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Kinetic exchange models of markets

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Understanding the distributions of income and wealth in an economy has been a classic problem in economics for more than a hundred years. Kinetic exchange models are multi-agent dynamic models inspired by the statistical physics of energy distribution, which try to explain the robust and universal features of income/wealth distributions. Today it is one of the main branches of Econophysics.


Data and Basic tools

In 1897, Vilfredo Pareto first found an universal feature in the distribution of wealth. After that, with some notable exceptions, this field had been dormant for many decades, although accurate data had been accumulated over this period. Considerable investigations with the real data during the last fifteen years revealed [1] that the tail (typically 5 to 10 percent of agents in any country) of the income/wealth distribution indeed follows a power law. The rest (bulk) of the population (i.e., the low-income population) follow a different distribution which is debated to be either Gibbs or log-normal.

Basic tools used in this type of modelling are probabilistic and statistical methods mostly taken from the kinetic theory of statistical physics. Monte Carlo simulations often come handy in solving these models.

Overview of the models

Since the distributions of income/wealth are the results of the interaction among many heterogeneous agents, there is an analogy with statistical mechanics, where many particles interact. This similarity was noted long back by Meghnad Saha and B. N. Srivastava [2] and also by Benoit Mandelbrot[3]. J. Angle [4] was the first to propose an elementary version of the stochastic exchange model. In the context of kinetic theory of gases, such an exchange model was first investigated by A. Dragulescu,V. Yakovenko [5]. The main modelling effort has been put to introduce the concepts of savings[6], [7] and taxation [8] in the setting of an ideal gas-like system. Basically, it assumes that in the short-run, an economy remains conserevd in terms of income/wealth and any monetary transaction therefore, represents a redistribution of money from one agent to another. Millions of such conservative transactions lead to a steady state distribution of money (gamma function-like in the CC model with uniform savings [6], and a gamma-like bulk distribution ending with a Pareto tail [9] in the CCM model with distributed savings [7]) and the economy converges to it. The distributions derived thus have close resemblance with those found in case of income/wealth distributions. Though this theory has been originally derived from the entropy maximization principle of statistical mechanics, it has recently been shown [10] that the same could be derived from the utility maximization principle as well, following a standard exchange-model with Cobb-Douglas utility function.


The exact distributions produced by this class of kinetic models are known only in certain limits and extensive investigations have been made on the mathematical structures of this class of models [11] . The general forms have not been derived so far.

Criticisms

This class of models has attracted criticisms from many dimensions [12] . It has been debated for long whether the distributions derived from these models are representing the income distributions or wealth distributions. The Law of conservation for income/wealth has also been a subject of criticism.



See also

References

  1. ^ A. Chatterjee, S. Yarlagadda, B. K. Chakrabarti (2005). Econophysics of Wealth Distributions. Springer-Verlag (Milan).{{cite book}}: CS1 maint: multiple names: authors list (link)
  2. ^ See p. 105 of M. Saha, B. N. Srivastava (1931). A Treatise on Heat. Indian Press (Allahabad).
  3. ^ B. B. Mandelbrot (1960). " The Pareto-Levy law and the distribution of income". International Economic Review. 1: 69.
  4. ^ J. Angle (1986). "The surplus theory of social stratification and the size distribution of personal wealth ". Social Forces. 65: 293–326.
  5. ^ A. Dragulescu, V. Yakovenko (2000). "The statistical mechanics of money". European Journal of Physics B. 17: 723–729. See also U. Garibaldi, E. Scalas, P. Viarenga (2007). "Statistical equilibrium in exchange games". European Journal of Physics B. 60: 241–246.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  6. ^ A. Chakraborti, B. K. Chakrabarti (2000). "Statistical mechanics of money: how savings propensity affects its distribution". European physical Journal B. 17: 167–170.
  7. ^ A. Chatterjee, B. K. Chakrabarti, S. S. Manna (2004). "Pareto law in a kinetic model of market with random saving propensity". Physica A. 335: 155.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  8. ^ S. Guala (2009). "Taxes in a simple wealth distribution model by inelastically scattering particles". Interdisciplinary description of complex systems. 7(1): 1–7.
  9. ^ A. Chakraborti, M. Patriarca (2009). " Variational Principle for the Pareto Power Law". Physical Review Letters. 103: 228701.
  10. ^ A. S. Chakrabarti, B. K. Chakrabarti (2009). "Microeconomics of the ideal gas like market models". Physica A. 388: 4151–4158.
  11. ^ B. During, D. Matthes, G. Toscani (2008). "Kinetic equations modelling wealth distributions: a comparison of approaches". Physical Review E. 78: 056103.{{cite journal}}: CS1 maint: multiple names: authors list (link) ,S. Cordier, L. Pareschi, G. Toscani (2005). "On a kinetic model for a simple market economy". Journal of Statistical Physics. 120: 253–277.{{cite journal}}: CS1 maint: multiple names: authors list (link)
  12. ^ M. Gallegati, S. Keen, T. Lux and P. Ormerod (2006). "Worrying Trends in Econophysics". Physica A. 441: 686–688. {{cite journal}}: |access-date= requires |url= (help)CS1 maint: multiple names: authors list (link)

Further reading





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