Organized crime, money laundering and legal economy: theory and simulations

Abstract

This paper proposes a dynamic model to simulate the relationships between the profits of organized crime, money laundering and legal investments. We develop a macro framework in which organized crime can increase its possibilities to invest in the legal sector by resorting to effective but costly money laundering schemes. The model explores the conditions under which the effectiveness of money laundering causes a positive trend in the legal assets owned by the criminal organizations. We use the model to simulate the total amount of legal wealth generated by organized crime through drug trafficking in different world regions, with particular attention to Europe.

Appendices

Appendix 1

In Sect. 2 we said that L(t) is a monotonic increasing function for both $f < {\frac{1}{{1 + r_{l} }}}$ and $r_{i} > {\frac{y}{1 - y}}$. This could be shown by taking the first derivative of L(t) and imposing that it should be greater than zero.

$$ \frac{dL}{dt} = {\frac{{f\left( {1 + r_{l} } \right)}}{{1 - f\left( {1 + r_{l} } \right)}}}yK_{0} \left( {1 - C} \right)\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t} \log \left[ {\left( {1 - y} \right)\left( {1 + r_{i} } \right)} \right] > 0. $$

(17)

Condition 17 could be satisfied also for both $f > {\frac{1}{{1 + r_{l} }}}$ and $r_{i} < {\frac{y}{1 - y}}$, but this eventuality is not reasonable because it will means that, given the actual values for the legal interest rate, f should be near to 100%, and this is incoherent with the economical data and with the common sense, because it will means that criminal will work without expending any money in consumption goods. According to these considerations we have that the range of variation of the share of money laundered reinvested in the legal market—i.e. f—has an upper extremum which is lower than 100%.

Let see now how the legal capital varies with the variation of the other parameters involved in our model.

For a fixed t we have:

$$ {{\frac{\partial L}{\partial f}} =\, }{\frac{{\left( {1 + r_{l} } \right)}}{{1 - f\left( {1 + r_{l} } \right)}}}yK_{0} \left( {1 - C} \right)\left[ {\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t} - 1} \right] $$

(18)

We know that this quantity will be always greater than zero thanks to the conditions quoted above; this means that L(t) will increase as f increases, precisely for $f \to {\frac{1}{{1 + r_{l} }}}$;

$$ {{\frac{\partial L}{{\partial r_{l} }}} = }{\frac{f}{{\left[ {1 - f\left( {1 + r_{l} } \right)} \right]^{2} }}}yK_{0} \left( {1 - C} \right)\left[ {\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t} - 1} \right] $$

(19)

This function is always positive, so L(t) will increase as r _l increases;

$$ {{\frac{\partial L}{{\partial r_{i} }}} =\, }{\frac{{f\left( {1 + r_{l} } \right)}}{{1 - f\left( {1 + r_{l} } \right)}}}yK_{0} \left( {1 - C} \right)\left[ {t\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t - 1} } \right] $$

(20)

The legal capital gets higher as r _i increases but its growing become sensible only when t > 1 because $\left( { 1+ r_{i} } \right)^{t - 1}$ become a positive power of r _i .

$$ \begin{aligned} {\frac{\partial L}{\partial y}} = & A\left[ {\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t} - 1} \right] - tyA\left[ {\left( {1 - y} \right)^{t - 1} \left( {1 + r_{i} } \right)^{t} } \right] = A\left\{ {\left[ {\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t} - ty\left( {1 - y} \right)^{t - 1} \left( {1 + r_{i} } \right)^{t} } \right] - 1} \right\} \\ = & A\left\{ {\left( {1 - y} \right)^{t - 1} \left( {1 + r_{i} } \right)^{t} \left( {1 - y - ty} \right) - 1} \right\} \\ \end{aligned} $$

(21)

where $A = {\frac{{f\left( {1 + r_{l} } \right)}}{{1 - f\left( {1 + r_{l} } \right)}}}\,K_{0} \left( {1 - C} \right)$

The legal capital decreases as the share of illegal money that needs to be laundered increases. The rationale for this is that gains coming principally from illegal traffics, therefore if the share of illegal capital that needs to be laundered increases, profits decrease.

$$ {{\frac{\partial L}{\partial \delta }} = WC_{1} \beta }. $$

(22)

where $W = {\frac{{f\left( {1 + r_{l} } \right)}}{{1 - f\left( {1 + r_{l} } \right)}}}\,yK_{0} \left[ {\left( {1 - y} \right)^{t} \left( {1 + r_{i} } \right)^{t} - 1} \right].$

The legal capital increases as the anti money laundering regulation decreases.

Appendix 2

See Tables 3, 4 and 5 and Fig. 12.

Table 3 Regional distribution of world drugs retail sales (US$ mill)

Table 4 Share (y) of crimes proceeds that needs to be laundered

Table 5 Examples of money laundering technical costs (C ₀ in US$)

Fig. 12

Global illicit drug market at the retail prices by regions (US$bn). Source Own elaboration on basis of data from United Nations (2005), pp. 131–142