[Commentary] EVIDENCE OF THINGS UNSEEN: CAUSALITY AND CONFOUNDING IN PATH MODELS OF YOUTH SUBSTANCE USE

Does discretionary income encourage youth tobacco use? If so, does this occur through the indirect pathway of youth alcohol use? This question is of obvious interest to public health researchers and to practitioners, not to mention millions of parents. It stems from an old question: are alcohol and tobacco substitutes or complements for youth [1, 2]? This is a proprietary concern for health economists, but it also concerns others. If tobacco and alcohol are complements, high excise taxes or more stringent youth access restrictions pertaining to one of these substances would bring the beneficial side effect of curbing youth consumption of the other. If these substances are substitutes, more stringent (for instance) tobacco regulation will have the unwanted side effect of encouraging youth alcohol use. Alcohol and tobacco are probably substitutes for youth who face stringent financial constraints. Alcohol and tobacco are probably complements if youth like to consume them jointly, or if exposure to one substance brings youth into settings that encourage experimentation with the other. Existing data suggest that youth smoking and drinking are strong complements [1]. A convincing attack on these relationships requires strong data and an econometric framework that clarifies what is observed. Zang et al. [3] provide a strong data set (the 2003 Ontario Student Drug Use Survey) and a useful path analysis framework through which they interpret the data. Under their framework, alcohol use provides a mediator between spending money and adolescent smoking. Youth with ready access to discretionary funds are more likely to drink. Drinking then provides opportunities and settings for tobacco experimentation and (perhaps) chronic use. In a (linear) mediator model they present it as follows: Here X includes diverse independent variables, including those which capture extra spending money, as asked in the survey: ‘Each week I can spend $__ any way I want’. Precise wording matters here. The question speaks to the availability of money for consumer items. Perhaps more importantly, it speaks to youths' discretion to spend as they wish. If this model is specified properly, the total estimated impact of a unit increase in discretionary monies on smoking is τ′ + αβ—the direct effect τ′ of discretionary monies, plus an indirect effect αβ through the channel of alcohol use. The ratio R = αβ/(τ′ + αβ) indicates the relative importance of indirect to total impacts of discretionary monies. This account is plausible, but I remain skeptical. Mediator models are, at bottom, particular genres of simultaneous equation models. These analyses are therefore vulnerable to confounding and specification errors. Mediator models are especially vulnerable to bias caused by unobserved individual and family traits correlated with both alcohol and tobacco use. Suppose, for example, that a common propensity for adolescent risk-taking induces a correlation between the residuals ε1 and ε2, which are otherwise uncorrelated with the X's. We can write: Here γ reflects the covariance of the two error terms; while υ is uncorrelated with ε2. We then have: Therefore, when γ is non-zero, OLS regression based on equation 1 will not recover the causal parameters τ′ and β. Instead, the alcohol coefficient will typically be upward-biased because it includes both the true causal β and the correlation that arises between the error terms. The total estimated effect on smoking of a 1-unit change in X will be, as before, τ′ + αβ. However, one attributes too high a proportion to the effects of X on youth alcohol use. Some algebra yields that the estimated ratio of indirect to total effects will be R(1 + [γ/β]). The relative bias is determined by the covariance in the error terms divided by β. Zang and colleagues discuss whether they have overlooked variables such as religious attendance that might be correlated with discretionary spending. Parents who monitor their children closely seem, all else equal, somewhat less likely than others to allow a 9th grader to spend $60 per week on discretionary consumer items. Equation 4 indicates a deeper problem: any unobservable correlated with both youth smoking and youth drinking can bias the results. These authors acknowledge these study limitations, although acknowledgement appears rather late in the day within the discussion section. They write, judiciously, that ‘the current study cannot be used to test the causal relationships among spending money, drinking and smoking, due to its cross-sectional design’. They wisely recommend longitudinal studies to unpack causal pathways suggested by their work. Zang et al. [3] also include some variables to capture unobserved family attitudes and traits. As always, however, the underlying data bring frustrating limitations. The authors account for parental attitudes regarding youth smoking; yet they cannot include parental attitudes regarding youth drinking. As the authors note, longitudinal studies could explore directly the specific circumstances surrounding youths' first tobacco use. One might reduce econometric problems by including a richer array of variables to capture individual and family factors. Such factors would include youths' risk preferences, which may promote multiple forms of substance use. Differences in parenting approaches and strategies may prove especially powerful. Several studies suggest that authoritative parenting is associated with later initiation of tobacco and alcohol use [4-6]. Data sets such as Monitoring the Future may allow greater leverage on these concerns. Independent of thorny issues of causality, the current findings suggest some useful advice. Alongside the usual recommendations, perhaps clinicians should advise parents to keep a closer watch on their children's financial lives. ‘It’s 10 o'clock. Do you know where your child's money is tonight?'

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