384 research outputs found
Growth and Fluctuations of Personal Income
Pareto's law states that the distribution of personal income obeys a
power-law in the high-income range, and has been supported by international
observations. Researchers have proposed models over a century since its
discovery. However, the dynamical nature of personal income has been little
studied hitherto, mostly due to the lack of empirical work. Here we report the
first such study, an examination of the fluctuations in personal income of
about 80,000 high-income taxpayers in Japan for two consecutive years, 1997 and
1998, when the economy was relatively stable. We find that the distribution of
the growth rate in one year is independent of income in the previous year. This
fact, combined with an approximate time-reversal symmetry, leads to the Pareto
law, thereby explaining it as a consequence of a stable economy. We also derive
a scaling relation between positive and negative growth rates, and show good
agreement with the data. These findings provide the direct observation of the
dynamical process of personal income flow not yet studied as much as for
companies.Comment: 9 pages, 4 figure
On Stable Pareto Laws in a Hierarchical Model of Economy
This study considers a model of the income distribution of agents whose
pairwise interaction is asymmetric and price-invariant. Asymmetric transactions
are typical for chain-trading groups who arrange their business such that
commodities move from senior to junior partners and money moves in the opposite
direction. The price-invariance of transactions means that the probability of a
pairwise interaction is a function of the ratio of incomes, which is
independent of the price scale or absolute income level. These two features
characterize the hierarchical model. The income distribution in this class of
models is a well-defined double-Pareto function, which possesses Pareto tails
for the upper and lower incomes. For gross and net upper incomes, the model
predicts definite values of the Pareto exponents, and , which are stable with respect to quantitative variation of the
pair-interaction. The Pareto exponents are also stable with respect to the
choice of a demand function within two classes of status-dependent behavior of
agents: linear demand (, ) and unlimited slowly
varying demand (). For the sigmoidal demand that
describes limited returns, , with some
satisfying a transcendental equation. The low-income distribution
may be singular or vanishing in the neighborhood of the minimal income; in any
case, it is -integrable and its Pareto exponent is given explicitly.
The theory used in the present study is based on a simple balance equation
and new results from multiplicative Markov chains and exponential moments of
random geometric progressions.Comment: 23 pages, 10 figure
Power-law distributions from additive preferential redistributions
We introduce a non-growth model that generates the power-law distribution
with the Zipf exponent. There are N elements, each of which is characterized by
a quantity, and at each time step these quantities are redistributed through
binary random interactions with a simple additive preferential rule, while the
sum of quantities is conserved. The situation described by this model is
similar to those of closed -particle systems when conservative two-body
collisions are only allowed. We obtain stationary distributions of these
quantities both analytically and numerically while varying parameters of the
model, and find that the model exhibits the scaling behavior for some parameter
ranges. Unlike well-known growth models, this alternative mechanism generates
the power-law distribution when the growth is not expected and the dynamics of
the system is based on interactions between elements. This model can be applied
to some examples such as personal wealths, city sizes, and the generation of
scale-free networks when only rewiring is allowed.Comment: 12 pages, 4 figures; Changed some expressions and notations; Added
more explanations and changed the order of presentation in Sec.III while
results are the sam
Large Alphabets and Incompressibility
We briefly survey some concepts related to empirical entropy -- normal
numbers, de Bruijn sequences and Markov processes -- and investigate how well
it approximates Kolmogorov complexity. Our results suggest th-order
empirical entropy stops being a reasonable complexity metric for almost all
strings of length over alphabets of size about when surpasses
The Economic Mobility in Money Transfer
In this paper, we investigate the economic mobility in some money transfer
models which have been applied into the research on wealth distribution. We
demonstrate the mobility by recording the time series of agents' ranks and
observing their volatility. We also compare the mobility quantitatively by
employing an index, "the per capita aggregate change in log-income", raised by
economists. Like the shape of distribution, the character of mobility is also
decided by the trading rule in these transfer models. It is worth noting that
even though different models have the same type of distribution, their mobility
characters may be quite different.Comment: 17 pages, 4 figures, 2nd versio
Power Law Distribution of Wealth in a Money-Based Model
A money-based model for the power law distribution (PLD) of wealth in an
economically interacting population is introduced. The basic feature of our
model is concentrating on the capital movements and avoiding the complexity of
micro behaviors of individuals. It is proposed as an extension of the Equiluz
and Zimmermann's (EZ) model for crowding and information transmission in
financial markets. Still, we must emphasize that in EZ model the PLD without
exponential correction is obtained only for a particular parameter, while our
pattern will give it within a wide range. The Zipf exponent depends on the
parameters in a nontrivial way and is exactly calculated in this paper.Comment: 5 pages and 4 figure
Asymptotic analysis of the model for distribution of high-tax payers
The z-transform technique is used to investigate the model for distribution
of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and
others. Our analysis shows an asymptotic power-law of this model with the
exponent -5/2 when a total ``mass'' has a certain critical value. Below the
critical value, the system exhibits an ordinary critical behavior, and scaling
relations hold. Above the threshold, numerical simulations show that a
power-law distribution coexists with a huge ``monopolized'' member. It is
argued that these behaviors are observed universally in conserved aggregation
processes, by analizing an extended model.Comment: 5pages, 3figure
Typical properties of optimal growth in the Von Neumann expanding model for large random economies
We calculate the optimal solutions of the fully heterogeneous Von Neumann
expansion problem with processes and goods in the limit .
This model provides an elementary description of the growth of a production
economy in the long run. The system turns from a contracting to an expanding
phase as increases beyond . The solution is characterized by a universal
behavior, independent of the parameters of the disorder statistics. Associating
technological innovation to an increase of , we find that while such an
increase has a large positive impact on long term growth when , its
effect on technologically advanced economies () is very weak.Comment: 8 pages, 1 figur
Killing-Yano tensors and some applications
The role of Killing and Killing-Yano tensors for studying the geodesic motion
of the particle and the superparticle in a curved background is reviewed.
Additionally the Papadopoulos list [74] for Killing-Yano tensors in G
structures is reproduced by studying the torsion types these structures admit.
The Papadopoulos list deals with groups G appearing in the Berger
classification, and we enlarge the list by considering additional G structures
which are not of the Berger type. Possible applications of these results in the
study of supersymmetric particle actions and in the AdS/CFT correspondence are
outlined.Comment: 36 pages, no figure
Directional mobility of debt ratings
In this paper we describe a method to decompose a well-known measure of debt ratings mobility into it's directional components. We show, using sovereign debt ratings as an example, that this directional decomposition allows us to better understand the underlying characteristics of debt ratings migration and, for the case of the data set used, that the standard Markov chain model is not homogeneous in either the time or cross-sectional dimensions. We find that the directional decomposition also allows us to sign the change in quality of debt over time and across sub-groups of the population
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