From Gibrat’s law to Zipf’s law through cointegration?

This article investigates the role of cointegration in the context of urban growth processes. It proposes the use of cointegration tests to distinguish between two versions of Gibrat’s law: a standard formalization with growth shocks that are iid across time and cities, and an alternative one with shocks that are only iid over time. It then shows that city-size distributions converge to Zipf’s law under the standard version of Gibrat’s law; in contrast, they are perfectly preserved under the alternative formalization. An empirical application to French data provides support for non-cointegrated city growth, and thus for the standard formalization