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On the Sources of Instability in the Rank‐Size Rule: Some Simple Tests of Gibrat's Law
Author(s) -
Vining Daniel R.
Publication year - 1974
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/j.1538-4632.1974.tb00517.x
Subject(s) - rank (graph theory) , curvature , simple (philosophy) , econometrics , mathematics , variation (astronomy) , combinatorics , physics , geometry , epistemology , philosophy , astrophysics
While the implications of the Simon model of urban growth, e.g., the rank‐size rule, have been explored in numerous papers, the assumptions of that model have not, to my knowledge, been subjected to empirical verification. This paper represents an initial attempt to do so, emphasizing those sources of variation in the growth of cities typically singled out in Simon's verbal statements of the model: births, deaths, rural‐urban, urban‐rural, and urban‐urban migration. It is found that over the recent past the assumptions concerning these components are all violated and violated in the direction of upward curvature away from the log‐linear relationship between city size and rank predicted by the model, an upward curvature which we in fact observe.