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Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century.

Ramos, Arturo (2019): Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century.

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Abstract

We review the classical Gibrat’s process for the population of city sizes. In particular, we are interested in whether the log-population process has stationary and independent (Gibrat’s Law for cities) increments. We have tested these characteristics for the case of the municipalities of Italy and Spain and the places of USA for a time span of more than one century. The results are clear: stationarity and independence are empirically rejected by standard tests. These results open theoretically the way for the observance of other city size distributions other than the lognormal and the double Pareto lognormal, something that in fact has already happened in the literature.

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