A Money Laundering Model - SSRN papers

Economics and Finance Review Vol. 1(11) pp. 42 – 47, January, 2012 Available online at http://www.businessjournalz.org/efr

ISSN: 2047 - 0401

A DYNAMIC MODEL OF ORGANIZED CRIME AND MONEY LAUNDERING Tito Belchior Silva Moreira1 Department of Economics - Catholic University of Brasilia (UCB): [email protected] Adolfo Sachsida Department of Economics - Catholic University of Brasilia (UCB): [email protected] Paulo Roberto Amorim Loureiro Department of Economics - University of Brasilia (UnB): [email protected]

ABSTRACT This paper analyzes a model of crime that emphasizes the relation between criminal practices and money laundering activities in a framework which leads to an optimal rule to repress and avoid criminality. This optimal rule shows that repressive and preventive actions against criminal practices must be applied in two situations: i) with an increase of criminal activities and, ii) with an increase of money laundering activities. Furthermore, the greater the effectiveness of anti-money laundering, the lower the repressive and preventive actions against organized crime must be. Keywords: crime, money laundering. JEL Classification: K40, K42 1. INTRODUCTION The process of money laundering is usually defined as any process that is carried out to disguise or cancel the nature or source of entitlement to money or property from criminal activities. This process is critical to the effective operation of virtually every form of transnational and organized crime. Anti-money laundering efforts, which are designed to prevent or limit the ability of criminals to use their ill-gotten gains, are both a critical and effective component of anti-crime programs (Moreira, 2007). As money laundering is a necessary consequence of almost all profit generating crime, it can occur practically anywhere in the world. Generally, money launderers tend to seek out areas where there is a low risk of detection due to weak or ineffective anti-money laundering programs. Because the objective of money laundering is to get the illegal funds back to the individual who generated them, launderers usually prefer to move funds through areas with stable financial systems. Money laundering is a threat to the good functioning of a financial system; however, it can also be the Achilles heel of criminal activity. In law enforcement investigations into organized criminal activity, it is often the connections made through financial transaction records that allow hidden assets to be located and that establish the identity of the criminals and the criminal organization responsible. When criminal funds are derived from robbery, extortion, embezzlement or fraud, a money laundering investigation is frequently the only way to locate the stolen funds and restore them to the victims. The possible social and political costs of money-laundering, if left unchecked or dealt with ineffectively, are serious. Organized crime can infiltrate financial institutions, acquire control of large sectors of the economy through investment, or offer bribes to public officials and even governments. In this vein, the economic and political influence of criminal organizations can weaken the social fabric, collective ethical standards, and

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Address for correspondence: SGAN 916, Módulo B, Sala A-117, Universidade Católica de Brasília – UCB, Mestrado de Economia de Empresas, Asa Norte, Brasília-DF, Brazil, 70.790-160. E-mail:[email protected] and [email protected]

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ultimately the democratic institutions of society2. Fundamentally, money-laundering is inextricably linked to the underlying criminal activity that generated it and allows criminal activity to continue. Most importantly, however, targeting the money laundering aspect of criminal activity and depriving the criminal of his ill-gotten gains means hitting him where he is vulnerable. Without a usable profit, the criminal activity will not continue. In this sense, this paper presents a model that shows a link between organized crime and the money laundering process where the objective of the policy maker is to minimize the index of criminal and money laundering activities. The result of the process of optimization leads to an optimal rule to reduce the criminal activities. In the criminal literature, there are not many formal models which explain the ties between illicit activity and the money laundering process. Camera (2001) has developed a general equilibrium model capable of characterizing the links between the availability of currency and the extent of illegal economics activities. She has shown that different stationary equilibria coexist contingent on the size of the returns to legal production, the severity of impediments from illicit output trades, and cash availability. Masciandaro (2000) has developed a macroeconomic model useful to the analysis of the relationship between the illegal sector, money laundering and legal economy. The model shows under which conditions a possible synergy can exist between general anti-crime policies and anti-money laundering regulation as general policies, and which may have an expansive effect on legal income, providing that anti-money laundering regulation shows some degree of effectiveness. Araújo and Moreira (2005) have analyzed the introduction of money laundering in a Sidrauski framework and have derived its optimal conditions. They show that (i) the effectiveness of anti-money laundering positively affects consumption, (ii) there exists equilibria solutions where legal and illegal activities coexist and, (iii) the steady state results allow us to conclude that where only legal activity exists, the welfare of the economy is greater than in an economy where legal and illegal activities coexist.3 The plan of the paper is as follows. In Section II an optimal rule is derived to combat the criminal activities and the final section provides conclusions and gives directions for further research. II. THE MODEL Let us assume two equations that describe criminals activities following the rules of equations (2.1) and (2.2). The first is a crime function where ct denotes the index of the criminal activities gap4, et is the index of repressive and preventive actions against criminal practices5 and u t is a stochastic shock, assumed to be normally distributed, defined as follows:

ct 1  1ct   2et  ut 1

(2.1)

Denote the criminal activities gap as the difference between the index of current crimes and the index that measures a minimum amount of crimes that is economically tolerable. We admit that the cost to reduce the current crimes to a level lower than this minimum is impracticable, i.e., the cost to do it is greater than the benefits. The lower the criminal activities target is, the greater the public spending with repression and prevention of crimes will be and, consequently, greater will be the taxes to finance them. On the other hand, if the public security authority wishes to greatly reduce criminality, given the public resources, then it will transfer public resources of other areas like education, health, and so forth, to the security area. In this context, because

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In countries which are in the transition stage of becoming democratic societies, this criminal influence can undermine the transition. 3 Very much has been written on creating regulations in order to devise mechanisms at the institutional level to monitor and deter the use of financial intermediaries in the recycling of illegal profits [see Masciandaro (1998,1999) Masciandaro and Filotto (2008) and Alexander (2000)] 4 The criminal practices described in equation (2.1) exclude the money laundering activities that are illegal activities as well. 5 A possible proxy for indexing repressive actions is the quantity of arrests. For preventive actions, a possible proxy could be the time spent by police patrols in a given area (which could eventually inhibit the practice of crimes). 43


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crime prevention and repression is costly, it may be more efficient to experience a crime than to prevent and repress it. In other words, the optimum amount of crime is positive6. Assume that coefficient

1  0 . This implies that criminal activities lead to more. Conversely, assume that  2  0 . The

2

reveals the effectiveness of repression and prevention against criminal practices.

Consider that et  e( yt ) , where yt is a quantity of public resources employed to combat crime. In this context, et / yt  0 7. Public resources can be spent on weapons, security equipment, technology to combat crime, hiring more police officers, more police patrols, more investigators to gather evidence of crimes, or any other instrument employed to combat crime. The greater these resources, the greater the conditions of the police to repress and prevent crime must be. Notice that the objective of many criminal acts is to make a profit for the individual or group that carries out the act. The activities of organized crime, which may include drug traffic, prostitution rings, illegal arms sales and smuggling, can produce large profits and create incentives to legitimize the ill-gotten gains through recycling money of illegal origin8. Money laundering enables the criminal to enjoy these profits without revealing their source. Furthermore, notice that without a usable profit, the criminal activity will not continue. The money laundering function is represented as:

mt 1  (1   )mt   ct  t 1

(2.2)

where mt is the index of the money laundering gap9, i.e., the difference between the index of current money laundering and the index that measures the minimum amount of money laundering activities that is economically tolerable. In the same way, we admit that the cost to reduce current money laundering to a level lower than this minimum is impracticable, i.e., the cost to make it is higher than the benefits. Furthermore,  t 1 is the stochastic shock not correlated with u t 1 . We denote 0    1 as an index that measures the performance of the effectiveness of anti-money laundering. Notice that mt positively affect mt 1 . This means that the performance of the policy maker to combat the money laundering activities will depend of the parameter  . Hence, if the effectiveness of the antimoney laundering is higher in period t, then the money laundering activities will drop in period t  1 . The cost of the activity of money laundering will depend on the effectiveness of the regulation of anti-money laundering; the more effective the regulation, the more expensive for the criminals to put the illegal activity into action. We assume that  also represents a proxy for the effectiveness of the regulation of anti-money laundering. We also admit that this regulation is exogenous. A key feature of the model is that public security policy affects the criminality activity through one channel. An expansion of public resources improves the conditions to repress and avoid the crime through the crime function and thus reduce the money laundering process according to the money laundering function. Note that the link between the index of the money laundering gap and the index of the criminal activities gap is denoted by   0 .

t the index of repressive and preventive actions against criminal practices et . The state variable in instant t is The policy maker chooses in instant

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Another way to analyze the index of the criminal activities gap is to define it as the deviation between the index of current criminal activities and the index of optimum criminal activities. The optimum amount of crime is the level at which the marginal victim cost equals the marginal protection cost (O’Sullivan ,2003).

ct 1 et  0. et yt

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Then,

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The index of criminal activities is formed by criminal practices like these which generate dirty money. Of course, for each index of money laundering there exists a correspondent index of criminal activities.

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st  (1   ) mt  ct

(2.3)

t  1ct   2et

(2.4)

while the control variable is

The optimal feedback rule10 will be given by

 t  Hst

(2.5)

Equations (2.1) and (2.2) can be rewritten as and

ct 1  t  ut 1

(2.6)

mt 1  st  t 1

(2.7)

Consider that the loss function is given by

L



1  Et   i  ct21  mt21 2 t 1



(2.8)

The objective of the policy maker is to minimize this loss function subject to

st 1  (1   ) st  (1   ) t 1    t   ut 1

(2.9)

where this equation is deduced taking the equation (2.3) one step forward and replacing into it the equations (2.6) and (2.7). In this sense, the loss function presented here is a law enforcement strategy. The concern of the public security authorities is to not only minimize criminality activities, but to also minimize money laundering activities. Define the value function as

1  V ( st )  min Et  ( ct21  mt21 )   V ( st 1 ) t 2 

(2.10)

where replacing Equations (2.6), (2.7) and (2.9) into the value function we obtain the equation (2.11):

1 1  V ( st )  min   Et ( t  ut 1 ) 2  Et ( st  t 1 ) 2   EtV (1   ) st    t   ut 1  (1   ) t 1  t 2 2  Solving problem (2.11) with respect to  t gives the first-order conditions:

  t    EtV (st 1 )  0 t

(2.12)

Applying the envelop theorem with respect to s t gives:

V (st )  st   EtV (st 1 ) (1   ) Multiplying Equation (2.13) by applying expectations:

(2.13)

 , substituting in Equation (2.12), taking this expression one-step forward and EtV ( st 1 )  Et ( st 1 ) 

 Et ( t 1 ) (1   ) 

(2.14)

Applying expectations in equation (2.9) and replacing it in equation (2.14) results in:

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The variable H is defined in equation (2.19) 45


EtV ( st 1 )  (1   t ) st    t 

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 Et ( t 1 )(1   ) 

(2.15)

Inserting Equation (2.15) in Equation (2.12) we have

t  

   (1   ) st  Et ( t 1 )       st     2   st

(2.16)

2

When the policy is established in instant t, s t is the state variable and thus the optimal policy rule has a

 t  Hst . Applying expectations in equation (2.5) and taking this expression one-step forward, Et (st 1 )  (1   )st   t we have (2.17) Et (t 1 )  HEt (st 1 )  H (1   )st   t 

quadratic form knowing that

Inserting (2.17) in Equation (2.16) gives the following quadratic form:





  (1   )H 2     2   (1   )2 H   (1  t )  0

(2.18)

Hence, the solution to equation (2.18) is given by (2.19)

H

 (    (1   ) 2   2  ) 

  (1   )       4( 2

2

2

2

 2 )(1   t )(1   )

 2    (1   ) A propriety of the quadratic function states that the product of the roots is

H1H 2  

(1   t )  (1   )

(2.20)

The root of interest is the one that satisfies the stability condition, which is the negative root

H 2 . In this case

(1   t ) needs to be positive. Finally, replacing H 2 in Equation (2.5) gives (2.21)

t 

 (    (1   ) 2   2  ) 

  (1   )       4( 2

2

2

2

 2 )(1   t )(1   )

 2    (1   )

st

The optimal rule for the index of repressive and preventive actions against criminal practices can be derived replacing the equations (2.3) and (2.4) in the equation (2.21).

et 

H 2 (1   )

2

mt 

 H 2  1 ct 2

Comparative static analysis based on the equation (2.22) shows that

(2.22)

et / mt  0 . In this sense when the

index of money laundering gap increases, the repressive and preventive actions against criminal practices must be improved by the policy maker. Observe that when the effectiveness of the anti-money-laundering is greater, the policy maker can operate with a lower level of repressive and preventive actions against criminal practices. Notice that et / ct  0 . This means that the greater the index of criminal activities gap is, the greater the repressive and preventive actions against criminal practices must be. III- CONCLUDING REMARKS This paper deduces an optimal rule to combat the criminal activities given the rules of crime and money laundering. The model shows that an increase in money laundering activities must raise the repressive and preventive actions against criminal practices. Furthermore, the larger the effectiveness of anti-money laundering, the lower the repressive and preventive actions against criminal practices must be. The static comparative also shows that an increase in the index of criminal activities must improve the repressive and preventive actions against criminal practices.

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This model can be tested empirically to analyze the optimal rule to repress and avoid criminality. It is necessary to estimate the equations (2.1) and (2.2) to obtain the parameters 1 ,  2 , (1   ) and  . To calculate H 2

from (2.19), it is necessary to know the values of the parameters  and  . These parameters are related to equation (2.10), i.e., the loss function. If targeting criminality is the priority of the policy maker then the relative weight of the index of the criminal activities gap in the loss function can be one,   1 . Parameter  represents the inter-temporal discount factor that can assume a value between zero and one. Moreover, a possible proxy for the index crime gap is the deviation between the index of crimes and their trend. Finally, there exists an interesting methodology to create an aggregate index for several kinds of crimes, money laundering or preventive and repressive actions against criminality, according to Goldstein et.al. (2000). REFERENCES Alexander, K. (2000). The International Anti-Money Laundering Regime: the Role of the Financial Action Task Force, Financial Crime Review, Fall, n.1, 2000: 9-27. Araújo, Ricardo A. de and Moreira, Tito B. S. (2005). An Intertemporal Model of Dirty Money. Journal of Money Laundering Control, Vol.8, : 60-62. Camera, Gabriele, (2001). . Dirty Money. Journal of Monetary Economics. Vol. 47, Issue 2, April, : 377-415. Goldstein, M.; Kaminsky, G.L.; Reinhart, C.M. (2000). Assessing financial vulnerability: an early warning system for emerging markets. Washington: Institute for International Economics. Masciandaro, D. (1998). Money Laundering Regulation: The Micro Economics. Journal of Money Laundering Control, Vol.2 , n.1: 49-58 Masciandaro, D. (1999). Money Laundering: the Economics of Regulation, European Journal of Law and Economics, no.3, May: 225-240. Masciandaro, D. (2000). The Illegal Sector, Money Laundering and Legal Economy: A Macroeconomic Analysis. Journal of Financial Crime. November, n.2, : 103-112. Masciandaro, D and Filotto, U. (2008). Money Laundering Regulation and Bank Compliance Costs. What Do Your Customers Know? Economics and Italian Experience. In Journal of Money Laundering Control. Moreira, Tito B. S (2007). A Two-Period Model of Money Laundering and Organized Crime. Economics Bulletin, Vol. 11, no. 3, : 1-5. O’Sullivan, Arthur (2003). Urban Economics. McGraw-Hill, 5th edition.

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