Evolution of the personal income distribution in the USA: high incomes

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

http://www.census.gov/hhes/income/dinctabs.html








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


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


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


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


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


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


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


conom

ic model


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


conom

ic model


The model (5)

The

mod

el - from m

icroeconom


conom

ic model

Only the persons with high L and S can reach the Pareto threshold


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


conom

ic model

http://www.census.gov/


The Pareto threshold

(HIGH INCOME DEFINITION)

Defining

the Pareto thre

shold

PERSONAL INCOME > MPareto(t) =

= MPareto(0)(GDP(t)/GDP(0)) (6)


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 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


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


Results: Distribution above $100K

Results fro

m m

odelling: the

PID

in the US

A is pre

defined


Results: Distribution above the Pareto threshold

Results fro

m m

odelling: the

PID

in the US

A is pre

defined


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

http://www.census.gov/population/www/projections/popproj.html






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


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

Education

Evolution of the personal income distribution in the USA: high incomes