Mental illness and the demand for alcohol, cocaine, and cigarettes.

Saffer, Henry ; Dave, Dhaval

I. INTRODUCTION

The U.S. Surgeon General (US Department of Health and Human Services [USDHHS] 1999) reports that the indirect costs of mental illness were $79 billion in 1990, and in 1996 the United States spent $69 billion on treatment of mental illness. Also, about 112,000 deaths in the United States each year are related to alcohol and illicit drug use (USDHHS 2002). In 1995, the economic cost of alcohol and drug abuse was $276 billion. This includes the costs of health care, motor vehicle crashes, crime, lost productivity, and other adverse outcomes. Tobacco use is responsible for additional 430,000 deaths per year among adults in the United States, representing more than 5 million years of potential life lost. Direct medical costs related to smoking total at least $50 billion per year. Both mental illness and the consumption of addictive goods are associated with increased levels of mortality, physical illnesses, nonfatal accidents, lost income, reduced productivity, and emotional damage caused to children by afflicted parents (McGinnis and Foege 1993; USDHHS 1999).

Diagnosable mental illness affects about 24% of the U.S. population in any given year, and about 43% of the population have had a diagnosable mental illness some time during their lives. There is considerable correlation between mental illness and the consumption of addictive goods. (1) The 24% of the population with a current mental illness consume about 38% of all the alcohol, 44% of all the cocaine, and 40% of all cigarettes. The 43% of the population who have had a period of mental illness sometime during their lives consume about 69% of all the alcohol, 84% of all the cocaine, and 68% of all cigarettes.

This article has two goals. The first goal is to empirically examine the effect of mental illness on the level of consumption of alcohol, cocaine, and tobacco. Raw data indicate that mental illness is associated with higher consumption of addictive goods. This may be due to uncontrolled factors, such as income or education. The research in this article examines the effect of mental illness holding other factors that affect addictive consumption constant while controlling for reverse causality and simultaneity. The second goal is to empirically estimate the price elasticity of alcohol, cocaine, and tobacco for individuals with a history of mental illness.

Although this study is primarily intended for economists, the subject matter is, in part, usually the domain of psychologists. As such, some definitions are needed from the outset. The U.S. Surgeon General (USDHHS 1999) describes mental illness as abnormalities in cognition, emotion, mood, and social function. The term "mental illness" is used to describe minor as well as major problems, and almost everyone experiences problems of this type at some time and to some degree. Mental illness is associated with an inappropriate level and duration of these problems. What is inappropriate and what is not is derived from social norms and is neither objective nor fixed. Despite these difficulties, a systematic approach to classification and diagnosis of mental illness has been developed by the American Psychiatric Association. The definition and criteria for diagnosis of specific mental illnesses are contained in the Diagnostic and Statistical Manual of Mental Disorders (DSM) (American Psychiatric Association 1987). Substance abuse and substance dependence refer to specific disorders defined in the DSM. Economists generally use the term "substance abuse" more loosely to refer to a harmful level of consumption of addictive goods. Because this article relies on the definitions of mental illness provided by the DSM, the term "substance abuse" is used only in its DSM context. However, mental illness is defined to exclude substance abuse and substance dependence disorders because the inclusion of these disorders would bias the mentally ill group to high addictive consumption.

The interaction between the consumption of addictive goods and mental illness is a complex process. Psychologists (see Kessler et al. 1996) have contributed greatly to this subject, but the economics literature makes very limited reference to it. However, economists have shown that price increases reduce the consumption of alcohol, illicit drugs, and tobacco as well as outcomes related to the consumption of these goods. Economists should therefore be interested in the interaction of mental illness and demand for these addictive goods. If mental illness alters demand, then the affected individuals may be more or less responsive to higher prices. If prices have less effect for this group, then treatment may be more important than tax increases and other supply reduction policies for the mentally ill. Alternatively, individuals with mental illness may be more affected by higher prices and may be more responsive to tax increases and other supply reduction policies. If this is true, then it is an added justification for higher taxes and other supply reduction activities, because these policies target high-consumption individuals.

There have been prior studies by psychologists of the causality between mental illness and addictive consumption. These studies suggest that causality between mental illness and addictive consumption may go in both directions. (2) Studies by Kessler et al. (1996) and Brady and Sonne (1999) find that individuals with mental illness are more likely to develop an alcohol or illicit drug disorder than other individuals. However, a review by the National Institute on Alcohol Abuse and Alcoholism (USDHHS 1993) finds that alcohol use at low doses may reduce certain psychiatric symptoms, but prolonged and high-dose alcohol consumption can have the opposite effect. Also a note by Leshner (2001) argues that illicit drug use may be a factor in the onset of mental illness. A study by Lasser et al. (2000) finds that mental illness increases the likelihood that an individual will smoke. However, studies by Breslau and Klein (1999) and Wu and Anthony (1999) have found that tobacco can have a causal effect on mental illness. None of these studies, nor any other prior studies that account for mental illness, consider the potential effect of prices in altering the pathology of these comorbidities.

Prior studies of addictive consumption by economists have considered differentials in price elasticities by use level and by demographic variables. Studies of alcohol demand by Manning et al. (1995) and Kenkel (1996) found that heavy drinkers were less responsive to price changes than moderate drinkers. A study by Grossman et al. (1998) finds that heavy drinking by youth is more price-responsive in the long run than in the short run. A study of alcohol and cocaine demand by Saffer and Chaloupka (1999) for a number of demographic groups finds negative price effects. Grossman and Chaloupka (1998) also found negative price elasticities in a study of cocaine consumption by youth. The Report of the Surgeon General (USDHHS 2000) lists 38 studies that indicate that higher tobacco prices or taxes reduce smoking for various demographic groups. None of these studies, nor any other prior studies that account for price, consider the effects of mental illness.

The remainder of the article is organized as follows. First, the estimation model is specified with a theoretical background model provided in Appendix A. A figure is provided to help clarify the relationships in the model. Next, the data set and empirical variables are described. A detailed description of the mental illness variable is contained in Appendix B. The next section describes the empirical strategy. This is followed by a discussion of the results and conclusions.

II. EMPIRICAL MODEL

Mental illness could affect the marginal utility derived from consumption of addictive goods. The reason for this is that consumption of addictive goods disrupts the flow of the neurotransmitter dopamine. This disruption is believed to be responsible for producing feelings of pleasure and reward. Individuals with mental illness may derive a greater marginal utility from these chemically induced feelings of pleasure and reward because they mask the symptoms of mental illness. Mental illness could also affect the rate at which the marginal utility diminishes, but there are no a priori expectations about the direction.

A demand function can be derived from a utility function with an addictive good, a nonaddictive good, and mental illness as arguments. In this utility function, the marginal utility of addictive consumption is assumed to be positive and diminishing, and the marginal utility of mental illness is assumed to be negative. The demand function is derived using a quadratic utility function in Appendix A. The derivation shows that if mental illness increases the marginal utility from consumption of the addictive good, then consumption will be higher. The model also shows that if mental illness affects the rate at which marginal utility diminishes, then price responsiveness will be affected.

The empirical demand function takes the form

(1) A = A(M,P,I,Z,[mu]),

where A is the addictive good, M is mental illness, P is the price of the addictive good, I is income, and Z are other relevant observable factors such as age, gender, and race. The demand for substances may also depend on other unobservable characteristics la, such as personality traits. Prior research has highlighted the potential structural endogeneity and simultaneity between mental illness and addictive consumption. To account for both of these sources of endogeneity requires specification of a probability of mental illness equation. The mental illness equation can be interpreted as a production function and is analogous to a physical health production function such as specified by Grossman (1972). In this case, however, rather than physical, it is mental and rather than health, it is illness that is "produced."

(2) M = M(A,H,L,I,Z,[mu])

In this equation, mental illness is produced by the consumption of the addictive good A, a family history of mental illness H, stressful life events L, income I, and other observable factors Z. The production of mental illness may also depend on unobservable characteristics la, which may be the same as those affecting substance use. Considerable research (USDHHS 1999; Kessler 1997) shows that family history of mental illness and stressful life events have a causal relationship to mental illness. These relationships are illustrated in Figure 1.

[FIGURE 1 OMITTED]

III. DATA

The empirical work employs the National Comorbidity Survey (NCS) with appended price data. The NCS was a congressionally mandated survey designed to study mental illness in the United States and is based on a stratified, multistage area probability sample of the noninstitutionalized civilian population aged 15-54 years. (3) The NCS uses the revised third edition DSM nomenclature to define mental illness. The survey, conducted in 1991, included 8,098 respondents, although only 5,877 respondents were asked more detailed questions on family background and stressful life events. The NCS limited tobacco use questions to 4,411 respondents. Of these respondents, 2,897 were asked detailed questions on family background and stressful life events.

The NCS includes a series of detailed questions regarding alcohol, cocaine, and tobacco consumption. These questions have been used to define alcohol, cocaine, and tobacco participation variables. These variables are each equal to zero for individuals who report that during the past 12 months they did not participate and otherwise are equal to one. (4)

The price of alcohol was estimated from data taken from the Inter-City Cost of Living Index, published quarterly by the American Chamber of Commerce Researchers Association (ACCRA). The ACCRA data contain the price of standard brands of beer, wine, and distilled spirits. The ACCRA samples only a few stores in each location. Because beer prices vary widely by store type and wine consumption is limited, distilled spirits price was selected as the price of alcohol. The alcohol price was matched to the individual records in the NCS by county FIPS code for 70% of the sample. Most of the remainder of the individuals were matched by using the price from a similarly sized community in the same state. Only 3.4% of the sample could not be matched by either method and were dropped from the alcohol regressions.

The price of cocaine was estimated from the U.S. Department of Justice, Drug Enforcement Agency's STRIDE data set. The total cost, purity, weight, and other information are recorded in the STRIDE data set. Total cost cannot simply be divided by number of grams to obtain price because the price of a gram is lower for larger purchases. Variation in purity and imperfect information about purity on the part of purchasers further complicate the issue. A regression of the log of total cost on the log of weight, the log of purity, and dummy variables for city and year were estimated. Imperfect information about purity is addressed by predicting purity based on the other regressors. To identify the total cost model, the coefficient of the log of predicted purity is constrained to equal the coefficient of the log of weight. The log of the price of one gram of pure cocaine is then given as the sum of the intercept, the relevant city coefficients, and the relevant time coefficients. This procedure eliminated variations in price or unit cost due to variations in weight or purity. The antilogarithm of this predicted price is the price of one unit of 100% pure cocaine. This price was then divided by the intercity cost of living provided by the ACCRA. The cocaine price was matched to the individual records in the NCS by county FIPS code for 64.3% of the sample. The remainder of the individuals were matched by state using a weighted average price computed using the Metropolitan Statistical Areas in the state.

The cigarette price data come from the Tobacco Institute and are matched to the NCS data by state. The price includes generic cigarettes and state and federal taxes. Because tax rates change during the year, a weighted average state and federal tax was used. The weights represent the proportion of the year the tax rate was in effect. The price and tax data are in cents per pack.

The component of the NCS that was used to collect data on mental illness is called the Composite International Diagnostic Interview (CIDI). The CIDI was developed by the National Institutes of Health, the World Health Organization, and the University of Michigan and is a nonclinician-administered instrument that generates psychiatric diagnoses. The instrument has undergone extensive testing for reliability and validity. The CIDI includes an extensive series of questions used to define a series of dichotomous mental illness variables. (5) A series of 12 nonsubstance-related disorder groups are defined in the data set. These disorders are defined for both past year occurrence and for occurrence any time during the respondent's life. Two dichotomous mental illness variables were defined as equal to one for the occurrence of any of these 12 disorder groups during the past year and during the lifetime. The 12 disorder groups are listed and described in Appendix B. In this article, an individual is defined as having a mental illness if they met the criteria for any one of the 12 non-substance abuse disorders. Alcohol and drug abuse and dependence refer to specific disorders defined in the DSM and are not included in the definition of mental illness used herein. This distinction is necessary because the topic of this article is the interaction of addictive consumption and nonsubstance-related mental illness. Inclusion of addictive consumption disorders with other disorders would bias the mental illness group toward high addictive consumption. Although mental illness is defined as a dichotomous variable, it is interpreted as an observable indicator for a continuous unobserved latent variable.

A series of demographic variables are also defined from data collected in the NCS. A set of dichotomous variables equal to one if the individual reports that they are black is defined. Also, a dichotomous gender variable is defined. A dichotomous measure equal to one for those currently married or living together is also defined. Continuous age and age squared variables are defined. A dichotomous religion variable is defined as equal to one if the respondent indicates affiliation with any religion. Finally, a continuous income variable was defined.

The NCS data set also contains information on the individual's family history. There is evidence (Kendler and Prescott 1998) that genetic factors can affect an individual's demand for addictive goods. Studies of genetic factors predict that a family history of addiction problems increases the probability of addiction problems. (6) However, the environmental link is ambiguous. Observing an alcohol or drug-abusing parent may deter a child from following the same path. Dichotomous parental alcohol abuse and dichotomous parental drug abuse variables were defined. These variables are equal to one if the natural mother had a problem with alcohol or drugs.

A family history of mental illness can also affect an individual's probability of mental illness. However, this variable would not directly affect an individual's addictive consumption. A dichotomous variable equal to one if the natural mother had periods of depression is also defined. (7)

The NCS data set also contains information on stressful life events that may have happened to the respondent. Nine stressful life event variables were defined. These variables include measures of crime, violence, and traumatic loss. Poor recall of events in the distant past or misreporting of these data is possible.

Summary definitions and weighted mean values for all variables used are presented in Table 1. The weighted means are presented in Table 1 for the full sample as well as for those with and without past year and lifetime mental illness.

IV. EMPIRICAL STRATEGY

The empirical work presented in this article is designed to estimate the effect of mental illness both on the level of consumption and the price elasticity of alcohol, cocaine, and tobacco. Neither question is ideally answered with a single estimation technique. To estimate the effect of mental illness on addictive consumption, recall equation (1), the demand for substances, and equation (2), the structural mental illness production function. Substituting equation (1) into equation (2) results in the reduced-form mental illness production function (3).

(3) M = M(P,H,L,I,Z,[mu])

The first empirical task is to estimate the causal effect of mental illness on addictive consumption. This task is complicated by two factors. The first is structural endogeneity or reverse causality wherein both outcomes may directly influence each other. Thus, not only does the demand for substances depend on mental illness, but the production of mental illness may also be a function of substance use. The second complication is statistical endogeneity or simultaneity wherein an individual's substance use and mental illness may be simultaneously determined by a common set of unobserved characteristics g, such as personality traits. Structural endogeneity and simultaneity will cause the error terms in the substance use and mental illness equations to be correlated. As a result, single equation estimation methods, such as ordinary least squares (OLS) or simple probit, will yield biased estimates because they ignore this interequation correlation. To consistently estimate the structural effect of mental illness on substance use, equations (1) and (3) are jointly estimated using full-information maximum likelihood bivariate probit. (8) The bivariate probit model is based on the assumption that the unmeasured determinants in equations (1) and (3) have a joint, bivariate normal distribution. This procedure is applicable because substance use (A) and mental illness (M) are measured as dichotomous variables. Bivariate probit accounts for the correlation [rho.sub.BP] between the error terms in both equations due to structural endogeneity and simultaneity (Greene 2000). If there is no endogeneity of either form, then [rho.sup.BP] is zero because the remaining error terms in both equations will be random and thus uncorrelated by definition. In this case, equation (1) can be consistently estimated with single-equation probit.

The second empirical task is to estimate differential price elasticities. To do this, the sample is divided into two groups. Models using these subsamples cannot be estimated with single equation techniques because selection in or out of mental illness may not be exogenous. The means in Table 1 indicate that alcohol, cocaine, and cigarette participation is more prevalent among individuals with any mental illness. The figures also reveal that mental illness is significantly correlated with other characteristics, such as income, education, and life events. Individuals with mental illness are more likely to use addictive substances, more likely to have lower levels of education and income, and more likely to be involved in stressful life events. As a result, the Heckman sample selection model is appropriate because sample selection may be endogenous. This model allows for all the coefficients to differ between the two groups. Because the dependent variables are dichotomous in both equations, the sample selection model is estimated via probit. Likelihood ratio tests can be performed to determine the need for estimation of separate equations.

Both the bivariate probit and the Heckman sample selection models require specification of the addictive good demand function and the mental illness production function. If these models are empirically estimated with the same covariate vector for both equations, identification would come purely from functional form restrictions. In practice however, such functional form restrictions are insufficient for identification. As a result, instruments that theoretically belong in one equation but not the other are employed for identification.

An intuitive understanding of identification in the model presented in this article is dependent on the definition of mental illness. Because mental illness is not a usual variable in economic research, some added discussion of the concept may be useful. Mental illness is a common occurrence with about a quarter of the population affected each year and with many individuals recovering without any intervention. This is because mental illness includes minor as well as major problems. (An extensive definition is presented in Appendix B.) The specification of equations (1) and (2) models the path of causation from a family history of mental illness and stressful life events to mental illness. That is, the mental illness problems of the parents and the individual's stressful life events will increase the probability of mental illness in the individual. The individual's probability of consuming addictive goods may increase as a result of mental illness. This specification assumes that a family history of mental illness and stressful life events do not directly enter the addictive good demand function. These variables have an indirect effect on addictive consumption through their effect on mental illness. Family history and stressful life events have a direct effect on mental illness, and mental illness has a direct effect on addictive consumption. Figure 1 illustrates these relationships.

Two criteria must be satisfied to determine whether these assumptions about the specification and identification of the model are valid. The first criterion is the exclusion restriction. The instruments that identify the addictive demand equations must have no direct effect in the structural addictive demand equation beyond their effect through mental illness. The second criterion is that these instruments have sufficient power to move the mental illness variable.

Instrumental validity is determined using tests developed in the context of two-stage least squares estimation (2SLS). (9) There are two tests of the exclusion restriction. The null hypothesis in these tests is that the exclusion restrictions are valid. That is, the identifying variables should not appear in the structural addictive demand equation. The first test for exclusion has been proposed by Davidson and MacKinnon (1993). In this test the residuals from the 2SLS model are regressed on the full instrumental set that includes the excluded instruments and the exogenous variables. The statistic n [R.sup.2] from this regression is distributed as a chi-square density function with degrees of freedom equal to the degree of overidentification. The second test of exclusion uses the method proposed by Bollen et al. (1995). This test is based on the principle that the reduced-form model is correct whether or not the exclusion restrictions are valid. Regardless of whether the instruments affect addictive good demand indirectly through mental illness or directly on their own, the reduced-form model will capture these effects. The structural addictive demand model estimated by 2SLS is correct only if the instruments for mental illness can validly be excluded from this equation. The test involves obtaining the value of the log-likelihood function from the reduced-form ([L.sub.RF]) and structural models ([L.sub.2SLS]). If the exclusion restrictions are valid, then the restricted log-likelihood from the 2SLS model should be similar to the unrestricted log-likelihood from the reduced-form model. The likelihood-ratio test, LR = --2([L.sub.SLS] - [L.sub.RF]), is distributed as chi-square with degrees of freedom equal to the degree of overidentification.

There is one test for the second criteria, which is that these instruments have sufficient power to move the mental illness variable. Nelson and Startz (1990) and Bound et al. (1995) recommend examining the joint F-statistic on the instruments in the first-stage regression to diagnose potentially weak instruments.

V. RESULTS

The first empirical issue that needs to be addressed is the potential endogeneity of mental illness and addictive consumption. A Wu-Hausman test was performed for each of the three addictive goods to test for any endogeneity. For each good, two sets of Wu-Hausman tests were performed by predicting both dependent variables with reduced-form equations and including the predicted values, along with the actual values, in the structural equations. (10) Both structural equations were then estimated with weighted OLS (see note 10). The predicted mental illness variables were significant in the alcohol and cigarette demand functions but not in the cocaine demand function. The second set of tests were performed by including the predicted addictive consumption variable in the mental illness structural equation. These tests never rejected exogeneity. However, because causality must go in either one or both directions, there is enough evidence to conclude that there is endogeneity with mental illness in cases of alcohol and cigarettes. The results from the Wu-Hausman tests are supported by the significance of [rho.sub.BP], the correlation coefficient of the error terms in the substance use and mental illness equations, from the bivariate probit models. [Rho.sub.BP] is reported in Table 2 for alcohol and cigarettes and is statistically significant at the 5% level, indicating endogeneity. In the case of cocaine, [rho.sub.BP] is statistically insignificant, indicating exogeneity, and so consistent estimates can be obtained with single equation probit specifications.

The failure to find evidence of endogeneity for cocaine might be due to the low prevalence of cocaine use. Only about 2% of the sample used cocaine in the past year. However, about 24% of the sample had a mental illness in the past year, and 43% had a mental illness sometime during their lives. Even if every cocaine user were mentally ill, they would comprise only 8% of all past year mentally ill individuals and 4% of all lifetime mentally ill individuals. That is, cocaine use is so minor a factor compared to other causes of mental illness that the exogeneity hypothesis cannot be rejected.

The second empirical issue is to examine the identifying instrumental variables. The Davidson and MacKinnon test results are reported as overidentification test A and the Bollen et al. test results are reported as overidentification test B in Table 2. In none of the cases can the null hypothesis that the exclusion restrictions are valid be rejected. That is, both tests, for both alcohol and cigarettes, show that the excluded variables do not belong in the addictive good equations. The instruments for lifetime and past year mental illness are indicators of nine stressful life events, an indicator of a family history of mental illness, and the number of psychiatrists in the respondent's county of residence. The joint F-statistics from the first stage regression are also reported in Table 2. In all cases the instruments excluded from the addictive demand functions are highly significant as a group in the mental illness equations. This shows that the instruments are strongly correlated with the mental illness variables. These tests show that the nine stressful life events, the family history of mental illness, and the number of psychiatrists do belong in the mental illness function. These identifying variables have no effect on addictive good demand beyond their effect on mental illness.

The first empirical question that this article seeks to answer is the effect of mental illness on alcohol, cocaine, and cigarette participation. To examine the effect of mental illness on addictive good participation, bivariate probit models were estimated for alcohol and cigarettes, and probit models were estimated for cocaine. All of the demand functions include either a past year or lifetime mental illness variable. The results are presented in Table 2. The mental illness marginal effects represent the increase in the probability of participation when the dichotomous mental illness variable switches from zero to one. These coefficients are all positive and generally significant (Table 2). A somewhat more intuitive concept results when the marginal effects are divided by the mean addictive good participation rate. The result is the percentage increase in the participation rate for those with mental illness over those without mental illness. Past year mental illness is found to increase alcohol participation by about 20%, and lifetime mental illness increases alcohol participation by about 26%. For cocaine, the increases are 26% and 66%, respectively. For cigarettes, the increases are 80% and 89%, respectively.

The bivariate probit estimates also include the effects of price and other variables on addictive good participation. This is interesting because the NCS data have never been used to estimate addictive good demand functions. The price-participation elasticities are negative 0.48, 0.63, and 0.71 for alcohol, cocaine, and cigarettes, respectively. The other independent variables are similar to prior empirical studies and are examined in the selection models presented next. One variable that has not been included in prior addictive demand studies is the effect of a family history of problems with the addictive good. The results show that a family history of alcohol problems has a positive effect on alcohol participation and a family history of drug problems has a positive effect on cocaine participation. There were no variables on family history of problems with tobacco in the NCS data set.

The second question that this article seeks to answer is the effect of mental illness on alcohol, cocaine, and cigarette price elasticities. To answer this question, Heckman selection models for alcohol, cocaine, and cigarette participation were estimated. These results are presented in Tables 3, 4, and 5, respectively. (11) Each table contains demand functions for those with and without both past year and lifetime mental illness. These tables also present the selection equation for past year and lifetime mental illness, which is the reduced-form mental illness equation described earlier. Each demand function contains the parameter [rho.sub.HS], which is proportional to the coefficient of lambda and measures the correlation between the error terms in the demand function and the selection equation. (12) A significant value for [rho.sub.HS] is evidence of endogenous selection. Each table also presents the results for two likelihood ratio tests for each pair of demand functions. The first likelihood ratio statistic tests for a significant difference between the price coefficients, and the second tests for a significant difference between the coefficients of all the included regressors.

The next empirical issue is whether different demand functions are needed for those with and without mental illness, and if so, is selection endogenous? The likelihood ratio tests indicate that the demand functions in all cases are significantly different between the two groups. These results imply that separate demand functions for those with and without mental illness are needed. [Rho.sub.HS] is significant for one equation in the alcohol and cocaine regressions. For cigarettes, however, [rho.sub.HS] is significant in all but one of the equations. Because at least one demand function in each pair for alcohol and cigarettes shows evidence of endogenous selection, to be consistent, all regressions are estimated as endogenous selection models. Inclusion of an insignificant lambda does not bias the other variables.

For alcohol participation, the price elasticities for both mental illness groups are larger than the corresponding coefficients for those without mental illness. For cocaine, one case has an insignificant price coefficient and should be ignored. In the other case, mental illness reduces price elasticity. For cigarettes the results are mixed, higher in one case and lower in the other. These results show that individuals with mental illness are price-responsive and that the elasticities are not substantively different from those who are not in the mentally ill group.

It is also interesting to examine the marginal effects for the other independent variables because they also differ between those with and without mental illness. The most interesting results are for religious adherence and family history. Religious adherence has a negative effect on addictive consumption, and it is a larger negative effect for those with mental illness. Family history increases consumption of alcohol and cocaine for the mentally ill, but the effect tends to be weaker for those without mental illness. Gender, race, income, age, and education mirror the results found in other studies of these goods with no systematic pattern across all three substances for those with and without mental illness.

Finally, Tables 3, 4, and 5 present results for the mental illness reduced-form equations. They are all very similar across the three substances and for past year and lifetime mental illness. There are few prior studies of mental illness production functions in the health economics literature. Prior studies of mental illness in health economics have mostly considered the effects of income and employment on mental illness. (13) This prior work does point to the potential endogeneity between mental illness and some of the included variables. However, because this article focuses on addictive consumption, the potential endogeneity between mental illness and other variables such as income and education is not addressed. Because of these biases, these estimation results should be viewed as only suggestive of the relationships.

The mental illness reduced-form equations correctly predict the dichotomous mental illness variables for about 70% of the sample. Income, education, and marriage have a negative effect on mental illness. Age has a parabolic relationship to mental illness indicating that the onset of metal illness decreases after the age of 40. Women are more likely to have a current year mental illness than men. However, there is no gender difference for lifetime mental illness. Being black also has a negative effect on lifetime mental illness but no effect on past year mental illness. The other variables include family history of depression and stressful life events. A depressed mother has a significantly positive effect on mental illness. The stressful life events are generally positive and significant, although the effects are stronger for past year mental illness.

VI. CONCLUSION

Economists have recommended price increases as a tool to reduce the consumption of addictive goods and their related costs. However, no research has specifically examined the interaction of price and mental illness on addictive consumption. The primary goals of this article were to determine whether mental illness has any causal effect on the level of consumption of addictive goods or on the price elasticity of addictive goods. The empirical models allow for the possibility of endogeneity and simultaneity between mental illness and addictive consumption. The empirical results show that mental illness increases participation in addictive goods and that mental illness has no substantive effect on the price elasticity. These results suggest that alcohol and tobacco taxes and drug interdiction are effective with this high-participation group. The results also suggest that an additional method of reducing consumption of addictive goods is to treat or subsidize the treatment of mental illness.

APPENDIX A: DERIVATION OF THE SUBSTANCE DEMAND FUNCTION

The individual maximizes the following utility function subject to an income constraint:

Max : U(A, X, M)

ST: PA + X = I.

To derive the demand curve, let the utility function be quadratic in A.

[U.sub.t] [[alpha].sub.1]A - (1/2)[[alpha].sub.2][A.sup.2] - [[alpha].sub.3]M + [[alpha].sub.4]X.

A is consumption of the addictive good, with corresponding price P; X is consumption of the nonaddictive good, with price normalized to one; I is current income; and M represents mental illness. In addition, the following restrictions are imposed on the parameters:

[U.sub.a] = [differential]U/[differential]A = [[alpha].sub.1] - [[alpha].sub.2]A > 0

[U.sub.aa] = [[differential].sup.2]U/[differential][A.sup.2] = -[[alpha].sub.2] < 0

[U.sub.m] = [differential]U/[differential]M = -[[alpha].sub.3] < 0.

The first and second conditions indicate positive but diminishing marginal utility of addictive consumption. The third condition shows that mental illness reduces utility. Furthermore, the marginal utility of current consumption and the extent to which it diminishes may vary with mental illness. To allow for this possibility, let [[alpha].sub.1] and [[alpha].sub.2] depend on M:

[[alpha].sub.1] = [[delta].sub.1] + [[delta].sub.2]M

[[alpha].sub.2] = [[theta].sub.1] + [[theta].sub.2]M.

If [[delta].sub.2] and [[theta].sub.1] are positive parameters, then mental illness raises marginal utility and lowers the rate at which it diminishes. The first-order condition for maximization with respect to A is: (14)

[[delta].sub.1] + [[delta].sub.2]M - ([[theta].sub.1] - [[theta].sub.2]M)A = [lambda]P.

Solving this condition for A yields the following current period demand for the addictive good,

A = [[psi].sub.1](M) - [[psi].sub.2](M)P

where

[[psi].sub.1] = ([[delta].sub.1] + [[delta].sub.2](M))/([[theta].sub.1] + [[theta].sub.2](M)) > 0

[[psi].sub.2] = [lambda]/([[theta].sub.1] - [[theta].sub.2](M)) > 0

Holding all else constant, [[psi].sub.1] represents the effect of mental illness on consumption. Mental illness has a positive effect on consumption if current marginal utility is higher or if marginal utility diminishes less for mentally ill individuals.

The effect of mental illness on the price responsiveness of consumption is given by the following derivative:

[[differential].sup.2]A/[differential]P[differential]M = -[differential][[psi].sub.2]/[differential]M.

If mental illness reduces the rate at which marginal utility diminishes such that [[theta].sub.2] is positive, then the price effect, given by negative [[psi].sub.2], rises in absolute value. In this case, mentally ill individuals will be more responsive to price. If, on the other hand, the extent of diminishing marginal utility is greater for the mentally ill, then the price effect is smaller in absolute value and this group will be less price responsive. (15)

The empirical results show that mental illness increases the consumption of all substances, ceteris paribus. This implies that [[delta].sub.2] is positive in all cases so that mental illness raises the marginal utility of consumption. For alcohol, we find that mentally ill individuals are also more price responsive, so that [[theta].sub.2] is also positive for them. Thus, for alcohol users, mental illness lowers the rate of diminishing marginal utility. In the case of cocaine and cigarettes, the evidence is mixed. However, even if [[theta].sub.2] is negative for cocaine and cigarette users, [[delta].sub.2] must still be positive because the mentally iii consume more cocaine and cigarettes. They must be deriving a higher marginal utility from consumption and this effect must be outweighing any other.

APPENDIX B: PSYCHIATRIC DISORDERS FROM THE NCS

The following disorders are defined as dichotomous in the NCS data set. The mental illness variable used in this study was defined as equal to one if any of these disorders were present.

1. Generalized anxiety disorder is defined by a protracted period of anxiety and worry, accompanied by multiple associated symptoms. These symptoms include muscle tension, easily fatigued, poor concentration, insomnia, and irritability.

2. Social phobia describes people with marked and persistent anxiety in social situations, including performances and public speaking. The critical element of the fearfulness is the possibility of embarrassment or ridicule.

3. Simple phobia includes common conditions characterized by marked fear of specific objects or situations. Exposure to either the object of the phobia, either in real life or via imagination or video, invariably elicits intense anxiety, which may include a panic attack.

4. Panic attack is a discrete period of intense fear or discomfort that is associated with numerous somatic and cognitive symptoms. These symptoms include palpitations, sweating, trembling, shortness of breath, sensations of choking or smothering, chest pains, nausea or gastrointestinal distress, dizziness or lightheadedness, tingling sensations, and chills or blushing and hot flashes. The experience generally provokes a strong urge to flee or escape from the place where the attack began.

5. Panic disorder is diagnosed when a person has experienced at least two unexpected panic attacks and develops persistent concern or worry about having further attacks or changes his or her behavior to avoid or minimize such attacks.

6. Agoraphobia comes from the ancient Greek meaning a fear of an open marketplace. Agoraphobia today describes severe and pervasive anxiety about being in situations from which escape might be difficult or avoidance of situations, such as being alone outside of home; traveling in a car, bus, or airplane; or being in a crowded area.

7. Post-traumatic stress disorder refers to the anxiety and behavioral disturbances and functional impairment that develop after exposure to an extreme trauma--such as rape, other severe physical assault, near death experience, witness to murder and combat--and persist for more than a month.

8. Major depression features one or more major depressive episodes, each of which lasts at least two weeks. The symptoms of major depression include expressed mood and loss of interest or pleasure. Other symptoms vary but might include sleep disorders, unusual weight changes, psychomotor changes, fatigue, feelings of worthlessness, diminished ability to concentrate, and thoughts of death.

9. Dysthymia is a chronic form of depression. Its early onset and unrelenting, smoldering course are among the features that distinguish it from major depressive disorder. It is sometimes associated with passive, avoidant, and dependent traits. There are fewer symptoms required than there are for major depressive disorder, but the duration is at least two years.

10. Bipolar disorder is a recurrent mood disorder featuring one or more episodes of mania or mixed episodes of mania and depression. Bipolar is different from major depressive by virtue of a history of manic episodes. It has a higher familial prevalence than major depressive disorder.

11. Mania is a mood disturbance that ranges from euphoria to irritability. It may include inflated self-esteem, decreased need for sleep, being more talkative, racing thought process, distractibility, increased goal-directed behavior, and increased activities that are risky.

12. Nonaffective psychosis is a summary category made up of schizophrenia, schizophreniform disorder, schizoaffective disorder, delusional disorder, and atypical psychosis.It is characterized by profound disruption in cognition and emotion affecting the most fundamental human attributes, such as language and thought. It can include hallucinations and delusions.

TABLE 1
Definitions and Weighted Means of Variables

 Means Full
Variable Definition Sample

Lifetime mental A dichotomous indicator equal to 0.432
illness one if the respondent is diagnosed
 with any of the 12 psychiatric
 disorders listed in the appendix, in
 their lifetime.

Past year A dichotomous indicator equal to 0.241
mental illness one if the respondent is diagnosed
 with any of the 12 psychiatric
 disorders listed in the appendix, in
 the past 12 months.

Alcohol A dichotomous indicator equal to 0.636
participation one for alcohol use in the past year.

Cocaine A dichotomous indicator equal to 0.022
participation one for cocaine use in the past year.

Cigarette A dichotomous indicator equal to 0.310
participation one for cigarette use in the past year.

Alcohol price Price of 750-ml bottle of scotch, 16.105
 measured in dollars.

Cocaine price Price of one pure gram of cocaine, 137.776
 measured in dollars.

Cigarette price Average price per pack of 162.390
 cigarettes, including generic brands,
 measured in cents.

Income Personal income of the respondent, 19.529
 measured in thousands of dollars.

Age Age of the respondent. 33.027

Age squared Square of age. 1205.783

Education Number of years of formal 12.884
 schooling completed by the
 respondent.

Female A dichotomous indicator equal to 0.509
 one if the respondent is female.

Married A dichotomous indicator equal to 0.602
 one if the respondent is married.

Black A dichotomous indicator equal to 0.107
 one if the respondent is black.

Religious A dichotomous indicator equal to 0.909
preference one if the respondent has preference
 for any religion.

Mom drink A dichotomous indicator equal to 0.070
 one if the respondent reported that
 their natural mother had a problem
 with drinking.

Mom drugs A dichotomous indicator equal to 0.044
 one if the respondent reported their
 natural mother abused prescription
 drugs or had a problem with illegal
 drugs.

Mom A dichotomous indicator equal to 0.325
depressed one if the respondent reported their
 natural mother being depressed for
 at least two weeks.

Combat A dichotomous indicator equal to 0.031
 one if the respondent had combat
 experience in a war.

Ever molested A dichotomous indicator equal to 0.072
 one if the respondent was sexually
 molested.

Terrible A dichotomous indicator equal to 0.111
experience one if the respondent had any other
 terrible experience.

Shock A dichotomous indicator equal to 0.120
 one if the respondent suffered
 a great shock because someone
 close to them experienced one of
 these traumatic events.

Robbed A dichotomous indicator equal to 0.057
 one if the respondent was robbed
 was burglarized in the past
 12 months.

Conflict A dichotomous indicator equal to 0.246
 one if the respondent had serious,
 ongoing tensions or conflicts with
 a relative, friend, neighbor,
 landlord/tenant, or someone at
 work or at school in the past
 12 months.

Separation A dichotomous indicator equal to 0.130
 one if the respondent had a long
 separation from a loved one in the
 past 12 months.

Death of A dichotomous indicator equal to 0.218
relative one if any close friend or close
 relative of the respondent died in
 the past 12 months.

Other event A dichotomous indicator equal to 0.117
 one if the respondent suffered any
 other major stressful event in the
 past 12 months.

Psychiatrist An indicator of the number of 0.033
availability psychiatrists in the respondent's
 county of residence.

 Lifetime Lifetime
 Mental Mental
Variable Illness = 1 Illness = 0

Lifetime mental -- --
illness

Past year 0.558 0.000
mental illness

Alcohol 0.673 *** 0.607
participation

Cocaine 0.035 ** 0.012
participation

Cigarette 0.396 *** 0.247
participation

Alcohol price 16.086 16.119

Cocaine price 137.418 138.049

Cigarette price 162.486 * 162.317

Income 16.971 *** 21.472

Age 32.877 33.141

Age squared 1195.204 1213.817

Education 12.625 *** 13.081

Female 0.550 ** 0.478

Married 0.584 0.615

Black 0.087 *** 0.123

Religious 0.894 0.920
preference

Mom drink 0.098 *** 0.049

Mom drugs 0.065 *** 0.028

Mom 0.449 *** 0.231
depressed

Combat 0.036 0.026

Ever molested 0.121 *** 0.035

Terrible 0.149 *** 0.081
experience

Shock 0.165 *** 0.087

Robbed 0.074 * 0.045

Conflict 0.363 *** 0.158

Separation 0.185 *** 0.088

Death of 0.230 0.209
relative

Other event 0.151 *** 0.090

Psychiatrist 0.051 0.020
availability

 Past Year Past Year
 Mental Mental
Variable Illness = 1 Illness = 0

Lifetime mental 1.000 0.251
illness

Past year -- --
mental illness

Alcohol 0.636 0.635
participation

Cocaine 0.032 * 0.019
participation

Cigarette 0.424 *** 0.275
participation

Alcohol price 16.160 16.087

Cocaine price 138.364 137.590

Cigarette price 162.542 162.342

Income 13.509 *** 21.441

Age 31.593 *** 33.483

Age squared 1113.796 *** 1235.000

Education 12.342 *** 13.057

Female 0.657 *** 0.462

Married 0.545 ** 0.620

Black 0.099 * 0.110

Religious 0.901 0.911
preference

Mom drink 0.102 *** 0.060

Mom drugs 0.067 *** 0.036

Mom 0.502 *** 0.269
depressed

Combat 0.024 * 0.033

Ever molested 0.147 *** 0.048

Terrible 0.150 *** 0.098
experience

Shock 0.194 *** 0.097

Robbed 0.078 0.051

Conflict 0.429 *** 0.188

Separation 0.239 *** 0.095

Death of 0.268 *** 0.202
relative

Other event 0.175 *** 0.098

Psychiatrist 0.017 0.038
availability

Notes. Maximum number of observations is 5,282. Asterisks indicate
that the difference between the two groups is significant as follows:
*** significant at 0.01 level, ** significant at 0.05 level, and
* significant at 0.10 level.

TABLE 2
Full Sample Models

 Cocaine
 Alcohol Partici-
Dependent Variable Participation (a) pation (a)

Lifetime mental illness 0.16683 -- 0.01457
 (2.68) (2.52)
Past year mental illness -- 0.12886 --
 (2.71)
Alcohol price -0.01839 -0.01922 --
 (-2.94) (-3.27)
Cocaine price -- -- -0.00010
 (-3.41)
Cigarette price -- -- --
Income 0.00332 0.00330 -0.00007
 (7.18) (-6.94) (-0.65)
Age 0.04279 0.04735 0.00919
 (7.06) (7.97) (5.78)
Age squared -0.00065 -0.00070 -0.00015
 (-7.92) (-8.62) (-5.95)
Education 0.02089 0.02029 -0.00083
 (4.66) (4.34) (-1.09)
Female -0.11923 -0.12775 -0.01900
 (-7.88) (-7.17) (-6.12)
Married -0.00975 -0.00641 -0.01711
 (0.55) (0.36) (-3.21)
Black 0.09241 0.10337 0.00592
 (-4.31) (-5.29) (1.04)
Religious preference -0.04288 -0.05042 -0.01418
 (-1.90) (-2.27) (-0.00)
Mom drink 0.03673 0.04797 --
 (1.68) (2.22)
Mom drugs -- -- 0.02091
 (3.18)
[Rho.sub.BP] (c) -0.2368 ** -0.1909 ** --
 (5.01) (6.09)
Price elasticity -0.466 -0.487 -0.626
Overidentification test A 11.45 11.51 --
Overidentification test B 11.66 11.74 --
F-test on instruments 87.98 *** 81.98 *** --
Number of observations 5,282 5,282 5,430

 Cocaine
 Partici-
 pation
Dependent Variable (a) Cigarette Participation (a)

Lifetime mental illness -- 0.27539 --
 (6.45)
Past year mental illness 0.00572 -- 0.24843
 (1.53) (4.94)
Alcohol price -- -- --

Cocaine price -0.00010 -- --
 (-3.17)
Cigarette price -- -0.00132 -0.00138
 (-3.26) (-3.21)
Income -0.00008 -0.00044 -0.00049
 (-0.74) (-0.73) (-0.80)
Age 0.01006 0.04491 0.05244
 (6.43) (7.63) (8.86)
Age squared -0.00016 -0.00058 -0.00067
 (-6.45) (-7.42) (-8.65)
Education -0.00111 -0.04865 -0.04976
 (-1.41) (-8.70) (-8.43)
Female -0.01970 -0.04661 -0.05870
 (-5.99) (-2.56) (-2.97)
Married -0.01805 -0.03200 -0.03759
 (-3.36) (-1.77) (-2.08)
Black 0.00479 -0.04800 -0.06743
 (0.85) (-1.17) (-1.69)
Religious preference -0.01551 -0.07355 -0.09173
 (-0.00) (-0.00) (-0.00)
Mom drink -- -- --

Mom drugs 0.02401 -- --
 (3.57)
[Rho.sub.BP] (c) -- -0.3686 *** -0.3307 ***
 (15.09) (16.93)
Price elasticity -0.626 -0.691 -0.723
Overidentification test A -- 8.60 10.48
Overidentification test B -- 8.03 10.72
F-test on instruments -- 135.27 *** 83.71 ***
Number of observations 5,430 2,898 2,898

(a) Models are estimated via bivariate probit. Marginal effects are
reported. Calculated standard errors (not shown) are clustered robust
by state. Asymptotic z-values are in parentheses. Overidentification
test A, based on Davidson and MacKinnon (1993), is distributed as
chi-square with 8 degrees of freedom. Overidentification test B,
based on Bollen et al. (1995), is the likelihood ratio test distributed
as chi-square with 8 degrees of freedom.

(b) Models are estimated via single equation probit. Marginal effects
are reported. Calculated standard errors (not shown) are clustered
robust by state. Asymptotic z-values are in parentheses.

(c) Chi-square values for the Wald test of [rho.sub.BP] = 0 are
reported in parentheses. For cocaine, [rho.sub.BP] is statistically
insignificant from the bivariate probit models, and so probit results
are presented (see text).

** Significant at 5% level.

*** Significant at 1% level.

TABLE 3
Alcohol Participation

 Lifetime
 Mental
 Illness
Dependent Variable Alcohol Participation (a) (b)

 Lifetime Lifetime
 Mental Mental
Sample Illness = 1 Illness = 0 All

Alcohol price -0.02068 -0.01444 -0.00100
 (-3.93) (-1.54) (-0.22)
Income 0.00293 0.00350 -0.00139
 (6.10) (3.88) (-3.42)
Age 0.02978 0.06081 0.04996
 (4.12) (3.89) (13.87)
Age squared -0.00047 -0.00090 -0.00062
 (-4.55) (-4.24) (-12.75)
Education 0.01022 0.03467 -0.02677
 (1.94) (5.98) (-9.36)
Female -0.08776 -0.16260 0.02267
 (-4.75) (-6.41) (1.27)
Married 0.00830 0.00284 -0.05535
 (0.55) (0.08) (-3.47)
Black -0.06513 -0.12483 -0.07039
 (-3.41) (-3.23) (-3.00)
Religious -0.05074 -0.02182 0.05360
preference (-2.15) (-0.51) (-2.82)
Mom drink 0.03064 0.06497 0.08953
 (1.21) (1.63) (3.11)
Mom -- -- 0.13058
depressed (10.90)
Combat -- -- 0.04309
 (0.84)
Molested -- -- 0.15116
 (5.61)
Robbed -- -- 0.07283
 (2.83)
Terrible experience -- -- 0.07991
 (3.64)
Shock -- -- 0.09446
 (3.57)
Conflict -- -- 0.14619
 (11.77)
Separation -- -- 0.09320
 (4.77)
Death of relative -- -- 0.01247
 (0.88)
Other event -- -- 0.05611
 (2.38)
Psychiatrist availability -- -- 0.00903
 (1.30)
[Rhon.sub.HS] (c) -0.2109 -0.2241 --
 (2.22) (2.07)
Price elasticity -0.494 -0.383 --
Test of price differences (d) 4.18 ** --
Test of 65.87 *** --
 difference in all
 Coefficients (d)
Number of observations 2,984 2,298 5,282

 Past Year
 Mental
 Illness
Dependent Variable Alcohol Participation (a) (b)

 Past Year Past Year
 Mental Mental
Sample Illness = 1 Illness = 0 All

Alcohol price -0.02458 -0.01526 0.00370
 (-4.03) (-1.72) (0.69)
Income 0.00368 0.00300 -0.00139
 (5.03) (4.44) (-3.01)
Age 0.03294 0.05503 0.02478
 (3.53) (6.21) (4.71)
Age squared -0.00050 -0.00081 -0.00032
 (-3.80) (-6.78) (-4.31)
Education 0.01158 0.02486 -0.02321
 (1.67) (5.37) (-7.00)
Female -0.05878 -0.16812 0.10295
 (-2.23) (-7.49) (5.03)
Married 0.00966 0.00284 -0.03915
 (0.42) (0.13) (-3.01)
Black -0.06615 -0.12021 -0.01229
 (-2.30) (-4.98) (-0.52)
Religious -0.07179 -0.02944 -0.00903
preference (-2.54) (-1.00) (-0.45)
Mom drink 0.04713 0.03961 0.01609
 (1.81) (1.27) (0.69)
Mom -- -- 0.12444
depressed (10.12)
Combat -- -- 0.01483
 (0.35)
Molested -- -- 0.10168
 (4.46)
Robbed -- -- 0.01197
 (0.51)
Terrible experience -- -- 0.04416
 (1.88)
Shock -- -- 0.07999
 (3.26)
Conflict -- -- 0.13923
 (10.73)
Separation -- -- 0.11411
 (5.86)
Death of relative -- -- 0.04183
 (4.22)
Other event -- -- 0.06081
 (2.90)
Psychiatrist availability -- -- 0.00049
 (0.08)
[Rhon.sub.HS] (c) -0.2157 -0.2194 * --
 (2.03) (3.82)
Price elasticity -0.625 -0.387 --
Test of price differences (d) 5.94 ** --
Test of 45.72 *** --
 difference in all
 Coefficients (d)
Number of observations 1,711 3,571 5,282

(a) Sample selection models are estimated as probit via Heckman's
two-step procedure. Marginal effects are reported. Calculated standard
errors (not shown) are clustered robust. Asymptotic z-values are in
parentheses.

(b) Probit selection equation. Marginal effects are reported.

(c) Chi-square values for the Wald test of [rho.sub.HS] = 0 are
reported in parentheses.

(d) Likelihood ratio test.

* Significant at 10% level.

** Significant at 5% level.

*** Significant at 1% level.

TABLE 4
Cocaine Participation

 Lifetime
 Mental
 Illness
Dependent Variable Cocaine Participation (a) (b)

 Lifetime Lifetime
 Mental Mental
Sample Illness = 1 Illness = 0 All

Cocaine price -0.00005 -0.00007 0.00022
 (-0.92) (-3.55) (1.59)
Income -0.00014 0.000005 -0.00122
 (0.88) (-0.09) (-3.24)
Age 0.00956 0.00270 0.04956
 (4.91) (2.30) (13.54)
Age squared -0.00016 -0.00004 -0.00062
 (-5.15) (-2.37) (-12.25)
Education -0.00137 0.000005 -0.02720
 (-1.20) (-0.01) (-9.70)
Female -0.02294 -0.00525 0.02520
 (-5.27) (-2.63) (1.40)
Married -0.01649 -0.00541 -0.05556
 (-2.83) (-2.12) (-3.36)
Black 0.00620 0.00141 -0.06978
 (0.86) (0.36) (-3.08)
Religious preference -0.01548 -0.00268 -0.05725
 (-3.06) (-0.98) (-2.96)
Mom drugs 0.02486 0.00567 0.07581
 (2.48) (1.38) (1.93)
Mom depressed -- -- 0.12969
 (11.28)
Combat -- -- 0.04860
 (1.02)
Molested -- -- 0.15820
 (6.00)
Robbed -- -- 0.06169
 (2.30)
Terrible experience -- -- 0.08291
 (3.80)
Shock -- -- 0.09045
 (3.35)
Conflict -- -- 0.14758
 (12.02)
Separation -- -- 0.09609
 (4.61)
Death of relative -- -- 0.01501
 (1.03)
Other event -- -- 0.05898
 (2.56)
Psychiatrist availability -- -- 0.00990
 (1.31)
[Rho.sub.HS] (c) 0.2355 -0.5102 * --
 (0.43) (3.05)
Price elasticity -0.196 -0.805 --
Test of price differences (d) 342.75 *** --
Test of difference in all 377.97 *** --
 Coefficients (d)
Number of observations 2,928 2,282 5,210

 Past Year
 Mental
 Illness
Dependent Variable Cocaine Participation (a) (b)

 Past Year Past Year
 Mental Mental
Sample Illness = 1 Illness = 0 All

Cocaine price -0.00011 -0.00007 0.00024
 (-1.99) (-2.29) (1.41)
Income -0.00020 -0.00005 -0.00138
 (-0.97) (-0.39) (2.88)
Age 0.01173 0.00730 0.02475
 (3.22) (4.99) (4.62)
Age squared -0.00018 -0.00012 -0.00032
 (-3.17) (-4.89) (-4.18)
Education -0.00074 -0.0012 -0.02317
 (-0.36) (-1.69) (-7.18)
Female -0.02369 -0.01847 0.10715
 (-2.95) (-3.60) (5.15)
Married -0.03033 -0.00765 -0.04360
 (-3.81) (-1.50) (-3.42)
Black 0.01550 -0.00085 -0.01670
 (1.23) (-0.19) (-0.71)
Religious preference -0.02114 -0.00794 -0.00732
 (-2.49) (-1.80) (-0.37)
Mom drugs 0.06174 -0.00012 0.00944
 (3.12) (-0.02) (0.28)
Mom depressed -- -- 0.12248
 (11.20)
Combat -- -- 0.01528
 (0.36)
Molested -- -- 0.10690
 (3.99)
Robbed -- -- 0.00245
 (0.10)
Terrible experience -- -- 0.04615
 (1.95)
Shock -- -- 0.08028
 (3.25)
Conflict -- -- 0.13584
 (10.76)
Separation -- -- 0.11667
 (5.72)
Death of relative -- -- 0.04191
 (3.77)
Other event -- -- 0.06091
 (3.03)
Psychiatrist availability -- -- 0.00327
 (0.45)
[Rho.sub.HS] (c) -0.0157 -0.1645 --
 (0.00) -0.39
Price elasticity -0.476 -0.507 --
Test of price differences (d) 26.73 *** --
Test of difference in all 62.40 *** --
 Coefficients (d)
Number of observations 1,677 3,533 5,210

(a) Sample selection models are estimated as probit via Heckman's
two-step procedure. Marginal effects are reported. Calculated standard
errors (not shown) are clustered robust. Asymptotic z-values are in
parentheses.

(b) Probit selection equation. Marginal effects are reported.

(c) Chi-square values for the Wald test of [rho.sub.HS] = 0 are
reported in parentheses.

(d) Likelihood ratio test.

* Significant at 10% level.

** Significant at 5% level.

*** Significant at 1% level.

TABLE 5
Cigarette Participation

 Lifetime
 Mental
 Cigarette Illness
Dependent Variable participation (a) (b)

 Lifetime Lifetime
 Mental Mental
Sample Illness = 1 Illness = 0 All

Cigarette price -0.00161 -0.00073 0.00012
 (-3.37) (-1.64) (0.24)
Income -0.00095 -0.00004 -0.00139
 (-0.87) (-0.06) (-2.37)
Age 0.05469 0.02717 0.05005
 (6.01) (3.86) (9.73)
Age squared -0.00074 -0.00032 -0.00063
 (-6.05) (-3.55) (-8.44)
Education -0.05935 -0.02998 -0.02549
 (-7.40) (-6.25) (-5.80)
Female -0.04134 -0.03361 0.03137
 (-1.23) (-1.79) (1.64)
Married -0.03211 -0.03375 -0.05842
 (-1.20) (-1.33) (-3.24)
Black -0.09906 -0.00643 -0.10897
 (-2.39) (-0.14) (-3.83)
Religious preference -0.07907 -0.06081 -0.03846
 (-1.80) (-1.58) (-1.27)
Mom depressed -- -- 0.13933
 (6.91)
Combat -- -- 0.03812
 (0.61)
Molested -- -- 0.17245
 (5.13)
Robbed -- -- 0.06348
 (1.65)
Terrible experience -- -- 0.08238
 (2.65)
Shock -- -- 0.08693
 (2.50)
Conflict -- -- 0.15401
 (7.88)
Separation -- -- 0.07995
 (2.94)
Death of relative -- -- 0.01990
 (1.07)
Other event -- -- 0.06116
 (1.93)
Psychiatrist availability -- -- 0.00755
 (1.40)
[Rho.sub.HS] (c) -0.2061 -0.4461 *** --
 (2.26) (7.77)
Price elasticity -0.661 -0.480 --
Test of price differences (d) 15.49 *** --
Test of difference in all 55.17 *** --
 Coefficients (d)
Number of observations 1,647 1,251 2,898

 Past Year
 Mental
 Cigarette Illness
Dependent Variable participation (a) (b)

 Past Year Past Year
 Mental Mental
Sample Illness = 1 Illness = 0 All

Cigarette price -0.00144 -0.00126 0.00051
 (-2.36) (-2.30) (0.96)
Income -0.00127 -0.00016 -0.00138
 (-0.96) (-0.30) (-2.26)
Age 0.05373 0.04856 0.02719
 (5.25) (7.85) (4.09)
Age squared -0.00072 -0.00061 -0.00035
 (-5.28) (-7.35) (-3.71)
Education -0.05357 -0.04535 -0.02449
 (-5.67) (-8.13) (-5.41)
Female -0.11448 -0.03236 0.10164
 (-3.14) (-1.64) (4.54)
Married -0.00091 -0.05042 -0.04188
 (-0.02) (-2.60) (-2.25)
Black -0.12573 -0.03835 -0.04339
 (-2.74) (-0.90) (-1.57)
Religious preference -0.10829 -0.08155 0.02722
 (-1.72) (-2.34) (1.04)
Mom depressed -- -- 0.12352
 (8.72)
Combat -- -- 0.01263
 (0.27)
Molested -- -- 0.13837
 (4.71)
Robbed -- -- -0.00657
 (-0.22)
Terrible experience -- -- 0.06029
 (2.23)
Shock -- -- 0.11412
 (3.49)
Conflict -- -- 0.15063
 (7.26)
Separation -- -- 0.10429
 (3.43)
Death of relative -- -- 0.04860
 (2.76)
Other event -- -- 0.06109
 (2.17)
Psychiatrist availability -- -- 0.00091
 (0.15)
[Rho.sub.HS] (c) -0.2545 ** -0.3697 ** --
 (5.34) (5.22)
Price elasticity -0.552 -0.744 --
Test of price differences (d) 5.39 ** --
Test of difference in all 43.88 *** --
 Coefficients (d)
Number of observations 950 1,948 2,898

(a) Sample selection models are estimated as probit via Heckman's
two-step procedure. Marginal effects are reported. Calculated standard
errors (not shown) are clustered robust. Asymptotic z-values are in
parentheses.

(b) Probit selection equation. Marginal effects are reported.

(c) Chi-square values for the Wald test of [rho.sub.HS] = 0 are
reported in parentheses.

(d) Likelihood ratio test.

* Significant at 10% level.

** Significant at 5% level.

*** Significant at 1% level.

ABBREVIATIONS

2SLS: Two-Stage Least Squares

ACCRA: American Chamber of Commerce Researchers Association

CIDI: Composite International Diagnostic Interview

DSM." Diagnostic and Statistical Manual of Mental Disorders

NCS: National Comorbidity Survey

OLS: Ordinary Least Squares

USDHHS: U.S. Department of Health and Human Services

(1.) Illicit drugs were limited to cocaine because the data set used in this study includes too few heroin users and there is very limited price data for other illicit drugs.

(2.) Some psychological dysfunctions are organic in nature and thus would not be related to addictive consumption.

(3.) The initial response rate was 82.6%. Based on previous evidence that survey nonrespondents have higher rates of psychiatric disorders than respondents, a supplemental survey was given to a random sample of these nonrespondents along with a financial incentive. About 4% of the sample was interviewed in late 1990.

(4.) Measurement error is a potential problem with all self-reported data on mental illness and substance use. A reinterview of 20% of the sample by clinical psychologists showed that there is no measurement error in the diagnosis of psychiatric disorders. Prior studies of substance abuse data have shown that the measurement error is reduced when the questions are part of a long survey instrument. In addition the use of dichotomous measures of alcohol, cocaine, and cigarette participation reduces measurement error.

(5.) These mental illness variables were created in a recode of the original data done by the University of Michigan. These mental illness variables are defined in accordance with DSM-III-R, which was current during the data collection period.

(6.) Although the probability of addiction increases, most children brought up in a household with an alcohol- or drug-abusing parent do not become abusers themselves.

(7.) There is a parallel question on father's depression, but it has too many missing values for inclusion.

(8.) The two structural equations (1) and (2) could also be estimated with bivariate probit, which is equivalent to estimating (1) and (3). If the bivariate probit model is applied properly, both should yield a consistent estimate of the causal effect of mental illness on substance use. The only difference is that the correlation between the disturbance terms in equations (1) and (3) is greater than that between equations (1) and (2). This is because the reduced-form mental illness equation (3) has netted out the effect of substance use, and thus its error now also appears as part of the disturbance term in the reduced form substance use equation.

(9.) As an alternative to bivariate probit, consistent estimates of equation (3) can also be obtained using a generalized least squares version of instrumental variables or weighted 2SLS. This is an application of the linear probability model. Because the variance of the error term in such a model is heteroscedastic and known to have the form [X.sub.i]B (1 - [X.sub.i]B), the observations can be appropriately weighted by the inverse of the standard deviation to obtain homoscedastic errors. Estimates from these weighted 2SLS models were essentially identical to those from the bivariate probit models. Differential price elasticities can also be estimated with weighted 2SLS, but this requires a mental illness interaction term that creates two endogenous right-hand-side variables. In addition, all of the other variables in the demand function may also differ between individuals with and without mental illness. This would require additional interaction terms and create a series of endogenous variables. The Heckman probit sample selection method bypasses these problems and provides a more streamlined estimation method while directly accounting for the dichotomous nature of the dependent variables.

(10.) Angrist (2000) and Heckman and MaCurdy (1985) show that 2SLS is an acceptable method of estimation in cases of endogenous dichotomous dependent variables. All of the functions were estimated with robust standard errors, clustered on state, to account for unobserved state-level heterogeneity.

(11.) Because these models also have dichotomous dependent variables in both the demand function and the selection function, they are estimated with the Heckprob procedure in Stata, using robust standard errors clustered on state.

(12.) The parameter [rho.sub.HS] represents the correlation between the error terms in the probit selection equation and the addictive demand equation in the Heckman sample selection models. If [rho.sub.HS] is significantly different from zero, then there is evidence of sample selection and single-equation techniques will yield biased results. Lambda is the inverse Mills ratio and is equal to [rho.sub.HS] times the standard error of the residual in the addictive demand equation. Lambda is proportional to the inverse of the probability that the individual is mentally ill.

(13.) Bjorkund (1985), MacFadyen et al. (1996), Mitchell and Anderson (1989), Hamilton et al. (1997), and Ettner et al. (1997) estimate mental health functions. The last study also used the NCS data but included only three independent variables.

(14.) [lambda] is the marginal utility of income.

(15.) The analysis applies to a continuous measure of consumption. Because the dependent variable used in this study is dichotomous for participation, it is not appropriate to analyze the effects with differential calculus. The reservation price [pi], defined by evaluating the marginal utility of A at A = 0, equals [[delta].sub.1] + [[delta].sub.2]M. Optimal consumption is zero if [pi] < [lambda]P or if [[pi].sup.*] < P, where [[pi].sup.*] = [pi]/[lambda] is the reservation price expressed in dollars. If mentally ill individuals have a higher marginal utility, they will have a higher reservation price. They will therefore be more likely to participate. Furthermore, if the mentally ill individual is initially not participating because [[pi].sup.*] < P, then the decline in P required to shift the status from nonparticipation to participation is smaller than if the individual were not mentally ill and had a lower reservation price. Thus, mental illness also tends to increase the participation response with respect to actual price.

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HENRY SAFFER and DHAVAL DAVE *

* We thank Michael French, Jenny Williams, Theodore Joyce, Michael Grossman, and the session participants at the International Atlantic Economic Conference 2001 and the Western Economic Association Conference 2001 for helpful comments. This project was supported by a grant from the National Institute of Mental Health to the National Bureau of Economic Research.

Saffer: Research Associate, National Bureau of Economic Research, 365 Fifth Ave., Suite 5318, New York, NY 10016-4309, and Professor, Kean University, Union, NJ 07083. Phone 1-212-817-7956, Fax 1-212-817-1597, E-mail hsaffer@gc.cuny.edu

Dave: Faculty Research Fellow, National Bureau of Economic Research, 365 Fifth Ave., Suite 5318, New York, NY 10016-4309, and Assistant Professor, Bentley College, Department of Economics, Waltham, MA 02452. Phone 1-212-817-7955, Fax 1-212-817-1597,

E-mail ddave@bentley.edu