The observed striking regularity of the wealth distribution at the high wealth range confirms the hypothesis made over a century ago by Pareto (1897). During the century since Pareto’s work, empirical evidence has been accumulated in support of his hypothesis (see, for example, Steindl, 1965; Atkinson and Harrison, 1978; Persky, 1992). This is a remarkable result because power-law distributions exhibit the special property that they have no characteristic scale. It may indicate that
the same dynamical rules of gains/losses apply across the entire economy independently of the particular sector or the wealth and sophistication of different investors (Anderson, 1997). Thus, the Forbes 400 data may provide useful information not only about the richest individuals, but also about the wealth of people in wealth percentiles far away from the top 400. These findings raise
the broader question about the origins of this form of the wealth distribution. While the physical properties of humans (such as height) as well as their mental and social abilities approximately follow Gaussian distributions that tend to be rather narrow, their wealths are very widely distributed and span over seven orders of magnitude (which, in terms of other human properties
such as IQ or height, would correspond to observing an individual with an IQ of 109, or an individual who is 10,000 mi tall). What is the underlying reason for the empirically observed power-law distribution of wealth? It has been suggested that the Pareto wealth distribution is a
consequence of the fundamental nature of the capital market, namely, of market efficiency and the multiplicative nature of the process of wealth accumulation via capital investment (Levy and Solomon, 1996; Levy, 2003).
It is however important to notice that in spite of what happens with most exponents in Statistical Physics may
change in time depending on the economical circumstances [5,12], making thus impossible the definition of some sort of universal scaling in this problem.
In spite of all the neglected effects we will see that this simple model is able to reproduce the observed wealth-distributions and generates reasonable first-degree
family relation networks. The main advantage of this model is that the network structure on which the wealth-exchange is realized is not a-priori put in the system. The network forms and converges to a stable topology in time, together with the wealth diversification in the system and the appearance of the Pareto distribution.
It is easy to realize that the chosen value of Wt will not change the nature of the results, but it simply rescales the values of the wealth. A simple computer exercise will also convince us that the above defined family-network model converges in time very quickly to a statistically invariant state both for the wealth distribution and network structure. Results for a relatively big lattice (N = 10000) and for realistic p = 0.3 and q = 0.7 values are presented in Figure 2. We see that roughly after 5 MCS, both the cumulative wealth distribution and the first two moments of the degree distribution converge to their stable limit.
On the other hand one can also check that the model has a well defined thermodynamic limit. As N increases, we obtain again that both the cumulative wealth distribution and the statistical properties of the network reach a stable
limit. Characteristic results for this variation are presented in Figure 3. As we can see from the figure, for reasonably big lattices N ≈ 10000, a stable limit is reached.
Extended computer simulations show, that for reasonable parameter values both the obtained cumulative wealth distribution function and network structure are realistic: (i) in good agreement with real measurement data we were able to generate cumulative wealth-distribution functions with Pareto-like power-law tails, (ii) the obtained Pareto index is close to the measured values, (iii) the cumulative
wealth distribution function for the low and medium wealth values is exponential as found in social data (iv) the Pareto regime is valid for the upper 5% of the society, (v) the generated first-degree family relation network is
realistic. We observed that in our model the initial wealth-diversification is realized through a strong anticorrelation between the wealth of the nodes and their number of links.
The novel aspect of our approach is however that the
network structure was not a-priori introduced in the model, but it got formed during the postulated wealth-exchange dynamics.
The power-law nature was also found to be true of wealth
distributions, albeit with a different exponent. The two distributions are not completely unrelated, as those who are significantly wealthy also have incomes far higher than the average individual or household. However, the distributions of income and wealth cannot be simply connected, and each have to be measured independently for a particular society. The occurrence of a qualitatively
similar distribution across widely differing geographical regions and economic development stages may be indicative of universal features of inequality in human societies.
Unfortunately, not many studies have been done on the distribution of wealth, which consist of the net value of assets (financial holdings and/or tangible items) owned at a given point in time. The lack of an easily available data
source for measuring wealth, analogous to income tax returns for measuring income, means that one has to resort to indirect methods
Observing the wealth distribution of a non-Western developing capitalist society, such as India, which until quite recently had a planned economy, will be not only instructive by itself but it will also provide necessary
comparison with the previous studies.
The Pareto exponent as measured from the wealth distribution is found to be always lower than the exponent for the income distribution, which is consistent with the general observation that, in market economies, wealth is much more unequally distributed than income.
Typically, the presence of power-law distributions is a hint for the complexity underlying a system, and a challenge for statistical physicists to model and study the problem. This is why Pareto law is one of the main problems studied in Econophysics.
Since the value found by Pareto for the scaling exponent was around 1.5, Pareto law is sometimes related to a generalized form of Zipf’s law [15] and referred to as Pareto-Zipf law. According to Zipf’s law, many natural
and social phenomena (distribution of words frequency in a text, population of cities, debit of rivers, users of web sites, strength of earthquakes, income of companies, etc) are characterized by a cumulative distribution function with a power-law tail with a scaling exponent close to 1.
This large variation of indicates the absence of universal scaling in this problem – a feature which models designed
to describe the wealth distribution in societies should be able to reproduce.
This model is based on a mean field type scenario with interactions of strength J among all the agents and on the existence of multiplicative fluctuations acting on each agent’s wealth. The obtained wealth distributions adjust well to the phenomenological P>(w) curve. Their mean-field results predict that Pareto index should increase linearly with the strength of interaction between the
agents and that = 1 for the case of independent agents (J = 0).
Both the experimental results and the models suggest that societies in which there is strong wealth-exchange among the agents are characterized by higher values
of the Pareto index, whereas societies of isolated agents, where each agent increases or decreases his wealth in a multiplicative and uncorrelated manner, are usually characterized by close to 1. Our measurement results on the Hungarian medieval society confirm this rule.
However, once such data is obtained, it could be of decisive importance, since such a society represents an idealized case, where the agents are acting roughly
independently. The underlying social network and the wealth exchange on it, are expected to have no major influence, since the aristocratic families were
more or less self-supporting and no relevant barter existed. This simplified economic system provides thus an excellent framework to test, in a trivial case, the prediction of wealth distribution models.
This cut-off is necessary since historians suggest that the database is not reliable in this ranges. With the above constraints, our final database [28] had data for 1283 noble families and 116 religious or city institutions.
Considering an average of five persons per family (a generally accepted value by the historians and sociologists specialized in the targeted medieval period)
we obtain that our sample contains around 6400 people. This represents the top 8% of the estimated 80000 aristocrats living in Hungary at that period, and 0.2−0.3% of the estimated total population (2.7 millions) of Hungary in 1550.
It is also observable from Figure 1, that the Pareto law breaks down in the limit of the very rich families, where the wealth is bigger than 1000 serf families. This is presumably a finite-size effect and such results are observable in other databases too ([5,9]).
Sources:
The Forbes 400 and the Pareto wealth distribution - Economics Letters 90 (2006) 290–295
A family-network model for wealth distribution in societies
Ricardo Coelho a, Zolt´an N´eda a,b,∗, Jos´e J. Ramasco a,c and Maria Augusta Santos a
Evidence for Power-law tail of the Wealth Distribution in India Sitabhra Sinha The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai -
600 113, India.
Wealth distribution and Pareto’s law in the
Hungarian medieval society G´eza Hegyi a,b, Zolt´an N´eda a,c,, and Maria Augusta Santos
the same dynamical rules of gains/losses apply across the entire economy independently of the particular sector or the wealth and sophistication of different investors (Anderson, 1997). Thus, the Forbes 400 data may provide useful information not only about the richest individuals, but also about the wealth of people in wealth percentiles far away from the top 400. These findings raise
the broader question about the origins of this form of the wealth distribution. While the physical properties of humans (such as height) as well as their mental and social abilities approximately follow Gaussian distributions that tend to be rather narrow, their wealths are very widely distributed and span over seven orders of magnitude (which, in terms of other human properties
such as IQ or height, would correspond to observing an individual with an IQ of 109, or an individual who is 10,000 mi tall). What is the underlying reason for the empirically observed power-law distribution of wealth? It has been suggested that the Pareto wealth distribution is a
consequence of the fundamental nature of the capital market, namely, of market efficiency and the multiplicative nature of the process of wealth accumulation via capital investment (Levy and Solomon, 1996; Levy, 2003).
It is however important to notice that in spite of what happens with most exponents in Statistical Physics may
change in time depending on the economical circumstances [5,12], making thus impossible the definition of some sort of universal scaling in this problem.
In spite of all the neglected effects we will see that this simple model is able to reproduce the observed wealth-distributions and generates reasonable first-degree
family relation networks. The main advantage of this model is that the network structure on which the wealth-exchange is realized is not a-priori put in the system. The network forms and converges to a stable topology in time, together with the wealth diversification in the system and the appearance of the Pareto distribution.
It is easy to realize that the chosen value of Wt will not change the nature of the results, but it simply rescales the values of the wealth. A simple computer exercise will also convince us that the above defined family-network model converges in time very quickly to a statistically invariant state both for the wealth distribution and network structure. Results for a relatively big lattice (N = 10000) and for realistic p = 0.3 and q = 0.7 values are presented in Figure 2. We see that roughly after 5 MCS, both the cumulative wealth distribution and the first two moments of the degree distribution converge to their stable limit.
On the other hand one can also check that the model has a well defined thermodynamic limit. As N increases, we obtain again that both the cumulative wealth distribution and the statistical properties of the network reach a stable
limit. Characteristic results for this variation are presented in Figure 3. As we can see from the figure, for reasonably big lattices N ≈ 10000, a stable limit is reached.
Extended computer simulations show, that for reasonable parameter values both the obtained cumulative wealth distribution function and network structure are realistic: (i) in good agreement with real measurement data we were able to generate cumulative wealth-distribution functions with Pareto-like power-law tails, (ii) the obtained Pareto index is close to the measured values, (iii) the cumulative
wealth distribution function for the low and medium wealth values is exponential as found in social data (iv) the Pareto regime is valid for the upper 5% of the society, (v) the generated first-degree family relation network is
realistic. We observed that in our model the initial wealth-diversification is realized through a strong anticorrelation between the wealth of the nodes and their number of links.
The novel aspect of our approach is however that the
network structure was not a-priori introduced in the model, but it got formed during the postulated wealth-exchange dynamics.
The power-law nature was also found to be true of wealth
distributions, albeit with a different exponent. The two distributions are not completely unrelated, as those who are significantly wealthy also have incomes far higher than the average individual or household. However, the distributions of income and wealth cannot be simply connected, and each have to be measured independently for a particular society. The occurrence of a qualitatively
similar distribution across widely differing geographical regions and economic development stages may be indicative of universal features of inequality in human societies.
Unfortunately, not many studies have been done on the distribution of wealth, which consist of the net value of assets (financial holdings and/or tangible items) owned at a given point in time. The lack of an easily available data
source for measuring wealth, analogous to income tax returns for measuring income, means that one has to resort to indirect methods
Observing the wealth distribution of a non-Western developing capitalist society, such as India, which until quite recently had a planned economy, will be not only instructive by itself but it will also provide necessary
comparison with the previous studies.
The Pareto exponent as measured from the wealth distribution is found to be always lower than the exponent for the income distribution, which is consistent with the general observation that, in market economies, wealth is much more unequally distributed than income.
Typically, the presence of power-law distributions is a hint for the complexity underlying a system, and a challenge for statistical physicists to model and study the problem. This is why Pareto law is one of the main problems studied in Econophysics.
Since the value found by Pareto for the scaling exponent was around 1.5, Pareto law is sometimes related to a generalized form of Zipf’s law [15] and referred to as Pareto-Zipf law. According to Zipf’s law, many natural
and social phenomena (distribution of words frequency in a text, population of cities, debit of rivers, users of web sites, strength of earthquakes, income of companies, etc) are characterized by a cumulative distribution function with a power-law tail with a scaling exponent close to 1.
This large variation of indicates the absence of universal scaling in this problem – a feature which models designed
to describe the wealth distribution in societies should be able to reproduce.
This model is based on a mean field type scenario with interactions of strength J among all the agents and on the existence of multiplicative fluctuations acting on each agent’s wealth. The obtained wealth distributions adjust well to the phenomenological P>(w) curve. Their mean-field results predict that Pareto index should increase linearly with the strength of interaction between the
agents and that = 1 for the case of independent agents (J = 0).
Both the experimental results and the models suggest that societies in which there is strong wealth-exchange among the agents are characterized by higher values
of the Pareto index, whereas societies of isolated agents, where each agent increases or decreases his wealth in a multiplicative and uncorrelated manner, are usually characterized by close to 1. Our measurement results on the Hungarian medieval society confirm this rule.
However, once such data is obtained, it could be of decisive importance, since such a society represents an idealized case, where the agents are acting roughly
independently. The underlying social network and the wealth exchange on it, are expected to have no major influence, since the aristocratic families were
more or less self-supporting and no relevant barter existed. This simplified economic system provides thus an excellent framework to test, in a trivial case, the prediction of wealth distribution models.
This cut-off is necessary since historians suggest that the database is not reliable in this ranges. With the above constraints, our final database [28] had data for 1283 noble families and 116 religious or city institutions.
Considering an average of five persons per family (a generally accepted value by the historians and sociologists specialized in the targeted medieval period)
we obtain that our sample contains around 6400 people. This represents the top 8% of the estimated 80000 aristocrats living in Hungary at that period, and 0.2−0.3% of the estimated total population (2.7 millions) of Hungary in 1550.
It is also observable from Figure 1, that the Pareto law breaks down in the limit of the very rich families, where the wealth is bigger than 1000 serf families. This is presumably a finite-size effect and such results are observable in other databases too ([5,9]).
Sources:
The Forbes 400 and the Pareto wealth distribution - Economics Letters 90 (2006) 290–295
A family-network model for wealth distribution in societies
Ricardo Coelho a, Zolt´an N´eda a,b,∗, Jos´e J. Ramasco a,c and Maria Augusta Santos a
Evidence for Power-law tail of the Wealth Distribution in India Sitabhra Sinha The Institute of Mathematical Sciences, C. I. T. Campus, Taramani, Chennai -
600 113, India.
Wealth distribution and Pareto’s law in the
Hungarian medieval society G´eza Hegyi a,b, Zolt´an N´eda a,c,, and Maria Augusta Santos