Ols estimation and the t test revisited in rank-size rule regression

Yoshihiko Nishiyama, Susumu Osada, Yasuhiro Sato

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)691-716
Number of pages26
JournalJournal of Regional Science
Issue number4
Publication statusPublished - 2008

ASJC Scopus subject areas

  • Development
  • Environmental Science (miscellaneous)


Dive into the research topics of 'Ols estimation and the t test revisited in rank-size rule regression'. Together they form a unique fingerprint.

Cite this