Scholarship demonstrates that urban systems follow a power law population distribution if the population has full labor mobility. Theoretically, subpopulations should also follow a power law population distribution if that subpopulation also has full labor mobility. Examining city population distributions for White and Black Americans across US metropolitan areas from 1910 to 2020 shows that the White distribution mostly conforms to both Zipf's and Gibrat's laws throughout this period. In contrast, the Black population does not follow either law until the second half of the 20th century, a result that is consistent with theories of restricted mobility out of the South for Black Americans during the Jim Crow era.

中文翻译：

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齐普夫定律的竞赛：种族和大都市人口规模 1910-2020

学术研究表明，如果人口具有充分的劳动力流动性，则城市系统遵循幂律人口分布。理论上，如果该亚群也具有充分的劳动力流动性，那么该亚群也应该遵循幂律人口分布。研究 1910 年至 2020 年美国大都市地区白人和黑人的城市人口分布表明，这一时期白人的分布大多符合齐夫定律和吉布拉特定律。相比之下，黑人直到 20 世纪下半叶才遵守这两项法律，这一结果与吉姆·克劳时代限制美国黑人离开南方的理论是一致的。