Smoking within the Household: Spousal Peer Effects and Children’s Health Implications

4.1 Data Description

The French health survey 2002–2003, carried out by the French National Statistical Institute (INSEE), includes data on the demography, socioeconomic status, health status, and health consumption of 25,000 households in France. Data were collected on about 40,797 individuals, interviewed three successive times. Adult individuals (over 18) were also required to fill an auto-evaluation, in which they were asked to report their perceived health and their prevention behavior, including alcohol and tobacco consumption. A similar but adapted questionnaire was proposed to kids aged between 11 and 17. Out of 30,997 adults in the survey, 25,931 complied and returned an auto-evaluation. We dropped the observations containing missing values either on the reported smoking habit or on the socio-demographic variables of interest. We also limit the analysis to adults being the household reference person or the partner of the reference person and in this subgroup, we consider only individuals with an age between 25 and 60. In the case of couples, we drop the households in which the husband is more than 60-years old. Our sample reduces this way to 12,770 adult individuals, 10,540 of which live in a couple.

Our endogenous variable is the smoking behavior. We construct a dummy equal to one if the individual reports being a smoker. An individual is considered a smoker if she reports to be smoking every day.

Individual variables include the age, a dummy equal to one if the level of education is above high school (HS), and the body mass index (BMI). Descriptive statistics on the whole adult population of the survey point to a negative correlation between smoking and BMI. Another variable susceptible to influence smoking behavior is the exposure to smoke at the workplace. This variable is self-reported by each individual and takes the form of a dummy equal to one if the individual is currently exposed to smoke at work. It is worth noticing that in France smoking bans in public places were not as strict in 2002 as they are today. Consequently the exposure at work variable exhibits some variability, and almost 15% of the individuals in our sample reported to be exposed to smoke at the workplace. Finally, the past smoking behavior is included in the analysis: in particular, we use the two years lagged smoking behavior. A two years period is short enough to reasonably assume that most couples did not change their partner; at the same time it is a period long enough to have some variation between past and current smoking behaviors. Taking longer lags would raise the problem of having to deal with individuals changing partner or moving from single to couple. We do not include in the explanatory variables the price of cigarettes for the simple reason that this price in France is regulated and homogeneous at the national level. Another variable that is often used in smoking models is the price (or the price variation) of cigarettes during the adolescence of the individual, that is to say when the individual was more likely to start smoking.^[4] We refrain from using this variable, since it would be the same for all individuals in the same age cohort, and thus reduce to a mere proxy for age.

Household-specific variables include the family income adjusted for the number of people in the household, according to the OECD-modified scale (assigning a weight of 1 to the household head, of 0.5 to each additional adult, and of 0.3 to each child), and a dummy variable taking value 1 if at least one child under the age of 15 belongs to the household. Note that the presence of children does not mean that these are the children of the reference individuals (they could be the children of just one of the two partners). For our purposes, this is not problematic, since we want to estimate the impact of the presence of children in the same household on the smoking behavior. Finally, we control for the number of children under age 15 living in the household.

4.2 Reduced Form Results on Smoking Behavior

In the first stage of the empirical analysis, we estimate a reduced form model in order to recover the estimated probability of smoking of each individual and the empirical analogue of her expected utility.

We run a logit regression where the endogenous variable is the smoking dummy. We include in the explanatory variables individual characteristics of both the individual and her partner, if any. In particular we include the past smoking behavior, in the form of a dummy taking value one if the individual smoked two years ago. We use a two years lag to have more variation across present and past smoking status without having to deal with changing partners. Remark that the correlation across past and present behavior is very high, probably because of addiction. In particular, in our sample, the probability of being a smoker is equal to 25.9%. However, this probability is equal to 85.6% for past smokers and to just 1.17% for people who did not smoke in the past. This piece of evidence shows that among adults quitting smoking is much more frequent than starting smoking.^[5] Since we control for the past smoking behavior, we will be able to look at the impact of spousal smoking on the probability of switching behaviors and in particular on the probability of smoking cessation.

We also include in the analysis the gender, the age, the education level and the current work exposure to smoke of the individual. Some household characteristics are also taken into account: for instance, we distinguish among individuals being singles and the ones living in couple. The number of children under 15 and the presence of at least one child under 15 are variables that are susceptible to influence smoking behavior. Finally, we include the family income, adjusted for the size of the household. Descriptive statistics for people living in couple and singles are reported in Tables 1 and 2.

The results of the reduced form logit regression are reported in Table 3. Heteroscedasticity-robust standard errors allowing for clustering at the household level are reported in parentheses.

The current smoking behavior is strongly correlated with the past smoking behavior, as expected. The level of education correlates negatively with the probability to smoke, as well as the BMI for people living in a couple. The presence of children does not display any correlation with the probability of smoking. For couples, the past smoking behavior of the partner has a positive and highly significant effect on the probability of smoking, while the partner’s level of education affects negatively the probability of smoking. These parameters, however, do not correspond to the structural model parameters. As pointed out by Clark and Etilé (2006), the effect of the partner’s past smoking behavior could be overestimated due to the exclusion of individual effects. The first step estimation is thus only instrumental to getting the estimated probability σ⌢ixi,xj that individual i smokes conditional on the observables. For our purposes, it does not matter whether the partner’s smoking behavior affects σ⌢ixi,xj directly or through the correlation of individual effects. All that matters is that σixi,xj is an unbiased estimate of the equilibrium individual beliefs, whose effect on smoking decisions we want to test. In order to recover the structural parameters, we use the Hotz–Miller inversion and we obtain an estimate of the expected utility from smoking for each of individual i:

Remind that, under our assumptions, σ⌢jxi,xj is a consistent estimate of the beliefs that individual i holds about the probability of smoking of her partner. In equilibrium, the beliefs coincide with the true probabilities. Thus, ΔEU^i(xi,xj) is the empirical analogue of the expected utility of individual i. We can then proceed with the second step of our analysis.

4.3 Structural Estimation of Smoking Behavior

Once an unbiased estimation of the expected utility from smoking has been recovered, it is possible to recover the parameters of the structural model under the sole moment condition discussed above, E[(ΔEU^i(xi,xj)−λ1xi−λ2σ^j(xi,xj)Di)]=0. In particular, we obtain estimates of the coefficients λ1=(λ,−p) and λ2=p+r+s. Both p and r+s are identified.

Remark that the assumption that allows us to recover these parameters is that partner’s characteristics xj enter the individual expected utility function only through the beliefs about the partner’s smoking behavior σ⌢jxi,xj and thus are excluded from the direct utility of the individual.

The results of the described regression are reported in Table 4. Bootstrap standard errors are reported in brackets.^[7]

The past smoking behavior affects positively the utility of smoking. The corresponding parameter is strongly significant and quantitatively important. This is not surprising, since the smoking behavior is persistent over time. Remember that, on the one hand, only about 15% of past smokers succeeded in giving up smoking by the time of the interview. On the other hand, individuals that were non-smokers two years before are very unlikely to start smoking. This accounts for the explanatory power of the past smoking behavior.

However, given the past smoking behavior, other variables significantly affect the present utility from smoking. Males seem to be more prone to smoke than women. The BMI is negatively correlated with the utility of smoking. This piece of evidence suggests that overweight people might be more concerned about the health damages of smoking; the fact that obesity and tobacco consumption could be substitute and not complements is not new to the literature (see for instance, Gruber and Frakes, 2006 and Flegal et al., 1995). Of course, the BMI is potentially an endogenous variable. Smoking might substitute excessive eating and affect individual weight. However, the causal relationship between BMI and tobacco consumption goes beyond the scope of this paper, and the cross-sectional nature of our data does not permit us to trace back the evolution of the BMI, which is the result of long-term decisions. The level of education is negatively correlated with the expected utility of smoking. This is an intuitive result in line with previous findings from the literature (see for instance Kenkel, Lillard, and Mathios 2006). The exposure to smoke at work has no significant effect on the utility of smoking. The results also suggest that the utility from smoking decreases as family income increases, which is in line with previous findings. The presence of at least one child and the number of children in the household do not have any significant effect on individual smoking. This result is counterintuitive but quite robust to different specifications and in line with previous findings (see Clark and Etilé 2006). Parents do not seem to perceive an extra cost of smoking with respect to non-parents. This may be due to the fact that we control for the past smoking behavior, which has a large explanatory power due to addiction. Also, note that in the first stage regression (Table 3), the number of children matters in explaining beliefs about the spousal smoking behavior. This suggests that the number of children might enter indirectly in the utility from smoking, through the spousal peer effect.

Let us now discuss the parameters corresponding to peer effects. On the one hand, the impact of the probability of smoking of the partner is positive and strongly significant. This effect corresponds in the theoretical model to p+r+s and is estimated to be 0.55. On the other hand, living in a couple has a negative and significant (at the 95% confidence level) effect estimated to be –0.34. The absolute value of this parameter corresponds to the cost of smoking when the partner does not, p. We can thus identify r+s. If the partner has a probability to smoke close to one, the individual expected utility function increases of around 0.55 in absolute value with respect to the case in which it is very unlikely that the partner will smoke. In the model, the presence of single individuals permits to decompose this effect. With respect to a single, an individual with a partner who smokes gets an extra utility from smoking. This extra utility is modeled through the parameter r+s and is estimated to be about 0.21. Conversely, with respect to a single, an individual with a non-smoking partner gets a loss of utility if she smokes. This loss, corresponding to the parameter p in the model, is estimated to be equal to –0.34.

These findings suggest that the smoking behavior of the partner influences the utility from smoking in two distinct ways. First, if both partners smoke, this increases the benefit that they can both extract from tobacco consumption. This is a smoking enhancing effect linked to the presence of a smoker in the household. Second, if just one partner smokes, she will have to bear a cost due to the fact that she lives with a non-smoker. This extra cost might be linked to the partner complaints or to the internalization of some of the passive smoke externality. Furthermore, it could be due to the fact that a smoker matched with a non-smoker might have to smoke outside the house or reduce her tobacco consumption.

Finally, note that the estimated λ2=r+p+s is smaller than four in absolute value. As shown in Section 3, this ensures that the Bayesian Nash equilibrium that we have empirically characterized is indeed unique.

The coefficients listed in Table 4 give us a qualitative idea of spousal peer effects. However, the results refer to the impact on the utility from smoking which is an ordinal quantity. Thus, they do not allow us to quantify the magnitude of the peer effects. As pointed out before, these magnitudes are important in order to measure the impact of smoking containment measures. In the next section, we present the marginal effects of spousal smoking behavior on the individual probability of smoking.

4.4 Marginal Effects

Given the estimated parameters, we now analyze the marginal effects of xi or xj (the characteristics of the partner of i) on the probability of smoking of an individual i. This probability is equal to

where F is the logistic function satisfying F′u=Fu1−Fu for all u.

Thus, we have

for the marginal effect of an individual characteristic on its own likelihood to smoke, and

for the marginal effect of a partner characteristic on the own likelihood to smoke.

Note that each individual characteristic has both a direct effect on the probability of smoking and an indirect effect through the partner’s probability of smoking. The direct effect of xi on the probability of smoking of i is λ1σixi,xj1−σixi,xj. The indirect effect due to the implied change in the probability of smoking of the partner is equal to λ2σixi,xj1−σixi,xj∂∂xiσjxi,xj. This indirect effect can either reinforce or reduce the effect of xi on the probability to smoke.

Substituting the same expressions for ∂∂xiσjxi,xj and ∂∂xjσjxi,xj in the previous equations, after some rearrangements we get:

and

The interaction effect increases the marginal effect of the own individual characteristics on the probability to smoke since

whenever λ2<4, which is the case empirically.

We estimated the marginal effect of continuous variables for each individual, and we take the averages on the whole sample. Concerning the BMI, for a person measuring 1m70 the effect of a 3 kilos weight increase reduces the probability of smoking by a factor equal to 0.20 percentage points on average (ranging from −2% to 0). An increase in annual income of 10,000 euros corresponds to a decrease in the probability of smoking of 3.7 percentage points on average.

In Table 5 we report the average marginal effect for the peer effect parameters. The standard deviations are obtained by bootstrap. For individuals living in couple, the effect of the probability that the partner smokes s+r+p is equal to

and is estimated to be equal to 0.02 for individuals living in couple. This effect ranges from 0 to 0.13 depending on the value of σi. This effect seems low, compared to the existing empirical literature; for instance, Cutler and Glaeser (2007) find that a smoking partner increases the individual probability of smoking of 40%. However, we are already controlling for the past smoking behavior for which we know that there is a strong path dependence. Thus, marginal effects on transitions from smoking to non-smoking are generally low. In addition to that, the average marginal effect for individuals that smoked in the past (t−2) goes up to 6.4%. The interpretation of this number is that a smoker is about 6.4 percentage points less likely to give up smoking if her partner smoking probability moves from zero to one. Remember that the unconditional probability to quit smoking is equal to 15%. The estimated peer effect is therefore relatively important.

The marginal effect p of being in a couple on the probability of smoking is calculated as the difference in the probability of smoking of individual i when the couple dummy, Di, passes from zero to one. Since for singles σˆj=0, in order to evaluate this marginal effect separately from the effect of σˆj, one has to keep σˆj fixed and equal for all the individuals in the sample. First, we impose σˆj=0. The average marginal effect over the full sample is equal to –1.5%. This figure goes up to –4.1% for individuals who smoked two years before. This result suggests that smokers living in a couple and expecting the partner not to smoke are 4.1 percentage points more likely to give up smoking than singles.

We also look at the marginal effect of being in couple imposing σˆj=1. The effect is much smaller than the previous one both for smokers and the full sample. As one would expect, the smoking deterring effect of living in a couple is smaller if the partner is expected to smoke with probability one. Living with a smoking partner increases the probability of smoking by a number (corresponding to s+r in the theoretical model) equal to the difference between the marginal effect of σˆj (corresponding to s+r+p) and the marginal effect of the couple dummy calculated at σˆj=1 (corresponding to −p). For past smokers, this increase is estimated to be equal to 1.7 percentage points.

The results from this section suggest that a non-smoking partner might reduce the individual utility from smoking. This effect might work through the three channels described above: consumption externalities, altruism and learning. If we were able to observe the qualitative aspects of the smoking behavior (smoke in/out, for instance), it would be possible to disentangle learning effects from consumption externalities and altruism, since the latter affect the behavior of the smoker. We do not observe these qualitative variables. However, in the next section, we consider partners with children and analyze the effects of parental smoking on the health of their children. If the deterring effect identified in this section reduces the individual utility through an obligation for the smoker not to smoke at home, we should find that, everything else equal, children whose both parents smoke are more exposed to passive smoking than children with a non-smoking parent. Thus, smoking externality and altruism seem to play a role in smoking spousal peer effects.

4.5 Gender-Specific Peer Effects

In a couple, male and female partners might be affected in different ways by the behavior of the partner. In this section we consider a different setting where the structural parameters p, r and s depend on gender. We denote the gender by g∈{f,m} where m refers to male individuals and f to female ones. The utility of individual i of gender g equals:

where xi=(x˜i,Di),λ1=(λg,−pg), λ2=pg+rg+sg, λ3=−rg. The parameters sg, rg and pg are expected to be non-negative for g=f,m.

We apply the same estimation method as in the previous sections. In the first stage regression (the results are omitted), we allow the parameters to be different for men and women. In the second stage, we estimate the gender-specific peer effects, by interacting the variables of interest, σˆj and the Couple dummy, with a dummy taking value one if the individual is male. The results of the analysis are reported in Table 6.

The results for the individual characteristics are very similar to the ones reported in Table 5, with the important exception of the gender dummy. Concerning the peer effects, however, there are some noticeable differences. Women seem to feel a higher peer pressure. In particular, the so-called smoking enhancing effect is greater for women than for men. The difference is statistically significant. In order to have a sense of the magnitude of these different effects, we calculated the average marginal effect of a smoking partner on the own probability of smoking. For both men and women, the probability of smoking is 2.1 percentage points higher if their partner smokes (the standard deviation is equal to 0.0060 and 0.0068, respectively).

The difference between men and women appears when computing the average marginal effect of σj for the subsample of past smokers. This is very high for women: a woman living in a couple is 6.8 percentage points less likely to give up smoking if her partner’s smoking probability goes from zero to one (with standard deviation equal to 0.0192). For past smoking men, this figure is only of 6.2 percentage points (standard deviation of 0.0183). Under our interpretation, these results suggest that women get more pleasure from smoking with their partner or internalize more the externality imposed on their partner. These results are in line with the findings of McGeary (2015), who shows that women are more likely to quit smoking if their partner suffers a negative health shock. Concerning the smoking deterring effect, represented by the parameter p, the results suggest that there are no significant differences between men and women.

The gender dummy has no significant explanatory power in this specification, while in the previous one it was significant. This suggests that gender affects the smoking behavior only through the interaction with the expectations on the partner’s smoking behavior.

4.6 Children’s Health and Parents’ Behavior

In this section, we study the relationship between the smoking behavior of parents and the number of non-chronic respiratory diseases of their children. The survey respondents were asked to report the diseases occurred to all household members between different waves of the survey. For each disease, they were asked when the disease occurred, its length, and whether it was chronic or not. Thus, the distinction between chronic and non-chronic diseases is based on the self-reported duration of the illness status. The reason why we focus on non-chronic conditions is twofold. First, we think that the relationship between chronic respiratory conditions and parental smoking behavior may be plagued by more severe endogeneity problems. Second, our aim is to test how the exposure of children to smoke depends on whether both parent smoke, or only one of them. We think that, for this purpose, looking at diseases occurring at the same time in which the smoking behavior takes place is more appropriate (rather than considering chronic diseases that surged in the past and that are likely to be correlated with past parental smoking).

We only include households in which the reference person lives in a couple. We also limit the analysis to the case in which the reference person is a man (only 10 households are removed) and is between the age of 25 and 60. There are 5,274 such households. For simplicity, in the following we will define the reference person as the husband and his partner as the wife, even though we do not control for their effective marital status. Overall, 2,791 such households have at least one child under the age of 15; 4,853 children live in these families. In these household, 670 husbands and 831 wives reported being smokers. In 374 cases both parents smoke (see Table 7).

We regress the number of non-chronic respiratory diseases on a set of individual variables, such as the age, the gender, the BMI of the child and a dummy equal to one if she is affected by a chronic respiratory condition; we also include in the regressors the number of children under 15 present in the household. The education level of both the mother and the father and their BMI are also taken into account, since these characteristics may influence the way parents care about the health of their children. Finally, we include two dummy variables summarizing parents’ smoking behavior: we distinguish the case in which both parents smoke and the one in which just one parent smokes.

In our data set the number of sicknesses and the level of health care consumption of children is reported by parents. This can lead to measurement problems if parents tend to misreport the health status of their children. In the case of respiratory diseases, this difficulty seems to be particularly strong since some parents might report to the interviewer problems such as a light flu, while others would not. If this reporting bias is correlated with the variables of interest, this can lead to a misinterpretation of the coefficients. For instance, if smoking parents tend to underestimate the health problems of their children, we might find no effect of smoking on the non-chronic respiratory diseases of children, even though passive tobacco exposure actually affects their health. In order to reduce this bias, we control for the total number of non-respiratory diseases and the total number of doctor visits for health matters different from the respiratory ones. These variables are useful to control the global health of the child and might capture the reporting bias of parents, if the latter is systematically the same for any health condition.

Another problem to take into account is endogeneity. On the one hand if a parent observes that her children are often sick, this may affect her smoking behavior. On the other hand, even though we control for chronic respiratory conditions, which have a high chance to affect both the parents’ behavior and the occurrence of non-chronic respiratory diseases, there could still be some correlation between our measures of parents’ tobacco consumption and some unobservables affecting the occurrence of non-chronic respiratory diseases. For instance, smoking parents might be less concerned with the health status of their children as they are less by their own health. This would lead to an overestimation of the effect of smoking on children’s health. Regressing naively the health status of children on the smoking behavior of parents might thus lead to biased results. In particular, the impact of smoking on children respiratory health could be underestimated. We try to overcome this problem using instruments. We use as instruments the age of both parents and their exposure to smoke at the workplace. The age of parents does not appear to be correlated with the error term once one controls for the age of children. We think that it is quite reasonable to consider the exposure to smoke at the workplace as exogenous to the health care of children by parents. Evans, Farrelly, and Montgomery (1999) using U.S. data showed that the sorting across jobs based on smoking status seems to be relatively weak. We perform an OLS and 2SLS regression. We run a Sargan test suggesting that the instruments are indeed valid (see Table 8).

Since we are dealing with count data (the number of respiratory diseases in the period of interest ranges from 0 to 4), we also run a Poisson regression and a Poisson regression with control functions in order to account for endogeneity (using the same instrumental variables as in the 2SLS). The latter estimates are obtained by a technique suggested by Blundell and Powell (2003). We perform a first stage regression of the endogenous variables on all exogenous variables and instruments and we use the residuals and polynomials of those residuals as additional control variables in the main regression. This seems to be a more appropriate estimation strategy, because of the zero inflated discrete distribution of the dependent variable.

Results of both the OLS and the IV regressions are reported in the first two columns of Table 8. Clustered standard errors at the household level are reported in brackets. The presence of chronic conditions seems not to influence the number of non-chronic respiratory diseases. However, the total number of doctor visits and the number of diseases different than respiratory both present positive and highly significant effect on the endogenous variable. As pointed out before, this could be due to the fact that these variables are proxies for the general health of the child. However, their positive impact might be linked to a systematic reporting bias of the parents. The age of the child affects positively the respiratory health of the child, as expected. The square of the age, the gender and the BMI have a small or insignificant effect in both specifications. The variable controlling for the number of children in the household presents a negative estimated parameter. This result seems counterintuitive since one could expect the presence of siblings to increase the risk to fall sick. The father’s education level seems to have a positive correlation with the respiratory diseases of children. The mother’s education and BMI have a small effect which is significant only under certain specifications. The fact that the father’s education increases the number of non-chronic respiratory condition is at first sight counterintuitive too. One explanation could be that more educated households tend to report more respiratory diseases. The family income has a negative and significant effect on the number of sicknesses.

The results on smoking variables are the ones presenting a particular interest in order to test our smoking model. In the OLS specification, the estimates suggest no significant effect of the smoking behavior of parents. In the IV regression, however, the fact that both parents smoke has a significant (at the 90% confidence interval) and positive effect on the respiratory diseases of children. Having just one parent smoking at home does not affect significantly the children’s health. The impact of the fact that both parents smoke is quantitatively very high (0.668), considering that in the period of observation, the average number of non-chronic respiratory diseases for children is equal to 0.3. If just one parent smokes, the effect of smoking on children seems to be null. This evidence supports the hypothesis that non-smoking parents might have a control role inside the household, protecting children from passive tobacco exposure.

In the third and fourth columns of Table 8, we report the results of the Poisson regressions. For most variables the results of the least square regression are confirmed. However, the parameters corresponding to the smoking behavior of parents are not significant in this specification.

These results weakly point toward a control role of a non-smoking parent. However, this first analysis does not take into account the number of cigarettes effectively smoked by each parents and thus lacks precision. We refine the analysis by looking at the effect of each cigarette smoked per day by household members. In particular, we constructed a variable corresponding to the daily tobacco consumption of the smoking parent when just one parent smokes, and a variable corresponding to the daily aggregate consumption when both parents smoke. No information concerning where these cigarettes are consumed is available. In particular, the available data does not allow us to know whether the parents smoke at home or not. The estimates of the smoking game suggest that when an individual is in couple with a non-smoker, this reduces its utility from smoking. Our interpretation is that this disutility might come from the fact that smokers living with non-smokers and having kids may be forced to smoke less at home or leave the house in order to smoke. Thus, we expect to see a smaller effect of each cigarette on the respiratory health of children when just one parent smokes instead of both.

In columns (a) and (b) of Table 9 we report the results of the OLS and the IV regressions. In the OLS regression, no effect of the smoking behavior is found. In the IV specification, the respiratory health of children seems to be affected by each extra cigarette that a parent smokes only if the other parent is also a smoker. The parameter is significant at the 95% confidence level. In column (3) of Table 9, we also include among the instrumented variables the square of the total number of cigarettes smoked by parents (if one or both smoke). This variable is meant to control for nonlinear effects of the number of cigarettes smoked. More precisely, we want to test for the hypothesis that the number of cigarettes matters only if a critical number of cigarettes is consumed (or that the negative effect on health is convex). The results seem to reject this hypothesis. Controlling for this variable, the marginal cigarette smoked leads to an increase of 0.06 in the number of respiratory diseases when both parents smoke. Again, no effect is detected in households where just one parent smokes. In columns (c) and (d), we report the results of a Poisson regression and of a Poisson with control functions (for endogeneity). The results are qualitatively similar to the previous ones. The number of cigarettes smoked in households where both parents smoke has a positive impact on the number of diseases.

As suggested by the medical literature (see for instance Cook and Strachan, 1999), younger children may be more sensitive to the smoking behavior of their parents. According to our model, this may be justified by the fact that younger children may spend more time with their parents and may thus be more exposed to parental smoking. In this case, a control role of non-smoking parents may be particularly important. To test for this intuition, we split the sample in two age groups: children below age 7 (included), and children between age 8 and 14 (included). The results for the smoking intensity model are reported in Table 10. At least in our Poisson specification, we find results similar to the ones above, but only for younger children. The number of cigarettes smoked has a negative impact on the respiratory health of children when both parents smoke, but not otherwise. The results also suggest some concavity in the effect of cigarettes on health. For children above age 8, we do not find any impact of parental smoking on non-chronic respiratory diseases. Thus, we think that the results of Tables 8 and 9 are mainly driven by younger children.

Finally, we reproduce the Poisson regressions of Tables 8 and 9, but using the dummy for chronic respiratory diseases as a dependent variable. We do not find a causal relationship between current parental smoking behavior and children’s chronic respiratory conditions (see Table 11 in Appendix 2). This result can be considered as some sort of placebo test. In fact, if chronic diseases are determined by the past smoking behavior of parents, which is correlated with current smoking behavior, we would find significant effects only if we were not able to disentangle the effect of current smoking from past behavior. The fact that current smoking does not affect chronic respiratory diseases after instrumentation suggests that our instruments are indeed valid and orthogonal to past smoking behavior of parents. Thus, we feel confident that the results for non-chronic diseases actually capture the current exposure of children to smoke and are not due to correlation with past behaviors.

Summarizing, there is some evidence that non-smoking parents exert a control role over smoking ones, in particular in protecting children from passive smoking. This points toward an interpretation of the empirical results of the smoking game in terms of consumption externalities or altruism. For instance, having one parent smoking 20 cigarettes a day may be less detrimental than having two parents smoking 10 cigarettes a day because of the unobserved change in behavior concerning smoking inside or outside, the smoker with a non-smoking partner being more likely to smoke outside.