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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

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

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.