Bulletin of Narcotics 1,2-2008

7/29/2019 Bulletin of Narcotics 1,2-2008

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Volume LX, 2008

Measurement issues indrug policy analysis


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UNITED NATIONS OFFICE ON DRUGS AND CRIME

Vienna

BULLETINON

NARCOTICSVolume LX, 2008

Measurement issues in

drug policy analysis

Selected papers from the Third Annual Conferenceof the International Society for theStudy of Drug Policy, held in Vienna

on 2 and 3 March 2009

UNITED NATIONSNew York, 2011


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Sandeep Chawla, Editor

United Nations Ofce on Drugs and CrimeVienna International Centre

PO Box 5001400 Vienna, Austria

Telephone: (+43-1) 26060-0Fax: (+43-1) 26060-5866

The Bulletin on Narcotics is available fromwww.unodc.org/unodc/en/data-and-analysis/Journals.html

The Ofce for Drug Control and Crime Prevention became the United NationsOfce on Drugs and Crime (UNODC) on 1 October 2002. UNODC includes the

United Nations International Drug Control Programme.

United Nations, February 2011. All rights reserved.

The views expressed in signed articles are those of the authors and do notnecessarily reect the views of the United Nations Secretariat.

The designations employed and the presentation of the material in thispublication do not imply the expression of any opinion whatsoever on the

part of the Secretariat concerning the legal status of any country,territory, city or area, or its authorities, or concerning the delimitation

of any frontiers or boundaries.

Publishing production: English, Publishing and Library Section,United Nations Ofce at Vienna.

UNITED NATIONS PUBLICATION

Sales No. E.11.XI.6

ISBN 978-92-1-148261-4

ISSN 0007-523X


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iii

PREFACE

The Bulletin on Narcotics is a United Nations journal that has been in continu-

ous publication since 1949. It is printed in all six ofcial languages o the

United NationsArabic, Chinese, English, French, Russian and Spanish.

The Bulletin provides inormation on developments in drug control at the

local, national, regional and international levels that can be o beneft to the

international community.

The present issue o the Bulletin, whose guest editor is Martin Bouchard

o Simon Fraser University in Canada, is ocused on measurement issues in

drug policy analysis. It consists o a selection o papers presented at the Third

Annual Conerence o the International Society or the Study o Drug Policy,

held in Vienna on 2 and 3 March 2009.

The United Nations Ofce on Drugs and Crime wishes to thank Melissa

Tullis o the Division or Policy Analysis and Public Aairs and Raggie Johanseno the Studies and Threat Analysis Section or editorial assistance in preparing

this issue.


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iv

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v

Reprints, purchases and subscriptions

All issues o the Bulletin on Narcotics (rom vol. I, No. 1 (1949), to the present issue)

are available on the website o the United Nations Ofce on Drugs and Crime

(http://www.unodc.org/unodc/en/data-and-analysis/bulletin/index.html).

The ollowing special issues o the Bulletin are also available as United Nations

publications:

1993

Policy issues relating to drug abuse and the human immunodefciency virus (HIV)

(vol. XLV, No. 1)

Drug testing in the workplace (vol. XLV, No. 2)

1994

The amily and drug abuse (vol. XLVI, No. 1)

Special issue on gender and drug abuse (vol. XLVII, Nos. 1 and 2)

1996

Special issue on rapid assessment o drug abuse (vol. XLVIII, Nos. 1 and 2)

1997 and 1998

Double issue on cannabis: recent developments (vol. XLIX, Nos. 1 and 2, and vol. L,

Nos. 1 and 2)

1999

Occasional papers (vol. LI, Nos. 1 and 2)

2000

Economic and social costs o substance abuse (vol. LII, Nos. 1 and 2)

2001

Dynamic drug policy: understanding and controlling drug epidemics (vol. LIII, Nos. 1

and 2)

2002

The science o drug abuse epidemiology (vol. LIV, Nos. 1 and 2)

2003

The practice o drug abuse epidemiology (vol. LV, Nos. 1 and 2)


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vi

2004

Illicit drug markets (vol. LVI, Nos. 1 and 2)

2005

Science in drug control: the role o laboratory and scientifc expertise (vol. LVII, Nos. 1

and 2)

2006

Review o the world cannabis situation (vol. LVIII, Nos. 1 and 2))

2007

A century o international drug control (vol. LIX, Nos. 1 and 2)

Requests or permission to reprint signed material should be addressed to the

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vii

CONTENTS

Page

Preace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Editorial: measurement issues in drug policy analysisby M. Bouchard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Capture-recapture methods to estimate prevalence indicators or the

evaluation o drug policiesby F. Mascioli and C. Rossi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Studies on public drug expenditure in Europe: possibilities and limitations

by F. Vander Laenen, L. Vandam and B. De Ruyver. . . . . . . . . . . . . . . . . . 27

Measuring the benefts o drug law enorcement: the development o theAustralian Federal Police Drug Harm Index

by R. Attewell and M. McFadden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 The association between the number o days o methamphetamine useand the level o earnings rom acquisitive crime among police detaineesin New Zealand

by C. Wilkins and P. Sweetsur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Modelling disorganized crime: the cannabis market

by C. Costa Storti and P. De Grauwe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79


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1

Editorial: measurement issues in drug policy analysis*

Martin bouchard

Assistant Professor, School of Criminology, Simon Fraser University, Canada

I am pleased to introduce this special issue o the Bulletin on Narcotics, which

consists o selected papers rom the Third Annual Conerence o the InternationalSociety or the Study o Drug Policy (ISSDP), held in Vienna on 2 and 3 March2009. The organizers o the ISSDP conerences have always insisted on using thistype o publication as a way to disseminate the important work on drug policythat is presented at their meetings, but also to keep stimulating policy researcho the highest standards. Selected papers rom the frst two conerences have beenpublished in Contemporary Drug Problems (vol. 35 (2/3), 2008) and the Inter-national Journal of Drug Policy (vol. 20 (6), 2009).

The publication o these special issues represents a unique opportunity to takethe pulse o the feld, and this issue o the Bulletin is no exception. While thenumber o research articles selected is relatively small, each one is a prime exam-ple o the quality and diversity o research presented at ISSDP conerences. Forexample, the collection o articles included in this issue contributes to understand-ing the connections between drugs and crime (Wilkins and Sweetsur), the (dis)organization o drug markets (Costa Storti and De Grauwe), the issue o publicexpenditures (Vander Laenen, Vandam and De Ruyver) and drug use prevalencein the evaluation o drug policy (Mascioli and Rossi), as well as to the develop-ment o drug harm indexes (Attewell and McFadden), an issue that has been theobject o a special workshop in Vienna. Although this collection o articles frstand oremost illustrates the variety o approaches taken in the analysis o drugpolicy, all authors share a concern or improving the measures and indicatorsavailable to do so. This interest in measurement issues is arguably one o the mostimportant actors or the uture o the feld.

The special issue opens with Mascioli and Rossis article (Capture-recapturemethods to estimate prevalence indicators or the evaluation o drug policies) onthe measurement o the prevalence o drug users in Italy. The authors make use ocapture-recapture methods, which have been shown to provide valid measurements

*The author would like to express his sincere gratitude to Melissa Tullis and Peter Reuter or theirgenerous contributions, and to the reviewers without whom this special issue would not have beenpossible.


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2 Bulletin onNarcotics, vol. LX, 2008

o populations o drug users in a variety o contexts and settings, and innovate overprevious studies in a number o ways. First, they use a single data set comprisingall individual drug users identifed by the Italian police in 2007, avoidingthe problem o matching records ound in multiple data set capture-recapture

studies. Second, they estimate prevalence rom three dierent methods (allwith slightly dierent assumptions), allowing or a proper triangulation o results.Third, they provide separate estimates or males and emales and or eightdierent age groups, including adolescents. They fnd that the prevalence ratesare highest or the 20-24 and 25-29 age groups, but that the capture andrecapture rates are highest or adolescent users. In other words, adolescent usersare detected and registered at a higher rate than users in other age groups.Because these estimates were derived rom police records, these results are oheightened importance or policymakers.

By analysing the concept o public expenditures, the second article, byVander and others (Studies on public drug expenditure in Europe: possibilitiesand limitations), raises the issue o measurement on the government side,examining how and how much public authorities actually spend on drug policy.The authors frst make the important distinction between public (directexpenditures by public authorities), private (expenditures o individuals and pri-vate organizations) and external (related to the consequences o drug use)

expenditures. Together, the authors argue, these three kinds o expenditure ormthe total social costs o drugs in society. With a clearer idea o the concepts,the authors then proceed to present the steps that need to be taken in order toestimate public expenditures. Their review o the methodological rameworksused in European studies on public expenditures leads to the identifcation ofve steps: defning the research scope (legal and/or illegal drugs?), identiyingthe major players responsible or drug policy, collecting the data (top-down orbottom-up approach?), classiying public expenditures (prevention, treatment,

law enorcement, etc.) and, fnally, calculating the actual expenditures romcollected data. The article is essential reading or researchers embarking onpublic expenditure estimation exercises.

The article by Attewell and McFadden (Measuring the benefts o drug lawenorcement: the development o the Australian Federal Police Drug HarmIndex) starts where the previous article let o. The authors document thedevelopment o a drug harm index in Australia and examine its utility as a

perormance measure or the Australian Federal Police. The article raises animportant question: are the actions o law enorcement agencies aimed atpreventing the importation o illegal drugs eective and, more importantly, whatis the appropriate perormance measure to answer this question? Assumptionsare inevitable in such exercises, and the authors o this paper make an importantone: that the drugs seized at the border do not reach drug users and, as such,the costs associated with the use o these drugs could have been avoided. Defnedas such, the drug harm index estimates a clear return on investment or each


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Editorial:measurement issues indrugpolicy analysis 3

dollar allocated to ederal drug law enorcement. The return on investment isespecially high or operations involving international partners where the potentialor larger seizures is greatest.

One o the greatest harms associated with drug use is the increase in drug-related criminalitythe ocus o the article by Wilkins and Sweetsur (Theassociation between the number o days o methamphetamine use and the levelo earnings rom acquisitive crime among police detainees in New Zealand).Drawing on the New Zealand version o the Arrestee Drug Abuse Monitoring(ADAM) survey on police detainees, the authors ocus on a specifc drug (meth-amphetamine) and its relationship to two money-generating oences (propertycrime and drug dealing). Several important eatures make this article worthy onote. First, the main dependent variable (criminal earnings) is a much richerindicator o criminal involvement (and criminal success [1]) than the presenceor number o crimes committed, and it is more likely to be directly associatedto levels o drug use [2]. Wilkins and Sweetsur fnd that the number odays over which methamphetamine is used is the strongest predictor o bothproperty crime and drug dealing earnings. Second, the authors control or theeect o other important determinants o earning levels, including the requencyo cannabis and alcohol use. Not only do they fnd that slightly dierentpredictors are associated with the level o earnings rom property crime and rom

drug dealing, but also that cannabis and alcohol use are signifcantly related onlyto the ormer, not to the latter. The implications or drug policy are straight-orward: preventing methamphetamine useheavy use in particularhas the clearpotential to reduce crime.

Although their ocus and analysis are completely dierent, the authors othe closing article o this special issue o the Bulletin (Modelling disorganizedcrime: the cannabis market) also deal with the issue o money. Costa Storti and

De Grauwe present a ascinating economic analysis o the structure o cannabismarkets in industrial countries. They start by emphasizing some o the peculi-arities o the cannabis market in comparison to the cocaine or heroin markets,the most important being the decentralization o production leading to a new-ound proximity between cannabis producers and users. The objective o theauthors is to build a theoretical model that takes these particularities intoaccount. An important assumption o the model is the presence o monopolisticcompetition, in other words that there are many potential suppliers competing

in a market characterized by asymmetric inormationa market in which thesellers have a better idea o quality than the buyers. Ater crating a model thattakes these eatures into account, the authors use such a model to analyse theeects o two phenomena: a change in remuneration and a change in the numbero seizures. Both scenarios have slightly dierent implications or the market,but both lead to the same overall eect: a decrease in the size o suppliers buta rise in their numbers, which makes or a more competitive market structure.Interestingly, Costa Storti and De Grauwes model leads to a conclusion that has


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been oered beore in other contexts [3, 4]: past a certain threshold,increases in the intensity o law enorcement may produce diminishing returnsby creating a larger number o targets that are increasingly difcult to detect.

References

1. Carlo Morselli and Pierre Tremblay, Criminal achievement, oender networks andthe benefts o low sel-control, Criminology, vol. 42, No. 3 (2004), pp. 773-804.

2. Christopher Uggen and Melissa Thompson, The socioeconomic determinants oill-gotten gains: within-person changes in drug use and illegal earnings, AmericanJournal of Sociology, vol. 109, No. 1 (2003), pp. 146-185.

3. Martin Bouchard, On the resilience o illegal drug markets, Global Crime, vol. 8,No. 4 (2007), pp. 325-344.

4. Mark A.R. Kleiman, The problem o replacement and the logic o drug law enorce-ment, FAS Drug Policy Analysis Bulletin, No. 3, 1997.


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5

Capture-recapture methods to estimate prevalenceindicators for the evaluation of drug policies

F. Mascioli*

Associate Professor of Statistics,

University La Sapienza, Rome

C. Rossi*Professor of Medical Statistics, University of Rome Tor Vergata, Rome

AbS T RACT

In the present paper several capture-recapture procedures in the presence of

a single source are compared to estimate the size of the population of drug users

that risks being registered for personal drug use under Italian law. It is the rst

time that this method is used in Italy for this particular subpopulation. Data sets

are based on police registration data for the year 2007 and have been provided by

the Italian Ministry of the Interior. In order to propose a means of evaluating theimpact of demand-reduction policies, particular attention has been devoted to

prevalence estimates for the younger age groups (those under 20 years of age), for

whom prevalence can be considered as a good proxy for incidence; in fact, incidence

indicators are more efcient in assessing the effect of policy intervention but are

more difcult to estimate.

Keywords: capture-recapture; truncated Poisson model; heterogeneity; prevalence;

incidence; calibration.

Introduction

Historically, capture-recapture procedures have been used to determine the sizeo an unknown animal population. However, such procedures may be appliedmore widely, or example to estimate the size o a human population with acertain disease or o a sub-group that is difcult to identiy because it is involved

in illegal activities.One such hidden population is that made up o drug users. Estimating the

size o this population using the administrative databases available in manycountries is important or assessing the eect o anti-drug policies at various

*This work was partially supported by the Open Society Institute. The authors would like to expresstheir deepest thanks to reviewers or their helpul comments and suggestions, and thank Daria Scacciatellior the valuable support in data analysis.


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levels o government. However, new trends in illicit drug markets are challengingor classical methods and defnitions, with the main problem being modelling datageneration processes in order to estimate the specifc subpopulation involved in agiven process. In act, dierent archives capture dierent subpopulations o drug

users. Data generation processes in each country strongly depend on drug lawsand their implementation, and on policy measures. On the basis o the laws andpolicies implemented, dierent hidden subpopulations become visible and riskbeing registered in a database, which means that estimation methods can only beused to measure the size o such subpopulations in relation to the databasesavailable. External inormation can be used to better speciy and estimate theextent o the problem.

Many capture-recapture contributions in public health use a modelling approachwith two or more sources or lists [1-5]. In the feld o drug use, these sources areoten hospitals, the police, amily doctors, etc. I subjects are identifed on two ormore occasions, estimates o the hidden population are based on the degree ooverlap between the resulting data sets.

Another approach involves a single list with repeated entries during theobservational period [6-11]. In such an approach, the frst step is to countrepeated entries o the same user and then to attempt to estimate the requency

o units missed by the sample, using inormation on the number o people oundduring the study period in that single list one time, two times, three times and soon. I an appropriate truncated count model can be ound and ftted to this typeo data, it is possible to estimate the unobserved requency o zero entries in thelist. When the ocus is on the population o drug users, police records provide thenumber o times an individual has been identifed; drug users who have never beenidentifed will not appear in the records. Count models dier in the way the countdistribution is specifed.

In contrast to the multiple-list approach, the one-list approach is less demand-ing in terms o data requirements, especially as it avoids all the matching problemsarising rom using dierent sources. In the literature, this counting approach iscommonly classifed as a capture-recapture model. The dierence is betweenstudies that examine repeated captures across multiple lists and those thatexamine repeated captures within a single list. In the feld o illicit drug research,the one-list approach has been applied to estimate prevalence o specifc

subpopulations o drug users, such as opiate users in Rotterdam [12], opiate usersin Western Australia [13], injecting drug users in Scotland [14], heroin and meth-amphetamine users in Bangkok [15], problematic cocaine users in Barcelona [16]and problem drug users in the Netherlands [17].

In this article, a particular application o the multiple captures modelwithin a single data source is presented with the aim o estimating the size o thepopulation o drug users at risk o being registered or personal drug use. This


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Capture-recapturemethods to estimate prevalence indicators 7

population is generated by the current legal ramework in Italy, specifcally byarticle 75 o Presidential Decree 309 o October 1990 (D.P.R. 309/90), whichprohibits the possession o all drugs.1 The resulting database makes it possible toollow recent trends in drug markets better than other administrative databases

resulting rom, or example, data on hospitalizations, arrests or drug-relatedoences, imprisonments, drug-related deaths and so on, which are commonlyemployed to estimate the size o the problem drug user population2 or otherproblematic subpopulations. This is shown clearly in the fgure below, where thesupply-side indicators are also reported or comparison and show similar behaviour;the example reers to recent trends in the cocaine market. The population studiedhere is generally younger than that reported in other databases. The mainsubstances used are: cannabis (about 70 per cent), cocaine (about 20 per cent)and synthetic drugs (4 per cent), whereas the problem drug user population inItaly mainly consumes opiates (more than 70 per cent) or cocaine (about 15 percent). This population is generally not involved in criminal behaviour (eitheracquisitive crime or drug dealing). The estimates obtained or this specifc popula-tion lend themselves better to comparison with estimates derived rom generalpopulation surveys or assessing the implementation and eectiveness o usingarticle 75 o the drug law or the early detection o drug users. The aim o article75 is dissuasion and secondary prevention or drug users.

Figure I. Supply and demand-related indicators related to cocaine in recentyears in Italy (drug users registered for personal use), 2000-2006

0

50

100

150

200

250

2000 2001 2002 2003 2004 2005 2006

Year

Indexnum

bers

Index numbers of persons registered for cocaine

Index numbers of operations concerning cocaine

Index numbers of cocaine seized (kg)

1Possession o drugs or personal use is punishable by administrative sanctions. A maximum quantityo drugs determines the threshold between personal possession and trafcking. I a person is ound inpossession o illegal drugs or the frst time, administrative sanctions are usually not applied, but theoender receives a warning rom the preect and a ormal request to rerain rom use.

2The term problem drug use is defned by the European Monitoring Centre or Drugs and DrugAddiction as injecting drug use or long duration/regular use o opioids, cocaine and/or amphetamines.


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In section II, data sources and the main methodological eatures are outlined;in section III, the data generation model is presented; in section IV, the resultsare summarized in tabular and graphical orm; and, in section V, conclusions aredrawn and urther developments are outlined.

Study design

The objective o the study is to apply a capture-recapture method to estimatethe prevalence o drug users at risk o being registered or personal possessionin Italy during 2007, according to the law presently in orce.3

The data set has been provided by the Italian Ministry o the Interior andcontains various contingency tables with aggregated data on individuals identifedby the police in 2007, divided by sex, age and number o times they wereregistered (once or more than once) during that year. Inormation on thegeographical area (district) in which the registration with the police took placeis also available. Individuals can be identifed at any time during the period oobservation. In our study, individuals were unequivocally identifed and recorded.

The procedure involves a single-source capture-recapture analysis in whichthree dierent estimators are compared. The three estimators are generatedthrough truncated Poisson modelling. The frst is the classical Horvitz-Thompsonestimator [18], while the other two, independently, developed by Zelterman [19]and Chao [20, 21], incorporate unobserved heterogeneity, relaxing theassumptions about homogeneity o capture probabilities. The reason or thiscomparison is that each o the estimators is based on dierent assumptions andany violation o those assumptions might invalidate the estimates.

To account or observed heterogeneity, stratifcation by age group, gender orboth, is also considered. The geographical covariate will be analysed in a uturepaper, as the size o the sub-groups obtained including all the observable covari-ates (age, gender and geographical area) does not permit statistical analysis.Variances and associated confdence intervals have been calculated or the threeestimators. The limitations o the methodology applied are also discussed.

Data generation model: the zero-truncated Poisson model

Police records were used to derive count data on how oten (once or more thanonce) each drug user was identifed, where repeated identifcations can occur at

3See www.emcdda.europa.eu/html.cm/index44943EN.html.


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Capture-recapture methods to estimate prevalence indicators 9

any time during the study period. We do not know the number n0

o individuals

who are identifed zero times (individuals who were not identifed but had a

positive probability o being identifed since they belonged to the target popula-

tion), but can estimate their number rom the observed requencies nj ( )j> 0 by assuming that nj is generated by a Poisson distribution that is truncated

below one. Then we were able to estimate the size o the hidden population o

target drug users by adding the estimate n0 o n0 to the number o identifed

drug users, or through calibration.

Let n n nk1 2

, ,..., be the requencies o individuals identifed 1, 2, ..., k times

in the time period considered, where k denotes the largest count observed, and

let p p pk1 2, ,..., be the associated probabilities o identiying individuals 1, 2, ...,

k times. We also denote by n the number o distinct individuals identifed, bym the total number o identifcations and by N the size o the drug user

population at risk o being identifed. Then

n n m in N n n ni

i

k

i

i

k

k= = = + + +

= =

1 1

0 1, , ... .

I p0

is known, the overall population o drug users can be estimated by

means o the Horvitz-Thompson estimator: ( )N n p= 10

, which represents

the number o observed cases identifed by the police, adjusted or the probabil-ity o being included in the database. This estimation method may be viewed

as a calibration method.

I p0

is unknown, dierent approaches lead to dierent estimates o p0

and N. We will concentrate on three dierent estimators suggested in the lit-

erature, without providing much detail. These estimators, obtained rom data

ollowing a Poisson distribution, are subject to the ollowing assumptions:

(a) That the population is closed;

(b) That the individual probabilities o being observed and re-observed

are constant during the study period;

(c) That the population o interest is homogeneous.

The frst assumption, known as the closure assumption, asserts that the true

population size, N, is unaected by migration, birth and death during the

period under review. In this particular study, we have chosen a period o oneyear because we want to estimate the one-year prevalence. Keeping the study

period short is one way o addressing the closure assumption. In our case, it is

hard to see how the size o the population o drug users could change signif-

cantly in a single year.


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The second assumption, i.e. constancy o (re)capture probability, does nottake into account the possibility o individuals showing a behavioural responseto the experience o being registered. Evidently, with respect to the data gener-ating process, this assumption is a restrictive one. Again, one way o dealing

with this assumption is to keep the time period under review as short as pos-sible, but not too short, otherwise the number o recaptures is likely to be zero.

Finally, the homogeneity assumption dictates that the probability o beingobserved and re-observed should not dier too much between dierent individualsand, in theory, this assumption should not cause too many concerns. The estima-tors o both Chao and Zelterman considered here are airly robust, in the sensethat both will underestimate the true size o the population in the presence o

heterogeneity [21, 22]. So, i heterogeneity is suspected, then it could be assumedthat the estimates are in the lower bounds o the true population size [23].

It is also possible to stratiy the data set and perorm a sub-group analysison groups that are more homogeneous and pool those estimates into a singleestimate oN.

All the estimators will produce underestimates oN in the presence o

heterogeneity, so we should expect that using regression-type estimators andintroducing more covariates will produce a higher estimate oN.

The Horvitz-Thompson estimator under Poisson homogeneity

A traditional approach assumes that the count o each individual is generatedby the same Poisson distribution with parameter l . Then l can be estimated

by maximizing the likelihood or the zero-truncated Poisson distribution. Theestimate o l o l leads to the estimate

p e0=

l and the Horvitz-Thompsonestimator becomes ( )N n p

HT= 1

0. The variance o N

HTcan be obtained [8].

To estimate l , another approach that has been used involves maximizingthe likelihood unction o the Poisson density via the EM algorithm in thecomplete data ramework [24]. Both approaches applied to our data led to thesame estimate or l , at the chosen level o accuracy. The variance or l can

be obtained rom the log-likelihood unction by the standard approach.

Including heterogeneity: the estimators of Zelterman and Chao

The assumption o homogeneity o identifcation probabilities is rarely met inpractice. The simple Poisson model is not exible enough to capture populationheterogeneity and will generally underestimate the size o the population.


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Zelterman proposed estimating p0

using only requencies nj, rom the zero-

truncated count distribution, where j is usually chosen to be 1 or 2. Theproposed estimator given by

exp( / )N

n

n nZ

=

1 22 1

has been shown to be robust

against model misspecifcations. A relatively simple variance ormula can be oundor NZ

[25, 26].

Chao suggested an estimator or the population based on a mixed Poissonmodel. Chaos estimator is given by / ( )N n n n

C= +

1

2

22 and provides a lower

bound or the population size, allowing or population heterogeneity.

As beore, a variance ormula or NC

can be derived [25, 26].

In order to use Chaos and Zeltermans estimators, as only n1

and n>1

wereavailable in the data set provided by the Italian Ministry o the Interior,4 n

2

was obtained by multiple imputation on the basis o l .

Both estimators are primarily based on the lower requency classes (n1

andn

2). People seen rarely (once or twice) are likely to bear a greater resemblance to

those never seen than to those seen very oten. In addition, the emphasis on thelower requency classes makes the estimators robust in the presence o heteroge-

neity, e.g. persons seen very oten may orm a dierent sub-group compared topersons seen rarely. The inuence o persons seen oten is weighted down in bothestimators; thereore, heterogeneity, i present, is likely to exercise a relativelyminor inuence. In practice, the underlying conditions that were assumed or thethree estimators and previously discussed are unlikely to hold.

The closure assumption is under control i the study period is short. A studyperiod o one year is generally considered satisactory, but a six-month period

might be better and will be used in a uture study as soon as adequate databecomes available.

The constant (re)capture probability is hard to control. I a drug userchanges his or her behaviour ollowing identifcation and i, as a result, theprobability o him or her being identifed decreases or increases, the independencestructure o the Poisson distribution is violated. As already mentioned, oneway o dealing with this assumption is to keep the study time period as short

as possible. However, using the Chao and Zelterman estimates minimizes theproblem. A generalized model could also be developed, but proper inormationmust frst be acquired by carrying out surveys among drug users.5

4Since the Italian Ministry o the Interior did not provide data speciying exactly how many timesindividuals were registered, the data generation process was adapted to the data set available.

5Some surveys will be conducted in Italy in 2010 or this purpose.


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A problem in spatial variation may also exist. At the national level, i thereare areas where the police are less likely to identiy drug users, then the modelftted to data or the entire country may not be valid. In that case, the popula-tion should, i possible, be stratifed by geographical area.6

Indeed, the approach to estimating drug use prevalence by capture-recapturemethods generally perorms better at the local level than at the national level,as it minimizes heterogeneity problems [27].

Covariate information

One method to account or observed heterogeneity described in the orm ocovariates is to stratiy the population and then pool the estimates into a singleestimate o N. This allows individuals with dierent characteristics to havedierent Poisson parameters. It is possible that the probability o being identifedor males is dierent to that o emales, or that younger drug users are lesslikely to be identifed.

In this study, demographic variables such as age and gender were consideredas important covariates. I all relevant covariates are included, estimators are

generally less biased and more precise, but i the strata contain too ew data,statistical problems can arise and uncertainties in the estimates increase, thussome compromise is necessary.

Condence intervals

Estimating variances or the three estimators allows a calculation o 95-per-cent

confdence intervals or N, according to the usual ormula: . var( )N N1 96 .

To improve the confdence interval or the three estimators, the log transorma-tion proposed by Chao [20] was used. A capture-recapture study produces anestimate that is the fnal stage o a process in which errors can be introduced atdierent stages. A confdence interval only takes into account sampling variations,not the uncertainty related to possible violations o the underlying assumptions.To calculate the variance or the three estimators, the new approach proposed by

van der Heiden et al. [8] and Bhning [26] was used. That approach breaks downthe variance into two components: the binomial variance due to samplingn unitsrom a population o size N and the variance due to estimation o the modelparameters.

6Recent analyses at the local level show that the covariate geographical area might have a greaterinuence than the age and gender covariates used in this paper. An estimated size o 558,000 (Horvitz-Thompson point estimate) has been obtained or the target population.


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Main results

Available data reer to subjects identifed by the police with a quantity o drugsor personal use only.7 In the ollowing tables, data and various estimates o

l and N are reported.

Table 1 presents available data, disaggregated by gender and age, as providedby the Ministry o the Interior in its annual report to the national parliament or2007. There are signifcant dierences between the numbers o individuals identi-fed in each age group, the highest number being observed in the group aged20-24. Estimates or l are also presented.

It must be observed that re-capture rates ( )n n>1 1 and estimated values orl are lower or emales than or males in each age group, which means thatthe emale population has a smaller chance o being identifed than the malepopulation. The same phenomenon appears in another set o data concerningdealers, analysed by Rossi and Ricci [28].

Tale 1. Data on registrations y gender and age, and point estimates for l

Data Estimates

Males

Age(years) n

1n

>1n

Recapture rate(percentage)

l

39 1 195 31 1 226 2.59 0.051

Total 21 962 663 22 625

No agecovariate 21 962 663 22 625 3.02 0.059

7See www.emcdda.europa.eu/publications/country-overviews/it.


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Tale 1. Data on registrations y gender and age, and point estimates for l(continued)

Data Estimates

Females

Age(years) n

1n

>1n

Recapture rate(percentage)

l

39 107 1 108 0.93 0.018

Total 1 925 32 1 957

No agecovariate 1 925 32 1 957 1.66 0.032

Confdence intervals based on Horvitz-Thompson estimates (see table 2), can becalculated in two ways: either applying the ormula . var( )N N1 96 ater a logtransormation or by substituting in the ormula

p e0=

l the lower and theupper 95-per-cent confdence limits or l . In either case, the intervals are notsymmetrical and this reects the act that N must be non-negative and islikely to be right-skewed.

Tale 2. Accuracy of the Horvitz-Thompson estimates

CI for l

Horvitz-Thompson

CI for NCI for N calculated

from l interval

Males

Age (years) 95 per cent CI 95 per cent CI 95 per cent CI

Age


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Age 35-39 (0.050, 0.054) 31 260 (23 246, 42 240) (30 242, 32 352)

Age >39 (0.049, 0.053) 24 657 (17 557, 34 845) (23 748, 25 642)

Total 409 244 (404 753, 412 013)

No age covariate (0.058, 0.06) 394 898 (379 028, 440 084) (391 423, 398 438)

Females

Age(years)

95 per centCI

95 per centCI

95 per centCI

39 (0.016, 0.02) 6 054 (1 254, 30 950) (5 350, 6 975)

Total 63 478

No age covariate (0.031, 0.033) 62 140 (44 317, 87 461) (60 290, 64 109)

In table 3, estimated capture rates ( )n NHT , estimated capture indexes, defned asCapI n N

HT = , and 95-per-cent confdence intervals or CapI(CapI CapI . ( ))1 96s

are presented. Dierences regarding estimated capture indexes between males and

emales are mostly signifcant, apart rom the case o some younger age groups.

Tale 3. Inference on capture rate ased on Horvitz-Thompson estimates

Males

Age(years)

NHT

Estimatedcapture

Estimatedcapture index

CapI

95 per centCI

39 24 657 4.97 0.22 (0.21, 0.24)

Total 409 244 5.53 0.24 (0.23, 0.24)

No age covariate 394 898 5.73 0.24 (0.23, 0.24)


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Tale 3. Inference on capture rate ased on Horvitz-Thompson estimates(continued)

Females

Age(years)

NHT

Estimatedcapture

Estimated captureindex

95 per centCI

39 6 054 1.78 0.13 (0.1, 0.17)

Total 63 849 3.07 0.18 (0.16, 0.19)

No age covariate 62 140 3.15 0.18 (0.17, 0.19)

To better check this gender eect, the odds ratio or gender was calculated or

each age group (see table 4). The p-values show that the dierence between thesexes, or each age group, is highly signifcant.

Tale 4. Inference on odds ratio for males and females

Ratio males : females

Age

(years) Identied Estimated population

odds ratio

(males : females) p-value39 11.35 4.07 2.88 0

Total 11.56 6.35 1.86 0

In order to take into account the unobserved heterogeneity, Chaos and Zeltermanspopulation size estimates were calculated and compared (see table 5). As expected,Zeltermans estimates were always greater than Chaos estimates.


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Tale 5. Chao's and Zeltermans estimates

Males

Age

(years) n

Imputed

n2 Chao

95 per

cent CI Zelterman

95 per

cent CI

39 1 226 27 27 671 (19 201, 40 133) 27 749 (19 979, 38 736)

Total 22 625 442 620 443 608

No agecovariate 22 625 587 422 566 (390 700, 457 190) 423 431 (393 226, 456 098)

Females

Age(years) n

Imputedn

2Chao

95 percent CI Zelterman

95 percent CI

39 108 1 5 832 (1 209, 29 861) 5 833 (1 155, 31 395)

Total 1 957 77 778 78 048

No agecovariate 1 957 25 70 580 (48 820, 102 450) 70 747 (51 045, 98 335)

Both Chaos and Zeltermans estimates are greater than the Horvitz-Thompsonestimates (except or the estimates regarding the sub-groups o emales aged30-34 and >39) (see table 6). Better estimates can be obtained taking into con-sideration the observed heterogeneity, whereas neglecting heterogeneity (specif-cally age) produces underestimation.


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Tale 6. Comparison of the three population estimates

Point estimates

Males

Age(years) Chao Horvitz-Thompson Zelterman

39 27 671 24 657 27 749

Total 442 620 409 244 443 608

No age covariate 422 566 394 898 423 431

Females


39 5 832 6 054 5 833

Total 77 778 63 848 78 048

No age covariate 70 580 62 140 70 747

Prevalence estimates per 1,000 inhabitants in the same age groups arepresented in table 7. For the frst and last age group, the reerence populationsare those aged 12-14 and 40-54. The highest relative prevalence is observed ormales and emales aged 18-19. This reects the peculiarity o the target population,which is quite dierent rom the problem drug user population, which is usuallyestimated as being much older.


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Tale 7. Estimates for N per 1,000 inhaitants

Males


39 4.33 3.86 4.34

Females


39 0.90 0.94 0.90

The Ministry o the Interior also provides tables o subjects who were iden-tifed one or more times in 2007 but who had been identifed or the frst time

in previous years (table 8). As only a ew or zero emales were registered oreach age group, it is possible to calculate N

HTonly or the total emale popula-

tion. Both re-capture rates and estimated capture rates (based on NHT

) aremuch higher or these individuals than or individuals identifed in 2007 or thefrst time (tables 1 and 3). This shows that what is being observed is a mixtureo at least two dierent subpopulations o drug users: old drug users, i.e. thoseat risk o being identifed or the frst time beore 2007, and new drug users,i.e. those at risk o being identifed or the frst time in 2007.


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Tale 8. Gender and, for males, age distriution of previously identiedsujects who were identied again in 2007

Males

Age(years) n

1n

>1n

Re-capturerate(percentage)

NHT

Estimatedcapture rate(percentage)

39 556 28 584 5.04 6 145 9.50

Total 7 115 491 7 606 6.90 61 910 12.29

Females

n1

n>1

n

Re-capturerate

(percentage)

NHT

Estimatedcapture rate(percentage)

Total 214 14 228 6.54 1 875 12.16

When comparing the age distributions o the two samples and two estimatedpopulations, the non-homogeneity is evident (table 9). The estimate o the emalepopulation identifed or the frst time beore 2007 was obtained by distributingNHT

=1875proportionally to the observed age distribution.

Tale 9. Age distriutions of the registered samples and the estimated

populations (percentage)

Registered sample Estimated population

Age (years)

First registration in2007 (samplesize=24,582)

First registration inthe previous years(sample size=7,834)

First registration in2007 (total=473,092)

First registration inthe previous years

(total=63,785)

39 5.43 7.89 6.49 10.07

Total 100.00 100.00 100.00 100.00


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The remarkably dierent behaviour o registered subjects in the frst threeage groups or the two subpopulations indicates that the estimated prevalencein the younger groups (under 20 years o age) can be used as a proxy or inci-dence rates in the same age classes. It is well known that incidence rates are

preerable to prevalence or evaluating drug policies. Unortunately, these ratesare difcult to estimate, especially or recent years and or non-problem drugusers [29]. Thus, being able to estimate prevalence or these age groups is veryvaluable. In act:

" Available methods only allow estimates o historical trends or theincidence o opiate use.

" Estimating recent trends or stimulants and new drugs is o much greater

interest or policymakers." New trends cannot be identifed using the same approach and data sets

as adopted or (historical) opiate users.

" Incidence estimates can be obtained rom prevalence estimates by usinginormation about age.

" Conditional distribution o age at frst use can be utilized to allocateprevalent cases to the various years and to estimate incidence.

In other words, we need to make a retrospective projection o the prevalentcases to obtain incidence rates.

Conclusion and further developments

Estimates o the population o drug users are essential or calibrating and assess-

ing drug policy, and the task o calculating these estimates is now o growinginterest at the European level. Apart rom the special case o problem drug users,the population o drug users has not generated many studies adopting capture-recapture methods in Europe.

This study is a frst attempt at deriving estimates or this particular subpopu-lation o drug users who are at risk o being identifed in Italy, so some limitationsin the results are to be expected. The analyses we perormed should be considered

a pilot study that presents initial fndings.

In order to apply control measures, administer available resources and establishrealistic working objectives, it is important to know as accurately as possible theextent to which the size o the drug user population is being underreported.

Both estimators NZ

and NC

appear to be airly realistic with respect tounderlying assumptions, but we are not sure i the constant recapture assumption


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is met or each individual over time. How does the violation o this hypothesisaect the results? Analysing patterns over a shorter time interval, or example sixmonths, might produce a better estimate than using data or an entire year. Withclassical truncated Poisson analyses, the time period is believed to exert a strong

eect on the prevalence estimates, but most prevalence estimates across Europehave used a one year period.

The methods that can be utilized to estimate prevalence depend heavily onthe nature o the available data. Although there should be exibility in the choiceo methods, there are perhaps some methods that provide more robust estimatesthan others, so we compared three dierent methodologies so as to be able toselect the best estimate.

Both Chaos and Zeltermans estimators produced about the same estimateso N , or each age group and or the total population. N

Zis slightly greater,

acting as a sort o upper bound estimator, which was expected.

Both Chaos and Zeltermans estimators perorm better than the Horvitz-Thompson estimator, which cannot handle heterogeneity. The assumption oheterogeneity in the population will not severely aect N

Cand N

Zrobust esti-

mators, but will result in underestimation o the true N by NHT

.

Truncated Poisson estimators are only capable o estimating the size o thegroup o individuals who have a latent non-zero probability o being identifed.Thereore, the results based on these estimators cannot be generalized to thewhole population o drug users. On the basis o the last general populationsurvey,8 the estimated population o drug users in Italy was about 3 million in2007 (2.5 million o whom were cannabis users), so we can say that at least 80per cent o the drug user population has a zero probability o being identifed.

In Italy, it is difcult to organize data sources with compatible identifers.Moreover, dierent data sources in general correspond to dierent target popula-tions and the database based on article 75 o the relevant law is not homogene-ous with the other databases generally available or estimating the problem druguser population.

The present study on the prevalence o drug use, which is based on a single

source, is more accurate than a study based on repeated identifcation acrossmultiple sources or our target population. In the presence o observed and unob-served between-subject heterogeneity, estimators derived rom mixture-modelscould be an improvement over Chaos and Zeltermans estimators, and this couldindicate a uture development or Italian data. Including urther covariates (such

8See www.governo.it/GovernoInorma/Dossier/relazione_droga_2008/relazione_droga_2008.pd.


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as geographical, behavioural, main substance, polydrug use) could also producemore accurate estimates. Preliminary analyses perormed on these data and basedon geographical strata show that these covariates might be more important thangender and age.

Presently, work is in progress to separately analyse data rom the largestmetropolitan areas and small cities and districts in order to incorporate latentinormation about the liestyle linked to metropolitan and small areas. Inormationabout the main substance o use will also be considered.

Future work should also concentrate on developing data sources withcompatible identifers so that capture-recapture studies can examine repeatedidentifcations across multiple sources.

References

1. Yvonne M. Bishop, Stephen E. Fienberg and Paul W. Holland, Discrete MultivariateAnalysis: Theory and Practice (Cambridge, Massachusetts, MIT Press, 1975).

2. R.M. Cormack, Log-linear models or capture-recapture,Biometrics, vol. 45, No. 2

(1989), pp.

395-413.3. Y. Hser, Population estimation o illicit drug users in Los Angeles county,Journal

of Drug Issues, vol. 23, No. 2 (1993), pp. 323334.

4. International Working Group or Disease Monitoring and Forecasting, Capture-recapture and multiplerecord system estimation 1: history and theoretical develop-ment, American Journal of Epidemiology, vol. 142, No. 10 (1995), pp. 1047-1058.

5. Elena Stanghellini and Peter G.M. van der Heijden, A multiple-record systems

estimation method that takes observed and unobserved heterogeneity into account,Biometrics, vol. 60, No. 2 (2004), pp. 510-516.

6. A.G. McKendrick, Applications o mathematics to medical problems, Proceedingsof the Edinburgh Mathematical Society, vol. 44, 1925, pp. 98-130.

7. David P.M. Scollnik, Inerence concerning the size o the zero class rom an incom-plete Poisson sample, Communication in Statistics: Theory and Methods,vol. 26,No. 1 (1997), pp. 221-236.

8. Peter G.M. van der Heijden and others, Point and interval estimation o the popula-tion size using the truncated Poisson regression model, Statistical Modelling,vol. 3, No. 4 (2003), pp. 305-322.

9. Dankmar Bhning and others, Mixture models or capture-recapture count data,StatisticalMethods and Applications, vol.14, No. 1 (2005), pp. 29-43.

10. Dankmar Bhning and Ronny Kuhnert, Equivalence o truncated count mixturedistributions and mixture o truncated count distributions, Biometrics, vol. 62,No. 4 (2006), pp. 1207-1215.


34/112


11. Martin Bouchard, A capture-recapture model to estimate the size o criminalpopulations and the risks o detection in a marijuana cultivation industry, Journalof Quantitative Criminology, vol. 23,No. 3 (2007), pp.221-241.

12. Filip Smit, Jaap Toet and Peter van der Heijden, Estimating the number o opiate

users in Rotterdam using statistical models or incomplete count data, in Methodo-logical Pilot Study of Local Level Prevalence Estimates (Lisbon, European MonitoringCentre or Drugs and Drug Addiction, 1997).

13. Y. H. Choi, and C. M. Comiskey, Methods or providing the frst prevalence estimateso opiate use in Western Australia, International Journal of Drug Policy, vol. 14,No. 4 (2003), pp. 297-305.

14. Gordon Hay and Filip Smit, Estimating the number o drug injectors rom needleexchange data, Addiction Research and Theory, vol. 11, No. 4 (2003), pp. 235-243.

15. Dankmar Bhning and others, Estimating the number o drug users in Bangkok2001: a capture-recapture approach using repeated entries in one list, EuropeanJournal of Epidemiology, vol. 19, No. 12 (2004), pp. 1075-1083.

16. M. T. Brugal and others, Prevalence o problematic cocaine consumption in a cityo southern Europe, using capture-recapture with a single list, Journal of UrbanHealth, vol. 81, No. 3 (2004), pp. 416-427.

17. Filip Smit, Margriet van Laar and Lucas Wiessing, Estimating problem drug useprevalence at national level: comparison o three methods, Drugs: Education,Prevention and Policy, vol. 13, No. 2 (2006), pp. 109-120.

18. D. G. Horvitz and D. J. Thompson, A generalization o sampling without replace-ment rom a fnite universe,Journal of the American Statistical Association, vol. 47,No. 260 (1952), pp. 663-685.

19. Daniel Zelterman, Robust estimation in truncated discrete distributions with appli-cation to capture-recapture experiments, Journal of Statistical Planning and Inference,vol. 18, No. 2 (1988), pp. 225-237.

20. Anne Chao, Estimating the population size or capture-recapture data with unequalcatchability, Biometrics,vol. 43, No. 4 (1987), pp. 783-791.

21. Anne Chao, Estimating population size or sparse data in capture-recapture experi-ments, Biometrics, vol. 45, No. 2 (1989), pp. 427-438.

22. Richard M. Wilson and Mark F. Collins, Capture-recapture estimation with sampleso size one using requency data, Biometrika, vol, 79, No. 3 (1992), pp.543-553.

23. European Monitoring Centre or Drugs and Drug Addiction, Methodological Pilot

Study of Local Level Prevalence Estimates (Lisbon, EMCDDA, 1997).24. Martin A. Tanner, Tools for Statistical Inference: Methods for the Exploration of

Posterior Distributions and Likelihood Functions, 3rd ed., Springer Series in Statistics(New York, Springer, 1996).

25. Dankmar Bhning and Victor J. Del Rio Vilas, Estimating the hidden number oscrapie aected holdings in Great Britain using a simple, truncated count modelallowing or heterogeneity, Journal of Agricultural, Biological, and EnvironmentalStatistics, vol. 13, No. 1 (2008), pp. 1-22.


35/112


26. Dankmar Bhning, A simple variance ormula or population size estimators byconditioning, Statistical Methodology, vol. 5, No. 5 (2008), pp. 410-423.

27. European Monitoring Centre or Drugs and Drug Addiction, Methodological Guide-lines to Estimate the Prevalence of Problem Drug Use on the Local Level (Lisbon,

EMCDDA, 1999).28. Carla Rossi and Roberto Ricci, Modelling and estimating illicit drug market as a

tool to evaluate drug policy: the case o Italy, paper prepared or the Third AnnualConerence o the International Society or the Study o Drug Policy, Vienna, 2-3March 2009.

29. G.P. Scalia Tomba, and others, Guidelines for Estimating the Incidence of ProblemDrug Use (Lisbon, European Monitoring Centre or Drugs and Drug Addiction,2008).


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27

Studies on pulic drug expenditure in Europe:possiilities and limitations

F. Vander Laenen

Professor, Institute for International Research on Criminal Policy,

Ghent University, Belgium

L. Vandam

Scientic Researcher, Institute for International Research on Criminal Policy,


b. De Ruyver

Professor, Institute for International Research on Criminal Policy,


D. Lievens

Scientic Researcher, Institute for International Research on Criminal Policy,

Ghent University, BelgiumAbS T RACT

The number of studies on public expenditure is growing in view of the growing

importance of the evaluation of drug policies. Public expenditure is an important

indicator of government efforts to tackle the drug problem.

Studying public expenditure and comparing the methodology and the results of

existing research is challenging. In the present article, the concepts and methodologies

used in studies of public expenditure are reviewed. Public expenditure and social cost

models are compared to determine their scope. The possibilities and limitations ofstudying drug budgets are discussed. A workable methodology for estimating public

expenditure on drugs is proposed.

Introduction

Since the 1990s, the evaluation o drug policy and policy programmes has becomeincreasingly important in western societies. An essential step in the evaluation

o drug policy is the estimation o public expenditure, since that makes it pos-sible to evaluate the commitments o governments in the feld o drug policy.

Canada and the United States o America have a long tradition o studyingpublic expenditure on drugs [1-9]. Since the start o the decade o the 2000s,the importance o this research theme has been increasingly recognized byresearchers and policymakers in Europe as well [10, 11]. The European Unionaction plan on drugs or the period 2000-2004 stated that evaluation was to be


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an integral part o the European approach to the drug phenomenon and thatthe European Monitoring Centre or Drugs and Drug Addiction (EMCDDA)should be an important contributor to that evaluation. Since 2001, EMCDDAhas underlined the importance o studies on public expenditure on drug policy

in States members o the European Union. In the most recent European Unionaction plans on drugs, or the periods 2005-2008 and 2009-2012, the estimationo public expenditure became one o the special points o interest.

The frst European studies on public expenditure on drugs were publishedin Sweden [12] and Luxembourg [13]. Since then, studies have ollowed in theNetherlands [14], Belgium [15, 16], France [17] and Germany [18]. Parallel tothe studies o national public expenditure, some studies have tried to compare

public expenditure on drugs in all European Union member States [19, 20]. In2004, Reuter, Ramstedt and Rigter proposed guidelines or the estimation opublic expenditure on drug policy throughout the European Union [21].

Studying public expenditure, in particular comparing the methodology and theresults o existing studies conducted in dierent countries o the European Union,is challenging. The existing studies use diering defnitions o public expenditure,and consequently, the object o analysis and the methodology applied dier.

The aim o the present article is to untangle the existing conusion withregard to public expenditure studies in the European Union. To that end, thisarticle reviews the concepts and methodologies used in studies on Europeanpublic expenditure on drug policy. Such an undertaking might stimulate thedevelopment o evidence-based policies in the European Union.

Method

The objective o the present article is to clariy the concept o public expenditureand examine existing methodologies used to calculate public expenditure on drugpolicy in the European Union. To that end, European studies dealing with theestimation o public expenditure were searched or by consulting search enginesand online scientifc databases. The databases o the Web o Science, PubMed andSociological Abstracts were consulted. In addition, the websites o EMCDDA andthe World Health Organization were searched. The terms public expenditure,

public expenditure study, public expenditure drugs, public expenditure ondrug policy, budget, spending, in combination with the terms drugs andsubstances, were used to screen the databases. Time periods were not deter-mined. The ocus was placed on studies estimating public expenditures in Euro-pean countries.

The search resulted in the identifcation o 10 studies on public expenditure[12-21]. Table 1 presents an overview o the studies reviewed in this article.


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Studiesonpublicdrugexpenditure in Europe:possibilities and limitations 29

Table

1.

Ten

studies

on

public

expenditurei

n

Europe

Study

Countriesstudied

Researchscope

Methodology

(a

)Collectionofdata

(b)Classication

Results,divisionofthepu

blic

expenditures

Origer(2002)

Luxembourg

Illicitdrugs

(a)Top-downapproach.

(b)Demandandharm

reduction,

supply-s

idereduction,research,

EuropeanUniondrugbudget.

Demandandharm

reduc

tion:

59%;supply-sidereduction:

39%;research:1%;European

Uniondrugbudget:1%.

KoppandFenoglio(2003)

EuropeanUnion

Illicitdrugs

(a)B

ottom-upapproach.

(b)Healthcareandlaw

enforcement.

Healthcare:25-30%;law

enforcement:70-75%

.

Ramstedt(2004)

Sweden

Illicitdrugs


(b)Prevention,

treatment,harm

reduct

ion,

law

enforcement.

Treatment:24%;enforcem

ent:

75%;prevention:1%;harm

reduction:0%.

Rigter(2004)

Netherlands

Illicitdrugs


(b)Prevention,

treatment,harm

reduct

ion,

law

enforcement.

Underitsdrugspolicy,the

Netherlandsspendsmuch

more

onenforcementthanon

prevention,

treatmentand

harm

reductioncombined.

DeRuyver,Casselmanan

d

Pele(2004)

Belgium

Illicitdrugs

(a)Bottom-upandtop-down

approaches.

(b)Research/epidemiology,

preve

ntion,

treatment,law

en

forcement,policy.

Research/epidemiology:1%;

prevention:4%;treatment

:38%;

law

enforcement:54%,p

olicy:

3%.

Postma(2004)

EuropeanUnion

Illicitdrugs


approaches.

(b)Pre

ventionandresearch,

treatm

ent,law

enforcement,

costofillness.

High-qualityinformation

on

drugexpenditureisurge

ntly

neededbutislackinginmany

countries.


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30 BulletinonNarcotics, vol. LX, 2008

Study

Countriesstudied

Researchscope

Methodology

(a

)Collectionofdata

(b)Classication

Results,divisionofthepu

blic

expenditures

Reuter,Ramstedtand

Rigter(2004)

EuropeanUnion

Illicitdrugs


(b)Prevention,

treatment,harm

reduct

ion,

law

enforcement.

Theprecisionofcurrent

expenditureestimatesis

very

low.

Comparisonsofthe

expenditureestimates

of

differentcountrieslackcredibil-

ity.

KoppandFenoglio(2006)

France

Illicitdrugs,

alcoholand

tobacco


(b)Classicationaccordingto

differentministries,police

forces.

Illicitdrugs:80.2

4%;alco

hol:

15.0

8%;tobacco4.6

9%

.

DeRuyverandothers

(2007)

Belgium

Illicitdrugs


approaches.

(b)Prevention,

treatment,law

en

forcement,others.

Prevention:3.8

2%;treatm

ent:

39.5

8%;law

enforceme

nt:

56.2

4%;other:0.3

6%

.

Mostardtandothers(20

10)

Germany

Illicitdrugs


(b)ClassicationoftheFunc-

tionsofGovernment(COFOG).

Publicorderandsafety:65

-70%;

health:30-35%;generalp

ublic

services: 1 (in absolute value). It can been shown thatin order or the model o monopolistic competition to have an equilibrium, e

11 is the markup.


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Equation (5) allows us to gauge the impact o exogenous changes to theretail price o cannabis. An increase in the wage rate (owing, or example, to anincrease in the risk premium) and an increase in the in-kind remuneration costhave an amplifed eect on the price o the drug produced by the markup, i.e.

=

p

w

i

11( ) and

=

pi

i

1(6)

It should be stressed that these eects apply to the short term. In the longrun, the profts o the drug suppliers are lost through competition through theentry o new drug suppliers. Long-run equilibrium is obtained by imposing azero proft condition

i= 0. We will also impose the condition that the equilib-

rium is symmetric, i.e. that prices and quantities are identical across drugsuppliers. This allows us to concentrate on the representative drug supplierwithout subscript, i.e. to ocus on a representative upper-level drug dealer.

Settingi= 0 in (4) and dropping the subscript i, the long-run equilibrium

condition is

p x w x x p xC + =( ) ( )1 0 (7)

Rearranging leads to pw x

xp

C=

++ +

( ) ( )1 (8)

or

pw

xw p

C

=

+ + +( )

( )1

1

(9)

It can be seen that this amounts to setting price equal to average cost.

We can derive the long-run eect o a change in the wage rate or in thein-kind remuneration. We have

= +

p

w x( )1

and

=p

(10)

We observe an important dierence between the eects o the two remu-neration schemes. In the wage remuneration scheme, the eect o an increasein the wage cost on the price declines with the size o the drug sales, while inthe in-kind remuneration scheme, the eect o a higher in-kind remuneration onthe price remains constant and is independent rom the scale o the supply. Thisimplies that in the wage remuneration scheme, there is an incentive or the


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Modelling disorganized crime: the cannabismarket 91

supplier to go or economies o scale, i.e. to increase supply so as to proft roma declining average cost. This incentive to increase supply is absent in the in-kind remuneration.

Finally, in order to close the model, we introduce the condition thatthe demand or cannabis is equal to the supply. Total demand is equal to theconsumption (c) o the representative consumer multiplied by the size o thepopulationL (the prevalence), i.e. cL. In equilibrium cL = x. We substitute thisexpression in (8)

pw

cLw p

C=

+ + +

( )( )

11

(11)

The equilibrium o the model is ully described by equations (5) and (11).These two equations determine the equilibrium value o the retail price (p) andthe consumption o drugs (c), in the short and long term, respectively.

We represent the short-term and long-term equilibria expressed in equations(5) and (11) graphically in fgure IV. The PP line is the graphical expression othe short term shown in equation (5). We assume here that the retail demandcurves are linear. As a result, the elasticity h is declining or increasing valueso c, i.e., the higher the drug use the less sensitive drug demand is to pricechanges. This eature o the demand curve is consistent with the evidencesuggesting that high-use drug users become addicted (dependent) so that theirdemand becomes less price sensitive (see box 2). This produces an upwardsloping PP line. The upward slope reects the act that with a higher level odrug consumption, the market power o the drug supplier is increased, allowinghim to apply a higher markup. This leads to a higher retail price.

The QQ line is the graphical representation o the long-run equilibriumcondition (11). The negative slope (which is readily seen rom equation (11))expresses the act that QQ is derived rom the average cost curve. Thus as con-sumption increases, drug suppliers are able to slide down their average costcurves. In the long run, this leads to a declining retail price.

The equilibrium values o the price and the consumption o the representa-

tive drug user are given by the intersection point o the PP and QQ lines. Atthis intersection point, short-term and long-term equilibria are satisfed simulta-neously. While the short-term equilibrium can be considered to be satisfed ateach point in time, this is not the case with the long-term equilibrium. In theollowing sections, we will analyse how changes in exogenous variables aectthis intersection point, i.e. how these shocks aect both the short- and long-runequilibrium. We do not go into a dynamic analysis o how the long-run equilib-rium is reached.


102/112


Figure IV. Equilirium of the retail market

p

c

P

P

Q

Q

p1

c1

The remuneration scheme and market structure

This model is then used to analyse how a changing composition o in-kind and

wage remuneration aects the equilibrium. Figure V shows how an increase ing (i.e. the relative importance o in-kind remuneration as compared to a remu-neration in wages) aects the short- and long-run equilibria. The eect o anincrease in g is to make the long-run QQ line (the average cost curve) atterand to shit it down (QQ). This can be seen rom equation (11). As a result,the equilibrium levels o consumption (o the representative consumer) or thedrug supplied by an individual supplier declines and so does the price. This doesnot mean that the representative consumer will reduce his drug use. It means

that he will now have the choice between more suppliers o cannabis, each owhich becomes smaller in size. Put dierently, in the new equilibrium point therewill be more suppliers o cannabis, which all have a smaller size. In order toshow the latter, we use equations (5) and (11) describing the short- and long-runequilibria. We can then solve or x (remembering the x = cL). This yields anexpression or the optimal size o the representative producer:

xw

w pC

=

+ +

( )( )

( )

1 1

1

(12)

We can now see that as g 1 0,x . The counterpart o this result is thatthe number o frms goes to infnity. We can show the latter as ollows. Thetotal population o workers can be divided into those who work in the cannabisindustry and those who do not.

L LC LL= + (13)


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Where L is the total population, LC the population working in the cannabisindustry and LL the population working in the legal sector.

L l LL x LL N x LLi

i

N

i

i

N

= + = +( )+ = +( )+= =

1 1

(14)

It ollows that NL LL

x=

+ (15)

We can conclude rom (15) that a decline in x coincides with an increasein the number o cannabis suppliers, N. In addition, since in an in-kind remu-neration system (i.e. g= 1) the fxed cost componenta drops out, we concludethat as g 1,N . Thus, an exclusively in-kind remuneration system leads

to a market structure o perect competition.

Figure V. Effect of increasing in-kind remuneration

p

c

PQ

Q

Q

Q

We can use this model to analyse important policy questions. The frstquestion we analyse is how drug seizures aect the retail market.

Impact of seizures

The way we model seizures is as ollows. We introduce in equation (1) the prob-ability that a certain percentage o drugs sold in the retail market is seized. Thisleads to a new defnition o the profts o supplier i:

i i i i i C i

p x s w u l p x= +[ ] ( ) ( )1 1 (16)


104/112


where s is the probability that the drug supplied by i will be seized. Thus weassume that the drugs distributed to the lower-level trafckers are not seizedbecause these do not reach the retail market but are consumed by the trafckers.Note that

inow has to be interpreted as expected profts.

The frst order condition or proft maximization is now given by

ps

w pi i C

=

+ +[ ]

1

1

11( ) (17)

This equation has the same interpretation as (5), that is, it describes theshort-term equilibrium. We observe rom (17) that when the probability o seizures

increases, the upper-level trafckers raise the retail price. Because o the existenceo a markup ( h

h -1), the price increase will be a multiple o the increase in the

probability o seizures. But this price increase will be smaller when consumersare more responsive to price rises (when h increases, that is, when the level oaddiction is smaller). Note also that the markup (

h

h -1) can be interpreted as

reecting higher expected costs that are due to the increases in the probability

o seizures.

The zero proft condition i

= 0 is imposed to obtain long-run equilibrium.It yields

ps

w

xw p

C=

+ + +

1

1

11

( )( )

(18)

Since in equilibrium x(1-s) = cN, (17) becomes

ps

w pw

cNC

=

+ +[ ]+

1

11 1( ) ( )

(19)

We can now analyse the eect o changes in the probability o seizuresbrought about by stricter law enorcement. We do this in fgure VI using thesame graphical procedure as in fgure V. An increase in s has the eect o shit-

ing both the PP curve and the QQ curve upwards. However, it can be shownthat the upward shit o the PP curve is higher than that o the QQ curve. Thiscan be seen by taking the partial derivative op with respect to s in equations(17) and (19). We obtain

From equation (17):

= ( )

+ +( )

p

s sw p

C

1

1

11

2( ) (20)


105/112


From equation (19):

=( )

+ +( )

p

s sw p

C

1

11

2( ) (21)

It can be seen that (20) > (21), showing that the upward shit o the PPcurve is higher than that o the QQ curve (see fgure VI).

We conclude that an increase in the probability o seizures raises the retailprice o drugs and reduces the amount o drug use (c declines). The latter eectollows rom the act that drug users are sensitive to a price increase. Note alsothat as the price increases and drug use declines, the price elasticity, h,increases.

Seizures have an interesting eect on the structure o the market in the longrun. The model predicts that increases in seizures reduce c. This implies by (15)thatN also increases (given thatx = cL). Thus, increases in seizures raise thenumber o higher-level trafckers who all have a smaller size. In this sense, lawenorcement (seizures) has the eect o changing the market structure, that is,it leads to more but smaller drug dealing organizations. As a result, the drugdealing business becomes less monopolistic and more competitive.

Figure VI. Effect of increases in the proaility of seizures

p

c

P

P

Q

Q

p1

c1

P

P

Q

Q

p2

c2

The risk of importing cannabis

In many countries, import o cannabis is subject to more stringent law enorce-ment than is domestic production. Empirical research has shown that home-


106/112


growing o cannabis plant is a way to reduce or avoid the risk o getting caught,because imports are more easily detected than domestic production, which isoten small-scale and indoor [7]. Importation requires lengthy transportation,imaginative concealing methods and evading border controls. Furthermore, the

penal status o cannabis cultivation remains ambiguous5*

or non-existent, and,consequently, some European law enorcement entities still disregard the impor-tance o detecting home-grown production. The latter is sometimes perceived tobe a small-scale problem, where the cost o detecting small units o cannabiscultivation is too high or the volume o cannabis seized.

We model this eature in the ollowing way. We defned the price o can-nabis as a weighted average o the price o the imported cannabis and the priceo domestically produced cannabis:

p p pC m d

= + q q( )1

We now assume that the import price pm

carries a risk premium, r, whichis a unction o the tightness o border controls:

p pm m

= + r

We substitute this expression into the short-term and long-term equilibriumconditions (5) and (11):

p w p pi m d=

+ + + + [ ]

11 1( ) ( ) ( ) (22)

pw

cLw p p

m d=

+ + + + +

( )( ) ( ) ( )

11 1

(23)

Taking the derivative op with respect to r yields the ollowing two expressions:

dp

d

=

1and

dp

d=

We obtain the same qualitative result as in the previous section, i.e. boththe short-term PP line and the long-term QQ line shit upwards, but the shitin the PP line is stronger than the shit in the QQ line. As a result, the retail

price increases, and the consumption o the representative user declines. Themarket structure eects are also qualitatively the same.

It should be stressed that the previous analysis should be completed byanalysing how the risk premium aects the import share, q. We have kept qconstant but it is clear that the risk premium is likely to lead to a shit towards

5See Gamella and Rodrigo (2004) or the Spanish situation [38].


107/112


the use o domestic cannabis, thereby reducing q. We leave this problem orurther research. Note also that a shit in the preerences o European consum-ers and trafckers towards indoor production has been observed.6

All in all, the empirical evidence and the existing studies suggest that thereis an exogenous dynamic that tends to reduce q, thereby avouring the uturedevelopment o home-grown production in replacement o imported cannabis.

Conclusions

In this paper, we have modelled the cannabis market, starting rom the ideathat this market can be characterized by two opposing orces. The frst orce

leads to more competition. Technological developments have made it possible toincrease the number o producers dramatically. In addition, production can nowbe done in virtually all countries. All this has led to more competition. Thesecond orce arises rom the asymmetric inormation between sellers and buyersand leads to monopolistic structures. Asymmetric inormation leads to the needto develop a network based on trust. Trust, in turn, allows the seller to chargea premium above marginal costs.

This combination o competitive and monopolistic orces led us to use amodel o monopolistic competition. We used this model to analyse the workingso the cannabis market. One o the questions that we studied was how the useo in-kind payments, which are widely observed in the cannabis market, aectthe market structure. We concluded that in-kind payments tend to increase thenumber o sellers and reduce their size.

We also analysed how the probability o having cannabis seized aects the

market structure. The model shows that a higher probability o having cannabisseized has the eect o changing the market structure, i.e. it leads to more butsmaller drug dealing organizations. As a result, the drug dealing business becomesless monopolistic and more competitive.

6Criminological and ethnographic studies report a set o actors that justiy this change in preerences[7, 8]. First, technological developments have allowed or the introduction o increasingly sophisticatedgrowing equipment, requiring know-how which is widely available, or instance on the Internet or in special-

ized magazines. Second, there is a wide availa

Documents

Bulletin of Narcotics 1,2-2008