Stochastic effects in a discretized kinetic model of economic exchange

M.L. Bertotti, A.K. Chattopadhyay, G. Modanese*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.
Original languageEnglish
Pages (from-to)724–732
Number of pages9
JournalPhysica A
Volume471
Early online date26 Dec 2016
DOIs
Publication statusPublished - 1 Apr 2017

Fingerprint

Kinetic Model
economics
Economics
Gini Index
Taxation
Langevin Equation
kinetics
Kinetic Theory
Redistribution
Welfare
System of Ordinary Differential Equations
Interaction
income
Stochastic Model
Linear Model
Complex Systems
Fluctuations
Model-based
Binary
kinetic theory

Bibliographical note

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

  • discretized Boltzmann equation
  • stochastic differential equations
  • income distributions
  • economic inequality
  • social mobility

Cite this

Bertotti, M.L. ; Chattopadhyay, A.K. ; Modanese, G. / Stochastic effects in a discretized kinetic model of economic exchange. In: Physica A. 2017 ; Vol. 471. pp. 724–732.
@article{caa1725731c044eebefa80a443d41ab8,
title = "Stochastic effects in a discretized kinetic model of economic exchange",
abstract = "Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.",
keywords = "discretized Boltzmann equation, stochastic differential equations, income distributions, economic inequality, social mobility",
author = "M.L. Bertotti and A.K. Chattopadhyay and G. Modanese",
note = "{\circledC} 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/",
year = "2017",
month = "4",
day = "1",
doi = "10.1016/j.physa.2016.12.072",
language = "English",
volume = "471",
pages = "724–732",
journal = "Physica A",
issn = "0378-4371",
publisher = "Elsevier",

}

Stochastic effects in a discretized kinetic model of economic exchange. / Bertotti, M.L.; Chattopadhyay, A.K.; Modanese, G.

In: Physica A, Vol. 471, 01.04.2017, p. 724–732.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Stochastic effects in a discretized kinetic model of economic exchange

AU - Bertotti, M.L.

AU - Chattopadhyay, A.K.

AU - Modanese, G.

N1 - © 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

PY - 2017/4/1

Y1 - 2017/4/1

N2 - Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.

AB - Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker–Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.

KW - discretized Boltzmann equation

KW - stochastic differential equations

KW - income distributions

KW - economic inequality

KW - social mobility

UR - http://www.scopus.com/inward/record.url?scp=85008400950&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2016.12.072

DO - 10.1016/j.physa.2016.12.072

M3 - Article

VL - 471

SP - 724

EP - 732

JO - Physica A

JF - Physica A

SN - 0378-4371

ER -