal point of view. A new methodology based on the Akaike information criterion is proposed. An extensive simulation study is carried out in order to prove the existence of this optimal point, under different assumptions about the underlying population. Several kind of populations are considered, including lognormal and population with heavy tails. Finally, the methodology is used for the optimal estimation of power laws in city size data sets for USA and Spain for several years.