Under federal law — and in some states — defendants must serve the entire sentence, with no possibility of time off for good behavior. So these sentences can be severe. A dealer convicted in the federal system of possessing 5 grams of crack (about one 40-millionth of annual U.S. consumption) would serve a minimum of five years. By way of comparison, the average time served for homicide is five years and four months.

The Models
The analysis was pursued in two complementary ways. First we analyzed the effect of enforcement programs directed at cocaine dealers who are typical of those arrested throughout the United States. These calculations were performed using a modified version of RAND's Controlling Cocaine model, which has been described briefly in OR/MS Today [Caulkins, 1995] and in detail in Operations Research [Rydell, Caulkins and Everingham, 1996]. The chief advantage of this model is that it is dynamic; it describes the year-by-year consequences of an intervention over the planning horizon.

We also created a new model of the cocaine market. The new model is much simpler because it is, in economists' lexicon, a comparative statics model. At the same time, it encompasses a richer description of the criminal justice system and is more flexible in the sense that it can analyze enforcement programs applied to specific classes, or subsets, of dealers.

The two models complement each other. The first can elucidate intertemporal patterns. The second is better for analyzing the effects of targeting interventions or modifying the details of a policy. A side benefit of creating two models is that their base case results could be compared to make sure they were consistent.

The details of the models are documented elsewhere, but before proceeding to the results, it is important to provide an intuitive understanding of how locking up suppliers of a mass market drug, such as cocaine, affects drug use and drug-related crime.

It does not do so primarily through incapacitation. Most incarcerated drug dealers can be replaced relatively quickly, and the new dealers will see that supply continues to satisfy demand. However, locking up dealers does drive up the price by acting as a sort of "tax." (Enforcement against retail sellers can also increase the non-dollar costs users pay to obtain drugs. It turns out that this "search time" mechanism is not the dominant one, particularly in the context of mandatory minimum sentences.) Dealers make so much money in part to compensate them for the risks they face. Raising the risks drives up the compensation they can command and, hence, the cost of distributing drugs. Those costs are passed on to users in the form of higher prices. Higher prices both suppress consumption of current users and also reduce initiation into use over time.

At one time it was thought that this price responsiveness was quite modest. But several recent empirical studies have concluded that use of drugs such as cocaine and opiates responds nontrivially to price changes. We take the consensus estimate to be that the "elasticity of demand" is about -1. In other words, when prices go up by a certain percent, consumption goes down by the same percentage.

Policy Options Evaluated
For the purposes of this article, longer sentences or mandatory minimum length sentences should be construed as a mixture of five- and 10-year sentences that average about 6.7 years served. Such sentences are typical of those given at the federal level.

Rather than estimate the effectiveness of such sentences in isolation, we compare imposing mandatory minimum sentences with simply expanding conventional enforcement. By expanding conventional enforcement we mean arresting, prosecuting and incarcerating more dealers than would be done under base case conditions, by incarcerating those dealers for just a year or two.

We consider applying both mandatory minimum sentences and expanding conventional enforcement to two types of dealers. The first are dealers typical of those arrested in the United States by all levels of government. The second are dealers arrested by federal agencies, such as the Drug Enforcement Administration (DEA), who are caught in possession of quantities that would trigger a federal mandatory minimum sentence. These individuals are higher-level dealers than the average dealer arrested in the United States since state and local agencies make most of the arrests, and they focus on lower level dealers.

There are differences between enforcement against higher-level dealers and enforcement against typical dealers. On the one hand, higher-level dealers are harder to arrest. On the other hand, each arrest produces greater seizures of cocaine, physical assets and financial assets. Also, there is a greater chance of an arrest leading to a conviction, and more damage is done per year of incarceration. So, per arrest, enforcement against higher-level dealers is more expensive but it also produces greater benefits. Hence, it is not obvious a priori which is more cost-effective.

As a foil, the effectiveness of the enforcement interventions was compared to that of treating heavy users. Note that the policy choice is not whether to incarcerate or treat a particular person. Rather, the choice is to fund greater enforcement against dealers or to fund greater treatment for a more or less distinct population of drug users. Treatment is assumed to cost about $2,000 per admission, to keep four out of five users off drugs while they are in the treatment program, and to prevent 13 percent of those treated from returning to their previous rates of consumption even after they have left treatment.

Central Finding
Figure 1 shows the central finding. Conventional enforcement is more effective at reducing cocaine use than is giving very long sentences, and enforcement directed against the higher-level dealers pursued by the federal government is more effective than is average enforcement. Neither enhanced sentences nor conventional enforcement, whether applied to federal or typical defendants, is as cost-effective, at the margin, as treating heavy cocaine users.

 
Figure 1

As an aside, this does not mean local enforcement has no role in drug control. If a violent street market erupted in your neighborhood, you should call your local police, not the DEA or a treatment agency. Local enforcement is needed to control street markets and associated externalities even if it not effective at suppressing drug use altogether.

These findings are quite important for drug policy, but they are probably neither surprising nor of great interest to the average operation research analyst. The results get more interesting when we examine the sensitivity of these conclusions to various factors.

Sensitivity with Respect to Type of Dealer Targeted
Contrasting the results for enforcement directed at high-level vs. average dealers suggests that targeting helps make enforcement more effective, particularly the longer sentences. However, the level of targeting associated with current federal mandatory minimum sentences is not enough to: (1) make enforcement more cost-effective than treatment, or (2) make mandatory minimum sentences more cost-effective than conventional enforcement. A natural question to ask is, How much targeting would it take to reverse the rank order of the program's effectiveness?

Figure 2 is a strategy region graph that can answer such questions. It shows regions where each of the three strategies — mandatory minimum sentences, conventional enforcement and treatment — are the most cost-effective way to spend an additional million dollars. The regions correspond to various levels of two key parameters.

 
Figure 2

The vertical axis represents how much cost is imposed on dealers per additional cell year. This parameter is not easily measured, but there is thin literature suggesting that for federal-level dealers a base case value of $85,000 per cell year is appropriate.

The horizontal axis displays the cost to the government of arresting a dealer. Our base case assumption was that a federal-level arrest costs $20,000, not including adjudication or incarceration costs. For these parameter values, treatment is the most cost-effective program.

How much cost would a cell year have to impose on dealers in order for enforcement to become as effective as treatment? The figure shows the answer is about $200,000. To put this in perspective, a second- or third-level wholesale dealer who sells drugs a kilogram at a time probably has profits of about $5,000 per kilogram sold. Such an individual would have to sell about 40 kilograms a year to have a profit of $200,000 per year. Risk compensation need not equal income, but one cost of being incarcerated is that one foregoes the ability to make money by selling drugs. (Drug selling and use certainly occur in prison, but random drug testing suggests that it occurs at much lower rates than is possible outside of prison.) This suggests that enforcement against third-level wholesale dealers and above may be more cost-effective than treatment.

A second insight comes from noting the conditions under which long sentences become more effective than conventional enforcement. If it costs more than $30,000 to arrest one of the dealers, then it is cost-effective to give them long sentences. If it costs less than $30,000, it is more cost-effective to use shorter, conventional sentences.

That makes sense because costs are imposed on dealers not just through incarceration but also by arrest itself (seizure of drugs and assets, disruption of operations, etc.). So, if it is easy to arrest dealers, conventional enforcement is superior because it does more arresting relative to incarcerating. But if it is hard to arrest dealers, those who are caught should be kept in prison for a long time.

Figure 2 also makes a more general point. It is not the case that long sentences are never effective, but rather that they are only cost-effective when applied to a certain special class of drug dealers: those who value their time very highly and who are quite difficult to catch. The problem with current mandatory minimum sentences is that, although they do not apply to all dealers, they also do not apply only to this particular class of dealers.

Sensitivity with Respect to Planning Horizon
The timing of benefits and costs associated with the different programs deserves comment. Treatment costs come early. A single episode of treatment rarely lasts much more than a year, so if someone enters treatment today, the costs accrue in the first year.

The benefits of successfully treating someone, however, accrue throughout the entire period during which they would have used cocaine had they not been treated, which can be many years. Addiction careers of 10 or 12 years are not uncommon.

In contrast, the public costs of the additional prison space required for longer sentences are not felt until after the end of the regular prison term the dealer would have received under conventional enforcement. And the costs of a five- or 10-year sentence continue to be felt well into the future.

The benefits of extending prison sentences occur immediately, though, because dealers will want more income today to compensate them for the risk of increased prison time. As a result, prices will go up and consumption will go down immediately, while the costs of the extended terms will stretch out into the future.

Thus treatment is like an investment. You pay now, but receive benefits for many years into the future. Extending sentences is like buying something with a credit card. You get the benefit right away, but the bill comes due later. Conventional enforcement is more like paying cash; both the benefits and the costs accrue relatively early.

Hence, the relative desirability of the programs depends on how far sighted the policy maker is, as Figure 3 illustrates. The vertical axis shows consumption averted per million dollars. The horizontal axis indicates the planning horizon, or the period over which benefits and costs are summed. (The base case uses a 15-year planning horizon, and within the planning horizon outcomes are still discounted at 4 percent per year.)

 
Figure 3

Shifting to a shorter time horizon implies ignoring events in the out years. With treatment that implies ignoring benefits, so the benefit to cost ratio declines. For longer sentences, ignoring future events implies ignoring costs, so the ratio increases.

To decision makers who only care about what happens in the next three years, long sentences appear to be more effective than conventional enforcement. For those who only care about what happens in the next two years, long sentences appear to be more cost effective than treatment. Politicians focused on the next election might have such short time horizons, but society generally wants to consider consequences more than two or three years in the future; otherwise we would never invest in research and development, educate children or screen for cancer.

Sensitivity with Respect to the Drug Control Objective
Reducing drug use is just one goal of drug policy. Another is reducing drug-related consequences, paramount among which is reducing drug-related crime. So we estimated these programs' effects on drug-related crime. The estimates are very rough; they are only intended to be ballpark estimates that give some idea of relative efficacy.

There are three types of drug-related crime. The first, sometimes referred to as a psychopharmacological crime, is related to intoxication or withdrawal. For example, if using cocaine leads to stimulant-induced paranoia, and that paranoia causes the user to assault someone, that would be a psychopharmacological crime.

The second, sometimes called economic-compulsive crime, occurs when drug users commit property crime to obtain money to buy drugs. The third type, systemic crime, refers to conflicts among participants in the black market for drugs. Since the transactions are illegal, disputes cannot be resolved in court and are often resolved through violence instead. The stereotype is dealers fighting over turf, but the modal systemic crime probably arises from a dispute over money or the quality of drugs between two people who were engaged in a transaction.

Psychopharmacological crime is caused directly by drug use itself. Economic-compulsive and systemic crime are driven by drug money. Depending on the specific crime and drug, these three categories account for roughly one-sixth, one-third and one-half of drug-related crime, respectively. Thus, most drug-related crime is actually motivated by drug money, not by drug use directly.

With this categorization, it is apparent that the amount of drug-related crime is a function of drug use and of spending on drugs. The analysis assumes psychopharmacological crime is proportional to the amount of drug use and economic-compulsive and systemic crime are proportional to the amount of spending on drugs. Those are strong and simplistic assumptions, but the goal is only to get a rough sense of these programs' ability to control drug-related crime.

Figure 4 contrasts the ability of federal mandatory minimum sentences, conventional enforcement against high-level dealers and treatment to control drug use, drug spending and drug-related crime. The middle set of bars shows the relative ability of the programs to reduce spending on cocaine. We can calculate spending because we know how the programs affect price and use, and spending is just the product of the quantity consumed and the price per unit.

 
Figure 4

Enforcement programs are not effective at reducing drug-related spending because they suppress use by driving up price. For instance, if price goes up by 10 percent, consumption will go down by about 10 percent, leaving spending almost unchanged.

The relative abilities of the three programs to control crime is a mixture of their abilities to control use and spending, weighted toward spending. Hence, the rank order of the programs with respect to their ability to reduce drug-related crime is the same as that for reducing drug use.

Summary
The policy implications can be summarized as follows: Mandatory minimum sentences for drug dealers are more cost-effective than the alternatives of additional conventional enforcement or treatment only if the sentences are targeted at high-level dealers who both have very high risk-premiums and are hard to catch. Also, such sentences might appear to be cost-effective to someone who is extremely myopic.

Absent those rather extreme conditions, enhanced sentences are not cost-effective. This result is true if reducing drug use is the objective. It is true with even greater force if the objective is to reduce drug-related crime. Hence, long sentences for drug dealers should be used selectively.

The implications of this analysis for operations research are of equal interest. First, operations research techniques can make a valuable contribution to policy analysis. They can introduce quantitative estimates of impacts and notions of effectiveness into a debate that otherwise would be mostly qualitative, and they can highlight issues that had not previously been identified. For example, before this study no one advocating or opposing the use of mandatory minimums had discussed the roles that either time horizons or the cost of arresting a dealer have in determining whether mandatory minimum sentences are the most effective tactic. Furthermore, policy makers find these analyses to be useful. This material has been briefed to policy makers at all levels of government. Drug czar Barry McCaffrey liked the study enough to issue a press statement stating that he supported its principal thesis.

Second, good sensitivity analysis can bring a fairly dry result to life. Conveyed in pictures and backed with clear "stories," they can give people without much analytical training (including policy makers, the media and the public at large) insight into fairly complicated issues.

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