世界经济 ›› 2018, Vol. 41 ›› Issue (9): 96-120.

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Zipf定律与Gibrat定律在中国城市规模分布中的适用性

魏守华1, 孙宁2, 姜悦3   

  1. 1. 北京外国语大学国际商学院 北京市海淀区西三环北路2号 100089;
    2. 南京大学经济学院 南京市汉口路22号 210093;
    3. 上海对外经贸大学贸易谈判学院 上海市长宁区古北路620号 200336
  • 出版日期:2018-09-10 发布日期:2018-09-17
  • 通讯作者: 魏守华,电子信箱:weish@nju.edu.cn E-mail:weish@nju.edu.cn
  • 作者简介:孙宁,电子信箱:18225526968@163.com;姜悦,电子信箱:1057296527@qq.com
  • 基金资助:
    国家自然科学基金项目"双重集聚外部性驱动下我国城市群的经济空间结构演变与政策引导"(71473115)及"中国城镇体系协调发展研究:测度、成因与绩效评价"(71873062)的资助。

The Applicability of Zipf's Law and Gibrat's Law to City Size Distribution in China

Wei Shouhua1, Sun Ning2, Jiang Yue3   

  • Online:2018-09-10 Published:2018-09-17

摘要: 本文在阐释Zipf定律和Gibrat定律的理论机制基础上,运用中国646个县级以上城市数据检验其在城市规模分布上的适用性。理论分析表明:Zipf定律服从Pareto分布,适合用Simon随机增长模型解释;Gibrat定律服从对数正态分布,适合用Gabaix人口迁移模型解释;Gibrat定律是Zipf定律的适用条件,近似Gibrat定律下可用修正的Zipf定律——上尾Pareto分布或双Pareto对数正态分布描述。基于中国人口普查数据的研究表明:646个县级以上城市总体不满足Gibrat定律,而表现为大城市和中小城市的两组对数正态分布;2000和2010年在截点分别为规模排序第375和第417位的城市时,Zipf定律的拟合效果最好,Pareto指数都在1.30左右,表明城市规模分布具有大城市主导特征;近似Gibrat定律下,双Pareto对数正态分布能较好地拟合中国城市规模分布律。

关键词: Zipf定律, Gibrat定律, 城市规模分布, Pareto分布

Abstract: Based on elucidating the theoretical mechanism of Zipf's law and Gibrat's law, this paper uses data from 646 cities at and above the county level to verify the applicability of the two laws to city size distribution in China. Theoretical analysis shows that Zipf's law obeys the Pareto distribution and applies to the Simon model of stochastic growth; Gibrat's law follows the log-normal distribution and applies to the Gabaix population migration model. Gibrat's law is the precondition for Zipf's law, while the adjusted Zipf's law for upper tail Pareto distribution, or the double Pareto log-normal distribution, is applicable when approximating to log-normal distribution. Based on the empirical evidence from the fifth (2000) and sixth (2010) National Population Census data, we draw the following conclusions:646 cities at and above the county level do not satisfy Gibrat's law in general, while a few large cities and most small-medium ones are presented by two log-normal distribution groups respectively in terms of growth rates that are different between groups and convergent within groups; when truncated city for 2000 and 2010 ranks 375th and 417th in size respectively, the fitting effects of Zipf's law reach to the optimal and the corresponding Pareto coefficients are both about 1.30, indicating that dominant characteristic of large cities on city size distribution; when approximating to Gibrat's law, double Pareto log-normal distribution can better describe the city size distribution in China by means of a combination of log-normal distribution in the main body and Pareto distribution in the long upper and lower tails.

Key words: Zipf's law, Gibrat's law, city size distribution, Pareto distribution

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