Simulation of Adaptive Response_a Model of Drug Interdiction

Mathl. Comput. Modelling Vol. 17, No. 2, pp. 37-52, 1993 0695-7177193 $6.00 + 0.00 Printed in Great Britain. AII rights reserved Copyright@ 1993 Pergamon Press Ltd

SIMULATION OF ADAPTIVE RESPONSE: A MODEL OF DRUG INTERDICTION

JONATHAN P. CAULKINS

H. John Heinz III School of Public Policy and Management

Carnegie Mellon University, Pittsburgh, PA 152134690, U.S.A.

GORDON CRAWFORD*

PETER REUTER

The RAND Corporation

2100 M St. NW, Washington DC 20037-1270, U.S.A.

Abstract-This paper presents a Monte Carlo simulation of the smuggling and interdiction of illicit drugs that explicitly allows for adaptation across routes and modes. The model is used to examine several issues surrounding the interdiction of cocaine shipments into the U.S. It suggests that baclc- of-the-envelope estimates of interdictions effectiveness may be overly optimistic if they neglect the existence of a backstop technology (smuggling small shipments over laud), the concavity of smugglers costs as a function of the fraction of all routes on which the interdiction rate is increased, and the fact that not all smuggling costs are caused by interdiction. When one considers these factors, it appears that only under truly exceptional ci rcumstances would one expect increasing interdiction to have a substantial impact on U.S. cocaine consumption.

1. INTRODUCTION

Drug interdiction, the seizing of drugs and smugglers as they travel from source countries to consumer countries, accounted for over $2 billion of the nearly $7.5 billion the U.S. federal government spent on drug law enforcement in fiscal year 1991. Since 1981, interdiction expenditures have grown almost four-fold in real terms [l].

This increase in interdiction resources has led to a dramatic increase in the quantity of drugs seized, particularly cocaine. In fiscal year 1981, federal agencies seized an estimated 1.7 metric tons of cocaine; in fiscal year 1986, 27.2 tons were seized. By 1990, the figure had risen to over 100 tons. During most of this period, however, estimated U.S. cocaine consumption rose and the

import price fell. Furthermore, the rise in cocaine consumption was far smaller than the increase in cocaine seizures.

This presents an apparent conundrum: interdiction was seizing a larger percentage of total shipments, so one might have expected that the import price should have risen rather than fallen. The apparent conundrum ceases to be troubling, however, when one realizes that smuggling and interdiction do not occur in a simple, static world governed by ceteris paribus. For example, smugglers may be willing to risk losing larger shipments because the replacement cost in the

source country has decreased, thus shifting the preferred combination of drugs and other items;

this might raise the share of drugs seized, while lowering total smuggling costs because fewer pilots, couriers and other agents are arrested.

Hence, the lesson taught by the apparent conundrum is that the complex interactions among

interdiction resources, the smuggling sector, and drug consumption require a systematic analysis.

The authors are indebted to Karen Isaacson for programrm ng and Patrick Murphy for research assistance.

This paper draws on a publication of the same name published by RAND in 1966 as N-2660. The research for this paper was funded by the Office of the Under Secretary of Defense for Policy. The writing of this paper was supported by the RAND Drug Policy Research Center which is funded by the Ford and Weingart Foundations. The opinions expressed are not necessarily those of RAND or its sponsors. *Gordon Crawford died in a plane crash in 1989.

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37

38 J.P. CAULKINS et al.

The dynamic model presented here, SOAR (Simulation of Adaptive Response), attempts to provide such an analysis by taking into account adaptations by smugglers in response to changes in the strategies of interdiction agencies. The model traces how this adaptation affects the ability of increased interdiction efforts to reduce drug use in the United States.

The rationale of SOAR is straightforward and ignores the complexity of strategic market behavior. As the perceived risks associated with particular routes and modes of smuggling change, so do smugglers preferences for how they bring drugs into the country. Increasing the risks associated with one route and mode, leaving all other risks unchanged, alters the distribution of routes and modes by which the drug enters the United States away from that route and increases the cost of bringing in a given quantity. Increased smuggling costs raise the import price which in turn raises retail prices. This effect on retail price, modeled very simply in SOAR, ultimately reduces consumption.

We chose to develop a simulation model, rather than estimate the parameters of a behavioral system, simply because of data constraints. This simulation model permits us to incorporate many sources of data of varying quality and to fill in blanks where there simply is no data by using educated guesses. To partially compensate for this uncertainty about parameter values, the discussion focuses on the models qualitative behavior, not the particular numerical values it produces.

Section 2 presents the basic rationale of the model. Section 3 describes the model in greater detail; further detail and a program listing are provided in [2]. Section 4 describes some exercises

that were performed to partially validate the model. Section 5 uses the model to examine the effect of increasing the interdiction rate of cocaine. Section 6 offers some concluding comments.

2. OVERVIEW OF THE DYNAMIC NETWORK MODEL

Several studies have developed models of drug smuggling and interdiction and could be considered as the starting points for our analysis [3-51. These models estimate the effectiveness of additional assets in increasing the probability of interdiction in given geographical areas where interdiction can be effective. Unfortunately, both these and the other models we have reviewed assume that the quantity smuggled and the means of smuggling through given areas remain constant, regardless of the level of interdiction.

In estimating the effect that particular assets could have in raising the amounts of drugs seized,

or the effect of seizures and interdiction on the cost of smuggling drugs, these models disregard the ability of the smugglers to adapt and change their mode and locale of operation. This approach may, therefore, overstate the effectiveness of a given asset, so we chose instead to use a dynamic (not steady-state) network model.

This model, like all models, is built around some simplifying assumptions, the most important of which we discuss here. The network model considers several routes from drug sources in Central and South America to the consumer in the United States. Because of the lack of route-specific data, however, we treat routes as generic; no effort is made to associate particular geographic routes with particular parameters.

The amount that a smuggler desires to send in any one shipment is fixed and is an input to the model. The user also specifies the mean time between shipments. Together, these parameters govern the expected amount shipped per unit time. The individual shipment size is modified

sometimes, however, because some modes have restrictions on the size of any single shipment. The model not only allows a choice among different routes and different modes (air, sea,

or land) at any given time, but also allows the modeling of the dynamic changes of smuggler preferences over time as perceptions of the risks associated with different routes and modes change. The smugglers perceptions of the risk along any given route are determined by the number of successful interdictions and shipments. That is, it is assumed that each smuggler has access to the experience of all smugglers in making that estimate.

Thus, the smugglers face a version of the two-armed bandit problem, in which a gambler has the option of playing either arm of a two-armed slot machine, each one having an unknown, and different, probability of loss. The gamblers optimal strategy, given no information about the probability of loss for either arm, is to predominantly play the machine that has given the best

Drug interdiction 39

ratio of winnings to attempts and occasionally play the other machine to insure that he or she is not being permanently misled by the luck of past plays. For a full exposition of this analysis,

see [S]. Mathematically, smugglers face a harder problem: not only are there more than two routes and

even more than two methods of smuggling, but also, as the drug law enforcement (DLE) forces change the focus and deployment of their interdiction assets, the risks of interdiction associated with a route change over time in ways unknown to the smugglers.

We have assumed a strategy for the smugglers that is in keeping with the spirit of the optimal

solution to the two-armed bandit problem and with the dynamic nature of the problem. A smuggler computes time-weighted estimates (more recent history is weighted more heavily than older history) of the probability of interdiction along every route and then randomly chooses a route on the basis of these estimates of interdiction. The seemingly safe routes are chosen more often than the seemingly more dangerous ones. The strategy is implemented within a Monte Carlo simulation because an analytical solution is not feasible.

The inputs to the model include the probability of interdiction for each route. Varying these probabilities models the time phased placement of DLE interdiction assets, i.e., the movement of additional resources to particular smuggling routes.

Very little of the structure of the model is rigorously defensible; too little is known about the operation of smuggling markets to permit formal estimation of the important relations. The goal is to capture the important facets as well as possible. When given a choice among assumptions in the absence of data, we have generally chosen the one that is most likely to produce a finding of effective interdiction. Since the overall conclusion is that interdiction is only modestly effective, these are conservative assumptions.

The model may be simplified when applied individually to marijuana or cocainesome of the legs may be deemed unimportant for a particular drug. The intent is to build a general model and make it applicable to an individual drug by suitable choice of parameters. Here we present only the cocaine results. Crawford and Reuter [2] also present results for marijuana, where the models validity is somewhat weakened by the existence of a substantial domestic marijuana production sector. The relevance of the model to heroin is difficult to determine; heroin is imported, but interdiction is a less targeted enforcement activity and dedicated smuggling vessels are rare. The other major drugs are mostly produced domestically in the United States.

The next section describes the model in greater detail, and Section 4 reviews some valida-

tion exercises that were conducted. Section 5 describes an application of the model to cocaine

smuggling.

3. DETAILS OF THE SOAR MODEL

The model is an event-based Monte Carlo simulation implemented in FORTRAN. Shipments are assumed to occur according to a Poisson process, with a rate parameter selected so that the expected number of shipments per unit time equals the user specified input value. For each shipment, a route is selected randomly with probability based on the results of previous smuggling attempts. The shipment may or may not be interdicted, depending on the probability of interdiction along the selected route. In either case, the necessary bookkeeping is done and the simulation moves on to the next shipment attempt.

The desired shipment size is an input parameter. In the runs described in Section 5, we used a value of 420 kg, which was the average size of a U.S. Customs cocaine seizure in 1991.

Each mode has an associated maximum shipment size. This parameter is intended to describe a typical professional shipment size, rather than a seizure of drugs that might be taken from a tourist or amateur smuggler. The data were taken from Drug Enforcement Administration [7] and Office of Technology Assessment reports [8] giving sizes of seizures and adjusted as deemed necessary.

The probability a given route is selected is proportional to the of taking that route (Ck), i.e.:

P{route k selected} = l/ck

Ck l/Ck

reciprocal of the expected cost

(1)

40 J.P. CAULKINS ef al.

The expected cost of sending a shipment of Q units of a drug on route k can be divided into three parts: (1) the regular costs of sending a shipment, (2) the risk compensation premium commanded by the crew, and (3) the expected cost of losing a shipment. The last is the product of the perceived probability of interdiction along that route (denoted PPIk) and the cost of losing a shipment. This can be expressed more formally as:

Ck = Cost_to_Shipt + Risk_Compensationk

+ PPIb (Q * Export-Price + Cost_if_Interdictedk). (2)

The perceived probability of interdiction (PPIk) is the fraction of all shipments sent along that route which were interdicted, adjusted so that information about more recent shipments is weighted more heavily than the outcomes of earlier shipments. It is computed as follows:

PPIk _ Cj Ii e-a(T-t*) xi e-b(T-ti) (3)

where the summation is taken over all shipments sent on route k, T is the current time, ti is the time of the i th shipment, and

Ii = {

1, if shipment i was seized,

0, otherwise.

The constant b is chosen to give go-day old data a fraction f of the weight of new data. That is: e- = f. For th e runs reported below, f = 0.1, so b M 0.02558, but other values are possible.

The Export-Price is simply the amount the smuggler pays an exporter in the source country per unit to obtain the drug. The value of $3,000 per kg of cocaine used below is intermediate to the export prices in the three principal source countries: Colombia, Peru, and Bolivia [7].

The Cost-to-Ship by this route includes all operating expenses associated with sending one shipment, irrespective of size, along a given route, except the risk compensation costs and the interdiction costs. Lacking more detailed data, we used the same cost to ship for all routes of a particular mode (air, sea, or land). We assumed that the costs to ship by sea ($19,200) were less than by air ($24,000). The land route was considered to be an expensive but safe route; hence, its cost was much higher ($144,000).

Personnel costs can be broken down into conventional wages and risk compensation. Con- ventional wages recompense individuals for their time and effort; they are independent of the perceived probability of interdiction and are incorporated in the Cost_to_Ship. Risk compensa-

tion recompenses individuals for the risks, principally of arrest and incarceration, to which they are exposed. It is assumed that the necessary risk compensation will increase non-linearly as a

function of the perceived risk, that is, of the PPI. The particular form used here was:

.

The proportionality constant was estimated from the average sentence given to convicted smugglers, the average rate of conviction of drug smugglers, and our guess of the earnings potential of the people at risk.

Assuming an air crew size of one, or occasionally two, people with reasonably high legitimate earning potential, the risk compensation was set at $1,440,000 for air shipments. Ship crews are larger. However, the potential earnings of most of the crew is much smaller, hence, the risk compensation for the entire crew was set at $480,000 for sea shipments. Because of the lack of earning potential of the single smuggler who carries cocaine over the land border, $12,000 was set as the risk compensation for land shipments.

If the shipment size exceeds the maximum allowed size for that mode, it is broken into several shipments and

the costs and other considerations are adjusted accordingly.


Using a risk compensation exponent (p) greater than one will result in risk compensation increasing super-linearly, an assumption that enhances the effectiveness of increasing interdiction. In the runs described below, we used a risk exponent of /3 = 2, resulting in the risk compensation

pay varying as the square of the PPI. The Cost_if_Interdicted should reflect all expected costs to the smuggler of replacing seized cap-

ital, establishing new personnel and contacts (where necessary), and of legal expenses associated with defending arrested personnel. It should also include the replacement costs of seized assets, but not seized drugs.

In the runs described below, the Cost_if_Interdicted for shipments were $240,000 by air, $48,000 by sea, and $6,000 by land. These estimates reflect our belief that smugglers will make a substantially greater effort to try to release an experienced pilot, or incur substantially more costs in replacing a pilot, than they would for a boat and ships crew. By contrast, we have been told that the people used to carry drugs across land borders are generally considered expendable. The seemingly low figure for the sea routes has also been influenced by Coast Guard observations that many smugglers boats are barely seaworthy.

Once the smuggler has selected a route, the model computes the probability of interdiction and determines whether the shipment was successful, based on that probability. One of the models inputs is the probability of interdiction along a given route in a given epoch, but that probability is adjusted to penalize smugglers who try to change tactics too quickly. Suppose the raw probability of interdiction on this route at this time is PI. Then with probability

P' = 1 - (1 - PI)R, (5)

the shipment is interdicted. The saturation factor, R, is equal to the maximum of 1 and the ratio of the rate of shipments over the recent past to the rate of shipments over the long past. In

particular,

R=max 1

rate of shipments in past 20 days

rate of shipments in past 120 days 1 (6)

Shipments are simulated for a run-in period to establish a basis for calculating R on the first day of the simulation.

The assumption here is that capacity along a route is the average rate of shipments over the last four months, and costs go up if this rate is exceeded in the last three weeks running. This method of calculating P implies that smugglers can slowly build the capacity of a route at little increase in risk, but substantially increasing throughput over a 20-day period can impose a large

increase in risk.

Equations (l)-(6) d escribe how SOAR processes each shipment. Those steps are repeated until the simulation has run for the time specified by the user, at which point the trial ends.

Since each trial is a simulation, successive trials will not produce identical results, raising the question of how many trials must be conducted for a given set of parameter values before the run-to-run variation averages out, leaving suitably precise estimates of the quantities of interest.

With SOAR, each Monte Carlo trial is itself a result of a large number of Monte Carlo experiments, so the run-to-run differences are usually small. We empirically verified the run-to-run variation in the averages of the reported statistics by repeating 20 sets of 10 runs. These 20 sets of 10 runs yield 20 independent observations of the output measures. (The output measures are the means of the output of 10 runs.) We looked explicitly at the following statistics: the average success rate, the average total cost to the smugglers, the average quantity interdicted, and the average number of attempts to use the land route. Using the results of these 20 sets of runs, we compiled statistics on the variation in the means of a set of 10 runs. (See [2] for details.)

Among these statistics, the number of attempts to use the land route can be expected to have the most variation because the other outputs are the results of action on all routes. Still, its coefficient of variation was a modest 0.046, suggesting that a confidence band of plus or minus 2 standard deviations around the mean would range from about 10 percent below the observed number of attempts to 10 percent above. The similar confidence bands around the other variables were even narrower on a percentage basis.


Hence, replicating a scenario as few as ten times gives adequately precise means, particularly in view of the rather large uncertainty about some of the parameter values. Still, to be conservative, we ran 20 trials for each of the results reported in Section 5.

4. MODEL VALIDATION

Model validation is always a concern, particularly with simulation models and most particularly with models of incompletely understood systems about which relatively few data are available, as is the case with drug smuggling. We certainly cannot claim that SOAR has been, or ever could be, validated rigorously, but this section briefly describes a range of exercises that were conducted which give us some degree of confidence that the model does not grossly distort reality.

Several SOAR runs were made in scenarios where all routes had identical interdiction probabilities and the shipments were small, equal size, and frequent. In these runs shipments do not saturate routes so the proportion of shipments interdicted in the model should be close to the probability of interdiction, which is an input. These scenarios can be analyzed with back- of-the-envelope calculations; upper bounds on the experimental error are easy to compute. The differences between the proportions computed in the model and the input probabilities have been small and well within the range of expected variations inherent in a Monte Carlo simulation.

Another of the exploratory series of runs held all parameters constant, except the mean time between shipments and the shipment size; the model dispatched a smaller number of larger shipments. Both the mean time between shipments and the shipments size were increased by the same multiplicative factor. The results were as expected: most output statistics remained fairly constant; but as the shipment size gets bigger, the amount shipped over a route per unit time becomes more random. As this occurs, routes occasionally become randomly saturated, and the proportion interdicted rises. This reflects our assumption that interdiction agencies react positively to increased flow rather than being flooded.

In another series of runs the parameters describing different routes were varied to make individual routes advantageous or expensive. The resulting proportion of drugs shipped along each route was compared with the proportion before parameters were adjusted. The long term averages of the amount of drugs shipped, by route, were as expected-the more expensive routes were rarely used, the less expensive ones dominated.

We also conducted runs to examine alternative methods of modeling smuggler adaptation. The method used in the model, and described in detail above, assumes that smugglers have perfect historical recall of all past shipments, successes, and interdictions. This modeling assumption is clearly favorable to the smugglers. To some extent this assumption is mitigated by another assumption-the smugglers are forced to make a weighted random choice of routes rather than using routes clearly perceived to be cheaper. The degree to which these assumptions bias the results in favor of the smugglers or the DLE forces is unknown.

Because of our concern about the effects of these assumptions, we varied the extent to which past history influenced the random choice. By increasing the dispersion among the weights until one weighting constant is several orders of magnitude greater than the others, we modeled a strategy where the smuggler always uses the route perceived to be the cheapest. By shrinking all the weights toward an average value we were able to model strategies where historical attempts and successes and perceived costs had little effect on the choice of routes.

In the runs without randomization, where the smuggler always used the route perceived to be the cheapest, we found that the delay between the deployment of DLE forces and the predictable response of smugglers became too obvious; there were clear strategies for the DLE that took advantage of the unduly predictable timing of smugglers reactions. The value of interdiction assets in these cases was seen to depend heavily on the degree to which the DLE deployments took advantage of the almost deterministic smugglers reactions. These scenarios lacked realism and robustness; small and seemingly inconsequential changes in DLE timing could have large effects.

Going to the other extreme and using randomization where perceived costs have little effect in the selection of routes also gave unreasonable results. Smugglers continued to use routes regardless of the high interdiction rates and high costs.


There is a broad middle ground where changes in the degree of randomization, and minor

changes in the scenario, had little effect. The model logic described here falls in this middle

ground. These runs provided confidence in the model and some understanding of the consequences of our chosen method, and alternative methods, of modeling adaptation.

These validation runs suggest that the models behavior conforms to our intuitive understand-

ing of the smuggling sector, but there is no guarantee that our intuition is right. That is, we may

have successfully modeled our own mental model, but not the real world. Nevertheless, given the quality and unavailability of data, the inability to run controlled experiments, and the dearth of natural experiments, it is difficult to conceive of truly satisfying validation tests.

5. AN APPLICATION OF SOAR

SOAR is a versatile tool which can be used to investigate a variety of issues related to inter-

diction, but here we examine the impact of a backstop smuggling technology (such as smuggling small shipments across a land border), the implications of not being able to increase the interdiction rate on all routes simultaneously, and the possible benefits of future increases in the

interdiction rate. Table 1 presents the common parameter values used for all of the runs. Individual runs are

distinguished by the interdiction rates specified for each route over time. Existing estimates of the

interdiction rate in a particular sector, regardless of the mode of smuggling, are of questionable accuracy. A good estimate of the interdiction rate along a route can be made only if there is good information about the amount of a drug being smuggled over the route. In the rare event that intelligence is available about the total flow through a sector, it is apt to be used to disrupt the smuggling along that route, and hence ceases to be descriptive of activity there.

Table 1. Summary of inputs.

Run-in period:

Simulated period:

Quantity delivered:

Export cost:

Desired shipment size:

Risk compensation exponent:

120 days

365 days

300.03 metric tons

93,OOO/kg

420 kg

2.0

Air Routes: I

cost to ship = Risk compensation proportionality constant =

Cost if Interdicted = -_ Maximum shipment size (kg) =

Sea Routes:

$24,000

$1,440,000

$240,000

2,000


Cost if Interdicted = __ Maximum shipment size (kg) =

Air Routes:

$19,200

$1(920,000

$48,000

16,000


Cost_if_Interdicted =

Maximum shipment size (kg) =

$144,000

$12,000

$6,000

50

For these reasons, we have been forced to rely on global estimates of the overall interdiction

rate, which were based on seizure data and consumption estimates, and have assumed that the probability of interdiction is equal on all routes and modes, except the expensive, but relatively


safe, land route. Since of all the parameters used in the model the interdiction rates are least well known, the results below are presented for ranges of interdiction rates.

Eleven routes were used in these runs: five air, five sea, and one land route. That choice, rather than 10 or 12 or 17, was arbitrary, but our desire to make the set of options available to the smuggler sufficiently rich suggested that the number of routes be no less than 10.

The land route is intended to model methods of smuggling that will probably remain viable regardless of the level of federal interdiction efforts, such as smuggling through ports of entry or

across remote areas of the Mexican border. Two types of analyses are reported. In the first, consumption is assumed to be constant at

300 tons per year-roughly the level of imports in 1991. Scenarios are then compared using a variety of measures produced directly by SOAR.

The second type of analysis incorporates the feedback to consumption and production that would result from elastic markets. They differ from the first series in that the quantity landed varies from run to run, and this quantity is the primary criterion for judging the effectiveness of the additional interdiction resources.

5.1. Consequences of the Existence of a Backstop Technology

In thinking about the impact of interdiction, a natural first approximation is to consider what would happen if interdiction rates increased simultaneously across all routes. Such thinking could be misleading, however, if there existed smuggling modes that were largely immune to increased interdiction, even if they were relatively little utilized at present because of their cost. Such a

mode may in fact exist for cocaine smuggling, namely bringing the cocaine across a land border in relatively small units.

To estimate the importance of such a backstop technology we compared two sets of runs. The first examined the impact of maintaining various probabilities of interdiction on all routes, including the land route, ranging from 0.0 to 0.75 in increments of 0.05. The second set of runs were similar except that the probability of interdiction on the land route was held steady at 0.10. It seemed obvious a priori that the effect of increasing interdiction rates would be diluted in the second set of runs, but the question was, by how much?

The answer, it turns out, depends on which outcome measure one uses. There are actually two probabilities of interdiction that could be of interest. One is the probability that a randomly chosen kilogram of a drug is seized in the interdiction process. The other is the probability that a randomly chosen shipment gets seized. If all shipments were the same size, or if all shipments

incurred the same risk of interdiction, these probabilities would be the same, but in general they are different.

We define the interdiction rate (PI) as the number of shipments interdicted divided by the number of shipments attempted. This is the more relevant figure for measuring the risk to which

smugglers agents are exposed, the number of individuals associated with a shipment being very

insensitive to shipment size. The other probability mentioned above would be estimated by the quantity seized divided by

the quantity attempted. This will be referred to as the seizure rate (f). Since shipments are of different sizes and routes have different probabilities of interdiction, these probabilities will not necessarily be equal. In particular, the interdiction rate is usually smaller than the seizure rate because overland shipments are smaller and less likely to be intercepted than sea or air shipments.

Figures 1 and 2 illustrate the difference. Figure 1 contrasts the overall interdiction rate, counting air, sea, and land routes, when there is and is not a backstop technology. When a backstop technology exists, as the interdiction rate on the air and sea routes increases, more shipments are sent by land and the overall interdiction rate plateaus.

As Figure 2 shows, however, since overland shipments are much smaller, the impact of the existence of a backstop technology on the seizure rate is much less dramatic.

The model user specifies the mean time between shipments, and hence the expected amount shipped, but because the simulation itself is random, it is not possible to ensure that exactly 300 tons are delivered. To facilitate comparisons, SOAR linearly scales the outputs so that 300 tons were delivered in each case, or more precisely, 822 kg/day * 365 days = 300.03 tons. In most cases, the scaling was by less than 1% and so does not distort the results in any noticeable way.

Drug interdiction 4.5

...... . . . . . . . . . . . . . . No Backstop / - Backstop ,... >

. ..* ..*

. .. ,... *

. .. /.J

/.*. ..*.

. . . . . . . . . . ... NO Backstop

0.6- - Backstop

0.0 0.2 0.4 0.6 0.6 0.0 0.2 0.4 0.6 0.8

Probability of Interdiction Probability of Interdiction

Figure 1. Fraction of shipments seized with Figure 2. Fraction of cocaine seized with

and without a backstop technology. and without a backstop technology.

Plots of the quantity seized tell an intermediate story. The quantity seized does not plateau

when a backstop technology exists, but the no backstop and backstop curves for the quantity seized diverge more dramatically than they do in Figure 2.

Rather than debating the relative merits of these measures, it might be more constructive to

turn to yet another. Ultimately the objective of interdiction is not to seize drugs, but rather to reduce consumption. Given the efficiency of domestic cocaine markets, interdiction does not generally accomplish this by creating spot shortages, but rather by increasing the cost of smuggling. Some fraction of this cost is passed through as an increase in the retail price, which in turn reduces consumption. Hence, it makes sense to examine the impact on the cost of delivering a kilogram of cocaine. (See Figure 3.)

t50000 @

.a $4ocm- E . . . . . . . . . . . . . .

?

No Backstop

- - Backstop

p

0.2 0.4 0.6 , Probability of Interdiction

Figure 3. Cost of smuggling one kilogram of cocaine with and without a backstop

technology.

The height of the curves and the point at which they begin to diverge appreciably depend on the parameter values, but the general shape is robust, and hence one can draw a number of conclusions.

KII 1712-E

46 J.P. CAULKINS el al.

The first is that for the range of interdiction rates thought to pertain for air and sea shipments over the last 15 years (probably at least 0.10, probably not more than 0.4), the existence of a backstop technology has had relatively little impact on the cost of smuggling cocaine into the U.S.

The second is that the cost of smuggling cocaine is a convex function of the probability of interdiction, and it begins to increase quite rapidly as the probability of interdiction moves beyond 0.4. This suggests that whatever the benefits of past increases in interdiction, further increases would generate more benefits per unit increase in the interdiction rate than they did in the past. Although this says nothing about the marginal benefit per dollar spent on interdiction, since it is not known whether the cost of achieving a one percent increase in the interdiction rate changes with the interdiction rate, it still suggests that it is worth investigating what order of magnitude the benefits might be.

As the interdiction rates on air and sea routes cross 40%, however, the existence of a backstop technology begins to make a difference; the convexity of the backstop curve in Figure 3 is substantially less pronounced than that of the no backstop curve. Since smuggling over land borders does occur and is difficult to stop by conventional interdiction efforts, such an investiga- tion should be based on the data from runs with a backstop technology, which are presented in Table 2.

Table 2. Impact of increased interdiction on air and sea routes with interdiction rate on land route fixed at 0.10.

PI on PI on Seizure Amount Cost/Kg Arrived by

Air & Sea All Routes Rate Seized (MT) Delivered Land (MT)

0.00 0.01 0.00 0 $3,000 0

0.05 0.06 0.05 17 $3,300 2

0.15 0.14 0.15 54 $4,100 8

0.20 0.18 0.20 74 $4,800 12

0.25 0.20 0.24 95 $5,500 17

0.30 0.22 0.29 121 $6,600 26

0.35 0.24 0.33 148 $7,800 34

0.40 0.25 0.37 178 $9,100 43

0.45 0.26 0.41 208 $10,600 54

Roughly speaking, the 1986 interdiction rate for air and sea routes was about 0.20, yielding an overall interdiction rate of about 0.18 [2]. By 1990-1991, the quantity seized was about 100 tons, suggesting that the interdiction rate on the air and sea routes was about 0.25.3 According to

the table, that should have represented an increase in the cost of smuggling of about $700. That increase, however, was swamped by a collapse in the export price in the source countries [7] and quite possibly also learning curve effects [9]. Hence, the model suggests that the massive increases in interdiction spending undertaken had the potential to increase import prices by roughly $700 per kilogram, but other factors masked its effect.

5.2. Impact of Further Increases in Inter-diction on Smugglers Costs

SOAR also allows one to make rough estimates of the impact of further increases in the interdiction rate. It is difficult to judge by how much interdiction rates might increase. On the one hand

3Note that the modest increase in the seizure rate was accompanied by a very substantial increase in the quantity seized because the quantity delivered increased dramatically to about 300 tons.


while inflation-adjusted spending on interdiction increased by 125% between 1986 and 1991 [l], the interdiction rate increased only modestly. One might conclude from this that it is unlikely

that interdiction rates could ever be increased much above 0.30 or 0.35. On the other hand, best estimates of the total quantity of cocaine smuggled increased by roughly the same amount between 1986 and 1991, so the number of dollars spent per kilogram smuggled did not change substantially. Hence, if it were true that the interdiction rate is determined more 6y the ratio of interdiction effort to the amount smuggled than by interdiction effort alone, one might be more optimistic about the prospects for greater increases in the interdiction rate. In particular, if the quantity smuggled leveled off while spending increased further or if the quantity smuggled decreased while spending remained constant, it is possible that the interdiction rate might increase noticeably.

Since our overall conclusion is that increased interdiction is unlikely to substantially affect U.S. consumption, we will be conservative and consider an optimistic scenario under which interdiction

rates increase from 0.25 to 0.5, at least on some routes. What impact would this have on the costs of smuggling and consumption?

A naive observer might argue that the amount seized per unit reaching the U.S. would triple (e.g., from 1 ton in 4 to 3 tons in 6), so the costs of smuggling should roughly triple. And/or one might argue that whereas before 314 of what was shipped got through, now only l/2 would get through, so consumption should fall by 33%. If one recognized that it is probably not feasible to

so drastically increase the interdiction rate on all routes, the naive observer might assume that these two figures could be scaled back proportionately. That is, raising the interdiction rate on half the air and sea routes would double the cost of smuggling a kilogram and cut consumption by 16.5%. Working with SOAR shows just how naive such back of the envelope calculations can

be. First of all, not all smuggling costs are costs of interdiction, and there is a backstop technology,

so the costs of smuggling would not triple. Table 2 suggests instead that even if the interdiction rate were increased on all routes, smuggling costs would increase by about 125% to $12,300 per kilogram delivered. That is a substantial increase, but costs would not triple.

The discrepancy becomes even more severe if the interdiction rate is not raised uniformly across all routes because smugglers can react. Figure 4 shows the impact on the cost of smuggling of raising the interdiction rate from 0.25 to 0.50 on various numbers of air and sea routes.

s14ow

54000 0

7

.

.

.

.

. .

. .

. l

'10 la0 lhl 281 282 3a2 383 483 414 584 5L5

Number of Air & Sea Roufes, Respectively,

on Which Interdiction Rate is Raised

Figure 4. The impact of increased interdiction on Figure 5. The impact of randomly rotating in-

the cost of smuggling one kilogram of cocaine. terdiction assets across routes.

814OOc

$12000 D e

it L.-z

0"

E $lOcOO

z

0"

E

2 SBOOO

;;

0"

; tliow

i-

54000

I-

. Fixed Routes 0 Varying Routes

0

0

.

0

0

0

.

. 0

0 .

.

0 .

0 . .

0 :

I&O 180 181 Z&1 2&Z 362 383 483 4&4 514 5&5

Number of Air & Sea Routes, Rospeclivcly,

on Which Interdiction Rate is Raised

If one raises the interdiction rate from 0.25 to 0.50 on half of the air and sea routes (in particular on 3 air and 2 sea routes), then one only raises the cost of smuggling by about $1600, which is


less than one-quarter of the roughly $6,800 increase one achieves by raising the interdiction rate on all routes. Hence, the naive observers linear scaling substantially overstates the expected benefits of a realistic program.

The problem, simply put, is that smugglers can learn to avoid those routes for which the

interdiction rate has been raised. Figure 5 illustrates this point by overlaying a plot of the smuggling costs if the interdiction rate were raised on various numbers of air and sea routes and the particular routes for which the rates were raised changed periodically in an unpredictable manner. 4 When no routes or all routes have their rates increased there is no difference between the fixed and varying strategies, but for intermediate numbers, by varying the location of increased interdiction, the DLE can mitigate some of the convexity displayed in Figure 4. The data for these runs are displayed in Table 3.

Table 3. Impact of increasing interdiction on fixed vs. varying routes with interdiction

rate on land route fixed at 0.10.

Total

cost

(billions)

# of Air SC Amount cost Amount Total cost Sea Routes Seized per/Kg Seized cost per/Kg

Affected (MT) Delivered (MT) (billions) Delivered

O&O 95 $5,500 95 $1,660 $5,500

l&O 97 $5,600 104 $1,760 $5,900

l&l 104 $5,900 115 $1,890 $6,300

2&l 111 $6,200 127 $2,040 $6,800

2&2 116 $6,500 142 $2,220 $7,400

3&2 128 $7,100 156 $2,440 $8,100

3&3 138 $7,600 174 $2,680 $8,900

4&3 152 $8,300 189 $2,880 $9,600

4&4 172 $9,200 201 $3,070 $10,200

5&4 199 $10,500 215 $3,330 $11,100

5&5 237 $12,300 237 $3,700 $12,300

$1,660

$1,700

$1,790

$1,890

$1,980

$2,140

$2,300

$2,490

$2,770

$3,160

$3,700

T Fixed Routes T Varying Routes

Unfortunately, if it were possible to raise the interdiction rate on a route some of the time, it would be possible to raise it most of the time. That is, it is probably not realistic to hope that DLE forces could be moved rapidly and unpredictably enough to make much of a difference, at least not without incurring substantial costs.

Hence, SOAR suggests that even if the DLE forces could double the interdiction rate on half of the air and sea routes, it would only increase smuggling costs by about $1,600 per kilogram (less than 30%), which is much less than the 100% increase a naive observer might have predicted.

5.3. Impact of Further Increases in Interdiction on Consumption

Let us now turn to the second question: by how much would such an increase reduce con-

sumption? A crude estimate to the answer to that question can be obtained by making some assumptions about three key elasticities:

n, = elasticity of the export price with respect to total shipments to the U.S., nd = elasticity of demand with respect to the retail price, and r]r = elasticity of the retail price with respect to the import price.

The first elasticity, n5, captures the effect of seizures on the replacement cost of drugs for smugglers. If price increases induced by higher seizures do not reduce consumption (demand) by as much or more than the amount seized, then total shipments from the source countries to the United States will rise [lo]. To persuade farmers to grow more and processors to refine more, it may be necessary for smugglers to offer higher prices at the point of export.

In particular, the varying routes were simulated by moving the DLE forces every 40 days over the course of a year and not letting the smugglers anticipate the moves.


There is no basis for systematic estimation of this price elasticity. Discussions with officials suggest that they believe it to be very low. In the short run, this perception is influenced by the apparent availability of very large inventories, which would dampen the price effect of increased

U.S. demand. In the long run, the fact that U.S. cocaine consumption is less than half of total source country production5 and that the resources required for production (low productivity land and rural labor) are in ready supply make it unlikely that prices would have to increase much to induce a higher supply of cocaine.

Our assumption is that a one percent increase in shipments to the United States requires a one percent increase in the export price, i.e., 71~ = 1.0. This is a larger effect than we actually believe is likely to hold, but it is a conservative assumption intended to allow for the possibility

that interdiction can have a large effect on export price, and hence on domestic consumption. The elasticity of demand for cocaine is simply not known. Some might think that demand

is perfectly inelastic because the users are addicted, but addiction is rarely so absolute and even drug users have a budget constraint. Cocaine consumption is not, in that sense, altogether different than consumption of other goods. In particular, it might bear some resemblance to consumption of the two most commonly used licit drugs, tobacco and alcohol, at least the first of which is highly addictive.

The elasticities of demand for tobacco and alcohol are also not known, but the central tendency of the studies reviewed by Manning el al. [ll] was -0.5. That is, consumption declined by 0.5% for every 1% increase in price. We will use this figure in the calculations below.6

The third elasticity (v,), the elasticity of the retail price with respect to changes in the import price, might seem innocuous, but it has been the subject of considerable debate. Conventional wisdom holds that it is quite small because retail prices are currently approximately ten times import prices. With competitive markets in the post-import distribution sectors, a $1 increase in the import price might be expected to raise retail price by only about $1.25, even allowing generously for the additional domestic inventory costs [12]. That would suggest an elasticity of retail to import price of only 0.125. This figure might be increased to 0.2 to account for non-enforcement risks that rise with the value of the drugs held in domestic transactions.

A second line of argument holds that since many of the costs of distributing drugs in the U.S. depend more on their value than on their weight or quantity, price increases might be passed through more on a percentage or multiplicative basis rather than an additive basis [13]. If all costs obeyed the multiplicative model then by definition the elasticity of retail prices with respect to input prices would be 1.0, since a one percent increase in import prices would translate to a

one percent increase in retail prices. Some distribution costs do depend on quantity rather than

value, however, suggesting that Q is between 0.2 and 1.0, but closer to 1.0. Below we will use both qP = 0.2 and qP = 0.9 and contrast the results obtained.

To use these elasticities, one starts with a base case. We use an interdiction probability of 0.25 on all air and sea routes and 0.10 on the land route (6 th line in Table 2) because it reasonably approximates current conditions. The various scenarios described in Table 3 are then considered.

To compute the change in consumption we also need estimates of the seizure rate and import price in the base case and scenarios of interest. The seizure rate in the base case is given in Table 2 as 0.24. It will be assumed that the feedback from the elastic markets has a negligible effect on the seizure rate and hence that the seizure rates (f) for the various scenarios can be computed directly from Table 3. For example, SOAR predicts that if the interdiction rate were raised on 3 air routes and 2 sea routes and not varied, 128 metric tons would be seized, so the seizure rate would be 128/(300 f 128).

The basis for computing the import price is the assumption that smugglers revenues cover their costs. Hence, from Table 2, for the base case the import price is just $5,500 per kilogram, the average cost per kilogram delivered. For the various scenarios described in Table 3, the cost per kilogram must be adjusted by the change in the export price relative to the base case price of $3,000 per kilogram.

5Consumption and seizures in the source countries and European consumption account for most of the rest.

Strictly speaking, the quantity used below is the elasticity of domestic removals with respect to price. Domestic

removals includes both consumption and domestic seizures, but consumption dominates removals so this distinction

is unlikely to be important.


Given these assumptions the elasticities can be used to write two equations relating the new export price (EP) to the new quantity delivered (QD). The first elasticity relates the percentage change in the export price to the percentage change in the amount shipped:

EP - $3,00O/kg

$3,OOO/kg (7)

where %3,00O/kg is the export price in the base case, and 300 tons is the amount delivered in the base case.

The remaining two elasticities allow one to relate the percentage change in the amount delivered to the percentage change in the import price:

300 tons - QD (Cost/kg + EP - %3,00O/kg) - $5,5OO/kg

300 tons = Id%

$5,5OO/kg > 1 (8)

where $5,5OO/kg is the import price in the base case. Table 4 presents the results obtained by solving Equations (7) and (8) for the various runs

described in Table 3 with the increased interdiction on fixed routes.7 Figure 6 plots the amount of cocaine landed when various numbers of air and sea routes have their probabilities of interdiction raised from 0.25 to 0.5 on both fixed and varying routes for both rip = 0.2 and vp = 0.9.

Table 4. Impact of increasing interdiction on fixed routes on consumption, export

prices, and value of exports.

# of Air &

Sea Routes

Affected

O&O

l&O

l&l

2&l

2&2

3&2

3&3

4&3

4&4

S&4

5&5

7)r = 0.20 np = 0.90

Amount Export Export Amount Export Export

Delivered Price Value Delivered Price Value

(MT) (g/kg) (billions) (MT) (S/kg) (billions)

300 $3,000 $1,180 300 $3,000 $1,180

299 $3,040 $1,190 297 $2,990 $1,170

297 $3,040 $1,220 290 $2,960 $1,160

296 $3,020 $1,230 283 $2,940 $1,140

294 $3,100 $1,260 276 $2,910 $1,120

290 $3,150 $1,300 264 $2,860 $1,080

287 $3,190 $1,340 253 $2,800 $1,040

284 $3,250 $1,390 240 $2,660 $960

278 $3,320 $1,450 223 $2,470 $860

271 $3,420 $1,540 192 $2,420 $770

260 $3,540 $1,650 155 $2,110 $590

Figure 6 suggests that the prospects of making a substantial dent in U.S. cocaine consumption by increasing interdiction rates are slim indeed. If the additive model holds (7,~~ = 0.20), then even if DLE doubles the interdiction rate on half of the air and sea routes, the amount of cocaine reaching the US would fall by only 3%-5%, depending on whether they could somehow re-deploy across routes in an unpredictable manner. If the multiplicative model holds, the corresponding

reductions in consumption are 12% and 20%. Such reductions are noticeable perhaps and are roughly in line with naive predictions, but they are still not particularly dramatic when one considers the effort which would be required to achieve them. The reductions in consumption only become substantial if the DLE can double the interdiction rate on all air and sea routes and the multiplicative model holds.

7The numbers reported in Tables 2 and 3 have been rounded off; the calculations used the original SOAR outputs

and rounded off at the end. Hence, the results in Table 4 may differ slightly from what one would obtain

reproducing the calculations using the numbers reported in Tables 2 and 3.

Drug interdiction

. . . . . * . . .

Flxed. elastkily-02 varying, elasUcny-g2

Fixed. elasgd94.9 vafyhg, elasudly-0.9

51

O&O 110 ,(L, 25, 2h2 362 363 453 434 534 535

Number of Air & Sea Roules, ReSPeCtiJelY, on Wl,lCll InlcrfJlctlon ROlD IS Rnlscd

Figure 6. The impact on consumption of increasing the interdiction rate.

It is also of some interest to consider export prices and revenues. Seizures, though a positive measure for interdiction forces in the United States, may create a problem for the drug control

forces in source countries, because under some circumstances they increase the demand for shipments and hence the income received by source country producers. Table 4 shows that if the additive model holds (qP = 0.20) total export revenues would actually rise as the interdiction

rate increased, and they would rise more quickly than deliveries fell.

6. CONCLUSIONS

This paper presents a Monte Carlo simulation of the smuggling and interdiction of illicit drugs that explicitly allows for adaptation across routes and modes. The Simulation of Adaptive Re- sponse (SOAR) model was then used to examine several issues surrounding the interdiction of

cocaine shipments to the U.S. The first lesson derived is that judgments as to the efficacy of interdiction efforts depend

significantly on the evaluation measure used. (See also [14].) Assuming a relatively safe but expensive land route is available, increasing interdiction rates on air and sea routes beyond 0.3 or so has essentially no impact on the overall interdiction rate (i.e., the fraction of shipments seized). The reason is simply that an increasing fraction of the drugs would be carried in small

shipments over relatively safe routes. If, in contrast, the measure of success were the seizure rate (fraction of all drugs seized) or simply the quantity of drugs seized, such increases in interdiction

rates would appear to be much more effective. The goal of interdiction, however, is not to seize drugs but rather to reduce consumption by

increasing prices, so none of these measures is particularly appropriate. Examining the impact on the smugglers cost per kilogram delivered is a reasonable metric for assessing the relative efficacy of various programs, and by making a few assumptions about elasticities, one can translate these effects on costs to impacts on consumption to get a sense of the absolute level of benefits increasing interdiction might bring.

Another lesson is that back-of-the-envelope estimates of interdictions effect on costs can be overly optimistic if they neglect the existence of a backstop technology (smuggling small shipments over the land border), the concavity of smugglers costs as a function of the fraction of all air and sea routes on which the interdiction rate is increased, and the fact that not all smuggling costs are caused by interdiction.

With respect to the backstop technology, SOAR suggests that the ability to smuggle small shipments over the land border did not play a decisive role in the lack of success of past increases in interdiction rates. It is more likely that any benefits they might have produced were swamped by falling export prices in the source countries. If interdiction rates on air and sea routes were


doubled from their current levels, however, smuggling by land could become more significant and blunt the impact of such an increase.

The SOAR model also shows that raising the interdiction rate on half the air and sea routes generates less than half the benefits of raising the interdiction rates on all routes. The extent of the concavity of the relation depends on how sharply the rates are being raised, but this result suggests that in general the DLE should strive to increase interdiction rates uniformly. Somewhat the same effect could be achieved by redeploying resources frequently and unpredictably to keep the smugglers from discovering which routes are relatively unprotected. Either way one looks at it, the moral is the same; there is no sense building a Maginot Line which can be outflanked.

When the impacts on smugglers costs are translated into changes in consumption, interdiction looks even less promising. Because demand for cocaine is probably somewhat inelastic and there is the very real possibility that the elasticity of retail prices with respect to import prices is on the order of 0.2, modest increases in smugglers costs may have essentially no impact on consumption. If the multiplicative model holds so that the elasticity of retail prices with respect to import prices is closer to unity, then increasing interdiction might have a noticeable, but still not dramatic, effect on consumption. Only in the most optimistic of all scenarios would there be a sizable impact on consumption.

One final point of interest is that, under quite plausible circumstances, increasing interdiction rates could have the negative side effect of increasing export revenues of traffickers in the source countries.

SOAR and its variants constitute an early effort to systematically analyze how interdiction can raise smugglers costs and lower consumption. More refined, data based versions of these models should be developed. The precise quantitative results presented will certainly not be replicated. We do believe, however, that a more extensive effort will replicate the finding that interdiction must be very stringent and the multiplicative model of the linkage between import and retail prices must hold for interdiction to greatly affect U.S. cocaine consumption.

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Documents

Simulation of Adaptive Response_a Model of Drug Interdiction