Volume 29, Issue 2

The City of Flint, Michigan, USA has experienced extreme population and economic variability in the past one hundred and fifty years. The City of Flint developed three comprehensive or master plans in order to assess available data, make projections and propose recommendations. The ways in which each plan proved to contain accuracies and failures is instructive for the practices of historical statistical methods and urban planning, particularly as it relates to spatial data. The three plans will be considered in three main sections: planning for population growth (1920), planning for regional rationalization (1960), and planning for a flexible future (2013). Population projections, residential density patterns, and economic and employment data will be reviewed and compared against the planning recommendations and realities. The relationship between statistics and spatial analysis is examined. Discussion is included on ways data and statistical analysis can be utilized for public decision-making and assist with governing.

After a hundred years of contributions, the debate about how to measure inequality is still open. We provide a brief review of the literature, showing that inequality has been assessed through a relative approach, from Gini's pioneering article [Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 73 (1914), no. 2, 1203–1248]. Analyzing historical census data for Flint and other American cities, we observe how mean values of income in population subgroups capture the shape of the distributions of income and their comparisons state the overall situation of inequality. Namely, we adopted the approach introduced in [Statistica & Applicazioni 5 (2007), no. 1, 3–27] to assess inequality. Our first findings show that prosperity is distributed unevenly across America's metropolitan areas. More interestingly, unbalanced wealth can be related to other concomitant facts [The New Geography of Jobs, Houghton Mifflin Harcourt, New York, 2012], such as population growth, income growth, unemployment rates and women participation to the labor force. Gaps between more and less educated areas were modest 40 years ago, but they have become quite large nowadays [Cities and skills, technical report, National Bureau of Economic Research, 1994].

The inequality analysis plays an important role since the beginning of the last century, in the economic, social and political debate. From the first pioneering paper of Gini, this subject has become more and more fascinating. The several tools proposed in the literature for evaluating the inequality belong basically to two families: on the one hand there are inequality curves which represent (also graphically) the local pattern of inequality in all segments of the considered population; on the other hand, inequality indexes (that often can be derived from a particular inequality curve) which summarize its measure in one number. Different indexes are needed to reveal different viewpoints toward inequality. In this paper, the features of the relatively new inequality I ( p ) curve are described. Beyond many theoretical results, also an empirical analysis based on real income data of Flint is performed.

In this paper we compare the ordinal rankings generated through Data Envelopment Analysis (DEA) methods to ordinal rankings generated by human decision makers. Through eliciting the total rank ordering for approximately 100 individuals on all of the four different datasets of Decision Making Units (DMUs), we compare the rankings generated by individuals to those generated by ten DEA methods. We observe that depending on the characteristics of the dataset one of the DEA methods performs better than the others in matching human decision makers.

We review several common discretization schemes and study a particular class of power-tail probability distributions on integers, obtained by discretizing continuous Pareto II (Lomax) distribution through one of them. Our results include expressions for the density and cumulative distribution functions, probability generating function, moments and related parameters, stability and divisibility properties, stochastic representations, and limiting distributions of random sums with discrete-Pareto number of terms. We also briefly discuss issues of simulation and estimation and extensions to multivariate setting.

We propose a new model that accounts for the asymmetric response of volatility to positive (`good news') and negative (`bad news') shocks in economic time series – the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of `bad' and `good' news processes given the past – the property that is important for statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.