Christian Schluter

Welfare Measurement and Measurement Error

The approximate effects of measurement error on a variety of measures of inequality and poverty are derived. They are shown to depend on the measurement error variance and functionals of the error contaminated income distribution, but not on the form of the measurement error distribution, and to be accurate within a rich class of error free income distributions and measurement error distributions. The functionals of the error contaminated income distribution that approximate the measurement error induced distortions can be estimated. So it is possible to investigate the sensitivity of welfare measures to alternative amounts of measurement error and, when an estimate of the measurement error variance is available, to calculate corrected welfare measures. The methods are illustrated in an application using Indonesian household expenditure data.

Why Are Child Poverty Rates Higher in Britain than in Germany? A Longitudinal Perspective.

We analyze why child poverty rates were much higher in Britain than in Western Germany during the 1990s, using a framework focusing on poverty transition rates. Child poverty exit rates were significantly lower, and poverty entry rates significantly higher, in Britain. We decompose these cross-national differences into differences in the prevalence of “trigger events” (changes in household composition, household labor market attachment, and labor earnings), and differences in the chances of making a poverty transition conditional on experiencing a trigger event. The latter are the most important in accounting for the cross-national differences in poverty exit and entry rates.

The Impact of Labour Market Dynamics on the Return-Migration of Immigrants

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.

Tails of Lorenz Curves

The Lorenz dominance criterion is the centre piece of inequality analysis. Yet, the appeal of this criterion, which requires considering Lorenz curves in their entirety, is undermined by the practical problem that many sample Lorenz curves intersect in the tails. The commonly used inferential methods, based on central limit theorem arguments, do not apply to the tails since these contain too few observations. By contrast, we propose a test procedure for distributions whose tails lie in the domain of attraction of the Frechet distribution, which fully takes into account the tail behaviour of Lorenz curves. Our experiments and empirical examples demonstrate the good performance of the proposed test: in many cases we are able to infer that despite sample tail crossings the population Lorenz curves do, in fact, exhibit Lorenz dominance.

Statistical inference with mobility indices

In order to make rigorous statistically inferences about levels of or changes in mobility, we derive the asymptotic distribution for the main representatives of the two classes of measures: indices based on inequality measures and transition matrices. An empirical example illustrates the discussion.

Upward structural mobility, exchange mobility, and subgroup consistent mobility measurement: U.S.-German mobility rankings revisited

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.

On the Problem of Inference for Inequality Measures for Heavy‐Tailed Distributions

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.

Weak convergence to the Student and Laplace distributions

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.

Discussion of S.G. Donald Et Al. And R. Davidson

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.

Size distributions reconsidered

ABSTRACT 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.