The demand for illicit drugs.
Saffer, Henry ; Chaloupka, Frank
I. INTRODUCTION
Illicit drug use and alcohol abuse imposes significant costs on
society and on the individual users. These costs include increased
crime, health problems, and employment problems. Because of these
considerable costs, government, at all levels, has made drug control and
the control of alcohol abuse important priorities. The federal
government has undertaken an aggressive program of interdiction of drug
shipments and eradication of drug crops in the field. The federal
government and the state governments have also increased their criminal
justice efforts.
In analyzing the effect of government drug control programs,
economists have applied the conventional supply and demand model to
illicit drug markets. The model includes a demand function that is
downward sloping with respect to price and a supply function that is
upward sloping or horizontal with respect to price. Drug programs like
interdiction and drug sanctions are assumed to reduce supply and raise
equilibrium price. Other policy options such as some form of drug
legalization could increase supply and reduce equilibrium price. The
effect of these policies on equilibrium quantity is dependent on the
elasticity of demand and on whether demand shifts. Since not much is
known about drug price elasticities, the potential effects of various
drug control policies remain a speculative exercise.
The purpose of this paper is to estimate the effects of alcohol and
drug prices on alcohol use and drug participation. Both own price and
cross price effects are estimated. There are few prior empirical studies of the effect of drug prices, because data have been difficult to
acquire. This paper makes use of newly available data on drug prices and
is the first paper to link these data to a nationally representative
drug use data set of 49,802 individuals. Estimates of drug price
elasticities are important empirical evidence that drug sales can be
characterized by market forces. Drug price elasticities are also
important in estimating the likely impact of policies that affect drug
prices and in estimating the effects of drug prohibition. Cross price
elasticities are important to estimate, since they suggest the likely
effects of policies such as an increase in alcohol taxes on illicit drug
participation and the effects of marijuana decriminalization on alcohol,
cocaine, and heroin use.
II. PRIOR STUDIES
While there are a number of prior studies of the effects of alcohol
prices and policies, there are few prior studies of drug prices and
polices. The reason for so few prior drug studies is the limited amount
of data on drug prices and the limited options for linking these data to
an individual record by residential area. This study uses a new data set
of cocaine and heroin prices from the Drug Enforcement Agency that was
linked to individual records by the Office of Applied Studies at the
Substance Abuse and Mental Health Services Administration.
Leung and Phelps (1993) provide a review of a number of recent
alcohol demand studies. The empirical literature provides considerable
evidence that shows increasing the price of alcoholic beverages to
decrease alcohol use. Alcohol demand studies generally estimate price
elasticities for beer, wine, and spirits separately. Most studies employ
aggregate data, but a few use individual data. Studies using aggregate
data find price elasticities for beer from about -.2 to about -1.0, for
wine from about -.3 to about -1.8, and for spirits from about -.3 to
about -1.8. Studies using individual data estimate price elasticities
for beer from about -.5 to about -3.0, for wine at about -.5, and for
spirits from about -.5 to about -4.0.
The few prior studies of the effect of decriminalization on
marijuana use generally find that marijuana decriminalization has no
effect on participation. Pacula (1994), Thies and Register (1993),
Dinardo and Lemieux (1992), and Johnston, O'Malley, and Bachman
(1981) all used samples of young people and found no effect of marijuana
decriminalization. Model (1992) found that decriminalization had a
significant positive effect on property crimes and a significant
negative effect on violent crimes, and Model (1993) found that
decriminalization increases marijuana use.
There are also a few prior empirical studies of the effect of drug
prices on drug use. Grossman and Chaloupka (1998) use a rational
addiction model and find cocaine price elasticities for youth ranging
from -.7 to -1.7. They also estimate cocaine participation elasticities
for youth of -.45 to -1.28. Bretteville-Jensen and Sutton (1996)
estimate a price elasticity of heroin of -1.23, van Ours (1995) finds a
price elasticity of -.7 to -1.0 for opium use and -.3 to -.4 for opium
participation. Dinardo (1993) finds no effect of price on cocaine use.
Nisbit and Vakil (1972) estimate the price elasticity of marijuana at
-.7 to -1.0.
III. DATA SET
The empirical models estimated in this paper are demand curves. The
basis of these empirical demand curves is the same theoretical demand
model that is used for legal goods. Theoretical drug demand curves are
derived in the usual fashion by maximizing individual utility subject to
a budget constraint consisting of the price of drugs and alcohol, other
prices, and income. The derived demand curves show that drug consumption
is negatively related to the own price and related, without a priori sign, to other prices, income, and taste. The demand curves in this
study are estimated with a pooled set of data from the 1988, 1990, and
1991 National Household Surveys on Drug Abuse (NHSDA). The pooled data
set consists of 49,802 observations, which is important since the larger
sample increases the number of drug users surveyed and the precision of
the estimates. The NHSDA are cross-sectional surveys of the U.S.
household population aged 12 or older and contain information on
socioeconomic characteristics as well as data on drug and alcohol use.
These surveys exclude residents of noninstitutional group quarters (that
is, college dormitories) and exclude residents of institutional group
quarters (that is, prisons). Also excluded are those people with no
permanent residence (that is, homeless and residents in transient
hotels). Less than 2% of the population is excluded. The excluded 2%
probably have a higher percentage of regular drug users than the
included 98%. These surveys are likely to be more representative of
occasional drug users rather than regular drug users. As a nationally
representative survey, the NHSDA has an important advantage over the
National Longitudinal Survey of Youth and Monitoring the Future surveys,
which are limited to youth. In addition to information on alcohol and
drug consumption, the surveys contain information on the gender, race,
ethnicity, personal income, and marital status for each individual
surveyed. County-level alcohol prices and state-level data on marijuana
decriminalization and drug prices have been appended to the individual
records.(1)
The 1988, 1990, and 1991 surveys are very similar, except for size.
The 1991 survey is over three times as large as the 1988 and 1990
surveys. The 1991 survey is larger, in part, because six primary
sampling units were oversampled. Each survey also oversamples persons
aged 12-17, Hispanics, and blacks. A summary of the variable definitions
and means are included in Table I. The means presented in this table are
weighted so that they are comparable to a random sample of the United
States.(2)
The dependent variables in this study are a continuous measure of
alcohol consumption and two dichotomous measures of marijuana, cocaine,
and heroin participation. The alcohol consumption variable measures the
number of days in the past 31 days that the individual had consumed
alcohol. Marijuana, cocaine, and heroin represent most of the illicit
drug use in the United States. The first illicit drug participation
variable is equal to one if the individual reports that he or she had
used the substance during the past year, and the second illicit drug
participation variable is for use in the past month.(3) The number of
individuals that report participation in the past year is about double
the monthly participation for all three drugs. Annual participation may
be interpreted as reflecting more occasional use, while participation in
the past month may be interpreted as more regular use.
The price of alcohol consists of the prices of beer, wine, and
distilled spirits. Data on the prices come from the American Chamber of
Commerce Research Association's quarterly Inter-City Cost of Living
Index (1988, 1990, 1991). This index contains prices, inclusive of taxes, for over 250 cities each quarter and was used to construct
county-level prices. These data were merged with the NHSDA on a PSU level.(4) A single alcohol price variable, the price of one pure liter
of alcohol, was created from the beer, wine, and spirits prices. This
computation was done by first computing the price per liter for each
beverage. The price of beer is reported for a six-pack. The price was
divided by 2.13, which is the number of liters in a six-pack. Since the
price of wine is reported for a 1.5-liter bottle the wine price was
divided by this number. Spirits prices are reported for a liter bottle.
Next, the these liter prices were divided by the percent alcohol in each
beverage (.04 for beer,. 11 for wine, and .41 for spirits). A weighted
average price of pure alcohol can now be computed. The weights are the
share of pure alcohol consumption represented by each beverage. These
weights are .569 for beer, .113 for wine, and .318 for spirits. These
weight data come from the Brewer's Association of Canada
International Survey. The price was then adjusted to the real value in
1982-84 dollars.
Prices for cocaine and heroin come from the U.S. Department of
Justice, Drug Enforcement Agency's (DEA) STRIDE (System to Retrieve
Information from Drug Evidence) data set.(5) DEA agents and police
narcotics officers purchase illicit drugs regularly. The price, purity,
weight, and other information are recorded in the STRIDE data set. One
reason these price data are collected is so that DEA agents will know
how much to offer when negotiating to buy from drug dealers. The price
data are fairly accurate, since inaccurate data would endanger these
agents. The STRIDE data set provided by the DEA to the National Bureau
of Economic Research (NBER) contains cocaine and heroin data from 1977
through 1989 and 1991 for approximately 144 cities or towns. This data
set has over 23,000 cocaine price observations and over 15,000 heroin
price observations.
TABLE I
Weighted Average Means from the Combined National Household Survey
of Drug Abuse 1988, 1990, 1991
Variable Definition and Mean
Alcohol Use The number of days alcohol was used in
the past 31 days, [Mu] = 3.49.
Heroin Participation Dichotomous indicator equal to one if a
respondent reports using heroin in the
past year, [Mu] = .0011; and past month
[Mu] = .0004.
Cocaine Participation Dichotomous indicator equal to one if a
respondent reports using cocaine in the
past year, [Mu] = .02; and past month,
[Mu] = .0085.
Alcohol Price The price of a liter of pure alcohol in
1983 dollars, [Mu] = $24.78.
Marijuana Participation Dichotomous indicator equal to one if a
respondent reports using marijuana in the
past year, [Mu] = .071; and past month,
[Mu] = .045.
Marijuana Decriminalized A dichotomous indicator equal to one for
states that have eliminated incarceration
as a penalty for most marijuana
possession offenses, [Mu] = .303.
Heroin Price Price of one pure milligram of heroin in
1983 dollars, [Mu] = $8.36.
Cocaine Price Price of one pure gram of cocaine in 1983
dollars, [Mu] = $111.47.
Real Income Total personal income in 1983 dollars,
[Mu] = $12,425.
Gender A dichotomous variable equal to one for
males, [Mu] = .479.
Marital Status A dichotomous variable equal to one if
married, [Mu] = .569. A dichotomous
variable equal to one if marital status
was missing is also included, [Mu] =
.033.
Age 12-20 A dichotomous variable equal to one if an
individual is 12-20 years of age, [Mu] =
.155.
Age 21-30 A dichotomous variable equal to one if an
individual is 21-24 years of age, [Mu] =
.197.
Black A dichotomous variable equal to one if an
individual self-reports that they are
black, [Mu] = .116.
Hispanic A dichotomous variable equal to one if an
individual self-reports that they are
Hispanic, [Mu] = .078.
Notes: Final sample size when missing values were excluded is
49,802. All data are weighted. The elasticities were computed with
unweighted data.
Information on the date and city of purchase, its total cost, total
weight in grams, and purity (as a percentage) are recorded in STRIDE.
The data must be adjusted because total cost rather than price is
recorded. If total cost were proportional to weight, price could be
calculated as the former divided by the latter. In fact, this is not the
case, because larger purchases tend to be wholesale purchases. Variation
in purity and imperfect information about purity on the part of
purchasers further complicate the issue. Therefore, the price of one
gram of pure drug was obtained, by year and city, from a regression of
the natural logarithm of the total purchase cost on the natural
logarithm of weight, the natural logarithm of purity, and dichotomous
variables for each city and year in STRIDE except one. Imperfect
information about purity is addressed by predicting purity based on the
other regressors. To identify the total cost model, the coefficient of
the natural logarithm of predicted purity is constrained to equal the
coefficient of the natural logarithm of weight. The natural logarithm of
the price of one gram of pure drug is then given as the sum of the
intercept, the relevant city coefficients, and the relevant time
coefficients. This procedure eliminated variations in price or unit cost
due to variations in weight or purity. The antilogarithm of this
predicted price is the price of one unit of 100% pure drug. The local
level prices were aggregated to the state level. This aggregation was
computed as a weighted average of all the represented cites in the
state. The population weights for each city were computed by dividing
the city population by the total population of all represented cities in
the state. The population data come from the City and County Databook
(1993), published by the U.S. Department of Commerce. Prices were
adjusted to their real value in 1982-84 dollars.
There are two issues regarding the price data that are important.
The first issue is the exogeneity of price. If drug supply is upward
sloping, then price and quantity would be endogenous. Since the
predicted price variable used in the regressions comes from a reduced
form model, however, it is uncorrelated with the error term in the
demand equation. The second issue is measurement error. Merging
individual level data with state level prices introduces a potential for
measurement error due to matching. Any measurement error created by the
matching problem is probably small since, in each state, most drug users
are in the larger urban areas and, for each state, the drug price data
comes mostly from the larger urban areas. If there is any matching
measurement error in the price data, it will bias the coefficient and
t-ratio downward. Thus, the reported coefficients and t-ratios are
conservative lower bound estimates.
Marijuana decriminalization is a law that specifically eliminates
criminal sanctions for possession of small amounts of marijuana.
Decriminalization of marijuana eliminates possible imprisonment for most
first offense possession violations. Oregon, in 1973, was the first
state to decriminalize marijuana. By 1978, 10 other states had followed,
substantially reducing the penalties associated with marijuana
possession. Decriminalization, by lowering the penalties associated with
marijuana use, is expected to increase marijuana demand.
Income and a group of dichotomous demographic variables have also
been defined. Total personal income is defined as income from all
sources including wages, self-employment, social security, public
assistance, child support and other pension income. These are age, race,
gender, and marital status. Two dummy age variables have been included
to allow for differential age effects. These dummies are for ages 12-20
and 21-30, with over 30 the omitted age category. Three dichotomous
variables equal to one if the individual reports that they are black,
Hispanic, or male, respectively, have also been defined. Marital status
may also affect drug use. A dichotomous variable equal to one if the
individual is married has been defined. Since there are a number of
missing values for this variable, a second variable was defined. The
second variable is defined as equal to one if the marital status data
are missing and the missing data on marital status are recoded to zero.
IV. REGRESSION RESULTS
Tables II-V present the estimation results for alcohol, marijuana,
cocaine and heroin, respectively.(6) The alcohol use equations were
estimated using ordinary least squares and the drug participation
equations were estimated using probit.(7) Five specifications for each
substance are presented. These specifications include alternative
combinations of the own price and other prices, or decriminalization,
along with a set of demographic variables and time dummies. These
alternatives are important since there is some collinearity between
prices. The first specification includes only the own price. The next
three specifications include the own price and one other price, or
decriminalization. The final specification includes all three prices and
decriminalization. For illicit drugs, the five specifications were
estimated for both participation in the past month and for participation
in the past year. The results for the economic variables, for each
substance, are discussed first. Since there is a fair amount of
redundancy in the demographic [TABULAR DATA FOR TABLE II OMITTED]
variables, these variables are discussed for all four substances as a
group.
Table II presents the results for alcohol use. The own price is
negative and significant in all five specifications. Marijuana
decriminalization is insignificant in one specification and negative and
significant in the other. The negative sign suggests substitution
between alcohol and marijuana. Cocaine and heroin prices are negative
and significant in all four specifications, suggesting complementarity.
The income variable is positive and significant in all five
specifications.
Table III presents the results for marijuana participation.
Decriminalization is positive and significant in all 10 specifications.
The cross price effect of marijuana decriminalization with alcohol is
insignificant in three of [TABULAR DATA FOR TABLE III OMITTED] four
specifications and negative and significant in one. The one significant
negative coefficient suggests complementarity. The cross price effects
of cocaine and heroin with marijuana are negative and significant in six
specifications and insignificant in two specifications. These two
insignificant coefficients are both for heroin, and both occur in the
specifications that include all three prices and decriminalization. The
lack of significance is probably due to collinearity between prices and
between prices and decriminalization. The significant cross price
effects suggest marijuana is a complement with both cocaine and heroin.
Income is insignificant in all five monthly participation equations and
positive and significant in all five yearly participation equations.
Table IV presents the results for cocaine. The price of cocaine is
negative and significant in 7 of 10 specifications. The three
insignificant coefficients are in specifications that include the price
of heroin. The cross price effect of alcohol with cocaine is negative
and significant in three of four specifications and insignificant in one
specification. The cross price effect of heroin with cocaine is negative
and significant in all specifications. The cross price effect of
marijuana with cocaine is insignificant in three of four specifications.
It is positive and significant in one yearly participation
specification. The significant coefficients suggest complementarity
between cocaine and the three other substances. The income variable is
insignificant in all monthly participation equations and positive and
insignificant in all but one yearly participation equations.
Table V presents the results for heroin participation. The price of
heroin is negative and significant in all 10 specifications. The cross
price effects of all three alternative substances with heroin are
insignificant in all specifications with the exception of alcohol in the
yearly participation equations. In these specifications alcohol is
negative and significant suggesting complementarity. The income variable
is negative and significant in 7 of 10 specifications.(8)
V. DISCUSSION
The regression results provide consistent evidence that alcohol use
and illicit drug participation respond to economic forces. The results
for the cross price effects provide evidence of complementarity, except
for alcohol and marijuana. The results can be used to estimate the
alcohol price elasticity, the effect of decriminalization on marijuana
participation, and the participation price elasticities for heroin and
cocaine.(9) These estimates are reported in the last row of tables II-V.
The average alcohol price elasticity is -.30 and is consistent with
other studies of alcohol price elasticities. The effect of marijuana
decriminalization was computed and the results show that
decriminalization increases marijuana participation in the past month by
about 8.4% and participation in the past year by about 7.6%. Using only
significant price coefficients, the average elasticity of cocaine
participation for the past month is -.28 and for the past year -.44. The
average elasticity of heroin participation for the past month is -.94
and for the past year -.82.(10)
The fairly consistent pattern of complementarity between substances
casts doubt on the gateway or domino theory of drug use. This gateway or
domino theory holds that use of one drug, such as marijuana, increases
the probability of going on to a stronger drug, such as cocaine or
heroin. If this theory were true, it is more likely that these drugs
would be substitutes. Complementarity suggests that [TABULAR DATA FOR
TABLE IV OMITTED] [TABULAR DATA FOR TABLE V OMITTED] drug users prefer
to use various drugs together rather than to substituted one for the
other.
The elasticities can be used to predict the effect of legalizing
cocaine and heroin. These estimates should be viewed with caution, since
several assumptions must be made in order to do the calculations.(11)
Legalization could take a number of alternative forms, depending on
whether only sanctions against buyers or sanctions against both buyers
and sellers were reduced and the magnitude of the reductions in
sanctions. The reduction of price is indirectly a policy option, since
price is a positive function of the level of sanctions. The potential
price reduction is considerable, since current sanctions result in a
retail price that is more than 10 times production costs, according to Reuter [1988]. Decreasing sanctions for possession of large quantities
drugs or for selling drugs would shift the supply curve downward.
Assuming that the demand curve remained fixed, the own price elasticity
could be used to estimate the change in participation of a given
decrease in price resulting from a change in sanctions. Assume that the
policy changes resulted in a decrease in the price of both drugs by 50%.
Under these assumptions the number of regular cocaine users would
increase by about 260,000 and the number of occasional cocaine users
would increase by about 1,400,000. In 1991 there were about 1.9 million
regular cocaine users and about 6.4 million occasional cocaine users.
Also, under these assumptions the number of regular heroin users would
increase by about 47,000 and the number of occasional heroin would
increase users by about 615,000. In 1991 there were about 100,000
regular heroin users and about 1.5 million occasional heroin users.(12)
These predictions could to some degree understate or overstate
changes in the number of drug users. The increase in drug use could be
understated if demand shifts to the right. Any change in drug sanctions
or enforcement that shifts the supply curve downward will probably also
shift the demand function to the right. On the other hand, the increase
in drug use could be overstated, since demand elasticities decrease at
lower prices. The demand elasticity is likely to be considerably lower
at a 50% lower price. Whether the estimates are overstatements or
understatements, the potential increase in public health problems are
not the extremes that some analysts predict. A complete analysis of drug
legalization should account for the costs of drug prohibition as well as
the benefits of drug prohibition.
We would like to thank Michael Grossman, John Dinardo, and Robert
Ohsfeldt for helpful comments. We would also like to thank Esel Yazici
and Ismail Sirtalan for programming assistance, Joseph Gfroerer and
Janet Greenblatt for assistance in merging the price data to the
National Household Survey of Drug Abuse, and Carolyn Hoffman for the
cocaine and heroin price data. This project was supported by grant RO1
DA07111 from the National Institute on Drug Abuse to the National Bureau
of Economic Research.
1. We are indebted to the Office of Applied Studies, Substance
Abuse and Mental Health Administration, for merging the price and
decriminalization data to the individual records in the NHSDA. With the
exception of one primary sampling unit in 1990 and six PSUs in 1991, no
locational identifiers are available due to confidentiality issues.
2. The data are weighted using the analysis weight variable in each
survey. The individual data are multiplied by the weight variable and
then divided by the sum of the weight variable for the survey. The means
for combined data are computed as a weighted average of weighted means
for the three surveys. These weights are defined as the sample size
divided by the total size of the three samples.
3. There is some continuous quantity data, but they do not use
standard measurement units, that is, bongs per day. There is also number
of days used during the past 30 days. A number of trial regressions done
with these number of days variables produced unstable and inconsistent
results. For these reasons these data were not used.
4. There was no American Chamber of Commerce Research Association
data available for Washington, D.C., so an average price from urban
Virginia and urban Maryland was used.
5. There are price data for marijuana from the Drug Enforcement
Agency's Domestic Cities Report. These prices are for retail and
wholesale commercial grade marijuana for 19 cities in 16 states. Use of
these data required a significant reduction in the number of
observations used in the analysis. A number of alternative estimates of
the price of marijuana were made with these data. The resulting price
variables were inconsistent with all other price data in the data set
and resulted in unstable coefficients when used in a series of
alternative demand specifications. For these reasons, these marijuana
price data were not used.
6. Several state fixed effects models, which resulted in
insignificant price coefficients, were also estimated. The inclusion of
state dummies tends to eliminate the effect of variables measured at the
state level, such as price.
7. According to Maddala (1983), weighted regressions are not
necessary since the sample design is based on exogenous variables.
8. The effects of income for all four substances might be affected
by education. The results for the remaining demographic variables
confirm the results found in other studies of alcohol and drug use.
9. The alcohol price elasticity was calculated as the price
coefficient times the mean alcohol price over mean alcohol use. The
effect of decriminalization was estimated by calculating the difference
between two distribution functions. The first distribution function is
computed using all the estimated coefficients and the mean values of all
the variables except for the decriminalization variable, which is set
equal to one. The second distribution function is identical with the
exception that the decriminalization variable is set equal to zero.
Cocaine and heroin price elasticities are estimated by multiplying the
normal density function of the estimated equation by the price variable
coefficient and then by the ratio of the mean price to mean
participation. The unweighted means were used in all these computations
rather than the weighted means which are reported in Table 1. The
unweighted means were used, since the estimated regression coefficients
are based on unweighted data.
10. Rational addiction models cannot be estimated with the NHSDA,
since past and future drug participation is not measured in the data
set. Studies of alcohol, cigarette and cocaine demand based on rational
addiction models, however, find long-run price elasticities that are
larger than those estimated by single-period models.
11. The calculations involve only own price effects because the own
price effects are estimated with more precision than cross price
effects.
12. The number of frequent heroin users is difficult to estimate,
since the sample excludes people with no permanent address and prison
inmates. The incidence of frequent heroin users is likely to be higher
in the excluded population than it is in the included population.
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Saffer: National Bureau of Economic Research Phone 1-212-953-0200
x108, Fax 1-212-953-0339 E-mail hsaffer@email.gc.cuny.edu
Chaloupka: Department of Economics (M/C 144), University of
Illinois at Chicago, Phone 1-630 801-0829 Fax 1-630 801-8870, E-mail
fjc@uic.edu