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The B.E. Journal of Economic Analysis & Policy

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Volume 17, Issue 3


Volume 6 (2006)

Volume 4 (2004)

Volume 2 (2002)

Volume 1 (2001)

Does Previous Marijuana Use Increase the Use of Other Drugs: An Almost Ideal Demand System Approach

Alexi Thompson / Yamaura Koichi
Published Online: 2017-06-01 | DOI: https://doi.org/10.1515/bejeap-2016-0069


From a policy standpoint, the legalization of marijuana may affect other drug markets. The Almost Ideal Demand Model is used to estimate drug substitution between the most common illegal street drugs in the US including cocaine, heroin, marijuana, and methamphetamines. We control for past marijuana consumption. Results indicate that past marijuana consumption does not contribute to increased current consumption of other drugs. Further, marijuana is a weak complement to methamphetamines but marijuana price changes do not affect heroin or cocaine consumption.

Keywords: marijuana legalization; drug substitution; Almost Ideal Demand System


About 20 % of worldwide marijuana users and 33 % of worldwide cocaine users are from North America (United Nations Office on Drugs and Crime 2016). The U.S. government has responded to its domestic drug problem by allocating large sums of funds for law enforcement, prevention and treatment, and interdiction. In 2010 alone, approximately $40 billion were used in the War on Drugs at the federal, state and local level. In addition, over $1 billion is spent annually for fighting drugs internationally, namely Mexican and Colombian drug cartels among others (Office of National Drug Control Policy 2016). Despite the US government’s efforts, US drug consumption continues to be a social problem.

Perhaps it is due to the largely ineffective War on Drugs, but slowly the social stigma attached to users of marijuana has softened. The current legalization of recreational marijuana in states including Colorado, Washington, and Alaska has brought national attention to this topic. According to marijuana legalization advocates, increased state tax revenues and thinning out overcrowded prisons are possible positive consequences. Previous studies find marijuana decriminalization does not affect usage (Pacula 1994; Thies and Register 1993; DiNardo and Lemieux 1992; Johnston, O’Malley, and Bachman 1981). Opponents believe that marijuana is a “gateway” drug. Increased consumption of marijuana, a relatively harmless drug, may lead to increased consumption of harder drugs including cocaine or heroin (Kandel and Yamaguchi 1993). Still, others find little evidence on the “gateway” effect of marijuana (Saffer and Chaloupka 1995).

Pudney (2003) describes various causes of the gateway effect of marijuana, including the addiction, access, and credibility effects. The addiction effect stipulates that if a user becomes addicted to marijuana he/she may seek harder drugs. The access effect suggests new drug users may come into contact with suppliers of harder drugs. Lastly, the credibility effect implies consuming relatively harmless drugs like marijuana may give users the impression that harder drugs are less harmful. Empirical evidence of the gateway effect is mixed. Pudney (2003) finds no statistical evidence while Fergusson, Boden, and Horwood (2006) do find a “gateway” effect. Kandel, Yamaguchi, and Klein (2006) discuss the difficulties involved in testing the gateway hypothesis. Results tend to depend on data, explanatory variables, and methods. Drug use data typically involves self-reported data which may lack reliability.

Substitutability between drugs may depend on the level of addiction as well as prices. The purpose of this paper is to see how drug consumption changes in response to changes in the price of drugs and past marijuana consumption. As more states begin to legalize marijuana, we can expect lower marijuana prices due to increase competition. From a policy standpoint, it is important to clarify how consumption of harder drugs may be affected due to the changes in the marijuana market.

This paper uses the Almost Ideal Demand System (AIDS) model of Deaton and Muellbauer (1980) which estimates a system of drug share demand equations. Past marijuana consumption is included as an explanatory variable in each share equation. Note this paper does not explicitly measure the “gateway” effect of marijuana. “Gateway” effect implies that marijuana is the first drug consumed that leads to the consumption of other drugs. Our consumption data does not differentiate between the type of user (first time user, casual user, or addict). Any positive effect of past marijuana consumption on current consumption of other drugs may include the gateway effect but also suggests the prevalence of polydrug use where users consume several types of drugs. Regardless, law enforcement may be interested in how the potential spread of marijuana legalization will affect the market of the other drugs in our study including cocaine, heroin, and methamphetamines.


Price and quantity of drugs comes from the System to Retrieve Information from Drug Evidence (STRIDE) developed by Fries et al. (2008) and published by the United States Drug Enforcement Agency (2016). Four street drugs are included in the data including cocaine, heroin, marijuana, and methamphetamines. Yearly data runs from 1986 to 2007. Unfortunately, STRIDE data is no further collected and 2007 is the latest year for which data is available. The quantity variable is the quantity of each drug confiscated, which is used as a proxy for the quantity of each drug consumed. We are assuming the more a drug is confiscated, the more it is consumed. STRIDE drug prices are prices that drug enforcement agents offer dealers prior to arrest. The number of cases used to calculate drug prices for each year is available on its website.1

The STRIDE dataset has been criticized as not being representative of actual drug prices (Horowitz 2001). We must note that the price of illegal drugs likely varies widely from state to state or from city to city. While STRIDE data does include drug prices from some major cities including Atlanta, the drug prices in Atlanta may be different from drug prices in rural Georgia, making it difficult to control for drug prices at the city or state level. In addition, as state policies have changed little with respect to drug decriminalization over the years, focusing on state-level data may yield little use with respect to policy changes (Pacula and Lundberg 2014; Pacula, Chriqui, and King 2003).

Despite the unavoidable issues concerning the data in STRIDE, undercover agents could potentially endanger themselves by offering prices not consistent with reality, therefore researchers assume STRIDE drug prices are reasonably accurate (Dobkin and Nicosia 2009). This dataset has been used in several previous studies (Dobkin and Nicosia 2009; Cunningham and Finlay 2015; DiNardo 1993; Reuter and Caulkins 2004). Drug prices in this study are at the national level. To help address the cross-state variation in drug prices, median prices rather than mean prices are used so that outlying prices will not affect data.


This paper employs the AIDS model, developed by Deaton and Muellbauer (1980), which empirically uses Zellner (1962) seemingly unrelated regression (SUR), estimating a system of four share equations; one for each drug.

The AIDS model takes the form wi=αi+Σj=1nβijln(pj)+γiln(x/P)+ψiln(pmc)+εi(1)

where wi is the share of the ith drug. Drugs in the study include cocaine, methamphetamines, heroin, and marijuana. Shares are calculated by dividing expenditures per drug by total drug expenditures. The coefficient αi is the constant in the ith share equation, pj is the price of the jth drug, x is total drug expenditures, pmc is past marijuana consumption, and βij, γi, and ψi are coefficients to be estimated. All variables are in natural logs (ln). P is an aggregate price index specified as ln(P)=λ0+Σiμiln(pi)+.5ΣiΣjφijln(pi)ln(pj)(2)

As the aggregated price index is difficult to estimate, most empirical studies adopt Stone (1953) Price Index, ln (P*) = Σiwiln(pi), the linear approximation of the price index. Eales and Unnevehr (1988) and Taljaard, Alemu, and Van Schalkwyk (2004) discuss simultaneity issues that may arise since wi is the dependent variable but is also included in Stone (1953) Price Index as a left-hand side variable. Eales and Unnevehr (1988) suggest lagging wi to avoid simultaneity issues, the technique in this paper. Thus, Stone (1953) Price Index takes the form, Σiwit1ln(pi).

Hunt-McCool, Kiker, and Ng (1994) discuss the shortcomings of the more common linear or log-linear approach to estimating illegal drug demand. Unlike these approaches, the AIDS approach is consistent with consumer demand theory (Deaton and Muellbauer 1980). Homogeniety and symmetry can be test for or imposed upon the system of equations. Despite its consistency with theory, to the authors’ knowledge, the AIDS model has not been used very often in drug demand studies. Jofre-Bonet and Petrey (2008) use the AIDS model to estimate own and cross-price elasticities between various illegal drugs while controlling for several variables including age and gender. This appears to be the first study that uses the AIDS approach while specifically attempting to see if previous marijuana consumption increases current consumption of other drugs.

Homogeneity and symmetry restrictions are imposed on the system of equations. The homogeneity restriction follows Σjβij=0

implying quantity demanded of the good stays the same if prices and expenditures change by same proportion.

Symmetry follows βij=βji(3)

suggesting consistency among drug choices.

Adding up requires budget shares to sum to unity therefore i=1na=1,i=1nγi=0,i=1nbij=0,i=1nψi=0

To avoid singularity, the marijuana share equation is dropped and later recovered with the adding up restriction. Table 1 shows the coefficient estimates from share equations and recovered estimates for the marijuana equation. Standard errors for the dropped equation approximated in Stata with the delta method.

Coefficients from the share equations are used to derive income and price elasticity estimates in Table 2. Before moving to Table 2, results from Table 1 have some interesting policy implications.2 Previous marijuana consumption (pmc) does not increase current consumption of harder drugs, and actually decreases current cocaine consumption. This substitution effect implies that a benefit from marijuana legalization, which would most likely increase marijuana consumption (Saffer and Chaloupka 1995), would be a decrease of cocaine consumption. Marijuana does appear to be addictive as previous marijuana consumption increases the current marijuana budget share. However, society may as a whole may benefit from relatively less cocaine consumption, especially since the ongoing drug wars, which can be violent, typically involves the cocaine trade.

Table 1:

Share Equations

Table 2:

Elasticity Estimates

Own price coefficients are positive and all statistically significant, suggesting all drugs are price inelastic. An increase in the price of a price inelastic good increases expenditures on the good as consumers are relatively insensitive to price changes. This result may be expected for addictive goods such as the drugs included in this study.

To the authors’ knowledge, only a few papers have used the AIDS model to study illegal drug substitution. Some focus solely on the addiction of alcohol and/or cigarettes including Fanelli and Mazzocchi (2004) and Aepli (2014). Jofre-Bonet and Petrey (2008) include data both on legal and illegal drugs in their drug-related AIDS empirical study. Our paper resembles this study with a few important exceptions. Most importantly, our paper focuses on the effect past marijuana consumption has on the shares of other drugs. Jofre-Bonet and Petrey (2008) include other explanatory variables but are all related to demographics (race, age, etc.). In addition, the authors obtain data using a classroom experiment with cocaine and heroin addicts as participants. The authors caution that participants may not behave in the same manner in a classroom setting as in the real world. Data from STRIDE may more closely reflect actual street-level prices. Both papers employ Stone (1953) Price Index. In our paper the share of the ith drug, wi is lagged one period.

The estimated coefficients and budget shares from the each SUR model in Table 2 reported are used to derive compensated (Hicksian) elasticities. The derivation of compensated elasticities is from Taljaard, Alemu, and Van Schalkwyk (2004). Income elasticities measure the percentage change in quantity demanded given a one percent increase in income and follow 1+(γi/wi)

where γi is the estimated coefficient on the expenditure term in eq. 1 and wi is the budget share of the ith drug.

Own price elasticities measure the percentage change in quantity demanded given a one percent change in price and follow 1+βijwi+wj

where βij is the own price coefficient with j = i, wi is the budget share of the ith drug and wj is the budget share of theith drug.

Cross-price elasticities measure the percentage change in quantity demanded of ith drug given a one percentage increase in the price of jth drug and follow βijwi+wj

where βij represents the cross-price coefficient of jth drug on the ith drug. A positive cross-price elasticity implies the drugs are substitutes and a negative cross-price elastic indicates the drugs are compliments. Table 2 reports derived compensated price and expenditure elasticities. All standard errors are estimated with the delta method.

With respect to income elasticities, we find cocaine is a luxury good. A 1 % increase in income increases quantity demanded of cocaine by 1.08 %. The data suggests heroin and marijuana are normal goods. A 1 % increase in income increases quantity demanded of heroin and marijuana by 0.64 % and 0.75 %, respectively.

Cocaine has a negative own price elasticity. A 1 % increase in the price of cocaine decreases quantity demanded of cocaine by 0.10 %. We find meth to be a giffen good. A 1 % increase in the price of meth increases quantity demanded by 0.51 %. In our study, this own price effect could be the result of solely focusing on addictive drugs and not including other goods (such as food). In addition this positive own price elasticity could reflect better quality. Heroin has a positive own price elasticity although it is not statistically significant. Marijuana is relatively inelastic, which is consistent with previous literature (Pacula and Lundberg 2014; Van Ours and Williams 2007) although the own price coefficient is not statistically significant in this study.

Negative cross-price elasticities indicate drugs are complements, while positive cross-price elasticities indicate drugs are substitutes. Heroin and meth are complements. A 1 % decrease in the price of heroin increases quantity demanded of meth by 0.89 %. A 1 % decrease in the price of meth increases quantity demanded of heroin by 0.40 %. None of the other cross-price elasticities are statistically significant. In general, our results indicate that there is not too much interaction across drug markets, which are consistent with previous studies (Cunningham and Finlay 2015).


In light of recent legalization and decriminalization of marijuana by US states, law enforcement may be interested in how legalization affects other drug markets. We use a theoretically consistent AIDS model to study the effects of previous marijuana consumption on present consumption of heroin, cocaine, and methamphetamines. Our results show that past marijuana consumption does not affect current consumption of other drugs included in the study and may lead to decreased consumption of cocaine. In addition, derived price elasticity estimates indicate drug users will not increase their consumption of heroin or cocaine with decreased marijuana prices (which we expect with its continued legalization). In general, previous marijuana consumption and marijuana price changes seem to have little effect on other drug markets.

Lastly, it must be noted that the results of the paper should be interpreted with some caution. The aggregation of data at the national level may not reflect drug substitutability at the state level. If marijuana legalization continues to be a decision made by US states, state-level data, rather than national-level data, may be more relevant in designing appropriate regulations. Unfortunately, state-level data spanning many years is not available through STRIDE. Future studies may be able to focus on drug substitutability at the state-level given data availability.


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    In addition to using the AIDS model, as a robustness check, we also estimate drug own –price, cross-price, and income elasticities using a translog functional form. The translog function estimates a system of drug share equations on drug prices and total drug expenditures. The AIDS model and translog model are similar with the only difference being drug expenditures are deflated by Stone (1953) Price Index in the AIDS model. See Thompson (2013) for a comparison between the two models. Although not reported here, the results from the translog model are similar to results from the AIDS model and do not affect the policy recommendations of the paper. With respect to previous marijuana consumption, the main variable of interest, previous marijuana consumption decreases current cocaine and heroin consumption and increases current meth consumption in the translog model. The increase in current meth consumption due to previous marijuana consumption is small (0.01 %). In the AIDS model, previous marijuana consumption decreases current cocaine consumption. 

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Published Online: 2017-06-01

Citation Information: The B.E. Journal of Economic Analysis & Policy, Volume 17, Issue 3, 20160069, ISSN (Online) 1935-1682, DOI: https://doi.org/10.1515/bejeap-2016-0069.

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