evolution of the personal income distribution in the usa: high incomes
DESCRIPTION
Modelling personal incomes in the USA as a physical systemTRANSCRIPT
Evolution of the personal income distribution in the USA: high incomes
Ivan O. Kitove-mail - [email protected]
http://www.ecokitov.narod.ru
First meeting of the Society for the
Study of Economic Inequality (ECINEQ)
Palma de Mallorca, July 20-22, 2005
‘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?
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
11/08/13 Evolution of the PID in the USA: high incomes4
Personal Income Distribution in the USA: 1994-2001(Data Source:.U.S. Census Bureau; "Detailed Income Tabulations from the CPS". Last Revised: August 26
2004; http://www.census.gov/hhes/income/dinctabs.html)
Two branches: “subcritical” and “supercritical”=Pareto distribution=High Incomes
Pareto threshold = Xm
Persona
l income d
istribution in the U
SA
: observatio
ns and features to m
odel
Xm
11/08/13 Evolution of the PID in the USA: high incomes5
Evolution of the number of people with income above $100K: 1994-2002
A linear increase with nominal GDP growth is expected and observed
Pe
rsonal inco
me distribution
in the U
SA
: observations and
features to model
11/08/13 Evolution of the PID in the USA: high incomes6
Normalized PIDs for incomes above $100K as a function of work experience
The distributions are very similar
Pe
rsonal inco
me distribution
in the U
SA
: observations and
features to model
11/08/13 Evolution of the PID in the USA: high incomes7
Normalized PIDs for incomes above $100K as a function of work experience - time dependence
Variation is minor.
Pe
rsonal inco
me distribution
in the U
SA
: observations and
features to model
11/08/13 Evolution of the PID in the USA: high incomes8
Evolution of the normalized PID in 1994 for incomes above a given threshold: >$0K (all personal incomes), >$10K, …, >$100K
The distributions for income above $60K are very similar:
SELF ODGANIZED CRITICALITY (SOC) - behaviour above (Pareto) threshold
Pa
reto income distribution as a rea
lization of self-org
anized criticality
11/08/13 Evolution of the PID in the USA: high incomes9
The model (1)
individual income - microeconomic model
dM(t)/dt= σ(t)-αM(t)/Λ(t) (1)
• M(t) is money income denominated in dollars [$]• 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)) (2)
Th
e model - from
microeconom
ic approa
ch to m
acroeconom
ic mode
l
11/08/13 Evolution of the PID in the USA: high incomes10
The model (2)
individual income - microeconomic model
Substitution Σ(t)=σ(t)/αEvolution law 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)) (2’)
The
mod
el - from m
icroeconom
ic approach to macroe
conom
ic model
11/08/13 Evolution of the PID in the USA: high incomes11
The model (3)
aggregate income - macroeconomic model
Σmin(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)
Substitution S(t)=Σ(t) /Σmin(t)
L(t)=Λ(t) /Λmin(t)
Distribution S1=2,…, S29=30
L1=2,…, L29=30
SiLj={2×2/900, 2×3/900, …, 2×30/900, 3×2/900, …, 3×30/900, …,
...
..., 30×30/900}.
The
mod
el - from m
icroeconom
ic approach to macroe
conom
ic model
11/08/13 Evolution of the PID in the USA: high incomes12
The model (4)
aggregate income - macroeconomic model
Mik(t)/(SmaxLmax)=(Σmin Λmin)(Si/Smax)(Lk/Lmax)
(1-exp(-(α/Λ minLmax)t/(Lk/Lmax))) (3)
Normalized form
M'ik(t) =Σmin(t)Λmin(t)S'iL'j{1-exp[-(1/Λmin)(α 't/L‘k)]} (3’)
Σmin (t)= Σmin (0)sqrt(GDP(t)/GDP(0))
Λmin (t)= Λmin (0)sqrt(GDP(t)/GDP(0)
Σmin (0)= Λmin (0)=1
The
mod
el - from m
icroeconom
ic approach to macroe
conom
ic model
11/08/13 Evolution of the PID in the USA: high incomes13
The model (5)
The
mod
el - from m
icroeconom
ic approach to macroe
conom
ic 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 incomes14
Mean personal income vs. work experience(Data Source: The U.S. Census Bureau, www.census.gov )
Tcr increases with economic growth economic growth:
Τ cr (t)= Τ cr (0)sqrt(GDP(t)/GDP(0) (4)
M(t)=M(Tcr)exp(-α (t-Tcr)/L)=SL(1-exp(-αTcr/L)) exp(-α1(t-Tcr)/L) (5)
Tcr The
mod
el - from m
icroeconom
ic approach to macroe
conom
ic model
11/08/13 Evolution of the PID in the USA: high incomes15
The Pareto threshold
(HIGH INCOME DEFINITION)
Defining
the Pareto thre
shold
PERSONAL INCOME > MPareto(t) =
= MPareto(0)(GDP(t)/GDP(0)) (6)
11/08/13 Evolution of the PID in the USA: high incomes16
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 thre
shold
11/08/13 Evolution of the PID in the USA: high incomes17
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 thre
shold
The curves diverge at income of $54K – the Pareto distribution threshold
11/08/13 Evolution of the PID in the USA: high incomes18
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 thre
shold
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 incomes19
Results: Distribution above $100K
Results fro
m m
odelling: the
PID
in the US
A is pre
defined
11/08/13 Evolution of the PID in the USA: high incomes20
Results: Distribution above the Pareto threshold
Results fro
m m
odelling: the
PID
in the US
A is pre
defined
11/08/13 Evolution of the PID in the USA: high incomes21
Distribution above the Pareto threshold: from 2002 to 2023
Results fro
m m
odelling: the
PID
in the US
A is pre
defined
Per capita real GDP growth rate = 1.6% per yearPopulation 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 incomes22
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 incomes23
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