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  • A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective
  • Tomoya Mori and Tony E. Smith

Japan experienced rapid urbanization after the World War II as indicated, for example, by the fact that the population share of Densely Inhabited Districts (DID), nearly doubled between 1950 and 2000, from 34.9 percent to 65.2 percent, while accounting for only 3.3 percent of the national land.1 Moreover, this rapid urbanization does not appear to be a simple proportional increase of economic activities in all urban areas. Rather, the spatial distributions of industries and population within the 258 metro areas (cities) of Japan are quite skewed. The population of the largest city, Tokyo, exceeded 30 million in 2000 and accounted for more than a quarter of the national population. The ten largest cities together accounted for more than a half of the national population. Moreover, if the industrial diversity of a given city is defined in terms of the number of industries exhibiting significant agglomeration within that city (see the section on cluster-based choice cities and industries below), then the population sizes of cities also appear to be highly correlated with their industrial diversities (see the section on the hierarchy principle). [End Page 175]

Against this background, our main interest is to ask whether these skewed spatial distributions of industries and population exhibit any clear relationship, or whether they might simply have happened by chance. In Mori, Nishikimi, and Smith (2008), a strong empirical regularity was identified between the size and industrial composition of cities in Japan. This regularity, designated as the Number-Average Size (NAS) Rule, asserts a negative log-linear relation between the number and average population size of those cities where a given industry is present, that is, of the choice cities for that industry. More recently, this same regularity (with comparable definitions of industries and cities) has been reported for the United States by Hsu (2008).

But despite the strong empirical regularity of the NAS Rule, there still remains the statistical question of whether such location patterns could simply have occurred by chance. Of particular importance here is the focus of this rule on the presence or absence of industries in each city, rather than on the percentage distribution of industries across cities. Indeed, chance occurrences of certain choice cities may be quite likely if, for example, one includes cities where only a single industrial establishment happens to appear. Hence there is a need to clarify exactly what constitutes a substantial industrial presence in a given city. Although it is possible to characterize substantial in terms of some threshold number or share of industrial establishments or employment, such conventions are necessarily ad hoc. Hence an alternative approach is proposed in a companion paper, Mori and Smith (2009b), which characterizes substantial in terms of significant industrial agglomeration. More specifically, this approach utilizes the statistical procedure developed in Mori and Smith (2009a) to identify spatially explicit patterns of significant clustering (agglomeration) for each industry. In this context, the desired choice cities for each industry are taken to be those (economic) cities that share at least a part of a significant spatial cluster for the industry and therefore are designated as cluster-based choice cities.

With this new definition, it is shown in Mori and Smith (2009b) that the NAS Rule not only continues to hold for Japan but in some ways is even stronger. In particular, the few industrial outliers identified for the NAS Rule in the original analysis of Mori, Nishikimi, and Smith (2008) are shown here to be without exception industries for which no significant spatial agglomerations can be identified. Hence these results serve to suggest that the NAS Rule may in fact be an observable consequence of underlying coordination between spatial agglomerations of industry and population.

But unlike the original analysis in Mori, Nishikimi, and Smith (2008), the NAS Rule in Mori and Smith (2009b) is examined only for 2001. To that end, [End Page 176] there remains the question of whether this rule continues to exhibit the same persistence over time that was seen in the original analysis. The results for 1981 have now been completed, and indeed they confirm persistence of...


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pp. 175-216
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Archived 2009
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