Earnings inequality in Germany has increased dramatically. Measuring inequality locally at the level of cities annually since 1985, we find that behind this development is the rapidly worsening inequality in the largest cities, driven by increasing earnings polarisation. In the cross-section, local earnings inequality rises substantially in city size, and this city-size inequality penalty has increased steadily since 1985, reaching an elasticity of .2 in 2010. Inequality decompositions reveal that overall earnings inequality is almost fully explained by the within-locations component, which in turn is driven by the largest cities. The worsening inequality in the largest cities is amplified by their greater population weight. Examining the local earnings distributions directly reveals that this is due to increasing earnings polarisation that is strongest in the largest places. Both upper and lower distributional tails become heavier over time, and are the heaviest in the largest cities. We establish these results using a large and spatially representative administrative data set, and address the top-coding problem in these data using a parametric distribution approach that outperforms standard imputations.

We consider tests of the hypothesis that the tail of size distributions decays faster than any power function. These are based on a single parameter that emerges from the Fisher–Tippett limit theorem, and discriminate between leading laws considered in the literature without requiring fully parametric models/specifications. We study the proposed tests taking into account the higher order regular variation of the size distribution that can lead to catastrophic distortions. The theoretical bias corrections realign successfully nominal and empirical test behavior, and inform a sensitivity analysis for practical work. The methods are used in an examination of the size distribution of cities and firms.

One often observed empirical regularity is a power-law behavior of the tails of some distribution of interest. We propose a limit law for normalized random means that exhibits such heavy tails irrespective of the distribution of the underlying sampling units: the limit is a t-distribution if the random variables have finite variances. The generative scheme is then extended to encompass classic limit theorems for random sums. The resulting unifying framework has wide empirical applicability which we illustrate by considering two empirical regularities in two different fields. First, we turn to urban geography and explain why city-size growth rates are approximately t-distributed, using a model of random sector growth based on the central place theory. Second, turning to an issue in finance, we show that high-frequency stock index returns can be modeled as a generalized asymmetric Laplace process. These empirical illustrations elucidate the situations in which heavy tails can arise.

Using administrative panel data on the entire population of new labor immigrants to the Netherlands, we estimate the effects of individual labor market spells on immigration durations using the timing-of-events method. The model allows for correlated unobserved heterogeneity across migration, unemployment, and employment processes. We find that unemployment spells increase return probabilities for all immigrant groups, while reemployment spells typically delay returns. © 2014 The President and Fellows of Harvard College and the Massachusetts Institute of Technology