Power Law Tails in the Italian Personal Income Distribution

We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977--2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of our analysis show a shift of the distribution and a change of the indexes specifying it over time. As regards the first issue, we test the hypothesis that the evolution of both gross domestic product and personal income is governed by similar mechanisms, pointing to the existence of correlation between these quantities. The fluctuations of the shape of income distribution are instead quantified by establishing some links with the business cycle phases experienced by the Italian economy over the years covered by our dataset.Comment: Latex2e v1.6; 14 pages with 10 figures; preprint submitted to Physica

A k-generalized statistical mechanics approach to income analysis

This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of k-generalized statistics, is derived that is particularly suitable to describe the whole spectrum of incomes, from the low-middle income region up to the high-income Pareto power-law regime. Analytical expressions for the shape, moments and some other basic statistical properties are given. Furthermore, several well-known econometric tools for measuring inequality, which all exist in a closed form, are considered. A method for parameter estimation is also discussed. The model is shown to fit remarkably well the data on personal income for the United States, and the analysis of inequality performed in terms of its parameters reveals very powerful.Comment: LaTeX2e; 15 pages with 1 figure; corrected typo

k-Generalized Statistics in Personal Income Distribution

Starting from the generalized exponential function $\exp_{\kappa}(x)=(\sqrt{1+\kappa^{2}x^{2}}+\kappa x)^{1/\kappa}$, with $\exp_{0}(x)=\exp(x)$, proposed in Ref. [G. Kaniadakis, Physica A \textbf{296}, 405 (2001)], the survival function $P_{>}(x)=\exp_{\kappa}(-\beta x^{\alpha})$, where $x\in\mathbf{R}^{+}$, $\alpha,\beta>0$, and $\kappa\in[0,1)$, is considered in order to analyze the data on personal income distribution for Germany, Italy, and the United Kingdom. The above defined distribution is a continuous one-parameter deformation of the stretched exponential function $P_{>}^{0}(x)=\exp(-\beta x^{\alpha})$\textemdash to which reduces as $\kappa$ approaches zero\textemdash behaving in very different way in the $x\to0$ and $x\to\infty$ regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law $P_{>}(x)\sim(2\beta\kappa)^{-1/\kappa}x^{-\alpha/\kappa}$. This makes the $\kappa$-generalized function particularly suitable to describe simultaneously the income distribution among both the richest part and the vast majority of the population, generally fitting different curves. An excellent agreement is found between our theoretical model and the observational data on personal income over their entire range.Comment: Latex2e v1.6; 14 pages with 12 figures; for inclusion in the APFA5 Proceeding

The Power-law Tail Exponent of Income Distributions

In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimising the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data for Australia and Italy.Comment: Latex2e v1.6; 8 pages with 3 figures; in press (Physica A

The k-generalized distribution: A new descriptive model for the size distribution of incomes

This paper proposes the k-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement - such as the Lorenz curve and the Gini coefficient - are given. A method for parameter estimation is also discussed. The model is shown to fit extremely well the data on personal income distribution in Australia and the United States.Comment: 12 pages with 8 figures; LaTeX; introduction revised, added reference for section 1; accepted for publication in Physica A: Statistical Mechanics and its Application

Una rilettura della crescita ciclica in Italia tra il 1861 e il 2009

Il lavoro fornisce una valutazione empirica dell'evoluzione economica di fondo e delle fluttuazioni cicliche in Italia per il lungo periodo di tempo dal 1861 al 2009. A tale scopo, l'analisi utilizza le ricostruzioni delle serie storiche di contabilit\ue0 nazionale elaborate da Fenoaltea (2005a,b, 2006) per il periodo 1861-1913 e da Rossi et al. (1993) per gli anni 1913-1970, insieme alle stime ISTAT dei conti economici nazionali dal 1970 al 2009. L'analisi di serie storiche annuali dall'Unit\ue0 al presente \ue8 condotta con l'obiettivo di riconsiderare la tesi dell'uniformit\ue0 nel corso del tempo dei cicli economici, implicita nell'approccio metodologico di gran parte della pi\uf9 recente ed accreditata letteratura sulle fluttuazioni di breve periodo\u2014in particolare, della teoria RBC. Dall'evidenza empirica presentata nel lavoro emergono infatti forti caveat contro questa ipotesi. Intanto, la struttura economica del paese lungo il sentiero di crescita muta nel corso del tempo, il che lascia ragionevolmente supporre che il comportamento ciclico dell'economia italiana di oggi non sia paragonabile a quello, per esempio, dell'Italia all\u2019indomani dell'Unit\ue0. Inoltre, investigando il ciclo economico italiano nel periodo considerato in base a diverse metodologie di analisi, sorgono notevoli perplessit\ue0 circa la possibilit\ue0 di individuare ed interpretare cambiamenti sistematici nel corso del tempo. Infatti, i risultati dell'analisi nel dominio temporale secondo l'approccio RBC mostrano in primo luogo una riduzione della variabilit\ue0 delle fluttuazioni nel secondo dopoguerra, che riflette la maggiore stabilit\ue0 delle componenti di domanda e di offerta. Inoltre, tutte le componenti del PIL e del valore aggiunto sono coincidenti e procicliche, sebbene il segno e l'entit\ue0 delle correlazioni di ogni singola componente con la serie di riferimento a livello aggregato si modifichino nel corso del tempo. Infine, integrando le statistiche descrittive nel dominio temporale con un'analisi dettagliata di cicli e fasi presi individualmente come nella tradizione NBER, i risultati segnalano nel complesso la presenza di asimmetrie tra cicli e fasi individuali, sia in termini di durata che di ampiezza, che offrono ulteriore supporto alla tesi dell'eterogeneit\ue0 delle fluttuazioni in Italia. Questa conclusione, che appare incompatibile con l'approccio dominante della letteratura RBC, ha delle conseguenze rilevanti per l'analisi delle fluttuazioni in particolare, e per la teoria macroeconomica in generale. L'ipotesi di somiglianza dei cicli economici rappresenta infatti un corollario della visione secondo cui gli agenti economici sono identici, per cui l'individuo rappresentativo pu\uf2 divenire nelle rappresentazioni formalizzate lo strumento analitico che consente di utilizzare per le grandezze aggregate i risultati ottenuti a livello microeconomico. Questa metodologia ha comportato, per quanto riguarda lo studio delle fluttuazioni, che gli strumenti di analisi fossero quasi esclusivamente quelli macroeconomici. Inoltre, essa preclude la possibilit\ue0 di individuare le determinanti causali nelle componenti microeconomiche se quest'ultime influenzano le grandezze aggregate. Per l'analisi delle fluttuazioni economiche occorre, dunque, una riconsiderazione degli strumenti analitici da utilizzare. L'analisi condotta in questo lavoro rivela infatti che le fluttuazioni costituiscono un evento complesso e per molti aspetti peculiare , di cui l'indagine aggregata rappresenta solo un primo passo. Se questo \ue8 vero, individuare le regolarit\ue0 empiriche del ciclo economico, trascurando i fattori che governano i cambiamenti di tali regolarit\ue0, non pu\uf2 che generare risultati, nella migliore delle ipotesi, parziali

The labour market and the distribution of income: an empirical analysis for Italy

This paper provides an empirical examination of the distribution of labour earnings in Italy. Using four waves of data from the Participation Labour Unemployment Survey, a database of information on the Italian labour market supply, we find the shape of the observed distributions to be positively skewed with a "fat" and long tail on the right. We also address the question of earnings dispersion by applying a "nested" decomposition procedure of the Theil inequality measure, which combines into a unified framework the standard decompositions by population subgroups and income sources. The empirical evidence obtained points to the key role played by the self-employees in shaping labour income inequality, especially at the upper extreme of the earnings distribution, and the emergence of non-standard forms of employment as an important feature of the contemporary workplace

The Pareto law and the distribution of labour income in Italy

This chapter provides an empirical examination of the distribution of labour earnings in Italy. Using data drawn from the 2005 and 2006 waves of the PLUS (See chapter 9) we find the shape of the observed distributions to be right-skewed and display a long right tail, which is adequately described by a Pareto-type model. This chapter also address the question of earnings dispersion by applying a nested decomposition procedure of the Theil inequality measure, which combines into a unified framework the standard decompositions by population subgroups and income sources. The empirical evidence obtained points to the key role played by the self-employees in shaping labour income inequality, especially at the upper extreme of the earnings distribution, and the emergence of non-standard forms of employment as an important feature of the contemporary workplace. The structure of the chapter is: after a brief introduction, data and methodological decisions are discussed; then it presents the empirical results obtained in the above analysis; finally, some concluding remarks and policy implications are drawn

Deterministic Digital Clustering of Wireless Ad Hoc Networks

We consider deterministic distributed communication in wireless ad hoc networks of identical weak devices under the SINR model without predefined infrastructure. Most algorithmic results in this model rely on various additional features or capabilities, e.g., randomization, access to geographic coordinates, power control, carrier sensing with various precision of measurements, and/or interference cancellation. We study a pure scenario, when no such properties are available. As a general tool, we develop a deterministic distributed clustering algorithm. Our solution relies on a new type of combinatorial structures (selectors), which might be of independent interest. Using the clustering, we develop a deterministic distributed local broadcast algorithm accomplishing this task in $O(\Delta \log^*N \log N)$ rounds, where $\Delta$ is the density of the network. To the best of our knowledge, this is the first solution in pure scenario which is only polylog$(n)$ away from the universal lower bound $\Omega(\Delta)$, valid also for scenarios with randomization and other features. Therefore, none of these features substantially helps in performing the local broadcast task. Using clustering, we also build a deterministic global broadcast algorithm that terminates within $O(D(\Delta + \log^* N) \log N)$ rounds, where $D$ is the diameter of the network. This result is complemented by a lower bound $\Omega(D \Delta^{1-1/\alpha})$, where $\alpha > 2$ is the path-loss parameter of the environment. This lower bound shows that randomization or knowledge of own location substantially help (by a factor polynomial in $\Delta$) in the global broadcast. Therefore, unlike in the case of local broadcast, some additional model features may help in global broadcast