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Data driven analysis and modelling of the wealth distribution
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Forbes, Samuel (2022) Data driven analysis and modelling of the wealth distribution. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3883999~S15
Abstract
We study the wealth distribution empirically with analysis of the UK wealth and asset survey and rich list data and focus on prominent factors of the distribution through mathematical modelling. Probability distributions for both debt and positive wealth are fitted to the wealth data concentrating on the time period 2008-2016. We fit power laws, a key property of the wealth distribution, to the upper tail and analyse the difference in power law exponents between the survey rich and the rich lists. We present an overview of potential agent based wealth models under the themes of hierarchy, exchange, feedback and multiplicative processes. Two of these models, one in each of the latter two categories, are studied in detail in the final main results chapters. Both models are characterised by a critical power γparameter, exhibit power law tails and eventually extreme inequality. The first is the balls in bins process with feedback originally studied in the combinatorics literature and only recently applied to wealth. We analyse theoretical aspects of this model as well as some general simulations. The second model, which we call a non-linear Kesten process, has not been studied before to our knowledge and is a generalisation of the Kesten process. This model was conceived by finding a rough power law relationship between agent’s wealth and their wealth returns. Agents evolve independently through time based on these returns. Due to the independence of agents we can run the model for a large number of agents and we do so for genera and realistic 2008 UK initial conditions. We conclude that a non-linear rich gets richer effect may be important when modelling the wealth distribution in times of growing inequality.
Item Type: | Thesis (PhD) | ||||
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Subjects: | H Social Sciences > HC Economic History and Conditions Q Science > QA Mathematics |
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Library of Congress Subject Headings (LCSH): | Income distribution -- Mathematical models -- Great Britain, Wealth -- Mathematical models -- Great Britain, Equality -- Mathematical models, Poverty -- Mathematical models, Probabilities, Great Britain -- Economic conditions -- 1945- | ||||
Official Date: | October 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Grosskinsky, Stefan ; Isaac, Alexander Karalis | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Extent: | vi, 143 pages : illustrations, charts | ||||
Language: | eng |
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