Modern urban growth literature frequently uses unit-root tests in order to check the empirical relevance of Gibrat’s law of random growth. The contradictory nature of the test results provided by this literature is most likely linked to the low power of unit-root tests. To address this problem, we apply unit-root testing to a large-sized sample of high-quality French census data covering an exceptionally long time span of more than two centuries. We add subsequent cointegration tests in order to detect the possible presence of cointegrated random growth, which may reflect the fact that cities with a similar economic structure react fairly similarly to exogenous growth shocks. According to the test results, the random growth hypothesis cannot be rejected for a very large majority of the tested French cities; on the other hand, the null hypothesis of absence of cointegration cannot be rejected in more than 95% of the cases. Our findings therefore provide empirical support for non-cointegrated random growth.

现代城市增长文献经常使用单位根检验，以检验吉布拉特随机增长定律的经验相关性。该文献提供的测试结果的矛盾性质很可能与单位根测试的低功效有关。为了解决这个问题，我们对大量高质量的法国人口普查数据样本进行了单位根检验，涵盖了长达两个多世纪的异常长的时间跨度。我们添加了后续的协整检验，以检测可能存在协整随机增长的情况，这可能反映出以下事实：经济结构相似的城市对外生增长冲击的反应相当相似。根据测试结果，绝大多数测试的法国城市都不能拒绝随机增长假设。另一方面，不存在协整的零假设在超过95％的案例中都不能被拒绝。因此，我们的发现为非整合随机增长提供了经验支持。