Evolution of the personal income distribution in the USA: high incomes
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(1) The document summarizes a presentation given at the Society for the Study of Economic Inequality conference on the evolution of personal income distribution in the USA, with a focus on high incomes. (2) It describes observations of US income distribution from 1994-2002 and presents a macroeconomic model to predict the distribution's shape and evolution over time based on self-organized criticality. (3) The model is shown to accurately predict the observed dependence of income distribution on work experience and its evolution over time for incomes above $100K as well as the Pareto threshold income level.
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(1)
M(t) is money income denominated in dollars [$]
t is the work experience expressed in some appropriate time units [time unit]
σ(t) is the capability to earn money [$/(time unit)]
α is the dissipation coefficient expressed in units [$/(time unit)]
Λ is the size of the earning means expressed in [$]
The Solution
M(t)=(σ/α)Λ(1- exp(-αt/Λ))
11/08/13
(2)
The model - from microeconomic approach to macroeconomic model
The model (1)
individual income - microeconomic model
dM(t)/dt= σ(t)-αM(t)/Λ(t)
Evolution of the PID in the USA: high incomes
9](https://image.slidesharecdn.com/ecineq-131108020145-phpapp01/85/Evolution-of-the-personal-income-distribution-in-the-USA-high-incomes-9-320.jpg)
![The model (4)
aggregate income - macroeconomic model
(1-exp(-(α/Λ minLmax)t/(Lk/Lmax))) (3)
Normalized form
M'ik(t) =Σ min(t)Λ min(t)S'iL'j{1-exp[-(1/Λ min)(α't/L‘k)]}
(3’)
Σ min (t)= Σ min (0)sqrt(GDP(t)/GDP(0))
The model - from microeconomic approach to macroeconomic model
Mik(t)/(SmaxLmax)=(Σ min Λ min)(Si/Smax)(Lk/Lmax)
Λ min (t)= Λ min (0)sqrt(GDP(t)/GDP(0)
Σ min (0)= Λ min (0)=1
11/08/13
Evolution of the PID in the USA: high incomes
12](https://image.slidesharecdn.com/ecineq-131108020145-phpapp01/85/Evolution-of-the-personal-income-distribution-in-the-USA-high-incomes-12-320.jpg)
Evolution of the personal income distribution in the USA: high incomes
- 1. First meeting of the Society for the Study of Economic Inequality (ECINEQ) Palma de Mallorca, July 20-22, 2005 Evolution of the personal income distribution in the USA: high incomes Ivan O. Kitov e-mail - ikitov@mail.ru http://www.ecokitov.narod.ru
- 2. ‘The ECINEQ conference will provide a forum for a rigorous analysis of inequality, welfare and redistribution issues, both at the theoretical and at the empirical level, as well as for a discussion of the policy implications of the research findings in this field.’ Does the inequality have economic roots?
- 3. Evolution of the personal income distribution in the USA: high incomes • Personal income distribution in the USA: observations and features to model • Pareto income distribution as a realization of self-organized criticality • The model - from microeconomic approach to macroeconomic model • Defining the Pareto threshold • Results from modelling: the PID in the USA is predefined • Conclusions
- 4. 2004; http://www.census.gov/hhes/income/dinctabs.html) Xm Two branches: “subcritical” and “supercritical”=Pareto distribution=High Incomes Pareto threshold = Xm 11/08/13 Personal income distribution in the USA: observations and features to model Personal Income Distribution in the USA: 1994-2001 (Data Source:.U.S. Census Bureau; "Detailed Income Tabulations from the CPS". Last Revised: August 26 Evolution of the PID in the USA: high incomes 4
- 5. Evolution of the number of people with income above $100K: 1994-2002 11/08/13 Personal income distribution in the USA: observations and features to model A linear increase with nominal GDP growth is expected and observed Evolution of the PID in the USA: high incomes 5
- 6. Personal income distribution in the USA: observations and features to model Normalized PIDs for incomes above $100K as a function of work experience The distributions are very similar 11/08/13 Evolution of the PID in the USA: high incomes 6
- 7. Personal income distribution in the USA: observations and features to model Normalized PIDs for incomes above $100K as a function of work experience - time dependence Variation is minor. 11/08/13 Evolution of the PID in the USA: high incomes 7
- 8. Evolution of the normalized PID in 1994 for incomes above a given threshold: >$0K (all personal incomes), >$10K, …, >$100K Pareto income distribution as a realization of self-organized criticality The distributions for income above $60K are very similar: SELF ODGANIZED CRITICALITY (SOC) - behaviour above (Pareto) threshold 11/08/13 Evolution of the PID in the USA: high incomes 8
- 9. • • • • • (1) M(t) is money income denominated in dollars [$] t is the work experience expressed in some appropriate time units [time unit] σ(t) is the capability to earn money [$/(time unit)] α is the dissipation coefficient expressed in units [$/(time unit)] Λ is the size of the earning means expressed in [$] The Solution M(t)=(σ/α)Λ(1- exp(-αt/Λ)) 11/08/13 (2) The model - from microeconomic approach to macroeconomic model The model (1) individual income - microeconomic model dM(t)/dt= σ(t)-αM(t)/Λ(t) Evolution of the PID in the USA: high incomes 9
- 10. The model (2) individual income - microeconomic model • Σ(t)=σ(t)/α Σ(t)= Σ(0)sqrt(GDP(t)/GDP(0)) Λ(t)= Λ(0)sqrt(GDP(t)/GDP(0) GDP(t) is real per capita GDP The Solution M(t)=Σ Λ(1- exp(-αt/Λ)) 11/08/13 (2’) The model - from microeconomic approach to macroeconomic model Substitution Evolution law Evolution of the PID in the USA: high incomes 10
- 11. The model (3) aggregate income - macroeconomic model Substitution S(t)=Σ(t)/Σ min(t) L(t)=Λ(t)/Λ min(t) Distribution S1=2,…, S29=30 L1=2,…, L29=30 The model - from microeconomic approach to macroeconomic model Σ min(t) and Λ min(t) are the nonzero minimum values for all the persons of the modified effective capability to earn money, Σ(t) and the size of earning means, Λ(t) SiLj={2×2/900, 2×3/900, …, 2×30/900, 3×2/900, …, 3×30/900, …, ... 11/08/13 ..., 30×30/900}. Evolution of the PID in the USA: high incomes 11
- 12. The model (4) aggregate income - macroeconomic model (1-exp(-(α/Λ minLmax)t/(Lk/Lmax))) (3) Normalized form M'ik(t) =Σ min(t)Λ min(t)S'iL'j{1-exp[-(1/Λ min)(α't/L‘k)]} (3’) Σ min (t)= Σ min (0)sqrt(GDP(t)/GDP(0)) The model - from microeconomic approach to macroeconomic model Mik(t)/(SmaxLmax)=(Σ min Λ min)(Si/Smax)(Lk/Lmax) Λ min (t)= Λ min (0)sqrt(GDP(t)/GDP(0) Σ min (0)= Λ min (0)=1 11/08/13 Evolution of the PID in the USA: high incomes 12
- 13. The model (5) The model - from microeconomic approach to macroeconomic model Only the persons with high L and S can reach the Pareto threshold 11/08/13 Evolution of the PID in the USA: high incomes 13
- 14. Mean personal income vs. work experience (Data Source: The U.S. Census Bureau, www.census.gov ) Tcr Τ cr (t)= Τ cr (0)sqrt(GDP(t)/GDP(0) M(t)=M(Tcr)exp(-α (t-Tcr)/L)=SL(1-exp(-αTcr/L)) exp(-α 1 (t-Tcr)/L) 11/08/13 The model - from microeconomic approach to macroeconomic model Tcr increases with economic growth economic growth: (4) (5) Evolution of the PID in the USA: high incomes 14
- 15. The Pareto threshold (HIGH INCOME DEFINITION) = MPareto(0)(GDP(t)/GDP(0)) 11/08/13 (6) Defining the Pareto threshold PERSONAL INCOME > MPareto(t) = Evolution of the PID in the USA: high incomes 15
- 16. The Pareto threshold - estimate (observed and predicted personal income distributions for the year 1999 – a portion of population with income below a given value) Defining the Pareto threshold 11/08/13 Evolution of the PID in the USA: high incomes 16
- 17. The Pareto threshold - estimate (observed and predicted personal income distributions for the year 1999 – a portion of population with income below a given value) Defining the Pareto threshold The curves diverge at income of $54K – the Pareto distribution threshold 11/08/13 Evolution of the PID in the USA: high incomes 17
- 18. Observed and predicted cumulative PIDs for 1999 – a portion of total income received by population with income below a given value. The ratio of the observed cumulative income of the population above the Pareto threshold (0.450) and the corresponding theoretical value (0.333) and is equal to 1.35. Defining the Pareto threshold This value is considered as an effective increase of the average capacity to earn money for people above the Pareto threshold 11/08/13 Evolution of the PID in the USA: high incomes 18
- 19. Results: Distribution above $100K Results from modelling: the PID in the USA is predefined 11/08/13 Evolution of the PID in the USA: high incomes 19
- 20. Results: Distribution above the Pareto threshold Results from modelling: the PID in the USA is predefined 11/08/13 Evolution of the PID in the USA: high incomes 20
- 21. Distribution above the Pareto threshold: from 2002 to 2023 Results from modelling: the PID in the USA is predefined Per capita real GDP growth rate = 1.6% per year Population projection - The US Census Bureau http://www.census.gov/population/www/projections/popproj.html 11/08/13 Evolution of the PID in the USA: high incomes 21
- 22. Conclusions (1) 1. In the high-income range, the PID in the USA is represented by a power law (Pareto) distribution 2. The Pareto distribution results from self-organized criticality (SOC) 3. The SOC effectively increases the capacity to earn money 4. A macroeconomic model is developed to predict the PID shape and the PID evolution, including the high-income range 5. The model predicts the observed dependence of the PID on work experience in the high-income range 6. The model predicts evolution of the dependence with time 11/08/13 Evolution of the PID in the USA: high incomes 22
- 23. Conclusions (2) 7. US society has structured personal incomes in a fixed manner 8. There is no economic means to change the PID: only social structure (ranking of the capability to earn money and size of earning means) produces the observed inequality 9. Socialism economically is less effective than capitalism due to the personal income limit 11/08/13 Evolution of the PID in the USA: high incomes 23