Marijuana should be illegal

Is Marijuana a Gateway Drug? Author(s): Jeffrey DeSimone Source: Eastern Economic Journal, Vol. 24, No. 2 (Spring, 1998), pp. 149-164 Published by: Palgrave Macmillan Journals Stable URL: http://www.jstor.org/stable/40325834 . Accessed: 18/11/2014 03:18

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IS MARIJUANA A GATEWAY DRUG?

Jeffrey DeSimone Yale University

INTRODUCTION

Marijuana is by far the most widely-used illicit drug. Though marijuana is a pow- erful intoxicant with subjective psychedelic-like effects that are more complicated than those of alcohol or cocaine, research has yet to show that marijuana consump- tion has harmful consequences. In truth, the primary cause for concern about mari- juana use may be that it potentially leads to the use of more hazardous illegal drugs such as cocaine. This premise arises from evidence that the overwhelming majority of adolescent and young adult cocaine users have previously used marijuana [O'Donnell and Clayton, 1982; Mills and Noyes, 1984; Yamaguchi and Kandel, 1984; Newcomb and Bentler, 1986; Kandel and Yamaguchi, 1993] and is known as the gateway hy- pothesis. Since the use of cocaine is associated with problems such as crime, child poverty, poor neonatal health, and the spread of HIV, a gateway effect of marijuana on cocaine could signify a sizable social cost of marijuana use.

Prior marijuana consumption may, however, predict current cocaine consump- tion without necessarily causing it. Marijuana use may simply be a marker of either observable personal characteristics or unobservable factors that make marijuana us- ers more likely to progress to cocaine use [Kleiman, 1992]. Conversely, marijuana may truly act as a gateway to cocaine in two fashions. Marijuana intoxication may spawn curiosity or diminish apprehension about trying more dangerous drugs. Or, the physiological and psychological benefits, say "euphoria" (from Stigler and Becker [1977]), induced by a certain level of marijuana consumption may decline over time, thereby prompting users to experiment with new drugs in an attempt to regain their original levels of euphoria [Kleiman, 1992].

The latter process above can be explained in terms of the economic model of ad- diction as specified by Becker and Murphy [1988] and Chaloupka [1991]. In this model, the cumulative past consumption of an addictive good represents an "addictive stock" that raises current consumption by creating both tolerance, through a negative mar- ginal utility, and reinforcement, through a positive effect on the marginal utility of current consumption. Grossman et al. [1996a] and Pacula [1997] find that marijuana is addictive in the sense that past use raises the likelihood of current use. Addictive marijuana can generate a gateway effect in two distinct ways. One is simply through contemporaneous complementarity of marijuana and cocaine. The other is through a direct positive effect of past marijuana consumption on the marginal utility of current

Eastern Economic Journal, Vol. 24, No. 2, Spring 1998

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consumption of other euphoria-producing goods such as cocaine, which may occur because the addictive stock is not of marijuana itself but rather of the euphoria pro- duced by marijuana. In this case, marijuana could conceivably serve both as a gate- way to cocaine and as a substitute to cocaine in the production of euphoria [Kleiman, 1992]. Evidence of negative cross-price effects between the two drugs, as reported by DeSimone [1997], Grossman et al. [1996b] and Saffer and Chaloupka [1996], implies contemporaneous complementarity but is also consistent with a direct intertemporal relationship because none of these studies disentangles past and current price ef- fects.

In combination, then, the empirical findings of addictive marijuana and negative cross-price effects suggest a gateway effect of marijuana on cocaine. Notwithstand- ing, no formal econometric evidence of the intertemporal relationship between the two drugs has been obtained to this point. This paper provides such evidence using data from the National Longitudinal Survey of Youth (NLSY). Though the study does not attempt to identify the causal mechanisms by which marijuana and cocaine are related, it is the first to estimate a structural effect of past marijuana demand on current cocaine demand. The results provide strong confirmation of the gateway hy- pothesis.

EMPIRICAL SPECIFICATION

To econometrically test the gateway hypothesis, the current demand for cocaine must be estimated, for a sample of individuals who have not previously used cocaine, as a function of past marijuana demand and current values of other variables that influence cocaine use. Using the subscript t to denote the current period and t -k to denote the period k years in the past, current cocaine consumption Ct is thus repre- sented as a function of past marijuana consumption Mt_k and a vector Xt of additional exogenous determinants,

(1) Ct=b0 + btMt.h + b2Xt + e,

A gateway effect exists if b1 > 0 in equation (1). Two empirical considerations make ordinary least squares (OLS) estimation of

equation (1) inappropriate. First, marijuana use is a function of many of the same variables that determine cocaine use.1 Although OLS on equation (1) holds Mt_k con- stant while estimating the direct effect of variables in Xt, some components of Xt may concurrently affect Ct indirectly through Mt_k. More importantly, Mt_k and Ct may be spuriously correlated because of unobserved factors that simultaneously affect the use of both types of drugs. For instance, tastes for intoxication or deviance are likely to vary positively with both marijuana and cocaine use. Meanwhile, other unobserved factors may lead individuals to choose one drug over the other as a producer of eupho- ria. Since all previous users of cocaine are excluded from the estimation sample, unobservables may in this situation reflect a preference for marijuana over cocaine in period t -k because marijuana is less costly, less dangerous, less stigmatized and more easily obtained. The regression assumption that Mt_k and ec are uncorrelated may

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IS MARIJUANA A GATEWAY DRUG? 15 1

thus be violated, resulting in bias and inconsistency in the OLS estimates of the pa- rameters of equation (1).

To account for the potential correlation between Mt_h and cc, a two-stage instru- mental variable (IV) regression procedure is employed. The first stage equation rep- resents past marijuana demand as a function of the exogenous variables Xt that affect current cocaine demand and a vector Zt_k of variables that affect past marijuana de- mand but not current cocaine demand,

(2) Mt_k = a0 + a2 X, + a2 Zt_k + em.

In theory the lagged values of X also belong on the right-hand side of equation (2), but are omitted from the empirical analysis because the variables in X are either time- invariant or highly correlated over time.2 Then, since the predicted value of Mt_k in equation (2) represents the component of Mt_k that is uncorrelated with the unobserv- able factors ec that impact Ct, equation (1) is typically estimated using this predicted value of Mt_k as a regressor in place of the observed Mt_k.

The second empirical concern is that Ct andMt_A are specified as binary indicators of drug use, since the gateway hypothesis posits a relationship between the use, rather than explicit quantities of consumption, of each drug.3 Because Ct is binary, equation (I) is most suitably estimated with a probit model. Smith and Blundell [1986] and Blundell and Smith [1989] show that equation (1) is consistently estimated with a probit that uses the observed value ofM^ but also includes the residual term em from equation (2),

(II) Ct = b0 + b1Muk + b2Xt + b3em + ec.

These studies also derive the expression for the correct asymptotic covariance matrix for the probit estimates of equation (I1). A limitation of this procedure is its assump- tion that the included endogenous variable, in this caseMt_ki is fully observed. Equa- tion (2) must therefore be estimated as a linear probability model. In order to correct for heteroskedasticity, equation (2) is first estimated by OLS to obtain predicted val- ues of Mt_k, and then reestimated by weighted least squares using the inverse of these predicted values as weights [Gujarati, 1995].

To improve on OLS, the set of instrumental variables Zt_k that is excluded from the cocaine demand equation must be highly correlated with Mt_k but uncorrelated with ec [Gujarati, 1995]. As is well known, nonzero correlation of Zt_k and ec will ren- der the IV estimates of equation (1) inconsistent. Moreover, Bound et al. [1995] illus- trates that the explanatory power of Zt_k is crucial for two reasons. First, if Zt_k is only weakly correlated with Mt_k, then even a weak correlation between Z<jk and ec can produce a large inconsistency in the IV estimates of equation (1) that may even sur- pass that of the OLS estimates. Second, IV estimates are biased in finite samples, and the magnitude of this bias approaches that of OLS as the explanatory power of Zt_k approaches zero. These empirical considerations must guide the choice of Zt_k in the analysis.

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152 EASTERN ECONOMIC JOURNAL

DATA

The primary source of data is the NLSY [Center for Human Resource Research, 1995]. Since 1979, the NLSY annually has collected detailed demographic and eco- nomic information from a cohort of 12,686 individuals originally aged between 14 and 22. In the 1984 and 1988 interviews, respondents were asked about their current and lifetime use of a variety of drugs, including marijuana and cocaine. Consequently, the relationship between cocaine demand in t=1988 and the demand for marijuana k=4 years previously is estimated for respondents who report no previous lifetime use of cocaine in 1984. Past year rather than lifetime measures of drug use are employed in an attempt to restrict attention to individuals who are persistent rather than experi- mental drug users, following the interpretation of Saffer and Chaloupka [1996] that annual participation reflects at least occasional use. The estimate here thus mea- sures the gateway from recurrent marijuana to cocaine use, which is more relevant for drug policy than one that also encompasses experimental drug use. As mentioned earlier, the drug use variables are binary indicators of consumption.

Note that NLSY respondents are between 23 and 31 years old in 1988, an impor- tant consideration since all existing evidence of a marijuana gateway comes based upon responses from individuals in their teens and early twenties. A specific concern is that the sample is highly selective because cocaine initiation declines with age in the NLSY. More precisely, even though only 17 percent of the respondents inter- viewed in 1984 had previously used cocaine and are thus excluded from the sample, this group is almost four times as large as the number of respondents in the sample reporting past year use in 1988. The estimate of the gateway effect reported here, therefore, may not hold at younger ages or for the population in general. In particu- lar, given that past year marijuana prevalence in the NLSY also fell over time, from 46 percent in 1980 to 32 percent in 1984, a gateway effect may not be detectable because precisely those individuals for whom the effect is likely to be strongest are not included in the sample.4 On the other hand, the finding of a gateway effect would mark an extension of the age range within which the phenomenon is considered to be consequential.

The set of explanatory variables included in the vector X^ is as follows. Race is represented by indicators of black and Hispanic ethnicity. Educational attainment measures human capital and is expected to be negatively correlated with drug de- mand, as is age and marriage. Males traditionally have higher rates of drug use than females. Indicators of living in a central city and in an SMSA outside a central city control for the possibility of increased availability of illegal drugs in urban areas. Indicators of a Catholic or nonreligious upbringing may reflect the presence or ab- sence of anti-drug values and attitudes. An indicator of the presence of both parents in the household at age fourteen is intended to capture parental supervision and may further capture family values that discourage drug use. Past year earnings will be positively associated with drug demand if drugs are normal goods.6 In addition, esti- mates of the average past year retail price of one pure gram of cocaine, imputed for over 140 cities using data from the Drug Enforcement Administration (DEA) on pur- chases made by undercover agents from 1977 to 1994, are matched to the individual

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IS MARIJUANA A GATEWAY DRUG? 153

NLSY responses.6 As previously mentioned, values of all time-varying variables are taken from the 1988, or current period, interview.

The set of instruments 7*M that identify marijuana use includes two measures of state-level penalties for marijuana possession and two additional variables that are expected to affect marijuana use through their influence on alcohol consumption. The marijuana penalty variables, which pertain to the possession of one ounce of mari- juana for first-time offenders in the state of residence of the respondent in 1984, are the maximum prison term and an indicator that fines are not assessed. Both of these variables are components of the expected cost of marijuana use and as such contrib- ute to the full price of marijuana.7 The expected cost of marijuana use, in terms of time, lost wages and stigma from being arrested and sent to prison, rises as the maxi- mum prison term increases from zero in ten states to a year in eighteen states and more than that in six others. Similarly, the expected monetary cost is lower in the two states, Massachusetts and Oklahoma, in which no fine can be levied compared to other states in which the maximum fine ranges from $100 (in ten states) to $2,500 or more (in seven states).8 The alcohol-related variables are the state excise tax on beer and an indicator of parental alcoholism or problem drinking. The beer tax is the tax on a case of 24 twelve-ounce beers containing 3.2 percent alcohol [Beer Institute, 1995]. If marijuana and alcohol are substitutes, as reported by DiNardo and Lemieux [1992], Model [1993] and Chaloupka and Laixuthai [1994], then marijuana demand will respond positively to increases in the beer tax, though Saffer and Chaloupka [1996] find evidence of the reverse relationship. Meanwhile, Cadoret [1992] and Merikangas et al. [1992] report an association between parental alcohol problems and filial drug use. This relationship may operate through alcohol use, since the pre- viously cited research on the chronological path of drug initiation shows that alcohol use almost always precedes the initiation of illegal drug use, while Kenkel and Ribar [1994] find that children of parents with alcohol problems are more likely to consume alcohol than others.

Although marijuana penalties could conceivably influence cocaine and marijuana use separately if they reflect sentiments towards illegal drug use in general [Model, 1993], the exclusion of the two marijuana penalty variables from the cocaine demand equation is natural because their direct impact is on marijuana demand. However, the exclusion of the two alcohol-related variables is more questionable. The rationale is the expectation that the consumption of alcohol is more closely related with that of marijuana than that of other illegal drugs like cocaine that are more dangerous and less socially acceptable. Besides evidence that alcohol use usually precedes the initia- tion of marijuana use even for the large fraction of marijuana users who do not progress to cocaine use, additional support for this exclusion strategy is given by Mills and Noyes [1984], Yamaguchi and Kandel [1984] and Newcomb and Bentler [1986], who fail to find a direct connection between past alcohol and current cocaine use. Never- theless, the propriety of this restriction and the full set of exclusions is empirically tested below, as is the power of the marijuana penalty variables and the full set of excluded instruments Z^ to explain the variation in marijuana use.

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154 EASTERN ECONOMIC JOURNAL

TABLE 1 Descriptive Statistics

(n=7,279)

Standard Mean Deviation

Dependent Variables Used Cocaine Past Year 0.057 0.232 Used Marijuana Past Year (in 1984) 0.246 0.431

Explanatory Variables Age 27.005 2.265 Education 12.683 2.437 Male 0.443 0.497 Black 0.270 0.444 Hispanic 0.162 0.368 Married 0.482 0.500 Central City Residence 0.143 0.350 SMSA Residence 0.595 0.491 Catholic Background 0.323 0.468 No Religious Background 0.039 0.193 Earnings Past Year (in 1000s) 17.663 15.111 Cocaine Price 123.620 30.144 Both Parents Present Age 14 0.691 0.462

Excluded Instrumental Variables Alcoholic Parent 0.215 0.411 Beer Tax (in 1984) 0.540 0.621 Maximum Jail Time for Marijuana (in 1984) 0.775 1.269 No Fine for Marijuana (in 1984) 0.036 0.187

Table 1 presents the means and standard deviations of the variables included in the analysis for the 7,279 respondents with complete data.9 Almost a quarter of the sample used marijuana in the year prior to the 1984 interview, but fewer than 6 percent used cocaine in the year preceding the 1988 interview. Table 2 exhibits the joint frequency of past marijuana and current cocaine demand. Even though 1984 marijuana nonusers outnumber users by a three-to-one margin, almost two-thirds of those who consumed cocaine in 1988 also consumed marijuana in 1984. A chi-square test of independence formally rejects the hypothesis that marijuana users are no more likely than nonusers to progress to cocaine use. However, more rigorous examination is necessary to determine whether this preliminary evidence of a gateway effect actu- ally represents a causal relationship.

A final point before proceeding to the regression results is that since drug use is an illegal activity, it may be underreported by NLSY respondents. Some evidence of underreporting exists for lifetime cocaine use in 1984 [Mensch and Kandel, 1988] and for both lifetime and past month marijuana and cocaine use, in both 1984 and 1988, in the modest (around 9 percent) fraction of interviews in which parents are present

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IS MARIJUANA A GATEWAY DRUG? 155

TABLE 2 Joint Frequencies of Marijuana and Cocaine Use

Used Cocaine Past Year 1988 Yes No Total

Used Marijuana Past Year 1984 Yes 270 1522 1792 No 147 5340 5487 Total 417 6862 7279

Chi-Squared Test of Independence: \2(1) = 383.8, p = 0.000

or that take place over the telephone [Hoyt and Chaloupka, 1994]. However, Sickles and Taubman [1991] provide evidence that reported past year drug use should be fairly accurate in both years. Furthermore, as long as marijuana use is truthfully reported, underreporting of 1988 cocaine use will only bias the estimate of the gate- way effect if this underreporting is correlated with 1984 marijuana use. But if the strong association between marijuana and cocaine use recorded in Table 2 also holds for cocaine users who report not using cocaine, so that marijuana users are more likely than nonusers to underreport cocaine, then the effect of underreporting of 1988 cocaine use but not 1984 marijuana use is to bias the estimated gateway coefficient towards zero.10 Such downward bias is exacerbated if lifetime cocaine use in 1984 is also underreported, as suggested by evidence from Johnston et al. [1988] that respon- dents who lie do so consistently over time, because the primary effect of underreporting in this case is to count respondents as current cocaine nonusers when in fact they should be excluded from the sample.11

RESULTS

Table 3 displays the regression results. Column 1 shows the estimates of equation (2), the first stage equation for marijuana use in 1984. The variables of primary con- cern are the excluded instruments Z^. The signs are as anticipated for the three of these variables for which prior expectations of the sign exist. The predicted likelihood of marijuana use is 3 percent lower in Nevada, which has the highest maximum prison term of six years, than in the ten states in which first-time marijuana possession offenses carry no prison sentence. The coefficient approaches statistical significance with ap-value of 0.136. The remaining three identifying instruments are statistically significant at all conventional confidence levels. Having an alcoholic parent increases the probability of marijuana consumption slightly more than living in a state with no fines for first-time marijuana possession. Meanwhile, the coefficient of the beer tax predicts that marijuana consumption is over 4 percent more probable in Wyoming, which has the lowest beer tax of $0.04, than in Alabama, which has the highest of $2.28. Although this evidence of complementarity between alcohol and marijuana contradicts the findings of DiNardo and Lemieux [1992], Model [1993] and Chaloupka and Laixuthai [1994], this result may not generalize because of the selection of the sample used here.

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156 EASTERN ECONOMIC JOURNAL

TABLE 3 Equations for Past Year Drug Demand

First Stage: Second Stage: WLS for 1984 Probits for 1988

Marijuana Use Cocaine Use 0) Í2a) Í2b)

Constant 0.422a 0.108b 0.177 (0.066) (0.054) (0.200)

Marijuana Use (in 1984) 0.292a 0.226 (0.074) (0.176)

Age -0.006a -0.0017 -0.0022 (0.002) (0.0012) (0.0015)

Education -0.001 -0.0028b -0.0028b (0.002) (0.0011) (0.0011)

Male 0.114a -0.006 0.002 (0.010) (0.009) (0.021)

Black -0.015 -0.011 -0.012c (0.012) (0.007) (0.007)

Hispanic -0.088a 0.002 -0.004 (0.015) (0.011) (0.017)

Married -0.070a -0.020b -0.024c (0.012) (0.008) (0.014)

Central City Residence 0.071a 0.0001 0.006 (0.017) (0.010) (0.015)

SMSA Residence 0.079a -0.006 -0.000003 (0.011) (0.009) (0.015)

Catholic Background 0.041a -0.001 0.002 (0.013) (0.007) (0.009)

No Religious Background 0.075a -0.025c -0.020 (0.028) (0.014) (0.018)

Earnings Past Year -0.0011a 0.0004c 0.0003 (in 1000s) (0.0003) (0.0002) (0.0003)

Cocaine Price -0.206 -0.184b -0.199b (in 1000s) (0.163) (0.093) (0.091)

Both Parents Present -0.015 0.001 0.0004 Age 14 (0.011) (0.006) (0.006)

Alcoholic Parent 0.065a 0.007 (0.013) (0.013)

Beer Tax (in 1984) -0.019a 0.001 (0.007) (0.006)

Maximum Jail Time for Marijuana -0.0053 (in 1984) (0.0036)

No Fine for Marijuana 0.057a (in 1984) (0.018)

Standard deviations are given in parentheses. In columns 2a and 2b, the constant indicates the probabil- ity of cocaine use when all variables are set to zero, while remaining coefficients represent the change in probability of cocaine use for a unit change in the explanatory variable while holding all other variables constant at their mean values. a. Significant at the 0.01 level. b. Significant at the 0.05 level. c. Significant at the 0.10 level.

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IS MARIJUANA A GATEWAY DRUG? 157

Of the other explanatory variables, those of greatest economic relevance are earn- ings and the price of cocaine. The results for these two variables contradict, to a great extent, evidence from Grossman et al. [1996a; 1996b] and Saffer and Chaloupka [1996] that marijuana is a normal good that is complementary with cocaine. Though the cocaine price does carry a negative coefficient, its effect is statistically insignificant. Moreover, the effect of earnings is negative and significant. An interpretation of these results, though, must consider the construction of the sample. As cocaine becomes more expensive, some respondents who would otherwise have initiated cocaine and therefore been excluded from the sample may instead substitute toward marijuana rather than away from illegal drugs altogether, contributing to the insignificance of the cocaine price. The same may occur as earnings declines, since the large expense of cocaine per dose may imply a large income effect. It does not necessarily follow that marijuana and cocaine use are unrelated, nor that marijuana is an inferior good, for the general population that also includes cocaine users. The only other surprising result is the significantly higher likelihood of use for Catholics, which again may be an artifact of the sample selection procedure if Catholic drug users are more inclined to use marijuana than cocaine as a producer of euphoria. The remaining explanatory variables have the expected relationship with marijuana consumption, and all are significant besides educational attainment, black racial status, and the presence of both parents in the household at age fourteen.

Column 2a of Table 3 gives the results for equation (I1), the second stage probit for 1988 cocaine demand. As previously discussed, past marijuana use is identified through the exclusion of both the two marijuana penalty variables and the two alcohol-related variables. The coefficients are reported in terms of the change in probability of co- caine use induced by a unit change in the explanatory variable while holding all other variables constant at their mean values, while the constant represents the probabil- ity of cocaine use when all variables equal zero. The crucial result, of course, is the statistically significant and extremely large positive effect of past marijuana use. In particular, past marijuana use raises the probability of consuming cocaine by more than 29 percentage points. This impact is clearly substantial, dwarfing that of the other explanatory variables, for realistic variations in their values, by a factor of at least ten. Not only is a strong gateway effect of marijuana on cocaine apparent, there- fore, but it is by far the most important factor in explaining current cocaine demand.

The relevance of economic factors is shown by the fact that besides earnings and the price of cocaine, only three other exogenous variables in column 2a are signifi- cant. The coefficients of the earnings and price variables indicate, in agreement with findings of Grossman et al. [1996b] and Saffer and Chaloupka [1996], that cocaine is a normal good with a downward-sloping demand curve. The magnitudes of these ef- fects, however, are modest. An increase in earnings of one standard deviation, or $15,000, raises the probability of using cocaine by just over half a percentage point, which is almost identical to the impact of lowering the price of cocaine by one stan- dard deviation, or $30. The implied price elasticity of -0.40 is, nonetheless, consis- tent with that estimated in the studies mentioned above. Meanwhile, the other sig- nificant results indicate that four additional years of education, marriage, and an

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TABLE 4 Specification Tests for Cocaine Use Probits

Model (a) Model (b)

First Stage F-statistic for Excluded Instruments 12.84 6.25 (0.000) (0.002)

Overidentification Test x2-statistic 1.577 0.523 (0.816) (0.770)

Second Stage x2-statistic for Alcohol Variables - 0.83 (0.660)

Hausman Test t-statistic 0.231a 0.164 (0.060) (0.152)

Hausman Test for (a) vs (b) - 0.067 (0.140)

Models (a) and (b) correspond to columns 2a and 2b, respectively, of Table 3. P-values are given in parentheses beneath F and x2-statistics, while standard deviations are given in parentheses beneath t- statistics. a. Significant at the .01 level.

upbringing that involves religion lowers the probability of using cocaine by 1, 2, and 2.5 percentage points, respectively. Again, though, the most notable characteristic of the significant coefficients is that their magnitudes are trivial in comparison with that of past marijuana use.

Table 4 reports the results of various tests regarding the specification of the IV procedure. The test statistics in column a correspond to the model of column 2a in Table 3. In the top row, the joint F-statistic for the excluded instruments Z^ verifies that these variables are highly correlated with marijuana demand, an essential con- dition for minimizing the standard errors of the IV estimates. Consequently, any inconsistency in the IV estimates arising from a weak nonzero correlation between Z^ and ec should be low relative to that of OLS. Following Bound et al. [1995], this F- statistic also implies that the inherent small sample bias in the IV estimates is only about 1 IF, or 8 percent, of the bias arising from OLS estimation.

The next row gives the statistic for a test of the validity of the overidentifying restrictions. If ZM is jointly correlated with ec and therefore should in reality be in- cluded in equation (I1), then the IV estimates of equation (I1) are inconsistent. Lee [1991] illustrates how a chi-square test statistic for the overidentifying restrictions, with degrees of freedom equal to the number of excluded instruments, can be ob- tained as a by-product of the IV regression methodology because, as Blundell and Smith [1989] show, the estimation procedure is a minimum chi-square method. The joint hypothesis that the excluded instruments neither belong in the second stage equation (I1) nor are correlated with the second stage residuals ec cannot be rejected at standard significance levels. More precisely, the extremely high p-value provides evidence that any correlation between Zw and ec is quite weak.

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IS MARIJUANA A GATEWAY DRUG? 159

The remaining statistic in column a of Table 4, appearing in the fourth row, is for a test of the exogeneity of past marijuana use in equation (I1). As Smith and Blundell [1986] show, the t-statistic for the coefficient of the first stage residual em, b3, in equa- tion (I1) provides an exogeneity test that is analogous to the standard Hausman test for exogeneity [Hausman, 1978]. Since the IV procedure is correctly specified, as the F and overidentification tests verify, any difference in the IV and OLS estimates of bv the gateway effect, arises because a nonzero correlation between Mw and ec affects the OLS but not the IV estimate. The exogeneity test statistic measures the magni- tude of this difference and thus indicates an OLS estimate of 0.061. Since the IV estimate is significantly larger than the OLS estimate, the latter must exhibit down- ward bias. This bias has two potential causes: observable factors that in reality affect cocaine use in part through marijuana use, and unobservable factors that increase past marijuana demand while decreasing current cocaine demand.

To disentangle these two sources of bias, I evaluate the IV estimates of the co- caine demand equation (I1) at mean values of the explanatory variables for marijuana users and nonusers (not reported here) while holding marijuana use constant and take the difference in predicted cocaine use between users and nonusers. I then do the same for the OLS estimates of equation (I1) (also not reported here). The differ- ence between these two quantities reveals that only 1.5 percentage points of the dis- crepancy between the IV and OLS estimates of the gateway effect represent effects of exogenous explanatory variables that in reality work through past marijuana use, but are incorrectly attributed by OLS to the variables themselves. Unobserved het- erogeneity must account for the remainder of the difference between the IV and OLS coefficients. More precisely, unobserved factors make marijuana users 21.6 percent- age points less likely than nonusers to consume cocaine. Unlike OLS, the IV method- ology is able to separate this unobserved heterogeneity from the true causal effect of marijuana use. This finding contradicts the conventional wisdom that the gateway effect is an artifact of unobserved variables that make both marijuana and cocaine consumption more likely, suggesting instead that unobserved substitutability of mari- juana and cocaine use masks an even greater effect of marijuana use than the OLS estimate of the gateway effect indicates. This result is not inconsistent with intertemporal complementarity of marijuana and cocaine use. It simply implies that marijuana users have actively chosen marijuana over cocaine as a producer of eupho- ria. The unobserved reasons for this choice make them, ceterisparibus, less likely to progress to cocaine use than others who have never used cocaine, even though these others may have been more likely to avoid illegal drugs altogether. Ironically, mari- juana users are subsequently more likely to use cocaine because of the substantial effect of marijuana use itself.

The variables in Z^ most likely to belong in the second stage equation (I1) are the alcoholic parent indicator and the beer tax. To further evaluate the validity of exclud- ing these two variables, I directly compare the specification discussed so far to an alternative specification in which these variables are included in equation (I1). Col- umn 2b of Table 3 shows the estimates of this alternative model. Not surprisingly, the effects of the exogenous variables are quite similar across the two IV equations. In

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addition, the estimated gateway effect in column 2b is much closer to that of column 2a than that of OLS. Because the standard error is more than twice as large as that in 2a, though, the estimate in 2b is not significantly different from zero and hence yields a much different implication than does the estimate in 2a.

Column b of Table 4 displays the results of the relevant specification tests for the model presented in column 2b of Table 3, allowing investigation of the sources of the variation between the two IV estimates of the gateway effect. The top two rows verify that this alternative model is also validly specified. The relative magnitudes of the F- statistics in columns a and b imply that the gateway estimate in column 2b of Table 3 will exhibit greater small sample bias than that in column 2a. It is thus expected that, as Table 3 indicates, the estimate in column 2b is closer to the OLS estimate than is that in column 2a. Meanwhile, the third row shows that the two alcohol-related vari- ables are jointly insignificant in the cocaine demand equation, which is not surprising given that neither individually approaches significance in Table 3. This result pro- vides explicit evidence that the two alcohol variables are validly excluded from the cocaine demand equation, which supports the more general conclusion from the col- umn a overidentification test statistic that the full exclusion restriction is valid. Fi- nally, the bottom two rows report the statistics for the exogeneity tests that compare the gateway coefficient in this model to those of the OLS and column a models, re- spectively. Though the model a estimate is significantly different from the OLS esti- mate, the estimate of this model is not significantly different from those of either column a or OLS because of the large standard error.

The combined results of the specification tests indicate that the primary conse- quence of the exclusion of the two alcohol-related variables from the cocaine demand equation is an increase in efficiency of the IV estimate of the gateway effect. Since these variables are highly related to past marijuana consumption but not separately related to current cocaine consumption, their exclusion does not alter the magnitude of the estimate of the gateway effect, but does provide the additional explanatory power necessary to reduce the standard errors enough to produce statistical signifi- cance. Furthermore, the evidence that alcohol use leads to cocaine use only through its strong complementarity with marijuana use is consistent with the hypothesis that a separate intertemporal link from alcohol to marijuana precedes the one from mari- juana to cocaine that is shown here.

CONCLUSION

This study has found evidence of a gateway from marijuana to cocaine that takes place at later ages than were previously thought relevant. Structural estimates ac- counting for unobserved heterogeneity that affects both marijuana and cocaine de- mand indicate that past marijuana use increases the probability of current cocaine use by twenty-nine percentage points. This effect is nearly three times as large as the one-in-ten increase that Kleiman [1992] cites as warranting a considerable expansion in efforts to control marijuana use. To put the magnitude of this result in perspective, preventing past marijuana use decreases the likelihood of cocaine initiation by an amount that is almost thirteen times greater than that brought about by a doubling

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IS MARIJUANA A GATEWAY DRUG? 161

of the average cocaine price, which any feasible enforcement effort is unlikely to ac- complish [Kleiman, 1992]. In order to most effectively deter cocaine use, therefore, some resources devoted to raising prices, which is the predominant focus of present U.S. drug policy, should be redirected towards the prevention of marijuana initiation by adolescents and young adults.

As a caveat, the estimate of the gateway effect obtained here suffers from several potential deficiencies as a result of data limitations. First, current and past drug use are crudely measured with a longtime interval between the two periods. Consequently, questions remain regarding the extent and persistence of marijuana use necessary to bring about cocaine use and the length of time between marijuana and cocaine initia- tion. Second, the gateway effect may be less pronounced for younger cocaine users who were excluded from the sample employed here. Earlier cocaine use may reflect a stronger inclination towards cocaine that makes it less likely to be preceded by mari- juana use. In addition, the unobserved factors found here to bias the OLS estimate towards zero may be an artifact of the substitution away from cocaine by marijuana users who have not tried cocaine by this relatively late age and may thus not be representative of unobservables for younger cohorts. Conversely, to the extent that late cocaine initiation reflects a lower propensity for intoxication, this estimate of the gateway effect may instead be conservative. Third, cohort effects may make this esti- mate inapplicable for the comparable age group today. In particular, the demand for illegal drugs has apparently shifted down in the last decade in response to attitudinal changes [SAMHSA, 1996].

Even conditional on the generalizability of the estimate obtained here, policy im- plications depend crucially on the contemporaneous relationship between marijuana and alcohol use. If these drugs are indeed complements, as indicated here and in Saffer and Chaloupka [1996], then policy should clearly aim to restrict youth mari- juana use. On the other hand, if these drugs are in fact substitutes, as several previ- ously cited studies have found, then restrictive marijuana policy involves a tradeoff between reducing future cocaine demand and increasing current alcohol demand. The latter is problematic because alcohol intoxication most likely involves greater health, accident and crime risks than marijuana intoxication. Similarly, policy impli- cations depend on the nature of the unobserved factors found here to be responsible for the inconsistency in the OLS estimates, since they reflect a component of the contemporaneous relationship between marijuana and cocaine. Namely, does the negative correlation between unobservables affecting marijuana and cocaine imply that restrictive marijuana policy would push teenagers and young adults to substi- tute cocaine for marijuana at an earlier age rather than simply block the gateway to cocaine use?

To further clarify policy goals, future research should attempt to identify the fun- damental relationships underlying the gateway from marijuana to cocaine. In par- ticular, empirical analysis should seek to establish the relative importance of mari- juana addiction, the contemporaneous relationship between marijuana and cocaine, and the direct intertemporal effect that exists because both drugs produce euphoria. For instance, Pacula [1997] reports evidence of both addictive marijuana and strong contemporaneous complementarity between alcohol and marijuana, but fails to find a

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162 EASTERN ECONOMIC JOURNAL

separate direct gateway from alcohol to marijuana.12 Comparable information for the gateway from marijuana to cocaine can delineate the role that reducing the persis- tence over time of marijuana use must play in the effort to avert the progression from marijuana to cocaine use.

NOTES

I am grateñil to Frank Chaloupka and Mike Grossman of the National Bureau of Economic Research for graciously providing the cocaine price data used herein, the Bureau of Labor Statistics for allow- ing my use of the restricted NLSY geocode data, and two anonymous referees and the editor for suggestions that substantially improved the paper.

1. Even though Mt_h is a predetermined variable in equation (1), this issue is empirically relevant because many determinants of marijuana and cocaine use are either time-invariant or highly corre- lated over time, as is marijuana consumption if it is indeed addictive.

2. For this reason, though I label equation (2) as a marijuana demand equation and later analyze it as such, it is more strictly interpreted as an instrumenting equation. It should be noted, though, that the use of lagged rather than current values of X does not change the estimates of equation (2) much.

3. In addition, data constraints dictate the use of binary measures of drug consumption, as discussed in the following section.

4. Lack of information on lifetime cocaine use in 1980 prevents the estimation of the relationship be- tween 19S0 marijuana use and 19S4 cocaine use.

5. All monetary variables are converted to 1982-84 equivalents using the CPI for all urban consumers. 6. As explained in detail in Grossman et al. [1996b], a regression of the price of the transaction on its

weight and purity and a set of city and year dummies is run and then used to predict a standardized price for each city and year. This procedure is similar to the ones developed by Caulkins [1994] and Saffer and Chaloupka [1996]. These standardized prices were generously supplied to me by Frank Chaloupka and Mike Grossman of NBER. I then created a past year price by taking a weighted average of the 1987 and 1988 prices for each city based on the interview month. Since a price esti- mate exists for at least one city in each state, each county of residence in the NLSY is assigned the price from the city within the same state that is geographically closest. Although the matching pro- cess introduces measurement error that most likely biases the estimates of the price elasticity of marijuana and cocaine demand towards zero, the imputed prices should be reasonably accurate for the large majority of the sample that resides in urban areas.

7. The retail price of marijuana would be the ideal instrumental variable for marijuana use. However, because DEA agents do not focus on apprehending marijuana dealers, the number of marijuana purchases recorded in the DEA database that generate the cocaine price estimates used here is insufficient to estimate a reliable price series for marijuana.

8. The maximum prison term yields almost identical results to the midpoint of the range of the poten- tial prison term, or any other weighted average of the minimum and maximum prison sentence, because the minimum prison term exceeds zero in only two states, Arizona (mandatory 1.5 years) and West Virginia (range from 3 to 6 months). Note that beyond the two included variables, other measures of state-level marijuana penalties, including minimum and maximum fines for possession and an indicator of decriminalization, are not significantly related to marijuana use.

9. The reasons for excluding the remaining 5,407 respondents from the original NLSY cohort are as follows. First, the 1,280 members of the military sample are not included, though in any event 1,079 of these respondents are dropped from the NLSY after 1984 and accordingly the necessary informa- tion for inclusion exists for only 113 people out of the original 1,280. An additional 1,320 respondents are not interviewed in one of the two years. The sample next omits the 397 individuals who are in the military (although drug price and penalty variables could not be matched for this group in any case because states of residence are not recorded for military respondents) and the 190 respondents who are incarcerated at the time of either interview, since these people may not have the same opportu- nity to consume illegal drugs as others. Another 120 individuals live outside the United States in

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IS MARIJUANA A GATEWAY DRUG? 163

either 19S4 or 1988, while an additional 1,484 respondents have consumed cocaine by the 1984 interview. The remaining exclusions occur because values are missing for one of the two drug use variables in 162 cases and for an explanatory variable in 454 instances.

10. A separate potential source of bias is the refusal of drug users to answer the survey questions on drug use. Refusal bias seems improbable, though, because missing values for either 19S4 marijuana or 19SS cocaine use are responsible for the exclusion of only 162 individuals. Moreover, although 156 of these respondents report marijuana use but not cocaine use, the prevalence of marijuana use among these respondents, 17.9 percent, is slightly lower than the prevalence of 24.6 percent among sample respondents.

11. To maintain unbiasedness under this scenario, underreporters must be less likely to use marijuana than others, rather than equally likely as in the case in which cocaine use is underreported only in 1988.

12. Though in her analysis marijuana plays the role of cocaine here, Pacula [1997] does not eliminate previous users of marijuana from her sample and therefore must consider marijuana addiction as an additional element of the intertemporal relationship between alcohol and marijuana.

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