Zipf's Law and Growth in Russian Cities

In current research is tested the hypothesis that the monthly average real wage and population distribution is submitted Zipf’s law. The main tasks that were determined in this work consist of estimation the “rank – size” rule equation for population and real wage data, testing that distributions of parameters have spatial correlation, building the dynamics of Pareto exponent by both distribution. In process of investigation I exploited econometric analysis instruments as OLS estimation method as well as spatial regression analysis tools as Moran I test and SAR model. The involvement of methods of spatial regression analysis is justified by the attempts to explain the fulfillment of Zipf’s law with existence of spatial interaction of factor distributions. It was resulted that the real wage and population distributions correspond to power law, however, the spatial distribution of population has negative interdependence, while the spatial interdependence of real wages is positive. Consequently, the type of spatial correlation does not influence at the Zipf’s law implementation. The trajectory of the Pareto indicator evolution differs greatly, in particular the Pareto exponent of population model was declining during the 18 years, whereas the real wage Pareto index was increasing for 11 years. In the first case, it means the sizes of cities converged according to the number of inhabitants, in the second case - the number of rich cities raised during the time interval. In addition, it was confirmed that when there are the imposing restrictions on the size of the population, the distribution of the sizes of cities becomes closer to Zipf's law.