Information Technology Reference
In-Depth Information
0.4
30
a
b
c
d
c) Compliance period
0.35
a) Total black market share
25
0.3
20
0.25
15
0.2
10
0.15
5
0.1
0
0
100
200
0
100
200
0.5
0.5
0.2
0.4
a
b
0.4
b) Black market
share of agents
0.3
a
b
c
d
0.3
0.2
0.2
0.15
0.1
0.1
0
0
0
816
24
0
816
24
0.1
1
0.4
0.8
c
d
0.3
0.6
0.05
0.2
0.4
0.1
0.2
0
0
0
0
100
200
0816
24
0816
24
time step
Fig. 2.
Time evolution for the participation in black market services for a society consisting of
15% a-type, 50% b-type, 20% c-type, and 15% d-type agents. The upper left panel compares
the extent and dynamics of black market participation for backaudit periods
b
p
= 5. The lower
left panel breaks down the participation probability to the individual agent types. The upper right
panel displays the average forced compliance period (or penalty) for the individual agent types
and the lower right panels show the corresponding distribution. Audit probability is
p
a
= 10% in
each case.
According to this analysis the size of the shadow economy in France and Germany is
15% and 16% of the official GDP, respectively, averaged over the period 1999 - 2007.
These numbers are supported by the data of Elgin and Oztunali (2012) which report
16
.
53% for OECD EU-countries in the period from 2001-2009.
Fig. 2a shows the dynamics of black market participation for the parameter set 'F'
appropriate to France and 15(50)% a(b)-type agents. Initial conditions are chosen such
that all agents but the a-types are set to white market participants so that the black
market share at time step 'zero' just reflects the percentage of selfish a-types. Note,
however, that the equilibrium result for large time steps does not depend on these initial
conditions. As can be seen from Fig. 2b the initial increase in the first time step is due to
the b-types which copy the black market participation from the a-type agents. In the fol-
lowing periods black market participation is reduced to the (back)audit and approaches
an equilibrium value after passing a transient regime. For this parameter set a-, b- and
d-type agends contribute equally with
5% to the total black market share. It is also
instructive to monitor the average compliance period of the convicted agents as shown
in Fig. 2c and the actual distributions which are displayed in the lower right panels of
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