Economic inequality and mobility in kinetic models for social sciences

Statistical evaluations of the economic mobility of a society are more difficult than measurements of the income distribution, because they require to follow the evolution of the individuals' income for at least one or two generations. In micro-to-macro theoretical models of economic exchanges based on kinetic equations, the income distribution depends only on the asymptotic equilibrium solutions, while mobility estimates also involve the detailed structure of the transition probabilities of the model, and are thus an important tool for assessing its validity. Empirical data show a remarkably general negative correlation between economic inequality and mobility, whose explanation is still unclear. It is therefore particularly interesting to study this correlation in analytical models. In previous work we investigated the behavior of the Gini inequality index in kinetic models in dependence on several parameters which define the binary interactions and the taxation and redistribution processes: saving propensity, taxation rates gap, tax evasion rate, welfare means-testing etc. Here, we check the correlation of mobility with inequality by analyzing the mobility dependence from the same parameters. According to several numerical solutions, the correlation is confirmed to be negative.Comment: 11 pages, 6 figures. Proceedings of the Sigma-Phi Conference on Statistical Physics, Rhodes, 201

Discretized kinetic theory on scale-free networks

The network of interpersonal connections is one of the possible heterogeneous factors which affect the income distribution emerging from micro-to-macro economic models. In this paper we equip our model discussed in [1,2] with a network structure. The model is based on a system of $n$ differential equations of the kinetic discretized-Boltzmann kind. The network structure is incorporated in a probabilistic way, through the introduction of a link density $P(\alpha)$ and of correlation coefficients $P(\beta|\alpha)$, which give the conditioned probability that an individual with $\alpha$ links is connected to one with $\beta$ links. We study the properties of the equations and give analytical results concerning the existence, normalization and positivity of the solutions. For a fixed network with $P(\alpha)=c/\alpha^q$, we investigate numerically the dependence of the detailed and marginal equilibrium distributions on the initial conditions and on the exponent $q$. Our results are compatible with those obtained from the Bouchaud-Mezard model and from agent-based simulations, and provide additional information about the dependence of the individual income on the level of connectivity.Comment: 17 pages, 5 figures. Proceedings of the Sigma-Phi Conference on Statistical Physics, Rhodes, 201

From microscopic taxation and redistribution models to macroscopic income distributions

We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution of the income distribution over the population and to explain the emergence of collective features based on the knowledge of the individual interactions. By making different choices of the framework parameters, we construct different models, whose long-time behavior is then investigated. Asymptotic stationary distributions are found, which enjoy similar properties as those observed in empirical distributions. In particular, they exhibit power law tails of Pareto type and their Lorenz curves and Gini indices are consistent with some real world ones.Comment: 12 pages, 4 figures. Version submitted to Physica A on Feb 15, 201

Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange

In our recently proposed stochastic version of discretized kinetic theory, the exchange of wealth in a society is modelled through a large system of Langevin equations. The deterministic part of the equations is based on non-linear transition probabilities between income classes. The noise terms can be additive, multiplicative or mixed, both with white or Ornstein–Uhlenbeck spectrum. The most important measured correlations are those between Gini inequality index G and social mobility M, between total income and G, and between M and total income. We describe numerical results concerning these correlations and a quantity which gives average stochastic deviations from the equilibrium solutions in dependence on the noise amplitude

Driving-induced crossover: from classical criticality to self-organized criticality

We propose a spin model with quenched disorder which exhibits in slow driving two drastically different types of critical nonequilibrium steady states. One of them corresponds to classical criticality requiring fine-tuning of the disorder. The other is a self-organized criticality which is insensitive to disorder. The crossover between the two types of criticality is determined by the mode of driving. As one moves from "soft" to "hard" driving the universality class of the critical point changes from a classical order-disorder to a quenched Edwards-Wilkinson universality class. The model is viewed as prototypical for a broad class of physical phenomena ranging from magnetism to earthquakes.Comment: 4 pages, 4 figure

Testing the preservation potential of early diagenetic dolomites as geochemical archives

Early marine diagenetic dolomite is a rather thermodynamically‐stable carbonate phase and has potential to act as an archive of marine porewater properties. However, the variety of early to late diagenetic dolomite phases that can coexist within a single sample can result in extensive complexity. Here, the archive potential of early marine dolomites exposed to extreme post‐depositional processes is tested using various types of analyses, including: petrography, fluid inclusion data, stable δ13C and δ18O isotopes, 87Sr/86Sr ratios, and U‐Pb age dating of various dolomite phases. In this example, a Triassic carbonate platform was dissected and overprinted (diagenetic temperatures of 50 to 430°C) in a strike‐slip zone in Southern Spain. Eight episodes of dolomitization, a dolostone cataclasite and late stage meteoric/vadose cementation were recognized. The following processes were found to be diagenetically relevant: (i) protolith deposition and fabric‐preservation, and marine dolomitization of precursor aragonite and calcite during the Middle–Late Triassic; (ii) intermediate burial and formation of zebra saddle dolomite and precipitation of various dolomite cements in a Proto‐Atlantic opening stress regime (T ca 250°C) during the Early–Middle Jurassic; (iii) dolomite cement precipitation during early Alpine tectonism, rapid burial to ca 15 km, and high‐grade anchizone overprint during Alpine tectonic evolution in the Early Eocene to Early Miocene; (iv) brecciation of dolostones to cataclasite during the onset of the Carboneras Fault Zone activity during the Middle Miocene; and (v) late‐stage regression and subsequent meteoric overprint. Data shown here document that, under favourable conditions, early diagenetic marine dolomites and their archive data may resist petrographic and geochemical resetting over time intervals of 108 or more years. Evidence for this preservation includes preserved Late Triassic seawater δ13CDIC values and primary fluid inclusion data. Data also indicate that oversimplified statements based on bulk data from other petrographically‐complex dolomite archives must be considered with caution