Presentation by Steve Kinsella, Ed Nell and Matthias Greiff, at the Agent-Based Modeling Session at the Annual Meeting of the Eastern Economic Association, February 2009

1. Introduction
The Model
Results
Conclusion
Interacting Heterogeneous Agents
Stephen Kinsella, Edward J. Nell, Matthias Greiff
February 27, 2009
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

2. Introduction
The Model
Econophysics
Results
Conclusion
Income Distributions and Econophysics
1
Econophysics
The Model
2
Labor Market
Education
Production
Demand
Banks
Structure of the Model
Results
3
Mobility
Income Distribution
Conclusion
4
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

3. Introduction
The Model
Econophysics
Results
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 initially
¯
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 Interacting Heterogeneous Agents

4. Introduction
The Model
Econophysics
Results
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 Interacting Heterogeneous Agents

5. of money conserva- same stationary distribution (7), as in the first model.
nary distribution of Computer animation for this model is also available on
Introduction
nential Boltzmann- the Web page [35]. Model
The
Econophysics
Results
The final distribution is universal despite different rules
Conclusion
for ∆m. To amplify this point further, Ref. [25] also con-
. (7) sidered a toy model, where ∆m was taken to be a ran-
d T Distribution of Money
dom fraction of the average amount of money of the two
is the “money
m
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- (Source:
bution of money exponential distribution for money
a symmet-
ulations. Solid curves: Fits to the Boltzmann-Gibbs law (7).
r a diffusion process.
Yakovenko 2008).
p around the m =Kinsella, Edward lines: The initial distribution of money. (Reproduced
Vertical
0
Stephen J. Nell, Matthias Greiff Interacting Heterogeneous Agents
from Ref. [25])

6. Introduction
The Model
Econophysics
Results
Conclusion
Critique & Modifications
Critique
Model is attractive in its simplicity but represents a rather
primitive picture of the market.
Agents are characterized only by their amount of money.
Data on wealth is rarely available, but data on income is.
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 Interacting Heterogeneous Agents

7. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
The Question
How is inequality of incomes generated?
Simple four sector model.
Conservation law should be fulfilled.
Model should produce exponential (or gamma) and power-law
distributions of income.
Inequality of income between and within classes should be
explained.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

8. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Characteristics of the Model
no representative agent
no utility 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 Interacting Heterogeneous Agents

9. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
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.
spend money on education.
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 Interacting Heterogeneous Agents

10. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Wage Bargaining
Hiring rule:
Each agents’ reservation wage is given by:
w (m, θ, o) : R3 → R+ .
Every unemployed worker is matched with a randomly chosen
firm.
If the firm’s res. wage exceeds the worker’s res. wage, they
sign a wage contract.
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.
Unemployed workers get a dole-income which is a fraction of
their reservation wage.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

11. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Ability & Education
Workers can be of five types.
no degree
college degree
BA degree
MA degree
PhD
Workers are born with innate abilities which they can augment
by further training and education. The workers skills can be
summed up in a measure of the workers productivity, θiw .
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

12. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Education Levels
PhD
MA
innate ability,
productivity
BA
College
a0'
a0 = innate ability
a0 me = money spend on education
me
θt+1 = f (θt , me , o)
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

13. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Production & Capacity Utilization
Think of the production sector as a vertically integrated linear
production model (neo-Ricardian).
In each market there will be winners and loosers, the higher
earnings of the successful are exactly balanced by the lower
earnings of the less successful.
If θw < θf worker performs inadequately (accidents,
slowdowns).
A firm produces its highest potential output if θw ≥ θf for all
employees.
min θw , θf
output=
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

14. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
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 its output.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

15. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
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 Interacting Heterogeneous Agents

16. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Banks
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 .
rr
Maximum 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 Interacting Heterogeneous Agents

17. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
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 Interacting Heterogeneous Agents

18. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
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 Interacting Heterogeneous Agents

19. Labor Market
Introduction Education
The Model Production
Results Demand
Conclusion Banks
Structure of the Model
Structure of the Model
At the beginning of the year agents buy or sell one-year bonds.
Workers die and get born.
Each month the following happens:
Wage bargaining, hiring and firing.
Effective Demand.
Education.
At the end of each year we collect data on income distribution
(and other data).
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

20. Introduction
The Model Mobility
Results Income Distribution
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 Interacting Heterogeneous Agents

21. Introduction
The Model Mobility
Results Income Distribution
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.
Positive interest rate reduces mobility.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

22. Introduction
The Model Mobility
Results Income Distribution
Conclusion
Income Distribution by Education
0.15
0.10
0.05
5 10 15 20 25
Figure: Income distribution for different levels of education.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

23. Introduction
The Model
Results
Conclusion
Conclusion
Workers are heterogeneous with respect to wealth, ability, and
opportunities.
Almost no restrictions on agents behavior.
Markets generate surpluses that go to the successful, gains are
carried forward through time.
Labor Market
Education
Differences in wealth, ability, and opportunity translate into
income inequality within and between classes.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

24. Introduction
The Model
Results
Conclusion
Problems
Workers income is 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 go bankrupt. (Interest rate on
borrowing > interest rate on lending.)
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

25. 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 (Irland 2000-2006).
Possible Extensions:
Introduce central bank.
Look at the effects of policy.
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents

26. Introduction
The Model
Results
Conclusion
Stephen Kinsella
stephen.kinsella@ul.ie
http://www.stephenkinsella.net
Edward J. Nell
ejnell@aol.com
Matthias Greiff
greiff@uni-bremen.de
http://matthiasgreiff.wordpress.com
Stephen Kinsella, Edward J. Nell, Matthias Greiff Interacting Heterogeneous Agents