A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective

An empirical regularity designated as the Number-Average Size (NAS) Rule was first identified for the case of Japan by Mori, Nishikimi and Smith [71], and has since been extended to the US by Hsu [50]. This rule asserts a negative log-linear relation between the number and average population size of cities where a given industry is present, i.e., of industry-choice cities. Hence one of its key features is to focus on the presence or absence of industries in each city, rather than the percentage distribution of industries across cities. But despite the strong empirical regularity of this rule, there still remains the statistical question of whether such location patterns could simply have occurred by chance. Indeed, chance occurrences of certain industry-choice cities may be quite likely if, for example, one includes cities where only a single industrial establishment happens to appear. An alternative approach to industry-choice cities is proposed in a companion paper, Mori and Smith [73], which is based on industrial clustering. More specifically, this approach utilizes the statistical procedure developed in Mori and Smith [72] to identify spatially explicit patterns of agglomeration for each industry. In this context, the desired industry-choice cities are taken to be those (economic) cities that constitute at least part of a significant spatial agglomeration for the industry. With respect to these cluster-based industry-choice cities, the central objective of the present paper is to reconfirm the persistence of the NAS Rule between the years 1981 and 2001, as first observed in Mori et al. [71]. Indeed the NAS Rule is in some ways stronger under this new definition of industry-choice cities in that none of outlier industries in the original analysis show any significant agglomeration, and hence can be excluded from the present analysis. A second objective is to show that there has been a substantial churning of the industry mix in individual cities between these two time periods, and hence that persistence of the NAS Rule is even more remarkable in this light. Finally, these persistence results are extended to both the Rank Size Rule and the Hierarchy Principle of Christaller [13], which were shown in Mori et al. [71] to be intimately connected to the NAS Rule.