Maison de l'économie et de la gestion d'Aix

424 chemin du viaduc, CS80429

13097 Aix-en-Provence Cedex 2

# Schluter

## Publications

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.

City size distributions are not strictly Pareto, but upper tails are rather Pareto like (i.e. tails are regularly varying). We examine the properties of the tail exponent estimator obtained from ordinary least squares (OLS) rank size regressions (Zipf regressions for short), the most popular empirical strategy among urban economists. The estimator is then biased towards Zipf’s law in the leading class of distributions. The Pareto quantile–quantile plot is shown to offer a simple diagnostic device to detect such distortions and should be used in conjunction with the regression residuals to select the anchor point of the OLS regression in a data-dependent manner. Applying these updated methods to some well-known data sets for the largest cities, Zipf’s law is now rejected in several cases.

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.

In economics, rank-size regressions provide popular estimators of tail exponents of heavy-tailed distributions. We discuss the properties of this approach when the tail of the distribution is regularly varying rather than strictly Pareto. The estimator then over-estimates the true value in the leading parametric income models (so the upper income tail is less heavy than estimated), which leads to test size distortions and undermines inference. For practical work, we propose a sensitivity analysis based on regression diagnostics in order to assess the likely impact of the distortion. The methods are illustrated using data on top incomes in the UK.

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.

We consider the role of unobservables, such as differences in search frictions, reservation wages, and productivities for the explanation of wage differentials between migrants and natives. We disentangle these by estimating an empirical general equilibrium search model with on-the-job search due to Bontemps et al. (1999) on segments of the labour market defined by occupation, age, and nationality using a large scale German administrative dataset.

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. Â© 2014 The President and Fellows of Harvard College and the Massachusetts Institute of Technology

This paper discusses aspects of the papers by S.G. Donald et al. and R. Davidson, which were presented at The Econometrics Journal sponsored special session on the econometrics of inequality measurement, held at the Royal Economics Society Meeting in Surrey in 2010.

We consider the class of heavy-tailed income distributions and show that the shape of the income distribution has a strong effect on inference for inequality measures. In particular, we demonstrate how the severity of the inference problem responds to the exact nature of the right tail of the income distribution. It is shown that the density of the studentized inequality measure is heavily skewed to the left, and that the excessive coverage failures of the usual confidence intervals are associated with excessively low estimates of both the point measure and the variance. For further diagnostics, the coefficients of bias, skewness and kurtosis are derived and examined for both studentized and standardized inequality measures. These coefficients are also used to correct the size of confidence intervals. Exploiting the uncovered systematic relationship between the inequality estimate and its estimated variance, variance stabilizing transforms are proposed and shown to improve inference significantly.

We formalize the concept of upward structural mobility and use the framework of subgroup consistent mobility measurement to derive a relative and an absolute measure of mobility that is increasing in upward structural mobility and compatible with the notion of exchange mobility. In our empirical illustration, we contribute substantively to the ongoing debate about mobility rankings between the U.S. and Germany by demonstrating that the U.S. typically does exhibit more upward structural mobility than Germany.