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Mathematical models of drug markets and drug policy
Mathl. Compui. Modelling Vol. 17,No. 2,p. ix-xi, Printed in Great Britain. AU rights reserved
1993
0695-7177/93 $S.OO+ 0.00 Copyright@
1993 Pergamon
Press Ltd
PREFACE MATHEMATICAL AND
MODELS OF DRUG DRUG POLICY
MARKETS
It is news to no one that both the distribution and consumption of illicit drugs and drug control measures impose substantial costs on many countries, particularly the United States. Unfortunately this state has only rarely prompted the kind of reasoned analysis which must precede thoughtful interventions designed to manage the problems and mitigate their costs. This special issue strives to report on and promote such reasoned analysis. Too often the response to the problems of illicit drugs are irresponsibly superficial. Politicians seeking votes proffer quick fixes such as minimum mandatory sentences and “boot camps” for drug offenders. Whether or not these policies, on balance, are beneficial is a subject for legitimate debate, but it is clear u ptiari that they are not “magic bullets” that will somehow solve all our ills. Others, usually after equally superficial analysis, suggest solving the problems by simply “legalizing” drugs. Such pundits often correctly point out that the costs associated with illicit drugs include costs created by enforcement and the drug’s illegality, not just their consumption. And they point out that the costs of enforcement are large, perhaps even larger than the costs due to consumption. What they usually overlook, however, is the fact that the costs of consumption are relatively modest, in no small part, precisely because so much effort is devoted to enforcement. Furthermore, even when advocates of legalization do recognize that consumption might increase, they typically make very optimistic forecasts and offer confidence intervals around the forecasts that are altogether too narrow. Given that the costs to the user, both pecuniary and otherwise, would fall dramatically, substantial increases in consumption are not inconceivable. And given how little we know about the extent and causes of current consumption, whatever point estimate seems most likely should be bracketed by very broad confidence intervals. Those who do not stoop to the quick fixes of Draconian measures or “legalization” are often left frustrated. The profits from dealing are so great; the recidivism rates are so high; and the evaluations of prevention programs so disappointing, that it is tempting to throw up one’s hands and say, “Nothing works; no program is any better than another. It is all hopeless.” Fortunately that is not the only alternative to superficial analysis. If one takes the time to delve into the complexities of the issues (and unlearn the caricatures foisted on the public by the media); if one approaches the issues with an open mind, free of ideological baggage; and if one adopts as an objective the minimization of the total harm done to society, then it is possible to conceive of concrete, feasible, constructive measures that could be taken to ameliorate one or more aspects of the problem. For a variety of reasons, this problem solving mindset can carry one even further if it is leveraged on some mathematical modelling and quantitative analysis. The first reason is simply unfamiliarity. Most leaders probably have no more than passing acquaintance with illicit drugs; most have neither been or known “junkies”; and few have spent much time in street markets for cocaine or heroin. A second reason is that many people’s intuitions, unguided by analysis, are easily fooled by the numbers involved. Some are simply large: for example, in 1990 over 25 million Americans used an illicit drug. Other numbers vary enormously in magnitude; for example, the largest seizure of cocaine (about 20 metric tons) is eight orders of magnitude larger than the typical retail purchases (0.2 grams). Typeset iX
by &S-‘&X
Y
J.P. CAULKINS
A third reason is that the participants in drug markets are intelligent actors who adapt to changing circumstances. Drug problems are not static; they evolve, often rapidly and in ways that thwart interventions. Furthermore the dynamics of drug use are complex. There may have been roughly the same number of cocaine users in the U.S. in 1990 as there were in 1985, but initiation rates were almost certainly lower and consumption much greater. Patterns of drug use do not simply scale up and down proportionately; they have histories and dynamics that must be analyzed and understood. Add to this the fact that there are multiple, often conflicting, objectives and the result is a complex problem domain that truly demands the rigor of mathematical modelling. Unfortunately there has not traditionally been much quantitative analysis of drug markets and drug policy. One can speculate about the reasons. Drug problems are relatively new, or at least newly prominent in public debate. Data are scarce. The subject is too applied and too “dirty” to merit respectable scholarship. It falls between the boundaries of disciplines that do not normally interact. Whatever the reasons, the net effect is that many of the issues in drug policy are virgin territory. Important work remains to be done in formulating problems, testing basic hypotheses, and proposing theories that synthesize and explain the experiences to date. This is a particularly exciting time because researchers and policy makers are beginning to cooperate, better data are becoming available, and a critical mass of quantitative drug policy analysts is forming that can cross-fertilize and incubate new ideas. Hence I am proud to introduce this special issue of Mathematical and Computer Modelling which is devoted to modelling drug markets and drug policy. What is perhaps most striking about this collection of articles is their diversity. One might have thought quantitative analysis related to illicit drugs would be limited to such tactical issues as the design of Coast Guard cutter interdiction patrol routes, but that is not at all the case. The articles herein literally go from the source to the street. Some are largely empirical; others present stylized models that build intuition. The techniques applied range from straightforward Monte Carlo simulation to network interdiction models. Briefly describing these articles underscores the wealth in their diversity. For much of the last decade, cocaine has been the illicit drug which has caused the greatest concern. Essentially all of the cocaine consumed in the U.S. is imported from South America, so not surprisingly many control efforts focus on limiting production in the source countries and/or interdicting shipments destined for the U.S. The first three papers focus on this aspect of drug control policy. Cocaine is not produced in one step or in one location; it moves through a number of processing stages, usually in locations which are physically dispersed. Hence, even within the source countries there is substantial trans-shipment of precursor chemicals and intermediate products such as coca leaf, base, and paste. In the first article in this volume, Wood uses a network interdiction model to examine attempts to disrupt these flows. He demonstrates that the problem is NP-complete even when interdicting an arc requires exactly one unit of resource, as would likely be the case with drug smuggling since smugglers seek to avoid interdictors rather than to overwhelm them militarily. he develops new integer programming models for the problem and derives inequalities that tighten the resulting LP relaxation. Kennedy ei al. approach source country control measures from another angle. They observe that such measures have received significant attention and not insignificant resources but are widely perceived of as having been ineffective. Advocates argue that this is primarily because governments in the source countries have not put their heart into the effort, but Kennedy et al. construct a simple, equilibrium economic model of the primary coca and cocaine producing countries which offers another explanation. Their model suggests that the very nature of the market dictates that source country interventions will have only modest effects on world market conditions and hence consumption. Caulkins el al. use a simulation model to reach a similarly pessimistic conclusion about efforts to interdict cocaine between the source countries and the United States, which is the largest consumer of cocaine. They suggest that simple, back-of-the-envelope calculations may overestimate the efficacy of interdiction if those calculations ignore the possibility that smugglers can adapt to changing circumstance and circumvent risky routes.
Preface
xi
The next two papers focus on domestic enforcement. DiNardo uses historical data on Drug Enforcement Administration (DEA) investigations, cocaine prices, and consumption to examine the relationship between these variables. He discusses some of the limitations and frustrations inherent in working with data on illicit activities. After recognizing these limitations, he concludes that the data, such as they are, do not provide evidence that regional and temporal variations in DEA enforcement activity explain variations in either the demand for or the price of cocaine. Kleiman, in a more stylized and more general analysis, offers an explanation for the lack of success of enforcement efforts. He observes that it is not so much the level of enforcement but rather the level of enforcement per violator which determines a violator’s risk. Hence, inasmuch as the increases in enforcement over the last decade followed large, if not larger, increases in the size of the market, it is perhaps not surprising that increasing enforcement efforts did not yield visible improvements. But Kleiman goes beyond simply offering another explanation for past failures; he offers a concrete suggestion for how enforcement could be used to beat back drug problems. He observes that for a given level of enforcement there are usually two stable equilibria, one with few violators and one with many. The only way to move from a high-level equilibria to a low-level equilibria is to apply massive pressure, more than one would need to sustain an equilibrium with a low-level of violation. As Kleiman explains, this suggests following a “divide and conquer” strategy, and Kleiman suggests how such a strategy might be implemented. Baker et al. turn their attention to another facet of drug control policy: drug testing. Drug testing programs present challenging operational questions regarding who is tested, how often, and under what circumstances. In the past these question have been addressed on an ad hoc basis, but Baker e2 al. combine decision theory and acceptance sampling methods to investigate costminimizing drug-testing strategies. Their analytical approach brings objectivity and efficiency to an area which has previously been dominated by guesswork and rules of thumb. Powers et al. develop a long-term, multivariate forecasting model that assesses the impact of social interventions on narcotics-related behavior. They then use their model in a simulation study to investigate the impact of changing methadone maintenance policies on narcotics use and property crime. This research both demonstrates the power of their methodology and the benefits of methadone maintenance. Probably the single greatest obstacle to effective drug policy analysis has been the lack of reliable data. The classic example of this is that we do not even always know how many drug users there are. Our ignorance is particularly severe with respect to specific geographic areas (as opposed to national totals) and/ or when the form of use is highly deviant, such as injecting drugs. Hence, it is appropriate to close this volume with Kaplan and Soloshatz’ elegant article. They apply straightforward models to AIDS data to estimate the number of drug injectors in New Haven. What makes this work especially valuable is that synthetic estimation techniques currently lack effective anchor points; Kaplan and Soloshatz’ estimate for New Haven provides just such an anchor and, hence, could improve estimates of the number of injecting users across the U.S. The articles in this volume were selected for their diversity, their clarity, and their relevance, and they stand out in those respects. Yet they barely scratch the surface of what can be done in quantitative analysis of drug markets and drug policy. I will close by inviting all who are intrigued by this subject to “join up”; drug policy presents a rare opportunity. A great deal of important and exciting work remains to be done, and one does not need a Ph.D. in drug policy to get started. On the contrary, what this field needs, as much as if not more than any other, is the synergistic interaction of the perspectives different disciplines can provide on this difficult problem area.
Jonathan
P. Caulkins Guest
Editor
1993
0695-7177/93 $S.OO+ 0.00 Copyright@
1993 Pergamon
Press Ltd
PREFACE MATHEMATICAL AND
MODELS OF DRUG DRUG POLICY
MARKETS
It is news to no one that both the distribution and consumption of illicit drugs and drug control measures impose substantial costs on many countries, particularly the United States. Unfortunately this state has only rarely prompted the kind of reasoned analysis which must precede thoughtful interventions designed to manage the problems and mitigate their costs. This special issue strives to report on and promote such reasoned analysis. Too often the response to the problems of illicit drugs are irresponsibly superficial. Politicians seeking votes proffer quick fixes such as minimum mandatory sentences and “boot camps” for drug offenders. Whether or not these policies, on balance, are beneficial is a subject for legitimate debate, but it is clear u ptiari that they are not “magic bullets” that will somehow solve all our ills. Others, usually after equally superficial analysis, suggest solving the problems by simply “legalizing” drugs. Such pundits often correctly point out that the costs associated with illicit drugs include costs created by enforcement and the drug’s illegality, not just their consumption. And they point out that the costs of enforcement are large, perhaps even larger than the costs due to consumption. What they usually overlook, however, is the fact that the costs of consumption are relatively modest, in no small part, precisely because so much effort is devoted to enforcement. Furthermore, even when advocates of legalization do recognize that consumption might increase, they typically make very optimistic forecasts and offer confidence intervals around the forecasts that are altogether too narrow. Given that the costs to the user, both pecuniary and otherwise, would fall dramatically, substantial increases in consumption are not inconceivable. And given how little we know about the extent and causes of current consumption, whatever point estimate seems most likely should be bracketed by very broad confidence intervals. Those who do not stoop to the quick fixes of Draconian measures or “legalization” are often left frustrated. The profits from dealing are so great; the recidivism rates are so high; and the evaluations of prevention programs so disappointing, that it is tempting to throw up one’s hands and say, “Nothing works; no program is any better than another. It is all hopeless.” Fortunately that is not the only alternative to superficial analysis. If one takes the time to delve into the complexities of the issues (and unlearn the caricatures foisted on the public by the media); if one approaches the issues with an open mind, free of ideological baggage; and if one adopts as an objective the minimization of the total harm done to society, then it is possible to conceive of concrete, feasible, constructive measures that could be taken to ameliorate one or more aspects of the problem. For a variety of reasons, this problem solving mindset can carry one even further if it is leveraged on some mathematical modelling and quantitative analysis. The first reason is simply unfamiliarity. Most leaders probably have no more than passing acquaintance with illicit drugs; most have neither been or known “junkies”; and few have spent much time in street markets for cocaine or heroin. A second reason is that many people’s intuitions, unguided by analysis, are easily fooled by the numbers involved. Some are simply large: for example, in 1990 over 25 million Americans used an illicit drug. Other numbers vary enormously in magnitude; for example, the largest seizure of cocaine (about 20 metric tons) is eight orders of magnitude larger than the typical retail purchases (0.2 grams). Typeset iX
by &S-‘&X
Y
J.P. CAULKINS
A third reason is that the participants in drug markets are intelligent actors who adapt to changing circumstances. Drug problems are not static; they evolve, often rapidly and in ways that thwart interventions. Furthermore the dynamics of drug use are complex. There may have been roughly the same number of cocaine users in the U.S. in 1990 as there were in 1985, but initiation rates were almost certainly lower and consumption much greater. Patterns of drug use do not simply scale up and down proportionately; they have histories and dynamics that must be analyzed and understood. Add to this the fact that there are multiple, often conflicting, objectives and the result is a complex problem domain that truly demands the rigor of mathematical modelling. Unfortunately there has not traditionally been much quantitative analysis of drug markets and drug policy. One can speculate about the reasons. Drug problems are relatively new, or at least newly prominent in public debate. Data are scarce. The subject is too applied and too “dirty” to merit respectable scholarship. It falls between the boundaries of disciplines that do not normally interact. Whatever the reasons, the net effect is that many of the issues in drug policy are virgin territory. Important work remains to be done in formulating problems, testing basic hypotheses, and proposing theories that synthesize and explain the experiences to date. This is a particularly exciting time because researchers and policy makers are beginning to cooperate, better data are becoming available, and a critical mass of quantitative drug policy analysts is forming that can cross-fertilize and incubate new ideas. Hence I am proud to introduce this special issue of Mathematical and Computer Modelling which is devoted to modelling drug markets and drug policy. What is perhaps most striking about this collection of articles is their diversity. One might have thought quantitative analysis related to illicit drugs would be limited to such tactical issues as the design of Coast Guard cutter interdiction patrol routes, but that is not at all the case. The articles herein literally go from the source to the street. Some are largely empirical; others present stylized models that build intuition. The techniques applied range from straightforward Monte Carlo simulation to network interdiction models. Briefly describing these articles underscores the wealth in their diversity. For much of the last decade, cocaine has been the illicit drug which has caused the greatest concern. Essentially all of the cocaine consumed in the U.S. is imported from South America, so not surprisingly many control efforts focus on limiting production in the source countries and/or interdicting shipments destined for the U.S. The first three papers focus on this aspect of drug control policy. Cocaine is not produced in one step or in one location; it moves through a number of processing stages, usually in locations which are physically dispersed. Hence, even within the source countries there is substantial trans-shipment of precursor chemicals and intermediate products such as coca leaf, base, and paste. In the first article in this volume, Wood uses a network interdiction model to examine attempts to disrupt these flows. He demonstrates that the problem is NP-complete even when interdicting an arc requires exactly one unit of resource, as would likely be the case with drug smuggling since smugglers seek to avoid interdictors rather than to overwhelm them militarily. he develops new integer programming models for the problem and derives inequalities that tighten the resulting LP relaxation. Kennedy ei al. approach source country control measures from another angle. They observe that such measures have received significant attention and not insignificant resources but are widely perceived of as having been ineffective. Advocates argue that this is primarily because governments in the source countries have not put their heart into the effort, but Kennedy et al. construct a simple, equilibrium economic model of the primary coca and cocaine producing countries which offers another explanation. Their model suggests that the very nature of the market dictates that source country interventions will have only modest effects on world market conditions and hence consumption. Caulkins el al. use a simulation model to reach a similarly pessimistic conclusion about efforts to interdict cocaine between the source countries and the United States, which is the largest consumer of cocaine. They suggest that simple, back-of-the-envelope calculations may overestimate the efficacy of interdiction if those calculations ignore the possibility that smugglers can adapt to changing circumstance and circumvent risky routes.
Preface
xi
The next two papers focus on domestic enforcement. DiNardo uses historical data on Drug Enforcement Administration (DEA) investigations, cocaine prices, and consumption to examine the relationship between these variables. He discusses some of the limitations and frustrations inherent in working with data on illicit activities. After recognizing these limitations, he concludes that the data, such as they are, do not provide evidence that regional and temporal variations in DEA enforcement activity explain variations in either the demand for or the price of cocaine. Kleiman, in a more stylized and more general analysis, offers an explanation for the lack of success of enforcement efforts. He observes that it is not so much the level of enforcement but rather the level of enforcement per violator which determines a violator’s risk. Hence, inasmuch as the increases in enforcement over the last decade followed large, if not larger, increases in the size of the market, it is perhaps not surprising that increasing enforcement efforts did not yield visible improvements. But Kleiman goes beyond simply offering another explanation for past failures; he offers a concrete suggestion for how enforcement could be used to beat back drug problems. He observes that for a given level of enforcement there are usually two stable equilibria, one with few violators and one with many. The only way to move from a high-level equilibria to a low-level equilibria is to apply massive pressure, more than one would need to sustain an equilibrium with a low-level of violation. As Kleiman explains, this suggests following a “divide and conquer” strategy, and Kleiman suggests how such a strategy might be implemented. Baker et al. turn their attention to another facet of drug control policy: drug testing. Drug testing programs present challenging operational questions regarding who is tested, how often, and under what circumstances. In the past these question have been addressed on an ad hoc basis, but Baker e2 al. combine decision theory and acceptance sampling methods to investigate costminimizing drug-testing strategies. Their analytical approach brings objectivity and efficiency to an area which has previously been dominated by guesswork and rules of thumb. Powers et al. develop a long-term, multivariate forecasting model that assesses the impact of social interventions on narcotics-related behavior. They then use their model in a simulation study to investigate the impact of changing methadone maintenance policies on narcotics use and property crime. This research both demonstrates the power of their methodology and the benefits of methadone maintenance. Probably the single greatest obstacle to effective drug policy analysis has been the lack of reliable data. The classic example of this is that we do not even always know how many drug users there are. Our ignorance is particularly severe with respect to specific geographic areas (as opposed to national totals) and/ or when the form of use is highly deviant, such as injecting drugs. Hence, it is appropriate to close this volume with Kaplan and Soloshatz’ elegant article. They apply straightforward models to AIDS data to estimate the number of drug injectors in New Haven. What makes this work especially valuable is that synthetic estimation techniques currently lack effective anchor points; Kaplan and Soloshatz’ estimate for New Haven provides just such an anchor and, hence, could improve estimates of the number of injecting users across the U.S. The articles in this volume were selected for their diversity, their clarity, and their relevance, and they stand out in those respects. Yet they barely scratch the surface of what can be done in quantitative analysis of drug markets and drug policy. I will close by inviting all who are intrigued by this subject to “join up”; drug policy presents a rare opportunity. A great deal of important and exciting work remains to be done, and one does not need a Ph.D. in drug policy to get started. On the contrary, what this field needs, as much as if not more than any other, is the synergistic interaction of the perspectives different disciplines can provide on this difficult problem area.
Jonathan
P. Caulkins Guest
Editor