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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.
Are parents altruistic or selfish? We contribute to the continuing debate of this question by proposing a simple test which is implemented using experimental data from the Mexican anti-poverty programme PROGRESA. Benefit eligibility is randomised. Our estimation strategy explicitly addresses potentially confounding factors and selection bias problems. We reject selfishness of parents in non-urban Mexico as PROGRESA beneficiaries spend more on child-related goods and do not increase spending on adult-related goods compared to parents in the control group. At the same time, we reject some rival theories.