Search

The paper provides a survey of results related to the "$\kappa$-generalized distribution", a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties, interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution field, such as the Gini index and the Lorenz curve. An extension of the basic model that is most able to accommodate the special features of wealth data is also reviewed. The survey of empirical applications given in this paper shows the $\kappa$-generalized models of income and wealth to be in excellent agreement with the observed data in many cases., Comment: LaTeX2e; 22 pages with 7 figures

Over the last decades, the distribution of income and wealth has been deteriorating in many countries, leading to increased inequalities within and between societies. This tendency has revived the interest in the subject greatly, yet it still receives very little attention within the realm of mainstream economic thinking. One reason for this is that the basic paradigm of "standard economics", the representative-agent General Equilibrium framework, is badly equipped to cope with distributional issues. Here we argue that when the economy is treated as a complex system composed of many heterogeneous interacting agents who give rise to emergent phenomena, to address the main stylized facts of income/wealth distribution requires leaving the toolbox of mainstream economics in favour of alternative approaches. The "k-generalized" family of income/wealth distributions, building on the categories of complexity, is an example of how advances in the field can be achieved within new interdisciplinary research contexts., Comment: LaTeX2e; 14 pages with 3 figures

In a recent paper in this journal [J. Stat. Mech. (2009) P02037] we proposed a new, physically motivated, distribution function for modeling individual incomes having its roots in the framework of the k-generalized statistical mechanics. The performance of the k-generalized distribution was checked against real data on personal income for the United States in 2003. In this paper we extend our previous model so as to be able to account for the distribution of wealth. Probabilistic functions and inequality measures of this generalized model for wealth distribution are obtained in closed form. In order to check the validity of the proposed model, we analyze the U.S. household wealth distributions from 1984 to 2009 and conclude an excellent agreement with the data that is superior to any other model already known in the literature., Comment: LaTeX2e; 23 pages with 6 figures; corrected typos

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 typos

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 Applications

This paper uses firm-level data recorded in the AMADEUS database to investigate the distribution of labour productivity in different European countries. We find that the upper tail of the empirical productivity distributions follows a decaying power-law, whose exponent $\alpha$ is obtained by a semi-parametric estimation technique recently developed by Clementi et al. (2006). The emergence of "fat tails" in productivity distribution has already been detected in Di Matteo et al. (2005) and explained by means of a model of social network. Here we show that this model is tested on a broader sample of countries having different patterns of social network structure. These different social attitudes, measured using a social capital indicator, reflect in the power-law exponent estimates, verifying in this way the existence of linkages among firms' productivity performance and social network., Comment: LaTeX2e; 18 pages with 3 figures; Journal of Economic Interaction and Coordination, in press

In this paper we sketch some reflections on the pitfalls and inconsistencies of the research program - currently dominant among the profession - aimed at providing microfoundations to macroeconomics along a Walrasian perspective. We argue that such a methodological approach constitutes an unsatisfactory answer to a well-posed research question, and that alternative promising routes have been long mapped out but only recently explored. In particular, we discuss a recent agent-based, truly non-Walrasian macroeconomic model, and we use it to envisage new challenges for future research., Comment: Latex2e v1.6; 17 pages with 4 figures; for inclusion in the APFA5 Proceedings

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 Proceedings

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)

We analyze three sets of income data: the US Panel Study of Income Dynamics PSID), the British Household Panel Survey (BHPS), and the German Socio-Economic Panel (GSOEP). It is shown that the empirical income distribution is consistent with a two-parameter lognormal function for the low-middle income group (97%-99% of the population), and with a Pareto or power law function for the high income group (1%-3% of the population). This mixture of two qualitatively different analytical distributions seems stable over the years covered by our data sets, although their parameters significantly change in time. It is also found that the probability density of income growth rates almost has the form of an exponential function., Comment: Latex2e v1.6; 16 pages with 5 figures

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