To Launder or Not to Launder: Modelling How the Value of Dirty Income Impacts the Marginal Deterrence of AML Policy

Samuel Haak

doi:10.1515/rle-2024-0115

Artikel

To Launder or Not to Launder: Modelling How the Value of Dirty Income Impacts the Marginal Deterrence of AML Policy

Samuel Haak

Veröffentlicht/Copyright: 11. Juli 2025

Veröffentlicht von

Veröffentlichen auch Sie bei De Gruyter Brill

Manuskript einreichen Informationen für Autor*innen

Aus der Zeitschrift Review of Law & Economics Band 21 Heft 3

Abstract

This paper develops a mathematical model of the criminal’s decision to launder money, in order to analyze the relationship between anti-money laundering (AML) policy and the incentive to commit crime. The model includes a measure of the value of dirty income for direct usage in consumption and investment, which is contrasted with the value of laundered money. The results demonstrate that increases in the strictness of AML policy cause criminals to shift away from laundering and towards spending dirty income directly. To the extent that dirty income provides a positive utility on the margin, deterrence effects from AML will be incomplete, as criminals are deterred from crime but not from laundering. Additionally, the value of dirty income is shown to present a confounding influence on the use of changes in money laundering volume to assess criminal welfare. These results suggest that efforts to improve AML regulations may be less effective at combating crime than previously supposed, and highlight the need for further research to understand how criminals use dirty income.

Keywords: money laundering; AML; microeconomics; crime; public policy

JEL Classification: K42; H10; G38

Corresponding author: Samuel Haak, Doctoral Candidate in Economics, Department of Accounting, Finance and Economics, Griffith University, Brisbane, Australia, E-mail: samuel.haak@griffithuni.edu.au

Acknowledgments

I wish to thank Andreas Chai (Griffith University), Nicholas Rohde (Griffith University), Alex Robson (Griffith University) and Kaiwen Leong (Griffith University) for supervising the writing of this paper. I would also like to thank Robert Alexander (University of the Sunshine Coast), Jackson Mejia (Massachusetts Institute of Technology), and an especially helpful anonymous peer-reviewer for their valuable comments. Needless to say, the usual disclaimer applies.

Appendix A: Proofs and Elaborations

A.1 Quadratic Utility Model

A.1.1 Assumptions

The following assumptions are utilized for the quadratic utility model in Equation (6):

Assumption 1a: 0 < M < Y
Assumption 1b: b > d
Assumption 2: β[dY + M(b − d − c − E _θ(θ)f)] < 1
Assumption 3: d > 1/βY
Assumption 4: b − c − θ(θ)f > 1/βY.

Assumptions 1a and 1b are also utilized in the case of the generalized Masciandaro model in Appendix A.2, while Assumptions 2–4 ensure the tractability of the model and the meaningful interpretation of results.

A.1.2 Simplification to Equation (1)

Proposition 1.

If:

d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p M ( b − f ) + β 2 f − 1 f M 2 + p β [ d Y f M + f M 2 ( b − d − c ) ] = 0 ,

then Equation (6) reduces to Equation (1).

Proof.

Starting with Equation (6), we take expectations over θ where E _θ(θ) = p to obtain:

E [ U ] = ( 1 − p ) d Y + M ( b − d − c ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p d Y + M ( b − d − c − f ) − β 2 [ d Y + M ( b − d − c ) − f M ] 2 .

Next, we expand the final quadratic term using the identity (x − y)² = x ² + y ² − 2xy, where x = dY + M(b − d − c) and y = fM:

E [ U ] = ( 1 − p ) d Y + M ( b − d − c ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p d Y + M ( b − d − c − f ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p β 2 f 2 M 2 + 2 d Y f M + 2 f M 2 ( b − d − c ) .

Grouping and rearranging terms to isolate the structure of Equation (1), we have:

E [ U ] = ( 1 − p ) ( b M − c M ) + p ( − c M − f M 2 ) + ( 1 − p ) d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p d ( Y − M ) + M ( b − f ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p β 2 f − 1 f M 2 + β 2 2 d Y f M + 2 f M 2 ( b − d − c ) .

We may also simplify using the identity (1 − p)z + pz = z, where:

z = d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 ,

and further rearrange to obtain:

E [ U ] = ( 1 − p ) ( b M − c M ) + p ( − c M − f M 2 ) + d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p M ( b − f ) + β 2 f − 1 f M 2 + p β [ d Y f M + f M 2 ( b − d − c ) ] .

Now finally, substituting for:

d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p M ( b − f ) + β 2 f − 1 f M 2 + p β [ d Y f M + f M 2 ( b − d − c ) ] = 0 ,

we are left with

E [ U ] = ( 1 − p ) ( b M − c M ) + p ( − c M − f M 2 ) ,

which is equivalent to Equation (1). □

A.1.3 Simplifying Parameter Restrictions

In this section, I show the parameter restrictions necessary to reduce the quadratic utility model to the original Masciandaro model. Such a limited case is unlikely to occur in reality, however, as it entails numerous, powerful assumptions–for example, that the constant term β governing the individual’s degree of risk aversion is exactly equal to the probability of laundering conviction; that the probability and severity of punishment should multiply to exactly 1/2; and that it is optimal for the individual to launder none of their criminal funds, even when the value of dirty income is zero.

Proposition 2.

Let:

E [ U 1 ] ≔ ( 1 − p ) ( b M − c M ) + p ( − c M − f M 2 ) E [ U 2 ] ≔ ( 1 − p ) ( b M − c M ) + p ( − c M − f M 2 ) + d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p M ( b − f ) + β 2 f − 1 f M 2 + p β [ d Y f M + f M 2 ( b − d − c ) ] .

If d = 0, β = p, b = f, pf = 1/2 and c ≥ (1 − p)/2p, then E[U ₁] = E[U ₂].

Proof.

To begin, we define:

A ≔ d ( Y − M ) − β 2 [ d Y + M ( b − d − c ) ] 2 + p M ( b − f ) + β 2 f − 1 f M 2 + p β d Y f M + f M 2 ( b − d − c ) ,

and X as the set of conditions:

X ≔ d = 0 β = p b = f p f = 1 2 c ≥ 1 − p 2 p .

Now, by Proposition 1, we know that:

A = 0 ⇒ E [ U 1 ] = E [ U 2 ] .

Therefore, if it can be shown that X ⇒ A = 0, then by transitivity of implications we have:

X ⇒ A = 0 ⇒ E [ U 1 ] = E [ U 2 ] X ⇒ E [ U 1 ] = E [ U 2 ] .

To evaluate whether X ⇒ A = 0, we first calculate the value of A under the condition that d = 0:

A = 0 ( Y − M ) − β 2 [ 0 Y + M ( b − 0 − c ) ] 2 + p M ( b − f ) + β 2 f − 1 f M 2 + p β 0 Y f M + f M 2 ( b − 0 − c ) = β p f − 1 2 ( b − c ) ( b − c ) M 2 + p M ( b − f ) + p f β f 2 − 1 M 2 .

Next, we impose β = p, b = f and pf = 1/2:

A = p 1 2 − 1 2 ( f − c ) ( f − c ) M 2 + p M ( f − f ) + 1 2 1 / 2 2 − 1 M 2 = p 1 2 − 1 2 ( f − c ) ( f − c ) M 2 − 3 8 M 2 .

Letting x ≔ f − c and rearranging to isolate M ²:

A = p x 1 2 − 1 2 x − 3 8 M 2 = p 2 x − x 2 − 3 8 M 2 .

Note that coefficient on M ² contains the quadratic function x − x ², which reaches its maximum value at the vertex:

− 1 2 ( − 1 ) = 1 2 .

Substituting this value into x − x ² gives the function’s maximum value:

1 2 − 1 2 2 = 1 4 .

Therefore, we have:

x − x 2 ≤ 1 4 ⇒ p 2 ( x − x 2 ) − 3 8 ≤ − 1 4 ,

since 0 ≤ p ≤ 1. Due to the negative coefficient on M ², it follows that for any M > 0, A < 0. However, if we allow M ≥ 0, then A = 0 if and only if M = 0, which occurs only when M* = 0 solves the individual’s utility maximization problem. To test this, we restrict the value of the expected utility function E[U ₂] according to the first four conditions in X:

E [ U 2 ] = ( 1 − p ) ( f M − c M ) + p ( − c M − f M 2 ) + p 2 x − x 2 − 3 8 M 2 ,

calculate the first and second derivatives with respect to M:^[18]

∂ E [ U 2 ] ∂ M = ( 1 − p ) f − c + 2 p 2 x − x 2 − 7 8 M ∂ 2 E [ U 2 ] ∂ M 2 = 2 p 2 x − x 2 − 7 8 ,

and evaluate these derivatives at M = 0:

∂ E [ U 2 ] ∂ M M = 0 = ( 1 − p ) f − c . ∂ 2 E [ U 2 ] ∂ M 2 M = 0 = 2 p 2 x − x 2 − 7 8 .

For M = 0 to represent a global optimum, we need:

∂ E [ U 2 ] ∂ M M = 0 ≤ 0 ∂ 2 E [ U 2 ] ∂ M 2 M = 0 < 0 .

Recalling that x = f − c and substituting f = 1/2p and c = (1 − p)/2p, the first and second derivatives become:

∂ E [ U 2 ] ∂ M M = 0 = ( 1 − p ) 1 2 p − 1 − p 2 p = 0 ∂ 2 E [ U 2 ] ∂ M 2 M = 0 = p 1 2 p − 1 − p 2 p − 1 2 p − 1 − p 2 p 2 − 7 4 = p − 7 4 < 0 ,

where the inequality follows from 0 ≤ p ≤ 1. Note that for all values of c ≥ (1 − p)/2p, we have E [ U 2 ] M ≤ 0 and E [ U 2 ] M M < 0 , meaning that X ⇒ M* = 0. Therefore, we conclude that:

X ⇒ M * = 0 ⇒ A = 0 ⇒ E [ U 1 ] = E [ U 2 ] X ⇒ E [ U 1 ] = E [ U 2 ] .

□

A.2 Generalized Masciandaro Model

A.2.1 Setup

Consider the following expected utility function for the prospective launderer:

(11) E [ U ] = ( 1 − p ) [ b M + d ( Y − M ) − c M ] + p [ b M + d ( Y − M ) − c M − f M α ] ,

or, equivalently:

(12) E [ U ] = d Y + M ( b − d − c ) − p f M α .

This model represents a more generalized form of Equation (1), with the addition of the parameter d, the application of benefits in both scenario (conviction and non-conviction), and alterations made to the punishment technology. For the latter case, it is assumed that social harm is an increasing and convex function of the amount of money laundered, and that the authorities aim to capture this convexity to some degree in the size of the punishment.^[19] This leads to a more generalized punishment of the form fM ^α, with α > 1.

A.2.2 Relations

First, we differentiate Equation (12) with respect to the parameters in the model:

(13) ∂ E [ U ] ∂ b = M ≥ 0 ∂ E [ U ] ∂ d = Y − M ≥ 0 ∂ E [ U ] ∂ c = − M ≤ 0 ∂ E [ U ] ∂ p = − f M α ≤ 0 ∂ E [ U ] ∂ f = − p M α ≤ 0 ∂ E [ U ] ∂ f = − p M α ≤ 0 .

If we restrict attention to amounts of laundering for which 0 < M < Y (Assumption 1a), then all of these inequalities become strict. In words, we can see that increases in both the value of clean income (b) and the value of dirty income (d) are positively related to overall expected utility, while the effect of an increase in the laundering cost parameters (p, f, c and α) is negative. Next, the expected utility function for money laundering is differentiated twice with respect to M, giving the necessary and sufficient conditions for a global maximum:

(14) ∂ E [ U ] ∂ M = b − d − c − α p f M α − 1

and

(15) ∂ 2 E [ U ] ∂ M = − ( α − 1 ) α p f M α − 2 < 0 ,

since α > 1. As in the original Masciandaro model, the function reaches its maximum where the individual chooses the utility maximizing amount of money laundering M*, which here is equal to:

(16) M * = b − d − c α p f 1 a − 1 .

In contrast to Equation (2), Equation (16) clearly shows that the relationship between the values of clean and dirty income to the individual and the transaction costs of laundering (b − d − c) is crucial in determining the utility maximizing amount of laundering. One interpretation of this is that because laundering carries an additional transaction cost, the amount that the individual will launder can be reduced to zero, even when dirty income is less valuable than clean income. Specifically, the utility maximizing amount of laundering is zero when:

(17) d = b − c .

Of course, if dirty income is assumed to provide no value, then the individual will always launder some positive amount, provided that the value of clean income outweighs the transaction costs of laundering (b > c).

Lastly, by taking first-order derivatives of (16) with respect to each parameter, we can see that the utility maximizing amount of laundering is increasing with respect to the value of clean income, and decreasing with respect to the value of dirty income, the transaction costs of laundering, and the AML policy parameters:

(18) ∂ M * ∂ b = ( b − d − c ) 1 α − 1 − 1 ( α − 1 ) ( α p f ) 1 α − 1 > 0 ∂ M * ∂ d = − ( b − d − c ) 1 α − 1 − 1 ( α − 1 ) ( α p f ) 1 α − 1 < 0 ∂ M * ∂ c = − ( b − d − c ) 1 α − 1 − 1 ( α − 1 ) ( α p f ) 1 α − 1 < 0 ∂ M * ∂ p = − ( b − d − c ) 1 α − 1 p ( α − 1 ) ( α p f ) 1 α − 1 < 0 ∂ M * ∂ f = − ( b − d − c ) 1 α − 1 f ( α − 1 ) ( α p f ) 1 α − 1 < 0 ∂ M * ∂ α = − b − d − c α p f 1 a − 1 α − 1 + α ⁡ ln b − d − c α p f α ( α − 1 ) 2 < 0 ,

for amounts of laundering where 0 < M < Y.

A.2.3 Simplification to Equation (1)

Proposition 3.

If d(Y − M) + pbM = 0 and α = 2, then Equation (11) reduces to Equation (1).

Proof.

We begin with Equation (11), which is expanded to a more easily manipulable form:

E [ U ] = ( 1 − p ) ( b M − c M ) + ( 1 − p ) d ( Y − M ) + p ( − c M − f M α ) + p d ( Y − M ) + p b M .

Using the identity (1 − p)x + px = x, with x = d(Y − M), we may simplify this expression to:

E [ U ] = ( 1 − p ) ( b M − c M ) + p ( − c M − f M α ) + d ( Y − M ) + p b M .

Substituting d(Y − M) + pbM = 0 and α = 2, we have:

E [ U ] = ( 1 − p ) ( b M − c M ) + p ( − c M − f M 2 ) ,

which is equivalent to Equation (1). □

References

Araujo, R. A., and T. B. S. Moreira. 2005. “An Inter-Temporal Model of Dirty Money.” Journal of Money Laundering Control 8 (3): 260–2. https://doi.org/10.1108/13685200510700552.Suche in Google Scholar

Ardizzi, G., C. Petraglia, M. Piacenza, F. Schneider, and G. Turati. 2014. “Money Laundering as a Crime in the Financial Sector: A New Approach to Quantitative Assessment, with an Application to Italy.” Journal of Money, Credit, and Banking 46 (8): 1555–90. https://doi.org/10.1111/jmcb.12159.Suche in Google Scholar

Attorney-General’s Department. 2016. Report on the Statutory Review of the Anti-Money Laundering and Counter-Terrorism Financing Act 2006 and Associated Rules and Regulations. Commonwealth of Australia. https://www.austrac.gov.au/sites/default/files/2019-07/report-on-the-statutory-review-of-the-anti-money-laundering.pdf.Suche in Google Scholar

Barone, R., D. Delle Side, and D. Masciandaro. 2018. “Drug Trafficking, Money Laundering and the Business Cycle: Does Secular Stagnation Include Crime?” Metroeconomica 69: 409–26. https://doi.org/10.1111/meca.12193.Suche in Google Scholar

Becker, G. 1968. “Crime and Punishment: An Economic Approach.” Journal of Political Economy 76 (2): 169–217. https://doi.org/10.1086/259394.Suche in Google Scholar

Black Economy Taskforce. 2017. Black Economy Taskforce (Final Report). Commonwealth of Australia. https://treasury.gov.au/sites/default/files/2019-03/Black-Economy-Taskforce_Final-Report.pdf.Suche in Google Scholar

Cullen, A. F. 2022. Commission of Inquiry into Money Laundering in British Columbia (Final Report – June 2022). Province of British Columbia. https://www.cullencommission.ca/files/reports/CullenCommission-FinalReport-Full.pdf.Suche in Google Scholar

Europol. 2016. Does Crime Still Pay? Criminal Asset Recovery in the EU. European Police Office. https://www.europol.europa.eu/cms/sites/default/files/documents/criminal_asset_recovery_in_the_eu_web_version.pdf.Suche in Google Scholar

Fanta, F., and H. Mohsin. 2011. “Anti-Money Laundering Regulation and Crime: A Two-Period Model of Money-in-the-Utility-Function.” Journal of Economic Cooperation and Development 32 (3): 1–20.Suche in Google Scholar

Ferwerda, J. 2009. “The Economics of Crime and Money Laundering Policy: Does Anti-Money Laundering Policy Reduce Crime?” Review of Law & Economics 5 (2): 903–29. https://doi.org/10.2202/1555-5879.1421.Suche in Google Scholar

Financial Action Task Force. 2022. FATF and INTERPOL Intensify Global Asset Recovery. https://www.fatf-gafi.org/en/publications/Methodsandtrends/FATF-INTERPOL-intensify-global-asset-recovery.html.Suche in Google Scholar

Financial Action Task Force. 2023. International Standards on Combating Money Laundering and the Financing of Terrorism & Proliferation: The FATF Recommendations. https://www.fatf-gafi.org/content/dam/fatf-gafi/recommendations/FATF%20Recommendations%202012.pdf.coredownload.inline.pdf.Suche in Google Scholar

Geiger, H., and O. Wuensch. 2007. “The Fight Against Money Laundering: And Economics Analysis of a Cost-Benefit Paradoxon.” Journal of Money Laundering Control 10 (1): 91–105. https://doi.org/10.1108/13685200710721881.Suche in Google Scholar

Harvey, J. 2008. “Just How Effective is Money Laundering Regulation?” Security Journal 28: 189–211.10.1057/palgrave.sj.8350054Suche in Google Scholar

Khadjavi, M. 2018. “Deterrence Works for Criminals.” European Journal of Law and Economics 46: 165–78. https://doi.org/10.1007/s10657-015-9483-2.Suche in Google Scholar

Leong, K., H. Li, N. Pavanin, and C. Walsh. 2022. The Effects of Policy Interventions to Limit Illegal Money Lending. IZA Discussion paper 15359. IZA Institute of Labor Economics.Suche in Google Scholar

Levi, M. 2022. “Money Laundering.” In Research Handbook of Comparative Criminal Justice, edited by D. Nelken, and C. Hamilton, 225–42. Cheltenham: Edward Elgar Publishing.10.4337/9781839106385.00023Suche in Google Scholar

Levi, M., P. Reuter, and T. Halliday. 2018. “Can the AML System be Evaluated without Better Data?” Crime, Law and Social Change 69: 307–28. https://doi.org/10.1007/s10611-017-9757-4.Suche in Google Scholar

Levitt, S., and S. A. Venkatesh. 2000. “An Economic Analysis of a Drug-Selling Gang’s Finances.” Quarterly Journal of Economics 115 (3): 755–89. https://doi.org/10.1162/003355300554908.Suche in Google Scholar

Masciandaro, D. 1998. “Money Laundering Regulation: The Micro Economics.” Journal of Money Laundering Control 2 (1): 49–58. https://doi.org/10.1108/eb027170.Suche in Google Scholar

Masciandaro, D. 1999. “Money Laundering: The Economics of Regulation.” European Journal of Law and Economics 7: 225–40.10.1023/A:1008776629651Suche in Google Scholar

Masciandaro, D. 2007. Economics of Money Laundering: A Primer. Working Paper 171. Paolo Baffi Centre Bocconi University.10.2139/ssrn.970184Suche in Google Scholar

Masciandaro, D., and R. Barone. 2008. “Worldwide Anti-Money Laundering Regulation: Estimating Costs and Benefits.” Global Business and Economics Review 10 (3): 243–64. https://doi.org/10.1504/gber.2008.019983.Suche in Google Scholar

Mungan, M. C., and J. Klick. 2015. “Discounting and Criminals’ Implied Risk Preferences.” Review of Law & Economics 11 (1): 19–23. https://doi.org/10.1515/rle-2014-0048.Suche in Google Scholar

Mungan, M. C., and J. Klick. 2016. “Identifying Criminals’ Risk Preferences.” Indiana Law Journal 91 (3): 791.10.2139/ssrn.2567048Suche in Google Scholar

Neilson, W. S., and H. Winter. 1997. “On Criminals’ Risk Attitudes.” Economics Letters 55 (1): 97–102. https://doi.org/10.1016/S0165-1765(97)00042-6.Suche in Google Scholar

Pol, R. 2018. “Uncomfortable Truths? ML=BS and AML = BS2.” Journal of Financial Crime 52 (2): 294–308. https://doi.org/10.1108/jfc-08-2017-0071.Suche in Google Scholar

Polinsky, A. M., and S. Shavell. 2000. “The Economic Theory of Public Enforcement of Law.” Journal of Economic Literature 38 (1): 45–76. https://doi.org/10.1257/jel.38.1.45.Suche in Google Scholar

Reuter, P. 2013. “Are Estimates of the Volume of Money Laundering Either Feasible or Useful?” In Research Handbook on Money Laundering, edited by B. Unger, and D. van der Linde, 243–64. Cheltenham: Edward Elgar Publishing.10.4337/9780857934000.00028Suche in Google Scholar

Unger, B., and J. den Hertog. 2012. “Water Always Finds its Way: Identifying New Forms of Money Laundering.” Crime, Law and Social Change 57: 287–304. https://doi.org/10.1007/s10611-011-9352-z.Suche in Google Scholar

United Nations Office on Drugs and Crime. 2011. Estimating Illicit Financial Flows Resulting from Drug Trafficking and Other Transnational Organized Crime (Research Report). https://unodc.org/documents/data-and-analysis/Studies/Illicit_financial_flows_2011_web.pdf.Suche in Google Scholar

Van Duyne, P. C. 1994. “Money-Laundering: Estimates in Fog.” Journal of Financial Crime 2 (1): 58–74. https://doi.org/10.1108/eb025638.Suche in Google Scholar

Van Duyne, P. C. 2003. “Money Laundering Policy: Fears and Facts.” In Criminal Finances and Organising Crime in Europe, edited by P. C. van Duyne, K. von Lampe, and J. L. Newell, 67–104. Nijmegen: Wolf Legal Publishers.Suche in Google Scholar

Walker, J. 1995. Estimates of the Extent of Money Laundering in and through Australia. https://ccv-secondant.nl/fileadmin/w/secondant_nl/platform/artikelen_2018/Austrac_1995_Estimates_report.pdf.Suche in Google Scholar

Walker, J., and B. Unger. 2009. “Measuring Global Money Laundering: “The Walker Gravity Model”.” Review of Law & Economics 5 (2): 821–53. https://doi.org/10.2202/1555-5879.1418.Suche in Google Scholar

Received: 2024-09-12

Accepted: 2025-06-02

Published Online: 2025-07-11

Sie haben derzeit keinen Zugang zu diesem Inhalt.

Artikel in diesem Heft

https://doi.org/10.1515/rle-2024-0115

Schlagwörter für diesen Artikel

money laundering; AML; microeconomics; crime; public policy