metadata: authors: 0: author: Villa,Edgar
1: author: Misas,Martha A.
2: author: Loayza,Norman V.
count: Colombia
docna: 0: docna: Illicit activity and money laundering from
            an economic growth perspective : a model and an application
            to Colombia
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,Financial Regulation & Supervision,Economic Growth,Employment and Unemployment,Crime and Society
teratopic: Industry,Macroeconomics and Economic Growth,Conflict and Development
abstracts: cdata!: This paper contributes to the economic
            analysis of illicit activities and money laundering. First,
            it presents a theoretical model of long-run growth that
            explicitly considers illicit workers, activities, and
            income, alongside a licit private sector and a functioning
            government. Second, it generates estimates of the size of
            illicit income and provides simulated and econometric
            estimates of the volume of laundered assets in the Colombian
            economy. In the model, the licit sector operates in a
            perfectly competitive environment and produces a licit good
            through a standard neoclassical production function. The
            illicit sector operates in an imperfectly competitive
            environment and is composed of two different activities: The
            first activity produces an illicit good that nonetheless is
            valuable in the market (for example illicit drugs); the
            second does not add value to the economy but only
            redistributes wealth (for example robbery, kidnapping, and
            fraud). The paper provides a series of comparative statics
            exercises to assess the effects of changes in government
            efficiency, licit sector productivity, and illicit drug
            prices. From the model, the analysis derives a set of
            estimable macroeconometric equations to measure the size of
            laundered assets in the Colombian economy in the period 1985
            to 2013. The paper assembles a data set whose key components
            are estimates of illicit income from drug trafficking and
            common crime. Illicit incomes increased drastically until
            2001, reaching a peak of nearly 12 percent of gross domestic
            product and then decreasing to less than 2 percent by 2013.
            The decline overlaps not only in a period of high economic
            growth, but also after the implementation of Plan Colombia.
            The data set is used to estimate the volume of laundered
            assets in the economy by applying the Kalman filter for the
            estimation of unobserved dynamic variables onto the derived
            macroeconometric equations from the model. The findings show
            that the volume of laundered assets increased from about 8
            percent of gross domestic product in the mid-1980s to a peak
            of 14 percent by 2002, and declined to 8 percent in 2013.
geo_reg_key: 119228,517191
repnme: repnme: Illicit activity and money laundering from
            an economic growth perspective : a model and an application
            to Colombia
display_title: Illicit activity and money
            laundering from an economic growth perspective : a model and
            an application to Colombia
listing_relative_url: /research/2016/02/25975794/illicit-activity-money-laundering-economic-growth-perspective-model-application-colombia
topicv3: Economic Growth m1326241 471,Money Laundering m1327000 2076,Crime m1439217 3041,Kidnapping m1439223 KID-3047,Unemployment m1504051 2747
publishtoextweb_dt: 2016-02-25T00:00:00Z
historic_topic: Industry,Macroeconomics and Economic Growth,Conflict and Development
no_of_pages: 66
author_keys: 0: author_key: 97109
model_extractions: WPS7578 Policy Research Working Paper 7578 Illicit Activity and Money Laundering from an Economic Growth Perspective A Model and an Application to Colombia _Edgar Villa Martha A. Misas Norman V. Loayza_ Development Research Group Macroeconomics and Growth Team February 2016
Policy Research Working Paper 7578

# **Abstract**

This paper contributes to the economic analysis of illicit activities and money laundering. First, it presents a theoretical model of long-run growth that explicitly considers illicit workers, activities, and income, alongside a licit private sector and a functioning government. Second, it generates estimates of the size of illicit income and provides simulated and econometric estimates of the volume of laundered assets in the Colombian economy. In the model, the licit sector operates in a perfectly competitive environment and produces a licit good through a standard neoclassical production function. The illicit sector operates in an imperfectly competitive environment and is composed of two different activities: The first activity produces an illicit good that nonetheless is valuable in the market (for example illicit drugs); the second does not add value to the economy but only redistributes wealth (for example robbery, kidnapping, and fraud). The paper provides a series of comparative statics exercises to assess the effects of changes in government efficiency, licit sector productivity, and illicit drug prices. From the model, the analysis derives a set of estimable macroeconometric equations to measure the size of laundered assets in the Colombian economy in the period 1985 to 2013. The paper assembles a data set whose key components are estimates of illicit income from drug trafficking and common crime. Illicit incomes increased drastically until 2001, reaching a peak of nearly 12 percent of gross domestic product and then decreasing to less than 2 percent by 2013. The decline overlaps not only in a period of high economic growth, but also after the implementation of Plan Colombia. The data set is used to estimate the volume of laundered assets in the economy by applying the Kalman filter for the estimation of unobserved dynamic variables onto the derived macroeconometric equations from the model. The findings show that the volume of laundered assets increased from about 8 percent of gross domestic product in the mid-1980s to a peak of 14 percent by 2002, and declined to 8 percent in 2013.

This paper is a product of the Macroeconomics and Growth Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at nloayza@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Illicit Activity and Money Laundering from an Economic Growth Perspective: A Model and an Application to Colombia<sup>�</sup>

Edgar Villa<sup>y</sup> , Martha A. Misas<sup>z</sup> and Norman V. Loayza<sup>x</sup> Abstract This paper contributes to the economic analysis of illicit activities and money laundering. First, it presents a theoretical model of long-run growth that explicitly considers illicit workers, activities, and income, alongside a licit private sector and a functioning government. Second, it generates estimates of the size of illicit income and provides simulated and econometric estimates of the volume of laundered assets in the Colombian economy. In the model, the licit sector operates in a perfectly competitive environment and produces a licit good through a standard neoclassical production function. The illicit sector operates in an imperfectly competitive environment and is composed of two di¤erent activities: The ...rst activity produces an illicit good that nonetheless is valuable in the market (for example illicit drugs); the second does not add value to the economy but only redistributes wealth (for example robbery, kidnapping, and fraud). The paper provides a series of comparative statics exercises to assess the e¤ects of changes in government e¢ ciency, licit sector productivity, and illicit drug prices. From the model, the analysis derives a set of estimable macroeconometric equations to measure the size of laundered assets in the Colombian economy in the period 1985 to 2013. The paper assembles a data set whose key components are estimates of illicit income from drug tra¢ cking and common crime. Illicit incomes increased drastically until 2001, reaching a peak of nearly 12 percent of gross domestic product and then decreasing to less than 2 percent by 2013. The decline overlaps not only in a period of high economic growth, but also after the implementation of Plan Colombia. The data set is used to estimate the volume of laundered assets in the economy by applying the Kalman ...lter for the estimation of unobserved dynamic variables onto the derived macroeconometric equations from the model. The ...ndings show that the volume of laundered assets increased from about 8 percent of gross domestic product in the mid-1980s to a peak of 14 percent by 2002, and declined to 8 percent in 2013.

JEL code: O10, O54, K14, K42 Keywords: Crime, Economic Growth, Drug Tra¢ cking, Money Laundering, Colombia

> �This paper is the result of collaboration between the Government of Colombia, members of the Colombian academic community, and the World Bank. We gratefully recognize the UIAF (Colombia), especially director Mr. Luis Edmundo Suarez and deputy director Mr. Javier Gutiérrez for their support. We thank María Camila Castellanos and, especially, Angela Hurtado for their superb assistance in building the data set used in this project; Wilson Martinez, former Prosecutor General of Colombia, for his practical advice; and Claudia Meza-Cuadra for her careful editorial assistance. We gratefully acknowledge the ...nancial and technical support of the World Bank in undertaking and completing this project. In this respect, we are particularly indebted to Yara Esquivel (Senior Financial Specialist), Jean Pesme (Financial Markets Integrity Practice Manager), Luis Serven (Senior Advisor Development Research Group), Emile van der Does de Willebois (Senior Specialist), Eva Gutierrez (Finance and Markets Program Leader), Daniel Lederman (Lead Economist), Barbara Cunha (Senior Specialist), Marjin Verhoeven (Senior Specialist), Quy-Toan Do (Senior Economist), Emily Adeleke (Finance and Markets Specialist), Alfonso García Mora (Practice Manager) and Roberto Aleu Biel (Consultant). We are grateful for the helpful comments of Alvaro Montenegro (Universidad Javeriana, Bogotá), Leonardo Duarte (Universidad Nacional de Colombia), Gonzalo Hernández (Universidad Javeriana, Bogotá), Munir Jalil (Universidad Nacional de Colombia), and Franz Hamman (Banco de la República de Colombia). We also wish to thank Daniel Flechas, Stephany Santacruz, Alejandro Gaviria, and Sebastián Zárate for superb research assistance for this project.

> yAssociate Professor of the International School of Economics and Business Administration. Universidad de La Sabana, Campus Puente del Común. Chía, Colombia. Email: edgar.villa@unisabana.edu.co.

> zAssociate Professor of the Economics Department. Ponti...cia Universidad Javeriana. Calle 40 No. 6-23, Edi...cio Gabriel Giraldo. Email: mmisas@javeriana.edu.co.

> xLead Economist of World Bank, Development Economics. Email: nloayza@worldbank.org.

1
# 1 Introduction

Money laundering has increased substantially in the last 20 years among developed and developing economies.<sup>1</sup> The economics literature on the long-run e¤ects of money laundering is limited as only a few papers consider the measurement and e¤ect of illicit activities–and associated laundering transactions— on capital accumulation and economic growth. Moreover, there is no consensus on whether there is a negative or positive relation between the funneling of “dirty money”into the ...nancial system and the growth prospects of the economy.<sup>2</sup> Some experts consider that illicit activities and money laundering have a negative economic e¤ect because they i) generate economic distortions that decrease the productivity of licit factors in the economy; ii) erode the ...nancial and real sectors that are in...ltrated by asset laundering, generating bankruptcy risks and ultimately ...nancial crises; and iii) undermine government institutions through corruption and capture. Other authors, however, suggest that illicit activities and money laundering can have a positive impact on economic growth, especially for developing economies, if they generate new resources that can enter the economy and fund productive investment.

This paper contributes to the economic analysis of illicit activities and money laundering in two interrelated ways. First, it presents a theoretical model of long-run growth that explicitly considers illicit workers, activities, and income, alongside a licit private sector and a functioning government. Second, it generates estimates of the size of illicit income and provides simulated and econometric estimates of money laundering in the Colombian economy.

On the theoretical contribution, the paper presents an overlapping-generation growth model with both licit and illicit activities. In the model, earnings from illicit activities can be in part “laundered” into the economy by consumption of licit goods and investment of physical capital. The model restricts attention to only one asset, capital. The licit sector, which operates in a perfectly competitive environment, produces a licit good using capital and labor through a standard neoclassical production function. The illicit sector, which operates in an imperfectly competitive environment, is composed of two di¤erent activities. The ...rst produces an illicit good (e.g., illicit drugs) that nonetheless is valuable in the market. The second activity does not produce anything new or add value to the economy but consists of illicit appropriation of somebody else’s income (e.g., robbery, kidnapping, and fraud). In a purely economic sense, the ...rst illicit activity can be characterized as productive, while the second one as redistributive.

In the model, young individuals self-select into working in either the licit or illicit sector depending on their subjective moral loss of undertaking illicit activities. Young individuals are endowed with a unit of time to work, receive at the end of their ...rst period of life an inheritance in the form of

> 1 See Boghean, C., (2001), Reuter and Truman (2004), Gilmore, W.C., (2006), Walker and Unger (2009).

> 2 Tanzi (1996), Prokhorov (2001A, 2001B), Masciandaro (2001). Ardizzi et al.(2013).

2
capital from their adult parents, and consume the licit good. Old individuals do not work, leave a bequest of capital for their o¤spring, and consume the licit good. The volume of illicit income is either consumed or saved by illicit households (young and old) much in the same way as licit households do. An important di¤erence, however, is that a part of illicit income is detected and con...scated by the government with a given probability, while the rest is either consumed or saved. Some of the savings from illicit income are funneled to fund capital investment, which can then be integrated into the licit economy through the bequests from the old to the young.

The last agent in the model is the government, which raises ...scal revenues from both taxes (from licit income) and con...scation proceeds (from illicit activities). It then uses this revenue to produce public goods for all households and to fund a police and judicial system that can detect illicit activities and con...scate their income. We solve the model, showing that it has a short-run equilibrium with illicit activities as well as a steady-state or long-run equilibrium. We perform a set of comparativestatic exercises to explore how changes in key parameters and exogenous variables a¤ect licit and illicit activities, their corresponding income, and key variables like public good provision, social welfare and aggregate savings for an economy.

On the empirical contribution of the paper, we generate estimates of illicit income derived from drug tra¢ cking and from common crime for the early 1980s to the early 2010s in Colombia. This period was characterized by a substantial increase in drug tra¢ cking in the 1980s and 1990s, and a considerable decline after 2000, coinciding with the country’s economic recovery and the implementation of Plan Colombia..Moreover, we use two quantitative methods to estimate the stock of laundered assets in the country’s economy. We ...rst use a calibration method based on a parameterization of the solution equation for laundered assets in the theoretical model. Next, we use a Kalman ...lter method for the estimation of an unobserved variable, which is an innovation in the crime literature.

To implement these quantitative methods, we develop a macroeconometric system of equations that is derived directly from the theoretical model. The system includes two equations: The ...rst one is a transition equation that speci...es the dynamic nature of asset laundering in the economy in terms of its determinants. The second is a measurement equation that represents the mechanisms through which asset laundering a¤ects the stock of physical capital in the economy. The estimable system is applied to data for Colombia in the period 1985 to 2013 in order to estimate the volume of assets and money laundered in this economy. We see our contribution as a ...rst step to measure and quantify these elusive unobservable but relevant variables for any economy.

On a normative perspective, we expect that this study can contribute to improve the country’s regulatory, preventive and anti-criminal systems by providing an economic analysis of the incentives, mechanisms, and e¤ects of illicit activities. Likewise, it can contribute by quantifying the size and e¤ects of illicit income and corresponding money laundering in the economy. Finally, the model and 3
empirical methods can be used later on to incorporate new data as it becomes available in Colombia, and more broadly, they can be used in other countries facing similar conditions.

The rest of the article is organized as follows. The second section presents a brief literature review on money laundering, while the third section presents a conceptual framework in order to guide the theoretical modelling. The fourth section develops the theoretical economic growth model with illicit activities. The ...fth section presents some comparative statics on key parameters of the model, while the sixth section develops the macroeconometric system used in estimation. The seventh section reviews the methods used to estimate the trajectory of the volume of assets laundered in the Colombian economy between 1985 and 2013. The eighth section introduces the data while the ninth section presents the empirical results. The ...nal section concludes.

# 2 Literature Review

This section presents a brief literature review on money laundering. We present this literature review in four parts: i) general concepts on the issues around money laundering as well as anti-money laundering policies, ii) theoretical models that have been developed to understand the main drivers of money laundering, iii) empirical and econometric estimations of shadow/underground economies and volumes of money laundering using various methods and ...nally iv) a review of the case of Colombia.

## 2.1 General Concepts

Kumar (2012) de...nes money laundering as the process by which large amounts of illegally obtained money (from drug tra¢ cking, terrorist activity or other serious crimes) is given the appearance of having originated from legitimate sources. The e¤ects of money laundering and of anti-money laundering policies (AMLP) on an economy are a subject of ongoing debate. Some economists argue that AMLP generate negative e¤ects on developing countries, since these countries could bene...t from illicit funds being laundered in their economies. Geiger and Wuensch (2006), for example, argue that complying with AMLP can become so costly that it back...res, increasing delinquency and therefore increasing the volume of money laundered. These authors believe that the bene...ts of AMLP are lower than the costs for society and thus question whether these regulations should be pursued in the ...rst place.

Other authors, such as Kumar (2012) and Bartlett and Ballantine (2002), argue that money laundering has signi...cant negative impacts on the development of a country. Kumar (2012), for example, argues that money laundering is a criminal activity against governments and countries, and notes that since the events of September 11 of 2001, it has been targeted as an activity that threatens national security because of its link with the ...nancing of terrorism. In general, the authors note that negative e¤ects of money laundering occur in three main sectors of the economy: 4
i) The ...nancial sector, which becomes vulnerable to the risks of harboring illicit funds and in turn has its reputation eroded with the banking system, ii) The real sector, which is adversely a¤ected as illicit funds are channeled to less e¢ cient sectors, leading to a distortion of exchange rates, in‡ation rates, money supply and eventually lowering the economic growth rate of a country. The real sector is also negatively impacted as corruption and delinquency increase, charging an implicit tax.

iii) The international commerce sector and capital markets, which are a¤ected since illicit funds distort a country’s imports and exports as well as capital ‡ows in and out of the country.

According to these authors asset laundering involves highly complex ...nancial operations around the world from those countries where the assets are generated to those countries that lack su¢ cient regulation. Moreover, it generates powerful criminal organizations that also have the political power to curb government policies for their bene...t.

Slim (2011), meanwhile, argues that money laundering has a di¤erent expected impact on an open economy than on a closed one at the macro level. The author argues that in a closed economy it generates an increase in money supply in the economy, an increase in consumption and economic activity in general, an increase in in‡ation and ...scal revenue for the government and the appearance of real estate bubbles. On the other hand, he argues that the e¤ects on an open economy vary. If the economy produces drugs and receives money laundered, then remittances increase, which increases the balance of payments. If the economy receives the illicit proceeds only temporarily, there is an increase in the current account de...cit due to an increase in imports which also revalues the currency. Finally, if the economy receives illicit proceeds permanently then there is a current account surplus and a revaluation of the currency which increases the in‡ow of foreign capital.

Another section of the literature focuses on understanding how the shadow economy (SE) works and on estimating its size within a given economy. For example, Eilat and Zinnes (2000) ...nd that in less developed economies the SE represents more than 50% of the economy, which suggests that it plays a key role in economic growth. The authors also argue that the SE acts as a cushion when the o¢ cial GDP decreases, by increasing opportunities to generate income in times of recession. This would imply a negative correlation between the size of the SE and GDP during a business cycle. The authors ...nd that the strength of this relation is not symmetric and depends on the business cycle, which could have inertia or hysteresis in the creation and destruction of the SE. The authors also ...nd that the SE is associated with negative e¤ects on private as well as public investments and seems to be positively related with greater monetary instability and ine¢ ciency in the allocation of resources. Furthermore, they argue that it disintegrates social norms, o¢ cial institutions and the rule of law. The authors identify three types of policies that can in‡uence or are a¤ected by the SE: (i) policies with multiple bene...ts: those that enhance economic liberalization, maintain macroeconomic stability, 5
enhance regulation, generate greater transparency and public participation, greater decentralization and a stronger rule of law, (ii) policies that attack the SE directly: tax cuts, better regulation and greater temporal policy consistency; and (iii) policies a¤ected by the presence of the SE: monetary and ...scal policy that ignore the size and the way the SE operates. Overall, the authors conclude that the concept of an SE is intrinsically vague and di¢ cult to estimate due to noisy data, which does not allow us to disentangle simultaneity issues between causes and e¤ects.

Tanzi (1999) also studies issues related to the SE and methods for measuring it. The author argues that the SE has been growing through time in most economies, which has made the o¢ cial licit measures of macroeconomic variables, such as national accounts of GDP, unemployment rates and the size of tax evasion, less precise. These variables in turn in‡uence and decrease precision of other macro economic variables, such as the ...scal de...cit, public debt and ...scal goals. In addition, Tanzi argues that the relationship between unemployment and the SE is ambiguous since the SE is more labor intensive than capital intensive due to the illicit or informal nature of the production of illicit goods and due to the fact that workers can labor in both the licit and the illicit SE. Finally, Tanzi emphasizes that tax evasion increases with the SE which in turn generates a negative impact on the ...scal revenues of a government. Spiro (1996) applies Tanzi’s methodology to estimate the shadow economy in Canada. He ...nds, counter intuitively, that for Canada, recessions were not a key factor for the expansion of the underground economy.

Finally, money laundering has been historically linked with drug tra¢ cking in the literature. There is a commonly held view among economists and researchers, such as Taylor (1992), that drugs are the fundamental illicit good produced that enhance asset and money laundering. Taylor argues that economic liberalization of markets as well as ...nancial markets across borders, such as the European Union, Canada or the United States, can increase drug tra¢ cking and thus money laundering. This problem is even more relevant today, more than 20 years later, given the issues around drug tra¢ cking on the Mexico and United States border.

# 2.2 Theoretical Models

One of the ...rst authors to construct a microeconomic model of money laundering which considers regulation is Masciandaro (1999, 2007). We present the basic model from the 2007 paper since it is more developed and pertinent for our purposes. Masciandaro builds a microeconomic model of money laundering in order to assess the impact of regulation. The author starts by assuming the existence of a criminal organization de...ned as a group of individuals that collaborate to exchange and produce illegal goods and services in the economy. The organization accumulates resources through its illegal activity and eventually faces a laundering decision. Following the principles of Beckerian crime models, Masciandaro proposes that money laundering by a professional launderer is 6
a decision that depends on two key factors: (i) the probability of detection and apprehension by law enforcement authorities, denoted p 2 (0; 1) and (ii) the penalty in case of being detected, denoted T (Y ) = tY<sup>2</sup> for t 2 (0; 1). The expected utility of a criminal organization that is risk neutral is then de...ned as U (Y ) = (1 � p) [B (Y ) � C (Y )] + p [�C (Y ) � T (Y )], where B (Y ) = (1 + r) Y are the bene...ts of laundering, where r is the licit return on the investment of the volume Y of money laundered, and C (Y ) = cY represents the costs of laundering money in either eventuality where c 2 (0; 1). Finally, the model assumes that if there is no money to be laundered, then the utility is normalized to zero. In this static environment the optimal amount of money to be laundered is simply found by maximizing the utility with respect to Y , yielding Y<sup>�</sup> =<sup><u>(1+r)(</u></sup> 2<sup>1</sup> pt<sup>�p)�c</sup> . This is a decreasing function in p, c and t yet increasing in r. The author then develops a macroeconomic model based on these microeconomic foundations in which money laundering is a fraction of criminal organizations’ income in the economy, i.e. AFI = m � ACI, where AFI represents illegal funds laundered, ACI represents criminal organizations’incomes and m 2 (0; 1). Moreover, total investment in the economy is composed of licit investment, ARL, and illegal investment, which is money laundered from the illegal sector AFI and depends on illegal income ACI. Hence, in this model, money laundered from criminal organizations increases the investment in the economy which positively a¤ects economic growth.

Silva et al. (2012) develop a simple dynamic model with no microeconomic foundations in order to relate crime, money laundering and anti-crime policies. They postulate a simple dynamic equation in which criminal activities are a function of their past level as well as repressive and preventive policies to counteract crime, which in turn depend positively on public resources and a stochastic shock. Since income from criminal activities must be laundered so that it can be used in the licit economy, the authors postulate a money laundering function in which it similarly depends on its past value and on criminal activities and a stochastic shock. A policy maker must choose the level of repressive and preventive policies as well as the level of crime that society will tolerate so as to minimize a quadratic loss function. A linear policy function is obtained that generates the fundamental policy result: the level of repressive and preventive anti-crime policies increases with the volume of money laundered.

Walker and Unger (2009) use a gravity model developed by Walker to estimate the volume of money laundered in Australia in 2004. The proposed model is a variation of the Newton gravity model which postulates that the ‡ow of goods between countries is related as in a Newtonian gravity model that does not have microfoundations. The model assumes that: i) crime generates income in all countries, ii) criminal income depends on the prevalence of di¤erent types of crimes and on the average pro...t per criminal o¤ense, iii) organized crime is more productive than simple crime, iv) crime is more pro...table in higher income countries, v) income inequality allows the existence of a criminal class even in poor countries and vi) not all criminal pro...t is laundered. The authors estimate the bene...ts of crime for the Australian economy to be between $2.8 and $6.3 billion Australian dollars 7
for 2004.

Using a methodology similar to Ingram et al. (1997) and Busato et al. (2006), Argentiero et al. (2008) calibrate a dynamic general equilibrium model to measure money laundering in Italy. They argue that econometric estimations have limitations since the key variable is unobservable leading to technical statistical issues. The authors develop a model that has a formal licit sector and an informal-criminal sector in which three main agents interact: i) licit ...rms that produce licit goods using capital and labor and illicit ...rms that produce illicit goods using labor and land; ii) households that pay taxes, demand both goods, demand money and supply labor and capital to both sectors of the economy; and iii) a government which collects ...scal revenue in the form of taxes from households and ...rms, and includes a central bank that supplies money to the economy. The authors ...nd that money laundering depends optimally on labor in both sectors, capital, prices and quantities of both goods. They calibrate the model and ...nd that money laundered as a proportion of Italian GDP has increased over time. They also ...nd a negative correlation between money laundering and GDP. In Argentiero et al. (2009), they apply their methodology to the United States and 15 countries in the European Union.

# 2.3 Empirical and Econometric Estimations

Unger (2009) describes a series of methods that have been used to assess the volume and mechanisms behind the phenomenon of asset laundering. These include: i) ...eld studies that help understand the way individuals and institutions behave in the presence of crime and asset laundering; ii) interviews and surveys of individuals that work in the di¤erent sectors in which asset laundering occurs, which help understand the di¤erent mechanisms through which asset laundering operates; iii) analyses of suspicious or unusual transactions that help understand some of the mechanisms used by criminals to launder their illicit income; iv) analyses of statistical discrepancies at the macro level in the balance of payments or money supply-demand that help understand the volume of the SE in which asset laundering operates; and v) the latent variable approach, in which asset laundering is viewed as an unobservable variable to estimate indirectly using statistical methods such as Multiple IndicatorMultiple Causes (MIMIC) and Dynamic MIMIC. These methods consist of using the software LISREL to estimate a system of linear structural equations of at least two types: i) a transition equation that relates the unobservable variable, in this case asset laundering, to its determinants, and ii) measure equations that relate observable indicator variables, e.g. money supply, GDP, capital stock, to the unobservable variable, which can be used to measure the impact of the unobservable variable. Unger (2009) also discusses other methods that have been used to estimate the volume of asset laundering like a Gravity Model as in Walker and Unger (2009). For an overview of structural linear models and MIMIC see Manzano and Zamora (2009), Schumacker and Lomax (2010), Kline (2011).

8
Using the DYMIMIC methodology Schneider (2007) estimates the volume of assets laundered and its time series trajectory between 1995 and 2006 for 20 OECD countries. The conceptual framework of the illegal economy used distinguishes between the SE, in which illegal goods are produced, and the underground or criminal economy, in which all types of criminal o¤enses are considered. All illegal income that comes from these sectors is potentially laundered. Schneider uses a transition equation which includes criminal activities and income distribution as determinants of asset laundering, while con...scated illegal income, number of o¤enders in the judicial system, and income per capita, are used as measure or indicator variables. The author ...nds that for economies like Italy, France and Great Britain, the SE decreased in size over the study period while the underground economy grew rapidly. An overview of some previous results by Schneider with his several coauthors is provided in Frey and Schneider (2000).

Like Schneider, Prokhorov (2001) considers the underground economy to be composed of a SE and a criminal economy where asset laundering is included in the latter. The author argues that a functioning licit economy cannot be separated from illicit activities and therefore argues that there must be an optimal level of illegality such that if surpassed society should coordinate to make it smaller. Prokhorov uses a MIMIC methodology where ...scal and non-...scal regulation, in‡ation, population below the poverty line, real income and unemployment rate are determinants of the transition equation for the ratio of the size of the underground economy to GDP. The indicator variables a¤ected by this latent unobserved variable include the monetary base, M2, foreign investment, crime rate and energy consumption over GDP. The estimation is carried out for Russia in the periods 1992-2001 and 20002004.

Tedds and Giles (2000), following Giles (1999), similarly use the MIMIC methodology to estimate the shadow economy of Canada and New Zealand using as indicator variables the growth rate of the economy, M3 and other monetary measures of money in circulation and male labor participation. As determinants of the SE they use self-employment income, crime rates, unemployment rates, tax rates relative to GDP and the in‡ation rate among others. The authors ...nd that these SEs have been growing over time. However, this type of methodology has been criticized by Breusch (2005).

# 2.4 The Case of Colombia

Colombia is an ideal country for studying asset and money laundering as it is one of the main drug producing countries in the world, particularly of marijuana and cocaine. It is also a country with high crime rates, particularly kidnapping for ransom and theft. Not surprisingly then, the domestic literature on Colombia has been dominated by the role of drugs in its economy which is considered the main predicate o¤ense of asset laundering. For an overview of drug tra¢ cking in Colombia up to 2001 see Thoumi (2002).

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Holmes and Gutiérrez de Piñeres (2006) argue that the drug trade has had negative e¤ects on the economy through: i) higher unemployment rates, (ii) an accelerating increase in the cost of real estate, (iii) a substitution from licit agricultural crops to illicit crops, like coca, (iv) an increase in smuggling that has increased asset laundering in the country, (v) lower investment levels in licit ...rms, (vi) an increase in land concentration in order to produce drugs, and (vii) an increase in long run inequality, among other things. Moreover, drugs have brought much violence to the country, generating forced displacement of people, the creation of illegal guerrillas and the proliferation of paramilitary groups involved in massacres and kidnapping since the 1980s.

Several approaches have been used to understand and estimate asset laundering as well as the shadow/underground activities of the Colombian economy. For example, Schneider and Hametner (2007) use a demand approach to estimate the SE in Colombia between 1976 and 2000. The authors ...nd that the SE grew between 1976-1985 and 1992-2000 and argue that this occurred because of an increase in taxes, higher unemployment and economic crises. They also ...nd a positive relationship between the overall economic growth of the economy and the SE. Arango et al. (2006) uses a latent variable approach to estimate the SE in Colombia using the Kalman Filter and an optimizing algorithm with transition and measure equations. They ...nd that the money supply in the Colombian economy has been a¤ected positively by the SE. Other studies like Amaya and Caballero (2011) try to estimate the aggregate volume of asset laundering in Colombia with basic accounting principles under certain adhoc assumptions.

Our approach combines several of the methodologies used in the literature. We develop a general equilibrium overlapping generations growth model to study the main determinants of asset laundering and the way that this activity a¤ects the capital stock of an economy. On this basis, we build a two linear structural equation macroeconometric model with a transition equation, which speci...es the determinants of asset laundering, and a measure or indicator equation for an observable variable a¤ected by asset laundering, in this case, the capital stock of the economy. This linear system is then taken to the data for the Colombian economy between 1985 and 2013 using two empirical methods: Calibration and Kalman Filter, where asset laundering is understood as a latent variable to be estimated.

The next section builds the conceptual framework on asset laundering to be used in the theoretical model.

# 3 Conceptual Framework on Asset Laundering

In the literature on asset laundering, there appears to be no consensus on the di¤erence between the terms laundered assets and laundered money. In some cases they are considered to be synonymous while in others the former contains the latter. Most de...nitions, though, focus mostly on criminal 10
<!-- Start of picture text --> Detected<br>a<br>Cr un ><br>Money<br>d<br>laundering<br>e<br>i<br>f<br>>) Asset | Asset<br>- accumulation laundering<br>RZ<br><!-- End of picture text -->
as redistributive. In the macroeconomic model that we develop below we assume that households directly attempt to launder their illicit income by investing in the only asset in the economy, called capital. After households place their funds in the ...nancial system to purchase capital law enforcement authorities detect the illicit origins of the funds with a certain probability. If detected, the illicit income is con...scated and used to fund the government. Asset laundering occurs when adult parents (old members of a household) leave an inheritance of capital to their young o¤spring. Once illicit capital is transferred from adult parents to their o¤spring this capital is fully integrated into the licit economy and the ...nancial sector lends these funds to licit ...rms so that they can replace and expand their capital stock.

# 4 An Economic Growth Model with Illicit Activity and Money Laundering

As previously described, part of the literature estimates asset laundering using simple empirical models, which make a number of ad hoc assumptions not clearly founded in theory. Though some theoretical models have been constructed and calibrated, none have done so in the context of a growth model. We believe that a growth model is necessary for understanding the main mechanisms through which asset laundering, an unobservable variable, a¤ects the capital accumulation of an economy. Moreover, using a dynamic model can help the macroeconometrics required to estimate the volume of assets laundered in an economy given that it allows identi...cation of structural parameters.

We consider an overlapping generations model similar to Diamond (1965) since it is a dynamic time discrete model which is not as simple as the Solow model nor as complex in terms of continuous time structure as the Ramsey model. Moreover, it is a structure that allows us to model the transmission of wealth from generation to generation through which assets are laundered and illicit assets are integrated into the licit economy which we believe is a key aspect of asset laundering in an economy. Finally, the model’s structure allows us to attain the Markov property used in empirical speci...cations of transition equation and measure equations that lend themselves to apply econometric techniques.

Next, we present an overview of the economy and some details of the environment which constitute the building blocks for the growth model to be developed. The economy is composed of four actors and activities.

i) Households, made up by a young and an adult generation that overlap in any given period. The young generation is born with a moral cost type for illicit activities as well as a time endowment that is o¤ered inelastically in the labor market either to work in licit or illicit activities, but not both. At the end of the period, the young generation receives licit or illicit income according to the type of work chosen at the beginning of the period and an inheritance in the form of capital from the adult (parent) generation. The young generation has to choose how much to save and consume of the licit 12
good out of total wealth at the end of their ...rst period of life. The adult generation at the beginning of the period puts savings (capital) from the previous period into the ...nancial sector and obtains a return at the end of the period. At the end of the period the adult generation decides the amount to transfer out of total wealth as an inheritance to their o¤spring and the amount to consume in licit goods. The young generation receives these savings and invests them in capital (the only asset in the economy), obtaining a return on them at the end of the period. We assume households have perfect foresight and that the only heterogeneity among households is their moral cost when young of working in illicit activities.

ii) Licit ...rms, that produce licit consumption goods, demanded by households when young and when adult. These ...rms operate in a perfectly competitive environment using a constant returns to scale technology that uses capital and licit labor and have perfect foresight. To simplify the analysis we assume that licit ...rms in the model are not corruptible.

iii) Illicit activities are of two types: i) those that produce an illicit good, such as drugs, for which the price and demand is determined by world markets, and ii) those that redistribute income, i,e. common crimes such as burglary, larceny, theft, motor vehicle theft, arson, shoplifting, robbery, kidnapping and extortion, all of which generate insecurity in the economy and aim to apprehend income from licit workers. Both types of illicit activities use a techonology that is labor intensive, consistent with the assumption that capital accumulation in this sector generates perfect detection from the government. Drug tra¢ cking operates in an imperfect competition environment where workers are not paid according to their marginal productivity but by a sales commission based on average production compatible with income sharing. Illicit labor markets are segmented in the sense that drug tra¢ cking ...rst hires the labor it needs to meet foreign demand and the remaining illicit workers are allocated to common criminal activities. Illicit income is not subject to income tax.

iv) A government that raises ...scal revenues from both taxes (from licit income) and con...scation proceeds (from illicit activities). It then uses this revenue to produce public goods for all households and to fund a police and judicial system that can detect illicit activities and con...scate their income, such that it maximizes a utilitarian social welfare function under a balanced budget in every period.

In the next section we outline the precise mathematical assumptions for each of these participants in the economy, and derive their corresponding optimal behavior, specifying the variables that each of these agents take as given.

# 4.1 Households

We ...rst describe licit and illicit households in order to characterize their behavior in terms of their optimal savings (in assets) and consumption decisions. Then we study the way they self select into illicit and licit activities. Assume that there are Ht households in period t and that the population 13
grows at the exogenous rate n > 0 such that Ht+1 = (1 + n) Ht. Each member of a household lives two periods, one as a young person and one as an adult. The two generations overlap in any given period of time such that the young in period t have only one parent that is adult in period t and was born in period t � 1. Since in each household in every period there are two individuals, then Ht also represents the young population in period t and therefore n is the fertility rate of youths that are born in every period.

Households are of two types, licit and illicit, where the former type works in licit activities while the latter works in illicit activities. Young individuals are born with a moral type and one unit of labor that they o¤er inelastically in their ...rst period of life to work either in the licit or illicit sector. Working decisions are based on moral types and potential incomes and are irreversible decisions in the sense that once a worker decides to o¤er their unit of time to work in the licit or illicit sector they cannot go back to the other sector. At the end of their ...rst period of life, young individuals receive a bequest in the form of capital (the only asset in the economy) from their adult parent, which is not subject to con...scation regardless of legality of origin.<sup>3</sup>

# 4.1.1 Preferences and Lifetime Utility

A generation consumes the licit good when young (denoted Ct<sup>y)andwhenadult(denotedC</sup> t<sup>a</sup> +1<sup>)and</sup> leaves a bequest to their o¤spring at the end of period t + 1 denoted ht+1. Adults do not work and discount at rate of � 2 (0; 1) their utility in period t + 1. The variable � represents the moral cost of working in illicit activities and is assumed to be heterogenous in the population such that in any given period, it takes two values � 2 ��; �<sup>�</sup> � where �><sup>�</sup> <u>�</u> � 1 such that fraction � of households have � = <u>�</u> while the complement 1 � � have � = �<sup>�</sup> . This re‡ects a time invariant heterogeneity in the moral cost of entering the illicit sector. We assume that the type � is bequeathed by the adult to the young generation at the beginning of the period in which the young are born. Lifetime preferences for a generation that lives period t as young and period t + 1 as an adult are represented by the following log utility function where I takes the value one if the young generation in period t works in illicit activities and zero otherwise and gt;t+1 denotes a government transfer that a generation in both periods would receive which represents social investments from the government in public goods and services bene...tting all households alike. The weight on the utility of these public goods and services for a household relative to the unity utility weight on consumption goods is � 2 (0; 1).

> 3 Ideally one would want to include more than one asset in the economy, say housing and a ...nancial asset like bonds, which combined could make up the capital of the economy. This would allow one to analyze the various incentives for illicit households to place their income in di¤erent types of assets that could also have di¤erent detection and con...scation probabilities attached to them. However, doing this is beyond the scope of this article because we are interested in modelling the basic aggregate mechanisms involved in asset laundering related to economic growth.

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# 4.1.2 Lifetime Wealth

The young generation born in period t is endowed with moral type � and with one unit of time to be used to work in a licit or illicit activity in the period, and which yields a disposable income. Licit labor income is equal to disposable wage income after tax and crime i.e. (1 � � t) (1 � �) wt where � t 2 (0; 1) denotes the income tax rate while � 2 (0; 1) denotes the fraction of income apprehended by common crime, which is assumed to be proportional to disposable licit income. Moreover, the young generation inherits h<sup>I</sup> t<sup>for I= 1; 0 of capital at the end of period t,which it receives as a bequest from</sup> the adult generation (parent). Therefore licit wealth for a young individual at the end of period t is de...ned as Wt<sup>0�h0</sup> t<sup>+ (1 ��t) (1 ��) wt.</sup> A young individual that becomes an illicit worker can work in either of two illicit activities in the economy, one that produces drugs in the economy or one that appropriates income from licit workers, i.e. common crimes. Wealth for an illicit worker at the end of period t is thus the bequest received plus the illicit income from one of these two illicit activities which we denote as Yt<sup>ifor i = D; R, where</sup> D stands for the illicit goods sector that produces drugs to export and satisfy a foreign demand while R stands for robbery or common crime.<sup>4</sup> Illicit incomes are detected and con...scated with probability qt in period t. Hence expected wealth for an individual that chooses to enter the illicit sector is Wt<sup>1�h1</sup> t<sup>+ (1 �qt) Y</sup> t<sup>i,fori = D; R.</sup> We assume that bequests that come from the proceeds of illicit activity in the previous period are no di¤erent to ones that come from a licit source in the sense that they are not subject to detection and con...scation by the government in period t. This is because adults that invest illicit income in the ...nancial system in period t are not detected and therefore can bequest their wealth to their o¤spring at the end of period t. Hence, bequests do not face the risk of detection and con...scation even though they retain for our analytic purposes their illicit nature.<sup>5</sup> In our model, then, this is the way by which illicit assets are fully integrated and laundered in the economy. The adult generation in period t are the owners of the capital in the economy, do not work and live o¤ what they saved when young plus the interest it earns.

# 4.1.3 Budget Constraint

The budget constraint for period t for a young individual is therefore

> 4 In this paper we refer to "drugs" as the illicit good being produced. This is because in the empirical section we use cocaine as the main illicit good produced in the Colombian economy and exported to foreign countries. Nonetheless, the theoretical model is general enough to incorporate any type of illicit good or service produced in the domestic economy for exportation. Other examples of illicit goods include weapons, illegal mining and human tra¢ cking.

> 5 This assumption is plausible for generations of 25 to 30 years, the length of time per generation to which the model corresponds. Even if laundered assets were to be detected after 20 years we assume reasonably that this wealth cannot be con...scated by law enforcement authorities. In this sense once bequests are transferred from parents to sons/daughters then no con...scation can be implemented for laundered assets even if detected. This assumption works well for our theoretical purposes, however we relax this assumption in the empirical section and allow with certain probability that laundered assests be con...scated even after being integrated into the licit economy.

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while in period t + 1 the individual when adult consumes Ct<sup>I;a</sup> +1<sup>andleavesabequestofhI</sup> t+1<sup>fromthe</sup> savings plus the accrued interest where it+1 is the real interest rate on one-period loans between periods t and t + 1. Combining these two restrictions yields the lifetime budget constraint

# 4.1.4 Time Line

Figure 2 shows the time line of household decisions during periods t and t + 1. At the beginning of period t, each household includes an adult and a young person born that period. The adult generation does not work and puts their savings (invests capital) into the ...nancial system. The young generation has one unit of time endowment and chooses to work in the licit or illicit sector depending on their moral type. At the end of period t, the adult generation gets a return on their investment (savings) and divides their wealth into a bequest for their o¤spring and consumption of the licit good. The young generation at the end of period t receives labor income, either licit or illicit, and the bequest in the form of capital from their adult parent, which is also licit or illicit in nature. The young generation then chooses the amount to save out of total wealth, which is transferred to the next period, while the rest is used to consume the licit good. This is repeated in period t + 1, as the young generation of period t becomes the adult generation of t + 1, which invests its savings in the ...nancial system while a new young generation is born in period t + 1 and has to choose to work in the licit or illicit sector. This dynamic continues inde...nitely into the future.

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<!-- Start of picture text --> Household period t<br>Adult generation Adult generation<br>puts savings from Cs leaves bequest<br>t-1 into financial and consumes<br>system licit good ;<br>| Household period t+1<br>Young generation Young generation Young generation Adult generation<br>born in t chooses receives bequest, becomes Adult leaves bequest<br>to work in licit or "consumes licit. “generation and and consumes<br>illicit sector good and saves puts savings from licit good<br>from total wealth t into financial<br>system |<br>Young generation Young generation<br>born in t+1 receives bequest,<br>chooses to work ~~~_ consumes licit<br>in licit or illicit good and saves<br>sector from total wealth<br><!-- End of picture text -->

<!-- Start of picture text --> B B n - ¢<br>BW<br><!-- End of picture text -->
where s (�) � 1+22��<sup>2</sup> �0; 3<sup><u>2</u></sup> � denotes the constant marginal propensity to save given out of total wealth, where s<sup>0</sup> (�) > 0 and s<sup>00</sup> (�) < 0.

Replacing these demand functions in the utility function gives us the indirect utility function for an individual in his lifetime which, after simplifying terms, becomes where � � 2� ln � � (1 + 2�) ln (1 + 2�).

4.1.6 Decision for Young Workers to Enter Licit or Illicit Sector Young individuals self select between the licit and the illicit sector. A young individual born in period t has to decide either to work in the licit sector or the illicit sector. If he chooses to work in the illicit sector, he enters drug tra¢ cking with probability "t , which yields illicit income Yt<sup>D, or common</sup> crime with probability 1 � "t, which yields illicit income Yt<sup>R</sup> stolen from licit workers. We assume that each type of illicit income is con...scated with the same probability qt and confronts the same penalty. Therefore the net expected illicit income becomes (1 � qt) �"tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> �.

A young worker chooses to work in the illicit sector rather than the licit one if and only if the indirect expected utility of the former activity is no less than the indirect utility of the latter Evaluating (7) at I = 1 and I = 0, canceling common terms and substituting for the wealth levels Wt<sup>1andW 0</sup> t<sup>,thisinequalityreducesto</sup> The threshold variable �<sup>b</sup> t is the moral cost such that a worker is indi¤erent between entering the licit or illicit sector of the economy. Condition (8) says that a worker with low enough moral cost (lower than threshold value<sup>b</sup> � t) would choose to work optimally in the illicit sector in period t, and otherwise would not. Note that<sup>b</sup> � t > 0 given that all variables involved are positive. Interestingly, the threshold value is decreasing in qt and wt yet increasing in �, Yt<sup>D,Y</sup> t<sup>R</sup> and � t. By assumption, individuals are heterogenous in the moral cost of entering the illicit sector such that there are two types � 2 ��; �<sup>�</sup> � where in each period of time there is fraction � 2 (0; 1) of the population that has parameter � = <u>�</u> while fraction 1 � � has parameter � = �<sup>�</sup> .<sup>6</sup> A su¢ cient condition for the existence

> 6 Ideally the heterogeneity would be a continuum such that the threshold type would determine whether a worker enters the licit or illicit sector, and changes in economic incentives would change the share of each in the population in a continuous manner. In this scenario individuals would not simply have either good or bad moral types but rather a more complex continuum of types ranging in moral cost. We use a simple binary set up for this heterogeneity to make the model tractable.

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of a positive fraction of illicit workers is that Yt<sup>e�(1 �qt)</sup> �"tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> � be su¢ ciently large such that �><sup>�</sup> �<sup>b</sup> t > <u>�</u> so that not all workers enter the illicit sector. In the section on the short run equilibrium we determine a su¢ cient condition for this to hold which then partitions young workers between illicit activities in period t given by L<sup>1</sup> t<sup>=Ht�andlicitactivitiesgivenbythecomplement</sup> L<sup>0</sup> t<sup>=Ht(1 ��)suchthatL1</sup> t<sup>+ L0</sup> t<sup>=Htforallt.Itisimportanttopointoutthatillicitactivities</sup> generate costs to the economy through the moral costs of young individuals that enter this sector and also generate a negative externality to licit households through crime.<sup>7</sup>

# 4.2 Licit Firms

Licit ...rms in the economy produce the licit good (C) using capital and licit labor. The capital used by ...rms in period t comes from asset holdings o¤ered as savings by adults in that period, which under perfect competition, is equal to the real interest rate it for each unit of capital. These ...rms operate in a perfectly competitive environment with perfect foresight and produce the licit good demanded by young and adult generations in period t through a Cobb-Douglas technology Xt = BKt<sup>�N 1</sup> t<sup>��</sup> where B > 0, � 2 (0; 1), K denotes capital and N denotes licit labor hired. Since the technology has constant returns to scale in capital and licit labor, then the representative ...rm produces Xt = HtCt for HtCt<sup>aadults and HtC</sup> t<sup>yyouths in the economy in period t.Under perfect competition the real cost</sup> of using a unit of physical capital is it and wt is the real wage. The representative ...rm maximizes pro...ts in a competitive environment taking as given the real interest rate and the real wage Perfect competition implies that licit ...rms have to satisfy the following ...rst order conditions We assume that licit labor is distributed between the real sector that produces the licit good and the government sector such that in either sector licit households earn wt. De...ne Pt � �tL<sup>0</sup> t<sup>,where</sup> �t 2 (0; 1), as the amount of licit labor hired by the government as policemen and judges in order to generate a detection and con...scation probability, while the complement Nt � (1 � �t) L<sup>0</sup> t<sup>isthe</sup> licit labor hired by licit ...rms. Moreover, de...ne capital per licit worker as kt �<sup><u>K</u></sup> L<sup>0</sup> t<sup><u>t</u>.Replacingthese</sup>

> 7 We do not model the disutility that crime generates to licit households besides the income they lose, for example due to the anxiety and fear it can generate in innocent victims. We do not think these utility costs are unimportant but rather choose to focus on the most simple set up in order to discuss the relevant issues concerning asset and money laundering. This approach, the standard approach in the economics of crime literature, is restrictive in this aspect but we believe it to be fruitful for our purposes.

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de...nitions in the ...rst order conditions yields Note that as the fraction �t of policemen and judges hired increases, then it decreases while wt increases.

# 4.3 Illicit Activities

There are two types of illicit activities: i) organizations that produce drugs (e.g. cocaine) in order to satisfy a foreign (exogenous) demand using a technology that is labor intensive and has positive but marginally decreasing returns; and ii) common crime activities that prey on licit workers in order to steal a fraction of their disposable wage after taxes. We assume that labor markets in this sector are segmented in the following way: illicit labor is allocated ...rst to the production of drugs in order to satisfy the exogenous foreign demand,and the rest of the supply of illicit labor is residually allocated to common criminal activities. Drug production is assumed to be more pro...table than common crime in every period.<sup>8</sup>

## 4.3.1 Drug Tra¢ cking

The main driver of the production of drugs is not a domestic market but overseas foreign markets. In particular, an economy like Colombia produces drugs mainly for export to other countries, specially to the United States and to Europe. For simplicity, we abstract from domestic drug demand and consider only that the exogenous foreign drug demand D<sup>e</sup> t motivates drug tra¢ cking in the domestic economy. Furthermore, we assume that the foreign price of drugs dt is determined by world markets where drug � tra¢ cking organizations produce drugs Dt with a technology that is labor intensive Dt = A lt<sup>1;D</sup> , � � the demand of illicit labor is denoted as lt<sup>1;D</sup> , and A > 0, � 2 (0; 1) are technological parameters. We assume that workers in this sector act as vendors and obtain a commission on total sales i.e. �tdtDt where �t 2 (0; 1) is the common sales commission.

Since all drug tra¢ cking organizations are assumed to be the same, consider a representative organization which is not subject to criminal predation by common criminals. Given that the production of drugs is realized to satisfy a foreign exogenous demand D<sup>e</sup> t, the technology implies that the demand for illicit labor in this sector is given by lt<sup>1;D</sup> = <u>DeAt</u> � which is perfectly inelastic. Moreover, total � �<sup><u>1</u></sup> revenue for the sector is given exogenously by dtD<sup>f</sup> t and, given that each drug tra¢ cker obtains �tdtD<sup>e</sup> t,

> 8 There is a huge literature on the "shadow economy" as an analytical concept that is measured using di¤erent estimation methods. We do not use this concept, because even though the production of illicit goods could be seen as pertaining to a "shadow economy" criminal activities that generate violence and predatory behavior should not be included in this concept. The nature of these criminal activities makes the concept of the shadow economy an inadequate term to use in our conceptual framework. A more reasonable term used would be "underground economy".

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Since both the quantity and the price are given for the representative organization, the common commission vt under an egalitarian income sharing rule is determined such that pro...ts are zero i.e. �<sup>D</sup> t<sup>= 0forallt.Henceweget��</sup> t<sup>=</sup> � DeAt � �<sup><u>1</u></sup> and income per illicit worker in this activity is given by Labor market segmentation is such that foreign demand for drugs determines the fraction of illicit labor hired into drug tra¢ cking. Therefore, the fraction of illicit households that work in this sector is e"t = min n1; H<sup>l</sup> <u>t</u><sup>1;D</sup> t� o. Under perfect foresight expectations, this corresponds to the probability that e an illicit household ...nds a "job" in the drug tra¢ cking sector i.e. "t = "t.<sup>9</sup>

# 4.3.2 Common Crime

The second type of illicit activity is common crime<sup>10</sup> that preys on licit workers<sup>11</sup> for pecuniary reasons. The representative criminal activity does not produce a good in the economy but generates a negative externality called robbery (R) and only uses illicit labor, denoted lt<sup>1;R</sup> . Total income from these activities is given by ITt<sup>R</sup> = Ht (1 � �) (1 � � t) �wt, where Ht (1 � �) represents the total number of licit workers in the population that earn disposable income (1 � � t) wt.<sup>12</sup> Hence, illicit workers in these activities obtain a fraction (1 � � t) �wt of licit workers’disposable income. Assuming that each

> 9 Even though pro...ts are zero which determines vt�<sup>ineachperiod,thisdoesnotcorrespondtoacompetitivesolution</sup> since illicit labor is not paid according to its marginal productivity based on a publicly known wage as in a competitive environment. Instead, it is paid according to an egalitarian income sharing rule based on average product. To see this, note that perfect competition would entail the following optimization problem

where $t would be the so called competitive illicit wage in the sector. Since the technology has decreasing returns in the only factor, pro...t would not necessarily be zero in a competitive equilibrium. Moreover, solving the problem would yield a standard demand for illicit labor given by The total supply of illicit labor is perfectly inelastic and is given by L<sup>1</sup> t<sup>=Ht�wherefractione"tHt�ofillicitworkers</sup> would work in drug tra¢ cking. Hence, equalizing demand and supply of illicit labor would yield $<sup>�</sup> t<sup>=</sup> (e"tH�dt�tA)<sup>1��.</sup> <u>1</u> Since our solution vt<sup>�=</sup> � DeAt � � is a sales commission then d$tD<sup>e�</sup> <u>t</u> t<sup>wouldbecomparablewithv</sup> t<sup>�.Notethat</sup> d$tD<sup>e�</sup> <u>t</u> t<sup>=v</sup> t<sup>�,</sup> showing that the solution derived above is not the solution under perfect competition. 10 This type of crime is composed of property crimes as well as violent crimes with a pecuniary motive like kidnaps, robbery, larceny, burglary and extortion.

> 11 For simplicity, we abstract from predation on illicit workers.

> 12 We are implicitly assuming that only young licit individuals are victims of crime since they are the licit workers in the economy that have labor income. Hence, common crime is assumed to prey on licit labor income and not capital income from assets.

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criminal has the same level of ability and so captures the same quantity of income from licit workers, illicit income from crime per worker is given by where the total number of illicit workers in these activities is given residually by lt<sup>1;R</sup> = Ht� (1 � "t) such that lt<sup>1;R</sup> + lt<sup>1;D</sup> = Ht� for all t. Note that Yt<sup>R</sup> is strictly decreasing in � since more workers in common crime activities yield less income per illicit worker.

As argued above, the expected (average) illicit income for a young individual when entering the illicit sector is given by Yt<sup>e�(1 �qt)</sup> �"tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> � where under perfect foresight the probability "t equals the fraction of illicit jobs available in drug tra¢ cking e"t while the complement 1 � "t equals the fraction of illicit "jobs" available in common crime activities 1 � e"t. Hence, Yt<sup>ecanbe</sup> thought of as the average illicit income a delinquent in the sector earns in period t. The segmentation of the labor market is consistent with rational choices of illicit workers under the su¢ cient assumption that Yt<sup>D</sup> > Yt<sup>R</sup> for all t and that demand for illicit labor in drug tra¢ cking is perfectly inelastic. Note that average real illicit undetected income is then which is strictly decreasing in �, � t and qt while strictly increasing in �, D<sup>e</sup> t and dt.

# 4.4 Government

The government has two functions in the economy. Its ...rst function is to generate a detection and con...scation probability qt of illicit incomes and its second is to provide a certain amount of public goods gt;t+1. The probability of detection and con...scation qt depends on a technology that hires licit workers and pays the same as licit ...rms while the amount of public goods gt;t+1 provided is determined jointly with qt. The government chooses these two levels in every period so as to maximize the social welfare function of licit households in period t, subject to a balanced budget constraint.

In order to do this, the government must also choose the licit income tax rate � t that determines part of its ...scal revenue. Though there are several ways to de...ne a social welfare function, we consider a simple utilitarian social welfare function of licit households which the government maximizes. To build this function we aggregate the indirect utility function (7) evaluated at I = 0 for all Ht (1 � �) licit households giving where the key assumption is that social welfare is only sensitive to the indirect utility of licit households.

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Let us build the revenue and expenditure functions for the government. In terms of cost, the government hires Pt � �tL<sup>0</sup> t<sup>workersatwagewtaspolicemenandjudgesinordertodetectand</sup> con...scate illicit incomes with the purpose of generating probability qt in the economy according to technology qt = � ~~q~~ HPtt<sup>,where�2(0; 1)isapositivee¢ciencyparameter.Thistechnologycaptures</sup> the intuitive idea that a greater number of law enforcement o¢ cers generates a greater marginal probability of detection and con...scation but with marginal decreasing returns.<sup>13</sup> Note that since L<sup>0</sup> t<sup>�Ht(1 ��)and�t2 (0; 1),replacingPt��tL0</sup> t<sup>inthetechnologyyieldsqt= �</sup> ~~p~~ �t (1 � �) which shows that qt 2 (0; 1) and that qt is a strictly increasing function of fraction �t and a decreasing one in �.

The government must choose Pt so as to minimize cost wtPt subject to <u>qt</u> = � ~~q~~ HPtt<sup>for a given level</sup> of <u>qt</u> 2 (0; 1) that is desired to be implemented. Since each licit worker is costly, to generate probability ~~2~~ <u>qt,</u> the government needs to hire P t =<sup>H</sup> �<sup><u>t</u></sup> <u>q</u><sup>2</sup> <u>t</u> workers. Hence, the cost function of generating <u>qt</u> is 2 given by<sup>Htw</sup> �<sup>2t</sup> <u>qt</u> which is an increasing convex function of wt and <u>qt,</u> as expected. Furthermore, the government provides a given level of public goods in the economy denoted as <u>gt;t+1,</u> which gives us the total expenditure function of the government The government’s ...scal revenue comes from income taxes paid by licit workers in the economy<sup>14</sup> i.e. Ht (1 � �) <u>�</u> twt, for a given level of taxes, <u>�</u> t 2 (0; 1), as well as the amount of illicit income con...scated from illicit workers i.e. Ht�qt �"tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> �. This gives total ...scal revenue as We assume that the government satis...es a balanced budget constraint in every period, R <u>(�</u> t; <u>qt)</u> = E <u>(qt; gt;t+1).</u> Therefore, in order to generate probability of con...scation qt, public good gt and tax rate level � t, the government solves the following problem Dft �1 Replacing the values for the term "tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> from equations (11), (12) and "t = <u>�</u> HAt�� yields "tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> =<sup><u>d</u></sup> H<sup><u>t</u></sup> <u>Dt</u><sup>e</sup> �t<sup>+</sup><sup><u>(1��</u>t)�</sup> �<sup><u>(1��)wt</u></sup> . Substituting into the balanced budget constraint and rearranging gives 13 Empirically one can think of there being di¤erent values of qt for each illicit activity on the grounds that society can have preferences for policy makers to target these two types of illicit activities di¤erently. However, for simplicity, in the theoretical part we consider qt to be unique in the problem that the government faces, which is equivalent to assuming that all illicit activities are targeted in the same way. We relax this assumption in the empirical section, considering di¤erent probabilities of detection and con...scation for the two types of illicit activity in the Colombian economy. 14 Note that the government does not charge income tax on capital earnings. For an economy like Colombia this assumption is reasonable since income tax comes mainly from labor and not from capital.

23
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found necessary and su¢ cient conditions for a solution (�<sup>�</sup> t<sup>; q</sup> t<sup>�) 2 [0; 1]2to problem (18).Nonetheless,</sup> the uniqueness of the solution is not guaranteed since the problem is non-linear and the objective function is not globally concave. In Appendix A we establish su¢ cient conditions for the uniqueness of the solution (�<sup>�</sup> t<sup>; q</sup> t<sup>�) 2 [0; 1]2toproblem(18).</sup> From equation (17) and the second equation of (19) the optimal (positive) level of public good provision chosen by the government is given by Note that gt;t<sup>�</sup> +1<sup>is positive and strictly increasing in q</sup> t<sup>�and ��</sup> t<sup>,given that these allow the government</sup> to increase its ...scal revenue. Moreover, gt;t<sup>�</sup> +1<sup>isstrictlydecreasingin�whichshowsthatthegreater</sup> fraction of workers dedicated to illicit activities in the economy, the more the provision of public goods in the economy deteriorates. Furthermore, from the technology to generate the probability of detection and con...scation we can determine �<sup>�</sup> t<sup>=</sup> �<sup>2</sup> (1qt<sup>�</sup> �<sup>2</sup> �)<sup>aswellasthenumberofworkershiredby</sup> the government as policemen and judges, Pt<sup>����</sup> t<sup>L0</sup> t<sup>.</sup> Finally, note that although we here assume that the government maximizes the utilitarian social welfare of licit households only, as in equation (13), the solutions would be the same if the government had maximized the social welfare of all workers de...ned as HtUt;t<sup>0</sup> +1<sup>i.e.as if all workers were dedicated</sup> to licit activities.

# 4.5 Capital Accumulation

The ...nancial system channels all savings from young individuals at the end of period t into the licit economy in order to match the investments of licit ...rms that expand the capital in period t + 1. To derive the equation for capital accumulation we follow the time line of Figure 1 and note that capital is the only asset in the economy, therefore aggregate bequests ht, that the adult generation gives the young generation at the end of period t, must equal net capital used, partly depreciated at the end of period t; plus the real interest that the capital generates where aggregate bequests in period t correspond to ht � Ht (1 � �) h<sup>0</sup> t<sup>+ Ht�h1</sup> t<sup>and�2 (0; 1)denotes</sup> the depreciation rate of capital. Moreover, aggregate wealth Wt at the end of period t, according to the time line, is composed of aggregate bequests (capital) plus aggregate labor income (licil and illicit) where aggregate wealth in period t is de...ned as Wt � Ht (1 � �) Wt<sup>0+ Ht�W 1</sup> t<sup>andaggregatelabor</sup> income is de...ned as Yt � Ht (1 � �) (1 � � t) (1 � �) wt + Ht�Yt<sup>e.Furthermore,accordingtothetime</sup> 25
line in Figure 1, wealth in assets after consumption at the end of period t is de...ned as where aggregate assets of licit and illicit origin correspond to the de...nition at � Ht (1 � �) a<sup>0</sup> t<sup>+Ht�a1</sup> t while aggregate consumption is de...ned as Ct � Ht (1 � �) Ct<sup>0;a</sup> + Ct<sup>0;y</sup> + Ht� Ct<sup>1;a</sup> + Ct<sup>1;y</sup> . h i h i Capital used for production of the licit good during period t + 1 must equal aggregate assets of licit and illicit origin at the end of period t Hence, replacing (24) in (25) and then replacing equations (22) and (23), we get which gives us a familiar equation for accumulation of capital where aggregate net investment de...ned as Kt+1 � (1 � �) Kt is equal to aggregate income minus consumption de...ned as Yt + itKt � Ct.

# 4.6 Short Run Equilibrium and Steady State

We do not de...ne a competitive equilibrium because illicit activities do not operate in a competitive environment. Instead we de...ne a short-run equilibrium with illicit activities for each period as a situation in which every agent chooses their corresponding control variables optimally such that workers self-select into licit and illicit activities when young, illicit labor markets are segmented while licit markets clear and prices and quantities are either determined outside the economy, say by world markets, or are determined as a function of capital per licit worker for each period. In Appendix A we show that there is a short-run equilibrium (not necessarily unique) with illicit activities for each period and a given level of capital per licit worker.

We de...ne a long-run equilibrium or steady state as a short-run equilibrium with illicit activities in which capital per licit worker is constant and positive over time i.e. kt = k > 0 for all t. From equation (25) and after replacing at � Ht (1 � �) a<sup>0</sup> t<sup>+ Ht�a1</sup> t<sup>andtheoptimallevelsofaI</sup> t<sup>forI= 0; 1</sup> from equation (6), we get where s (�) � 1+22��<sup>2(0; 1)isthemarginalpropensitytosaveoutoftotalwealth.Substitutingfor</sup> wealth levels using ht � Ht (1 � �) h<sup>0</sup> t<sup>+ Ht�h1</sup> t<sup>andequation(22)yields</sup> 26
Dividing both sides of this last equation by Ht+1 (1 � �), capital per licit worker is de...ned as kt � Ht(1K�t �)<sup>,andusingHt+1=(1 + n) Htforallt,wegetthefundamentalcapitalaccumulation</sup> equation in terms of kt Note that in a short-run equilibrium, the licit real wage (wt) and the real interest rate (it) are determined as functions of capital per licit worker by equation (9). Moreover, the optimal income tax rate (� t) is determined by equation (19), which is implicitly a function of the licit real wage, wt and the optimal detection and con...scation probability, qt<sup>��,whichisgivenbyanimplicitfunction</sup> qt<sup>��</sup> = q (kt; �t; �t�1) where �t�1 corresponds to predetermined variables in period t and constant parameters such that and where �t corresponds to variables exogenous variables that the government takes as given, i.e. �t � (Ht; dtD<sup>e</sup> t; �; �; �; �; �; �; �).

Hence, qt<sup>��</sup> is a function of kt and kt�1 which implies that �t = �(<sup>2</sup> <u>q(1t</u><sup>��</sup> �<sup><u>)</u></sup> �<sup>2</sup> )<sup>and �tare also functions of</sup> kt and kt�1. Furthermore, we have that Yt<sup>R</sup> �<sup><u>(1��</u></sup> �<sup>t</sup> (1<sup><u>)�</u></sup> �<sup><u>(1</u></sup> "<sup>�</sup> t)<sup><u>�)wt</u></sup> which shows that it is also a function of kt and kt�1 while "t and Yt<sup>D</sup> are independent variables of capital per licit worker. Finally, since h<sup>0</sup> t�1<sup>; �t�1</sup> and wt�1 are themselves functions of �t�2 � �(kt�2; �; �), by backward iteration it must be the case that they are functions of all values of k from k0 up to kt�1, which we denote as kt�1 = (kt�1; ::; k0). Hence equation (27) is a t order non-linear di¤erence equation in capital per licit worker. Importantly, the vector kt�1 directly a¤ects only qt<sup>��,�tand�tandtheseareallvariablesboundedintheinterval</sup> [0; 1], which is key to proving the existence of a steady state. The following proposition, which is proved Appendix A, establishes that the model has a long-run equilibrium or steady state (not necessarily unique).

Proposition 1 There is at least a steady state k > 0 that satis...es equation (27).

# 5 Comparative Statics

In this section we study the short-run e¤ects on aggregate savings, public good provision, and social welfare when the following parameters are changed: a) e¢ ciency in the technology of common criminals (�), b) price of drugs (d), c) e¢ ciency of the government to generate the probability of detection and 27
con...scation (�) and d) e¢ ciency of the licit sector to produce the licit good (B). We keep the optimal income tax ...xed in these short run comparative static exercises since we believe that in the short run income taxes are di¢ cult to change and would adjust slowly to any of the changes studied. The following table summarizes the main comparative e¤ects for these parameter changes in a short-run equilibrium with illicit activities which is shown to hold in the appendix.

|Variable|E¢ ciency of<br>common crime|International<br>drug cocaine|E¢ ciency of<br>government|Productivity of<br>private licit sector|
|---|---|---|---|---|
|Delinquent incentives|+|+|-|-|
|Aggregate savings|-|+|-|+|
|Public goods|+|+|+|+|
|Social welfare|-|+|+|+|
|||Table 1|||

In the following subsections we report the intuition for these comparative analysis results.

# 5.1 E¢ ciency of Common Crimes

An increase in the e¢ ciency of common crimes i.e. ��> 0 increases illicit incomes from these activities. It does not alter the allocation of illicit labor across both illicit activities given that production of cocaine is still assumed to be more pro...table for a young individual that opts to work in the illicit sector in a short run equilibrium. However it does increase in principle the potential incentives to enter the illicit sector because the average returns for young workers increase. We discuss "potential" e¤ects here rather than actual e¤ects because the binary moral cost set up, which simpli...es the analysis, has the restrictive nature of not allowing a smooth change in the fractions of licit and illicit workers. Though a "continuous" shift of workers from licit to illicit activities is not possible, the model allows for the possibility of a quantum change, from no illicit activity to some, and vice versa. An increase in the e¢ ciency of common crimes also increases the optimal probability of detection and con...scation which would in principle generate an ambiguous e¤ect for delinquent incentives. Nonetheless the more likely case is that the net e¤ect should be positive for a low level of the probability of detection and con...scation which seems the relevant case to consider. Illicit incomes from common crimes as well as average incomes in the whole illicit sector increase, while licit incomes decrease, generating a redistribution of income from licit to illicit households and since there are more licit households in the economy then the net e¤ect is a decrease in national savings (a¤ecting capital accumulation adversely in the next period). Furthermore, since a greater e¢ ciency of common crimes triggers an increase in the probability of detection and apprehension then there is an increase in public goods provided in the economy since this is ...nanced by con...scation of illegal incomes. Finally, the more likely case is that an increase in common crime e¢ ciency reduces social welfare since this is sensitive to the decrease in licit incomes in the economy which should more than compensate for the increase in public goods provided.

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# 5.2 Price of Cocaine

An increase in the price of cocaine, i.e. �dt > 0, which is determined by foreign markets, leads to an increase in illicit incomes from drug tra¢ cking. The increase in average illicit income would increase potential incentives for young workers to enter the illicit sector. Again the optimal probability of detection and con...scation is increased in this situation since it responds positively to an increase in dt which would in principle generate an ambiguous e¤ect on delinquent incentives. Again the more likely case to arise is a positive net e¤ect on delinquent incentives for economies with low levels of detection and con...scation. Furthermore, an increase in the price of illicit drugs would generate a type of Dutch disease, since an increase in dt is equivalent to increasing the relative price of the illicit good (cocaine) with respect to the price of the licit good which has been normalized to one. Hence, an increase in the relative price of drugs generates higher potential incentives that attract more labor resources into the ine¢ cient illicit sector deteriorating the labor resources for the licit sector. On the other hand public goods provided increase with dt since this change triggers an increase in the optimal probability of detection and con...scation and therefore more resources would the government have from illicit activities. Moreover, given that licit disposable incomes in a short run equilibrium are una¤ected with an increase in dt while illicit incomes from cocaine tra¢ cking are increased then national savings are increased with dt which bene...ts capital accumulation in the next period. Finally, social welfare is increased since licit households bene...t from the increase in public goods provided.

Note that a simultaneous increase in common crime e¢ ciency and the international price of cocaine would generate an ambiguous e¤ect on national savings which shows that money laundering in this model does not necessarily generate positive incentives for capital accumulation.

# 5.3 E¢ ciency of Government

An increase in the e¢ ciency of the government, i.e. ��, increases the optimal probability of detection and con...scation which decreases illicit incomes and therefore the delinquent incentives to enter the underground sector in the economy. Since public goods provision depends positively on the optimal probability of detection and con...scation then we would have an increase in the optimal level of public goods provision. Moreover, licit disposable incomes are una¤ected and since social welfare is increasing in the provision of public goods then social welfare would increase. Furthermore, aggregate savings would decrease since licit incomes are una¤ected, given that the government does not give back to households con...scated income, while illicit incomes are decreased.

# 5.4 Productivity of Licit Firms

An increase in the productivity of licit ...rms, i.e. �B, increases the wage in the economy and therefore of disposable licit incomes. It also generates a decrease in the optimal probability of detection and 29
con...scation since licit labor is more expensive and a larger polic force is less sustainable. Hence, ...scal revenue increases which then generates an overall increase in the provision of public goods. There is also an increase in both the licit disposable income and average illicit income which generates an increase in aggregate savings. Importantly, an increase in the e¢ ciency of licit ...rms deteriorates the potential incentives to enter the illicit sector, since licit wages are increased more than average illicit income is. The increase in disposable income as well as in the provision of public goods generates an increase in social welfare. This explains the signs reported in the table 1.

# 6 Macroeconometric Model

This section builds the macroeconometric model as a two equation system derived directly from the conceptual framework of the OLG model developed above. This macroeconometric model is built in order to estimate the volume of asset laundering in the Colombian economy in a given period of time. The ...rst equation in the macroeconometric model, called the transition equation, speci...es the dynamic nature of asset laundering activity in the economy in terms of its determinants. The second equation, called a measure equation, represents the mechanism through which accumulation of laundered assets a¤ects capital accumulation in the licit sector of the economy.

## 6.1 Transition and Measure Equations

As conceptualized in the OLG model developed above, asset laundering is the part of total capital that is placed and integrated into the licit economy and thus assists in the production of the licit good. Recall that by assumption young individuals inherit their moral type and capital as a bequest from their adult parent. This means that illicit adult parents bequest capital to their young children that was accumulated illicitly in the previous period during which the adult parent was a young illicit worker. Hence, bequests that come from illicit activities at the end of period t constitute the net stock of laundered assets, in the form of capital, after adjusting for partial depreciation at the end of period t and any return on it, measured by it where ALt denotes the stock of capital of illicit origin laundered by the end of period t, which is assumed to depreciate at the same rate � 2 (0; 1) as capital from licit sources. Wealth of illicit origin at the end of period t is composed of bequests (capital) from illicit activities plus illicit labor income while wealth in assets from illicit sources after consumption at the end of period t is de...ned as 30
where consumption by illicit households at the end of period t is Ct<sup>1�C</sup> t<sup>1;a</sup> + Ct<sup>1;y</sup> . Hence, the volume of assets laundered and used as licit capital for the production of the licit good during period t + 1 must equal aggregate assets of illicit origin plus the capitalization of these assets’return Hence, replacing (30) in (31) and then using equations (28) and (29) we get the transition equation of asset laundering lagged by one period where Ct<sup>1�C</sup> t<sup>1;a</sup> + Ct<sup>1;y</sup> and Yt<sup>e�(1 �qt)</sup> �"tYt<sup>D</sup> + (1 � "t) Yt<sup>R</sup> �. Asset laundering a¤ects the capital accumulation of the licit sector of the economy, which generates the mechanism through which the latent variable ALt a¤ects the accumulation of capital in the economy. Recall equation (26) that corresponds to the dynamic equation for the accumulation of capital where Yt represents the aggregate labor income (not including the returns to capital) from licit and illicit sources. Substituting Ht (1 � �) h<sup>0</sup> t<sup>+Ht�h1</sup> t<sup>=(1 + it��) Ktfromequation(22)into</sup> this last equation, using the de...nition Ht�h<sup>1</sup> t<sup>=(1 + it��) ALtfromequation(28)andreplacing</sup> Ht (1 � �) h<sup>0</sup> t<sup>= �(1 + it��) Ktforsome�2 (0; 1) ;wegetthefollowingmeasureequationwhichwe</sup> lag by one period The intuition for this equation is simple in that the capital stock in period t is a function of the capital stock in period t�1, which corresponds to the licit part and its net return � (1 � � + it�1) Kt�1, plus illicit capital laundered plus its net return (1 � � + it�1) ALt�1, plus the aggregate savings in the economy (licit and illicit) which correspond to Yt�1 � Ct�1.

# 6.2 Linear Equation System

The empirical model to be constructed follows from the two linear equations (32) and (33). We assume that Ct<sup>1</sup> �1<sup>= (1 �s (�)) Y</sup> t<sup>e</sup> �1<sup>,i.e.thatillicitconsumptionofthelicitgoodC</sup> t<sup>1</sup> �1<sup>isequaltoafraction</sup> of illicit undetected income Yt<sup>e</sup> �1<sup>.Sinceillicityoungworkershavethesamepreferencesaslicityoung</sup> workers, this fraction is the marginal propensity to consume 1 � s (�), where s (�) = 1+22��<sup>.This</sup> method is used because the consumption of illicit households is not directly observable. Substituting these into the transition equation (32) and rearranging common terms yields the following transition equation 31
Note that assets laundered (AL) is lagged in the measure equation (33) which complicates the estimation process we use later on. To avoid this, we substitute for ALt�1 (1 + it�1 � �) in (33) using (1 + it�1 � �) ALt�1 = ALt � s (�) Ht�1�Yt<sup>e</sup> �1<sup>fromthetransitionequation(34),yieldinganequation</sup> with ALt in period t as the key unobservable to estimate We also replace in this last equation the de...nition of aggregate labor income which yields, after rearranging terms In order to obtain an estimable linear system, we must de...ne measures of theoretical variables and assume values for some parameters. In what follows we present the empirical variables used to approximate the theoretical counterparts involved in the linear system in equations (34) and (35).

# 7 Data

The period of analysis for the empirical section is 1985 to 2013, during which we observe variables at an annual frequency for the Colombian economy. Several of the empirical variables needed for the estimation, however, are not directly observable, particularly those related to illicit activities. The structural equations (34) and (35) suggest a way to create these variables using observable ones.

Firstly, we observe the amount of cocaine con...scated by Colombian authorities and estimate the aggregate amount of projected cocaine production every year for the Colombian economy. The estimated projected production of cocaine is a proxy variable for actual production, based on a measure of the land size used to grow coca. From this, we obtain an estimate of the probability of detection and con...scation of cocaine for period t We assume in the case of cocaine production that once it is detected by law enforcement authorities, no illicit income is generated from it, which is consistent with the idea that cocaine production is destroyed once it is detected.

32
Overall illicit income earned by drug lords in Colombia from cocaine tra¢ cking can be estimated using the estimated projected production and price of cocaine. The relevant cocaine price however is not clear, as local prices of cocaine are quite low while international prices from the United States during the period of study are too high. Caulkins and Reuter (2010) report cocaine prices from raw production in Colombia up to the retail prices in the United States for the years 1997, 2000 and 2007. They note that the export cocaine price in the ports of Colombia is around one-third of the mid-level wholesale price reported in the United States while the import cocaine price in the ports of the United States corresponds roughly to two-thirds of the mid-level wholesale price reported inside the United States. Assuming that somewhere between the ports of Colombia and the United States, Colombian drug lords deliver their production to others that continue the tra¢ cking in the United States, the cocaine price relevant for estimating the illicit income of Colombian drug lords would be between these two bounds. Accordingly, we use a price of half the mid-level wholesale cocaine price per kilogram reported for the United States by UNODC, as in the following measure Note that we use the consumer price index with base year 2005 to get illicit aggregate income from cocaine tra¢ cking in pesos in real terms. Hence, the aggregate real undetected illicit income from cocaine production per year RUICOCt is given by the following proxy variable Similarly, we do not observe total potential income from common crimes but only income from reported crimes. We use National Police Department statistics for the period under study on the income stolen through common crimes against property which includes 56 o¤enses, such as robbery, theft, burglary, motor vehicle theft, larceny etc., and excludes drug tra¢ cking from aggregate values. This allows us to obtain the following measure of reported income stolen where �tqt measures the probability of detection and con...scation of income from common crimes for some �t > 0. This re‡ects the idea that empirically (though not in the theoretical model, where qt is determined to be the same for both illicit sectors) the probability of detection and con...scation of income from cocaine can be di¤erent than for common crimes.

Importantly, this empirical variable only includes reported crimes while we also need to consider undetected crimes. To adjust these values we must take into account the reporting rates for these types of crimes. According to Soares (2004a, 2004b) there is a huge di¤erence between o¢ cial statistics on 33
~~(~~ --) ~~(;~~ -) ~~(-~~ - ) ~~(~~ -) ( ~~C~~ -) ~~G-~~ ))

-( ~~C~~ -) ~~G-~~ ))
We use reported Colombian GDP in constant 2005 pesos as a proxy for licit aggregate income that includes both private as well as public income (RGDP ) in the following way We also use an estimate of aggregate real consumption in the Colombian economy, an observable quantity, obtained from National accounts We use a measure of the real stock of capital (KS) for the Colombian economy, for which more than one estimate is available. We use the measure of real aggregate capital stock in each period from the Departamento Administrativo Nacional de Estadísticas (DANE), Colombia’s National Bureau of Statistics Finally, for our calibration measure of laundered assets we use the real interest rate which can be obtained by using the Fisher identity which says that the real interest rate (RIR) plus one is equal to the nominal interest rate plus one divided by the in‡ation rate plus one, yielding the following measure All of the data used were collected by the Unidad de Información y Análisis Financiero (UIAF) from September 2013 to March 2014.<sup>18</sup> All macroeconomic time series come from o¢ cial sources, mainly from the Banco de la República of Colombia, National Bureau of Statistics DANE, National O¢ ce of Taxes and Customs DIAN, National Planning Department DNP and Treasury Department. Data on crimes and drugs come from the Ministry of Defense, National Police Department, National Institute of Prisons INPEC, United Nations O¢ ce on Drugs and Crime UNODC, Ministry of Justice and the District Attorney’s O¢ ce. Although the data were initially to be collected quarterly for the period 1999 to 2013, data limitations made this unfeasible. Hence, data were collected at an annual frequency for 1985 to 2013, which a¤ected the size of the time series. Not all of the data collected were used since the theoretical model guided the ...nal data necessary for the application of the estimation methods. Descriptive statistics for the variables used in the estimation are reported in Table 2.

> 18 We thank the support of the Director of the UIAF Luis Edmundo Suárez and deputy director Javier Gutiérrez. We also thank especially Angela Hurtado from the UIAF for her superb assistance in constructing the data set used in this article. The UIAF did an excellent job in ...nding the best data available for the development of the empirical part of this project and assisted us in selecting the necessary information to construct the main time series required at the annual frequency and to obtain the relevant literature on asset laundering from national and international sources.

35
<!-- Start of picture text --> 14%<br>12%<br>:A<br>8% :: A\/ —RUII/ real GDP<br>: tet ++++ RUICOC/ real GDP<br>6% : y = -RUIC/real GDP<br>= Soy<br>4% SDVn<br>2% + > , ma,<br>we. wort tan YN o e-< -—_ -. 4 ---—-+ s Pom Lote,~~ eT.<br>0%<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text -->
<!-- Start of picture text --> 3.50<br>2.50<br>—real KS / real GDP<br>2.00<br>1.50<br>1.00<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text -->
i) calibration and ii) Kalman ...lter with an optimizing algorithm. The ...rst method relies on the transition equation while the second takes both the transition and the measure equation into account.

# 8.1 Estimable Linear System

The proxy variables de...ned in the previous section can be used to construct a macroeconometric estimable linear system with error forms for the structural equations (34) and (35). The error form of the equations comes from noting that the observable variables used in the structural equations are given at the country level and thus, may include aggregated measurement errors. This implies a stochastic error term in the macroeconometric linear system given that we must assume the existence of conditional distributions of the dependent variables with respect to the conditioning independent variables such that all variables have ...nite ...rst and second moments, which yields for t = 1985; :::; 2013. Reduced form parameters are de...ned in terms of deep structural parameters The errors u<sup>AL</sup> t and u<sup>K</sup> t of equations (44) and (45) are de...ned as where is the conditioning vector of variables in the measure equation and the homoskedastic variances of the two equations are denoted as �<sup>2</sup> AL<sup>and�2</sup> K<sup>.Thede...nitionoftheerrorsre‡ectstheassumptionthat</sup> we have a complete set of conditioning variables such that no omitted relevant variable problem arises in the linear equation system.

38
# 8.2 Calibration Method

First we use the transition equation in equation (34), calibrate the parameters s (�) and � and use the variables RUIIt�1 and RIRt�1 from equations (39) and (43) as proxy variables for �Ht�1Yt<sup>e</sup> �1<sup>and</sup> it�1 respectively. The marginal propensity to save out of income for Colombia is around 0:17. This value is obtained by regressing aggregate real consumption on real GDP (both in 2005 pesos) and a constant, which yields a marginal propensity to save of 0:83. Under log utility speci...cation, which we use in the theoretical part, the complement 1 � 0:83 = 0:17 is an estimate of the marginal propensity to save out of income. Assuming that this is equal to the theoretical marginal propensity to save out of wealth, we ...nd that s (�) = 0:17. The depreciation rate is assumed to be � = 0:05, as is standard in the growth literature. To implement the calibration method we need an initial value of the capital stock laundered for t � 1 = 1984. According to UNODC (2011), 75% of illicit undetected income enters the licit economy as laundered assets. This belief is supported to an extent by the UIAF of Colombia (see UIAF, 2014). On this basis we assume that 75% of average illicit income from 1984 to 1988 relative to average licit income in the same period is proportional to assets laundered in 1984 relative to the capital stock of the economy averaged from 1984 to 1988. Hence, a simple estimate of total illicit capital laundered is given by the following equation which assumes that AL0 is proportional to average KS. Recall that in the theoretical model periods correspond to generations, thus covering 20-30 years and that the way illicit income is laundered in capital investments is through bequests from parents to their o¤spring. The model assumes that after 30 years there is no con...scation of assets even if their illicit origins have been detected. However, in 1996, a judicial reform in Colombia gave law enforcement authorities the ability to con...scate assets that were laundered years before. Thus, since yearly data is available, we allow for con...scation of assets laundered in previous periods in the empirical estimation of assets laundered and take this into account in the empirical calibration.

For 2010 to 2014, we observe the amount of laundered assets con...scated by Colombian authorities. Nonetheless, we do not observe this amount from 1996 to 2009, despite this being after the judicial reform of 1996. For this time period, we assume that the volume of con...scated assets is proportional to illicit income RUII in each period where �t is equal to zero from 1985 to 1997, given that the 1996 judicial reform was not implemented until 1997. After that year, we assume that �t grows at the same rate as the probability of detection 39
and con...scation of cocaine from equation (36), which can be seen as a proxy of gains in the e¢ ciency of law enforcement authorities. The ...nal value of �t for 2013 is found using the average amount of assets con...scated in the Colombian economy from 2010 to 2014, an observable quantity, divided by the average illicit income from cocaine and common crime, as in the RUII measure of equation (39), e giving �2013 = 0:2. We then work backwards using the growth rate of qt from 1997 to 2013 to impute the values of the fraction of assets con...scated by Colombian authorities between 1998 and 2012.

The calibrated transition equation comes from equation (34) where we replace the depreciation rate and the marginal propensity to save and subtract the assets con...scated by Colombian authorities after 1997. This gives us the following dynamic equation for aggregate asset laundering Substituting equation (48) into this last equation and regrouping terms we get where 11998 is an indicator variable that takes the value one for 1998 onwards and zero otherwise.

This equation is similar to a perpetual inventory equation for capital accumulation of the form Kt = (1 � �) Kt�1 + It where It denotes gross investment in period t while Kt is the capital stock. Assets laundered depreciate at the same rate as licit capital which is similar to the term (1 � �) Kt�1 while the term It is equal to the amount of income generated from illicit assets laundered RIRt�1ALt�1 plus the term �0:17 � �t�1 � 11998� � RUIIt�1 that represents the amount of undetected illicit income saved by illicit households in the economy in period t � 1 and which enters the licit economy in period t, increasing the laundered capital stock in that period.

We can also obtain a decomposition of assets laundered from undetected income from cocaine and from common crime using equation (49) and replacing total illicit undetected income RUIIt with the variables RUICOCt or RUICt from equations (37) and (38) respectively and assuming that �t is the same for both types of illicit activities.

Calibration in itself is closely attached to theoretical deep structural parameters of a given model and since ALt is an unobservable quantity we cannot check whether the calibration works in the sense of reproducing an observed time series. Nonetheless it has the appeal of being consistent with the theory and can give us a trajectory consistent with the fundamentals of the Colombian economy.

# 8.3 Kalman Filter

The empirical methodology of the Kalman ...lter uses not only the transition equation (44) but also the measure equation (45) based on a state-space time invariant representation. In what follows we 40
present the state-space representation that is used in this empirical method following the literature on time series as in Harvey (1994), Hamilton (1995), Engle and McFadden (1999) and Durbin and Koopman (2005). The state-space representation of the system consists of the transition equation which can be written using the standard matrix notation in this literature e for t = 1985; ::; 2013, where �t = ALt, Wt = [RUIIt�1], �t = u<sup>AL</sup> t , T = �2 and � = �1 under the restriction that the intercept is zero according to the theoretical model, with E (�t) = 0 and variance �� = �<sup>2</sup> AL<sup>.Themeasureequationcanberepresentedasthefollowingstate-spacerepresentationfor</sup> t = 1985; ::; 2013 in its standard notation in the literature, following Harvey (1994) where the indicator variable is Yt = KSt, the explanatory variables are denoted as according to equation (45) and the parameters are de...ned as Z = [�5] and where the stochastic variable "t = �u<sup>K</sup> t � is such that E ("t) is a constant and the variance is given by �" = ��<sup>2</sup> K�. Note that in the estimation method of the Kalman ...lter we impose the following restrictions according to de...nitions in equation (46): �0 = �0 = 0 and �3 = �1. With these three restrictions and 29 observations for the period 1985 to 2013 we have only 8 parameters to estimate which gives us at least 21 degrees of freedom. We use the same initial value A0 for AL1984 as in equation (47). The initial values for the parameters T , �, Z and � were obtained by peforming 1200 replications of uniform distributions on intervals that corresponded to the theoretical values expected. In Appendix B we describe the recursive optimizing algorithm that is used in combination with the Kalman ...lter to estimate the system of equations (50) and (51).

# 9 Empirical Results

In this section we report the main trajectories for the key unobservable ALt for the two di¤erent methods used to estimate this stock for the Colombian economy from 1985 to 2013.

41
<!-- Start of picture text --> 60,000<br>50,000<br>40,000 —AL calibrated from Aggregate Illegal<br>Income (billion pesos of 2005)<br>30,000 Bs 5 a Sa tes ve, +++» ALpesos calibratedof 2005) from Cocaine (billion<br>oy = -AL calibrated from Common Crime<br>20,000 . =~o 7 == --—. (biilion of pesos 2005)<br>“ ee<br>Bid a cm<br>= Pe<br>LOjOOO «fae<br>- wee<br>()<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text -->
<!-- Start of picture text --> 6.0%<br>-4.0%a —AL calibrated / KS<br>3.0%aa ae 7 eatbracacseanet®<br>: we = -AL calibrated Common<br>OA on 7 os *, Crime/ KS<br>2.0% . oa _ -—- ~~ “ee, =<br>- --- petra t aa "ee<br>- °° Poe ~ ~<br>aeot® eee? ~- ~<br>1.0% =<br>0.0%<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br>20%<br>- OS<br>-14%12%aKN —AL calibrated Aggregate Illegal<br>10%Ynpe income. / reer eor<br>- re +++» AL calibrated Illegal Income<br>: “He from Cocaine / real GDP<br>8% +7 ne mae<br>woe . *s, = AL calibrated Illegal Income<br>6% pte A as tty, from Common Crime/ real<br>ee a GDP<br>- ~<br>4% = a<br>wenenene® ~ ~<br>2%<br>0%<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text -->
# 9.2 Kalman Filter Results

The Kalman ...lter estimates of the transition and measure equations in (44) and (45) with initial condition (47) are the following, based on 1,200 replications for t = 1985; ::; 2013: where the optimizing procedure converges more than 90% of the time in the 1,200 replications. Recall that the only restrictions imposed in the estimation procedure was that the coe¢ cient associated with RCONS be ...xed at �1 and zero values for the intercepts.

All of the estimated coe¢ cients of the Kalman ...lter are positive, which is consistent with the structural deep parameter values in equation (46). In terms of magnitudes, the results are consistent with the theory since the values of the estimated coe¢ cients are quite close to the expected theoretical values. For example, in equation (44) the parameter �2 associated with ALt�1 should theoretically be close to a value just less than one, corresponding to values of the depreciation rate and the expected real interest rate in (46). The value obtained using the Kalman ...lter is 0:951. Furthermore, the structural model predicts that the parameter �5 associated to ALt in the measure equation (45) should be equal to 1. The Kalman ...lter obtains the value 1:1974, also quite close to the expected theoretical value. Finally, the coe¢ cient �2 in the measure equation (45) is expected to be less than one. The Kalman ...lter obtains the value 1:083 ,which is slightly larger than one. So overall the signs and magnitudes of the reduced form parameters are close to the expected theoretical structural counterparts.

The magnitude of the coe¢ cients associated with RUII in the transition equation and the measure equations are quite interesting. On the one hand, the coe¢ cient in the transition equation is 0:1458, which is quite close to 0:17, the calibrated coe¢ cient associated with this variable in equation (49). On the other hand, the coe¢ cient associated with RUII in the measure equation is rather low, 0:0084. This shows that RUII is not a strong determinant of the capital stock of the Colombian economy yet does strongly a¤ect the accumulation of laundered assets.

44
<!-- Start of picture text --> 45,000<br>40,000<br>—ee a<br>—25,000iY ae<br>— AL Kalman (billions of<br>2005 pesos)<br>— UE<br>10,000<br>5,000<br>()<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text --> <!-- Start of picture text --> 12.0%<br>-rr AN<br>/ ~ UY<br>6.0% —AL Kalman / real GDP<br>== AL Kalman / KS<br>4.0%<br>¢poetttt tenn e_ -<br>_- o” we. ~.,<br>2.0% mewn wee wee w ewe<br>0.0%<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text -->
<!-- Start of picture text --> 50,000<br>45,000<br>40,000 aN<br>~YS<br>25,00020,000 PF US —ALFilter (billions average calibrated of pesos 2005)and Kalman<br>10,000<br>5,000<br>0<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2008 2005 2007 2009 2011 2013<br><!-- End of picture text -->
<!-- Start of picture text --> 16%<br>14% 7 <<br>77 x.<br>, \<br>12%<br>‘N<br>/ ~ eA.<br>7 N<br>10%<br>¢ ‘XN<br>7 Ny = -AL average calibrated and<br>2% i a ~ Kalman filter/ real GDP<br>—— — AL (calibrated and Kalman<br>6% averaged)ged) // KS<br>4% |, Si<br>2%<br>0%<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013<br><!-- End of picture text -->
illicit income behind them constitutes the process of asset laundering.

Using the model, we perform some comparative statics to trace the e¤ects of exogenous changes in the “e¢ ciency”of common crime, the price of cocaine, the e¢ ciency of the government in ...ghting crime, and the productivity of licit ...rms. The summarized results are as follows: a) “E¢ ciency”of common crime: an increase in the “e¢ ciency”of common crime increases illicit income from this activity, without altering the allocation of illicit labor across the two types of illicit activity given that production of illicit drugs is assumed to be more pro...table. The increase in the e¢ ciency of common crimes generates an increase in expected illicit income, which increases the potential incentives for young people to enter the illicit sector. Moreover, it generates a redistribution of income from licit to illicit agents, has a negative e¤ect on capital accumulation as it decreases the incentives to save and has a negative e¤ect on the level of public goods provided by the government reducing overall social welfare.

b) Price of illicit drugs: an increase in the price of illicit drugs increases illicit income from drug tra¢ cking. The increase in average illicit incomes increases the potential incentives to enter the illicit sector. It has an ambiguous impact on capital accumulation, positive through asset laundering but negative through the disincentive to save due to common crime. An increase in the price of illicit drugs generates a type of Dutch disease since it increases the relative price of the illicit good (cocaine) with respect to the price of the licit good which generates potential incentives that attract more labor resources to enter the ine¢ cient illicit sector, thus deteriorating potential labor resources available to the e¢ cient licit sector.

c) Government e¢ ciency: an improvement in government e¢ ciency increases the probability of detection and con...scation while allowing a decrease in the optimal tax rate. Under certain conditions, the level of public goods increases since the additional revenue from the con...scation of illicit income compensates for the decline in tax revenue. Moreover, social welfare improves since both disposable licit income and public goods provided increase in the economy. Furthermore, aggregate savings increase since the increase in licit disposable income more than compensates for the decrease in illicit income. Finally, the improvement of government e¢ ciency does not alter the allocation of labor across the two illicit activities but decreases the potential incentives to enter the illicit sector for young workers.

d) Productivity of licit ...rms: an improvement in the productivity of licit ...rms generates an increase in licit wages, which turns into higher disposable licit income even though the optimal income tax rate rises. This creates higher incentives for licit rather than illicit activities. Moreover the provision of public goods increases as do aggregate savings and capital accumulation leading to an improvement in social welfare.

Overall, the e¤ects of asset laundering on savings and social welfare are ambiguous. If asset 48
laundering comes mainly from drug tra¢ cking, then it may have a positive e¤ect on aggregate savings and social welfare in the economy, while if it comes mainly form common crime then it has a clear negative e¤ect on aggregate savings and social welfare. Hence, the common belief of some economists that asset laundering activities are always good for economic growth does not hold. On the other hand the opposite belief of some regulators that consider asset laundering activities to be always harmful for social welfare is also not always the case.

On the empirical contribution of the paper, we generate estimates of the size of illicit income for cocaine exports and common crime and provide simulated and econometric estimates of asset laundering in the Colombian economy. For this purpose, a macroeconometric speci...cation is derived from the theoretical model described above.

An important contribution is the development of a data set for this purpose, in which the key components are estimates of illicit income from drug tra¢ cking and common crime. Illicit income from drug tra¢ cking is calculated as the volume of cocaine production (from UNODC) times the average of the point-of-export and US point-of-import price of the drug, minus the portion con...scated by the authorities. Income from common crime is computed as the value of reported property crime (from police sources), adjusting by the rates of o¢ cial underreporting.

Estimates of the volume of laundered assets in the Colombian economy in the period 1985 to 2013 are developed using two empirical methodologies. These methodologies are based on a macroeconomic system of equations that is derived directly from the theoretical model. The system includes two equations. The ...rst is a “transition” equation that speci...es the dynamic nature of asset laundering in the economy in terms of its determinants and the second is a “measurement”equation that represents the mechanism through which asset laundering a¤ects the capital stock of the economy. The methodologies used are: i) a calibration based on a parameterization of the transition equation and ii) a Kalman ...lter method based on both the transition and the measurement equation.

The estimates of illicit income, money laundering, and laundered assets are reasonable according to the history of Colombia and are consistent with the dominant role cocaine tra¢ cking played in the 1990s in the country until the implementation of Plan Colombia in the early years of the new century. Figure 12 presents a summary of the results.

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<!-- Start of picture text --> 16%<br>14% poe<br>| ‘.<br>. \ --***Income from Drug<br>12% Trafficking/GDP<br>10% - : .‘ [ - ~ : x ‘N<br>8% -' 7's. = Crime/GDP<br>6%<br>:<br>2% = SS arr — - Stock of Laundered<br>Berm maw’. Vee ~ oom lee<br>mee set” - alee 7 - Stipes Assets/GDP<br>0%<br>1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 # £2013<br><!-- End of picture text -->