Peer Effects and Selection Effects on Smoking among Canadian Youth

Peer Effects and Selection Effects on Smoking among Canadian YouthAuthor(s): Brian V. KrauthSource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 38, No. 3(Aug., 2005), pp. 735-757Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/3696056 .

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Peer effects and selection effects on

smoking among Canadian youth Brian V. Krauth Department of Economics, Simon Fraser

University

Abstract. A number of studies have indicated that peer smoking is a highly influential factor in a young person's decision to smoke. However, this finding is suspect, because the studies often fail to account for selection and simultaneity bias. This paper develops an econometric model of youth smoking that incorporates both peer effects and selection effects. Identification is achieved by using the degree of selection on observables as a proxy for the degree of selection on unobservables. The results indicate that peers have some influence on a young person's decision to smoke, but that influence is much weaker than is suggested by reduced form models. JEL classification: C35, 112

Effets des pairs et effets de selection sur la decision de fumer des jeunes au Canada. Un nombre d'etudes ont montr6 que le fait que les pairs fument est un facteur tres important dans la decision de fumer d'une jeune personne. Cependant ce r6sultat pose probleme parce que ces 6tudes ne prennent souvent pas en compte les biais de selection et de simultaneit6. Ce m6moire developpe un modele 6conometrique du comportement de fumeur chez les jeunes qui incorpore i la fois les effets des pairs et les effets de s6lection. On arrive i une identification en utilisant le degr6 de selection sur les sujets observables comme mesure approximative du degre de selection des sujets non-observables. Les r6sultats indiquent que les pairs ont une certaine influence sur la decision de fumer d'une jeune personne mais que cette influence est bien plus faible que ce que suggerent les modeles de forme r6duite.

This paper has benefited by comments from two anonymous referees, Stephen Coate, Kevin Milligan, Phil Oreopoulos, Lisa Powell, and Anindya Sen, as well as seminar participants at SFU, the 2003 CEA meetings, the 2003 Canadian Public Economics Group meetings, the 2003 Society for Computational Economics meetings, and the 2003 North American Summer meetings of the Econometric Society. All errors are mine. Email: [email protected]

Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 38, No. 3 August / aofit 2005. Printed in Canada / Imprime au Canada

0008-4085 / 05 / 735-757 / ? Canadian Economics Association



736 B.V. Krauth

1. Introduction

Youth smoking is a major public health concern in much of the world. The World Health Organization (Mackay and Eriksen 2002, 36) estimates that 4.2 million individuals die every year from smoking-related conditions. Health Canada (2002) estimates that over 45,000 Canadians die from smoking every year, and that the social cost to Canadians from tobacco use is over $15 billion per year. As a result, governments often spend large sums on programs to reduce tobacco use. For example, in 2001 the federal government of Canada instituted the Federal Tobacco Control Strategy, a program with a budget of $500 million over its first five years. Because tobacco is highly addictive and most smokers begin when they are teenagers (Mackay and Eriksen 2002, 28), such tobacco control efforts are primarily focused on discouraging young people from starting to smoke. The research literature on tobacco control has a similar focus on youth. Research using behavioural data has generally found that peers are highly influential in the decision of a young person to smoke (Mackay and Eriksen 2002; Tyas and Pederson 1998); as a result, attempts to alter the social context of youth smoking represent a 'major component of the Canadian government's efforts to reduce tobacco use' (Mintz et al. 1997). Because they represent an externality, peer effects may also be used to justify increased tobacco control efforts. For example, Kenkel, Reed, and Wang (2002) calibrate a rational addiction model of lifetime tobacco use and find that the optimal tobacco tax increases by over 50% when peer effects are included. In spite of the apparent consensus, the influence of peers in youth smoking is far from well established. Most empirical studies in the literature fail to account for both endogenous peer selection and the simultaneity of choice among peers, both of which may lead a researcher to dramatically overestimate the strength of peer influence (Manski 1993).

This paper uses data from Health Canada's 1994 Youth Smoking Survey (YSS) (Stephens and Morin 1996) to estimate the strength of peer influence in smoking among Canadian youth. I use a simulation-based structural estimation method developed in Krauth (2005a) which explicitly allows for both endogenous peer selection and simultaneity of choice. The structural estimator addresses simultaneity by treating the group outcome as an endogenous variable, and addresses selection by explicitly allowing correlation in unobservables between peers. The model is non-parametrically identified by assuming equal correlation in observable and unobservable characteristics. In addition, informative bounds can be placed on the strength of the peer effect under substantially weaker assumptions. As discussed in section 1.1, below, this structural approach is complementary to recent attempts to measure peer effects in youth smoking using instrumental variables (Gaviria and Raphael 2001; Norton, Lindrooth, and Ennett 1998) or panel data methods (Engels et al. 1997; Wang, Eddy, and Fitzhugh 2000) and has some significant advantages over these other approaches.



Peer effects and selection effects 737

The empirical results reported in this paper indicate that peers are influential but not as influential as would be suggested by a 'naive' probit model that treats peer smoking as an exogenous regressor. The naive estimates indicate a very strong peer effect: the probability of smoking for a representative individual with five close friends increases by 15 percentage points in response to one friend becoming a smoker. Point estimates for the structural model imply a much lower but still positive peer effect; the representative individual's probability of smoking increases by 5 percentage points in response to one friend becoming a smoker. The interval estimates reported in the paper indicate that this finding is not highly sensitive to moderate violations of the identifying assumption. Accounting for peer selection and simultaneity thus reduces but does not eliminate the apparent influence of peers on youth smoking.

1.1. Related literature Because of the addictive nature of smoking, much of the research into the determinants of smoking behaviour deals with youth smoking. Among adults, the strongest predictor of current smoking is smoking as a young person. For example, Gruber and Zinman (2001) find that 75% of adult current or former smokers began before their 19th birthday. The literature on youth smoking has found a number of variables that are closely associated with a young person's smoking behaviour in multiple surveys. These variables include parental or sibling smoking, performance in school, race and ethnicity, and prices (Gruber and Zinman 2001), though DeCicca, Kenkel, and Mathios (2002) argue that the common finding of a high price elasticity of youth smoking is an artefact of correlation between prices and unobserved local factors. Peer smoking is also, in the words of a recent review article, 'consistently found to be related to smoking initiation, maintenance, and intentions' (Tyas and Pederson 1998). However, the finding of a close statistical association between peer smoking and a respondent's own smoking does not necessarily imply a causal relationship. Indeed, as Manski (1993) notes for studies of peer effects in general, selection and simultaneity imply that the statistical association may dramatically overstate the strength of any causal relationship. While this issue has been known for some time, it is only recently that empirical studies of youth smoking that attempt to account for selection and simultaneity have appeared. These studies have used either instrumental variables or panel data methods.

In the public health literature, concern with selection issues has been addressed mostly using panel data. These papers (e.g., Engels et al. 1997, Wang, Eddy, and Fitzhugh 2000) do not usually use regression-based econometric analysis, but rather, they ask whether smoking tends to precede or follow membership in a peer group of smokers. If membership in a peer group of smokers predicts transition into smoking, this is interpreted as evidence for a peer effect. If smoking predicts transition into a higher-smoking peer group, this is interpreted as evidence for a selection effect. They note that initial smoking appears to be associated with subsequent moves into a



738 B.V. Krauth

higher-smoking peer group, but initial membership in a higher-smoking peer group is not strongly associated with initial non-smokers becoming smokers. This result is generally taken to mean that correlation in smoking among peers is caused primarily by selection effects, not by peer effects. However, these results are somewhat weakened by the absence of a formal model of youth decision making. For example, if peer effects operate without a significant lag, current behaviour of group members may not be strongly associated with future changes in group behaviour even if peers are highly influential. While the results from these longitudinal studies provide some evidence for selection, they may actually have little to say about the strength of peer influence.

In the economics literature, the dominant approach uses peer group characteristics to instrument for the endogenous average peer choice. This approach produces consistent estimates under simple but strong assumptions. First, the usual validity requirement implies that the instruments can have no direct impact on the individual's probability of smoking, only an indirect effect through their impact on the smoking of the individual's peers. In this context this condition imposes particularly strong restrictions on the set of acceptable instruments: only group-level averages of the individual-level variables already in the regression can be used and even then only (Brock and Durlauf 2000) if there is no direct behavioural effect of the characteristics of an individual's peers (in the language of the literature, if there are no 'contextual effects'). It should be noted that while this restriction is followed by some researchers (Gaviria and Raphael 2001), others (Norton, Lindrooth, and Ennett 1998; Powell, Tauras, and Ross 2003) have used group characteristics (for example, population density of the neigh- bourhood the group lives in) that cannot in principle be valid instruments - if they have a direct impact on the group's average behaviour, they must have a corresponding direct impact on the behaviour of individual group members. A second assumption made in these studies, and one that has not previously been emphasized, is that the generally non-linear individual-level discrete choice model somehow aggregates into a linear group-level relationship between average peer smoking and average peer characteristics. This approach is internally consistent only if individual behaviour follows the unrestricted linear probability model (LPM). Gaviria and Raphael use the LPM for the individual-level regression, accepting a somewhat unappealing individual-level model as the cost of internal consistency, while Norton, Lindrooth, and Ennett and Powell, Tauras, and Ross assume a linear aggregate model and a non-linear (probit) individual model, sacrificing internal consistency for a more appealing individual-level model.

The structural approach pursued in this paper shares two important assumptions with the IV approach: absence of contextual effects, and absence of correlation between an individual's unobservable characteristics and the observable characteristics of peers. The remaining two identifying assumptions described in this paper - an equilibrium selection rule and equal within-peer- group correlation in observable and unobservable characteristics - in a sense are substitutes for the IV studies' assumption of a linear aggregate relationship,




TABLE 1 Summary statistics for YSS data, 9,210 observations

Variable Mean Std. Dev.

Current smoker 0.231 0.421 Number of friends 6.140 2.804 Fraction of friends smoking 0.425 0.368 Age on 1/1/94 16.815 1.406 Attending school 0.851 0.356 Performs above average in school 0.287 0.453 Performs below average in school 0.032 0.177 Number of smokers in house 0.828 1.038 Has seen ads for tobacco-sponsored events 0.463 0.487

as they are needed for identification once consistent aggregation is taken seriously. Because the IV and structural methods share some identifying assumptions, and each has plausible but arguable additional assumptions, these approaches can be viewed as complementary. Although the structural approach to measuring peer effects in youth behaviour is fairly novel, there is a recently growing literature in econometrics on empirical models of binary games. Kooreman (1994) and Tamer (2003) develop econometric models of interdependent binary choice for the special case with two group members and no selection effect. Krauth (2005a) and Kooreman and Soetevent (2002) extend this approach to an arbitrary group size and incorporate inter-peer correlation in characteristics (i.e., peer selection). The primary advantages of the structural approach are that it generates quantitative behavioural predictions more directly than the panel data approach, and that it allows for more flexibility in the choice of identifying assumptions than the IV method.

2. Data

The primary data source is the 1994 Youth Smoking Survey (YSS), a national survey of Canadian youth aged 10-19. Summary statistics for the YSS data, with cleaning and imputations as described below, are reported in table 1. In addition to information on a respondent's smoking behaviour and that of his or her peers, the YSS also reports several potentially relevant demographic and environmental factors, including province of residence. Information on province of residence is critical, because many important policies such as tax rates and restrictions on access or usage vary across provinces. The YSS is divided into two components: a school-based sample of 10-14-year-olds, and a household-based sample of 15-19-year-olds. I restrict attention to the household sample, which has 9,491 observations. Of these, 281 observations are dropped because the respondent reports having no friends or fails to report his or her own smoking behaviour or friends' smoking behaviour, leaving 9,210 observations to be used in estimation. For all other variables, missing values are



740 B.V. Krauth

replaced with the sample mean. This imputation affects a total of 430 observations (419 for the 'seen ads ...' variable and 13 for the '# smoking in household' variable). To verify that this handling of missing data does not drive any of the results, the basic regressions reported in this paper were re-estimated (1) with a specification that also included a binary variable indicating whether any imputations had been made on the observation, and (2) with a data set in which these 430 observations had been dropped. Both of these alternative methods yielded almost no change in parameter estimates.

The econometric model has two endogenous variables: a binary variable indicating whether the respondent is a current smoker and a discrete variable indicating the fraction of the respondent's close friends that smoke. In keeping with the conventional definition in the smoking literature, a 'current smoker' is defined as an individual who reports smoking at least one cigarette in the past 30 days and over 100 cigarettes in his or her lifetime. In addition to being asked about his or her own smoking, each respondent is asked both how many close friends he or she has and how many of them smoke. Respondents can claim up to 95 close friends. To keep the computational cost of the estimator reasonable, those respondents who claim more than 6 close friends are coded as having 6 close friends, and the fraction of their close friends who smoke is rounded to the nearest sixth. For example, if a person identifies 10 close friends, 7 of whom smoke, this is recoded as having 6 close friends and (6"7/10) = 4.2

, 4 close

friends who smoke. This recoding affects 3,405 observations. Note that the YSS is based on a stratified random sample of individual

youth, rather than on a group-based sample. This has two implications that complicate estimation of the model. First, we observe only the characteristics of the respondent, not those of his or her peers. With a group-based sample (for example, a survey of all students in a random sample of Canadian secondary schools), the within-peer-group correlation in characteristics could be estimated directly. With an individual-based sample like the YSS, this correlation is still non-parametrically identified, as discussed in section 3.4, below, but identification is less direct. The second issue created by the use of an individual-based sample is that there is no assurance that a respondent's own smoking and that of his or her peers are reported consistently. In particular, the average self-reported smoking rate of YSS respondents (23.1%) is substantially lower than the rate of smoking they report for their friends (42.5%). This is most likely due to a combination of smokers' falsely self-identifying as non- smokers and respondents overestimating the smoking rate of peers. This inconsistent reporting must be accounted for in the structural econometric model. Section 3.5 discusses this study's treatment of inconsistent reporting.

3. Model

The econometric model is similar in spirit to the standard model of discrete choice with social interaction effects due to Brock and Durlauf (2001). Both




the model and estimation method are described in greater detail in Krauth (2005a).

3.1. Preferences and peer groups In the model, each individual is a member of a peer group. Peer groups are indexed by g E Z+, and group g has ng > 2 members, where ng is exogenous and may vary across groups. Within each peer group, individuals are indexed by i, so that the pair i,g identifies an individual. Each member of a given peer group is influenced symmetrically by each other member, and there are no cross-group influences.

Individuals choose either to smoke (si,g = 1) or not (si, = 0). An individual's utility function ui,g(s,g) satisfies the following:

ui,g (l) - Ui,g(O) = a + Xi,g + AZg + 'YSi,g + Ei,g, (1)

where xi,g is a vector of individual-level exogenous variables (e.g., ethnicity, sex, parental and sibling behaviour, disposable income), z, is a vector of group- level exogenous variables (e.g., prices, school characteristics, or aggregate fixed effects), si, is the fraction of the other group members that smoke:

__ 1

S•i,g =

ng- 1 (2)

and 6i, is an unobserved individual-level term. The yig term is an 'endogenous peer effect,' in the terminology of Manski (1993); otherwise this is a standard discrete choice model of youth smoking. Note that the model does not include what are known as 'contextual effects,' in which the characteristics (as opposed to smoking behaviour) of one's peers have a direct effect on the net utility benefit from smoking. Since Manski (1993) pointed out the difficulties in doing so, empirical researchers rarely attempt to simultaneously estimate endogenous effects and contextual effects. It is more common (e.g., Gaviria and Raphael 2001; Hoxby 2000; Sacerdote 2001) to simply ignore one or the other and note that the estimated endogenous (contextual) effect could be reinterpreted as contextual (endogenous). That caveat applies to this article as well. An individual will prefer to smoke (st,g = 1) if and only if his or her incremental utility from doing so is positive. However, because this incremental utility depends in part on the average choice of peers (ig), predictions on the behaviour of individuals cannot be derived in isolation. Instead, it is necessary to analyse equilibrium behaviour.

3.2. Equilibrium The equilibrium concept used is Nash, supplemented with a selection rule to deal with multiplicity of Nash equilibria. Given the exogenous variables, the endogenous variables are given by a Nash equilibrium in pure strategies of a complete information simultaneous move game, where player i,g's strategy is given by si,g and his or her payoff function is described by equation (1). For a non-empty set of realizations for the exogenous variables, there are multiple Nash equilibria. That set has



742 B.V. Krauth

(probability or Lebesgue) measure zero for y = 0, positive measure for y > 0, and grows as y increases (Krauth 2005b). As a result, an equilibrium selection rule must be imposed to pin down a unique likelihood function for the data. The importance of correctly specifying the selection rule depends on y; when 7 is close to zero, all selection rules imply similar behaviour because Nash equilibrium is almost always unique. Misspecification in the equilibrium selection rule will have little effect on distinguishing between 'no peer effect' and 'some peer effect' but may lead to inconsistent estimates of the magnitude of a given peer effect (Krauth 2005a).

The selection rule chosen for this study is the 'low-activity' equilibrium: each group plays the Nash equilibrium which has the fewest smokers. This selection rule is chosen because it corresponds to the steady state of the myopic best-reply dynamics reached when agents start as non-smokers. Given that young people are born as non-smokers, such dynamics may be a reasonable approximation to youth behaviour, provided that quitting is rare. Although there is some debate in the literature over whether smoking cessation programs can be effective for youth, the consensus remains that teen smokers rarely independently quit while still teenagers (Sussman et al. 1998). In the YSS data, over 90% of those who have smoked 100 or more cigarettes in their lifetime are current smokers at the time of the survey.

3.3. Peer selection and correlation in characteristics As indicated in the introduction, the model estimated in this paper allows for the likelihood that a young person's choice of friends is not entirely random. This is done by incorporating a reduced-form correlation in observable characteristics and in unobservable characteristics across members of the same peer group. That is, the exogenous variables are identically distributed across all individuals in the population, and are independent across members of different peer groups but are not independent across members of the same peer group. Although it might be desirable to formally model the process of selecting one's peer group, estimating such a model would require substantially more detail on group composition than is available in the YSS or many other data sets.

The details are as follows. The joint distribution of the individual-level exogenous variables is assumed to be multivariate normal across the group members. For a group of size ng = 3, the exogenous observable characteristics

xi,g and the exogenous unobservable characteristics e,g:

fX1,g ( / -

"2 px Px 0 0 0 \ 3X2,g I

px02 2 pxx02 0 0 0

/X3,g

,oN

Px0 Px2 02 0 0 (3) NN (3) l,g 0 ' 0 0 0 1 pc p '

C2,g 0 0 0 0 p, 1 p J E3,g \ 0 0 0 p, p, 1 /

where the parameter vector p/3 reflects the marginal impact of the xi,g variables on the incremental utility from smoking, the parameter px is the between-peer




correlation in (a P3-weighted sum of) observable characteristics, the parameter 02 is the individual-level variance in the /-weighted sum of observable characteristics, and the parameter p6 is the between-peer correlation in the unobservable characteristics. Equation (3) is written for ng= 3; the distribution is defined analogously for other values of ng.

Equation (3) defines a probability distribution with several useful characteristics. First, with the exception of the dependence across peers, the distribution corresponds to that in a standard probit model. In particular, for each individual, the conditional distribution of unobservables has Ei.glXig N(0,1). Unlike a standard probit model, this model allows for correlation in both observable characteristics (Px) and unobservable characteristics (p6) across group members, as would occur when young people are prone to selecting friends who are similar to themselves. The 'naive' analysis pursued in much of the literature on peer effects implicitly assumes that random selection of peers (p, = px = 0).

Because of the strong functional form assumptions, the model is almost certainly identified without further restrictions. As discussed in section 3.4, non-parametric identification requires a restriction on p,, the between-peer correlation in unobservables. The primary restriction used in this paper is that the correlation is the same as the correlation in observables; that is, p6 = px. The idea of selection on observables to construct a proxy for selection on unobservables was first proposed by Altonji, Elder, and Taber (2005) to correct for selection bias in measuring the effect of attending a Catholic school. These authors demonstrate that equality in these two correlations will hold (in expectation) if the observables are a random subset of a large set of relevant variables. Alternatively, if the observed variables are more highly correlated between peers than are the unobserved variables, the equal- correlation point estimate of the peer effect will be biased downwards. This is a distinct possibility, as personal information that is particularly easily gathered in surveys (race, sex, age) may also be more easily observed by potential friends. In any case, the model can also be estimated under alternative restrictions on p6, including interval restrictions. As a result, the results reported in this paper allow readers with different beliefs about the selection process to construct their own range of estimates consistent with both the data and their prior beliefs.

3.4. Identification One potential concern in the estimation of complex non-linear structural models is how the parameters are identified from the data. This section provides a brief heuristic discussion of nonparametric identification of the model from individual-based survey data. The argument is a condensed version of one provided in Krauth (2005a).

The key to identification is the treatment of both own choice and peer choice as endogenous variables. Consider the conditional expectation functions

E(Si,glXi,g, Zg, Si,g) and E(SiglXig, Zg, Si,g), both of which are identified in the YSS data. The parameter (vector) /3 is identified because &E(si,g Xi,g, Zg, Si,g)/&Xi,g is increasing in /3, and the parameter (vector) A is identified because



744 B.V. Krauth

&E(SglXi,g, Zg, Si,g)/aZg is increasing in A. Identification of the peer effect 7 and the selection effect p, is more complex. First, note that dE(si,gJXi,g, Zg, Si,g)/&Si,g is increasing in both

, and p6. In other words, within-group similarity in

behaviour can be explained either by peer effects (high ~y) or by within-group similarity in unobserved characteristics (high p6). However, note that

OE(si,glxi,g, Zg, si,g)/Xi,g is increasing in Px but not increasing in y. Combined with the equal-correlation assumption, this provides a route to identification:

OE(Si,glxi,g, Zg, si,g)/Xi,g is used to identify px (and thus p6, because of the equal- correlation assumption), then OE(si,gxi,g, Zg,

Si,g)/si,g is used to identify -y. To

place the argument in more concrete terms, both high correlation in characteristics and strong peer effects imply that smokers are more likely to have friends who smoke than non-smokers. Only high correlation in characteristics, however, implies that among smokers, those who have the observable characteristics of a likely smoker (e.g., parents who smoke) are more likely to have friends who smoke than those who do not have such characteristics.

3.5. Actual smoking and reported smoking The YSS data exhibit clear signs of inaccurate reporting on smoking of respondents and/or their friends: 23.1% of respondents are self-identified as current smokers, whereas 42.5% of their friends are identified as smokers. Given that the respondents and friends are drawn from the same population, this difference is likely caused by some combination of respondents underreporting their own smoking and/or overreporting that of their peers. This is a known issue in the youth smoking literature, but is of particular relevance in this paper because the basic structural model is inconsistent with differential smoking rates between respondents and their peers. Norton, Lindrooth, and Ennett (2003) provide a recent discussion of the main issues in misreporting of smoking behaviour by youth. First, despite efforts by survey collectors to emphasize and ensure confidentiality, young people tend to systematically underreport their own smoking. Audit studies compare self-reported smoking with breath or saliva tests and usually find substantial underreporting among youth (Wagenknecht et al. 1992). Second, young people also tend to overestimate the extent to which their peers smoke. Smokers have a particularly high propensity to overestimate the fraction of their peers who smoke, an example of what psychologists call the 'false consensus' effect.

In order to close the model and have a well-defined likelihood function it is necessary to explicitly model the connection between actual behaviour and reported behaviour. Unfortunately, the data provide limited information on this connection. In the light of these limitations, the model of reporting behaviour used here is quite simple. First, it is assumed that peer smoking is reported truthfully. Second, it is assumed that smokers falsely report as non-smokers with a fixed probability Pr. Let ri,g indicate whether a person self-reports as a smoker. Then:

Si,g with probability Pr ri'g

0 with probability 1 - p,' (4)




where Pr is a parameter. Note that conditional on si,, r,, is independent of all other variables, and that

E(ri,g) (5) p, (5) PrE(Sig)

The parameter Pr can thus be estimated using the sample analogue to this expression.

The assumption that all inconsistency in reporting is the result of random underreporting of one's own smoking is debatable and is not testable using the YSS data. Ultimately, the solution to this problem is to gather better data, but some sensitivity analysis can provide a rough guide to the robustness of the conclusions in this paper to the specification of the reporting process. The two main concerns are that reporting rates may vary with observable characteristics or outcomes, and that the difference between self-reported smoking and reported peer smoking may actually be due to respondents' overreporting the smoking of their peers rather than underreporting their own smoking. To address the first concern, the structural model has been estimated allowing Pr to be a function of z, (i.e., reporting rates vary by province). The results are nearly identical to those obtained from the baseline model with homogeneous reporting rates. It would also be nice to allow reporting rates to vary with the individual-level variables (xig), but such a model is not identified from the YSS data.

To address the second concern, I have constructed a set of simple Monte Carlo experiments reported in table 2. In each these experiments, 100 simulated data sets are created, each with 1000 individual-level observations from the structural model described in this section and with parameter values set as in Krauth (2005a). Specifically, there are five members in each peer group, a = 0,

xi,g is a N(0,1) scalar variable, f = 1, and there is no aggregate variable (zg). The peer effect y and the selection effect p Px = P, vary across experiments, as does the reporting behaviour of individuals. Three cases of reporting behaviour are considered: truthful reporting of both own and peer smoking, 50% underreporting of own smoking, and 50% overreporting of peer smoking. With each simulated data set, the structural model is estimated twice, once with the 'underreporting-corrected' version of the model used in this paper and once with the uncorrected version (which assumes truthful reporting). The results in table 2 show that, while the underreporting-corrected estimator has some degree of bias when applied to data that feature overreporting of peer smoking rather than underreporting of own smoking, it still performs much better than the uncorrected estimator.

4. Estimation

Given the model outlined in section 3, this section describes how the model is estimated using the YSS data. Let N be the number of observations in the data.



746 B.V. Krauth

TABLE 2 Average results across 100 Monte Carlo simulations of model under different reporting schemes and estimation methods

Parameter values Avg - in simulations

Case p 7 Corrected for underreporting Uncorrected

Accurate reporting 0.25 0.0 0.075 0.056 0.25 0.5 0.543 0.499 0.00 1.0 1.014 0.982

50% of smokers 0.25 0.0 0.008 0.000 self-identify 0.25 0.5 0.499 0.000 as non-smokers 0.00 1.0 1.004 0.234

50% of nonsmokers 0.25 0.0 0.158 0.000 identified by peers 0.25 0.5 0.516 0.023 as smokers 0.00 1.0 1.047 0.528

NOTE: Parameter values not described in the table correspond to those in the 'baseline' case in Krauth (2005a).

Because the YSS is a household-based random sample from a large population, it can be assumed that each observation represents a member of a different peer group. Without loss of generality, let the gth observation in the data set be identified as describing person 1 of group g.

4.1. Naive estimator The naive estimator is simply a standard maximum likelihood probit estimator that treats average peer behaviour s as an exogenous variable. Note that since s is not exogenous, this estimator is not consistent. Two naive estimators are reported: a 'basic' estimator and an 'underreporting-corrected' estimator. Both use standard maximum likelihood methods to estimate a variation on the standard probit equation:

Pr (rl,g = lxl,g,zgS,g) = p,•(a

+ -x-,g

+ Azg + Y's,g), (6)

where 1 is the CDF for the standard normal distribution, and all right-hand- side variables are treated as exogenous. The basic naive estimator is calculated by estimating (6) under the restriction Pr = 1 (so that (6) reduces to the usual probit equation), while the underreporting-corrected naive estimator is calculated by estimating (6) with p, = (~N lr1,g)/(CN lSl,g).

The remaining coefficients are estimated by maximum likelihood.

Because the two naive models and the structural models do not have identical functional forms, comparison in magnitude of coefficient estimates across the models should be performed with care. The appropriate comparison would be of approximate marginal effects for a representative individual on the probability of being a self-reported smoker. For simplicity let the representative individual be a hypothetical person who has observable characteristics




such that Pr(rl,g = 1lx,g, Zgsi,g) is equal to the rate of self-reported smoking in the population. Denoting that rate by r, differentiating equation (6) implies that the marginal effect of xl,g is given by pr (-l'(r/pr))3. The tables of results in section 5 report coefficient estimates as well as the factor by which they can be multiplied to generate marginal effects.

4.2. Structural estimator: point estimates The structural model described in section 3 is estimated by the simulated maximum likelihood (SML) method developed in Krauth (2005a). The vector of parameters to be estimated is

SE- (p,,a,',,YL,o',Px,P~). (7)

Observations are indexed by g; observation g in the data set is treated as describing person 1 in group g. For each observation, the GHK simulator (Hajivassiliou, McFadden, and Ruud 1996) is used to estimate the conditional likelihood Pr(rl,g, sl,glXl,g, z,; 0). This approximate conditional likelihood is then logged and added up across all observations to give

N

L(0) -Z In Pr(rlgSl,g

1,g g) (8) g= 1

where Plr is the simulation-based estimate of the true probability Pr, and 1(0) is thus a simulation-based estimate of the true log-likelihood function L(O). The parameter vector 0 is then chosen to maximize the conditional log-likelihood subject to the restrictions:

( -1

,P (maxg (ng) (9)

S>O 0 (10)

Pc = Px. (11)

Restriction (9) ensures that the peer group covariance matrix is positive defi- nite. The non-negativity constraint on the peer effect in restriction (10) is necessary for computational purposes; this constraint does not bind for this particular data set. However, it should be noted that if y is exactly zero, the bootstrap method used to estimate the covariance matrix of estimates is inconsistent (Andrews 2000), and the t-statistic for y has a non-standard asymptotic distribution. As a result, significance tests for y are not performed in this paper. Finally, equation (11) gives the equal-correlation restriction discussed in section 3.3.

Krauth (2005a) describes the estimation method and its properties in detail and reports the outcome of various Monte Carlo experiments. Relevant results in that paper include:



748 B.V. Krauth

1. If the model is correctly specified, the structural estimator of the peer effect is consistent and has much lower bias than the naive probit estimator.

2. Although the structural model assumes that the explanatory variables are normally distributed, deviations from normality (including discrete or binary explanatory variables) do not have a substantial effect on parameter estimates. This is important here because the explanatory variables in the YSS are all discrete.

3. The equilibrium selection rule has no effect on parameter estimates when the peer effect is zero; in that case equilibrium is always unique. The potential bias due to an incorrectly specified equilibrium selection rule increases gradually in the strength of the peer effect. In this application, that implies the finding that there is a substantial peer effect would be robust to alternative selection rules, though the magnitude of the effect may be somewhat under- or overestimated if the selection rule is misspecified.

4. The variance of the estimator depends strongly and negatively on the explanatory power of the individual-level observables. This explanatory power can be characterized by a pseudo-R2 statistic

(0"2(Xi;,g)/2(/Xi,g -Zg Eig)).

When the observables have strong explanatory power, the peer effect will be more precisely estimated. In this application, the explanatory power of the observables is sufficient to achieve a reasonable degree of precision in the estimated peer effect, as indicated by the estimated standard error.

4.3. Structural estimator: interval estimates As the equal-correlation assumption (11) reflects a strong restriction on the model, one might also wish to explore the effect of alternative or weaker restrictions. While some sort of restriction on p, is needed for non-parametric point identification, it is possible to place informative bounds on the peer effect under interval restrictions on p,.

Bounds on the peer effect are constructed as follows. Choose some arbitrary P E [0,1). Estimate the model, replacing the equal-correlation restriction (11) with the restriction:

Pc = P. (12)

Define the function -((P) as the point estimate of the peer effect 7 under the restriction (p, = P). This function can then be used to construct bounds on the peer effect. Let [Po,P1] be an arbitrary closed subinterval of [0,1). Then:

Pc E [Poi] = E [ min -(P), max

s(P)]. (13) p• ? [PoP,] == "#

[Pe[PoP,

PG olPG [PoPi

The bounds defined in such a way are consistent and efficient (Krauth 2002). Because the selection of a plausible interval restriction on p8 is a subjective




matter, in presenting results I report values for the function -(p,) at several points and leave the reader to apply the formula (13). It should be noted that it is possible to calculate values of -$(P) only at a finite number of points in the interval, implying that the true minimum or maximum may not be found. However, the theorem of the maximum implies that -(P) is continuous, implying that checking a sufficiently fine grid of points in the interval will yield a reasonable approximation to the true minimum and maximum. In addition, experience with the estimator suggests that -j(P) is strictly decreasing, though that conjecture is more difficult to prove. If true, this would imply one only needs to calculate

"(Po) and

"(P1) to place bounds on 7y.

Another alternative to interval estimation is to estimate both Px and p, under the restriction

,= 0 (14)

in place of (11). The resulting estimates answer the question, 'How high does the within-group correlation in unobservables need to be to explain the observed within-group correlation in behavior without peer effects?'

5. Results

Table 3 reports point estimates using both naive and structural estimators. Estimated standard errors are calculated for the naive estimators using the standard asymptotic approximation, and calculated for the structural model using the simple bootstrap with 200 replications. Province-level fixed effects are also included in all regressions, but are omitted from the tables. These fixed effects control for variations in cigarette prices, taxes, and availability across jurisdictions, as well as possible cultural or environmental differences between provinces. The fixed effects are treated as aggregate variables (z, in the model), while all other characteristics are treated as individual-level variables (xi,g in the model). All coefficients are reported as defined in the model rather than in terms of marginal effects, so each column also reports a 'Factor for marginal effects,' calculated as described in section 4.1. Multiplying a coefficient by this factor yields the estimated marginal effect of the associated variable for a representative individual (in this case, defined to be an individual with characteristics implying a conditional probability of smoking equal to the population mean). Table 3 also reports a pseudo-R2 measure for the structural model that characterizes the explanatory power of the individual-level variables. As noted in section 4.2, precise estimation of the peer effect in the structural model depends on the explanatory power of the individual-level variables.

As the table shows, all three models yield results for the effect of non-peer influences which are consistent with those commonly seen in the literature. Older youth, youth who are no longer attending school, and youth who are not doing well in school are noticeably more likely to smoke. The presence of smokers in the household is a particularly strong predictor of youth smoking:



750 B.V. Krauth

TABLE 3 Point estimates for both naive and structural models

Variable Naive probit Naive with underreporting Structural model

Reporting rate (Pr) 1.000 0.543 0.543 - (0.009) (0.009)

Selection effect (Px, pe) - - 0.237

- - (0.068) Peer effect (7) 2.240 3.626 1.255

(0.055) (0.119) (0.270) Age on 1/1/94 0.091 0.164 0.101

(0.014) (0.025) (0.028) Attending school -0.328 -0.517 -0.587

(0.051) (0.100) (0.100) Above avg in school -0.192 -0.297 -0.551

(0.046) (0.075) (0.060) Below avg in school 0.227 0.458 0.634

(0.089) (0.181) (0.200) # smokers in house 0.258 0.453 0.629

(0.016) (0.036) (0.046) Seen ads for events 0.242 0.367 0.292 sponsored by tobacco (0.037) (0.066) (0.057) Factor for marginal effects 0.304 0.213 0.213

(Pr sed-1R (Prsr))) Pseudo-R2 of x vars 0.136 0.304 0.413

(&2(fXi,g)/'2(•iXi,g + AZg + Ci,g))

NOTES: Province-level fixed effects also included, but not reported. Estimated standard errors in parentheses.

based on the estimated marginal effect, one additional smoker in the household is associated with a 7-9 percentage point increase, depending on the model, of the probability a young person will be a smoker. Given that 23.1% of the sample smokes, this is a very large effect. Exposure to advertising through event sponsorship (subject to fewer legal restrictions in Canada in 1994 than at present) also appears to be associated with youth smoking, although the direction of causation is unclear.

Table 3 also shows that estimates from all three models imply a substantial peer effect. To interpret the peer effect coefficients in a more concrete manner and to facilitate comparison across models and with earlier results in the literature consider a simple thought experiment. Begin with a representative individual who has five close friends (the median in the YSS data), all non- smokers, and has a set of observed characteristics (including average peer choice) such that the model predicts his or her probability of self-reporting as a smoker to be exactly 23.1%, the mean in the YSS data. Suppose that 20% of the relevant peer group (e.g., one of the five friends) suddenly switches from a non-smoker to a smoker. By how much would the model predict the representative individual's probability of smoking increases? This quantity, both for the models estimated here and for a few other recent studies, is reported in table 4.




TABLE 4 Comparison of estimated peer effects in this paper and in other studies

Source (peer group) Method of identification Implied A Pr(smoke)

Wang et al. (1995) (4 best friends) Naive 38.3%-53.2% Norton et al. (1998) (neighbours) Naive 24.0%-47.0%

IV 24.8%-75.0% Alexander et al. (2001) (schoolmates) Naive 24.2% Gaviria and Raphael (2001) (schoolmates) Naive 3.1%

IV 3.1% Auld (2005) (close friends) Naive 7.3% Norton et al. (2003) (3 best friends) Naive 10.5% (schoolmates) Naive 7.9% Powell et al. (2003) (schoolmates) Naive 11.1%

IV 10.8% This paper (close friends) Naive 15.6%

Naive w/underrep. 15.1% Structural, equal corr. 5.4%

NOTES: To facilitate comparison across different models, results are stated in terms of the increase in probability that a representative individual will be a self-reported smoker in response to a 20% (or one friend) increase in peer smoking. See text for details.

The results for this paper in table 4 suggest that the naive model substantially overstates the strength of peer influence in youth smoking, but peer influence remains strong once selection and simultaneity are accounted for using the structural model. The models estimated here imply that the representative individual's probability of being a self-reported smoker will increase by more than 15 percentage points (from 23.1% to 38.3-38.7%) in response to one of his or her closest friends becoming a smoker. This is an extremely large effect, but one that is actually much smaller than that found by Wang et al. (1995) and only somewhat larger than that found by Norton, Lindrooth, and Ennett (2003). However, as the table shows, much of this apparent peer effect is actually an artifact of selection and simultaneity. Specifically, the baseline structural model, with equal correlation in observables and unobservables, implies only a 5 percentage point increase (from 23.1% to 28.5%) in the representative individual's probability of being a self-reported smoker. Although the comparison is imperfect because this study considers close-friend peer effects rather than school-level peer effects, the results here are in clear contrast with those found in IV studies. In those studies (Norton, Lindrooth, and Ennett 1998; Gaviria and Raphael 2001; Powell, Tauras, and Ross 2003), the naive and 'corrected' estimates are nearly identical, implying that there



752 B.V. Krauth

TABLE 5 Point estimates of structural model under alternative choice of explanatory variables

Alternative specifications

Variable (1) (2) (3) (4)

Reporting rate (p,) 0.543 0.543 0.543 0.543 (0.009) (0.009) (0.009) (0.009)

Selection effect (px, pe) 0.256 0.188 0.264 0.056 (0.078) (0.107) (0.079) (0.188)

Peer effect (7) 1.180 1.342 1.132 1.716 (0.288) (0.385) (0.277) (0.670)

Age on 1/1/94 0.088 0.173 0.108 0.086 (0.021) (0.021) (0.021) (0.023)

Attending school -0.539 -0.552 -0.834 (0.087) (0.088) (0.203)

Above avg in school -0.547 -0.511 -0.512 (0.056) (0.053) (0.163)

Below avg in school 0.658 0.670 0.870 (0.149) (0.140) (0.432)

# smokers in house 0.614 0.645 0.602 (0.051) (0.051) (0.049)

Seen ads for tobacco- 0.292 0.233 0.275 sponsored events (0.053) (0.058) (0.073)

School no-smoking -0.112 rule (0.051)

Job 0.034 (0.049)

Job no-smoking 0.005 rule (0.082)

Trying to lose weight 0.121 (0.048)

Pseudo-R2 of x vars 0.411 0.344 0.392 0.210

(O'(/3Xi,g)/l2(/Xi,g + AZg + Cig))

NOTES: Province-level fixed effects also included, but not reported. Estimated standard errors in parentheses.

really is no endogeneity problem with peer behaviour. This result is suspicious in the light of the common finding (Engels et al. 1997, Wang, Eddy, and Fitzhugh 2000) that young smokers in low-smoking peer groups tend to move to higher-smoking peer groups over time. Reconciling this conflict in findings is a clear avenue for future research.

In the structural model, the estimated peer effect depends critically on the estimated correlation in unobservable characteristics p,. Because this correlation is identified through some fairly strong assumptions, it is important to check the robustness of findings to changes in those assumptions. First, because of the key role that within-group correlation in observable characteristics plays in identification of the peer effect, one may be concerned that the peer effect estimate is sensitive to the choice of characteristics to include. Table 5 provides a robustness check by estimating the model with alternative choices of explanatory variables.




TABLE 6 Estimated peer/selection effect under alternative identifying restrictions

Parameter estimates Implied

Identifying restriction - Px PE A Pr(smoke)

PE = Px 1.251 0.237 0.237 5.4% (0.270) (0.071) (0.071)

p. = 0.0 1.745 0.201 - 7.5% (0.059) (0.028)

p = 0.1 1.499 0.231 - 6.5% (0.072) (0.028)

p. = 0.2 1.260 0.261 - 5.4% (0.066) (0.028)

p. = 0.3 1.040 0.286 - 4.4% (0.068) (0.032)

p = 0.4 0.795 0.318 - 3.4% (0.091) (0.036)

p = 0.5 0.578 0.349 - 2.5% (0.095) (0.044)

pE = 0.6 0.400 0.353 - 1.7% (0.095) (0.041)

P. = 0.7 0.155 0.374 - 0.6% (0.119) (0.041)

y = 0.0 - 0.420 0.738 - (0.033) (0.035)

NOTES: Estimated standard errors (30 bootstrap replications for each restriction) in parentheses. 'Implied A Pr(smoke)' is the percentage-point increase in probability that a representative individual will be a self-reported smoker in response to a 20% (one friend) increase in peer smoking. See text for details.

As the table shows, the estimated peer effect is quite robust to alternative choices of explanatory variables. The one case where the estimated peer effect changes substantially is specification (4), where the variable describing the number of smokers in the home is dropped. Because that variable is an important one, the pseudo-R2 drops substantially, as does the precision of the estimated peer effect. Even so, none of the four specifications would lead to a revision of findings.

Another option for robustness checking is to replace the equal correlation assumption (p, = Px) with a point or interval restriction on p6, as described in section 4.3. The results for that approach are reported in table 6 and are depicted graphically in figure 1. To place the coefficients reported in table 6 in context, the last column in the table restates them in the same terms as in table 4: the implied percentage point change in a representative individual's probability of being a self-reported smoker in response to one of his or her five closest friends becoming a smoker. As these results show, the core findings from the baseline model are quite robust to a wide range of values for p6. Even if p, is substantially larger than the baseline model's estimate, the data imply a non-trivial peer effect. At the same time, even in the absence of a selection effect (p6 = 0), the structural model's implied change in the probability of being a self-reported smoker of 7.5



754 B.V. Krauth

co

S o

" naive estimate (w/underreporting correction) 0

"O- naive estimate (no underreporting correction) cr 0

E

E SML point estimate E Alternative SML estimates

0)o 0

a

o

c

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Selection effect (rho_e)

FIGURE 1 Estimated marginal peer effect (ypr I(<-'(-li/Pr)))

for alternative assumptions about selection effect (ps). NOTES: Individual points represent point estimates from naive probit models or baseline structural model with equal-correlation assumption. Ellipse is 95% joint confidence ellipse for structural model point estimate. Solid line represents alternative estimates of marginal peer effect as a function of the assumed value of p,; shaded region around it depicts a pointwise 95% confidence interval.

percentage points is well below both the naive model's 15 percentage points and previous estimates of close-friend peer effects in the literature.

Taking the results in this paper as a whole, the structural model applied to the YSS data provides robust evidence that the smoking behaviour of close friends has a moderate influence on a young person's own smoking behaviour, though this influence is substantially weaker than the influence implied by some previous studies.

6. Conclusion

It has long been known that naive estimation leads to upwardly biased measures of peer effects. For years, empirical researchers have used naive estimation with a few caveats in the absence of credible ways of compensating for simultaneity and peer selection. In recent years there has been an increased awareness of selection bias, and a number of valuable papers have used instrumental variables or panel methods to evaluate the strength of peer effects in youth smoking and other contexts.

This paper has used an alternative but complementary approach: the estimation of an equilibrium model of discrete choice that explicitly incorporates




the possibility of relative homogeneity within peer groups. As with structural estimation in general, this approach has the advantages of theoretical clarity and the ability to make predictions on the equilibrium response of behaviour to changes in incentives. In addition, the method is flexible enough to provide informative bounds on the peer effect under weaker restrictions than are needed for point identification, providing a valuable means of performing sensitivity analysis. In this case, there is also the advantage that estimation does not require complex data sets or natural experiments, but needs only standard survey data. While natural experiments have proved a valuable tool in the analysis of social interactions, they are not available in all questions of interest. Natural experiments will be particularly hard to find if the relevant peer group is formed informally (like groups of close friends) rather than by some central authority (like classrooms). In the absence of natural experiments, applied researchers will continue to investigate the question of peer effects in youth smoking using the tools available. For example, at least two recently published papers by prominent public health researchers (Alexander et al. 2001; Norton, Lindrooth, and Ennett 2003) estimate peer effects without any attempt to deal with simultaneity or selection.

Under the fairly strong assumption of equal correlation in observables and unobservables, I find that the estimated peer effect is substantially lower than the naive estimate, but is still quite large. Less restrictive assumptions lead to interval estimates, but the intervals associated with relatively weak restrictions are also well below the naive estimate and well above zero. These empirical results suggest a middle ground between extreme scepticism and blind faith on the existence of peer effects in youth smoking: under reasonable but arguable assumptions, the data suggest that peers are moderately influential in a young person's decision to smoke.

This research can be extended in a number of useful ways. The recent work of Tamer (2003) on estimation in the presence of multiple equilibria can be applied to investigate the role of equilibrium selection. The methodology can also be applied to newly available school-based data sets used in Alexander et al. (2001) or Norton, Lindrooth, and Ennett (2003), which sample all students in a given school and ask students to identify their friends directly. Not only will such data provide a more consistent measure of peer choice because all behaviour is self-reported, but it may also provide more detailed information on how peer influence works across complex social networks. Finally, an important open question is why the IV and structural methodolo- gies provide such contrasting results.

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Peer Effects and Selection Effects on Smoking among Canadian Youth