Testing Taylor's law in urban population dynamics worldwide with simultaneous equation models

Knowledge of long-term population trends is still incomplete at the global scale. In this perspective, human and animal ecology has intensively studied the relationship between the Mean (M) size and the Variance (V) of specific attributes of subpopulations within a given regional system. One of the best-known relationships between these two attributes suitable to describe long-term population trends is governed by Taylor's law (TL). The present article contributes to the recent literature on population trends worldwide by testing the long-term relationship (1950-2015) between the overall variance and mean in the total population of 1857 metropolitan agglomerations in 155 countries classified into 9 world macro-regions. To estimate the unknown parameter(s) of the V-M relation we made use of a simultaneous equation system using both linear (classical TL) and quadratic specifications, with the aim of ascertaining a wide range of simplified (or more complex) association rules between the two dimensions of demographic change. The empirical results show that TL is verified in all nine cases, although a quadratic relationship provides slightly better results than the classical, linear relationship. More specifically, similar estimates for both linear and quadratic relationships were characteristic of 'new' demographic continents with more recent and intense urbanization processes (the Americas, and African and Asian countries). The predominance of quadratic relationships characterized regions with long-established urbanization processes, such as Europe, Russia, and, partly, China and the Middle East. The relevance of the TL for a refined understanding of urbanization mechanisms worldwide, and the importance of a quadratic term for distinguishing metropolitan systems that have experienced different development paths, were finally discussed.