Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity

Stojkoski, Viktor; Jolakoski, Petar; Pal, A.; Sandev, Trifce; Kocarev, Ljupčo; Metzler, Ralf

doi:10.1098/rsta.2021.0157

Cited by 38 publications

(21 citation statements)

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“…We conclude by noting that in this paper we discussed mixing in terms of wealth mobility, but the same concept can be used for studying income dynamics (Stojkoski et al, 2021b(Stojkoski et al, , 2022a. In this context, studying the relationship between mixing and measures of income mobility may represent a fruitful avenue for future research.…”

Section: Relaxation Time and Standard Measures Of Mobility In Rgbmmentioning

confidence: 89%

Measures of physical mixing evaluate the economic mobility of the typical individual

Stojkoski¹

2022

Preprint

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Measures of economic mobility represent aggregated values for how wealth ranks of individuals change over time. Therefore, in certain circumstances mobility measures may not describe the feasibility of the typical individual to change their wealth ranking. To address this issue, we introduce mixing, a concept from statistical physics, as a relevant phenomenon for quantifying the ability of individuals to move across the whole wealth distribution. We display the relationship between mixing and mobility by studying the relaxation time, a statistical measure for the degree of mixing, in reallocating geometric Brownian motion (RGBM). RGBM is an established model of wealth in a growing and reallocating economy that distinguishes between a mixing and a non-mixing wealth dynamics regime. We show that measures of mixing are inherently connected to the concept of economic mobility: while certain individuals can move across the distribution when wealth is a non-mixing observable, only in the mixing case every individual is able to move across the whole wealth distribution. Then, there is also a direct equivalence between measures of mixing and the magnitude of the standard measures of economic mobility. On the other hand, the opposite is not true. Wealth dynamics, are however, best modeled as non-mixing. Hence, measuring mobility using standard measures in a non-mixing system may lead to misleading conclusions about the extent of mobility across the whole distribution.

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Section: Relaxation Time and Standard Measures Of Mobility In Rgbmmentioning

confidence: 89%

Measures of physical mixing evaluate the economic mobility of the typical individual

Stojkoski¹

2022

Preprint

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“…Stojkoski et al [ 14 ] explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and income mobility, the feasibility of an individual changing their position in the income rankings. Fitting the model to empirical data for the income share of the top earners in the USA, they find evidence that the income dynamics are consistently in a regime in which non-ergodicity characterizes inequality and immobility.…”

Section: Kinetic Models Of Wealth Distributionmentioning

confidence: 99%

Kinetic exchange models of societies and economies

Toscani

Sen

Biswas

2022

Phil. Trans. R. Soc. A.

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The statistical nature of collective human behaviour in a society is a topic of broad current interest. From formation of consensus through exchange of ideas, distributing wealth through exchanges of money, traffic flows, growth of cities to spread of infectious diseases, the application range of such collective responses cuts across multiple disciplines. Kinetic models have been an elegant and powerful tool to explain such collective phenomena in a myriad of human interaction-based problems, where an energy consideration for dynamics is generally inaccessible. Nonetheless, in this age of Big Data, seeking empirical regularities emerging out of collective responses is a prominent and essential approach, much like the empirical thermodynamic principles preceding quantitative foundations of statistical mechanics. In this introductory article of the theme issue, we will provide an overview of the field of applications of kinetic theories in different socio-economic contexts and its recent boosting topics. Moreover, we will put the contributions to the theme issue in an appropriate perspective. This article is part of the theme issue ‘Kinetic exchange models of societies and economies’.

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“…This is the most popular model for log-price processes due to the consideration of no arbitrage, see Delbaen and Schachermayer [12][13][14]. Some future literature about the stochastic volatility models can be found in Stojkoski et al [15], Zheng and Wang [16], Bouchaud and Potters [17], and Fouque et al [18], and references therein. We assume that the volatility process {σ t , t ≥ 0} is of form:…”

Section: Setting and Assumptionsmentioning

confidence: 99%

Testing for the Presence of the Leverage Effect without Estimation

Liu

2022

Mathematics

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Problem: The leverage effect plays an important role in finance. However, the statistical test for the presence of the leverage effect is still lacking study. Approach: In this paper, by using high frequency data, we propose a novel procedure to test if the driving Brownian motion of an Ito^ semi-martingale is correlated to its volatility (referred to as the leverage effect in financial econometrics) over a long time period. The asymptotic setting is based on observations within a long time interval with the mesh of the observation grid shrinking to zero. We construct a test statistic via forming a sequence of Studentized statistics whose distributions are asymptotically normal over blocks of a fixed time span, and then collect the sequence based on the whole data set of a long time span. Result: The asymptotic behaviour of the Studentized statistics was obtained from the cubic variation of the underlying semi-martingale and the asymptotic distribution of the proposed test statistic under the null hypothesis that the leverage effect is absent was established, and we also show that the test has an asymptotic power of one against the alternative hypothesis that the leverage effect is present. Implications: We conducted extensive simulation studies to assess the finite sample performance of the test statistics, and the results show a satisfactory performance for the test. Finally, we implemented the proposed test procedure to a dataset of the SP500 index. We see that the null hypothesis of the absence of the leverage effect is rejected for most of the time period. Therefore, this provides a strong evidence that the leverage effect is a necessary ingredient in modelling high-frequency data.

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Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity

Cited by 38 publications

References 58 publications

Measures of physical mixing evaluate the economic mobility of the typical individual

Measures of physical mixing evaluate the economic mobility of the typical individual

Kinetic exchange models of societies and economies

Testing for the Presence of the Leverage Effect without Estimation

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