The document discusses agent-based models for studying taxation and tax evasion. It covers: 1) What agent-based models are and how they differ from equilibrium and representative agent models by simulating autonomous agents. 2) Research on modeling tax evasion as an individual decision weighing penalties and using an ABM to account for heterogeneous taxpayers. 3) The specifics of the ABM model used, which assigns agents utility functions based on income, public spending preference, and risk preferences to determine tax declaration.

1. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Agent-based models: tax evasion and trading
Research day 2012
Paolo Pellizzari
1 Dipartimento di Economia
Ca’ Foscari - Venezia
19 June 2012

2. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Agent-based models
An ABM is a computational model for simulating
the actions and interactions of autonomous
agents (individual, collective entities,
organizations or groups) with a view to assessing
their effects on the system as a whole
Microsimulation, individual-based models,
heterogeneous-agents models...
1 Numerous agents at different scales
2 Decision-making heuristics
3 Learning and adaptation (as opposed as equilibrium)
4 Interaction and environment
History: John Conway, The game of life; Thomas
Schelling, segregation; Robert Axelrod, repeated prisoner
dilemma; Craig Reynolds, flocks...

3. Agent-based models Taxation and evasion An ABM model Results Tobin tax
What ABMs are not
Equilibrium models (based on infinite rationality and
knowledge)
1 How do you get to the equilibrium?
2 Is the equilibrium attainable?
3 Is an equilibrium realistic?
Representative agent models
1 All agents are the same or behave as if they are the same
2 The representative agent disagrees with all the agents in
the economy (segregation)
Analytical models
1 ABMs use numerical methods, simulations, ANT...

4. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Taxation and evasion
Allingham and Sandmo (1972): model tax evasion as an
individual decision
1 gamble (report or cheat)
2 portfolio choice (safe or risky asset)
The taxpayer maximizes
E[U] = (1 − q)U(I − τ X ) + qU(I − τ X − f (I − X )),
with respect to reported income X
“This is hardly public economics; in fact it’s very private”,
Kolm from Cowell and Gordon (1988)
ABMs (and a massive body of research) take into account
public expenditure, heterogeneous taxpayers, distinct
opportunities to cheat, networks and contagion, noisy
information, bomb crater effects...

5. Agent-based models It is assumed here that tax compliance can be achieved through increasing levels of
Taxation and evasion An ABM model Results Tobin tax
power and trust; however, the resulting compliance is enforced in the former case and vol-
untary in the latter case. The impact of changes in one dimension is assumed to depend on
the level of the other dimension, resulting in the stylized figure shown in Fig. 1. It shows
the proposed ‘‘slippery slope’’ framework graphically in a three-dimensional space with
The slippery slope
the power of authorities, trust in authorities, and tax compliance as dimensions.
We start the description of the characteristics of the framework in the front corner of
Fig. 1. In conditions where trust in authorities is low and the power of authorities is weak,
it is likely that citizens seek to maximize their individual outcomes by evading taxes, bring-
ing compliance to a minimum. (a) Moving along the left edge, along the power dimension
Kirchler, Hoelzl, Wahl (2008): compliance depends on
under conditions of low trust, compliance increases with the power of the authorities to
raise audit and detection probabilities and to inflict severe fines. Taxpayers have less and
power of tax authorities and trust in the tax authorities...
less incentives to evade, because the expected outcome of non-compliance falls below the
expected outcome of compliance. Increasing power of the authorities is likely to result in
there is enforced and voluntary compliance
enforced compliance. The curvature results from an assumption of diminishing returns:
Voluntary tax compliance
Enforced
tax compliance
Maximum
Compliance
High
Minimum Trust
in authorities
High
Power Low
of authorities Low
Fig. 1. The ‘‘slippery slope’’ framework: enforced tax compliance and voluntary tax compliance depending on the
The slippery slope and the tax morale dynamically evolve
power of the authorities and trust in the authorities.

6. Agent-based models Taxation and evasion An ABM model Results Tobin tax
An ABM model
N heterogeneous agents have utility
Ui = Ui (yi , Gi ).
We assume multiplicative utility
1 (1−ρi )
Ui = yi Giαi .
1 − ρi
Amount paid by an individual is
Ti = τ di Ii = τ Xi .
yi after tax income;
Gi perceived per capita public expenditure;
ρi relative risk aversion parameter;
αi relative intensity of preference public/personal;
Ii exogenous income;
di fraction of declared income.

7. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Individual behavior: low vs high α
Taxation should not exceed one third of
wealth. More than that? It’s a robbery.
Silvio Berlusconi: low α!
Taxes are a beautiful thing because they are a
civilized way of contributing to the common good.
T. Padoa-Schioppa: shockingly high α.

8. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Individual behavior: low vs high α
Taxation should not exceed one third of
wealth. More than that? It’s a robbery.
Silvio Berlusconi: low α!
Taxes are a beautiful thing because they are a
civilized way of contributing to the common good.
T. Padoa-Schioppa: shockingly high α.

9. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Individual behavior: low vs high α
Taxation should not exceed one third of
wealth. More than that? It’s a robbery.
Silvio Berlusconi: low α!
Taxes are a beautiful thing because they are a
civilized way of contributing to the common good.
T. Padoa-Schioppa: shockingly high α.

10. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Societal slippery slope
Figure 3 – Simulated slippery slope: societal compliance rate
1
2
The slope
3
dependsrate =the distribution of individual traits. rate = 30%
a) tax on 20% b) tax
4
5
6
7 1
8 0.95
0.9
9 0.85
0.8
0.75
10 0.7
0.65
11 0.6
0.55
12 0.5
0.45
13
0.4
0.35
0.3
14 0.25
0.2
15 0.15
0.1
16 1.0
0.05
0 1.0
17
0.9 1 0.9
0.8 0.9 0.8
0.7 0.8 0.7
0.7
18 trust index
0.6
0.5
0.4 0.4
0.5
0.6
pow er index
trust index
0.6
0.5
0.4
19 0.3
0.2
0.1
0.2
0.3 0.3
0.2
0.1
0.
20
21
22 b) with tax rate = 40% c) with tax rate = 50%
23

11. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Societal slippery slope
lippery slope: societal compliance rate
The slope dependsrate = 30%
b) tax on the distribution of individual traits.
1 1
0.95 0.95
0.9 0.9
0.85 0.85
0.8 0.8
0.75 0.75
0.7 0.7
0.65 0.65
0.6 0.6
0.55 0.55
0.5 0.5
0.45 0.45
0.4 0.4
0.35 0.35
0.3 0.3
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 1.0 0
1 0.9 1
0.9 0.8 0.9
0.8 0.7 0.8
0.7 0.6 0.7
0.6 trust index 0.5 0.6
0.5 pow er index 0.5 pow er index
0.4 0.4 0.4
0.3 0.3 0.3
.2 0.2 0.2
0.1
c) with tax rate = 50%

12. 13 0.35
Agent-based models Taxation and evasion An ABM model 0.3 Results Tobin tax
14 0.25
0.2
15 0.15
0.1
16 1.0
0.05
0 1.0
17
0.9 1 0.9
Societal slippery slope
18
0.8
trust index
0.7
0.6
0.5
0.4 0.4
0.5
0.6
0.7
0.8
pow er index
0.9 0.8
trust index
0.7
0.6
0.5
0.4
19 0.3
0.2
0.1
0.2
0.3 0.3
0.2
0.1
0.2
20
21
The slope
22 depends tax rate =distribution of individual traits. tax rate = 50%
b) with on the 40% c) with
23
24
25
26
27 1
0.95
28 0.9
0.85
29
0.8
0.75
0.7
30 0.65
0.6
31 0.55
0.5
32 0.45
0.4
0.35
33 0.3
0.25
34 0.2
0.15
35 0.1
0.05
36 1.0
0.9
0.8
1
0 1.0
0.9
0.8
0.9
37 trust index
0.7
0.6
0.6
0.7
0.8
trust index
0.7
0.6
0.5 0.5
38 0.4
0.3 0.3
0.4
0.5 pow er index 0.4
0.3
39
0.2 0.2 0.2 0.2
0.1 0.1
40
41
42

13. 0.4 0.4
Agent-based models0.35
0.3
Taxation and evasion An ABM model 0.35
0.3
Results Tobin tax
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 1.0 0
0.9
Societal slippery slope
0.5
0.6
0.7
0.8
0.9
1
0.8
trust index
0.7
0.6
0.5
0.5
0.6
0.7
0.8
0.9
1
pow er index 0.4 pow er index
0.4 0.4
0.3 0.3 0.3
0.2 0.2 0.2
0.1
The slope depends on the = 50%
c) with tax rate distribution of individual traits.
1 1
0.95 0.95
0.9 0.9
0.85 0.85
0.8 0.8
0.75 0.75
0.7 0.7
0.65 0.65
0.6 0.6
0.55 0.55
0.5 0.5
0.45 0.45
0.4 0.4
0.35 0.35
0.3 0.3
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 1.0 0
1 0.9 1
0.9 0.8 0.9
0.8 0.7 0.8
0.7 0.6 0.7
0.6 trust index 0.5 0.6
0.5 pow er index 0.5 pow er index
0.4 0.4 0.4
0.3 0.3 0.3
0.2 0.2 0.2
0.1

14. Agent-based models Taxation and evasion An ABM model Results Tobin tax
The Tobin tax “revival”

15. Agent-based models Taxation and evasion An ABM model Results Tobin tax
The Tobin tax “revival”

16. Agent-based models Taxation and evasion An ABM model Results Tobin tax
The Tobin tax “revival”

17. Agent-based models Taxation and evasion An ABM model Results Tobin tax
The Tobin tax “revival”

18. Agent-based models Taxation and evasion An ABM model Results Tobin tax
The Tobin tax “revival”

19. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Theoretical (vs empirical) side
James Tobin proposed a tax on all currency trades. If the idea is
applied to financial assets the tax is dubbed transaction tax (TT).
The intended effect was originally to put a penalty on short-term
speculation and cushion price fluctuations.

20. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Theoretical (vs empirical) side
The idea can be traced back to Keynes (1936):
The introduction of a substantial Government trans-
fer tax on all transactions might prove the most ser-
viceable reform available, with a view to mitigating the
dominance of speculation over enterprises. . .

21. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Theoretical (vs empirical) side
Barack Obama on financial risk-taking, January 20th 2010:
The fact is, these kinds of trading operations can crea-
te enormous and costly risks. . . This kind of trading of-
ten puts banks in direct conflict with their customers’
interests. . .
So if these folks want a fight, it’s a fight I’m ready to
have.

22. Agent-based models Taxation and evasion An ABM model Results Tobin tax
(theoretical vs) Empirical side
There are “few” cases of practical application of a TT,
hence ingenuity is needed to assess the empirical
evidence
Hau (2006) showed that bigger transaction costs do not
reduce the volatility of the Paris Bourse
Hu (1998), quite politely wrote “the evidence is not
consistent with the hypothesis that stock transaction tax
can reduce trading and volatility”
Umlauf (1993) analyzed the Swedish market where a TT
was in place for years. . . almost all trades moved to the
London Stock Exchange!

23. Agent-based models Taxation and evasion An ABM model Results Tobin tax
ABMs: comparison of Dealership vs CDA
Taken from Pellizzari and Westerhoff (2009)
1 Realistic market model
Our heterogeneous agents (myopic, F, C, N + switching)
produce returns with reasonable stylized facts (not shown)
2 Reconcile theoretical and empirical literature
In theory there is infinite liquidity that is instead
endogenously fluctuating in real markets
3 Is the tax working?

24. Agent-based models Taxation and evasion An ABM model Results Tobin tax
ABMs: comparison of Dealership vs CDA
Taken from Pellizzari and Westerhoff (2009)
1 Realistic market model
Our heterogeneous agents (myopic, F, C, N + switching)
produce returns with reasonable stylized facts (not shown)
2 Reconcile theoretical and empirical literature
In theory there is infinite liquidity that is instead
endogenously fluctuating in real markets
3 Is the tax working?

25. Agent-based models Taxation and evasion An ABM model Results Tobin tax
ABMs: comparison of Dealership vs CDA
Taken from Pellizzari and Westerhoff (2009)
1 Realistic market model
Our heterogeneous agents (myopic, F, C, N + switching)
produce returns with reasonable stylized facts (not shown)
2 Reconcile theoretical and empirical literature
In theory there is infinite liquidity that is instead
endogenously fluctuating in real markets
3 Is the tax working?

26. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Does the tax work?
1 Reduction in volume
The turnover is notably reduced in all protocols, due to
inactivity of most short-term agents
2 Reduction in volatility
Reduction in a CDA is negligible (as predicted by empirical
papers). However, if exogenous liquidity is provided
(Dealership) price fluctuations are dampened
3 Reduction in distortion
There is (almost) no effect in both markets. Hence, the tax
is unlikely to make prices closer to fundamentals

27. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Does the tax work?
1 Reduction in volume
The turnover is notably reduced in all protocols, due to
inactivity of most short-term agents
2 Reduction in volatility
Reduction in a CDA is negligible (as predicted by empirical
papers). However, if exogenous liquidity is provided
(Dealership) price fluctuations are dampened
3 Reduction in distortion
There is (almost) no effect in both markets. Hence, the tax
is unlikely to make prices closer to fundamentals

28. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Does the tax work?
1 Reduction in volume
The turnover is notably reduced in all protocols, due to
inactivity of most short-term agents
2 Reduction in volatility
Reduction in a CDA is negligible (as predicted by empirical
papers). However, if exogenous liquidity is provided
(Dealership) price fluctuations are dampened
3 Reduction in distortion
There is (almost) no effect in both markets. Hence, the tax
is unlikely to make prices closer to fundamentals

29. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Does the tax work?
1 Reduction in volume
The turnover is notably reduced in all protocols, due to
inactivity of most short-term agents
2 Reduction in volatility
Reduction in a CDA is negligible (as predicted by empirical
papers). However, if exogenous liquidity is provided
(Dealership) price fluctuations are dampened
3 Reduction in distortion
There is (almost) no effect in both markets. Hence, the tax
is unlikely to make prices closer to fundamentals

30. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Good readings
1 Joshua M. Epstein et al., Toward a Containment Strategy
for Smallpox Bioterror: An Individual-Based Computational
Approach, book, wp...
2 Korobow, A., Johnson, C., Axtell, R. (2007). An
Agent-based Model of Tax Compliance with Social
Networks, National Tax Journal, vol. 60(3), 589-610
3 Ronald L. Goettler, Christine A. Parlour, Uday Rajan,
Equilibrium in a Dynamic Limit Order Market, The Journal
of Finance, Vol. 60, No. 5 (Oct., 2005), pp. 2149-2192
Thank you

31. Agent-based models Taxation and evasion An ABM model Results Tobin tax
Good readings
1 Joshua M. Epstein et al., Toward a Containment Strategy
for Smallpox Bioterror: An Individual-Based Computational
Approach, book, wp...
2 Korobow, A., Johnson, C., Axtell, R. (2007). An
Agent-based Model of Tax Compliance with Social
Networks, National Tax Journal, vol. 60(3), 589-610
3 Ronald L. Goettler, Christine A. Parlour, Uday Rajan,
Equilibrium in a Dynamic Limit Order Market, The Journal
of Finance, Vol. 60, No. 5 (Oct., 2005), pp. 2149-2192
Thank you