Here is a talk delivered at the Eastern Economic Association Meetings, Feb 26--March 1, 2009.

1. Introduction
The Model
Results
Conclusion
Endogeneous Inequality
Stephen Kinsella, Edward J. Nell, Matthias Greiff
Annual Meeting of the Eastern Economic Association
February/March 2009, New York City
February 21, 2009
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

2. Introduction
The Model Distributions of Income
Results Econophysics
Conclusion
Income Distributions and Econophysics
1
Distributions of Income
Econophysics
The Model
2
Behavioral Rules
Structure of the Model
Results
3
Model without bank
Introducing debt
Mobility
Conclusion
4
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

3. Introduction
The Model Distributions of Income
Results Econophysics
Conclusion
Income Distribution
Vilfredo Pareto, “Ecrits sur la courbe de la repartition de la
richesse”, ch. 2, Librairie Droz, Geneve, (1896) 1965.
David G. Champernowne, “A model of income distribution”,
EJ, 1953.
Benoit Mandelbrot, “The Pareto-Levy Law and the
Distribution of Income”, IER, 1960.
John Angle (1983-. . . ), The Inequality Process.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

4. Introduction
The Model Distributions of Income
Results Econophysics
Conclusion
Conservation Principle
Conservation Law
Idea from physics: conservation of energy.
In econophysics: conservation of money.
We cannot keep track of all goods consumed.
A simple econophysics model
n agents, each agent has m Dollars
total amount of money M = n × m ¯
each period two agents are drawn and a random amount of
money is transferred from one agent to the other
nonnegativity constraint, mi ≥ 0
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

5. Introduction
The Model Distributions of Income
Results Econophysics
Conclusion
Distribution of Money
distribution of money converges to a Boltzmann-Gibbs
exponential distribution (entropy increases)
thermodynamic equilibrium P(m) = c × e −m/m
¯
m: money temparature, c: normalizing constant
¯
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

6. nential Boltzmann- the Web page [35].Introduction
The final distribution is universal despiteof Income rules
The Model Distributions different
Results Econophysics
for ∆m. To amplify this point further, Ref. [25] also con-
Conclusion
. (7) sidered a toy model, where ∆m was taken to be a ran-
Distribution of Money dom fraction of the average amount of money of the two
d Tm is the “money
agents: ∆m = ν(mi + mj )/2. This model produced the
average amount of
where M is the total
ts. 5 5
N=500, M=5*10 , time=4*10 .
5] performed agent- 18
y transfers between 16
n the same amount !mquot;, T
of agents (i, j) was 14
3
as transferred from 12
Probability, P(m)
was repeated many
log P(m)
2
ility distribution of 10
animation videos at 1
8
itory period, money
0
6
nary form shown in 0 1000 2000 3000
Money, m
n is very well fitted 4
2
e considered in Ref.
amount was fixed 0
0 1000 2000 3000 4000 5000 6000
cally, it means that Money, m
s for the same price
shows that the ini- FIG. 1 Histogram and points: Stationary probability distri-
dens toFigure: Boltzmann-Gibbs P (m) obtained in agent-based computer sim-
bution of money exponential distribution for money
a symmet- (Source:
ulations. Solid curves: Fits to the Boltzmann-Gibbs law (7).
r a diffusion process.
p around the m = 0 2008). lines: The initial distribution of money. (Reproduced
Yakovenko Vertical
from Ref. [25])
e boundary, because
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

7. Introduction
The Model Distributions of Income
Results Econophysics
Conclusion
Critique & Modifications
Critique
Model is attractive in its simplicity but represents a rather
primitive picture of the market.
Agents are characterized by their amount of money.
Modifications
Heterogeneous agents (in terms of money, abilities,
opportunities, and savings rates).
Ability changes as agents spend money on education.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

8. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
The Question
How is inequality of incomes and wealth generated?
Simple four sector model.
Conservation law should be fulfilled.
Model should produce exponential and power-law distributions
of income.
Model should be more realistic but not too complex.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

9. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Characteristics of the Model
no representative agent
no utility function
no production function
no rational expectations
large number of heterogeneous agents
individual behavior is unpredictable
individuals follow simple rules
indeterminacy at the micro level (random selection from a
given distribution)
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

10. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Four Sectors
In the simplest version of our model we have three sectors.
Workers...
search for work.
work for a wage or get dole.
spend money on consumption (demand).
Firms...
hire workers.
pay wages.
receive revenue from selling output.
Government: collects taxes and provides dole.
Add banking sector later.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

11. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Wage Bargaining
Each agents’ reservation wage is given by:
w (m, a, o) : R3 → R+
Hiring rule:
Every unemployed worker is matched with a randomly chosen
firm.
Provided that the firm has enough money to pay the wage,
wF W
they sign a wage contract with probability p = min w W , w F .
w
Firing rule: If a firm has not enough money to pay all its
employees, layoff workers until the firm can pay the wagebill
for the remaining workers.
Wage payment rule: Employees get their wages.
Dole payment rule: Unemployed workers get a dole-income
which is a fraction of their reservation wage.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

12. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Demand
Each agent (workers and firms) spends money on average
once a month.
Agents save a fraction of their money sm, (s ∈ [0, 1]).
The agent (=buyer) spends a random fraction u (u ∈ U [0, 1])
of his remaining money (1 − s)m on consumption,
∆m = u(1 − s)m.
A fraction t∆m goes to the government as tax income (t =
tax rate).
The remaining part (1 − t)∆m is transferred to seller.
The seller is a firm. The probability that a particular firm is
choosen is proportional to the sum of its employees’ abilities.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

13. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Ability & Education
Modelled in a rather crude way.
Assume that a fraction of money is spend on education.
Ability increases by η = U [0, o] ∆m.
But more sophisticated versions are possible...
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

14. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Government
Government is passive (no government spending besides dole).
Spend money on dole.
Collect taxes on consumption.
Increase tax rate if government deficit, decrease if surplus.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

15. Introduction
The Model Behavioral Rules
Results Structure of the Model
Conclusion
Structure of the Model
Each month the following happens:
Wage bargaining.
Demand.
At the end of each year we collect data on income distribution
(and other data).
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

16. Introduction
Model without bank
The Model
Introducing debt
Results
Mobility
Conclusion
Income Distribution
0.14
0.12
0.10
0.08
0.06
0.04
0.02
5 10 15 20 25 30
Figure: Probability density function for 95% of incomes and exponential
distribution.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

17. Introduction
Model without bank
The Model
Introducing debt
Results
Mobility
Conclusion
Banks: zero interest rate
debt is permitted (negative money)
unlimited borrowing has to be precluded
total amount of debt is limited by minimum reserve
requirement for banks, M = M0 r
maximal debt of any agent is limited by, mi > −md ∀i
¯
debt: increase in money temparature
Money supply ’increases’ (money multiplier) but conservation
law is still fulfilled!
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

18. Introduction
Model without bank
The Model
Introducing debt
Results
Mobility
Conclusion
Bond Market
Introduce a market for one-year bonds.
Agents can save (buy bonds) or get a loan (sell bonds).
Higher interest rate r increases supply and reduces demand.
Trading at disequilibrium.
Interest rate r adjusts.
r increases if excess demand for bonds.
r decreases if excess supply for bonds.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

19. Introduction
Model without bank
The Model
Introducing debt
Results
Mobility
Conclusion
Interest Rate Adjustment
r
r
supply
supply
r2
r1
r1
demand
demand
t t+1
Figure: Excess demand in the bond market.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

20. Introduction
Model without bank
The Model
Introducing debt
Results
Mobility
Conclusion
Measuring Mobility
N
1 0 − log mi1 |
i=1 | log mi
Mb = N
Two time period framework.
Money at time t: m0 = (m1 , m2 , . . . , mN ) .
0 0 0
Money at time t + 10: m1 = (m1 , m2 , . . . , mN ) .
1 1 1
Source: G.S. Fields & E.A. Ok, “Measuring Movement of Income”,
Economica (1999).
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

21. Introduction
Model without bank
The Model
Introducing debt
Results
Mobility
Conclusion
Mobility
mobility
1.5
1.4
1.3
1.2
1.1
1.0
0.9
spending
0.2 0.4 0.6 0.8
Figure: Absolute mobility and spending.
Higher savings → lower mobility.
Higher mobility if debt is allowed for.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

22. Introduction
The Model
Results
Conclusion
Conclusion
summarize main results from our model
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

23. Introduction
The Model
Results
Conclusion
Problems
Workers income is now wage income plus interest earned /
paid (on bonds).
Income can get negative if interest payment > wage income.
A possible solution: Restrict borrowing and introduce a
minimum wage such that income from minimum wage is
sufficiently high to pay interest.
Or: Allow for agents to get bankrupt. (Interest rate on
borrowing > interest rate on lending.)
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

24. Introduction
The Model
Results
Conclusion
Further research and possible extensions
Further research:
Allow for more than one bank.
Look at firm size distribution.
Fit model to actual data.
Possible Extensions:
Add production technology and growth.
Introduce central bank.
Look at the effects of policy.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality

25. Introduction
The Model
Results
Conclusion
Conclusion
http://www.stephenkinsella.net
http://matthiasgreiff.wordpress.com
http://www.newschool.edu/...
Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality