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The relationship between illegal drug prices at the retail user and seller levels.

I. INTRODUCTION

The hierarchical nature of illegal drug markets is well known. Drugs such as marijuana and cocaine reach consumers through multi-level distribution networks. Typically, a dealer at a given market level buys a quantity of drugs, repackages that quantity into a number of smaller units, and sells these repackaged units at a markup to either lower-level dealers or users. As drugs move down the distribution chain, therefore, their per unit prices increase.

Price markups are much greater for illegal drugs than for legal goods. Little is known, however, about the underlying determinants of these markups. The two main competing theories hold that markups are either a fixed amount or a fixed percentage of the original price. These theories correspond to a price change at one market level passing through to lower market levels either additively or multiplicatively, respectively, prompting Caulkins (1990) to label the theories as the additive and multiplicative models.

The important distinction between the two models is in their predictions regarding the effect of a change in the wholesale price of an illegal drug on the retail price. Suppose, for example, that retail seller (i.e., low-level wholesale) and user prices for cocaine are $50 and $100 per pure gram, respectively (roughly their mean values during the 1990s), and that a reduction in enforcement efforts lowers the retail seller price to $25. The additive model implies that the retail user price will also fall by $25, to $75, representing a decrease of 25%. Meanwhile, the multiplicative model implies a retail user price reduction of 50%, to $50. Restrictive drug policy that increases wholesale prices is thus more effective when the relationship between wholesale and retail prices is multiplicative rather than additive.

Suppose that the price elasticity for past year participation in cocaine use is -0.4 (from DeSimone and Farrelly 2003). The above retail seller price decline would then increase the number of cocaine users by 10% if the additive model holds but by 20% if the multiplicative model holds. According to the Office of National Drug Control Policy (ONDCP 2001c) estimate that 5.74 million individuals were cocaine users in 2000, the difference in the two predictions represents 574,000 users, or about 0.2% of the U.S. population.

In light of their differing implications for the potential impact of successful wholesale level drug enforcement on drug demand, information on which of the two models more accurately describes illegal drug markets is highly relevant for illegal drug policy. The recent report of the National Academy of Sciences Committee on Data and Research for Policy on Illegal Drugs (Manski et al. 2001) acknowledges that little is known about the effectiveness of current drug policy in general and drug law enforcement in particular (p. xi) and specifically notes that evidence regarding how changes in wholesale prices affect retail prices would be useful to illegal drug policy makers (p. 161).

The only published study that conducts direct empirical tests of the additive and multiplicative models is Caulkins (1994), who analyzes 1977-91 data on median cocaine prices in eight U.S. cities. (1) Estimates from regressions of gram-level prices on ounce-level prices, as well as those for regressions of gram and ounce prices on kilogram prices, strongly reject the implications of the additive model but correspond closely with those of the multiplicative model. These results support the observation by Kleiman (1992) that the ratio of retail to wholesale cocaine prices remained approximately constant during the 1980s even as prices at both levels fell dramatically. Similarly, ONDCP (2001a) estimates a correlation of 0.46 between monthly retail and wholesale cocaine prices, with a $1 retail price increase associated with a wholesale price increase of just 7 cents. However, Caulkins and Reuter (1998) point out that the multiplicative model seems implausible closer to the origins of the distribution chain, because large variations in monthly coca leaf prices are not paralleled in retail price series.

Information on market organization is arguably even more important for marijuana than for cocaine. Marijuana is the most widely used illegal drug in the United States. ONDCP (2001c) estimates that in 2000 there were 12.1 million marijuana users. Moreover, marijuana use can lead, in a causal sense, to the use of more dangerous drugs like cocaine (DeSimone 1998). However, only anecdotal evidence exists on pricing structures in the marijuana market. Kleiman (1989) approximates that the markup at each distribution level is between 40% and 200%. In addition, for several types of marijuana, Caulkins and Padman (1993) find that the relationship between prices and transaction size is consistent with the predictions of the multiplicative model but not with those of the additive model.

This study empirically tests the additive and multiplicative models using 1985-2000 data on transactions at the lowest end of the distribution chains, that is, the retail seller and user levels, for marijuana and cocaine. It examines metropolitan area prices measured quarterly for marijuana and annually for cocaine. In contrast to the findings of Caulkins (1994) and much of the descriptive evidence outlined, regression results for both drugs convincingly reject the multiplicative model in favor of the additive model.

II. THE ADDITIVE AND MULTIPLICATIVE MODELS

As Caulkins (1994) explains, (2) the theoretical arguments for each model presume that illegal drug prices reflect production costs. For a given drug, this can be written as

(1) [P.sub.U] = [P.sub.S] + c,

where [P.sub.U] denotes the standardized price (per bulk gram for marijuana, per pure gram for cocaine) when purchased by retail users, [P.sub.S] denotes the standardized price when purchased by retail sellers (from mid-level distributors), and c represents the cost of moving a standardized unit from the retail seller to retail user level. The crucial difference between the two models is in their assumptions over whether the distribution cost, c, is a function of the value of the drug.

The additive model assumes that c is constant and therefore independent of [P.sub.S]. The price paid by retail users thus represents a fixed markup over that paid by retail sellers, and an increase in [P.sub.S] brings about an equivalent increase in [P.sub.U]. The additive model reasonably characterizes most legal goods, for which distribution costs are generally proportional to quantity. Though the illicit nature of the drug trade raises the likelihood that value matters, costs such as those for packaging, transportation, and storage are likely to depend primarily on physical weight. Similarly, sanctions on illegal possession of drugs increase with the quantity possessed, and the risk of arrest for dealers increases with the quantity sold.

In contrast, the multiplicative model assumes that distribution costs depend primarily on package value. This implies that the markup from the retail seller to user level is a percentage of the original price, so that c = k[P.sub.S] and

(2) [P.sub.U] = [P.sub.S] + k[P.sub.S] = (1 + k)[P.sub.S].

Even marijuana, which is much cheaper than cocaine, has at times been worth nearly its weight in gold at the retail level. The high value-to-weight ratios for illegal drugs suggest that value might be more important than quantity in determining distribution costs. Compare, for example, the cost of distributing two 1-pound packages of marijuana, one worth $2,000 and the other worth only $1,000. The payment required to discourage theft and the risk of robbery would be about double for the more expensive package. Moreover, under highly price-inelastic demand, dealer consumption would cost almost twice as much in the more expensive case. Consequently, the cost of distributing the package that is twice as expensive could be close to twice as much.

The preceding arguments suggest a simple way to empirically distinguish between the additive and multiplicative models. Equations (1) and (2) indicate that both models are nested in the regression equation

(3) [P.sub.U] = [alpha] + [beta][P.sub.S] + [epsilon],

where [epsilon] is a disturbance term that is uncorrelated with [P.sub.S]. The difference between the models is in their predictions about the coefficients [alpha] and [beta]: The additive model implies that the constant term [alpha] = c = [P.sub.S] - [P.sub.U] and the slope [beta] = 1, whereas the multiplicative model implies that [alpha] = 0 and [beta] = (1 + k) = [P.sub.U]/[P.sub.S].

The empirical analysis estimates equation (3) using ordinary least squares. The unit of observation is the metropolitan area, at which prices vary by quarter for marijuana and year for cocaine. Standard errors are calculated under the assumption that observations are independent across metropolitan areas but not necessarily within metropolitan areas across time, and corrected for heteroscedasticity of unknown form (e.g., White 1980). Because the predictions of the models regarding [alpha] and [beta] apply simultaneously, F-statistics for the joint hypothesis that the two coefficients equal their predicted values are used to test the validity of each model.

III. DATA

All price data used in the analyses come from the Drug Enforcement Administration (DEA) and have been converted to 1982-84 values using the Consumer Price Index for all urban consumers.

A. Marijuana

The source of the marijuana price data is the Illegal Drug Pricel Purity Report, published by the DEA Intelligence Division. The report contains estimates of the minimum and maximum marijuana price in 19 U.S. cities for purchases of two types of marijuana, commercial-grade and sinsemilla, in both ounce and pound quantities. The data are quarterly from the fourth quarter of 1985 to the fourth quarter of 2000 (but are missing in the second quarter of 1988 and the fourth quarter of 1998). (3) The sample cities are the center cities of the 19 domestic DEA divisions excluding El Paso, which did not contribute price data until 1999 and in which ounce prices are never observed. Data on average content of THC, the primary psychoactive chemical in marijuana, show that as of 2000, the potency of sinsemilla (13.2%) is more than twice that of commercial grade (6.1%).

Distribution levels in illegal drug markets are not precisely defined, especially in the case of marijuana, for which networks have more fluidity and lateral links than those for cocaine and heroin (Caulkins and Padman 1993). However, it is likely that the ounce and pound quantities for which prices are reported refer to purchases by retail users and sellers, respectively. The DEA and ONDCP commonly report retail prices in per ounce terms and wholesale prices in per pound terms. The National Narcotics Intelligence Consumers Committee (NNICC 1998) reports that retail dealers often purchase single-pound quantities from midlevel distributors of imported marijuana and from domestic cultivators. ONDCP (2001b) indicates that the most common vehicle for smoking marijuana is a joint, which typically contains around 0.4 g of marijuana and generates approximately four hours of intoxication, but retail user purchases in units of an ounce are quite common. Kleiman (1989) similarly regards the ounce quantity as representative of a large street-level purchase. In its analysis of marijuana prices, ONDCP (2001a) assumes that purchases of less than 100 g, about 3.5 ounces, are retail purchases, and acknowledges that many marijuana users buy the drug in ounce bundles. ONDCP (2001a) further assumes that the next highest distribution level includes purchases between 100 g and a kilogram (i.e., 3.5 ounces and 2.2 pounds).

Six separate (but not independent) analysis samples, representing minimum prices, maximum prices, and midpoints of the minimum and maximum price for commercial grade and simsemilla, are constructed. In each, an observation consists of a city and quarter in which both ounce and pound prices are observed. Because THC content is not reported by city, prices per bulk gram are used.

B. Cocaine

Cocaine price data come from the System to Retrieve Information from Drug Evidence (STRIDE) database. When an undercover agent of the DEA (or occasionally another federal, state, or local agency) makes a drug purchase in an attempt to arrest a dealer, the price is recorded in STRIDE. Because an unreasonable offer would make the dealer suspicious and hence endanger the agent, STRIDE prices are likely to be realistic but might not accurately represent market values because they reflect preferences of enforcement agents rather than consumers (Manski et al. 2001, p. 107). (4)

STRIDE contains 75,244 cocaine purchase during the 1985-2000 period. After eliminating eight observations with recorded weights of zero, logged purity is regressed on logged gram weight and year indicators. The observed price is then divided by expected pure weight, that is, weight multiplied by fitted purity from this regression, to convert the price into pure gram terms. The use of fitted rather than observed purity adjusts for the fact that buyers do not know purity at the time of purchase and avoids discarding the roughly 3% of observations with recorded purities of zero (Caulkins 1994). Finally, 476 observations with pure gram prices below one-twentieth or above 20 times the year-specific mean are dropped. Overall, 74,760 observations, or 99.4% of the original sample, are retained. Excluding price observations that seem unrealistic follows Caulkins (1994) and ONDCP (2001a), although the criteria are less strict in that some low and high price observations that would be omitted by their outlier filters are kept.

The next task is to group purchases into distinct market categories corresponding to the retail seller and user levels by choosing a threshold weight to divide the two categories and another to represent the largest weight to be considered a seller purchase. As with marijuana, these categories are not precisely defined, although they are commonly referred to as the ounce and gram levels, respectively, because street dealers often purchase ounce (28.35 g) quantities that are repackaged and sold to retail users in gram and "eightball" (one-eighth ounce) quantities (Caulkins 1994; DEA 2001; NNICC 1998; ONDCP 2001a, 2001b). For instance, Caulkins (1994) uses 4 and 100 bulk grams as upper limits for the gram and ounce categories, respectively, whereas ONDCP (2001a) uses cutoffs of 10 and 100 pure grams, corresponding at their average purity value of 65% to about 15 and 140 bulk grams. The author therefore specifies four different bulk weight upper limits of 3.5, 7, 10.5, and 14 g (i.e., one-eighth, one-quarter, three-eighths, and one-half of an ounce) for the gram level, and 84, 112, 140, and 168 g (i.e., 3, 4, 5, and 6 ounces) for the ounce level, and performs separate analyses for each of the resulting 16 gram and ounce threshold pairs. (5) The gram level thresholds are roughly bounded by those from Caulkins (1994) and ONDCP (2001a), which are proportionally far apart from each other and seem to be the lowest and highest reasonable values to specify given available information about retail user and seller purchases. In contrast, because the upper ounce thresholds implemented by Caulkins (1994) and ONDCP (2001a) are proportionally much closer together, the author also uses alternative values that are both below and above theirs.

Once the two distribution levels are established by choosing a pair of weight cutoffs, the last step is to create the analysis samples used to compare gram and ounce prices. A geographic market is defined as a metropolitan statistical area or (when they exist) primary netropolitan statistical area. For each year and geographic market, the market price at a given distribution level is defined as either the median or mean price per pure gram, depending on the specification, and observations are omitted if there are fewer than three STRIDE purchases at both the gram and ounce levels.

IV. RESULTS

A. Marijuana

Table 1 displays summary statistics as well as the equation (3) estimation results for marijuana. The left and right panels pertain to commercial grade and sinsemilla varieties, respectively, with the number of ounce-pound price pairs being 817 for the former and 555 for the latter. The mean midpoint of the ounce price range over the period is $3.31 per bulk gram for commercial grade and almost twice as high for sinsemilla, which is consistent with sinsemilla being roughly twice as potent. Pound prices, as expected, are lower than ounce prices. The difference between ounce and pound prices is larger for sinsemilla than for commercial grade, whereas the ounce to pound price ratio is almost 2 for commercial grade but somewhat smaller for sinsemilla.

In all six specifications, the estimated coefficients differ significantly from those predicted by the multiplicative model, which implies an intercept of 0 and a slope equal to the ratio of the ounce and pound price. However, the parameter estimates correspond closely with those predicted by the additive model, which implies a slope of 1 and an intercept equal to the difference between the ounce and pound price. The two F-statistic rows indicate the statistic and p-value of the F-test for the joint hypothesis implied by each model. As expected from the individual coefficient estimates, each joint F-test strongly rejects the multiplicative model, with significance levels below 0.01 in five of six models and just above 0.01 in the remaining model, but none are close to rejecting the additive model, with p-values of 0.6 or above in all six regressions.

More precisely, the additive and multiplicative models are extremes on a continuum. Because some distribution costs depend on weight and others on value, the true model could well be some mixture of the two. However, in columns 1-4, the estimated slope is less than 1 while the estimated intercept is greater than the ounce-pound price difference, meaning that the slight departures from the additive model in these specifications are in the opposite direction from that predicted by the multiplicative model, that is, the point estimates are even further away from those implied by the multiplicative model than are those implied by the additive model. Even in column 5, for which the parameter estimates are "closest" to those predicted by the multiplicative model, both the intercept and slope are 2.02/2.38 [approximately equal to] (1.61 - 1.09)/0.61 [approximately equal to] 85% of the way from the multiplicative to the additive model, implying that the correct "mixed" model for marijuana is at least 85% additive and at most 15% multiplicative. For marijuana, therefore, the additive model appears to describe the relationship between ounce and pound prices much more accurately than does the multiplicative model.

B. Cocaine

Table 2 contains cocaine price results for regressions that specify the median price observation from the given metropolitan area and year as the price for that market level, whereas Table 3 shows estimates from analogous models that use mean prices from each area and year. Each table is divided into four quadrants representing different threshold weights dividing the gram and ounce levels, and each quadrant has four columns corresponding to different upper weight limits for the ounce level. The samples include between 838 and 1,112 gram-ounce price pairs, with higher threshold weights allowing for larger samples because some metropolitan area/year cells gain enough observations to enter the sample, that represent between 171 and 186 metropolitan areas.

Again as expected, mean ounce prices are substantially below mean gram prices, and consequently means for both fall as the threshold weight that divides the gram and ounce levels rises. For market medians (Table 2), average gram- and ounce-level per pure gram prices vary from $129 and $59 for the lowest upper weight limit (3.5 g) to $89 and $51 for the highest upper weight limit (14 g), producing gram-ounce price ratios of between 1.7 and 2.2 and differences of between $37 and $71. Because the distribution of individual transaction prices is skewed, average per pure gram prices are higher for means (Table 3) by $18-20 at the gram level and $2-3 at the ounce level, correspondingly resulting in higher price ratios (between 2 and 2.4) and differences (between $53 and $86).

The parameter estimates reject the multiplicative model and support the additive model even more strongly than for marijuana. Of the 32 specifications presented in Tables 2 and 3, the pair of coefficient values implied by the multiplicative model is rejected by joint F-tests at the 0.001 level in 28 models and at the 0.005 level in the remaining 4 models, corresponding to the use of market-level means with the lowest weight threshold for the gramounce distinction. Meanwhile, the additive null hypothesis cannot be rejected in any of the specifications, with p-values of close to 0.5 in the aforementioned four models and no less than 0.78 in remaining models.

Because value composes a larger proportion of distribution costs for cocaine than marijuana, in principle it seems less likely that the pure additive model would hold for cocaine than for marijuana. In the first four columns of Table 2, however, both the slopes and intercepts are virtually identical to the values that the additive model predicts, and the p-values for the joint F-tests for those coefficients are thus equal to 1. Moreover, in the remaining columns of Table 2 and the bottom right quadrant of Table 3, once again both the intercepts, which are greater than the price differences, and the slopes, which are less than 1, are even further from the values implied by the multiplicative model than are the values implied by the additive model. In the remaining quadrants of Table 3, the intercepts and slopes are between the values predicted by the two models. But even in the upper left quadrant specifications that least disagree with the multiplicative null hypothesis, the estimated parameters imply a mixture that is three-quarters additive and only one-quarter multiplicative. The results for cocaine thus again provide very strong evidence against the multiplicative model and in support of the additive model.

To address the possibility that the introduction of crack cocaine in the mid- to late 1980s altered the structure of low-level cocaine markets, all models are reestimated with data on cocaine prices from only 1991-2000. (6) Although regression slopes are larger and constant terms are smaller than those shown in Tables 2 and 3, that is, the values of both are always in between those predicted by the additive and multiplicative models, coefficient values are still always closer to those predicted by the additive model. In particular, of the 32 specifications analogous to those shown in Tables 2 and 3, the multiplicative model is rejected at the 0.01 level in 28 cases and at the 0.05 level in the other 4 cases (corresponding to the use of mean prices for the highest gram threshold weight), whereas the additive model is never rejected at the 0.01 level, is rejected at the 0.05 level in only 5 specifications (four corresponding to the use of mean prices at the lowest gram threshold weight), and cannot be rejected at the 0.10 level in the other 27 cases. Thus the conclusion that the multiplicative model is overwhelmingly rejected in favor of the additive model still holds.

These findings contradict those of Caulkins (1994), in which the estimated coefficients in regressions of gram prices on ounce prices strongly reject the implications of the additive model but correspond extremely closely with those of the multiplicative model. Although both studies use STRIDE data and the same regression specification (equation 3), they differ in many respects beyond that. One difference is in the time periods examined: Caulkins analyzes data from 1977-91, whereas the present data span 1985 to 2000. It could be that the model describing the retail-level pass through shifted from multiplicative to additive between the late 1970s and mid-1980s, when crack was introduced, although one would not expect such diametrically opposing results given that almost half of the data periods overlap. The studies also differ markedly in geographic coverage: Caulkins's data included only 83 observations from 8 cities, 6 of which are in the Northeast corridor with the remaining two in the upper Midwest, whereas the present smallest sample contains 838 observations from 171 different metropolitan areas spread across the United States.

Perhaps most important, the studies use different methods to construct the analysis samples from the raw STRIDE data. Caulkins (1994) uses a much tighter outlier filter in which per pure gram prices less than one-fourth or greater than four times the market level average are omitted, after which a city-specific filter based on distance from the median price eliminates additional observations. Furthermore, Caulkins standardized prices by applying an exponential quantity discount factor; for example, the per gram price of a purchase with expected pure weight of one-half gram is assumed to be [2.sup.[beta]] times as much as the actual price, where [beta] ~ .75 is estimated from STRIDE, rather than twice the actual price. This could impose some multiplicativity to the structure of the quantity discount across market levels, which is what our studies ultimately are designed to estimate. Because the author lacks data from the late 1970s and early 1980s, he cannot attempt to replicate Caulkins's analysis, and instead simply notes the most transparent differences between the studies.

V. CONCLUSION

The results of this analysis provide strong support for the hypothesis that changes in marijuana and cocaine prices paid by retail sellers are passed through additively to retail users, but soundly reject the hypothesis that such price changes are passed through multiplicatively. The central implication is that drug enforcement at wholesale levels is less effective in raising retail prices than it would be if the multiplicative model was operative. Research indicating that drug demand is priceresponsive (e.g., DeSimone and Farrelly 2003; Saffer and Chaloupka 1999) suggests that wholesale-level drug enforcement is thereby less effective in reducing drug consumption than would otherwise be the case. These implications apply directly to enforcement operations targeted at retail-level sellers as well as drug laws that penalize possession and sales more severely as the weight of the drug possessed or sold increases. Because price increases above the retail seller level are eventually passed to retail sellers through various wholesale dealers, implications with regard to the effectiveness of the considerable resources targeted toward interdiction and (for marijuana) domestic cultivation are similar. Moreover, this evidence suggests that markups closer to the beginning of the distribution chain could be additive as well, especially in light of the anecdotal evidence from Caulkins and Reuter (1998) cited in the introduction, although import price changes of small magnitudes would represent large proportionate price changes at that level.

The results are also relevant for enforcement policies aimed at the retail level. In particular, the rejection of the multiplicative model means that a potential shift in enforcement intensity from the retail to wholesale level is a relatively less desirable option than otherwise. Because a price increase of a specified amount at the wholesale level translates to a similar price increase at the retail level, the allocation of enforcement resources across these two market levels should be based solely on costs of raising the price by a specified amount and external costs and benefits of harassment. Rejection of the multiplicative model also enhances the relative attractiveness of both nonprice retail-level enforcement strategies, such as disruptive tactics designed to increase the search times required for users to find sellers (Kleiman 1992), and demand-side strategies, such as increasing resources for drug treatment programs.

An important caveat is that the coefficient estimates here represent simple linear correlations between prices at the retail user and seller levels that do not necessarily imply a causal relationship running from the retail seller to user level. For instance, ONDCP (2001a) finds evidence that to some extent wholesale prices have followed (rather than led) retail prices, perhaps because wholesale purchases are bound by prior contractual arrangements, whereas retail purchases are not. More generally, it is possible that common omitted factors such as enforcement resources or demand conditions simultaneously influence prices at several distribution levels. It is also possible that the relationship between prices at the two market levels varies across geographic areas or time, so that a more appropriate model would include multiple intercept and slope terms. However, the data employed here are not suitable for estimating a model with such nuances. The ideal data for this exercise, consisting of repeated observations of matched pairs of prices at the retail seller and user levels from particular locations, simply do not exist.

REFERENCES

Caulkins, J. P. The Distribution and Consumption of Illicit Drugs: Some Mathematical Models and Their Policy Implications. Doctoral dissertation, MIT, Cambridge, Mass., 1990.

______. Developing Price Series for Cocaine. Santa Monica, Calif.: RAND, 1994.

Caulkins, J. P., and R. Padman. "Quantity Discounts and Quality Premia for Illicit Drugs." Journal of the American Statistical Association, 88(423), 1993, 748-57.

Caulkins, J. P., and P. Reuter. "What Price Data Tell Us about Drug Markets." Journal of Drug Issues, 28(3), 1998, 593-612.

DeSimone, J. "Is Marijuana a Gateway Drug?" Eastern Economic Journal, 24(2), 1998, 149-64.

DeSimone, J., and M. C. Farrelly. "Price and Enforcement Effects on Cocaine and Marijuana Demand." Economic Inquiry, 41(1), 2003, 98-115.

DEA (Drug Enforcement Administration). Drug Trafficking in the United States. Washington, D.C.: U.S. Department of Justice, 2001.

Kleiman, M. A. R. Marijuana: Costs of Abuse, Costs of Control. New York: Greenwood Press, 1989.

_______. Against Excess: Drug Policy for Results. New York: Basic Books, 1992.

Manski, C. F., J. V. Pepper and C. V. Petrie, eds. Informing America's Policy on Illegal Drugs: What We Don't Know Keeps Hurting Us. Washington, D.C.: National Academy Press, 2001.

NNICC (National Narcotics Intelligence Consumers Committee). The Supply of Illicit Drugs to the United States. Washington, D.C.: U.S. Department of Justice, 1998.

ONDCP (Office of National Drug Control Policy). The Price of Illicit Drugs: 1981 through the Second Quarter of 2000. Washington, D.C.: Office of Programs, Budget, Research, and Evaluations, 2001a.

_______. Pulse Check. Trends in Drug Abuse. Washington, D.C.: Office of Programs, Budget, Research, and Evaluation, 2001b.

_______. What America's Users Spend on Illegal Drugs, 1988-2000. Washington, D.C.: Office of Programs, Budget, Research, and Evaluation, 2001c.

Pietschmann, T. "Price Setting Behavior in the Heroin Market." Working Paper, United Nations Office on drugs and Crime, 2005.

Saffer, H., and F. Chaloupka. "The Demand for Illicit Drugs." Economic Inquiry, 37(3), 1999, 401-11.

White, H. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity." Econometrica, 48(4), 1980, 817-38.

JEFF DESIMONE*

*The author is grateful to Bob Janice of the DEA for help in obtaining and understanding the STRIDE price data, Mike Grossman and Rosalie Pacula for sharing their marijuana price data, and two anonymous referees for providing suggestions that substantially improved the quality of the paper.

DeSimone: Assistant Professor, Department of Economics, University of South Florida, 4202 E. Fowler Ave., BSN 3403, Tampa, FL 33620-5500, and Faculty Research Fellow, National Bureau of Economic Research. Phone 1-813-974-6514, Fax 1-813-974-6510, E-mail jdesimon@coba.usf.edu

ABBREVIATIONS

DEA: Drug Enforcement Administration

NNICC: National Narcotics Intelligence Consumers Committee

ONDCP: Office of National Drug Control Policy

STRIDE: System to Retrieve Information from Drug Evidence

1. In addition, Pietschmann (2005) seeks to test the two models using data on opiate prices along the supply chain between Afghanistan and Western Europe surrounding the dramatic reduction in production during the Taliban ban.

2. This section borrows heavily from Caulkins (1994).

3. Prices are rarely observed in all four quarters for a given year and city. Lists of time periods included for each city in the marijuana samples and metropolitan area in the cocaine samples are available from the author.

4. STRIDE also contains data on marijuana prices, but they are not useful for this analysis because their scarcity precludes the ability to construct cross-sectional geographic units representing different markets. During the sample period there are an average of only 175 observations per year, one-third of which are from the District of Columbia.

5. Retail crack purchase quantities generally range from one-twentieth to one-half of a gram (DEA 2001; ONDCP 2001b).

6. These results are not shown but are available on request from the author.
TABLE 1 Relationship between Marijuana Prices at the Ounce and Pound
Levels

 (1) (2) (3)
 Commercial Grade (n = 817)
Measure Minimum Midpoint Maximum

Mean ounce price 2.24 3.31 4.38
Mean pound price 1.11 1.77 2.42
Difference 1.13 1.54 1.96
Ratio 2.01 1.87 1.81
Intercept 1.33 (0.19) 1.64 (0.28) 2.17 (0.37)
Slope 0.82 (0.18) 0.95 (0.15) 0.92 (0.14)
Additive F-statistic 0.54 [0.593] 0.06 [0.939] 0.19 [0.832]
Multiplicative F-statistic 23.71 [0.000] 19.75 [0.000] 21.11 [0.000]
[R.sup.2] 0.08 0.22 0.26

 (4) (5) (6)
 Sinsemilla (n = 555)
Measure Minimum Midpoint Maximum

Mean ounce price 4.89 6.31 7.73
Mean pound price 2.72 3.93 5.13
Difference 2.17 2.38 2.60
Ratio 1.80 1.61 1.51
Intercept 2.34 (0.38) 2.02 (0.65) 2.53 (0.66)
Slope 0.94 (0.18) 1.09 (0.19) 1.01 (0.15)
Additive F-statistic 0.10 [0.903] 0.17 [0.843] 0.01 [0.993]
Multiplicative F-statistic 19.67 [0.000] 5.42 [0.014] 7.41 [0.005]
[R.sup.2] 0.24 0.40 0.43

Notes: Measure indicates whether the price in each city/year is the
minimum, maximum, or midpoint of the reported range. Difference
represents the difference between the mean ounce and mean pound prices,
and ratio represents the mean ounce price divided by the mean pound
price. The intercept and slope are from an ordinary least squares
regression of ounce price on pound price and a constant. SEs that adjust
for within-metropolitan area clustering and arbitrary heteroscedasticity
appear in parentheses beside coefficients. The additive F-statistic
tests the joint hypothesis that the intercept equals the difference
between the ounce and pound price means and the slope equals one. The
multiplicative F-statistic tests the joint hypothesis that the intercept
equals 0 and the slope equals the ratio of ounce and pound price means.
p-values appear in brackets beside F-statistics.

TABLE 2 Relationship between Median Cocaine Prices at the Gram and Ounce
Levels

 (1) (2) (3)

Gram threshold 3.5 g 3.5 g 3.5 g
Ounce threshold 84 g 112 g 140 g
n 838 842 843
Metropolitan areas 171 171 171
Mean gram price 128.84 128.82 128.73
Mean ounce price 59.11 58.65 58.18
Difference 69.72 70.17 70.55
Ratio 2.18 2.20 2.21
Intercept 69.73 (13.26) 70.11 (13.24) 70.43 (13.08)
Slope 1.00 (0.23) 1.00 (0.23) 1.00 (0.23)
Additive F- 0.00 [1.00] 0.00 [1.00] 0.00 [1.00]
 statistic
Multiplicative F- 13.87 [0.000] 14.12 [0.000] 14.60 [0.000]
 statistic
[R.sup.2] 0.25 0.25 0.26

 (4) (5) (6)

Gram threshold 3.5 g 7 g 7 g
Ounce threshold 168 g 84 g 112 g
n 843 985 990
Metropolitan areas 171 181 182
Mean gram price 128.73 109.09 109.40
Mean ounce price 58.13 55.56 55.30
Difference 70.61 53.53 54.10
Ratio 2.21 1.96 1.98
Intercept 70.43 (13.06) 59.20 (10.18) 59.70 (10.12)
Slope 1.00 (0.23) 0.90 (0.19) 0.90 (0.19)
Additive F- 0.00 [1.00] 0.16 [0.856] 0.15 [0.858]
 statistic
Multiplicative F- 14.64 [0.000] 17.00 [0.000] 17.47 [0.000]
 statistic
[R.sup.2] 0.26 0.26 0.26

 (7) (8) (9)

Gram threshold 7 g 7 g 10.5 g
Ounce threshold 140 g 168 g 84 g
n 992 993 1,042
Metropolitan areas 182 182 187
Mean gram price 109.31 109.28 102.30
Mean ounce price 54.89 54.80 53.71
Difference 54.41 54.47 48.59
Ratio 1.99 1.99 1.90
Intercept 59.90 (10.03) 59.76 (10.11) 53.89 (9.81)
Slope 0.90 (0.19) 0.90 (0.19) 0.90 (0.19)
Additive F- 0.15 [0.861] 0.14 [0.871] 0.15 [0.863]
 statistic
Multiplicative F- 17.91 [0.000] 17.64 [0.000] 15.26 [0.000]
 statistic
[R.sup.2] 0.26 0.26 0.28

 (10) (11) (12)

Gram threshold 10.5 g 10.5 g 10.5 g
Ounce threshold 112 g 140 g 168 g
n 1,049 1,053 1,055
Metropolitan areas 188 188 189
Mean gram price 102.58 102.40 102.33
Mean ounce price 53.57 53.08 52.96
Difference 49.01 49.32 49.37
Ratio 1.91 1.93 1.93
Intercept 54.01 (9.79) 54.29 (9.67) 54.10 (9.76)
Slope 0.91 (0.19) 0.91 (0.19) 0.91 (0.19)
Additive F- 0.13 [0.876] 0.13 [0.875] 0.12 [0.888]
 statistic
Multiplicative F- 15.40 [0.000] 15.92 [0.000] 15.63 [0.000]
 statistic
[R.sup.2] 0.28 0.28 0.29

 (13) (14) (15)

Gram threshold 14 g 14 g 14 g
Ounce threshold 84 g 112 g 140 g
n 1,087 1,103 1,108
Metropolitan areas 185 186 186
Mean gram price 88.70 89.06 88.98
Mean ounce price 52.02 51.79 51.28
Difference 36.68 37.26 37.71
Ratio 1.71 1.72 1.74
Intercept 43.08 (9.24) 43.24 (9.23) 43.69 (9.09)
Slope 0.88 (0.18) 0.88 (0.18) 0.88 (0.18)
Additive F- 0.24 [0.784] 0.21 [0.808] 0.22 [0.803]
 statistic
Multiplicative F- 11.06 [0.000] 11.17 [0.000] 11.74 [0.000]
 statistic
[R.sup.2] 0.31 0.31 0.31

 (16)

Gram threshold 14 g
Ounce threshold 168 g
n 1,112
Metropolitan areas 186
Mean gram price 89.01
Mean ounce price 51.23
Difference 37.79
Ratio 1.74
Intercept 43.78 (9.09)
Slope 0.88 (0.18)
Additive F- 0.22 [0.801]
 statistic
Multiplicative F- 11.85 [0.000]
 statistic
[R.sup.2] 0.31

Notes: Thresholds are the upper bulk gram weight cutoffs for the
corresponding level. Difference represents the difference between the
mean gram and mean ounce prices, and ratio represents the mean gram
price divided by the mean ounce price. The intercept and slope are from
an ordineary least squares regression of gram price on ounce price and a
constant. SEs that adjust for within-metropolitan area clustering and
arbitrary heteroscedasticity appear in parentheses beside coefficients.
The additive F-statistic tests the joint hypothesis that the intercept
equals the difference between the gram and ounce price means and the
slope equals 1. The multiplicative F-statistic tests the joint
hypothesis that the intercept equals 0 and the slope equals the ratio of
the gram and ounce price means. p-values appear in brackets beside
F-statistics.

TABLE 3 Relationship between Mean Cocaine Prices at the Gram and Ounce
Levels

 (1) (2) (3)

Gram threshold 3.5 g 3.5 g 3.5 g
Ounce threshold 84 g 112 g 140 g
n 838 842 843
Metropolitan areas 171 171 171
Mean gram price 149.19 149.11 149.01
Mean ounce price 63.82 63.44 62.81
Difference 85.38 85.67 86.19
Ratio 2.34 2.35 2.37
Intercept 63.22 (19.02) 63.51 (18.97) 64.25 (18.78)
Slope 1.35 (0.31) 1.35 (0.31) 1.35 (0.31)
Additive F- 0.72 [0.487] 0.74 [0.480] 0.74 [0.479]
 statistic
Multiplicative F- 5.88 [0.003] 6.06 [0.003] 6.34 [0.002]
 statistic
[R.sup.2] 0.32 0.32 0.32

 (4) (5) (6)

Gram threshold 3.5 g 7 g 7 g
Ounce threshold 168 g 84 g 112 g
n 843 985 990
Metropolitan areas 171 181 182
Mean gram price 149.01 128.45 128.72
Mean ounce price 62.73 58.83 58.55
Difference 86.28 69.62 70.17
Ratio 2.38 2.18 2.20
Intercept 64.14 (18.78) 65.27 (12.32) 64.56 (12.42)
Slope 1.35 (0.31) 1.07 (0.22) 1.10 (.22)
Additive F- 0.75 [0.474] 0.06 [0.937] 0.11 [0.899]
 statistic
Multiplicative F- 6.31 [0.002] 14.59 [0.000] 14.05 [0.000]
 statistic
[R.sup.2] 0.32 0.27 0.28

 (7) (8) (9)

Gram threshold 7 g 7 g 10.5 g
Ounce threshold 140 g 168 g 84 g
n 992 993 1,042
Metropolitan areas 182 182 187
Mean gram price 128.60 128.57 120.92
Mean ounce price 57.96 57.90 56.24
Difference 70.64 70.66 64.68
Ratio 2.22 2.22 2.15
Intercept 64.29 (12.60) 64.23 (12.62) 61.70 (11.52)
Slope 1.11 (0.23) 1.11 (0.23) 1.05 (0.22)
Additive F- 0.13 [0.876] 0.14 [0.872] 0.04 [0.965]
 statistic
Multiplicative F- 13.53 [0.000] 13.63 [0.000] 15.08 [0.000]
 statistic
[R.sup.2] 0.28 0.28 0.28

 (10) (11) (12)

Gram threshold 10.5 g 10.5 g 10.5 g
Ounce threshold 112 g 140 g 168 g
n 1,049 1,053 1,055
Metropolitan areas 188 188 189
Mean gram price 121.15 120.98 120.89
Mean ounce price 56.03 55.40 55.32
Difference 65.11 65.58 65.58
Ratio 2.16 2.18 2.19
Intercept 61.02 (11.60) 60.10 (11.91) 59.97 (11.94)
Slope 1.07 (0.22) 1.10 (0.23) 1.10 (0.23)
Additive F- 0.07 [0.937] 0.11 [0.895] 0.12 [0.890]
 statistic
Multiplicative F- 14.52 [0.000] 13.35 [0.000] 13.39 [0.000]
 statistic
[R.sup.2] 0.28 0.29 0.29

 (13) (14) (15)

Gram threshold 14 g 14 g 14 g
Ounce threshold 84 g 112 g 140 g
n 1,087 1,103 1,108
Metropolitan areas 185 186 186
Mean gram price 106.71 106.90 106.83
Mean ounce price 54.06 53.80 53.16
Difference 52.64 53.10 53.67
Ratio 1.97 1.99 2.01
Intercept 55.90 (9.98) 54.86 (10.03) 54.31 (10.28)
Slope 0.94 (0.19) 0.97 (0.20) 0.99 (0.20)
Additive F- 0.06 [0.945] 0.02 [0.984] 0.00 [0.998]
 statistic
Multiplicative F- 16.55 [0.000] 15.77 [0.000] 14.66 [0.000]
 statistic
[R.sup.2] 0.28 0.29 0.29

 (16)

Gram threshold 14 g
Ounce threshold 168 g
n 1,112
Metropolitan areas 186
Mean gram price 106.83
Mean ounce price 53.14
Difference 53.69
Ratio 2.01
Intercept 54.28 (10.28)
Slope 0.99 (0.20)
Additive F- 0.00 [0.998]
 statistic
Multiplicative F- 14.80 [0.000]
 statistic
[R.sup.2] 0.29

Notes: Thresholds are the upper bulk gram weight cutoffs for the
corresponding level. Difference represents the difference between the
mean gram and mean ounce prices, and ratio represents the mean gram
price divided by the mean ounce price. The intercept and slope are from
an ordinary least squares regression of gram price on ounce price and a
constant. SEs that adjust for within-metropolitan area clustering and
arbitrary heteroscedasticity appear in parentheses beside coefficients.
The additive F-statistic tests the joint hypothesis that the intercept
equals the difference between the gram and ounce price means and the
slope equals 1. The multiplicative F-statistic tests the joint
hypothesis that the intercept equals 0 and the slope equals the ratio of
the gram and ounce price means. p-values appear in brackets beside
F-statistics.
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Author:Desimone, Jeff
Publication:Contemporary Economic Policy
Geographic Code:1USA
Date:Jan 1, 2006
Words:7367
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