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.
REFERENCES
American Psychiatric Association. Diagnostic and Statistical Manual
of Mental Disorders, 3rd ed., revised. Washington, DC: American
Psychiatric Association, 1987.
Angrist, D. "Estimation of Limited-Dependent Variable Models
with Dummy Endogenous Regressors: Simple Strategies for Empirical
Practice." National Bureau of Economic Research Technical Working
Paper No. 248, 2000.
Bjorkund, A. "Unemployment and Mental Health: Some Evidence
from Panel Data." Journal of Human Resources, 20(4), 1984, 469-83.
Bollen, K., D. Guilkey, and T. Mroz. "Binary Outcomes and
Endogenous Explanatory Variables: Tests and Solutions with an
Application to the Demand for Contraceptive Use in Tunisia."
Demography, 32(1), 1995, 111-31.
Bound, J., D. Jaeger, and R. Baker. "Problems with
Instrumental Variables Estimation when the Correlation between
Instruments and the Endogenous Explanatory Variable Is Weak."
Journal of the American Statistical Association, 90(430), 1995, 443-50.
Brady, K., and S. Sonne. "The Role of Stress in Alcohol Use,
Alcoholism Treatment and Relapse." Alcohol Research and Health,
23(4), 1999, 263-71.
Breslau, N., and D. Klein. "Smoking and Panic Attacks: An
Epidemiological Investigation." Archive of General Psychiatry, 56,
1999, 1141-47.
Davidson, R., and J. MacKinnon. Estimation and Inference in
Econometrics. New York: Oxford University Press, 1993.
Ettner, S., R. Frank, and R. Kessler. "The Impact of
Psychiatric Disorders on Labor Market Outcomes." Industrial and
Labor Relations Review, 51(1), 1997, 64-81.
Greene, W. H. Econometric Analysis. New Jersey: Prentice Hall,
2000.
Grossman, M. The Demand for Health: A Theoretical and Empirical
Investigation. New York: Columbia University Press, 1972.
Grossman, M., and F. Chaloupka. "The Demand for Cocaine by
Young Adults: A Rational Addiction." Journal of Health Economies,
17, 1998, 427-74.
Grossman, M., F. Chaloupka, and I. Sirtalan. "An Empirical
Analysis of Alcohol Addiction: Results from Monitoring the Future."
Economic Inquiry, 36(1), 1998, 39-48.
Hamilton, V., P. Merrigan, and E. Dufresne. "Down and Out:
Estimating the Relationship between Mental Health and
Unemployment." Health Economics, 6, 1997, 397-406.
Heckman, J., and T. MaCurdy. "A Simultaneous Equations Linear
Probability Model." Canadian Journal of Economics, 18(1), 1985,
28-37.
Kendler, K., and C. Prescott. "Cocaine Use and Abuse and
Dependence in a Population Based Sample of Female Twins." British
Journal of Psychiatry, 173, 1998, 345-50.
Kenkel, D. "New Estimates of the Optimal Tax on Alcohol."
Economic Inquiry, 34(2), 1996, 296-319.
Kessler, R. "The Effects of Stressful Life Events on
Depression." Annual Review of Psychology, 1997, 191-214.
Kessler, R., R. Crum, L. Warner, C. Nelson, J. Schulenberg, and J.
Anthony. "The Lifetime Co-Occurrence of DSM-III-R Alcohol Abuse and
Dependence with Other Psychiatric Disorders in the National Comorbidity
Survey." Archives of General Psychiatry, 54, 1996, 313-21.
Lasser, K., W. Boyd, S. Woolhandler, et al. "Smoking and
Mental Illness." Journal of the American Medical Association, 284,
2000, 2606-10.
Leshner, A. "Drug Abuse and Mental Disorders: Comorbidity Is
Reality." NIDA Notes, 14(4), 2001, 3-8.
MacFadyen, A., H. MacFadyen, and N. Prince. "Economic Stress
and Psychological Well-Being: An Economic Psychology Framework."
Journal of Economic Psychology, 17, 1996, 291-311.
Manning, W., L. Blumberg, and L. Moulton. "The Demand for
Alcohol: The Differential Response to Price." Journal of Health
Economics, 14(2), 1995, 123-48.
McGinnis, J., and W. Foege. "Actual Causes of Death in the
United States." Journal of the American Medical Association, 270,
1993, 2207-12.
Mitchell, J., and K. Anderson. "Mental Health and the Labor
Force Participation of Older Workers." Inquiry, 26, 1989, 262-67.
Nelson, C., and R. Startz. "The Distribution of the
Instrumental Variables Estimator and Its t-Ratio When the Instrument Is
a Poor One." Journal of Business, 63(2), 1990, 125-40.
Saffer, H., and F. Chaloupka. "The Demand for Illicit
Drugs." Economic Inquiry, 37, 1999, 401-11.
U.S. Department of Health and Human Services. Eighth Special Report
to the U.S. Congress on Alcohol and Health. Rockville: National
Institute on Alcohol Abuse and Alcoholism, 1993.
--. Mental Health: A Report of the Surgeon General. Rockville: U.S.
Department of Health and Human Services, 1999.
--. Reducing Tobacco Use: A Report of the Surgeon General.
Rockville: National Institute on Alcohol Abuse and Alcoholism, 2000.
--. Healthy People 2010, Volume II (second edition). Online
document available at www.health. gov/healthypeople, 2002.
Wu, L., and J. Anthony. "Tobacco Smoking and Depressed Mood in
Late Childhood and Early Adolescence." American Journal of Public
Health, 89, 1999, 1837-40.
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