Cross Ranking of Cities and Regions: Population vs. Income

This paper explores the relationship between the inner economical structure of communities and their population distribution through a rank-rank analysis of official data, along statistical physics ideas within two techniques. The data is taken on Italian cities. The analysis is performed both at a global (national) and at a more local (regional) level in order to distinguish "macro" and "micro" aspects. First, the rank-size rule is found not to be a standard power law, as in many other studies, but a doubly decreasing power law. Next, the Kendall and the Spearman rank correlation coefficients which measure pair concordance and the correlation between fluctuations in two rankings, respectively, - as a correlation function does in thermodynamics, are calculated for finding rank correlation (if any) between demography and wealth. Results show non only global disparities for the whole (country) set, but also (regional) disparities, when comparing the number of cities in regions, the number of inhabitants in cities and that in regions, as well as when comparing the aggregated tax income of the cities and that of regions. Different outliers are pointed out and justified. Interestingly, two classes of cities in the country and two classes of regions in the country are found. "Common sense" social, political, and economic considerations sustain the findings. More importantly, the methods show that they allow to distinguish communities, very clearly, when specific criteria are numerically sound. A specific modeling for the findings is presented, i.e. for the doubly decreasing power law and the two phase system, based on statistics theory, e.g., urn filling. The model ideas can be expected to hold when similar rank relationship features are observed in fields. It is emphasized that the analysis makes more sense than one through a Pearson value-value correlation analysis.Comment: 34 pages, 13 figures, 6 tables, 81 references; prepared for Journal of Statistical Mechanics: Theory and Experiment (JSTAT

Religion-based Urbanization Process in Italy: Statistical Evidence from Demographic and Economic Data

This paper analyzes some economic and demographic features of Italians living in cities containing a Saint name in their appellation (hagiotoponyms). Demographic data come from the surveys done in the 15th (2011) Italian Census, while the economic wealth of such cities is explored through their recent [2007-2011] aggregated tax income (ATI). This cultural problem is treated from various points of view. First, the exact list of hagiotoponyms is obtained through linguistic and religiosity criteria. Next, it is examined how such cities are distributed in the Italian regions. Demographic and economic perspectives are also offered at the Saint level, i.e. calculating the cumulated values of the number of inhabitants and the ATI, "per Saint", as well as the corresponding relative values taking into account the Saint popularity. On one hand, frequency-size plots and cumulative distribution function plots, and on the other hand, scatter plots and rank-size plots between the various quantities are shown and discussed in order to find the importance of correlations between the variables. It is concluded that rank-rank correlations point to a strong Saint effect, which explains what actually Saint-based toponyms imply in terms of comparing economic and demographic data.Comment: 55 pages, 70 refs., 21 figures, 15 tables; prepared for and to be published in Quantity & Qualit

Assessing the Inequalities of Wealth in Regions: the Italian Case

This paper discusses region wealth size distributions, through their member cities aggregated tax income. As an illustration, the official data of the Italian Ministry of Economics and Finance has been considered, for all Italian municipalities, over the period 2007-2011. Yearly data of the aggregated tax income is transformed into a few indicators: the Gini, Theil, and Herfindahl-Hirschman indices. On one hand, the relative interest of each index is discussed. On the other hand, numerical results confirm that Italy is divided into very different regional realities, a few which are specifically outlined. This shows the interest of transforming data in an adequate manner and of comparing such indices.Comment: to be published in Quality and Quantity; 23 pages; 1 figure; 23 tables; 19 reference

Dynamic Programming via Measurable Selection

The aim of this paper is to provide the proof of a Dynamic Programming Principle for a certain class of stochastic control problems with exit time. To this end, a Measurable Selection Theorem is also proved

Stochastic Ising model with flipping sets of spins and fast decreasing temperature

This paper deals with the stochastic Ising model with a temperature shrinking to zero as time goes to infinity. A generalization of the Glauber dynamics is considered, on the basis of the existence of simultaneous flips of some spins. Such dynamics act on a wide class of graphs which are periodic and embedded in $\mathbb{R}^d$. The interactions between couples of spins are assumed to be quenched i.i.d. random variables following a Bernoulli distribution with support $\{-1,+1\}$. The specific problem here analyzed concerns the assessment of how often (finitely or infinitely many times, almost surely) a given spin flips. Adopting the classification proposed in \cite{GNS}, we present conditions in order to have models of type $\mathcal{F}$ (any spin flips finitely many times), $\mathcal{I}$ (any spin flips infinitely many times) and $\mathcal{M}$ (a mixed case). Several examples are provided in all dimensions and for different cases of graphs. The most part of the obtained results holds true for the case of zero-temperature and some of them for the cubic lattice $\mathbb{L}_d=(\mathbb{Z}^d, \mathbb{E}_d)$ as well.Comment: 31 pages, 6 figures, Accepted for publication in "Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistiques

Exhaustion of resources: a marked temporal process framework

This paper deals with the exhaustion of a replenishable resource, one of the main topics in environmental research. To examine this problem, we construct a mechanism to estimate the probability of depletion under a very small set of assumptions. The stock of the resource is assumed to evolve accordingly to a marked temporal process generated by the shocks occurring in the environment. Our setting is eminently theoretical, and constitutes an effective extension of some important models of stochastic growth regarding sustainability and ruin analysis. Furthermore, the validity of the model is supported through the evidence relative to the paradigmatic cases of water resource planning and oil reserves

Long run analysis of crude oil portfolios

This paper deals with the analysis of the long-run behavior of a set of mispricing portfolios generated by three crude oils, where one of the oils is the reference commodity and it is compared to a combination of the other two ones. To this aim, the long-term parameter related to the mispricing portfolio are estimated on empirical data. We pay particular attention to the cases of mispricing portfolios either of stationary type or following a Brownian motion: the former situation is associated to replication portfolios of a reference commodity; the latter one allows to implement forecasts. The theoretical setting is validated through empirical data on WTI, Brent and Dubai oils

Economic growth, corruption and tax evasion

In this paper, we explore tax revenues in a regime of widespread corruption in a growth model. We develop a Ramsey model of economic growth with rival but non-excludable public good which is financed by taxes which can be evaded via corrupt tax inspector. We prove that the relationship between the tax rate and tax collection, in a dynamic framework, is not unique, but is different depending on the relevance of the shame effect. We show that growth rates - both of income and of tax revenues - decrease, as the tax rate increases, for all types of shame effect countries but they differ in how the growth rate decreases as the tax rate increases: the rate of decrease is higher in low shame countries than in high shame countries.

Roots and Effects of Investments' Misperception

This work deals with the problem of investors' irrational behavior and financial products' misperception. The theoretical analysis of the mechanisms driving wrong evaluations of investment performances is explored. The study is supported by the application of Monte Carlo simulations to the remarkable case of structured financial products. Some motivations explaining the popularity among retail investors of these complex financial instruments are also provided. Investors are assumed to compare the performances of different projects through stochastic dominance rules and, to pursue our scopes, a new definition of this decision criteria is introduced.

Asymptotic convergence of weighted random matrices: nonparametric cointegration analysis for I(2) processes.

The aim of this paper is to provide a new perspective on the nonparametric co-integration analysis for integrated processes of the second order. Our analysis focus on a pair of random matrices related to such integrated process. Such matrices are constructed by introducing some weight functions. Under asymptotic conditions on such weights, convergence results in distribution are obtained. Therefore, a generalized eigenvalue problem is solved. Differential equations and stochastic calculus theory are used.Co-integration, Nonparametric, Differential equations, Asymptotic properties.