Discussion Paper No. 600

MEASURING PEER EFFECTS ON YOUTHSMOKING BEHAVIOR

Ryo Nakajima
The Sixth ISER-Moriguchi Prize (2004)
Awarded Paper

March 2004

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

M P E  Y
S B
R N ∗New York University(March 2004)

Abstract
This paper examines the role of peer effects in smoking behavior using data of
middle and high school students in the United States. I present a random utility
model that explicitly incorporates complementarity between individual and peersmokings. A Markov process model of smoking interactions between individuals
is presented, under the assumption that such interactions occur frequently. I estimate the structural parameters of the model using a steady state distribution thatis uniquely determined by the Markov process . The empirical results strongly
support the presence of positive peer effects in smoking behavior among young
people. Interestingly, peer interactions are found to be stronger within the samegender than across genders. The same result is found for race. Moreover, a multiplier effect is found. The impact of a tax on youth smoking increases by a factorof 1.5 when peer interactions are present.

JFL Classification: C15, C35, C63, I12

Correspondence: Ryo Nakajima, Department of Economics, New York University, 269 Mercer Street 7th Floor New York, NY 10003; e-mail: rn231@nyu.edu∗

I would like to thank my thesis advisor Christopher Flinn for his guidance and supervision.
I also would like to thank for valuable comments from Donghoon Lee and Giorgio Topa andhelpful comments received from Victor Aguirregabiria, Robert Axtell, Alberto Bisin, Nobuyuki
Hanaki, Daiji Kawaguchi, Tsunao Okumura and participants at the 2003 CIEF Conference (North
Carolina), the 2003 JEA meeting (Tokyo) and seminars at Sophia University (Tokyo), Yokohama
National University (Yokohama) and Institute of Social and Economic Research, Osaka University.
All errors are my own.

1. I NTRODUCTION
During the last three decades, federal and local government tobacco policies have achieved
a dramatic reduction in the number of adult smokers in the United States. The same progress,
however, has not been made for American youth. For example, the proportion of teenage
smokers increased from 28 percent to 37 percent between 1992 and 1997 in the United States(Johnston et al. 2001).
A striking pattern in youth smoking data is the large differences between gender andrace groups. Summarizing the four national surveys undertaken, the Report of the Surgeon
General concludes that trends in youth smoking prevalence among gender and race groups
have moved in very different directions during the last 30 years(U.S. Department of Healthand Human Services 1994).
In a series of econometric studies, smoking demand functions were estimated for young
people in an attempt to explain the observed differences in youth smoking behavior between
groups. These studies found significant variation in price responsiveness across groups:
young men and blacks are more responsive to cigarette price changes than are young women
and whites.1 However, these results raise the question of why gender and race affect theelasticity of demand for smoking.
One explanation is that the underlying cause of these difference is the intensity of peerinteractions. DeCicca et al. (2000) hypothesize that peer interactions can lead to “bandwagon
effects” (Liebenstein 1950) on consumption, which raise the demand for cigarettes whenothers are smoking. Changes in cigarette prices have not only a direct effect on consumption,
but also an indirect one—changes in the consumption level of the peer group as a whole
affect the demand of individual group members. Thus, differences in the intensity of suchinteractions could account for differences in the price elasticity between groups.2.
In this paper, I investigate the importance of peer interactions in youth smoking behavior.
The hypothesis to be tested is that the probability that an individual smokes is positively
related to the fraction of smokers in his or her peer group. Data from the 2000 National Youth
Tobacco Survey (NYTS) are used to test this hypothesis. This survey contains informationon the prevalence of a variety of tobacco products among middle and high school students
in the United States.
There are two empirical problems in estimating the magnitude of peer interactions.
The first problem is that regressing a person’s behavior on the behavior of his or her peers
is inappropriate. This would seem to be a natural way to estimate peer effects. However,as argued in Case and Katz (1991), peer choice is endogenous. This endogeneity creates asimultaneity problem. Peer choice, which enters a person’s utility function, is also affectedby that person’s choice. Thus, the regression would have an error term that is correlatedwith peer choice, which is an explanatory variable. Standard econometric theory states that
estimates from the regression would be biased and inconsistent as a result.

1
2

See Chaloupka and Pacula (1999),Gruber (2000), and the Report of the Surgeon General(1998).
Similar consumption externalities have been found by Becker (1991).
1

The second problem is that outcomes that are due to other factors are mistakenly attributed
to peer effects. Manski (1993) argues that it is possible that peer effects may be indistinguishable from such omitted factors. An example may clarify this point. Suppose that there is ahigh smoking rate among teenagers in a neighborhood. This may be because they face thesame cultural attitudes towards tobacco in the neighborhood, or because they have similar
backgrounds as a result of their choices about where to live. One might see this as evidenceof peer effects because each person’s smoking seems to be due to smoking by others in theneighborhood. However, peer effects are absent because all smoking behavior in the neighborhood is due to other common factors. Failure to control for these effects may bias theestimation of peer effects.
This paper develops a method for estimating peer effects that accounts for both simultaneity and unobserved common factors. Simultaneity is addressed by treating peer outcomesas an endogenous variable that is determined by the model itself. The joint distribution ofoutcomes is considered in terms of probabilities. Unobserved common factors are dealt withby including fixed effects in the model. These fixed effects represent unobserved common
factors that affect all members in a neighborhood.
I start with a simple dynamic model of peer interactions that determines the smoking
behavior of young people. A Markov process model of smoking interactions between individuals is presented, under the assumption that such interactions occur frequently. Treating
current smokers in their peer group as exogenous, individuals’ conditional smoking choices
describe transition probabilities.
I estimate the structural parameters of the model using a steady-state distribution that is
uniquely determined by the Markov process. The distribution arises from below through repeated interactions between individuals. The steady-state distribution is assumed to specify
the cross-sectional distribution of smoking profiles at any point in time. Hence, it is used
to formulate the likelihood function. The structural parameters of the model are estimatedusing the maximum likelihood method.
Two sets of maximum likelihood estimates are obtained. The first controls for a variety
of individual and county characteristics, which are augmented by the Census data. Since
the likelihood function is intractable, it is approximated using a simulation method. Simulated samples are drawn from the Markov process introduced to describe smoking interactions. This technique was developed by Geyer and Thompson (1992). The second set of
maximum likelihood estimates incorporates fixed effects into the model to account for unobserved common factors specific to neighborhoods. I suggest that these fixed effects represent
unobserved neighborhood-related factors. The drawback of this approach is the associatedincrease in nuisance parameters. This problem is solved by using the conditional maximum
likelihood method proposed by Andersen (1970).
In this paper, I focus on school cohorts as an approximate definition of peer groups. Because the data set used in this paper does not include information about the structure of peergroup relations, it is necessary to make assumptions about the composition of a person’s
peer group. I assume that smoking interactions occur mainly between people at the sameschool. Since the NYTS uses samples in each school of students taking the same compulsory courses, these samples comprise students who probably see, study and play with each2other every day. Thus, this assumption is realistic. Moreover, I argue that peer interactions
relate to gender and race. Thus, I estimate both gender-specific and race-specific peer effects
on youth smoking behavior.
The empirical results provide compelling evidence for the existence of peer effects on
young people’s smoking behavior. The estimates show that peer effects are positive andhighly significant. Furthermore, peer interactions are found to be stronger within genders
than between genders. The same result is found for race. Furthermore, these strong peer
effects are robust to the inclusion of county-specific fixed effects. These findings support
the hypothesis that youth smoking patterns are due to peer effects rather than unobserved
neighborhood characteristics.
The paper also examines the expected response of youth smoking behavior to changes insmoking policies. Policy experiments based on the model estimates show that a 10 percent
increase in the tax on cigarettes could reduce the youth smoking rate by about 2 percent.
Moreover, a multiplier effect is found. The impact of a tax on youth smoking increases by afactor of 1.5 when peer interactions are present.
The paper is organized as follows. In section 2, I present the behavior model of smoking
interactions and describe the basic assumptions of the model. In section 3, I describe theempirical specification of the model and the estimation technique. In section 4, I describe
the data set and provide descriptive information on the variables used for estimation. In
section 5, I report the estimation results, including those from the fixed-effects model used
to account for unobserved heterogeneity between counties. In section 5, I also report theresults of policy experiments. Section 6 concludes the paper. Proofs and derivations of someancillary results are presented in the appendices.
2. M ODEL
2.1. Behavioral Model
I construct a simple interaction model based on the social capital hypothesis of (Becker
1992) to describe youth smoking behavior. The critical feature is that a person’s chance of
becoming addicted to smoking increases with exposure to the “social capital,” which is astock of influences from other persons. Although several alternative models are possible,3 I
adopt a simple framework by using a parameterization of the random-utility model proposedby Brock and Durlauf (2000).
Suppose that there are N persons. Persons are indexed by i ∈ I ≡ (1, · · · , N ). Suppose
person i ∈ I is deciding whether to smoke cigarettes. The smoking state of person i isdenoted by yi , which takes the form of the following binary choice:(+1 if smoking,yi =−1 otherwise.
Let y denote a smoking profile, which is an N × 1 vector of smoking states for all N
persons. That is, y = (y1 , · · · , yN )0 . Let Ω represent all possible states of y; y ∈ Ω.
3

See Glaeser and Scheinkman (2000) for various social interaction models.
3

For person i ∈ I, the latent utility from smoking is given byX(1)yi∗ = bi (xi ) +ρij yj + ²i .
j6=i

There are two components to utility. The first utility component incorporates systematic
utility (bi (xi )) and a stochastic idiosyncratic taste shock (²i ). In what follows, let xi ⊂ RK
be a 1 × K vector of individual characteristics for person i, and let ²i ∈ R be a random
taste shock for person i with a distribution F (²). I assume that the variable xi is observable
by everyone, but that the variable ²i is private information
known only by person i.4 The
P
second utility component involves the social capital ( ρij yj ), which is the sum of smoking
outcomes of other persons. The parameter ρij measures conformity; i.e., the degree to which
person i behaves like person j. If ρij > 0, person i’s smoking utility yi∗ is higher when
person j smokes (yj = +1) than when person j does not smoke (yj = −1). In short, theparameter ρij represents the peer effect between person i and j.
As in the standard utility-maximization framework, decisions are made to maximize utility. While smoking utility is given by Equation (1), non-smoking utility is normalized tozero. An individual with positive latent utility chooses to smoke; that is, person i chooses
smoking, yi = +1, if yi∗ ≥ 0, and chooses non-smoking, yi = −1, if yi∗ < 0. Let y−i bea smoking profile comprising the smoking states of the (N − 1) persons other than personi, so that y−i ≡ (yj , j ∈ I\{i})0 . Then the probability that person i smokes, (yi = +1),
conditional on xi and y−i , is given byZ(2)πi (yi = +1|xi , y−i ) =f (²i )d²i ,{²i ∈R|yi∗ >0}

where f denotes the density function of the error distribution F .
2.2. A Stochastic Process
In this section, I develop a stochastic process in which each person continually updates
his or her smoking status. I assume that smoking decisions are not once-and-for-all events.
Many studies in developmental psychology (e.g., Flay et al. (1983)) argue that most teenagers
repeat experimentation with smoking sufficiently often to acquire the smoking habit. Each
person’s smoking state develops in discrete steps, and it is therefore convenient to use discrete time, t = 0, 1, 2, · · · ∈ Z. Let yit and xti denote the smoking state and a vector ofcharacteristics of person i at time t.
The specification of the stochastic process relies heavily on local interaction models oflearning and adaptive behavior in game theory (e.g., Blume (1993) and Ellisson (1993)).
The key features are inertia and adaptive behavior.
Inertia implies that once a decision is made, it defines behavior for some time. Supposethat each person makes a decision at randomly chosen intervals.5 In a sufficiently smallinterval of time, it is unlikely that two or more persons will make decisions simultaneously.
4

For example, a random variable ²i could be interpreted as exposure to psychological stress that may leadto the onset of smoking.
5
For example, the timing of decisions could be, but need not be, described by a Poisson process.
4Let dt ∈ I be the person who makes a decision at time t. Then a sequence of decisions isdenoted by (d0 , d1 , d2 , · · · ).
Adaptive behavior implies that a person makes a decision by considering the current, notexpected future, rewards of each choice. Let yi∗t be the latent utility from smoking of person
i at time t. Then, analogous to the latent-utility model (Equation (1)), I assume thatX(3)
yi∗t = bi (xti ) +ρij yjt−1 + ²ti .
j6=i

In the present context, adaptive behavior means that person i at time t chooses between
yit = +1 if yi∗t ≥ 0 and yit = −1 if yi∗t < 0, treating other persons’ choices yjt−1 asexogenous. In other words, each person updates his or her choice by responding to thedecisions of others observed in the previous period.
The smoking decision described by Equation (3) does not incorporate addiction. The
rational addiction model (e.g., Becker and Murphy (1988)) implies that a person’s current
smoking consumption is determined by his or her past and expected future smoking consumption. Although addiction is a determinant of adult smoking, there are two reasons why
it might not be important for young people. First, as Chaloupka (1991) shows empirically,
young people tend to have higher rates of time preference for future smoking decisions thando older people. Therefore, it might be reasonable to assume that youths’ current smoking
demand is not influenced by expected future smoking consumption. Second, as explained in
section 4, data show that young people have low levels of past smoking consumption. Therefore, one can assume that the stocks of addictive capital have negligible effects on youths’
current smoking consumption. In future research, an empirical model of peer interactions
with addiction and rational expectations is estimated.6 The simpler specification, without
the stock of addiction, is adopted because it seems appropriate for a study of youth smoking
decisions.
To specify the probability structure of the model, the timing of decisions is crucial. If
decisions occur simultaneously, the discrete-choice model presented above yields multiple
equilibria (see Heckman (1978), Bresnahan and Reiss (1990) and Tamer (2003)). A modelwith multiple equilibria has neither a unique reduced form probability nor a well-defined
joint probability distribution. In this case, estimation by maximum likelihood is not feasible.
The specific way in which I model smoking interactions is through a discrete-time Markov
process in which each person updates his or her smoking choice sequentially over time.
Markov models are often used to study complex interactions between economic agents (e.g.,Föllmer (1974); Blume (1993); Ellisson (1993); Young (1993); see also Topa (2001) for ant 0) ∈ Ω be a smoking profile at time t, and let
empirical application). Let yt ≡ (y1t , · · · , yN
t 0
N
K
t
t
x ≡ (x1 , · · · , xN ) ∈ R × R be background characteristics at time t. Consider a sequence, y0 , y1 , y2 , · · · . The transition from one state to another is given as follows. At timet, person dt makes a decision given others’ choices in the previous period. Since Equation(3) represents latent utility, the conditional probability πi (i.e., Equation (2)) specifies the
person’s stochastic choice, while other persons’ choices remain unchanged. Thus, a new6

For example, Bisin et al. (2002) study rational expectations equilibria of a model with peer interactions andincomplete information.
5

profile yt+1 evolves from yt = ω ≡ (ω1 , · · · , ωN ) according to the following transition: forξ ∈ {−1, +1},(
ξ if i = dt ,yit+1 =
ωi if i 6= dt ,with Prob(yit+1 = ξ|xt ) = πi (yi = ξ|xti , y−i = ω−i ). I refer to the stochastic processof a sequence of smoking profiles that is defined by the transition probability above as aninteraction process. Because the transition probability at time t + 1 is independent of its
history before time t, the interaction process follows a Markov process on a finite state
space.
I make four assumptions, which are described below. The first assumption is that peer
effects are symmetric between persons. The second assumption concerns the error distribution. The third assumption requires that smoking decisions change more frequently thanyouth background characteristics. The fourth assumption requires that every person be able
to make a decision in each time period.
Assumption 1. Peer effects are symmetric ρij = ρji between any two persons i, j ∈ I.
Assumption 2. A shock is independent between persons and over time, is identically distributed, and has the logistic distribution F (²ti ) = exp(²ti ) /[1 + exp(²ti )].
Assumption 3. The vector of characteristics is time invariant: xt = x for any period t =0, 1, 2, · · · .
Assumption 4. Prob(dt = i) > 0 for any person i ∈ I and any period t = 0, 1, 2, · · · .
The following results describe the properties of the steady state of the interaction process.
(Proofs are presented in the appendix.)
Theorem 1. Let assumptions 1–4 hold. (i) The interaction process has a unique steady-state
distribution P ∗ such that for any ω and ω 0 ∈ Ω
lim Prob(yt = ω|y0 = ω 0 , x0 = x) = P ∗ (y = ω|x).

t→∞(ii) The steady-state distribution P ∗ is given by(4)ÁX
P (y = ω|x) = exp Q(ω|x)
exp Q(η|x),
∗

”∈Ω

where
(5)

Q(ω|x) =1X
1X
ωi bi (xi ) +ρij ωi ωj ,
2 i
2 i<j

for ω ∈ Ω.
The main implication of this result is that the sequence of smoking profiles y0 , y1 , y2 ,· · · , yT converges to a unique distribution P ∗ as T becomes large, whatever its initial distribution.
6

It is important to note that the model does not have multiple equilibria. The steadystate distribution P ∗ represents the proportion of time that the process spends in each state.
Although some states of the smoking profile may occur more often than others, in principle,
the distribution P ∗ allows each state to be revisited. Thus, the stochastic process does notconverge to a few distinct equilibria.
3. E MPIRICAL S TRATEGY
3.1. Maximum Likelihood
In this section, I discuss the estimation of the behavior model. The basic idea is thatan observed smoking profile can be taken as a realization of the steady-state distribution
P ∗ . Given data on the smoking choices yi and background characteristics xi of all i ∈ N
persons, the steady-state distribution P ∗ described above can be used as a likelihood function
to estimate the model cross-sectionally.
In the absence of information about the structure of a person’s peer group, the empirical
specification assumes that a person’s school cohort represents a well-defined peer group.
Evidence from the sociology and social psychology literature indicates that the majorityof middle and high school students choose as their peers fellow students from the sameschools.7 I assume that a person interacts daily with others in the same school. In otherwords, smoking interactions occur within, not between, schools.
Suppose that there are S different schools. Each person attends one of the finite numberof non-overlapping schools, which are indexed by s ∈ {1, 2, · · · , S}. Let Is ⊂ I denote a
set of persons at school s and Ns ≡ |Is |. Let ys ≡ (yi , i ∈ Is )0 be a smoking profile at schools, which is a vector of smoking states of Ns persons, and let xs ≡ (xi , i ∈ Is )0 be an Ns × K
matrix of individual characteristics of Ns persons at school s. In what follows, I use Ωs todenote all possible states of ys . Then ys ∈ Ωs .
To apply the model to the observed data (ys , xs ) for each school s ∈ {1, 2, · · · , S}, I
consider the following assumption on the data generation process. Let Ps ≡ {Prob(ys =ω s |xs ) : ω s ∈ Ωs } be the distribution of ys conditional on xs in the population under consideration. For any s ∈ {1, · · · , S}, Ps = P ∗ , where P ∗ is the steady-state distributionof the interaction process described above. Simply put, this assumes that the smoking profile observed at each school is distributed according to this steady-state distribution P ∗ that
describes the smoking interaction process.
The objective is to estimate the structural parameters (bi , ρij : i, j ∈ I) of the latent-utility
model (Equation (1)). However, identification of the parameters requires the imposition of
restrictions. The first identifying restriction concerns the parameterization of the systematicpart of the utility function.
Assumption 5. Perceived benefits from smoking are a linear combination of backgroundcharacteristics. For any i ∈ I, bi (xi ) = α + xi β, where α is a scalar and β is a 1 × K
parameter vector.
7

Shrum et al. (1988), based on studies of friendship structure of students from grades three to 12 in a 1981–
1982 survey, report that more than 95 percent of friendship links are within the same school.
7

The second assumption is that peer interactions depend on the types of person who match.
Suppose that there are G different types of person, which are indexed by g ∈ {1, 2, · · · , G}.
Let Ig denote a set of persons of type g. Then, one can state the following.
Assumption 6. Interactions are uniform for each type. That is, between person i of type g
and person j of type g 0 in school s, peer effects are defined by ρij = ρgg0 /Ns .
Peer effects are weighted by the number of persons in school s, which is Ns , so that they
are independent of school size. Note that assumption 1 (i.e., ρij = ρji ) implies that peer
effects are symmetric between groups, which in the present context implies ρgg0 = ρg0 g for
all g, g 0 ∈ {1, · · · G}.
As an example, I consider the gender of students. The most consistent finding of the literature on peer groups (e.g., Shrum et al. (1988) and McPherson et al. (2001)) is that students
tend to choose school friends of the same gender. Let g ∈ {M, F }, where M and F represent
male and female respectively. Then, gender determines within-gender and between-genderpeer effects. I use ρM M to denote peer effects between a pair of persons of type M , andρM F to denote peer effects between a pair of persons of type M and type F . The terms ρF F
and ρF M are defined analogously. Since ρM F = ρF M by the assumption of symmetric peer
effects, the identified parameters are (ρM M , ρM F , ρF F ), or (ρM M , ρF M , ρF F ).
Given these assumptions, the likelihood of a smoking profile ys can be defined. Letρ ≡ {ρgg0 } be a vector of peer effects involving ρgg0 s for all g, g 0 ∈ {1, · · · , G}. Then the2
structural parameters to be estimated are θ = (α, β, ρ) ∈ Θ ⊂ R1+K+G . Because thesteady-state distribution is given by P ∗ (Equation (4)), the likelihood of ys conditional on
xs at school s is given by
Á X
∗
(6)
P (ys = ω s |xs , θ) = exp Q(ω s |xs , θ)
exp Q(η s |xs , θ).
” s ∈Ωs

By analogy to Equation (5),8 one obtains:
1X
1 X
(7)
Q(ω s |xs , θ) =ωi (α + xi β) +
ρij ωi ωj .
2 i∈I2 i<j∈Iss

The structural parameter θ can be estimated by maximum likelihood. The contribution to
the log likelihood by school s is given byX(8)
exp Q(η s |xs , θ).
`s (θ) = Q(ys |xs , θ) − log” s ∈Ωs

The overall likelihood function combines the likelihood contributions of all schools; `(θ) =Ps `s (θ). Accordingly, a maximum likelihood estimator is defined by θ̂ = arg max„∈Θ `(θ).
8

The Q function can be also written explicitly in terms of the type-based peer effect ρgg0 :



X
X
X
X
X
X
1
1
ρgg0 
Q(ω s |xs , θ) =ωi  
ωi  .
ωi (α + xi β) +
2 g
4 g
Ns
0
Ig

g

8

Ig

Ig 0

In practice,Pthe log likelihood function `(θ) requires the computation of a normalizing
constant term ”∈Ω exp Q(η|x, θ) (itself a function of the structural parameters). However,
the exact calculation cannot be implemented analytically, and good analytical approximations are not available. Even for a moderate sample size, the computation is prohibitively
expensive.9
I use an approach proposed by Geyer and Thompson (1992), which involves approximating the likelihood function `(θ) by using Monte Carlo simulations. The basic idea is toadopt an importance-sampling approach to the normalizing constant term through the use ofsimulated samples. Let samples (y0 , y1 , y2 , · · · , yT ) be drawn from the interaction processdescribed in section 2, in which the structural parameter is given by ψ ∈ Θ. After many repetitions, T , the samples eventually converge to the steady-state distribution P ∗ (ω|x, ψ), although they are neither independent nor distributed exactly according to P ∗ (ω|x, ψ). Thesesimulated samples can be used to apply the Monte Carlo method in the same way as could
independent samples from the distribution P ∗ (ω|x, ψ). Define the following function for an
arbitrary fixed parameter ψ:10
(9)

¸
T ·
1 X exp Q(yt |x, θ)`T (θ; ψ) = Q(y|x, θ) − log,
T t=1 exp Q(yt |x, ψ)

where the school subscript s is henceforth suppressed for convenience. Given ψ and thesample size T , let θ̂ T = arg max„∈Θ `T (θ|ψ), which is known as a Monte Carlo maximum
likelihood estimator. Geyer and Thompson (1992, pp.658–659) show, under mild conditions,that the Monte Carlo estimator θ̂ T converges almost surely to the exact estimator θ̂ as T →∞, whatever ψ.
For example, if N = 100, it is necessary to sum over 2100 ' 1030 different states. Even a gigantic
supercomputer with 100 teraflops performance, which can complete a 1014 summand in a second, would takea few hundred million years to compute the summation once!
10
The maximized function `T (θ; ψ) is a multiplicative constant to a Monte Carlo approximation of the log∗(y|x,θ)likelihood ratio of θ against ψ. That is, `T (θ; ψ) ∝ log[ PP∗ (y|x,ψ)], where9·P ∗ (y|x, θ)logP ∗ (y|x, ψ)¸==The last equality follows from the identityP
exp Q(η|x, θ)
P η∈Ω
=
exp
Q(η|x, ψ)η∈Ω=PQ(y|x, θ)η∈Ω exp Q(η|x, θ)− log P
Q(y|x, ψ)η∈Ω exp Q(η|x, ψ)·¸Q(y|x, θ)
exp Q(y|x, θ)− log E.
Q(y|x, ψ)
exp Q(y|x, ψ)X"

exp Q(η|x, θ)
exp Q(η|x, ψ)·P
exp Q(η|x, ψ)η∈Ω exp Q(η|x, ψ)η∈Ω·¸X exp Q(η|x, θ)∗P (η|x, ψ) .
exp Q(η|x, ψ)

η∈Ω

9

#

4. DATA D ESCRIPTION
The main data set used for estimation is the 2000 National Youth Tobacco Survey (NYTS).
The survey was conducted by the American Legacy Foundation in collaboration with the
CDC Foundation during the spring semester of the academic year 2000.11 The 2000 NYTS
is a school-based nationally representative sample of students from grades six to 12. Threehundred and sixty schools were selected, and approximately five full classes in a required
subject (e.g., English or Social Studies) across grades six to 12 were randomly selected fromeach participating school. All students in the selected classes were eligible to participate.
In all, 35,828 students in 324 schools completed questionnaires. The school response rate
was 90.0%, and the student response rate was 93.4%, which resulted in an overall response
rate of 84.1%. Students completed an anonymous, self-administered questionnaire in theclassroom, containing questions about tobacco use (bidis, cigarettes, cigars, kreteks, pipes,
and smokeless tobacco), exposure to environmental tobacco smoke, the ability of minors topurchase or otherwise obtain tobacco products, knowledge of and attitudes to tobacco, andfamiliarity with pro- and anti-tobacco media messages.
Several sample restrictions are imposed on the data set. First, the samples are restricted to
students of the four major races in the United States (whites, blacks, Hispanics and Asians).
Other races (i.e., American Indians, Native Hawaiians and other Pacific Islanders) are excluded from the samples.12 Second, the samples are also restricted to students in schools
for which the 2000 NYTS collects at least ten male and female students.13. Additional restrictions due to missing observations reduce the sample size to N = 29, 385 students andthe number of schools to S = 305. Therefore, about 80 percent of the full sample is used
for estimation. I imposed this restriction to ensure that a reasonable number of observations
were available for computing meaningful average smoking outcomes for each peer group.
The average sample size per school is 96.344 students with a standard deviation of 24.823
students. Maximum and minimum sample sizes are 193 and 23 respectively.
A dichotomous measure of smoking was constructed for all respondents. Each student
was asked the following question: “During the past 30 days, on how many days did you
smoke cigarettes?” If the answer was “none”, the student was classified as a non-smoker,
otherwise the student was classified as a current smoker.14. Table 1 reports the percentages ofcurrent smokers for gender and different races. As shown, the average proportion of current
smokers among middle and high school students is 18.95 percent. Comparing smoking rates
between races reveals a pattern that has also been found in recent national surveys (e.g.,
the Monitoring the Future Survey). This finding is that white youths smoke more than
Hispanic youths, who in turn smoke more than black and Asian youths. Figure 1 presents
the distribution of school smoking rates. Variation in smoking between schools is high: the11

The publicly available data set and codebook can be obtained from the website of the American Legacy
Foundation (http://www.americanlegacy.org). See also Center for Disease Control and Prevention[CDC] (2001) for an overview of the results from this survey.
12This led to 1, 153 students (3.22 percent) being dropped.
13
This led to 957 students (2.67 percent) from 13 schools being dropped.
14
This type of smoking variable has been widely used as a smoking participation measure in previous studiesof youth smoking decisions (e.g., Chaloupka and Grossman 1996, Gruber and Zinman 2000)
10

highest proportion of current smokers is about 60 percent and the lowest is close to zero. For
compatibility with the behavior model above, the binary smoking-choice variable is set toyi = +1 if person i is a current smoker, otherwise it is set to yi = −1.
All respondents were also asked about the frequency and intensity of their cigarette smoking. I defined different measures of the frequency and intensity of cigarette smoking. For
the frequency of smoking, six categories were defined: (1) never smoked; (2) non-smoker;(3) smoker for 1–2 days; (4) smoker for 3–9 days; (5) smoker for 10–29 days; and (6) daily
smoker (all 30 days). Those who have never smoked (1) deny even trying a puff of cigarette,
and non-smokers (2) have tried cigarettes but deny smoking in the past 30 days. For theintensity of smoking, six categories were defined: (1) individuals who do not smoke (nocigarettes); (2) individuals who smoke less than one cigarette per day (< 1 cigarette); (3)individuals who smoke one to five cigarettes per day (1–5 cigarettes); (4) individuals who
smoke six to ten cigarettes, or half a pack, per day (6–10 cigarettes); (5) individuals who
smoke 11 to 20 cigarettes, or up to one pack, per day (11–20 cigarettes); and (6) individuals
who smoke more than 20 cigarettes, or more than one pack, per day (> 20 cigarettes). Table
2 presents information on the frequency and intensity of cigarette smoking.
As shown in Table 2, the students sampled did not have high levels of past cigarette consumption. For example, most students were not regular smokers: more than 95 percent ofstudents were not daily smokers, and about 85 percent of students did not smoke at all or
had smoked at least 1–2 days within the last 30 days. Smoking intensity was also low: about
90 percent of smokers smoked less than half a pack of cigarettes per day. Thus, one mightreasonably characterize the students as “chippers”; i.e., just beginning to get addicted.
I have included a number of independent variables to control for factors that are thought
to influence youth smoking decisions. The first set of such variables contains information
on students’ personal background characteristics and attitudinal attributes towards smoking.
I include the following personal background characteristics that are reported in the 2000
NYTS: grade dummies; race dummies (for whites, blacks, Hispanics and Asians); weekly
income in dollars (from paid jobs and other sources such as allowances); an employment
dummy; an indicator of other smokers in the family; several indicators of school-based tobacco prevention programs (school-based program 1 practices ways to say “No” to tobacco;school-based program 2 explains why people of your age smoke; school-based Program 3
explains that most people of your age don’t smoke; school-based program 4 explains theeffects of smoking); and indicators of exposure to smoking on TV and in movies. To explore
the effects of cigarette taxes on smoking participation, I have also included the federal andstate excise taxes (in dollars) on cigarettes per pack as of 31 May 2000.15 The data set isfrom Orzechowski and Walker (2001). Descriptive statistics for these control variables arepresented in Table 3.
The second set of control variables reflect the characteristics of the neighborhoods inwhich the students live. Since the 2000 NYTS data do not provide any information on
15

Cigarette taxes at 31 May are used because the 2000 NYTS was carried out during the spring semester.
However, the estimation results are robust to changes in the period used. In fact, New York is the only statethat raised the cigarette tax substantially during 2000: the state tax increased from $0.56 to $1.11 per pack on 1
March. Using either $0.56 or $1.11 as the New York state tax does not materially affect the estimation results.
11the neighborhoods from which the samples are taken, I have supplemented information on
county characteristics by other data sources. By exploiting information on counties fromthe 2000 Census (Summary Tape File 3A) and the 2000 Uniform Crime Reporting Program
Data (County-level Detailed Arrest and Offense Data), I have incorporated 35 county characteristics as control variables. To control for endogenous selection into neighborhoods, I
have included as many attributes as possible that may affect families’ decisions to locate ina given county. All the county variables used for estimation are listed in the appendix.

5. E MPIRICAL R ESULTS
5.1. Basic Estimation Results
In this section, I compute maximum likelihood estimates of the structural parametersθ = (α, β, ρ) of the behavioral model of smoking decisions. The Monte Carlo techniquedescribed in section 3 is used to obtain the maximum likelihood estimates; i.e., the likelihood functions are approximated using simulated samples obtained from the interaction
process introduced in section 2.16 All estimates are calculated with a final Monte Carlo sample size of 10, 000 experiments.17 The estimated parameters from the benchmark model ofyouth smoking behavior are reported in Tables 4 and 5.18 The point estimates of the county
variables are presented in the appendix.
Table 4 reports the estimated coefficients of the background characteristics. As shown,almost all variables are significant and have the expected signs. The estimates provide some
support for the idea that grade, race, sex, income and work experience significantly affectthe probability that a student is a current smoker. All these results are consistent with theexisting literature (e.g., Gruber (2000)). It is interesting to note that the coefficients of othersmokers in the family are highly significant, which suggests that youths are highly likely
to smoke if their parents and siblings also smoke. The evidence that family influences areimportant determinants of youth smoking is also consistent with previous empirical studies(e.g., Emery et al. (2001)). For ease of exposition, I treat the model specified in column
16

I start the interaction process from the observed smoking profile in data. Before collecting Monte Carlosamples, I discarded the first 10, 000 draws on the grounds that the steady state might not have been attainedby those the draws. Arguably, 10, 000 draws is sufficient for the process to reach its steady state. Then I
collected simulated samples at intervals of two spacing periods to reduce autocorrelation between samples.
Hence, to obtain T = 10, 000 simulated samples, 30, 000 draws must be made from the Markov chain. A
similar sampling procedure has also been suggested by Geyer and Thompson (1992).
17
The Monte Carlo sample size of T = 10, 000 is chosen arbitrarily. However, the sizes of the simulations
are of little practical significance. I re-estimated the model using simulations of T = 30, 000 and T = 50, 000.
The associated estimation results were virtually identical to those obtained from simulations of T = 10, 000.
18
Although theoretically unimportant, a good choice of ψ enhances the performance of the maximum likelihood estimator. The estimate of ψ from the standard logit regression seems a natural choice. However, for thisdata set, its use often produced simulated samples that yielded a likelihood function without maxima, and so
the logit estimate is not a good choice. Therefore, I use a heuristic approach that searches for ψ iteratively. To
be specific, I started with ψ from the standard logit estimate. Then, the one-step Newton–Raphson procedure
updated ψ. Repeated updating (about 100 times) yields the appropriate value of ψ.
12(3) of Table 4 as the best-fitting model because all the individual background characteristics
except the constant term are statistically significant at the 5 percent level.19
As far as the school-based prevention programs are concerned, the estimates in Table
4 suggest that some of them reduce youth smoking rates. Specifically, school program 1(practice ways to say “No” to tobacco) and school program 2 (which explains why youths
smoke cigarettes) significantly reduce youth smoking. The significant reduction in youth
smoking due to school-based program 1 is consistent with previous research, which suggeststhat prevention programs that teach students how to cope with peer pressure to smoke arevery effective deterrents to youth smoking.20 Curiously, however, the coefficient on schoolbased program 3 (which explains that most youths do not smoke cigarettes) is positive andsignificant, while the coefficient of school-based program 4 (which explains the effects ofsmoking) is negative but insignificant. These rather surprising results may indicate that
school-based programs 1 and 2 are responsible for most of the preventative effects of schoolbased programs.
All coefficients of cigarette taxes, which appear in the bottom rows of Table 4, indicate
negative and significant effects of taxation on youth smoking; i.e., higher taxes may deter
youths from smoking. These results are consistent with the findings of a number of empiricaleconometric studies on youth smoking (e.g., Lewit et al. (1981); Chaloupka and Grossman(1996); Gruber (2000)). To illustrate the impacts of cigarette taxes on youth smoking, later I
derive the tax elasticities of the youth smoking participation rate.
The estimates of peer effects (ρM M ,ρF F , ρM F ) are reported in Table 5. Several importantresults emerge. First, all estimates are positive and highly significant. The peer effects are
fairly large from a policy perspective. Suppose, for example, that a student moves from aschool in which none of his or her peers smoke cigarettes to one in which 50 percent of thestudents smoke cigarettes. My results predict that in such a case, the probability of smoking
would increase by 24 percentage points (from 3 percent to 27 percent) when evaluated at the
sample means of the other variables. Such an effect is substantial.
Peer effects generate social multipliers. If socioeconomic conditions change, each student’s smoking behavior changes not only because of the socioeconomic change but also
because the smoking behavior of the peer group changes. Thus, socioeconomic change hasboth direct and indirect effects on youth smoking behavior. The social multiplier, which isdefined as the ratio of the total effect to the direct effect, is the factor by which the externality raises the direct effect through peer interactions. Consider the following hypotheticalsituation. Suppose that school-based program 1 (practice ways to say “No” to tobacco) is
newly introduced to schools. A prediction based on the estimated parameters shows that theyouth smoking rate would fall by 3.68 percentage points from 19.71 percent to 16.03 percent. The total reduction in youth smoking can be decomposed into the direct and indirectcomponents. For this example, the direct effect is 2.36 percentage points while the indirect
effect is 1.32 percentage points. Thus, the social multiplier effect of smoking program 1 is
1.56.
19

The estimates of other specifications are available on request.
See Report of the Surgeon General (1998), chapter 6 (Efforts to Prevent Tobacco Use Among Young
People).
20

13

It is interesting to compare estimates of social multipliers from regression-based models
in other papers with those obtained in this paper. Krauth (2001) computed social multipliers
for a change in the smoking rate of high school seniors (12th graders) in response to an
aggregate shock. These estimated social multipliers are between 1.77 and 2.51, dependingon the data set used.21 In Gaviria and Raphael (2002), a social multiplier is estimated for achange in drug use (cocaine or marijuana) by 10th graders in response to a change in drug
use by their parents.22 Their estimated social multiplier is 1.34. Even though modelingframeworks and data are very different, these estimates are similar to those obtained in thispaper. Hence, my estimates are not unreasonably large.
Table 5 shows that the magnitudes of ρM M and ρF F are not significantly different, while
the within-gender peer effects (ρM M , ρF F ) are significantly larger than the between-genderpeer effect (ρM F ). In fact, the within-gender peer effects are more than twice as large as
the between-gender peer effect. This finding suggests that peer interactions are stronger
within genders than between genders. In other words, when making smoking decisions,male students seem to be more influenced by their male friends than their female friends,
while female students seem to be more influenced by their female friends than their malefriends. Consistent with the peer network literature in sociology (e.g., Shrum et al. (1988)),
this result supports the premise that smoking interactions are gender specific.
An interesting extension is to estimate race-based peer effects. Several studies in sociology (e.g., Shrum et al. (1988)) provide evidence that peer groups are formed along racial
lines. If there is race homogeneity in peer groups, one would expect peer interactions todiffer between racial groups. To explore this possibility, I estimate peer effects that are assumed to be constant within racial groups but different between racial groups. Assuming thattype g is defined by race, the following peer effects are considered: ρ = (ρW W , ρBB , ρHH ,ρW B , ρBH andρHW ), where the subscripts W , B and H represent whites, blacks and Hispanics respectively. This specification of peer effects implies the within-race peer effects
ρW W , ρBB and ρHH , and the cross-race peer effects ρW B , ρBH and ρHW . In the estimationthat follows, I ignore effects for Asian students. Since Asian students comprise less than 5
percent of the total sample, there is an insufficient number of schools with at least one Asianstudent. Hence, all Asian students are excluded from the samples used for estimation.
One drawback with the estimation of race-based peer effects is that this requires further
subsampling of the data set. As shown in Table 6, many schools are racially segregated.
The table shows that almost 100 schools (approximately 30 percent) contain students fromonly one racial group. Most of these schools contain only white students. These racially
uniform schools cannot be used to estimate between-race peer effects. In the estimation that
follows, I use only samples of students in schools in which there are more than two racial
groups, each of which contains at least 10 students. With these restrictions, the sample size
is N = 13, 622 individuals and the number of schools is S = 156. This is about 40 percentof the original sample size.
21

The data source used by Krauth (2001) is the Monitoring the Future (MTF) survey for the period between
1976 and 1988, and the 1993 Teenage Attitudes and Practices Survey (TAPS).
22
Gaviria and Raphael (2002) use data obtained from the 1990 Follow-up Question of the National Education Longitudinal Study (NELS).
14

The estimates of the peer effects ρ are given in Table 7. Since the estimated coefficients ofthe background characteristics are broadly similar in sign and significance to those in Table
4, estimates of β are not presented. Table 7 shows that all point estimates of within-race
peer effects (ρW W , ρBB and ρHH ) are positive and statistically significant at the 1 percent
level for all races. While peer effects between white students ρW W are of a similar magnitude to those between Hispanic students ρHH , peer effects between black students ρBB aresmaller, but remain substantial. Peer effects between white and Hispanic students ρW H are
positive and significant, as are those between black and Hispanic students ρBH . However,peer effects between white and black students ρW B are statistically insignificant, and notalways positive. This suggests that there are no peer interactions between white and black
students, or negligible ones, relating to their smoking decisions. If white and black students
hardly interact with each another, as the results suggest, there would be no social multiplierbetween the two races. This suggests that an aggregate shock that increases the smoking rateof white (or black) students would not necessary raise the smoking rate of black (or white)students. As a result, smoking rates could differ for these two racial groups.
Finally in this section, the results in Table 7 suggest that the within-race peer effects ρW W ,ρBB and ρHH are substantially larger than the between-race peer effects ρW B , ρHW and ρBH .
Table 5 shows similar results for gender-based peer effects. As shown, this tendency is clear
among white and Hispanic students. This is illustrated in Table 7 by substantially larger
values for the within-race peer effects ρW W and ρHH than for the between-race peer effects
ρW B and ρHW . This implies that white and Hispanic students take account of peer behavior
among students of their own race, rather than other races, when making smoking decisions.
For black students, point estimates of the peer effects show that ρBH > ρBB > ρW B , but thenull hypothesis that ρBH is significantly larger than ρHH cannot be rejected. This suggeststhat when making smoking decisions, black students are equally influenced by black andHispanic students, but are hardly influenced by white students.
5.2. Omitted Neighborhood Characteristics
While there is evidence of strong peer effects, there are two possible sources of omitted
variables bias, as suggested by Manski (1993). The first is the environmental and institutional characteristics of a neighborhood, and the second is the shared individual characteristics of a neighborhood. In the present context, (i) students in a neighborhood may be exposed
to common unobserved perceptions (or cultural attitudes) towards or against tobacco and (ii)students in a neighborhood may share unobserved predispositions that lead them to smoke
as a result of their families’ self-selection into the neighborhood. The effect of these omitted
variables, which affect everyone in a neighborhood, may be mistaken for peer effects.
To examine the possibility of omitted variables bias, I add to the model fixed effects that
explicitly account for unobserved heterogeneity between neighborhoods. Fixed-effects models have been used in recent studies of peer effects (e.g., Bertrand et al. (2000); Arcidiacono
and Nicholson (2002); and Weinberg et al. (2002)). I assume that everyone living in the same
county may be affected by a common unobserved factor. If the unobserved heterogeneity isconstant for persons in the same county, it can be accounted for by the county-specific fixed
effects.
15

The primary assumption of the fixed-effects model is that a county-specific factor, whichis unobservable to researchers, affects all persons in the same county. So, the latent-utility
model is modified as follows. Let ` ∈ {1, · · · , L} denote a county, where L is the number ofcounties in the sample.23 Let δ` represent the unobserved factor specific to county `, which
affects all students in the county. Denote the vector of county factors by δ = (δ1 , · · · , δL ). I
assume that the systematic utility of person i in county ` is given bybi (xi ) = δ` + xi β.

(10)Similarly, the latent utility of person i is given by yi∗ = bi (xi ) + ²i ; smoking yi = +1 ischosen if yi∗ ≥ 0, and non-smoking yi = −1 is chosen if yi∗ < 0.
In the following description of the model, the likelihood function is derived for eachcounty. I use y` and x` to denote the smoking profile and background characteristics incounty ` respectively. Let I` denote the persons in county `. Then y` ≡ (yi , i ∈ I` ) is thesmoking profile for county ` and x` ≡ (xi , i ∈ I` ) denotes background characteristics incounty `. Let Ω` denote all possible states of y` such that y` ∈ Ω` . Given the parameterθ = (δ, β, ρ), the log likelihood function of county ` is given byX(11)`` (θ) = Q(ω ` |x` , θ) − log
exp Q(η ` |x` , θ)
” ` ∈Ω`

P

The overall log likelihood is `(θ) =` `` (θ), and the maximum likelihood estimator isθ̂ ≡ arg max„∈Θ `(θ).
One problem with the maximum likelihood method described above is that it is inconsistent when N → ∞. This happens if the number of peer groups is fixed. This is thewell-known “incidental parameter” problem (Neyman and Scott 1948). Andersen (1970)
suggests that the problem can be solved if the likelihood function is conditional on the minimum sufficient statistic for incidental parameters. In the present context, the likelihood
function `(θ) must be conditioned on the minimum sufficient statistic for the fixed-effects
parameter δ` .
The conditional log likelihood function canPbe derived as follows. It is straightforward toshow that the minimum statistic of δ` is τ` = i∈I` yi , which is the total number of smokers
in county `. Define all possible states of the smoking profile given the restriction that the
number of smokers is fixed at τ` as follows:)(¯¯X
ωi = τ` .
B` ≡ ω ` ∈ Ω` ¯¯i

The conditional probability P ∗ given τ` isÁ X
P (ω ` |x` , θ; τ` ) = exp Q1 (ω ` |x1` , θ 1 )exp Q1 (η ` |x1` , θ 1 ).

(12)

∗

” ` ∈B`

23

There are L = 146 counties in the sample.
16

(Details of the derivation are given in the appendix.) Thus, the conditional likelihood isgiven byX
(13)
`1` (θ 1 ) = Q1 (ω ` |x1` , θ 1 ) − log
exp Q1 (η ` |x1` , θ 1 )” ` ∈B`

where x1` is a matrix of independent variables that includes individual background characteristics (e.g., grade dummies and race dummies). In other words, x1` includes neither
a constant nor county-specific variables (e.g., cigarette taxes and other county attributes).
θ 1 = (β 1 , ρ) and β 1 are unknown parameters corresponding to x1` . In this case, it can beshown that the Q1 function does not depend on the nuisance parameter δ` as follows:
1X
1 X
Q1 (ω ` |x1` , θ 1 ) =(14)
ωi x1i β 1 +ρij ωi ωj .
2 i∈I2 i<j∈I``

Note that the summation in the normalizing constant is taken over by the states in the smoking profile that satisfy the restriction given by τ` .
Because of its computational complexity,24 the conditional log likelihood function `1` (θ 1 )must be calculated by using the Monte Carlo technique described in section 3. By analogy
to Equation (9), I define a Monte Carlo conditional likelihood function for an arbitrary fixedparameter ψ 1 as
" T#
X exp Q1 (yt |x, θ 1 )(15)`1T (θ 1 ; ψ 1 ) = Q1 (y|x, θ 1 ) − log,
t |x, ψ )
exp
Q
(y
1
1
t=1
where the subscript ` is suppressed for convenience.
The simulated samples (y0 , y1 , y2 , · · · , yT ) used to construct `1T (θ) are realizations froma stochastic process that converges to the conditional distribution P ∗ (ω ` |x` , θ 1 ; τ` ), which
is given by Equation (12). It should be noted, however, that the interaction process used tocompute the Monte Carlo unconditional log likelihood function (i.e., Equation (9)) cannot
be used to obtain these simulated samples. This is because it generates samples that do notconverge to the conditional distribution P ∗ (ω ` |x` , θ 1 ; τ` ), but converge to the unconditional
distribution P ∗ (ω ` |x` , θ 1 ).25 In the appendix, I present an example in which the stochastic
process has the conditional distribution P ∗ (ω ` |x` , θ 1 ; τ` ) as its limiting distribution.
I estimate the structural parameter θ 1 = (β 1 , ρ) using the model with county fixed effects.
Using the stochastic process described in the appendix, the estimates are obtained by using
the Monte Carlo conditional maximum likelihood method described above. The estimates
are obtained from a final Monte Carlo sample size of T = 10, 000, with a spacing of two fullscans between simulated samples (see footnote 16).
Table 8 reports the point estimates of the coefficients β 1 for individual background characteristics. Compare these results with those in Table 4 in which fixed effects are not controlled¡ ¢Since the set B has N
τ distinct states, computational effort rises geometrically with the sample size N .
25
Clearly, the Markov chain of the interaction process does P
not converge to Equation (12) asymptoticallyeither. Suppose that yt = ω ∈ B at time t with the restriction i ωi = τ . Let yt+1 = ξ be generated
fromP
the Markov chain. Suppose that dt+1 = j ∈ N occurs. Then ξj can be different from ωj . Thus ξi 6= τ . It
follows that yt+1 = ξ 6∈ B occurs with a positive probability.
24

17

for. The point estimates of the coefficients β 1 are similar. All signs are as before, and thevariables that are significant in Table 4 are also significant in Table 8.
Table 9 shows the estimated peer effects ρ. These peer effects are gender based: ρ =(ρM M , ρM F , ρF F ). The magnitudes of the peer effects in Table 9 are smaller than those in
Table 5. For example, when county fixed effects are accounted for, the within-gender peer
effects (ρM M , ρF F ) decrease from 1.67 to 1.54 and from 1.62 to 1.46 respectively, while
the between-gender peer effect (ρM F ) decreases from 0.77 to 0.59. These are not dramatic
decreases. The results in Table 9 show that these peer effects are all statistically significant,which suggests that peer groups substantially affect individual smoking behavior.
I also estimate the race-based peer effects ρ = (ρW W , ρBB , ρHH , ρW B , ρBH , ρHW ) for
white, black and Hispanic students, using the model with county fixed effects. The results
are reported in Table 10. These point estimates are directly comparable with those presented
in Table 7. The standard errors of these estimates are larger, which indicates that the point
estimates are not as precise as those shown in Table 7. This may explain why not all racedbased peer effects are statistically significant in Table 10. The estimated peer effects based on
the inclusion of the fixed effects are smaller than those in Table 7. The difference is marked
for the between-race peer effects. For example, the signs of the peer effects ρW B and ρBHhave changed in all specifications. However, these effects are not statistically significant
because the standard errors of the estimates are large. In addition, some within-race peer
effects remain positive and statistically significant. The point estimate of ρW W is statisticallysignificant at the 1 percent level, and the point estimate of ρBB is statistically significant at
the 10 percent level.
In summary, many of the estimated peer effects from the model with the fixed effects(Table 9 and 10) are qualitatively similar to those from the model without the fixed effects(Table 5 and 7). The estimation results show that the inclusion of county-specific fixed
effects does not eliminate the peer effects, which suggests that the estimated peer effects
are not biased by the omission of county-level unobserved factors. The evidence of strong
peer effects reinforces the conclusion that peer effects are not mainly driven by unobservedcounty characteristics.

5.3. Policy Experiments
To reduce youth smoking, it is essential to know whether smoking policies are effective.
In this section, I evaluate the effects of smoking policies on youth smoking behavior. To dothis, I repeat experiments by simulating smoking profiles from the model using the parameter
estimates from the best-fitting specification from column (3) of Tables 4 and 5. Based on
1000 experiments, I compare the average values of the simulated smoking profiles undercurrent polices and hypothetical policies.
The first policy experiment relates to cigarette taxes. Table 11 reports the predicted smoking rates under a variety of hypothetical taxes. As expected, smoking rates decrease ascigarette taxes increase. The last row of Table 11 reports the elasticities of the smoking
18

participation rate with respect to the tax rate.26 These elasticities range from 0.193 to 0.210
for the tax increases considered. This implies that a 10 percent increase in federal and statetaxes reduces smoking rates among middle and high school students by roughly 2 percent.
An important question about smoking prevention policies is whether higher cigarette taxes
can achieve meaningful reductions in youth smoking. For example, Healthy People 2000 sets
the objective of more than doubling average federal and state taxes on cigarettes to $2.00 per
pack. According to the results in Table 11, a tax increase of 120 cents per pack (a cigarette
tax of $2.10 per pack) could reduce the smoking rates of middle and high school students by
4.74 percentage points, from 18.95 percent to 14.21 percent. Although this reduction is far
short of the target set by Healthy People 2000, which is to reduce youth smoking to half its
current rate, tax plays a significant role in reducing youth smoking.
There are both direct and and indirect effects of tax on smoking. Table 12 reports thedecomposition of the total tax effect into the direct effect on individual outcomes and theindirect effect, which operates through peer-group interactions.27 The last line of Table 12
reports the estimated social multiplier, which is the factor by which the externality raises the
direct effect through peer interactions. As shown, the multipliers range from 1.525 to 1.649,
which imply that peer effects raise the direct tax effect on youth smoking by a factor of morethan 1.5. The evidence of significant multiplier effects on the tax elasticities supports the
hypothesis that peer interactions strongly affect youth smoking behavior.
The second policy experiment relates to school-based smoking prevention programs. Given
that the estimates strongly suggest that school-based smoking program 1 (practice ways to
say “No” to tobacco) is likely to reduce youth smoking, I assess the impact of this programon youth smoking prevalence.
Table 13 shows the results of policy experiments in which school program 1 is implemented at different levels of intensity. The baseline smoking rates are computed under theassumption that all students are exposed to the same intensity level of the school-based program, which is the average level of intensity observed in the sample. Predicted smoking rates
are then computed for various hypothetical average levels of intensity of the smoking program. The implied elasticities show that a 10 percent increase in the average intensity levelof the school-based smoking program leads to a 0.53–0.82 percent decrease in the youth
smoking rate. This finding suggests that a school-based policy is not as effective as tax policy in discouraging youth smoking. For example, the reduction achieved by a tax increaseof 20 cents requires an increase in the intensity level of the school based program of about
20 percentage points.

26

Each tax elasticity is calculated as (∆y/y)/(∆τ /τ ) where ∆y is the predicted change in the smoking
rate due to the assumed tax change ∆τ , y is the average smoking rate in the baseline simulation, and τ is theaverage tax rate for the relevant sample.
27
I compute the direct effects as follows. Given that y denotes a simulated smoking profile, I computePΛi ≡ Λ(−xi β̂ − j ρ̂ij yj ) for person i, where Λ is the c.d.f of the logistic distribution, β̂ and ρ̂ are estimatedparameters, and xi is a vector of characteristics including a hypothetical tax. The predicted smoking prevalence
due to the direct tax change is calculated as the average of Λi .
19

6. S UMMARY AND C ONCLUSIONS
If peer behavior influences individual behavior, youth smoking can differ between groups.
I have used a micro data set that records the smoking behavior of middle and high school
students to examine the hypothesis that peer interactions play an important role in explaining
variations in youth smoking behavior.
The model presented in this paper specifies how each person’s smoking behavior is related
to the smoking behavior of their peers through utility. The behavior model incorporates autility-maximization framework using the standard parameterization of the discrete-choice
literature. Smoking interactions between individuals are modeled by using a Markov process, which produces a unique cross-sectional distribution of smoking profiles. This distribution is used as a likelihood function from which to estimate the model.
The model was estimated using a maximum likelihood method. The estimates show thatpeer effects are positive and statistically significant, and are important determinants of youth
smoking. The results are robust to the inclusion of the fixed effects that control for unobserved heterogeneity between counties; i.e., peer effects remain significant. Furthermore,
peer effects generate substantial externalities that lead to a more than 1.5-fold increase in the
direct tax effects on youth smoking behavior. These empirical results represent consistentevidence of peer effects on youth smoking behavior. Peer effects are so important that youths
succumb to smoking because of the influence of their peers.
I suggest that the framework developed in this paper could be applied to analyses of othertypes of behavior associated with social interactions. Recent economic studies have incorporated social interactions on the basis that interactions directly affect preferences. The
empirical approach used in this paper provides a tool for testing the existence and estimating
the magnitude of social interactions in settings in which there are direct interactions between
individuals. Finding evidence of social interactions would enhance the practical relevanceof such models.

20

A PPENDIX A. P ROOFS AND D ERIVATIONS OF E QUATIONS
A.1. Proof of Theorem
Amemiya (1975) shows the conditions under which a set of conditional logistic probabilities can specify the joint probability in a multivariate model. Let zi ∈ {0, 1} andz ≡ (z1 , · · · , zN ) ∈ {0, 1}N ≡ Ξ. Consider the following conditional logistic probability of zi given z−i :
Ã
!
X
(16)
Prob(zi = 1|z−i ) = Λ bi (xi ) + 2
ρij zj ,j6=iwhere Λ(x) = (1 + exp(−x))−1 is the c.d.f. of the logistic distribution. Amemiya (1975)shows that, under assumption 1 (i.e., ρij = ρji ), the conditional logistic probabilities (Equation (16)) determine at most one joint probability: For ξ ∈ Ξ,X
(17)
Prob(z = ξ|x) = exp Qξ (ξ|x)/exp Qξ (η|x),
”∈Ξ

where
(18)

Qξ (ξ|x) =Xbi (xi )ξi + 2

Xiρij ξi ξj .

i<jMaking use of the above result, I show that a set of conditional probabilities πi (Equation(2)) for i ∈ I determines the joint probability P ∗ (Equation (4)). Under assumption 2 (i.e.,
F (²) = Λ(²)), πi is written asÃ!
X
πi (yi = +1|y−i ) = Λ bi (xi ) +ρij yj .
j6=iUsing the variable transformation z = (y + 1)/2 reveals that the same probability mass as
πi is assigned by
!
Ã
X
X
ρij .
ρij zj −Prob(zi = 1|z−i ) = Λ bi (xi ) + 2
j6=i

j6=i

Therefore, by analogy to Equation (17) and Equation (18), the conditional probabilities πi
for i ∈ I determine the joint probability
X(19)
Prob(z = ξ|x) = exp Qξ (ξ|x)/exp Qξ (η|x),
”∈Ξ

where
(20)

Qξ (ξ|x) =XiÃbi (xi ) −

X
j6=i

!
ρij

ξi + 2Xρij ξi ξj .

i<jEquation (19) can be expressed in terms of y using the variable transformation as¯ ¶µω + 1 ¯¯Prob(y = ω|x) = Prob z =
x .
2 ¯
21

Hence, this is equal to(21)µ

Prob(y = ω|x) = exp Qξ

¯ ¶ÁX
¯ ¶
µ
ω + 1 ¯¯
η + 1 ¯¯xexp Qξ
x .
2 ¯
2 ¯
”∈Ξ

Equation (20) implies that
Ã
!µ
¯ ¶
¶
µ
X
X
X µ ωi + 1 ¶ µ ωj + 1 ¶¯
ωi + 1
ω + 1¯x=bi (xi ) −
ρij
Qξ
+2
ρij
2 ¯
2
2
2
i
i<j
j6=i
1X
1X
bi (xi )ωi +ρij ωi ωj + constant.
=
2 i
2 i<j
Recall that Equation (5) isQ(ω|x) ≡
Then,

µ
Qξ

(22)

1X
1X
bi (xi )ωi +ρij ωi ωj .
2 i
2 i<j

¯ ¶
ω + 1 ¯¯
x = Q(ω|x) + constant.
2 ¯Combining Equation (22) with Equation (21) yields Equation (4). Therefore, I have shownthat Equation (2) determines Equation (4) such thatP ∗ (yi = ωi |x, y−i = ω−i ) = πi (ωi |xi , ω−i ),(23)for any ω ∈ Ω and i ∈ I.
I now investigate the interaction process y0 , y1 , y2 , · · · ,yT . The transition probability ofi = dt is given byt−1
Prob(ydt t = ωdt |xt , y−dt = ω−dt ) = πdt (ωdt |xdt , ω−dt ),under assumption 3 (i.e., xt = x for any t). Given Equation (23), this is equal to
t−1
t−1
∗ t
Prob(ydt t = ωdt |xt , y−dt = ω−dt ) = P (ydt = ωdt |x, y−dt = ω−dt ).

In mathematical terms,
(24)

t−1
Prob(yit = ωi ) = P ∗ (ydt t = ωdt |x, y−dt = ω−dt ) · Prob(y−dt = ω−dt ).

Geman and Geman (1984, Theorem A) prove that Equation (24) implies that the above
Markov chain converges to P ∗ as t → ∞ whatever the initial profile y0 ; namely,
lim Prob(yt = ω|y0 = ω 0 , x0 = x) = P ∗ (y = ω|x).

t→∞

The only necessary condition for convergence is that a sequence of (d0 , d1 , d2 , · · · ) contains any i ∈ N infinitely often, which is ensured by assumption 4 (i.e., Prob(dt = i) > 0
for any i and t). This proves result 1.
¤
22

A.2. Derivation of the Conditional Probability P ∗ on τ
In the following derivation, I use a decomposition of the vector of characteristics xi . Let
x1i denote a vector of individual characteristics (e.g., grade dummies, race dummies), and let
x2i denote a vector of constant and county characteristics (e.g., cigarette tax and other county
characteristics). The x2i does not change across individuals in county `. The parameters aredecomposed into β = (β 1 , β 2 )0 , where β 1 and β 2 denote vectors of unknown parametersthat correspond to x1i and x2i respectively.
Using the above notation, the Q function is written as
1X
1X
Q(ω ` |x` , θ) =ωi (δ` + x1i β 1 + x2i β 2 ) +ρij ωi ωj .
2 i
2 i<j
P
Under the restriction that τ` = i ωi , this is equal to
1X
1X
1X
Q(ω ` |x` , θ) =(δ` + x2i β 2 )τ` +ωi x1i β 1 +ρij ωi ωj
2 i
2 i
2 i<j
= C` + Q1 (ω ` |x1` , θ),P
where I define C` ≡ 21 i (δ` + x2i β 2 )τ` .
The rule of conditional probability implies

Á X
P ∗ (y` = ω ` |x` , θ).
P (y` = ω ` |x` , θ; τ` ) = P (y` = ω ` |x` , θ)∗∗

! ` ∈B`

This is equal toÁP
exp Q(ω ` |x` , θ)
exp Q(ω ` |x` , θ)P!` ∈B`P (y` = ω ` |x` , θ; τ` ) = P” ` ∈Ω` exp Q(η ` |x` , θ)
” ` ∈Ω` exp Q(η ` |x` , θ)ÁX= exp Q(ω ` |x` , θ)
exp Q(η ` |x` , θ)∗

” ` ∈B`ÁX= exp C` exp Q1 (ω ` |x1` , θ)
exp C` exp Q1 (η ` |x1` , θ).
” ` ∈B`The term exp C` , which is constant, is canceled out. This is equal to Equation (12).

¤A PPENDIX B. I NCLUDED C OUNTY- SPECIFIC VARIABLES
B.1. 2000 Census data
The following county-specific variables are provided by the 2000 Census Data, Summary
Tape File 3.
Persons 0-18: The percentage of persons between the age of 0 and 18 in the county.
Persons 65+: The percentage of persons of the age of 65 and older in the county.
Asian persons: The percentage of Asian persons in the county.
23

Black persons: The percentage of black persons in the county.
Hispanic persons: The percentage of Hispanic persons in the county.
Single-mother families: The percentage of female householder families; no husband present;with own children under the age of 18.
One-person families: The percentage of one-person non-family households.
Persons with grandchildren: The percentage of persons of the age of 30 and older wholive with their own grandchildren under the age of 18.
Persons who divorced: The percentage of persons of the age of 15 and older who had been
divorced.
Unemployed workers: The percentage of unemployed persons over the civilian labor forceof the age of 16 and older.
Workers with management jobs: The percentage of persons of the age of 16 and older
employed in management; business; and financial operations occupations.
Workers with professional jobs: The percentage of persons of the age of 16 and older
employed in professional and related occupations.
Workers with construction jobs: The percentage of persons of the age of 16 and older
employed in construction; extraction; and maintenance occupations.
Workers with farming jobs: The percentage of persons of the age of 16 and older employed in farming; fishing; and forestry occupations.
Workers with sales and office jobs: The percentage of persons of the age of 16 and older
employed in sales and office occupations.
Workers with service jobs: The percentage of persons of the age of 16 and older employed
in service occupations.
Persons below poverty level: The percentage of persons with income below the poverty
level.
Persons who graduated high schools: The percentage of persons of the age 16 and older
with a high school diploma or more.
Persons who graduated colleges: The percentage of persons of the age 16 and older witha college degree or more.
Persons enrolled in public schools: The percentage of persons of the age of 3 or older who
are enrolled in a public school at present.
Persons enrolled in high schools: The percentage of persons of the age of 3 or older who
are enrolled in a high school at present.
24Persons enrolled in colleges: The percentage of persons of the age of 3 or older who areenrolled in a college at present.
Persons enrolled in graduate schools: The percentage of persons of the age of 3 or older
who are enrolled in a graduate or professional school at present.
Persons in armed forces: The percentage of persons between the age of 18 and 64 who are
in armed forces.
Persons in veteran status: The percentage of persons between the age of 18 and 64 whoare civilian veterans.
Persons migrated from foreign countries: The percentage of persons who were born inthe countries other than United States.
Persons moved in last 5 years: The percentage of persons who moved in the county in last
5 years.
Median household income: in 1999 U.S. $, includes wage or salary income, self-employment
income, interest, dividend or net rental income, social security, public assistance, retirement
income, and other.
Median housing value: Median housing value in 1999 U.S. $ of owner occupied noncondominium housing units in the county.
Vacant housing units: The percentage of all housing units that are vacant in the county.
Private vehicles occupancy: The percentage of workers of the age 16 and older who owns
private cars, vans and trucks.
Urban area rate: The percentage of urbanized area over total area in the county.
B.2. 2000 Uniform Crime Reporting Program Data
The following county-specific variables are provided by the 2000 Uniform Crime Reporting Program Data: County-level Detailed Arrest and Offense Data.
Crime index: The percentage of arrests and offenses for the Uniform Crime Reports index
crimes (murder, rape, robbery, aggravated assault, burglary, larceny, auto theft and arson)over the population in the county.
Juveniles crime: The percentage of arrests and offenses of juveniles for the Uniform Crime
Reports index crimes (murder, rape, robbery, aggravated assault, burglary, larceny, auto theft
and arson) over the population in the county.
Juveniles crime (drug abuse): The percentage of arrests of juveniles for violations of narcotic drug over the population in the county.
25

A PPENDIX C. A N E XAMPLE OF A M ARKOV C HAIN
The following Markov chain has the conditional distribution P ∗ (ω|x, τ, θ), which is given
by Equation (12), as the steady-state distribution. Given xt = x and yt = ω ∈ B at time t,
construct ξ ∈ B by swapping two elements of ω. For example, let i and j be the randomly
selected pair of persons (i, j ∈ N ). Then ω = (ω1 , · · · , ωi , · · · , ωj , · · · , ωN ) generates
ξ = (ω1 , · · · , ωj , · · · , ωi , · · · , ωN ).
Consider a Markov chain in which a new profile yt+1 evolves from yt according to(ω with probability α(ω, ξ),
yt+1 =
ξ with probability 1 − α(ω, ξ).
Here, I define½¾Q1 (ω|x, θ)α(ω, ξ) = min,1 .
Q1 (ξ|x, θ)The Markov process states that the next candidate value is proposed by swapping choices
between the randomly selected individuals, and is then accepted or rejected according to thepotential function at the candidate value relative to the potential function at the current value.
Such an algorithm is often referred to as the Metropolis sampling algorithm in the statistical
literature. See Chib and Greenberg (1996) for an introduction to the Metropolis algorithm
and its application to econometric problems.
Some important points should be noted about the above Markov process.
First, the Markov process satisfies the summation
restriction imposed by B. Suppose thatP
ω = (ω1 , · · · , ωN ) ∈ B with the restriction i ωi = τ . Since just two
P of ω are
Pelements
swapped to construct ξ = (ξ1 , · · · , ξN ) at the next step, it follows that i ξi = i ωi = τ ,and thus ξ ∈ B. Because either yt+1 = ω or yt+1 = ξ, it follows that yt ∈ B implies
yt+1 ∈ B.
Second, the Markov process is aperiodic. This is because the algorithm states that theprobability that the next draw is the same as the current draw is positive. This happens when
the proposed sample is rejected.
Finally, the Markov process is irreducible. To move from state ω to state ω 0 , find thecoordinates whose values in ω and ω 0 are different, and swap these two values. Continue
swapping until ω and ω 0 agree. If pairs swapped are chosen randomly, such a transition
from state ω to state ω 0 occurs with positive probability for any ω, ω 0 ∈ B. That meansthat there is a positive probability of reaching any state from any other state in finite steps,
so that the process visits all the states of B. The standard result shows that if the Markov
process is aperiodic and irreducible, it converges asymptotically. In particular, a sequencey0 , y1 , y2 , · · · converges in terms of its distribution to the conditional distribution given by
Equation (12).

26

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27

Geyer, Charles J. and Elizabeth A. Thompson, “Constrained Monte Carlo Maximum Likelihood for Dependent Data,” Journal of The Royal Statistical Society, Series B, 1992, 54, 657–699.
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28

TABLE 1. Smoking Rates (Percentages) by Gender and Race Subgroups in Sample

Race
White
Black
Hispanic
Asian
Total

GenderMale Female
21.829 22.192
15.499 11.153
18.111 13.507
17.237 11.425
19.874 18.059

29

Total
22.01213.15815.74514.48618.951TABLE 2. Smoking Frequency and Intensity

Intensity/day
0 cig
<1cig
1-5cigs
6-10cigs
11-20cigs> 20cigs
Sum

Frequency/30days
Never
NonSmokers Smokers Smokers
Smokers Smokers 1-2 days 3-9 days 10-29 days
16680
5391
0
0
0
0
0
741
209
48
0
0
608
929
919
0
0
22
63
163
0
0
2
10
59
0
0
0
3
9
16680
5391
1373
1214
1198

Sum
Daily
Smokers
0 22071
4
1002
485
2941
518
766
387
458
199
211
1593 27449

Never Smokers: those who deny ever trying a puff or two of cigarettes.
Non-Smokers: those who endors trying cigarettes, although deny smoking within 30 days.
Daily Smokers: those who smoke everyday within 30 days.

30

20
18
16

Frequency (Percent)

14
12
10
8
6
4
2
0

0

0.1

0.2

0.3

0.4
0.5
0.6
Average Smoking Rates

0.7

0.8

F IGURE 1. Distribution of School Smoking Rates

31

0.9

TABLE 3. Descriptive Statistics for Individual Background Variables Used in Estimation

Variable

Minimum

Maximum

MeanStandard
Deviation

0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.36500

1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
46.71429
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.00000
1.45000

0.15604
0.16259
0.15635
0.13788
0.13977
0.10756
0.049940.169040.186910.293810.02646
0.077810.09074
6.43774
0.395630.405160.83573
0.862790.27043
0.422680.220800.561020.89206

0.362900.36900
0.363190.34478
0.346760.309830.217830.37479
0.389850.455510.160510.267870.28724
8.36576
0.488990.490930.37053
0.344080.444190.49399
0.414800.49627
0.32863

7th Grade (0-1 Dummy)
8th Grade (0-1 Dummy)
9th Grade (0-1 Dummy)
10th Grade (0-1 Dummy)
11th Grade (0-1 Dummy)
12th Grade (0-1 Dummy)
Asian (0-1 Dummy)Black (0-1 Dummy)
Hispanic (0-1 Dummy)
White Male (0-1 Dummy)
Asian Male (0-1 Dummy)Black Male (0-1 Dummy)
Hispanic Male (0-1 Dummy)
Weekly Income (U.S. Dollar)
Working Dummy (0-1 Dummy)
Smokers in Home (0-1 Dummy)
See Actors Smoking in TV (0-1 Dummy)
See Actors Smoking in Movie (0-1 Dummy)
School Program 1 (0-1 Dummy)
School Program 2 (0-1 Dummy)
School Program 3 (0-1 Dummy)
School Program 4 (0-1 Dummy)
Cigarette Tax (U.S. Dollar)

School Program 1: Practice ways to say “No” to tobacco
School Program 2: Taught reasons why people your age smoke
School Program 3: Taught that most people your age don’t smoke
School Program 4: Taught about the effects of smoking

32

TABLE 4. The estimated coefficients of individual background characteristics in the baseline model (smoking choices among students in grades six to12): The estimates are calculated by using the Monte Carlo maximum likelihood method
Parameters(Coefficient on)
Constant
7th Grade
8th Grade
9th Grade10th Grade
11th Grade
12th Grade
Asian
Black
Hispanic
White Male
Asian Male
Black Male
Hispanic Male
Weekly Income
Working Dummy
Smokers in Home
See Actors Smoking in TV
See Actors Smoking in Movie
School Program 1
School Program 2
School Program 3
School Program 4
Cigarette Tax
Asymptotic standard errors are in parentheses.
33(1)xi β Specifications
(2)

(3)

-0.68177(3.69140)0.47755(0.08802)0.94492(0.08213)
0.98692(0.08437)
1.07936(0.08838)
1.07958(0.09053)
1.15153( 0.09397)-0.54672( 0.13176)-0.80229(0.07247)-0.39855(0.07055)-0.12576( 0.06984)
0.47027(0.17744)
0.24751(0.11557)
0.22300(0.10729)
0.02878(0.00231)
0.31798(0.04204)
0.96354(0.03308)
0.05762(0.04963)
0.05875(0.05656)-0.19903( 0.04626)-0.09634(0.04450)
0.14327(0.04733)-0.01018(0.04179)-0.23608( 0.09212)-0.03845(3.53725)
0.46843(0.08763)
0.93562(0.08088)
0.97299(0.08285)
1.06156(0.08718)
1.05034(0.08826)
1.13572(0.09157)-0.54873(0.12929)-0.80005(0.07182)-0.41438(0.06743)-0.14919(0.06733)
0.43158(0.17336)
0.20722(0.11408)
0.18893(0.10414)
0.02903(0.00224)
0.32408(0.04144)
0.96556(0.03181)
0.06059(0.04968)-0.20304(0.04410)-0.10557(0.03855)
0.16336(0.04570)-0.21771(0.08868)-0.87633(3.58852)
0.46602(0.08605)
0.93465(0.08058)
0.99142(0.08340)
1.07325(0.08789)
1.06054(0.08822)
1.15289(0.09232)-0.54734(0.12993)-0.79480(0.07200)-0.42327(0.06971)-0.13157(0.06944)
0.44862(0.17580)
0.27635(0.11248)
0.25128(0.10617)
0.02911(0.00226)
0.32637(0.04216)
0.96087(0.03222)
0.07542(0.04378)-0.18129(0.04499)-0.11811(0.03880)
0.14783(0.04590)-0.20983(0.08925)

TABLE 5. The estimated peer effects in the baseline model (smoking choices
among students in grades six to 12): The estimates are calculated by using
the Monte Carlo maximum likelihood method
Peer Effects(1)

xi β Specifications
(2)

ρM M

(3)

1.70269
1.66938
1.66987(0.20653)(0.19879)(0.20741)
ρF F
1.658281.73793
1.62800(0.20407)(0.19796)(0.20646)
ρM F
0.727500.74057
0.76848(0.16668)(0.16465)(0.17157)
Asymptotic standard errors are in parentheses.

34

TABLE 6. Distribution of Schools with Respect to Racial Composition:
Number of Schools in Each Category
Percentage of Each Race Group
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
White
48
29
16
15
17
22
29
25
38
79
Black
180
41
27
21
15
6
4
6
8
10
Hispanic 187
32
28
16
12
6
5
6
16
10

35

TABLE 7. Estimated raced-based peer effects (smoking choices among students in grades six to 12): The estimates are calculated by using the Monte
Carlo maximum likelihood method
Peer Effects(1)

xi β Specifications
(2)

ρW W

(3)

1.55833
1.58750
1.53104(0.20126)(0.19402)(0.20347)
ρBB
0.77466
0.797520.72025(0.36861)(0.36423)(0.36913)
ρHH
1.44520
1.39753
1.45932(0.36970)(0.35295)(0.35689)
ρW B
0.015680.03009-0.00037(0.25102)(0.25006)(0.25667)
ρW H
0.719630.756150.71113(0.27574)(0.26759)(0.28123)
ρBH
0.99595
0.947100.88158(0.33315)(0.33104)(0.34128)
Asymptotic standard errors are in parentheses.

36TABLE 8. The estimated coefficients of individual background characteristics in the model with fixed effects (smoking choices among students ingrades six to 12): The estimates are calculated by using the Monte Carlo
conditional maximum likelihood method
Parameters(Coefficient on)

xi β Specifications
(2)

(1)

(3)

Constant---

7th Grade

0.52662(0.09180)
1.01922(0.08510)
1.01244(0.09690)
1.19693(0.10006)
1.21891(0.10136)
1.31568(0.10745)-0.64295(0.14644)-0.90837(0.08222)-0.34677(0.07724)-0.13693(0.07756)
0.58284(0.19558)
0.25413(0.11848)
0.21696(0.11501)
0.03073(0.00242)
0.30452(0.04563)
0.96465(0.03522)
0.07796(0.05369)
0.05611(0.05931)-0.20497(0.04906)-0.07463(0.04742)
0.15234(0.04949)-0.03682(0.04494)-

0.52286(0.09025)
1.00826(0.08356)
0.98488(0.09490)
1.17840(0.09764)
1.19134(0.10007)
1.29056(0.10483)-0.63722(0.14265)-0.90505(0.07740)-0.35483(0.07665)-0.16880(0.07588)
0.52515(0.18740)
0.21341(0.11556)
0.16202(0.11355)
0.03055(0.00242)
0.31242(0.04442)
0.96668(0.03420)-

0.50752(0.09007)
0.99930(0.08502)
1.00323(0.09374)
1.17205(0.09762)
1.18839(0.09815)
1.29675(0.10376)-0.65163(0.14941)-0.89120(0.07982)-0.37839(0.07645)-0.12908(0.07682)
0.58495(0.19418)
0.30129(0.11746)
0.25584(0.11223)
0.03084(0.00241)0.31701(0.04414)
0.95985(0.03567)
0.09351(0.04759)-

8th Grade
9th Grade10th Grade
11th Grade
12th Grade
Asian
Black
Hispanic
White Male
Asian Male
Black Male
Hispanic Male
Weekly Income
Working Dummy
Smokers in Home
See Actors Smoking in TV
See Actors Smoking in Movie
School Program 1
School Program 2
School Program 3
School Program 4
Cigarette Tax
Asymptotic standard errors are in parentheses.
37

0.05994(0.05173)-0.20845(0.04788)-0.09275(0.04181)
0.15958(0.04791)--0.18925(0.04754)-0.10200(0.04177)
0.14387(0.04903)-

TABLE 9. The estimated coefficients of peer effects in the model with fixed
effects (smoking choices among students in grades six to 12): The estimates
are calculated by using the Monte Carlo conditional maximum likelihood
methodPeer Effects(1)

xi β Specifications
(2)

ρM M

(3)

1.52090
1.47377
1.54619(0.24665)(0.25002)(0.25164)
ρF F
1.48030
1.60347
1.46383(0.24326)(0.23562)(0.24089)
ρM F
0.52547
0.566420.58560(0.20739)(0.20826)(0.20620)
Asymptotic standard errors are in parentheses.

38TABLE 10. The estimated coefficients of race-based peer effects in the modelwith fixed effects (smoking choices among students in grades six to 12): The
estimates are calculated by using the Monte Carlo conditional maximum likelihood method
Peer Effects(1)

xi β Specifications
(2)

ρW W

(3)

1.49926
1.50204
1.47278(0.31725)(0.30838)(0.31973)
ρBB
0.781700.73457
0.63131(0.53012)(0.52385)(0.52662)
ρHH
0.51174
0.51186
0.58596(0.55511)(0.54107)(0.53320)
ρW B-0.18108-0.24148-0.25722(0.37773)(0.37937)(0.38538)
ρW H
0.29493
0.368710.30975(0.43672)(0.43398)(0.42431)
ρBH-0.44739-0.42444-0.48892(0.52332)(0.51826)(0.53077)
Asymptotic standard errors are in parentheses.

39TABLE 11. Simulated Smoking Prevalence Following Tax Increases

Predicted smoking rates
Estimated tax elasticities

Baseline
Simulation
18.94820
18.056
0.210

Hypothetical tax increases (cent)
40
60
80
100
17.223 16.407 15.65d 14.922
0.203 0.199
0.194 0.190

All values are computed from the average over 1000 experiments.
Tax elasticities are based on the average tax of 89.26 cent in sample.

40120
14.2130.199

TABLE 12. Decomposition of Tax Effects on Smoking PrevalenceType of effects
Total effects
Direct effects
Social multipliers

20-0.892-0.541
1.649

Hypothetical tax increases (cent)
40
60
80
100
120
-1.725 -2.540 -3.294 -4.026 -4.735-1.070 -1.600 -2.121 -2.614 -3.106
1.612 1.588 1.553 1.540 1.525

All values are computed from the average over 1000 experiments.
Social multiplier is defined by the ratio of total effect to direct effect.

41

TABLE 13. Simulated Smoking Prevalence Following Implementation of
School-based Smoking Program 1

Predicted smoking rates
Estimated elasticities

Baseline Hypothetical School Program increases (percent)Simulation
10
20
30
40
50
18.64018.078 17.924 17.522 17.172 16.813
0.082 0.052 0.054
0.053
0.053

All values are computed from the average over 1000 experiments.
Elasticities are based on the average school program of 27.04 percent in sample.

42

A PPENDIX D. A PPENDIX TABLES FOLLOWTABLE 14. the estimated coefficients of county characteristics in the modelwith fixed effects (smoking choices among students of 6-12th grades): The
estimates are calculated by the Monte Carlo maximum likelihood methods
Parameters(Coefficient on)
Persons 0-18
Persons 65+
Asian persons
Black persons
Hispanic persons
Single-mother families
One-person families
Persons with grandchildren
Persons who divorced
Unemployed workers
Workers with management job
Workers with professional job
Workers with construction job
Workers with farming job
Workers with sales and office job
Workers with service job
Persons below poverty level
Persons graduated high school
Persons graduated college(1)xi β Specifications
(2)

(3)

-0.00531(0.02280)
0.00251(0.00790)
0.00627(0.00530)
0.00327(0.00344)
0.00491(0.00223)
0.00550(0.01550)-0.02210(0.00882)-0.04468(0.02475)-0.01008(0.01431)
0.04817(0.01418)-0.01377(0.01210)-0.01541(0.01209)
0.01764(0.01191)-0.01132(0.01191)
0.00966(0.00844)
0.00188(0.00983)-0.00474(0.01062)-0.01024(0.00596)
0.01706(0.00769)-0.00856(0.02216)
0.00311(0.00768)
0.00618(0.00521)
0.00290(0.00334)
0.00575(0.00221)
0.01185(0.01373)-0.02406(0.00860)-0.04420(0.02395)-0.01058(0.01412)
0.04412(0.01388)-0.01315(0.01164)-0.01704(0.01188)
0.01721(0.01140)-0.01089(0.01141)
0.00675(0.00816)
0.00190(0.00931)-0.00575(0.01013)-0.01058(0.00580)
0.01802(0.00743)-0.00226(0.02218)
0.00332(0.00787)
0.00655(0.00525)
0.00356(0.00341)
0.00531(0.00222)
0.00581(0.01518)-0.02212(0.00873)-0.04561(0.02453)-0.00903(0.01425)
0.04669(0.01400)-0.01367(0.01160)-0.01614(0.01180)0.01608(0.01161)-0.01188(0.01178)
0.00829(0.00814)
0.00129(0.00957)-0.00318(0.01028)-0.00911(0.00595)
0.01838(0.00746)(continued on next page)
Asymptotic standard errors are in parentheses.

43Parameters(Coefficient on)(1)

xi β Specifications
(2)

(3)

(continued from previous page)
Persons enrolled in public schools

0.00192(0.00391)-0.02973(0.03017)-0.00853(0.01254)
0.07041(0.05416)
0.02012(0.01215)
0.01126(0.01091)-0.03224(0.01757)-0.01254(0.00362)
0.35930(0.38911)-0.31850(0.09055)-0.00103(0.00264)-0.00305(0.00272)-0.00385(0.00136)-0.01649(0.01373)
0.00732(0.01442)
0.18146(0.16581)

Persons enrolled in high schools
Persons enrolled in colleges
Persons enrolled in graduate schools
Persons in armed forces
Persons in veteran status
Persons imigrated from foreign countries
Persons moved in last 5 years
Median household income
Median housing value
Vacant housing units
Private vehicles occupacy
Urban area rate
Crime index
Juvenile crime
Juveniles crime (drug abuse)
Asymptotic standard errors are in parentheses.

44

0.00112(0.00376)-0.02786(0.02911)-0.00784(0.01204)
0.06842(0.05306)
0.01924(0.01184)
0.01234(0.01049)-0.03264(0.01680)-0.01212(0.00346)
0.31293(0.37372)-0.30472(0.08617)-0.00402(0.00129)-0.00181(0.00258)-0.00315(0.00257)-0.01675(0.01334)
0.00668(0.01397)
0.19590(0.16016)

0.00196(0.00391)-0.03177(0.02927)-0.00872(0.01206)
0.06650(0.05368)
0.01878(0.01196)
0.01312(0.01089)-0.03157(0.01691)-0.01241(0.00350)
0.36120(0.37826)-0.31418(0.08860)-0.00249(0.00271)-0.00102(0.00260)-0.00384(0.00128)-0.01898(0.01386)
0.00880(0.01427)
0.18956(0.16496)