OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION*
研究了秩规模回归中OLS估计量的性质，发现t统计量在零假设下渐近发散，导致传统t检验严重的第一类错误；通过构造修正的临界区域，重新检验了24个国家的城市规模分布，发现仅1个国家拒绝齐普夫定律，远少于以往研究。
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.