Pareto's law and sample size: A case study of China's urban system 1984-2008

While Pareto's law has been widely supported by empirical evidence in urban studies, past studies have focused on finding best fits for city rank-size distribution. A main concern with Pareto's law is the truncation of sample selection, for which few studies have examined it directly. This study tests three existing threshold methods (number threshold, size threshold, and urban population percentage threshold) using China's city system as a case study. In addition, this study proposes a new method based upon the percentage threshold of the total number of cities. A systematic analysis is applied to examine the relationship between Pareto exponent and sample size using different threshold methods. The results show that Pareto exponent is sensitive to sample size and the truncation point. Including only large cities is problematic because a slight change in the truncation point will yield quite different results of Pareto exponent. In addition, the new method, the percentage threshold of the total number of cities method, presents an advantage over previous methods, in that this method yields a consistent set of results over a wide range of thresholds. Finally, when using this new method with China's city system, the Pareto exponent presents a turning point in 1996, representing China's transition from a planned economy to a more market oriented economy during that period.