2
The RAND Study

Assumptions, Data, Methods, and Findings

The RAND study, Controlling Cocaine: Supply Versus Demand Programs (Rydell and Everingham, 1994), develops a model of the market for cocaine in the United States and selects parameter values to make the model consistent with some empirical evidence. The study then uses the model to assess the cost-effectiveness of four alternative strategies for reducing cocaine consumption: source-country control, interdiction, domestic enforcement, and treatment of heavy users.

Modeling the Market for Cocaine: Qualitative Features

The RAND model seeks to explain the aggregate consumption of cocaine in the United States as the outcome of a long-run competitive market process in which the price of cocaine adjusts to balance supply and demand. The model has a complex detailed structure, but Figure 1 describes some of the essential qualitative features. The demand curve shows the quantity of cocaine that American consumers wish to purchase at any given price. The supply curve shows the quantity that producers would be willing to sell at any given price. The intersection of the supply and demand curves is the market equilibrium: the price at which the quantities demanded and supplied are equal, so that the market is in balance.

The downward sloping shape of the market demand curve reflects the usual economic assumption that the quantity of a product demanded



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2 The RAND Study Assumptions, Data, Methods, and Findings The RAND study, Controlling Cocaine: Supply Versus Demand Programs (Rydell and Everingham, 1994), develops a model of the market for cocaine in the United States and selects parameter values to make the model consistent with some empirical evidence. The study then uses the model to assess the cost-effectiveness of four alternative strategies for reducing cocaine consumption: source-country control, interdiction, domestic enforcement, and treatment of heavy users. Modeling the Market for Cocaine: Qualitative Features The RAND model seeks to explain the aggregate consumption of cocaine in the United States as the outcome of a long-run competitive market process in which the price of cocaine adjusts to balance supply and demand. The model has a complex detailed structure, but Figure 1 describes some of the essential qualitative features. The demand curve shows the quantity of cocaine that American consumers wish to purchase at any given price. The supply curve shows the quantity that producers would be willing to sell at any given price. The intersection of the supply and demand curves is the market equilibrium: the price at which the quantities demanded and supplied are equal, so that the market is in balance. The downward sloping shape of the market demand curve reflects the usual economic assumption that the quantity of a product demanded

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FIGURE 1 RAND model of long-run market supply and demand for cocaine in the United States. varies inversely with its price. The unusual feature of Figure 1 is that the market supply curve also slopes downward. The RAND study bases its downward sloping supply curve on three assumptions. The first assumption is that the price at which a given quantity of cocaine is supplied to the market equals the average cost per unit of producing this quantity (Rydell and Everingham, 1994:53). This assumption is standard in the long-run analysis of competitive markets because free entry and exit of producers implies that profit must be zero for the marginal producer (Panzar and Willig, 1978). In this framework, the market supply curve in Figure 1 measures the average cost of producing any given quantity. The second assumption in the RAND study is that the resources used in the production of cocaine are available to producers at a constant price per unit, regardless of how much of these resources are used in the production of cocaine (pp. 52, 95). Hence, the marginal cost of producing an additional unit of cocaine does not change with the quantity produced. The third assumption is that supply-control policies generate production costs that grow at a slower rate than output (pp. 53, 95): As production rises, the ratio of seizures to the quantity of cocaine produced falls. Hence, the second and third assumptions together imply that average cost declines with quantity produced. In the RAND model, cocaine control policies would reduce the con-

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sumption of cocaine and increase its price. Source-country control, interdiction, domestic enforcement, and other supply-control policies would shift the average cost curve up, while leaving the demand curve unchanged. The result would be a new equilibrium with a higher price and lower consumption than would be observed in the absence of such policies. Drug treatment programs and other demand-control policies would shift the demand curve down, while leaving the average cost curve unchanged. The result again would be a new equilibrium with a higher price and lower consumption than in the absence of such policies. The RAND study does not specifically address the possibility that some cocaine control policies may affect both demand and supply. For example, domestic enforcement activities may reduce supply by disrupting the distribution of cocaine. They also may reduce demand by deterring cocaine purchases by incapacitating users and by making arrested users subject to mandatory treatment programs. The RAND study only entertains a limited form of incapacitation effects. It is of interest to compare the qualitative predictions of the RAND model with those of models that make the usual assumption that supply curves slope upward. In models with upward sloping supply curves, supply-control policies would yield increases in price and decreases in consumption, and demand-control policies would yield decreases in price and decreases in consumption. Thus, from a qualitative perspective, the RAND model and models that assume upward sloping supply curves make common predictions about the effects of policy on consumption and about the effect of supply-control policies on price, but they make opposite predictions about the effect of demand-control policies on price. Modeling the Market for Cocaine: Quantitative Features Qualitative analysis does not carry one very far toward the objective of assessing the cost-effectiveness of alternative policies in reducing cocaine consumption. To make predictions about the magnitudes of policy effects, it is necessary to specify particular shapes for the demand and supply curves and to specify how these curves shift with changes in cocaine control policy. The RAND study accomplishes this in two steps. First, it posits demand and supply models with specific functional forms. The demand model describes a dynamic process of cocaine use, with some individuals moving over time between no use, light use, and heavy use. The quantity of cocaine by the persons in a use category, as well as the transitions between categories, are assumed to be sensitive to prices (pp. 74-76). The model assumes that light and heavy users have the same constant price elasticity of demand. That is, given a 1 percent decrease in price, the

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study assumes that the quantity of cocaine demanded by light and heavy users always increases by the same constant percentage. Similarly, the model assumes that the rates of transitions between categories have the same absolute constant price elasticity. That is, given a 1 percent decrease in price, it assumes that the inflow of users into higher consumption categories always increases by the same percentage and that the outflow always decreased by the same percentage. The model does not specify how nonprice variables, such as criminal sanctions on users, affect the demand for cocaine. The supply model describes a multistage process of cocaine production and distribution, from the growing of coca leaf in source countries to the retail marketing of cocaine in the United States. Production costs at each stage are assumed to equal the sum of the value of inputs, processing costs, and costs generated by cocaine control policies. The demand and supply models have several free parameters. The second step in model specification is to select values for these parameters. The values in the RAND study were chosen in part to make the model consistent with available data and the findings of previous empirical studies and in part on the basis of educated guesses. Formal statistical methods were not used to estimate parameter values, to describe their uncertainty, or to evaluate the sensitivity of the model's predictions to the parameter values assumed. Table 1 displays the key parameters, the range of values entertained for them, and the sources of information used to choose this range. The "elasticity of market demand" parameter measures the sensitivity of quantity demanded to price. The RAND baseline analysis assumes that the price elasticity of demand equals -0.50: that is, a 1 percent increase in price generates a 0.50 percent decrease in the quantity of cocaine demanded, by both light and heavy users. This choice for the elasticity parameter was motivated by reference to empirical analyses of other psychoactive substances, namely, cigarettes and alcohol. The price elasticities of demand for cigarettes and alcohol have been estimated to lie between 0 (which means that changes in price have no effect on demand) to nearly -2.0 (which means that a 1 percent change in price generates a 2 percent drop in quantity demanded) (Manning et al., 1991). Most analyses find that the elasticity lies between 0 and -1.0. Given this range of estimates, the RAND study argues that a price elasticity of demand for cocaine of -0.5 is a "reasonable" assumption (p. 75). To assess the sensitivity of findings to this assumption, the study entertains values between -0.38 and -0.75. The "elasticity of market supply" parameter measures the sensitivity of quantity supplied to price. The RAND supply model requires that the average cost curve in Figure 1 be downward sloping; hence, the study

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TABLE 1 The Values of Selected Supply and Demand Market Parameters Used in the Simulations Reported in the RAND Study Parameter Low Baseline High Sources Elasticity of Market Demanda -0.38 -0.50 -0.75 Extrapolated from previous studies on cigarettes and alcohol, as reported in Manning et al. (1991) Elasticity of Market Supplya -2.7 -3.6 -6.6 Educated guess Drug Treatment Effectsb       TOPS data as reported in Hubbard et al. (1989) In-treatment 79.0% 79.0% 79.0% Post-treatment 9.9% 13.2% 16.5% Supply-Control Policies Elasticity of processing cost with respect to seizures 0.22 0.44 0.66 Crawford and Reuter (1988) Productivity of additional control budget dollars 0.70 0.80 0.90 Educated guess NOTE: The parameter values in the table are found in Rydell and Everingham (1994): Table 3.1 (p. 20), Table E.1 (p. 96), and Table F.1 (p. 107). a The percentage change in quantity demanded or supplied that results from a 1 percent increase in price. The elasticity of supply is not constant for all prices, but is instead an estimate based on "runs of the cocaine-control model" (p. 96). b These values are weighted averages of treatment effectiveness for residential and non-residential programs. entertains only negative values for the supply elasticity parameter. The baseline analysis assumes that the price elasticity of supply equals -3.6, implying that a 3.6 percent decrease in the quantity supplied requires a 1 percent increase in average costs (Table E.1). This choice is based on a "rough appreciation of discussions and general reading about the cocaine supply process" (p. 71). For purposes of sensitivity analysis, the study entertains values ranging from -2.6 to -6.6.1 1   In the RAND model, the average cost function does not have the constant-elasticity form. That is, the price elasticity of supply varies with average costs, and there is no single price elasticity of supply that applies for all prices. These elasticity measures are estimates based on "runs of the cocaine control model" as reported in Table E.1 in the RAND study (p. 96). The estimates are derived by varying a parameter, which regulates the fraction of seizure costs associated with the relative (as opposed to the absolute) size of the seizure. As this fraction increases from 0 to 1, seizures become increasingly related to total production, and the supply curve becomes increasingly elastic.

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The RAND model uses two parameters to measure the effectiveness of drug treatment programs that seek to reduce cocaine consumption by heavy users. The programs are assumed to have both an in-treatment and a post-treatment effect on drug use. The in-treatment effect measures the degree to which cocaine use decreases during the period that a person is undergoing the treatment program. The baseline analysis assumes that 79 percent of heavy users stop consuming cocaine while in-treatment (p. 20). The post-treatment effect measures the effect of treatment on the rate of transition of heavy users into the light use and no-use categories. The baseline analysis assumes that treatment programs cause 13.3 percent of treated heavy cocaine users to desist from heavy use after treatment (p. 20). These choices for the two treatment effect parameters are motivated by reference to statistics from the Treatment Outcome Prospective Study (TOPS) reported in Hubbard et al. (1989). TOPS collected program and client interview follow-up data in various treatment programs in 10 cities. The data include information on residential and nonresidential and public and private treatment programs. However, the programs studied primarily treated heroin users, not cocaine users. The final set of parameters in Table 1 are intended to measure the effectiveness of supply-control policies. In the RAND supply model, each stage of cocaine production may be subjected to control activities, which affect costs of production. Supply-control activities impose direct costs on producers through product seizures and financial penalties, and they impose indirect costs as producers seek to avoid seizures and penalties. It is assumed that the costs imposed by control activities are additive at each stage of production. That is, a dollar increase in average cost at any stage of production leads to a dollar shift upward in the industry average cost curve shown in Figure 1. The RAND study assumes that increases in the budget for supply-control activities generate additional seizures of cocaine and that seizures increase production costs. There are two key parameters. The "productivity of additional control budget dollars" measures how increases in the supply-control budget translate into additional seizures. The model assumes that increases in the supply-control budget lead to higher seizures, but with diminishing returns. As this parameter ranges from 0.70 to 0.90 in the RAND sensitivity analysis, "additional budget" is assumed to be increasingly effective in yielding seizures. The range of values entertained for the parameter is based on a "rough appreciation of discussions and general reading about the cocaine supply process" (p. 71). The other parameter is the "elasticity of processing cost with respect to seizures," which measures how seizures affect the cost of cocaine production. In the baseline analysis, the elasticity of the processing cost with

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respect to seizures is assumed to equal 0.44, implying that a 1 percent increase in seizures increases the unit cost of production by 0.44 percent. This number comes from the Simulation of Adaptive Response (SOAR) model, which explored how processing costs increase as producers seek to avoid sanctions (Crawford and Reuter, 1988). Cost-Effectiveness Findings of the RAND Study With the market model fully specified, the RAND study is able to evaluate the relative cost-effectiveness of demand-control and supply-control policies, given the current allocation of resources.2 The primary criterion used is the cost of achieving a specified reduction in U.S. cocaine consumption, namely, a 1 percent reduction in the 15-year discounted value of consumption. The RAND study also estimates the cost of achieving a 1 percent reduction in the number of users, as well as the cost of achieving both a specified reduction in drug-related crimes and an increase in productivity. One policy is deemed to be more cost-effective than another if the RAND model predicts that it achieves the objective at lower cost. The central finding of the RAND study is that treatment of heavy users, a demand-control policy, is much more cost-effective than all three of the supply-control policies considered—source-country control, interdiction, and domestic enforcement. In the baseline analysis, the least costly supply-control policy is domestic enforcement. The study predicts that spending on domestic enforcement, which in the RAND model acts to increase the average cost of production and reduce consumption by those who are arrested, would have to increase by $246 million to reduce cocaine consumption by 1 percent; in contrast, spending on treatment of heavy users would have to increase by only $34 million. Thus, the cost of achieving a 1 percent reduction in consumption through domestic enforcement is predicted to be 7.3 times the cost of achieving the same reduction through treatment of heavy users. The costs of achieving this reduction through source-country control and interdiction policies are predicted to be even higher, 23.0 and 10.8 times the cost of treatment, respectively. 2   In 1992, the base year for the RAND study, the United States spent nearly $13 billion on cocaine control programs. Approximately 93 percent of the total was spent on supply-control activities, with the largest fraction devoted to domestic enforcement. According to the RAND report (pp. 4 and 70), nearly $9.5 billion was spent on domestic enforcement, $1.7 billion on interdiction, $0.9 billion on source-country control, and $0.9 billion on treatment.

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While the quantitative conclusions of the RAND study depend on the specific parameter values chosen, the basic qualitative conclusion does not vary across the range of parameter values considered in the sensitivity analyses performed; see Table 1. The study finds that, in all cases, the cost of achieving the target consumption reduction through supply-control policies is at least twice the cost of achieving it through treatment of heavy users (Table F.9, p. 110). Assessment The RAND study develops a potentially useful framework for understanding the functioning of the market for cocaine at a high level of aggregation. It reports a serious effort to describe the behavior of producers and users and the manner in which cocaine-control policies may affect consumption and prices. The study is innovative and sophisticated in comparison with previous analyses of cocaine control policy. These positive features notwithstanding, the RAND study makes many unsubstantiated assumptions about the processes through which cocaine is produced, distributed, and consumed. Plausible changes in these assumptions outside the range examined in the sensitivity analyses may change the main qualitative conclusions of the study, not just the quantitative findings reported. The central finding—that treatment of heavy users is much more cost-effective in reducing cocaine consumption than are supply-control policies—depends on assumptions that are too questionable to guide the formation of cocaine control policy. The rest of this chapter details the committee's main concerns: the RAND estimates of effects of drug treatment programs, the models of cocaine supply and cocaine demand, and the study's efforts to evaluate the model posed. It is important to stress that these concerns do not lead the committee to conclude either that the RAND findings are necessarily incorrect or that alternative conclusions should have been drawn. Rather, the committee concludes that the findings reported in the RAND study—both quantitative and qualitative—are not persuasive. The main contribution of the RAND study is conceptual rather than empirical: The study produces a potentially useful framework for thinking about the operation of the market for cocaine, it does not yield usable findings on the relative cost-effectiveness of alternative policies in reducing cocaine consumption. Estimates of Effects of Drug Treatment Programs on Cocaine Use As described above, the RAND study uses two parameters—measured in-treatment and post-treatment effects—to quantify the effective-

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ness of treatment programs in reducing cocaine use. The values chosen for these parameters influence the cost of achieving reductions in cocaine use through treatment programs. Having credible values is essential to the RAND finding that treatment is cost-effective relative to supply-control policies. Unfortunately, the data and inferential methods used to select the parameter values displayed in Table 1 seem inappropriate. The TOPS Data The RAND study bases its estimates of treatment effectiveness on the Treatment Outcome Prospective Study (TOPS). TOPS is a study of drug abuse treatment effectiveness that included more than 11,000 patients in 41 treatment programs in 10 cities between 1979 and 1981 (Hubbard et al., 1989; Rydell and Everingham, 1994).3 Samples of patients were followed 1 year, 2 years, and 3-5 years post-treatment (Fletcher, Tims, and Brown, 1997). TOPS focused largely on treatment effectiveness for heroin users, specifically, those in methadone maintenance settings. Hubbard et al. make only the most general distinctions between types of treatment, and the programs observed were those in operation in the period 1979-1981. These years were well before the cocaine epidemic of the 1980s, when cocaine became widely available and inexpensive, and prior to the appearance of the crack form of cocaine. Moreover, there are many differences between the treatments available for heroin addiction and for cocaine addiction (O'Brien, 1997). Most notably, there is no current medication for cocaine comparable to methadone with its well-documented ability to reduce heroin use. Hence, it is not clear that the TOPS data provide information relevant to the evaluation of current treatment programs for heavy cocaine users. Inferential Problems Even if the TOPS data did accurately characterize cocaine treatment programs for heavy users, the RAND interpretation of the data is open to 3   TOPS is one of three comprehensive studies of drug abuse treatment effectiveness sponsored by the National Institute on Drug Abuse (NIDA). The first study was the Drug Abuse Reporting Program (DARP), which assessed more than 44,000 clients in 52 treatment programs from 1969 to 1973. More than 50 treatment programs were included in the sample, and a subset of those studied were revisited 6 and 12 years post-treatment (Institute of Medicine, 1996). The DARP was followed by the TOPS, which was followed in 1989 by the Drug Abuse Treatment Outcome Study (DATOS). The intent of DATOS is to provide information on the effectiveness of drug abuse treatment in typical, stable programs (Fletcher et al., 1997).

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question. Depending on the process by which users are selected into treatment programs and the determinants of dropout from such programs, the RAND interpretation of the data may make treatment programs seem more or less cost-effective than they actually are. Consider, first, the parameter measuring in-treatment effects. This parameter is taken to be the fraction of TOPS sample members who desist from drug use while participating in their treatment programs. No comparison group is invoked to predict what fraction would have desisted in the absence of treatment. Instead, it is assumed that, in the absence of treatment, all TOPS sample members would continue their pre-TOPS use patterns.4 To assess the validity of this assumption requires knowledge of the process by which cocaine users are selected into treatment programs. The assumption is reasonable if users are randomly drawn into treatment. But to the extent that users enter treatment programs voluntarily, it is reasonable to think that people who choose to enter treatment programs tend to be motivated to desist from drug use. In contrast, to the extent that users are mandated into treatment by the criminal justice system, it may be that people who enter treatment programs tend not to be so motivated.5 Thus, observed declines in drug use during the period of treatment may reflect the characteristics of people who seek or are coerced into treatment, not the effects of treatment programs. The true in-treatment effect may be much lower or higher than the estimate in the RAND study. Next, consider the parameter measuring post-treatment effects. To evaluate this parameter, the RAND study compares the post-treatment average drug use of members of the TOPS sample who completed their treatment programs with the post-treatment average drug use of TOPS subjects who began treatment but dropped out within 3 months. This comparison is appropriate under the assumption that people who drop out of their treatment programs are similar, on average, to people who complete treatment. Suppose, however, that treatment dropouts are more predisposed to drug use than are those who complete treatment. If dropouts are more severely addicted or less motivated or have fewer social supports than those who complete treatment, then the observed differences in post-treatment drug use of dropouts and completers may reflect differences in the characteristics of these two groups, not the effect 4   For those not in-treatment, the RAND study formalizes a dynamic model of initiation, intensification, and desistance. 5   The leverage of the criminal justice system may provide an incentive for the coerced participants to reduce consumption while in-treatment, so observed declines in drug use may reflect the effects of coercion rather than the effects of treatment participation per se.

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of treatment programs. The people who complete their treatment programs may be those who are more likely to reduce their drug use, whether or not they receive treatment. The true post-treatment effect may be smaller than estimated by RAND, or even zero.6 Or, if dropouts are less predisposed to drug use than are those who complete treatment, the true effect may be larger than estimated by RAND. The RAND study asserts that its baseline estimate of post-treatment effects may understate treatment effectiveness for another reason: ''To the extent that treatments lasting less than three months have some effect, the calculation underestimates the effectiveness of cocaine treatments" (Rydell and Everingham, 1994:89). This assertion may have merit if TOPS dropouts are an appropriate comparison group for TOPS completers. However, the appropriateness of using TOPS dropouts as a comparison group for TOPS completers is not addressed in the RAND study. There is no discussion of the attributes of the two groups prior to treatment and no attempt to account for any pretreatment differences that may exist. The study does not even consider whether, for example, dropouts and completers had the same drug use patterns prior to treatment. Even if the in-treatment and post-treatment parameters are evaluated correctly in the RAND study, these values pertain only to people of the TOPS sample, that is, only to people who actually were enrolled in-treatment during the period of TOPS data collection. Expansion of treatment programs from their historical levels to the higher levels contemplated in the RAND study may require reaching out to groups of drug users who have neither sought treatment nor been coerced by the criminal justice system into receiving treatment.7 These groups may be much more or much less susceptible to successful treatment than are the members of the TOPS sample: it is simply not known. At heart, the committee's concern about the RAND interpretation of the TOPS data is that the RAND study disregards well-understood, fundamental problems that arise in attempting to infer treatment effects from observational data on treatment outcomes in heterogeneous populations: see, for example, Campbell and Stanley (1963), Cochran (1965), Cook and Campbell (1979), Manski (1995), Rosenbaum (1995), and Manski and Nagin (1998). Many empirical studies have found a strong statistical 6   The true effect could even be negative, if treatment has a deleterious effect on some clients. 7   To the extent that people who enter treatment programs are placed there by the criminal justice system, expansion of treatment programs may require expansion of domestic enforcement activities. However, entry into treatment may be limited by the availability of space in existing programs.

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association between drug use and such variables as school dropout and delinquency: see, for example, Elliot, Huizinga, and Menard (1989), Elliot and Voss (1974), and Mensch and Kandel (1988a, 1988b). It is well appreciated that these statistical associations do not by themselves imply that school dropout or delinquency induces drug use, nor vice versa. For example, Anglin and Hser (1990:407) state in a review essay: "By the end of the 1970s, however, it had become generally recognized that pre- and post-treatment studies were subject to serious methodological shortcomings." Yet the RAND study, without substantiation, assumes that statistical associations between treatment and drug use in the TOPS data imply real treatment effects. The sensitivity analysis reported in the RAND study does not satisfy the committee's concerns; it only varies the post-treatment effectiveness parameter, leaving the in-treatment parameter fixed at the baseline value of 79 percent. The study observes that, even if one of the two treatment effect parameters were set equal to zero, the other parameter (fixed at its baseline value) would suffice to show that treatment programs are more cost-effective than are supply-control polices (Rydell and Everingham, 1994:xv, 20). The RAND report does not, however, evaluate the sensitivity of findings to joint changes in the values of the two treatment parameters. Clearly, if both parameters are zero, treatment would be an ineffective means of reducing consumption. Modeling the Supply of Cocaine The committee has several substantive concerns about the RAND model of the market supply of cocaine. Questionable aspects of the model include the assumption of a downward sloping industry average cost curve, the assumption of an additive process by which control activities affect production cost, the use of seizures to measure the extent of control activities, and the assumption that the market for cocaine equilibrates by price alone. In each case, the assumption tends to downplay the cost-effectiveness of supply-control policies. Shape of the Average Cost Curve Inferences on the effects of supply-control policies depend critically on the assumed shape of the average cost curve. The RAND supply model, described above, assumes that price equals the average cost of cocaine production, that the marginal cost of production is constant, and that the level of seizures grows at a slower rate than the quantity of cocaine produced. Together, these assumptions imply that the industry

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average cost curve is downward sloping. Yet there is no compelling case for any of these three assumptions. We consider each in turn. Price Equals Average Cost According to the RAND report, substantial monetary profits are earned in each of the six stages of production. The assumption of the RAND model is that the market for cocaine is competitive; hence, the profits exactly compensate producers for the risks they take and the processing costs they incur. If, on the contrary, some profits are economic rents that more than compensate for costs and risks, then the industry average curve will be upward sloping (see, e.g., Bresnahan, 1989). Constant Marginal Cost The assumption of constant marginal cost is plausible only if all of the factors of cocaine production and distribution—the land for growing coca leaf, the skilled labor and chemicals used in producing cocaine from coca, the dealers who market the drug, etc.—are available in perfectly elastic supply to the cocaine industry. This is a strong assumption, contrary to the usual idea that resource constraints make production in an industry increasingly more costly with each additional unit produced. If there are resource constraints relevant to the production of cocaine, the cocaine average cost curve slopes upward, if all else is equal. Supply-Control Policies Impose Fixed Costs In the RAND model, industry average cost declines as a consequence of an unsubstantiated assumption about the effects of supply-control policies. Such policies are assumed to generate seizures that increase less, proportionally, than output. Hence, the average cost of production falls as production rises.8 Suppose, to the contrary, that the fraction seized rises with production: then the fraction of production making it to market may not increase with the level of production; it may decrease. If so, the average cost of production increases with production. Changes in any of the three RAND assumptions could easily generate an upward sloping market average cost curve for cocaine. A sensitivity analysis can explore the range of plausible assumptions, but the RAND sensitivity analysis only entertains downward sloping curves. This matter is of potential consequence for assessment of the cost-effectiveness of 8   The simplest version of this model, which is considered in the appendix to this report, occurs when supply-control policies impose fixed costs on producers. In this case, the level of seizures does not vary with the amount of cocaine produced so that the average cost of production falls with the total output.

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alternative policies, but the complexity of the RAND model makes it impossible to judge the implications from the report itself. The most satisfactory way to judge the implications would be to reprogram the RAND model to permit upward sloping average cost curves and then to perform new sensitivity analyses. This is not a feasible activity for the committee, but we did find it feasible to formulate and analyze a relatively simple model that expresses the main features of the RAND model. This model is presented in the appendix; it can be used to assess how the cost-effectiveness of supply-control policies varies with the assumed shape of the average cost curve that determines industry supply. The analysis in the appendix indicates that the RAND assumption of a downward sloping average cost curve restricts the responsiveness of equilibrium cocaine consumption to the intensity of supply-control activities. Consider, for example, the setting of Figure 2, which is based on the market model in the appendix. The figure describes an initial condition in which the equilibrium consumption of cocaine is point A. The aggregate demand curve is downward sloping. Two different baseline average cost curves are shown, both of which are consistent with this equilibrium. Consistent with the RAND model, baseline average cost 1 indicates a negative relationship between the quantity supplied and the market price. In contrast, baseline average cost 2 is positively sloped. The figure also portrays the two baseline average cost curves shifted upward, reflecting a higher intensity of supply-control activities that increase FIGURE 2 Simulated effects of added seizures given upward and downward sloping average cost curves. NOTE: See text for discussion and see appendix for a formal presentation of the model.

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seizures by a fixed amount. The two shifted curves are labeled post-intervention average cost 1 and 2.9 What is the effect on equilibrium cocaine consumption? If the operative average cost curve is downward sloping, as assumed in the RAND report, the new equilibrium consumption of cocaine is point B. If the operative average cost curve is upward sloping, the new cocaine consumption is point C. Thus, given the model presented in the appendix, the responsiveness of consumption to the increased intensity of supply-control activities will be understated if the market average cost curve is incorrectly assumed to be downward sloping.10 Supply-Control Policies and Average Production Costs A major issue in assessing supply-control policies is the way that disruptions at different stages of the cocaine production and distribution process generate increases in average production costs. The RAND study assumes that the mechanism is additive: that is, a dollar of cost added at any stage of the process implies a dollar increase in average cost. In contrast, a multiplicative model would assume that a given percentage increase in cost at one stage of the process will be passed through proportionally at each later stage. Suppose, for example, that coca base costs $1 per gram in the supplying country but that this amount of coca base transformed into cocaine costs $100 per pure gram when distributed in the United States. Under the additive model, increasing the source-country cost of coca base to $2 per gram would increase the cost of cocaine distributed in the United States to $101 per gram. Under the multiplicative model, the cost of cocaine in the United States would increase to $200 per gram. The choice between these two models has clear consequences for the assessment of supply-control activities. In the additive model, supply-control activities at early stages of the cocaine production process have only additive effects on average production costs. In the multiplicative 9   The baseline case supposes that seizures equal 0, while the post-intervention case supposes that seizures equal 0.5. Under both average cost 1 and 2, the baseline equilibrium outcome is A (price = 1.0, quantity = 1.0). Under average cost 1, the post-intervention outcome is B (price = 1.64, quantity = 0.78). Under average cost 2, the post-intervention outcome is C (price = 2.57, quantity = 0.62). 10   A particularly revealing case occurs when the demand curve is perfectly elastic. That is, suppose the demand curve is horizontal. In this extreme case, a downward sloping average cost curve implies that interdiction would increase the equilibrium quantity consumed. In contrast, an upward sloping supply curve would imply that consumption would fall.

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model, such activities obviously have much larger effects. The RAND study, by assuming the additive model, strongly restricts the potential sensitivity of cocaine market outcomes to source-country control and interdiction relative to what it would be under the multiplicative model. The committee does not find compelling evidence in favor of either model. Caulkins and Reuter (1998) finds some evidence for a multiplicative model of the cocaine market and rejects an additive model. The question of pass-through of raw materials costs into the costs of final products has been studied much more extensively in some legal markets for which extensive wholesale and retail data are available. Such markets include foods and fuels, where the cost of the raw material (wheat or crude oil) is a small fraction of the cost of the final product (say, shredded wheat cereal or unleaded premium gasoline). Studies of the effect of fluctuations of raw materials costs on final product costs have tended to reject both the additive and multiplicative models in favor of a hybrid model, one in which fluctuations in raw materials costs are passed through more than additively but less than multiplicatively (see, e.g., Okun, 1981). From a theoretical perspective, there are no persuasive reasons to argue for either the additive model or the multiplicative model. Some elements of non-raw-material costs are likely to be sensitive to raw material costs including insurance costs in legal markets and risk premiums in illegal markets. Other elements, such as transport costs, may be independent of the cost of the raw material. Overall, neither the pure multiplicative nor additive model need hold.11 Seizures as a Measure of Supply-Control Activity The measure used to characterize the intensity of supply-control activities can influence findings on the cost-effectiveness of such activities. In the RAND study, the primary measure of supply-control activities—source-country controls, interdiction, or domestic enforcement—is the amount of cocaine that is seized. The study justifies use of this measure by asserting that seizures and supply-control activities are monotonically related and, hence, that seizures appropriately measure the intensity of supply-control activities (Everingham and Rydell, 1994:62). 11   A theoretical model yielding a hybrid result supposes that each stage of production has a monopolistic firm that marks up the price over marginal cost. If the marginal cost at each stage includes raw materials as well as other prime costs (such as labor and fuel), then the retail cost will be a complex compounded markup of raw material and other prime costs.

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Seizures, however, may not accurately measure the intensity of supply-control activities. There are some policies that may successfully disrupt supply without seizing any cocaine whatsoever. In fact, it is easy to imagine situations in which increasing control activities increases production costs while reducing seizures. Consider, for example, interdiction activities that aim to restrict the transport of cocaine to the United States, say, by interception of shipments in the Caribbean. Such policies may deter producers from attempting to make shipments. If so, seizures may fall as the intensity of supply-control activity rises. Nonprice Effects of Supply-Control Activities The RAND model assumes that supply-control activities affect the drug market by raising production costs and, hence, equilibrium drug prices. The operation of illegal markets, such as that for cocaine, however, may be more complicated than the operation of the simple legal markets in competitive models of market equilibrium. In such legal markets, price movements may suffice to balance supply and demand for the good or service. In illegal markets, however, both drug producers and consumers must reckon with important nonmonetary aspects of participation in the drug market. The relevant nonmonetary factors may include search costs and fear of stigma or imprisonment. The RAND study abstracts from these considerations and assumes that price movements suffice to equilibrate the market for cocaine. Yet important supply-control activities, particularly local law enforcement, act primarily by raising the nonmonetary costs of participation in the drug market. In this respect, as in the others discussed above, the RAND analysis may underestimate the cost-effectiveness of supply-control activities. Modeling the Demand for Cocaine The committee's concerns about the RAND model of demand for cocaine fall into two categories. First, accepting the RAND model's form, there is the matter of what value to use for its price elasticity parameter. Second, there are a host of reasons to question whether a demand model of the RAND type suffices to characterize the effects of control policies on cocaine use. The Price Elasticity of Demand The value of the price elasticity parameter used in the RAND study has important consequences for the study's findings on the cost-effectiveness of supply-control policies. To restate a point made above, the RAND

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model assumes that supply-control policies affect the drug market by raising average production costs and, hence, equilibrium drug prices. The magnitude of the associated reduction in drug consumption is determined by the price elasticity of demand. The more negative this elasticity is, the less steeply sloped the demand curve is, and the more effective are supply-control policies in reducing cocaine consumption. Figure 3 presents several possible supply and demand elasticities. The initial condition of equilibrium consumption of cocaine is point A. The baseline average cost curve is downward sloping, as assumed in the RAND model. Two different demand curves are shown, both of which are consistent with this equilibrium. The steeper demand curve has price elasticity -0.5, and the less steep one has elasticity -1.0. The figure also portrays a new average cost curve, shifted upward, reflecting a higher intensity of supply-control activities. What is the effect on equilibrium cocaine consumption? If the operative demand curve is the one with elasticity -0.5, the new equilibrium consumption of cocaine is point B. If the operative demand curve is the one with elasticity -1.0, the new cocaine consumption is point C. Thus, the responsiveness of consumption to the increased intensity of supply-control activities is sensitive to the elasticity of demand. There is a substantial literature on the price elasticity of demand for psychoactive substances, particularly for legal substances, such as alcohol FIGURE 3 Simulated effects of added seizures given elastic and inelastic curves.

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and tobacco. The literature for illegal substances is much less well developed. For some time, the conventional wisdom was that the demand for illegal substances is relatively price inelastic. Reflecting this belief, the RAND study chose a baseline value of -0.50 and performed a sensitivity analysis entertaining values between -0.38 and -0.75. Recent studies, however, suggest that the demand for cocaine may actually be much more price elastic, perhaps -1.0 or even more negative (see Caulkins, 1995b; Grossman et al., 1996). If the price elasticity of demand is, in fact, less than -0.75, the RAND analysis understates the cost-effectiveness of supply-control activities. The Complex Response of Cocaine Consumption to Prices The RAND demand model, with its single price elasticity of demand parameter, abstracts from much of the complexity of the behavior that determines cocaine use. As noted above, supply-control policies may affect cocaine use by altering the search costs, stigma, and other nonmonetary factors relevant to current and potential cocaine users. In this section, we call attention to some of the complexity of the response of cocaine consumption to prices. The RAND study assumes that light and heavy users of cocaine share the same sensitivity to price, in the sense that their consumption changes by the same percentage given a specified percentage change in price. This may be a justifiable simplifying assumption for an exploratory analysis, but it does not seem justifiable for a study that purports to draw strong policy conclusions, as does the RAND study. The addiction process may imply that price affects desistance from drug use differently than the way it affects initiation. The effects of price on initiation and intensification of drug use may be quite different as well. It is commonly thought that light drug users are more price sensitive than are heavy users, whose addiction drives behavior. However, heavy drug use may require such sufficient expenditure that income effects become prominent, which would imply strong sensitivity to price changes. For all of these reasons, it seems unlikely that a single price elasticity can adequately characterize how cocaine use responds to the price of cocaine. Another simplification in the RAND model of the demand for cocaine is the absence of any consideration of cross-price elasticities with respect to other psychoactive substances, both legal and illegal. Some experts believe that there is strong complementarity across substances, that lowering the price of one drug stimulates demand for other drugs; others believe that different drugs are substitutes, that lowering the price of one drug tends to reduce the use of other legal or illegal drugs (see Kleiman, 1992; Rasmussen and Benson, 1994; Zimmer and Morgan, 1997). The

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committee does not have the information to reach a judgment on these alternative perspectives, but it is clear that understanding patterns of complementarity and substitution among drugs is essential to understanding the effects of control policies on drug use. Evaluating the Reliability of the Model The RAND study formulates and applies a model of the cocaine market in the United States that is complex in some respects and simplistic in others. The model imposes a large set of unsubstantiated assumptions. When assessing the study, the committee conscientiously tried to focus on substantive issues that might arguably change the qualitative findings reported. As discussed above, plausible changes to the RAND assumptions about the effectiveness of treatment programs and the shapes of the demand and average cost curves might well modify or possibly even negate the study's findings. Hence, the committee concludes that the findings lack sufficient persuasiveness to be used as a basis for policy formation. A general methodological concern is that the RAND study offers no systematic approach to evaluation of the model, or its various elements, as a description of the actual cocaine market. Common approaches to model evaluation include the performance of statistical tests of individual equations or of the entire model, assessment of the accuracy of out-of-sample predictions, and comparisons of the predictions of the model with those of other models of the same phenomena. The sensitivity analyses reported in the RAND study are limited in scope and, in any case, do not take the place of efforts to evaluate the model empirically. It is troubling that the study makes no attempt to check the predictions of the model against the historical record. For example, the study makes no attempt to use the model to interpret the substantial decline in the domestic price of cocaine without any consequent increase in the consumption of cocaine that occurred during the 1980s. Conclusions The RAND study is best thought of as conceptual research, offering a coherent way to think about the cocaine problem. The study documents a significant effort to identify and model important elements of the market for cocaine. It represents a serious attempt to formally characterize the complex interaction of producers and users and the subtle process through which alternative cocaine control policies may affect consumption and prices. The study establishes an important point of departure for

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the development of richer models of the market for cocaine and for empirical research applying such models to evaluate alternative policies. However, the RAND study does not yield usable empirical findings on the relative cost-effectiveness of alternative policies in reducing cocaine consumption. The study makes many unsubstantiated assumptions about the processes through which cocaine is produced, distributed, and consumed. Plausible changes in these assumptions can change not only the quantitative findings reported, but also the main qualitative conclusions of the study. The study is also seriously deficient in its use of the Treatment Outcomes Prospective Study (TOPS) data to estimate the effectiveness of cocaine treatment programs. Hence, the findings of the RAND study do not constitute a persuasive basis for the formation of cocaine control policy.