 OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION*Yoshihiko Nishiyama, Susumu Osada and Yasuhiro Sato Journal of Regional Science, 2008, vol. 48, issue 4, 691-716 Abstract: ABSTRACT The rank‐size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the t test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the t statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the t statistic explodes asymptotically even under the null, indicating that a mechanical application of the t test yields a serious type I error. To overcome this problem, critical regions of the t test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005). By using the same database as that used in Soo (2005), we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual t test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries. Date: 2008 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jregsc:v:48:y:2008:i:4:p:691-716 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of Regional Science is currently edited by Marlon G. Boarnet, Matthew Kahn and Mark D. Partridge More articles in Journal of Regional Science from Wiley Blackwell |
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