Figure 4: ETS Exposure, by age and smoking status
6 Empirical Framework
6.3 Functional Form and Model Selection
My analysis begins by examining the effects of public smoking bans on smoking prevalence, using the binary current participation variable that indicates whether or not an individual smokes. Smoking prevalence is important to policymakers in Argentina because of the health implications associated with smoking. Numerous studies have found large and significant differences in both disease risk and life expectancy between smokers and nonsmokers. I measure determinants of smoking prevalence among both the general population and those individual with any smoking history prior to the survey. The regressions that are estimated using a standard logit model take the following form (in log odds):12
log[P(Ct>0) P(Ct=0) ]=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt (10) log[P(Ct >0 |St>0) P(Ct =0 |St>0) ]=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt
where the first represents the probability of smoking any quantity of cigarettes in period t, and the second represents the probability of smoking any quantity of cigarettes in period t conditional on having smoked at some point in the past. I use a positive addictive stock variable to differentiate individuals with any smoking history from those who have never smoked a cigarette.
12 Note that Greek letters α, δ, σ, and ε differ across equations, but they are kept similar in the depiction of my
After determining the effects of smoking bans on the proportion of the population that smokes, I look more specifically at smoking intensity, or the level of smoking. I begin with an analysis of the regularity of smoking. I use a multinomial logit approach with a base outcome of not smoking at all (Rt = 0), and two alternate outcomes of smoking occasionally (Rt = 1) and
smoking heavily (Rt = 2). The coefficients estimated for these two outcomes represent the
relative likelihood that an individual is that “type” of smoker compared to the likelihood that the individual is a nonsmoker. The regressions take the following functional form:
log[P(Rt= j) P(Rt =0) ]=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt, j=1, 2 (11) log[P(Rt= j|St >0) P(Rt =0 |St>0) ]=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt, j=1, 2
As done with smoking prevalence, these equations are estimated using the general population and those individuals with a smoking history. The multinomial logit estimator allows for different marginal effects of explanatory variables on each regularity outcome.
In addition to observing participation and regularity, I observe the smoking intensity of individuals who choose to smoke currently. Health outcomes are known to differ across non- smokers and smokers, as well as among those who smoke at different levels, so the findings of this analysis have important health implications.13 For that reason, after evaluating the effect of the smoking bans on the proportion of the population that smokes and the proportions that smoke occasionally and heavily, I investigate the effect of the ban on smoking intensity among smokers. Due to the differences in behavior and addictive stock between those that smoke occasionally
13While many previous studies have focused on the health risks associated with duration of smoking rather than intensity of smoking, studies have shown that there is a positive and significant correlation between smoking intensity and risk for smoking-related illnesses. Shields and Wilkins (2013), for example, found such a relationship in their study of smoking intensity and heart disease in Canada.
and those that smoke everyday, I also estimate the effects of the policy on smoking intensity for occasional smokers and heavy smokers separately, as these individuals may react differently to the smoking bans. These regressions take the following form:
Ct|Ct>0=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt (12) Ct|Rt =1=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt Ct|Rt=2=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt
As mentioned previously, the number of cigarettes smoked per day is technically reported as a count variable, but it can be modeled as a continuous variable as well. In order to complete a robust analysis of the effects of smoking bans on smoking intensity, the variable is analyzed in both forms. I use an ordinary least squares (OLS) approach to model the smoking intensity variable, as well as its natural log, as continuous variables. I also conduct a quantile regression of the smoking intensity variable for all smokers to determine whether the public smoking bans have had different effects at different levels of smoking intensity. To explore the sensitivity of the estimated marginal effects of the ban to distributional assumptions, I also use a generalized linear model (GLM) with a gamma distribution. A gamma distribution is selected over a negative binomial distribution and Poisson distribution due to the nature of the data and the fit of each distribution. Figure A2 of the Appendix presents a visualization of each of these three distributions fitted using the actual smoking intensity data (conditional on being a current smoker) and plotted against it, and it is clear that the gamma distribution fits most closely.
I conclude my investigation of the effects of public smoking bans on by examining individual reports of environmental tobacco smoke exposure, a public health concern that
presents significant and often underestimated health risks.14 While my previous analyses focus on modeling individual determinants of one’s own smoking behavior, this analysis investigates individual responses directly affected by the smoking behavior of other individuals. The binary dependent variable that indicates whether an individual reports being regularly exposed to ETS in public places (Ot) is analyzed using a standard logit model with the following form:
log[P(Ot=1) P(Ot =0)]=α0+α1Xt+α2Et+α3It+α4Nt+α5Pt C +δBt+σt+σp+εt (13) log[P(Ot=1 |Ct=0) P(Ot =0 |Ct =0) ]=α0+a1Xt+a2Et+a3It+a4Nt+a5Pt C +δBt+σt+σp+εt
Where the first captures the effects of determinants on exposure response of all individuals regardless of own smoking behavior, and the second captures the marginal effects on exposure to those individuals who do not currently smoke.