An inter‐temporal model of dirty money
| Pages | 260-262 |
| Date | 01 July 2005 |
| DOI | https://doi.org/10.1108/13685200510700552 |
| Published date | 01 July 2005 |
| Author | Ricardo Azevedo Araujo,Tito Belchior S. Moreira |
| Subject Matter | Accounting & finance |
Journal of Money Laundering Control Ð Vol. 8 No. 3
An Inter-Temporal Model of Dirty Money
Ricardo Azevedo Araujo and Tito Belchior S. Moreira
INTRODUCTION
This paper presents a basic model by which a represen-
tative agent chooses how to allocate his savings opti-
mally between money of legal origin and dirty
money. The agent holds the laundered
1
money of ille-
gal origin, from which the money laundering process
generates a positive transaction cost, ie positive laun-
dering costs due to transforming illegal money into
legal money. The basic framework follows previous
work by Sidrausky (1967) on money in the utility
function. This paper analyses the welfare of such an
economy as a result of money laundering, as well as
the conditions to reduce the incentives to transforming
illegal money into legal. This incentive can be mini-
mised if the eectiveness of anti-money laundering
increases.
THE MODEL
The model has a representative agent who is eligible for
being involved in illegal and legal activities concomi-
tantly, based on an adapted concept of the `legal-crim-
inal economy'.
2
He distributes his time between both
activities. A fraction of his time is spent in the legal
sector. The remaining fraction of his time (1 ÿ)is
allocated to deviating illegal government transfers
(x2) in the form of currency that circulates in the econ-
omy as dirty money, m2. However, dirty money does
not have an immediate purchasing power within the
legal economy and must be laundered ®rst in order
for its illegal source to be concealed. Hence, there are
costs due to the laundering technology adopted. The
cost of the money laundering activity will depend on
the eectiveness of the anti-money laundering regu-
lation; the more eective the regulation, the more
expensive for the criminals to put the illegal activity
into action. We assume that "also represents a proxy
to the anti-money laundering regulation eectiveness,
where 0 1. We also assume that this regulation
is exogenous and occurs at the source on x2, ie in the
act of transferring government money. In this case,
only a fraction of x2, namely (1 ÿ")x2, becomes m2.
The production function in the legal sector is
assumed to be Cobb-Douglas.
YFK;LKL1ÿ1
where Kis the stock of capital, Lis the labour force and
is the share of capital. Accordingly, the product per
worker may be written as:
yfk;k1ÿ2
where yand kare output and capital stock per capita.
The rental price of labour, the wage rate, is denoted by
wand ris the rental price of capital.
3
We assume that
there is an illegal sector, in which the representative
agent embezzles part of the government transfers.
4
Formally:
x21ÿ1ÿ"1ÿ3
where 0 1 It is possible to understand as the
elasticity between the illegal government transfers
and the time allocated to illegal activity. In the same
line of thought, the parameter 1ÿcan be under-
stood as the elasticity between the illegal government
transfers and a proxy to the ineectiveness of the regu-
lation of anti-money laundering.
The household can hold its wealth in the form of
money of legal origin, m1, clean money, and money
of illegal origin, m2, dirty money. Furthermore, the
household can hold its wealth in the form of capital.
Its budget constraint is given by
_m1_m2
_
kyÿcx1ÿm11ÿ"x2ÿm2
4
where c,x1and stand for consumption, legal govern-
ment transfers and in¯ation rate respectively. Consid-
ering that am1m2kand substituting (3) into
(4) and considering that ywrk, the budget con-
straint may be rewritten as:
_awraÿm1ÿm2ÿ cx1ÿm11ÿ"
1ÿ1ÿ"1ÿÿm25
Each household solves the following maximisation
problem:
Max
c;m1;m2; V1
0
uczm1;m2eÿtdt 6
subject to equation (5), where uc;zm1;zm2>0 and
ucc;zm1m1;zm2m2<0. Let be the co-state variable
associated with equation (5) at time t. Note that ais a
state variable, and c,m1,m2and are control variables.
Page 260
Journalof Money Laundering Control
Vol.8, No. 3, 2005, pp. 260± 262
#HenryStewart Publications
ISSN1368-5201
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