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The effect of illicit drug use on the labor supply of young adults.

Adolescence to Early Adulthood." American Journal of Public Health 74(7):660-66.

Kandel, Denise B., and K. Yamaghuchi. 1987. "Job Mobility and Drug Use: An Event History Analysis." American Journal of Sociology 92(4):836-78.

Killingsworth, Mark. 1983. Labor Supply. Cambridge: Cambridge University Press.

Maddala, G. S. 1983. Limited Dependent and Qualitative Variables in Econometrics. Cambridge, Mass.: Harvard University Press.

I. Introduction

There is widespread concern over the negative effects of illicit drug use on the workforce. Hundreds of companies in the United States have developed extensive alcohol and drug abuse programs alternatively aimed at prevention, detection and treatment of employees who use illicit drugs, and as detailed in Hayghe (1991) the numbers continue to grow. The federal government has also been quite active in its effort to control illicit drug use, particularly in the workplace. The Drug Free Workplace Act of 1988 requires federal government contractors to maintain drug free workplaces, and executive order 12,564 requires all federal agencies to establish drug free workplace policies. There is a general concern in the country that the ability of our workers is being seriously impaired by illicit drug use.

One of the most frequently cited consequences of illicit drug use is the consistency of labor force participation, including chronic absenteeism, although there have been relatively few systematic studies of the labor market effects of illicit drug use.(1) Johnson and Herring (1989) find that illicit drug use among young adults leads to delayed entry into the labor market. Kandel and Davies (1990) using data from the National Longitudinal Survey of Youth (NLSY), and Kandel and Yamaguchi (1987) using regional data, find that illicit drug use is positively correlated with weeks unemployed and increased job mobility (for example, quits) among young adults. Using a somewhat older and more limited sample, White et al. (1988) find no effect of illicit drug use on labor force participation. In one of the first studies found in the economics literature, Kagel et al. (1980) using a novel experimental design, report no significant effects of marijuana use on hours of work of young adults. More recently, Zarkin et al. (1992) find a slight negative impact of illicit drug use on weeks worked per year and skipped work days. The Zarkin et al. study uses a sample of individuals 18 and older drawn from the 1990 National Household Survey of Drug Use (NIDA 1991). Gill and Michaels (1992) and Register and Williams (1992) both use the NLSY data set and find significant effects of illicit drug use on labor force participation. Gill and Michaels (1992) report that a broad measure of past drug use is negatively correlated with the probability of being currently employed, but that a variable measuring use of hard drugs has no impact on the employment probability. The mixed nature of the Gill and Michaels (1992) findings also characterize the findings of Register and Williams (1992), who report that past marijuana use has a negative impact on the probability of being employed, but that cocaine use has no effect. Most of these studies present some evidence suggesting that among young adults, drug users work less hours than nonusers over the course of the year. In addition, Gleason et al. (1991) report that 7 percent of respondents in the NLSY reported drug use on the job as of 1984. Thus, it is possible that drug users will be devoting less actual time to work, even if they are technically working the same amount of hours as comparable nonusers.

If illicit drug use is in fact responsible for a reduction in the labor supply of individuals, the economic implications of such an occurrence are significant. The reduced labor market experience of drug users will result in a decrease in the amount of worker on-the-job training, and other human capital investments associated with the employment relationship. The lower levels of human capital accumulation will decrease the productivity of the U.S. workforce, increase production costs, and lead to diminished living standards. These negative consequences of illicit drug use are what underlie the government's "war on drugs," and the explosion in private employer concern over illicit drug use.

This paper analyzes the effects of illicit drug use on the labor supply of a sample of young adults using data from the National Longitudinal Survey of Youth (NLSY). In particular, the paper investigates whether the frequency and timing of marijuana and cocaine use are systematically related to the quantity of labor supplied. As was noted above, there have been very few systematic studies of the effects of illicit drug use in the labor market, and even fewer based on economic theory. Thus, this paper makes a contribution in two ways. First, it outlines the relevant economic theory, and applies it to the problem of illicit drug use and labor supply. Second, it uses micro-data to obtain both cross-sectional and panel data estimates of the effects of illicit drug use on labor supply, and addresses several previously ignored empirical problems. The cross-sectional results of this paper are consistent with the findings found in most of the previous research, and suggest that illicit drug use has large negative effects on labor supply. The longitudinal results, however, suggest that illicit drug use does not appear to have a significant adverse impact on the hours of work supplied to the market. In particular, it is found that the effect of illicit drug use on labor supply is quite variable, and that there does not appear to be a common experience with regard to the relationship between illicit drugs and labor supply.

The balance of the paper will be divided into the following parts. The next section presents a simple theoretical model of drug use and labor supply. This section sets forth a framework of analysis, and specifies the ways in which drug use can be incorporated into the more general theory of consumer behavior. Section III describes the empirical model used to estimate the effects of illicit drug use on labor supply. This section is followed by a description of the data, including sample design and important variable definitions. A presentation of the results will follow the data section, and the paper will end with a summary of the main findings.

II. Analytical Model of Drug Use and Labor Supply

The most straightforward way in which to incorporate illicit drug use into a labor supply model is to treat illicit drugs as a consumption good. Following Becker and Murphy (1988), an age specific utility function of the following general form can be specified;

(1) |U.sub.t~ = u(|L.sub.t~, |D.sub.t~, |S.sub.t~, |X.sub.t~),

where L is the amount of leisure, D is the quantity of illicit drugs, S is the stock of drug consumption capital, X is a composite good representing other consumption, and t = 1 to T indexes age. The inclusion of the stock of drug consumption capital in the utility function is a distinguishing feature of the current problem. Presently, it is assumed that drugs are potentially an addictive good as defined in Becker and Murphy (1988). Given the above preferences, a cost function can be defined that indicates the minimum cost of obtaining a certain level of utility. The cost function can be written as,

(2) |C.sub.t~ = c(|W.sub.t~, |V.sub.t~, |P.sub.xt~: |U.sub.t~ = u(|L.sub.t~, |D.sub.t~, |S.sub.t~, |X.sub.t~)).

In Equation (2), W is the wage, V is the price of current drug consumption which consists of two parts, the market price of illicit drugs and the user cost associated with the drug consumption capital, and |P.sub.x~ is the price of other consumption.(2) The compensated demand functions for leisure (L), and illicit drugs (D), can be obtained by differentiating Equation (2) with respect to wages and the price of drugs. These demand functions will in general depend on all prices and the level of utility. For example, the demand for leisure can be represented as follows;

(3) |L.sub.t~ = f(|W.sub.t~, |V.sub.t~, |P.sub.xt~, |U.sub.t~).

From an empirical point of view, Equation (3) is limited, due to the fact that V, the price of current drug consumption, including the user cost associated with the drug consumption capital, is never observed, nor is the level of utility. A partial solution to this problem is to use the conditional cost function to represent preferences, as developed by Pollak (1969), Browning (1983), Browning and Meghir (1991). In the conditional cost framework, illicit drugs are treated as a conditioning variable that affect preferences, but are not of primary interest (Browning and Meghir 1991). The consumer minimizes the cost of achieving a certain level of utility, given that the quantity of some goods (for example, illicit drugs) are predetermined.(3) Thus, Equation (2) can be rewritten as follows;

(4) |C.sub.t~ = c(|W.sub.t~, |D.sub.t~, |P.sub.xt~: |U.sub.t~ = u(|L.sub.t~, |D.sub.t~, |S.sub.t~, |X.sub.t~)),

where the quantity of the conditional variable is substituted for its respective price. The model can be put into an intertemporal framework by assuming that the lifecycle conditional cost function is additive, which implies that preferences are implicitly separable.(4) This specification is completely consistent with the idea that illicit drugs are an addictive good, since each age specific conditional cost function includes the current quantity of illicit drugs which is determined by past and future consumption. The age specific, compensated conditional demand functions can be derived from the lifecycle counterpart to Equation (4), and for leisure this derivation results in the following;

(5) |L.sub.t~ = g(|W.sub.t~, |D.sub.t~, |P.sub.xt~, U),

where demand for leisure will be a function of prices, quantities of the conditioning variables, and the unobserved level of utility (Browning 1983). The model assumes perfect foresight and complete certainty, which implies that the consumer knows all future prices, and takes account of the effect of current drug use on future utility and wages. The model outlined above can be easily extended to the family. The utility function would then include all family members' (for example, husband and wife) leisure and the quantity of drugs would refer to total household consumption of drugs.(5)

As noted by Browning and Meghir (1991), the use of conditional cost functions, and the resulting conditional demands, has several advantages. First, the conditional approach eliminates the need to specify the underlying model of the conditioning goods, which in this case is the current consumption of illicit drugs.(6) Second, the conditional approach is empirically valid even when individuals are at a corner solution, which is a common occurrence with regard to drug use. Third, the conditional approach eliminates the need to use measures of the "full" price of illicit drugs, which are not observable. Finally, since the primary purpose of this paper is to identify the effect of illicit drug use on labor supply, the conditional approach facilitates the direct estimation of such an effect, as opposed to simply the sign and magnitude of the cross price effect.

II. Effect of Illicit Drug Use on Labor Supply

In terms of the conditional demand approach outlined above, an increase in illicit drug use will result in an increase or decrease in leisure, depending on whether leisure and drugs are net complements or substitutes. Since it is a model of compensated demand, there is no income effect. It seems reasonable to expect drug use and leisure to be complements, thus, the expectation is that drug use will decrease labor supply, and increase leisure. This expectation is based on the assumption that the household production of the commodity that uses illicit drugs as an input is a relatively time intensive activity; given the physiological effects of most illicit drugs, individuals probably do not substitute greater quantities of drugs for time in the production of some good, say "euphoria" as in Stigler and Becker (1977). Thus, persons who consume drugs would be expected to have a preference for a more time intensive consumption bundle than comparable nonusers.

On the other hand, if drug use is a goods intensive activity, we would expect increased drug use to be positively related to labor supply. The production of "euphoria" might necessitate a much greater market input component (in other words, drugs) than time (leisure) input. In addition, Becker and Murphy (1988) suggest that drug users will have a higher rate of time preference than nonusers, and thus would prefer current consumption, including leisure, to future consumption.

III. Empirical Model of Drug Use and Labor Supply

The specific functional form of Equation (5) used in this paper is a modified version of that found in Browning, Deaton, and Irish (1985). In their paper, the authors (BDI) derive a theoretically consistent empirical demand function that is linear in parameters, and in which the unobserved component related to lifetime utility enters additively.(7) In addition, the demand function specified by BDI is consistent with the conditional cost framework used in this paper.(8) This particular form of the demand function is advantageous to work with since it can be estimated using OLS methods, and the unobserved variables can be eliminated using the fixed effect estimator. As in Browning and Meghir (1991), the introduction of the conditioning variable (in other words, illicit drugs) into the empirical model can be achieved by making the parameters associated with the price variables in the cost function, dependent on the quantity of illicit drugs. If it is also assumed that other consumption is separable from leisure and illicit drug use, the following model will result;

|Mathematical Expression Omitted~,

where everything is as defined previously, |H.sub.t~ = T - |L.sub.t~ is the hours of work, O|W.sub.t~ indexes the own or respondent's wage, S|W.sub.t~ indexes the spouse's wage (in a family labor supply model), |Z.sub.t~ is a vector of exogenous variables, including among others the number of children of various ages, the respondent's age and education, the a's are parameters to be estimated, and e is a stochastic error term. Illicit drug use is expected to be an endogenously determined variable, and in light of this fact an appropriate estimation method needs to be implemented. In this paper, an instrumental variables (IV) approach will be used.

Before turning to the problems of measurement error and sample selection, one additional point relating to Equation (5a) needs to be addressed. The wage of the spouse (S|W.sub.t~) is not observed in the data, but the spouse's age and education are included. In place of the ratio of wages found in Equation (5a), the spouse's age and education are included in the vector |Z.sub.t~, thereby making the identification of the instrumental parameter |a.sub.2~ impossible. The age and education of the spouse are the primary determinants of the spouse's wage. Since the main purpose of the paper is to identify the effects of drug use, and not to estimate the structural cross wage effect, Equation (5a) will be estimated as a semi-reduced form.(9)

Given the data that will be used in the analysis, both the wage and quantity (in other words, frequency) of drug use might be expected to be measured with error. The wage is treated as an exogenous variable, but is calculated using annual hours of work which results in the wage being endogenous in a statistical sense. In addition, drug use is expected to be endogenous. Thus, it is appropriate to use some type of instrumental variables in place of these two measures. The primary instruments that will be used to estimate the wage will be the individual's age, actual past labor market experience, education, and score on the armed forces qualification test.(10) The instruments that are used to estimate the drug use measures are several personal and family characteristics such as the respondent's age, education, household composition at age 14, frequency of religious attendance in 1979, and a measure of their perceived self-esteem.(11) As Kaestner (1991) demonstrates, the wage and drug use are also expected to be simultaneously determined, and thus, the regressions that estimate both of these measures will be reduced form estimates.

Equation (5a) still suffers from the empirical problem associated with the presence of nonworkers, and will have to be estimated using appropriate methods. An individual's hours of work and market wage are only observed for those who work, and thus, Equation (5a) will be estimated for a sample of employed individuals. As is well known, this type of "sample selection" criteria tends to result in biased estimates of the true parameters (Heckman 1976). In this paper, the two stage procedure due to Heckman (1976, 1979) will be implemented, although other methods were tried and yielded qualitatively the same results.(12)

The empirical analysis was carried out in the following order. First, a reduced form labor force participation model is estimated by standard probit methods, which yields estimates of the inverse mills ratio used to correct for sample selection bias. Second, a reduced form drug demand model is estimated using the entire sample. Next, a reduced form wage model is estimated using a sample of employed individuals, and correcting for sample selection. Finally, a semi-reduced form labor supply model is estimated using the predicted wage and predicted drug use, on a sample of employed individuals correcting for sample selection. The only equation that contains structural parameters is the labor supply model. This equation is identified since several of the exogenous variables that are used to predict both the wage and illicit drug use are excluded by assumption from the labor supply model. These variables include two indices measuring the respondent's psychological outlook, the respondent's adolescent family structure, mother's education, the respondent's religiosity and prior involvement in illegal activities.(13)

The empirical analysis will be implemented using two separate years of cross-sectional data, 1984 and 1988, and on a panel of data consisting of the two cross sections. Estimation using the limited panel will allow for the identification of the unobserved fixed effect in the model, which is potentially quite important. The cross-sectional estimates will suffer from the omitted variable bias associated with the unobserved characteristics of the individual, but remain informative since they will provide a set of estimates that are comparable with previous cross sectional estimates. The empirical strategy is identical for the cross-sectional and longitudinal samples, although there are some significant differences. The differences will be easier to describe when the panel data estimates are presented, so the relevant discussion will be delayed until that point in the paper.

As the previous two sections have detailed, the empirical implementation of a labor supply model including a potentially addictive good like illicit drugs is quite complex. Several theoretical and statistical assumptions have been made that impose strong restrictions on the model. Previous research has shown that the parameter estimates of the labor supply model may be significantly changed by using an alternative set of assumptions (Mroz 1987; Browning, Deaton, and Irish 1985; Browning and Meghir 1991). Thus, the results of this analysis need to be interpreted in the context of these considerations.

IV. Data

The data used in the analysis come from the National Longitudinal Survey of Youth (NLSY) which is a longitudinal survey of the labor market experiences of young adults (Center for Human Resource Research 1990). The starting year of the survey was 1979 and included an initial sample of approximately 12,500 youths aged 14-21 at that time. The survey has been updated each year since 1979 with a broadening array of purposes and questions. The data contain detailed information on a respondent's labor market experience, family and personal background, and illicit drug use. Central to the purposes of this paper are the questions related to respondent's illicit drug use. In 1984, and again in 1988, the respondent was asked questions about their lifetime and current use of several illicit drugs, most notably marijuana and cocaine.(14)

The sample used in the analysis was selected based on the following criteria, which were established to eliminate several sources of heterogeneity. The respondent had to be at least 21 years old in 1984, be living independently or with their parents, but not in jail or other temporary quarters (for example, dormitory), and the respondent could not be enrolled in school, or have served in the miliary at any time between 1984 and 1988. In addition, those observations with missing data were deleted.(15) These restrictions resulted in a sample size of approximately 4,200 individuals in 1984, and 4,100 individuals in 1988. Descriptive statistics of the variables used in the analysis can be found in the appendix. All analyses were done separately by marital status and gender. The analyses were done separately on the basis of marital status due to the expected impact of other family member characteristics (for example, wage) on the respondents labor supply.(16) Separating the sample on the basis of gender is consistent with the many previous studies of labor supply (see Killingsworth 1983) that have demonstrated significant differences between male and female labor supply parameters.

The illicit drug use questions are limited in two major respects. First, as suggested by Mensch and Kandel (1988), there appears to be some underreporting in the NLSY 1984 wave, particularly with regard to cocaine use. The exact nature of the underreporting is not known, but Mensch and Kandel (1988) suggest that underreporting is more common among relatively light users, compared to more heavy users of illicit drugs, and more pronounced among females and minorities. Although, the analysis accounts for a simple (in other words, random) type of measurement error, the underreporting issue remains a problem. The second problem related to the drug use questions, is the absence of a measurement of quantity of use; only the frequency of drug use is measured. Although frequency and quantity have been shown to be highly correlated, the two measures are clearly not equivalent (Stein et al. 1988). In fact, Stein et al. (1988) report that the quantity of drug use is a more powerful predictor of problems associated with illicit drug use. In addition the frequency of use was interval coded with relatively large groupings. This fact results in a more complex estimation strategy. As was noted above, instruments for the drug variables are obtained from auxiliary regressions, and given that the data on the frequency of drug use are discrete, simple OLS estimates will not be appropriate.

Table 1 is a frequency distribution of illicit drug use for the sample under examination, and presents the data by gender and marital status. One finding of note in Table 1 is the relatively large increase between 1984 and 1988 in the percentage of respondents reporting some lifetime use of cocaine. In 1984 about 15.7 percent of the married male sample and 8.9 percent of the married female sample report some prior cocaine use, and by 1988 these same figures are 26.6 percent and 16.9 percent. The same pattern can be observed for the sample of single individuals. The increase in the initiation into cocaine use over this age range is consistent with previous studies (Kandel and Logan 1984, Raveis and Kandel 1987). A surprising finding is that the percentage of respondents who report cocaine use in the last year is basically unchanged between 1984 and 1988, even though there was a substantial increase in the number of lifetime users.
Table 1
Distribution of Total Sample by Frequency of Drug Use by Marital Status and

           Married        Single        Married        Single
            Males         Males         Females        Females
           N     %       N      %       N      %       N      %

Lifetime Frequency of Cocaine Use

0         555   84.3     995   78.3     965   91.1   1,002   84.5
1-9        55    8.4     118    9.3      52    4.9      87    7.3
10-39      19    2.9      72    5.7      21    2.0      47    4.0
40-99      13    2.0      41    3.2       7    0.7      27    2.3
100+       16    2.4      44    3.5      14    1.3      23    1.9

0         706   73.4     588   61.9   1,011   83.1     716   74.0
1-9       161   16.7     188   19.8     127   10.4     145   15.0
10-39      44    4.6      81    8.5      51    4.2      57    5.9
40-99      24    2.5      44    4.6      17    1.4      28    2.9
100+       27    2.8      49    5.2      11    0.9      21    2.2

Cocaine Use Past Year

(No) 0    618   93.9   1,060   83.5   1,018   96.1   1,065   89.8
(Yes) 1    40    6.1     210   16.5      41    3.9     121   10.2

(No) 0    892   92.7     783   82.4   1,169   96.1     869   89.9
(Yes) 1    70    7.3     167   17.6      48    3.9      98   10.1

Lifetime Frequency of Marijuana Use

0         203   30.9     367   28.9     482   45.5     456   38.4
1-9       163   24.8     302   23.8     305   28.8     341   28.8
10-39      87   13.2     122    9.6     101    9.5     131   11.0
40-99      49    7.4     137   10.8      71    6.7      84    7.1
100+      156   23.7     342   26.9     100    9.4     174   14.7

0         299   31.1     262   27.6     524   43.1     346   35.8
1-9       253   26.3     254   26.7     367   30.2     299   30.9
10-39     121   12.6     124   13.1     142   11.7     137   14.2
40-99      84    8.7      80    8.4      78    6.4      58    6.0
100+      205   21.3     230   24.2     106    8.7     127   13.1

Marijuana Use Past Year

(No) 0    455   69.1     687   54.1     870   82.2     823   69.4
(Yes) 1   203   30.9     583   45.9     189   17.8     363   30.6

(No) 0    758   78.8     633   66.6   1,088   89.4     755   78.1
(Yes) 1   204   21.2     317   33.4     129   10.6     212   21.9

Initiation into marijuana use has generally ceased over the age range observed for the current sample, as evidenced by the relatively unchanged prevalance of lifetime marijuana use, and the number of respondents who report using marijuana during the past year declines dramatically between 1984 and 1988. This pattern of marijuana use is evident for both married and single individuals. These figures imply a general decline in illicit drug use consistent with the data from the recent National Institute on Drug Abuse (NIDA) household surveys.

In general the prevalence of marijuana use is much higher than that of cocaine, as is the proportion of users who report relatively heavy marijuana use. It is also apparent that single individuals engage in more drug use than married people, and men have a greater frequency of use than women. Single men exhibit the greatest frequency of drug use; over 38 percent have tried cocaine by 1988, and over 72 percent have reported some marijuana use. Finally, the prevalence of illicit drug use among employed individuals (not shown), is very similar to that reported in Table 1. In fact, a comparison of means between the employed and not at work samples indicated that in most cases there were no significant differences in their patterns of illicit drug use. Indeed, when there were significant differences, the employed were observed to have higher levels of usage.

The levels of reported drug use in the 1988 NLSY survey compare favorably to those reported in the 1988 National Household Survey (NHS) on Drug Abuse (National Institute on Drug Abuse 1988). The sample of male respondents used in this paper have an age range of 25-32, and report lifetime prevalence of cocaine use of 32.3 percent, the exact same figure as that reported in the NHS survey for a similarly aged (26-34) group of males. For marijuana use, the curent NLSY male sample report a lifetime prevalence of use of 70.7 percent, compared to 68.1 percent for the NHS. The same pattern is observed for the current NLSY sample of women, compared to those in the NHS. The women in the current sample report virtually the identical prevalence of cocaine use, 20.9 percent compared to 21.0 percent in the NHS, and a slightly greater prevalence of marijuana use, 60.2 percent compared to 56.2 percent in the NHS. This finding raises questions about the extent of underreporting in the NLSY, and particularly whether there was in fact substantial underreporting in 1984, as suggested by Mensch and Kandel (1988). Furthermore, Sickles and Taubman (1991) report on an unpublished NLS study that counters the Mensch and Kandel (1988) criticism, and suggests that the self reports of illicit drug use in the NLS are reliable.

There is a certain degree of inconsistency in the self-reports of drug use in the NLSY that may have implications for the empirical results that follow. In an attempt to find out the potential magnitude of the measurement error in the data, the internal consistency of the respondent's reported drug use in 1984 was compared to their reported use in 1988. For marijuana, approximately 12 percent of those who reported some prior use as of 1984, report no prior use as of 1988, and for cocaine the same figure is 19 percent. In response to this finding, all models were estimated twice, once using the original drug variables, and another time using an internally consistent drug variable; that is, if the respondent reported prior drug use as of 1984, but no prior drug use as of 1988, the reported drug use as of 1988 was replaced with the 1984 value. The results of the two analyses were qualitatively the same, and the text reports those results that used an internally consistent measure.

The measure of labor supply used in this paper is the number of hours worked in the past 12 months on all jobs reported during this period. The hours of work measure refers to the usual number of hours worked per week times the number of weeks worked at the job(s) the respondent held during the past year. This measure of labor supply ignores the loss of work time due to absenteeism, a potentially important source of hours variation among drug users, and is a clear limitation of the current study. Labor force participation is defined as having worked for pay at some time during the past year.

A variety of measures of illicit drug use were used in the following regression analyses. Two linear measures of the lifetime frequency of illicit drug use were used; one measure took on values ranging from 0 to 4, corresponding to the coding scheme used in the survey, and which is listed in Table 1, and the other used the midpoints of the intervals used by the survey to code drug responses. A series of dummy variables were also created to represent the frequency of lifetime illicit drug use. For marijuana, the categories were the following, no use, 1-39 times, and 40 or more times of use. For cocaine, the categories were no use, 1-9 times, and 10 or more times of use. The differences in the way the data were collapsed reflect the differences in the distribution of users across the drug types. In addition, a dummy variable indicating membership in the relatively higher drug use categories was used separately. A measure of past year use of illicit drugs was also used in the analysis. The only information in the data was whether or not the person used marijuana or cocaine in the past year, and the variable was coded as a dummy variable with one indicating past year use.

The rest of the variables used in the analysis are somewhat standard, except for experience, and several of the variables used to predict drug use. Experience is the actual experience, and is the sum of actual weeks worked since 1975. As predictors of drug use, several personal and family background measures were included in the analysis, namely; a respondents score on a series of questions relating to self-esteem (ESTEEM) as measured in 1980, the respondents score on a series of questions measuring an individual's feeling of control over the world (ROTTER) as measured in 1980, the frequency of religious attendance (RELIGION) prior to 1979, and the number of illegal acts (ILLACT) committed prior to 1980. Details of the questions that constitute those variables can be found in the NLS handbook (Center for Human Resources 1990).

V. Cross-Sectional Estimates

As noted above, the cross-sectional estimates of a labor supply model are subject to a serious misspecification bias, since there are important unobserved variables that have been omitted from the model which are expected to be correlated with the other explanatory variables (for example, illicit drug use). The cross-sectional estimates, however, will provide a link to prior research and serve as a benchmark, and for these reasons a brief review of the findings are included. Although not specified in Equation (5a), a measure of nonearned income was included in the cross sectional model in keeping with the tradition found in the literature. To some extent, nonearned income is expected to be correlated with the omitted unobservable variables. This variable along with the wage and drug use measures are all treated as endogenous, and the actual values have been replaced with their respective predicted values. The predicted value of illicit drug use was obtained in a variety of ways, corresponding to the particular form of drug use involved. The predicted value for the linear measures of lifetime use was obtained by an OLS regression, the predicted value of the dummy variables representing lifetime use were obtained by an ordered probit procedure, and the predicted value of current use was obtained from a binary probit regression. In the dummy variables case, the predicted probability of being in a certain category of drug use was used in place of the actual value.(17)

Three separate samples were used in all of the analyses contained in this paper; a combined sample of married and single respondents, and separate samples chosen on the basis of marital status. When estimating the labor supply model using the combined sample, variables related to the respondent's spouse, and the variables measuring the number of children were interacted with a marriage dummy variable. For each sample, five separate models were estimated using one of the different measures of drug use; two linear measures of lifetime use, a set of dummy variables representing different levels of lifetime use, a dummy variable indicating relatively heavy use, and a dummy variable indicating current use. The measure of lifetime drug use, which may include current use, and current drug use were not entered together in the same model, due to severe problems of multicollinearity. The problem of multicollinearity also provides the explanation for why the models are estimated separately by type of illicit drug.

The cross-sectional results are listed in the appendix. The results indicate that an increased frequency of marijuana use is associated with lower levels of labor supply for men, with somewhat larger and more significant effects for married as opposed to single men, and in 1988 as compared to 1984. For example, those married men who have used marijuana 40 or more times in their life, are expected to work between 503 (Model 3) and 587 (Model 4) hours less per year than comparable men using the 1984 estimate, or between 342 and 339 hours less per year using the 1988 estimate. In the case of cocaine, there does not appear to be any significant impact of cocaine use on the hours of work for males as of the 1984 interview. This conclusion is reversed, however, by 1988, and cocaine use is associated with less hours of work for both married and single men. For example, a married male who has used cocaine 20 times is expected to work 230 (Model 2) hours less than a similar male who is a nonuser. The same figure among single men would be 112 hours.

Among the female sample, it appears that increased marijuana use is only significantly related to hours of work for the sample of single women in 1988. Among this sample, those who used marijuana in the past year are expected to work 554 hours less than similar nonusers. A single women who has used marijuana 40 or more times in her life is expected to work between 518 (Model 4) and 587 (Model 3) hours less than a nonuser. In the case of cocaine, the only significant result is for current or past year cocaine use among single women in 1988, and this is only marginally significant at the .10 level.(18)

VI. Panel Data Estimates

As suggested above, the presence of important unobserved individual characteristics, such as the level of lifetime utility, may cause the cross-sectional estimates to be biased. In order to account for these unobserved effects, the labor supply model represented was reestimated using a limited panel of data formed from the two cross-sections of 1984 and 1988. The empirical estimates were obtained from a model of first differences which will yield unbiased estimates if the unobserved characteristics, and their effects, are time invariant. For illustrative purposes, the empirical model can be written as follows:

(6) | + |b.sub.0~ + |b.sub.1~ |X.sub.i~ + |b.sub.2~| + |b.sub.3~ U + |,


(7) | = |a.sub.0~ + |a.sub.1~|X.sub.i~ + |a.sub.2~| + |b.sub.3~U + |,

where H represents hours, X are time invariant exogenous variables, D represents time varying drug use, U is the level of lifetime utility, i = 1 to N indexes respondents, t = 1 to T indexes time, the b's and a's are parameters to be estimated, and the e's are error terms. The model was estimated in the following first differenced form;

(8) | - | = (|b.sub.0~ - |a.sub.0~) + (|b.sub.1~ - |a.sub.1~)|X.sub.i~ + |b.sub.2~| - |a.sub.2~| + | - |

The above formulation imposes no restrictions on the estimates across years, except that the effect of the unobserved time invariant characteristic is constant.

This unrestricted form also facilitates estimation of the predicted values used as instruments for the conditioning variables. For example, restricting the coefficients on current drug use to be equal in Equation (8), would necessitate that an instrument for the first difference of drug use be obtained. Since in this case drug use is a binary measure, this would necessitate estimating a nonlinear, panel data (in other words, fixed or random effect) model which as illustrated by Chamberlain (1982, 1984) is a nontrivial task. As currently formulated, instruments for drug use and wages are obtained on the levels of these variables using both years (1984 and 1988) exogenous variables.(19) The use of levels for the right hand side variables, as compared to first differences, will also reduce the effect of measurement error as a source of bias, particularly in the case of the binary variables. Jakubson (1986) demonstrates that in the case of binary variables measurement error can lead not only to a downward bias, but to the wrong sign.

The empirical estimates also account for sample selectivity due to nonparticipation, although among the married male sample the problem is ignored since over 95 percent of all married males in the matched sample work in both years. The method is an extension of the Heckman (1976, 1979) procedure. First, define V = |e.sub.i~ - | from Equation (8). Next, note that only individuals who are observed to work in both years are used in the analysis. Corresponding to the two participation decisions, there will be two latent variables defined by two auxiliary linear regression models with error terms |U.sub.1~ and |U.sub.2~. If it is assumed that V, |U.sub.1~, and |U.sub.2~ are distributed as trivariate normal, then instead of the simple binary probit selection model as is usually the case, a bivariate probit selection model is appropriate.(20) The bivariate probit model corresponding to the participation decisions will include an unobserved person specific effect, and to obtain consistent estimates of the selection terms (in other words, lambdas) it will be necessary to account for this fact. This can be done by using the results found in Chamberlain (1980), and the ideas behind his random effects probit model. The unobserved person effect is assumed to be linearly related to the leads and lags of the exogenous variables, and by including these variables in the selection model for each year, and estimating this reduced form, consistent estimates of the selection terms can be obtained. There is no inconsistency in treating the unobserved person effect as a Chamberlain type of random effect in the selection model, and a fixed effect in the hours model, since in the linear case (in other words, hours), the two treatments are identical. The assumptions that underlie this correction procedure are quite strong, but feasible alternative procedures are few.

Three samples of data were created from the original two cross sections. The first sample consists of individuals who were married in 1984, and who remained married to the same partner through 1988. The second sample consists of individuals who were single in 1984 and remained single through 1988. The last sample consists of all individuals present in both survey years with complete sets of data in each year. In this sample the spouse related variables are interacted with a marriage dummy variable corresponding to the formulations used in the cross sectional analysis. The sample selection criteria related to age, school enrollment and the military also applies to these longitudinal samples. Finally, only the linear measures of lifetime drug use, and the binary measures of current drug use are used in the analysis. The omission of the categorical measures of lifetime drug use from the analysis was based on the instability of the cross sectional results relating to this variable. In addition several other models which included the first differenced form of the drug use variables were estimated, two of which appear in Table 3 below.(21) These alternative specifications were used to test whether the results of Table 3 are sensitive to the expected multicollinearity between the current (1988) level of drug use and its lagged value (1984). In general, the results were not very sensitive to the choice of specification.

The essential relationship being identified in the longitudinal analysis is the relationship between changes in hours and changes in drug use, although the above formulation is not in the standard first difference form. In many studies this relationship is hard to identify due to little variation in hours, some or most of which is measurement error. In the current samples, there appears to be a relatively good deal of variation in hours between two time periods. The mean change in hours is 271 for males with a standard error of 826, and for females the same figures are 146 and 803. A related question is how much variation is there in drug use, and to what extent this variation is due to measurement error. In the case of cocaine, 15 percent of the male sample are observed changing their status with respect to past year use, and 21 percent increase their lifetime use. Among the female sample, 10 percent are observed changing their status with respect to past year cocaine use, and 16 percent increase their lifetime use of cocaine. For marijuana, 26 percent of the males change their status as past year users, and 18 percent increase their lifetime use. The same figures for the female sample are 20 percent and 18 percent respectively. Table 2 details the extent of the changes in drug use between 1984 and 1988 for past year marijuana and cocaine use for the total sample of matched respondents who were employed in both years.

Table 3 lists the parameter estimates associated with the drug use measures of equation (8). The signs on the 1984 values of drug use have been reversed for ease of exposition, since the regression package assumes an additive form of the model. Examining the results pertaining to males, the left half of Table 3, it can be seen that there does not appear to be a consistently significant relationship between marijuana use and hours of work. In contrast to the cross sectional estimates, the point estimates of the effect of increased lifetime use are positive, although the standard errors are quite large. For current or past year marijuana use, the results are insignificant, but negative for the sample of single respondents and the total sample, which includes those respondents changing marital status between the four years. Again, the standard errors of the estimates are quite large. In the case of cocaine use, the results are similar to those for marijuana in that the signs of the effects change across samples, and the estimates have relatively large standard errors. A significant negative effect is observed, however, for the measure of lifetime cocaine use among the total sample of respondents.
Table 2

Changes in Drug Use Status--Past Year Marijuana and Cocaine Use

                                      1988 Drug Use
                           Marijuana                   Cocaine
                    Nonuser         User         Nonuser        User
1984 Drug Use     N      (%)     N      (%)     N     (%)     N     (%)

Nonuser           795    (53)     95    (6)
User              297    (20)    303   (20)
Nonuser                                       1,197    (80)   108   (7)
User                                            110     (7)    75   (5)

Nonuser           874    (69)     64    (5)
User              193    (15)    145   (11)
Nonuser                                       1,104    (87)    61   (5)
User                                             69     (5)    42   (3)

Note: All percentages will not add to 100 percent due to rounding. The sample
on which these numbers are based consists of all respondents present and
employed in both survey years (1984 and 1988).

The results of Table 3 are quite disconcerting, and raise several questions. Theoretically, the effect of one type of drug use, say cocaine, should be consistent across marital status, although the nature of the relationship between illicit drugs and leisure could differ by drug type. The illicit drug under examination and leisure should be complements or substitutes regardless of an individual's marital status. If, however, the imprecise measure of drug use used in this paper is related to the true measure differently according to marital status, then the variability of the results is expected.

The right hand side of Table 3 presents the longitudinal results for the female sample. As was the case for males, there is a good deal of variability in the results across drug use types and marital groups, and the standard errors are relatively TABULAR DATA OMITTED large. Large, negative effects of current marijuana and cocaine use are observed for the samples of single women and all women. Among the married women, however, current marijuana use is associated with large positive effects, that in one case approach commonly accepted levels of statistical significance.

The findings with regard to the other variables raises a question about the commonly found way longitudinal estimates of labor supply are obtained. It is almost universal to find that the empirical model restricts the coefficients on wages, and other important variables, to be time invariant. The results of this paper suggest otherwise. The parameter estimates associated with the wages and other variables from different years often differed dramatically from each other. The effect of time invariant variables also differed over time. The results associated with two representative models can be found in the appendix.

The impact of illicit drug use on labor supply may be most evident in regard to an individual's labor force participation, as opposed to their (conditional) hours of work. To test this hypothesis, an analysis of the effect of marijuana and cocaine use on labor force participation was implemented using the limited panel data. The analysis of labor force participation using panel data, however, presents several substantial empirical problems. As demonstrated by Chamberlain (1982), the nonlinear nature of these models prohibits the use of the simple fixed effect estimates. In addition, there is the endogeneity of illicit drug use that further complicates the analysis, as does the categorical nature of the drug use variables.

In light of these considerations, the empirical framework chosen for this analysis was based on the correlated random effects model of Chamberlain (1980, 1982). This model was chosen because it does not necessitate first differencing the drug use measures which is impractical given the categorical drug use data, and the endogenous nature of illicit drug use.(22) The results (not shown) of this analysis were consistent with those reported in Table 3. The parameter estimates of the effect of illicit drug use were imprecisely estimated, particularly with regard to past year use, and had different signs depending on the measure of drug use and the sample. The majority of the results indicated a positive effect of illicit drug use on labor force participation, The significant empirical problems associated with this analysis, however, demand that these results be interpreted with caution and represent an area of future research.

VII. Conclusion

This paper has presented an empirical analysis of the effects of drug use on labor supply. Based on previous research, and the theoretical model currently presented, it was expected that drug use would most likely have a negative impact on the hours of work supplied to the market, though a positive result could not be ruled out. The findings of this paper do not appear to be totally consistent with such an expectation. In the cross-sectional results, the effect of illicit drug use on labor supply tended to be negative, and large in magnitude, particularly in 1988. The longitudinal estimates however, were less supportive of the hypothesized relationship. The parameter estimates were not in general negative, as in the cross-section, and the variability of the estimates was also much greater. If, as is often argued in the literature, the longitudinal estimates are to be preferred, there appears to be no systematic effect of illicit drug use on labor supply. Furthermore, a preliminary analysis of the effect of illicit drug use on labor force participation yielded qualitatively similar results.

Taken at face value, these results would have important policy implications. They would suggest that drug use among young adults is a highly idiosyncratic experience that has different effects on different people. It should be pointed out that these results are not inconsistent with anecdotal evidence concerning the severe adverse impact on young adults' lives of heavy and continuous illicit drug use. The evidence contained in this paper pertains to a broad range of drug users, and the interest has been focused on estimating an average effect of drug use. It is this average effect that is not systematic. There does not appear to be a common experience with regard to drug use and labor supply, and public policies should reflect this fact if they are to be effective and cost efficient. The goal of policy would be to identify those individuals for which illicit drug use does become problematic, and further research is clearly needed in this area.

The results of this paper should be viewed as preliminary. The current analysis suffers from several problems, most notable of which is poor measures of drug use. Only very crude measures of illicit drug use were available, and the variability of the parameter estimates associated with drug use might very well be a function of this fact. The neoclassical model of labor supply, the starting point of this analysis, has also suffered from its share of empirical refutation. Several of the theoretical and statistical assumptions used throughout the paper are quite restrictive. These qualifications are important and necessitate more work in this area.
Appendix Table 1

Mean Values of Variables Used in Analysis, Married Sample

                              1984                     1988
                        Male      Female         Male         Female
Variable                Mean       Mean          Mean          Mean

Black                   0.144      0.129        0.180        0.152
Hispanic                0.164      0.173        0.149        0.161
AFQT                   64.650     66.902       65.380       67.408
Experience            241.725    173.188      415.806      318.944
Age                    24.595     24.305       28.715       28.730
Education              11.839     12.152       12.077       12.286
Spouse Age             23.099     26.769       26.965       31.153
Spouse Educ            12.090     12.295       12.514       12.548
Num Chil Age 0-2        0.371      0.409        0.326        0.303
Num Chil Age 3-5        0.299      0.373        0.432        0.472
Num Chil Age 6-17       0.161      0.209        0.499        0.735
Religion                2.965      3.220        2.957        3.231
Self-Esteem Scale      32.757     32.258       32.628       32.280
Rotter Scale            8.723      8.725        8.629        8.632
Num Illegal Acts       10.699      3.318       10.710        3.349
Two Par Age 14          0.825      0.812        0.831        0.823
Two Par Age 18          0.629      0.612        0.662        0.637
Mother's Education      9.869     10.001        9.894       10.074
Live with Parents       0.043      0.042        0.019        0.036
Urban                   0.676      0.739        0.700        0.740
Unemployment Rate       3.514      3.538        2.624        2.658
North East Reg          0.138      0.155        0.160        0.187
North Central Reg       0.295      0.260        0.267        0.242
Southern Reg            0.403      0.398        0.388        0.398
Miss Mother's Ed        0.070      0.045        0.077        0.045
Miss Experience         0.021      0.015        0.072        0.045
Observations            658        1,059        962          1,217
Appendix Table 2

Mean Values of Variables Used in Analysis, Single Sample

                                  1984                  1988

                             Male      Female      Male      Female
Variable                     Mean       Mean       Mean       Mean

Black                        0.353      0.379      0.375      0.416
Hispanic                     0.161      0.124      0.179      0.133
AFQT                        58.723     59.465     57.219     58.144
Experience                 194.287    162.804    339.579    281.819
Age                         23.739     23.964     28.246     28.511
Education                   11.857     12.056     11.702     11.912
Num Chil Age 0-2             0.032      0.182      0.053      0.132
Num Chil Age 3-5             0.019      0.259      0.064      0.300
Num Chil Age 6-17            0.004      0.218      0.059      0.677
Religion                     2.820      3.187      2.746      3.210
Self-Esteem Scale           32.137     31.537     32.017     31.532
Rotter Scale                 8.669      8.977      8.778      8.951
Num Illegal Acts            14.005      6.077     13.196      5.994
Two Par Age 14               0.733      0.718      0.719      0.678
Two Par Age 18               0.598      0.564      0.576      0.519
Mother's Education           9.705      9.895      9.464      9.620
Live With Parents            0.587      0.431      0.346      0.217
Urban                        0.795      0.799      0.811      0.792
Unemployment Rate            3.385      3.363      2.595      2.578
North East Reg               0.202      0.200      0.194      0.174
North Central Reg            0.231      0.239      0.223      0.240
Southern Reg                 0.380      0.394      0.399      0.419
Miss Mother's Ed             0.072      0.049      0.081      0.057
Miss Experience              0.028      0.018      0.102      0.052
Observations                 1,270      1,186        950        967






1. In comparison to illicit drugs, there have been many more studies of the effects of alcohol use on labor market outcomes. Mullahy (1992) surveys the literature relating to alcohol use and the labor market.

2. Since changes in current consumption will alter the stock of drug consumption capital, the price of current consumption should include the effects of changes in the stock on utility. It is assumed that the changes in the stock of drug consumption capital are instantaneous.

3. The conditional framework has also been used to model goods that are rationed, as in Blundell and Walker (1982), but in the current case, illicit drugs are not rationed. The consumer is able to choose their optimal level, and at this point the conditional and unconditional cost functions will yield equal values.

4. For a discussion of implicit separability see Deaton and Muellbauer (1980) or Browning, Deaton, and Irish (1985).

5. An apparent drawback of the empirical model is that the measure of drug use actually used refers only to the respondent, and not the household. This implies that the drug use of one spouse is separable from the drug use of their partner.

6. This is a real advantage given the complexity of modeling the demand for addictive goods. See the papers by Chaloupka (1991) and Becker, Grossman, and Murphy (1991) for a discussion of the empirical analysis of the demand for an addictive good.

7. The demand function implies that preferences are "quasi-homothetic". See Browning, Deaton and Irish (1985) for further discussion.

8. Equations 5.8 and 5.9 in Browning, Deaton, and Irish (1985, p. 521) illustrate that the empirical demand function specified in equation (5a) in the text can be derived using the consumer's profit function or the cost function. The only difference between the two specifications is that instead of the unobserved price of utility, the lifetime level of utility enters into the model when the cost function is used.

9. In addition, the use of the semi-reduced form provides a way to sidestep the problem of the spouse not working. In essence the age and education of the spouse are capturing the effects of the actual wage for working spouses and the reservation wage for nonworking spouses. To the extent that the functional form of the empirical model becomes more ad-hoc, this procedure introduces the possibility of specification bias.

10. Several of the variables will be entered into the regression in a quadratic form (experience) or as a series of dummy variables (education). In addition, several geographic measures and demographic variables will be included in the model.

11. See the appendix for a complete list of the variables used to predict drug use, as well as the variables used to predict the wage.

12. The Heckman procedure was also estimated by FIML methods with virtually identical results, although in a few cases the LIMDEP software did not converge. The alternative method for correcting selectivity bias due to Olsen (1981) was also implemented. The results were quite similar to those reported in the table. In addition, the issue of selectivity due to nonworkers was ignored, and the results were again similar to those reported.

13. The empirical model can be represented as follows:


H = f(D, W, X) + |U.sub.h~, D = g(H, W, Y) + |U.sub.d~ W = h(D, Z) + |U.sub.w~ P = k(D, W, X) + |U.sub.p~

Reduced Form

D = |g.sup.1~(X,Y,Z) + |V.sub.w~ W = |h.sup.1~(X,Y,Z) + |V.sub.w~ P = |k.sup.1~(X,Y,Z) + |V.sub.p~

where H = hours, D = drugs, W = wage, P = a latent variable which has a corresponding indicator equal to one if the individual works, X, Y, and Z are exogenous variables, and the |U.sub.i~ and |V.sub.i~ are error terms. All estimates were obtained from the reduced form except for the hours model.

14. The 1988 survey limited the illicit drug use questions to include only marijuana and cocaine.

15. The sample selection criteria used in the paper are intended to reduce unobserved heterogeneity in the sample, but they also may have eliminated those individuals for whom drug use has the greatest adverse impact. For example, respondents who are in jail have been excluded from the analysis, although there are very few respondents in the data who are in fact in jail.

16. Empirically, tests of the validity of this strategy were carried out using the cross sectional samples, and a reduced form model of hours of work, including a correction for sample selection. The results of these tests indicated that the parameter estimates differed by marital status, and that a simple dummy variable indicating married was not sufficient to account for the differences. The results were less strong for the male sample, but significant at the .05 level. Limiting the sample on the basis of marriage, however, gives rise to the possibility that the parameter estimates of the labor supply model will be biased if marriage and drug use are jointly determined.

17. The use of the predicted values on the right hand side has important implications for the standard errors derived from the OLS regression on hours. The estimated standard errors from the OLS regression are smaller than the true estimates (Murphy and Topel 1985, Maddala 1983). The derivation of the true standard errors would be quite complex given the nature of the auxiliary regressions, sample selection and instruments for qualitative variables, and beyond the scope of this paper.

18. The parameter estimates associated with the other variables in the model are similar to previous estimates found in the literature. The female uncompensated own wage elasticity evaluated at the mean number of hours was in the .4 to .5 range in 1984, and .1 to .3 range in 1988 for the different samples. The presence of young children resulted in a significantly lower level of labor supply for women. Among the male samples, the own wage uncompensated elasticity was between .35 and .45 in 1984, and approximately .3 in 1988. The presence of children had no significant impact on male labor supply.

19. For example, respondents' past experience in 1984 and 1988 are entered into the regression of the 1984 wage. Inclusion of exogenous variables from other years is consistent with Chamberlain's (1982, 1984) correlated random effects model for panel data. In the linear case (in other words, wage), this model is identical to a fixed effect model, but in the nonlinear case this model allows a relatively simple way to obtain panel data estimates for discrete variables.

20. A bivariate probit procedure is preferable, but due to problems of obtaining estimates that would converge using the LIMDEP software and this data set, separate probits were used instead. When bivariate probit estimates could be obtained, the results were virtually identical to those obtained when using the separate probits, even when the correlation of the underlying random variables was significant.

21. For example, a dummy variable was created that indicated whether the person was a current user in both 1984 and 1988, or had become a current user in 1988, versus never being a current user, or being a current user in 1984 and not being a current user in 1988. Another variable was a dummy variable that indicated a person became a heavy user in 1988 as compared to 1984. None of the results from these models differed significantly from those reported in the text.

22. The model can be written as follows:

(9) LF|P.sub.1~ = |a.sub.0~ + |a.sub.1~|D.sub.1~ + |Phi~ + |e.sub.1~,

(10) LF|P.sub.2~ = |a.sub.0~ + |a.sub.1~|D.sub.2~ + |Phi~ + |e.sub.2~,

(11) |Phi~ = |b.sub.0~ + |b.sub.1~|D.sub.1~ + |b.sub.2~|D.sub.2~ + v,

where LFP is a binary indicator of labor force participation, D represents drug use, |Phi~ is an unobserved person specific effect, |a.sub.i~ and |b.sub.i~ are parameters, and |e.sub.i~ and v are error terms that follow independent normal distributions. The model is a reduced form model. The structural parameters, |a.sub.i~, are obtained by substituting Equation (11) into the other equations, and imposing cross-equation restrictions on the |b.sub.i~, using a minimum distance estimator (Chamberlain 1984). A problem is that illicit drug use, |D.sub.i~, is endogenous and the predicted nature of illicit drug use needs to be incorporated into the derivation of the appropriate covariance matrix of the reduced forms (Maddala 1983). In addition, the minimum distance estimator uses the matrix formed by the outer product of the first order conditions, which depend on the estimated parameters, and the derivation of this matrix may also be affected by the predicted nature of drug use. In this paper, the minimum distance estimates are obtained using a covariance matrix that ignores the predicted nature of the drug variables.


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Author:Kaestner, Robert
Publication:Journal of Human Resources
Date:Jan 1, 1994
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