Power of personalized smoking cessation: A quantitative lifecycle framework for policy evaluation

2.1 On genotype-demographic heterogeneities and smoking

The health economics literature finds that male smokers typically smoke more cigarettes per day (CPD) than female smokers and that blacks are less likely to smoke and smoke less than whites. There exists a substantially positive effect of education on health, in particular, better-educated smokers are more likely to quit smoking than less-educated smokers. By using a more precise gene-related measure, addicts may raise smoking intensity in response to higher cigarette taxes in contrast to the conventional predictions, whereas there is an adverse effect of smoking bans on passive (second-hand) smokers (Adda and Cornaglia (2006, 2010)).

We identify several stylized facts based on cross-sectional data from PSID (1999–2011): (i) about 1 out of 4 of the US adult population (whites and blacks at age above 18) smokes, with the average CPD almost one and a half packs (14);³ (ii) the average expenditure on tobacco accounts for an nonnegligible share (6.5%) of an addict's labor income; (iii) while the share of smokers differs little across genders and races, it varies substantially by education, with almost 30% of non-college educated but less than 10% of college educated being smokers; (iv) males smoke more than females, whites smoke more than blacks, and the noncollege educated smoke more than college educated; (v) while the noncollege educated white males have the highest average CPD, the noncollege educated black females have the highest smoking expenditure to labor income share.⁴

Figure 1 plots lifecycle smoking behavior, using the average data moments of each age group by regarding the data as multiple waves of cross-sections.⁵ First, the left panel of Figure 1 shows that the share of smokers in the population declines with age, indicating quitting by smokers over time. While the reduction in smoking prevalence is commonly identified in both economics and medicine literature, it is noted that as the sample size is trimmed down sharply due to deaths, the average outcomes become more volatile for age cohort beyond 65. Second, two smoking intensity measures that incorporate quitting and survival probability are presented in the middle panel (smoking expenditure to labor income ratio) and in the right panel (population average CPD). The smoking expenditure share declines sharply before age 30 and the downward trend continues through the remaining life course. The population average CPD exhibits a relatively stable pattern up to age 50 and then a downward trend, which is consistent with the smoking likelihood pattern discovered by Darden, Gilleskie, and Strumpf (2018).⁶

Turning now to the cessation data (Chen et al. (2012)) to be used in our quantitative analysis,⁷ we note that the share of H1, H2, and H3 genotypes among smokers is about 25%, 43%, and 32%, respectively. While the shares of the three genotypes do not vary significantly by gender or education, they do by race. In particular, panel A of Table 1 shows that whites have a much larger share of the H3 haplotype than blacks and blacks have a much larger share of the H1 haplotype than whites, while the share of the H2 haplotype is similar for both. Additionally, panel B of Table 1 summarizes the smoking behavior of the three genotypes in terms of CPD, indicating that H1 smokers are the lightest smokers, whereas H3 smokers the heaviest smokers.⁸

2.2 On smoking cessation and treatment effectiveness

Extensive research supports the effectiveness of counseling and pharmacological interventions in increasing smoking cessation rates among smokers. Successful counseling boosts the motivation to quit by personalizing the costs and risks of the patient's tobacco use. Seven medications are also approved by the Food and Drug Administration (FDA) for treating nicotine dependence.

Medical studies suggest that, among the three genotypes, H3 smokers (the high-risk haplotype) are less able to quit, more likely to smoke longer or inhale more deeply; thus, the risk in mortality is higher for H3 (cf. Kortmann et al. (2010) and Chen et al. (2015a)). Panel C of Table 1 presents the quitting behavior of the three genotypes. The quit rates are taken from the experiment data in Chen et al. (2012),⁹ adjusted by a 25% relapse rate.¹⁰ Interestingly, despite belonging to the high risk group, H3-type smokers are most responsive to medication treatment compared with the other two genotypes. The quit rate is only 16.8% for H3-type smokers if only counseling is provided and 35.5% with medication and counseling. This quit rate, however, is essentially unchanged for H1-type smokers (34.9% regardless of the provision of medication), and for H2 smokers, it is 25.3% without medication and 36.0% with medication. Moreover, conditional on genotype and treatment, college educated smokers have a substantially higher quit rate than noncollege educated smokers.¹¹

3.1 The basic environment

Time is continuous. An individual's life starts at $$ when she acts as a decision maker (who may be referred to as a young adult).¹⁵ Her life ends at T, which is endogenous.

3.2 Optimization

Consider an individual of type $$ that summarizes genotypes, work efficiency driven by gender/race/education, natural health deterioration rate by gender, and initial smoking habit (=0 for nonsmokers). The baseline dynamic optimization problem in the absence of treatment can be conveniently divided into three steps.

3.3 Responses to treatment under voluntary take-up and government intervention

As documented in the medical literature, smoking cessation is difficult to achieve, especially for noncasual smokers.²⁴ As shown by Koçak et al. (2015), although 70% of smokers desire to quit, only 46% of them have made an attempt to quit and less than 10% quit for an extended period. Government interventions, however, by providing financial incentives, can significantly increase the probability of participating in and completing a smoking cessation program by smokers, thereby enhancing cessation success (Volpp et al. (2009)). Moreover, this literature suggests take-up of cessation treatment as nonbehavioral, and hence, we shall view take-up rates as exogenous probabilities and instead focus on modeling responses to treatment, given a cessation program. We shall not model smoking relapse either because medical evidence also suggests it most likely nonbehavioral.²⁵ Thus, we simply adjust the quit rates from Chen et al. (2012) by a relapse probability (25%) to be used as the targeted moments in our numerical applications.

4.1 Baseline calibration

We calibrate the model to fit targeted moments of both smokers and nonsmokers. While we consider demographics as the only source of heterogeneity for nonsmokers, smokers are also allowed to be heterogeneous in initial smoking habits and smoking-associated genotypes. In particular, we categorize smokers into 6 groups based on initial habits, $$, determined by adolescent smoking (at age 18). Smokers with different genotypes, indicated by $$, differ in their preference for smoking, α, and habit scaling parameter, $$. We also incorporate heterogeneous work efficiency, θ, for eight demographic groups (by gender/race/education) as well as differential natural health deterioration rates, δ, by gender. Accordingly, there are 144 ($$) groups of smokers and 8 groups of nonsmokers in total.

Some parameters are determined outside the model, by normalization or by direct data measurement. We normalize the efficiency wage rate, w, to one and set the subjective time discount rate, ρ, to 0.02 to fit the average US wealth-income ratio of about 7 (Glover, Heathcote, Krueger, and Ríos-Rull (2020)). The growth rate of consumption, g, is set to equal to that of output per capita in the US (1.8%) to ensure long-run balanced growth, and hence, the real interest rate becomes $$. Lacking good panel data on wealth, we set initial wealth to be 15% of average initial labor income as permanent flow income converted to capitalized value: $$.

The initial stock of health at age $$ is normalized to $$ under which the threshold health level at death is calibrated at $$ to match the average mortality rate and average life expectancy of the US population.²⁷ The health investment curvature parameter ϵ is set to 0.3, following Hall and Jones (2007), to produce a reasonable health investment profile.

Because smoking drops by half at age 65, we apply the half-life formulation to compute the habit adjustment parameter: $$. To capture individuals' incomplete knowledge about the detrimental health effect of smoking, we use the empirical finding by Kenkel (1991) that for 7 illnesses that can be caused by smoking, respondents surveyed (including both smokers and nonsmokers) are aware of 5.5 on average. We therefore assume that individuals' belief of $$, that is, $$, to be 1/4 lower than $$.²⁸ Moreover, recall that $$ measures the detrimental health effect resulting from second-hand smoke. We set q to be 0.125 based on the finding in Pickett et al. (2006) that, even in US counties with extensive smoke-free law coverage, the exposure to second-hand smoke for nonsmokers is about 12.5%.

Based on the PSID data, initial smoking habits are given by $$.²⁹ The correspondent population shares of the six groups are $$. We set the gender (male-to-female) ratio of $$ to be 1.6 within each $$ group, based on the PSID data on youth's CPD, and compute $$ for each gender in each $$ group accordingly. Notably, to which $$ group a smoker belongs is assumed independent of genotype, to be consistent with the medical evidence that the formation of initial smoking habits is largely influenced by environment rather than by genes.

In the labor economics literature, the wage-tenure profile estimation usually yields an experience return at 3–5%. We thus use the average to set $$. Then to align health-based and experience-based human capital, we jointly calibrate κ and $$ to match income peak age of around 52 and the peak to initial income ratio of about 2.27, as documented in Guvenen, Karahan, Ozkan, and Song (2021). This yields $$ and $$. Regarding the extent to which bequest is a luxury good, we match our figure $$ with that in De Nardi (2004), which gives $$.

We calibrate θ for each of the eight demographic groups using PSID labor income of household heads aged between 23 and 26, normalized to an average of one. We do this for three reasons. First, the vast majority of people have completed education and started working by age 23. Second, their health may have not been significantly affected by smoking by age 26. Third, the experience may have yet contributed much to their labor income. In Table 2, we report the population share of each group among smokers and the calibrated value of θ for each group. As can be seen, the college educated all have higher than average work efficiency and are thus expected to have higher labor income, controlling for age. Blacks with no college degree, on the contrary, have much lower work efficiency, and hence, lower labor income within the same age cohort. In addition, there is a gender gap that leads to higher labor income for males than for females. Such gaps are larger for whites than for blacks. These implied patterns are in line with the labor economics literature.³⁰

Denote y as labor income and Y as total income (labor plus interest income, which is of greater relevance, especially for the retired). There are three functional forms to be specified: (i) health valuation: $$; (ii) detrimental health effects of smoking: $$ (where $$ ensures that $$ rises with age); (iii) health investment efficacy: $$. We are thus left with 20 parameters to be calibrated within the model: $$, χ, $$, B, η, $$, $$, $$, ν, $$, p, μ, α, and $$ by genotype, and δ by gender. They are jointly calibrated to meet the quitting threshold expression (8), as well as the 19 targeted moments: (i) 4 expenditure/bequest shares: consumption expenditure share ($$), health investment share ($$), smoking expenditure to labor income share ($$), and bequest-asset ratio measured by the share of total assets that come from bequests ($$); (ii) 1 smoking and 2 health investment gradients: age 50 to 25 smoking ratio ($$), health investment at age 38 and 60 to initial investment ratio $$; (iii) 2 smoking population shares: shares of smokers at age 50 and 65 ($$ and $$); (iv) 7 life year measures: the average life expectancy for nonsmokers and smokers ($$, $$) and for males and females ($$, $$), and 3 age-dependent life year gains as a result of smoking cessation at age 30, 40, and 50 ($$, $$, and $$); and (v) 3 average smoking levels by genotype ($$).

All expenditure and income measures are based on the US data averaged across individuals and over time. The consumption share is measured by the ratio of consumption (excluding tobacco consumption and private health expenditure) to GDP, from Penn World Table 6.3 (average over 1998–2007). The health investment share is measured by the average healthcare cost-to-GDP ratio, from the World Bank 1998–2010. We find an average individual invests about 15% of her income in health. The smoking expenditure ratio is computed as an average household head's smoking expenditure over labor income, using data from PSID (1999–2011).³¹ More specifically, smoking expenditure ps is computed by multiplying (tax-included) price of per pack of cigarettes, CPD from PSID, and 365 days in a year. We find an average individual (weighted average of smokers and nonsmokers) spends about 1.6% of her labor income on smoking. We set the bequest-asset ratio to 0.6, following De Nardi (2004). The smoking gradient (age 50 to 25) is set to 0.46, based on Holford et al. (2014);³² and the two smoking population shares are computed from PSID. The two health investment gradients are based on Hall and Jones (2007). The average life expectancy of the US population is 78 years, based on the World Bank data (1998–2011), and females live about 5 years longer than males on average. From Jha et al. (2013), the gap of life expectancy between smokers and nonsmokers is 12 years, and the average life year gain for smokers who quit at the ages 30, 40, and 50, respectively, are 10, 9, and 6 years. These give us life expectancy and life year gain figures. Finally, the smoking intensity of three genotypes is based on the CPD data from Chen et al. (2012) converted to model units.

We calibrate the 20 parameters jointly within the model by minimizing the distance between the model and the targeted values given the threshold expression (8). The algorithm for calibrating these parameters is as follows. We first choose a set of values for the parameters (initial guesses), and then solve the model for the 144 groups of smokers and 8 groups of nonsmokers. Next, given the population share of each group, we compute the weighted average of the targets from the model and compare them with the corresponding targeted values. The process reiterates until the sum of all gaps between model and data moments converges. Table 3 summarizes the parametrization, with panel A reporting predetermined parameters and panel B reporting parameters calibrated within the model. Table 4 presents the model fit, data versus model moments, showing a good fit overall.

The only imperfect match is the overestimation of smoking population shares, which is essentially due to the absence of cessation treatments in the baseline calibration. Recall that Koçak et al. (2015) show that despite 70% of smokers wanting to quit, only 46% of them have made such an attempt and less than 10% maintain abstinence for an extended period. Assume any such attempts include uses of formal treatments (counseling or counseling and medication), as well as usage of over-the-counter treatments (nicotine patch/inhaler/nasal spray/gum). Then we may view a general treatment rate, or a take-up rate (without a government intervention), as $$, and a share of smokers who quit with voluntary treatment as $$. Taking this into account would sufficiently close the gap in the share of smokers between the model and data.

4.2 Calibrating cessation treatment effects

We now calibrate the smoking cessation treatment effects under voluntary take-up and under policy-induced participation. According to Volpp et al. (2009), smokers receiving sufficient financial incentives have significantly higher rates of participating in and completing a smoking cessation program, and hence, have a significantly higher quit rate. Our calibration of treatment responses is based on the experimental data from Chen et al. (2012), which involves quit rates by genotype, education, age, and treatment (i.e., counseling or counseling plus medication). We use these quit rates as the targets for calibrating policy-induced treatment effects because their experiment provided free cessation treatment.³³ To back out the quit rates under voluntary take-up, we borrow the numbers from Koçak et al. (2015) and estimate the average quit rate under voluntary treatment to be 21.7%.³⁴ We then compute the ratio of average quit rates under policy-induced treatment and under voluntary treatment to be 1.6 and use it to back out the quit rates under voluntary take-up for smokers by genotype, education, age, and treatment.

Since the experimental data from Chen et al. (2012) contains only heavy smokers, we exclude light smokers and focus on smokers with initial smoking habits given by $$; the correspondent population shares of the five groups are $$.³⁵ To calibrate heterogeneous responses to different types of treatment, namely counseling versus counseling plus medication, we need more within the genotype-demographic cell variations in $$ – with only five groups of $$, the quitting response may be too lumpy, leading to imprecise calibration outcomes. It is known that self-reported CPD figures are concentrated on a quarter pack, half a pack, one pack, and one pack and a half (5, 10, 20, and 30). As such, it is uninformative to use the distribution of $$ directly. We instead interpolate 3 additional data points in between each pair of figures (one-quarter, half, and three-quarters). This gives us 17 data points in $$ within each of the 24 cells by genotype and demographics: $$, with corresponding population shares given by {0.024, 0.037, 0.050, 0.063, 0.076, 0.076, 0.076, 0.076, 0.076, 0.074, 0.072, 0.069, 0.067, 0.057, 0.046, 0.036, 0.025}. Again, the gender ratios of $$ are set to be the same across all 17 $$ grids. Moreover, Chen et al. (2012) focus on two major age groups, 25–44 (average 37) and 45–66 (average 52), and show differential quit rates across the two groups. We follow by examining the quitting responses of young (37) and old (52) addicts.

4.3 Lifecycle pattern

Before turning to the main policy evaluation task, it is informative to illustrate how genotype heterogeneity affects individual smokers' lifecycle choices and to compare the lifecycle pattern of several key indicators to the data.

Table 7 presents a comparison in key indicators for each genotype of smokers, nonsmokers, and the respective population weighted averages. As can be seen, life expectancy of smokers is 11–12 years shorter than nonsmokers. H3-haplotype smokers live slightly shorter than other haplotypes, consistent with medical evidence that CHRNA5 is associated with increased mortality (Halldén et al. (2016)). Smokers spend about 6–7% of labor income on tobacco, thus having a lower share of other consumption than nonsmokers.

The health expenditure ratio in row 5 may seem to be low for smokers compared with nonsmokers, given that more health maintenance is needed by addicts. This arises from the large life year gap between smokers and nonsmokers, and the sharply increasing health care expenditure at very advanced ages when diminishing returns kick in. This raises the average healthcare expenditure ratio of nonsmokers over the life span. If we trim everyone's life span to 60 years (i.e., the shortest life years among all groups of smokers), then smokers' average health investment share becomes 7 percentage points higher than nonsmokers' (see the last row of Table 7).³⁶

Figure 2 displays the lifecycle pattern of several key indicators, contrasting an average nonsmoker and an average smoker. First, while nonsmokers have higher labor income than smokers, the total income gap is even more substantial because of greater asset accumulation toward later stages of life. Second, health investment share of smokers is slightly higher than that of nonsmokers until the late 60s, since smoking-deteriorated health requires stronger effort to maintain; the health investment share, however, rises substantially for nonsmokers at more advanced ages due to their longevity.³⁷ Third, the death hazard, defined as the mortality rate at a given age conditional on survival up to that age, is higher for smokers than for nonsmokers at any point in life. At age 37, the death hazard is 0.0163 for smokers and 0.0154 for nonsmokers; the gap widens to 0.0518 versus 0.0383 at age 65. For most periods of life, smoking contributes to over half of the death hazard of a smoker (see details in Supplemental Appendix D).

To compare model predictions with the data, we report in Table 8 three gradients of total income, health investment share, and health capital at age 37, 52, and 65 (relative to age 23 for the income and health gradients). The first two ages are the two treatment ages used for policy evaluation. Because these are untargeted moments, they serve as an additional validation of our calibrated model.³⁸

The results indicate that smokers have a flatter total income gradient than nonsmokers and that our model prediction of the pattern is correct despite over prediction at older ages (due to our simplified setting of asset income). Meanwhile, the health investment share gradient is steeper at older ages, in line with the literature (e.g., De Nardi, French, and Jones (2010)). While the overall prediction for nonsmokers captures the rising pattern with a sharp increase toward the end of a lifetime, that of smokers is somewhat of—the model underpredicts an average smoker's health investment share at age 52 but overpredicts it at age 65. This might be due to smoking-led serious diseases occurring at the 50s, and sample trimming of older smokers as a result of death (with the surviving ones being increasing representative of those biologically resilient to cigarette exposure). Since we do not model large health shocks or the small biologically resilient group, we end up fitting the average smoker's hump-shaped health investment share in the data with a smooth and positive trend that more reasonably captures a representative smoker's lifecycle pattern of health investment. Overall, our model yields a downward health capital gradient: to an average nonsmoker, health capital drops at an increasing rate from age 23 to age 65 and an average smoker's health falls by even more, especially at older ages.

5.1 Method

We compare the effectiveness of the following three government policies, two standard medication policies (S, $$), and one personalized medication policy (P), all under the same budgetary cost. Thus, whichever policy yields greater value of effectiveness is by construction more cost effective. The three smoking cessation policies are specified as follows:

Policy S is a proxy for the standard policy that recommends that all smokers receive counseling and medication, whereas policy $$ is a proxy for some real world policy under which some smokers only receive counseling, while others receive counseling and medication. Neither policy takes smokers' genotypes into account. By contrast, policy P is personalized based on the genotype: (i) smokers receive a rebate only if they have taken a genetic test, and (ii) only those with genotypes responsive to medication would receive a rebate for medication treatment.

Several remarks regarding the treatment policies are in order.

First, the size of the subsidy in the benchmark case under policy S ($1400 per person) is adequate for covering the full cost of the counseling and medication treatment ($1050; see the detailed breakdown below) and for compensating the time cost of taking treatment ($350, about 1% of an average smoker's labor income, since treatment takes about 1% of average annual working hours). The inflation-adjusted amount matches with the subsidy offered in the cessation experiment conducted by Chen et al. (2012) that provides free treatment and compensates for the time cost.³⁹

Second, while the size of the budget regarding 10% coverage of smokers in the benchmark case under policy S is only for illustrative purposes, the total budget figure is feasible in practice and the subsidy rate in our experiment is viewed a feasible, conservative figure.⁴⁰

Third, the three policies have equal total budgets. Given that the shares of the three genotypes among smokers are 0.25, 0.43, and 0.32 for H1, H2, and H3 (Chen et al. (2012); Bergen et al. (2013)), we compute the fraction of smokers to be subsidized under policy P as 12.2% to meet the budget.

Fourth, the value of each type of rebate in policy P is based on the treatment or test cost. We estimate the monetary cost to be $150 for counseling, $900 for medication, and $200 for a genetic test. We thereby set the full rebate under policy P to be the same as policy S ($1400) to cover the test, counseling, and medication for H2 and H3 smokers, and then set the value of each type of rebate to be proportional to the cost of the corresponding treatment or test.

Fifth, policy $$ is designed to mimic policy P, except not being gene-based. It covers not only the same fraction of smokers as policy P (12.2%), but also the same fraction to receive counseling (3.1%) and to receive both counseling and medication (9.1%) as policy P. Moreover, those subsidized only for counseling under $$ receive the same amount of subsidy as the H1 smokers under P, and those subsidized for both counseling and treatment under $$ receive the same amount of subsidy as the H2 and H3 smokers under P. A comparison between policies $$ and P, therefore, isolates the effectiveness of personalized medication.

We carry out the policies on smokers aged 37 or 52. We solve the model for each group of smokers with different genotypes, demographics, and initial smoking habits (thus, $$ groups in total) when they are subsidized by a policy at 37 or 52. When modeling the cost of treatment or the genetic test, we also consider time cost (i.e., time needed for traveling, waiting, and receiving treatment), and convert the time cost into labor income losses using the hourly wage of each group (using PSID data). Based on medical practice, we estimate that it takes about 9 hours to receive counseling, 7.5 hours for medication, and 2 hours for a genetic test.

We employ six measures for policy comparison: (Measure 1) share of smokers that can be subsidized, (Measure 2) quit rates of subsidized smokers, (Measure 3) Consumption Equivalent (CE) of subsidized smokers, (Measure 4) Income Equivalent (IE) of subsidized smokers, (Measure 5) value of a statistical life (VSL) gains of quitters, and (Measure 6) one-time wealth transfer as a fraction of lifetime income for quitters and for subsidized smokers. While Measure 2 is standard, Measure 1 is an extra extensive margin that has often been overlooked in previous studies. The omission of this extensive margin effect would bias the cost-effectiveness analysis significantly, particularly because of the nature of personalized medical treatment. Measures 3–6 require further explanation.

Furthermore, we take into account voluntary take-up of treatment, since subsidizing smokers who would have taken up treatment even without subsidy would bias the overall policy effectiveness. We incorporate two margins into CE and IE to reflect policy effectiveness net of voluntary take-up. First, the policy induces smokers who would have not taken up treatment into cessation programs. According to Volpp et al. (2009), these are about 65% of smokers.⁴¹ Second, for those who would have taken treatment without intervention, the policy increases their probability of completing the cessation program, and hence, their probability of quitting—a margin that has been calibrated in Section 4.2. We assume all voluntary take-ups involve both counseling and medication treatments, which produces a conservative measure of net policy effectiveness.

Based on IE, we compute the VSL gain from quitting by multiplying a smoker's VSL without quitting (discussed below) by her IE with quitting. The gain measured by a one-time wealth transfer in the year of policy implementation can also be computed as IE (without adjustment for life years in this case) multiplied by her lifetime labor income.

Notably, our CE and IE measures are more general than the typical measure by QALYs in the literature of medicine and health. In contrast with QALYs, our lifetime utility-based effectiveness measures account for time discounting and diminishing marginal valuation. Moreover, our measures consider differential utility weights that are calibrated to the data. Furthermore, our measures incorporate heterogeneous individuals' dynamic responses. This is important because such responses vary across individuals over the life course.

5.2 Validating the quantitative model: Value of a statistical life

The value of a statistical life (VSL) helps validate our key measure of IE for constructing a dollar measure of effectiveness. By normalizing the value of death to zero (which can be simply obtained by setting $$ for all individuals and $$ for smokers, all at their subsistence levels), one may compute VSL as the dollar value of willingness to pay for a living status on average. This is done by first computing CE and IE as the percentage decrease in lifetime utility from life to death and then multiplying IE by average income of an individual to obtain a dollar measure. We finally convert permanent flow income to capitalized dollar value at age 45 (average age of a licensed driver in the US as we plan to compare our VSL with empirical estimates by Ashenfelter and Greenstone (2004)) based on the real interest rate of 3.8% and the life expectancy of smokers and nonsmokers.⁴²

We estimate VSL for smokers and nonsmokers of all subgroups and their population-weighted average. Since smokers have lower average work efficiency than nonsmokers ($$ vs. 1.03), lower average labor or replacement income (277 vs. 289 efficiency wage units) and lower life expectancy (69 vs. 81 years), their VSL is lower than nonsmokers. The VSLs for type H1, H2, and H3 smokers are estimated as 2.125, 2.209, and 2.187 million US dollars, largely comparable across genotypes. Given the population weights for the three genotypes, the (weighted) average VSL of a smoker becomes 2.181 million US dollars. The VSL of an average nonsmoker is computed as 2.665 million US dollars. Thus, VSL of an average smoker is 18% lower than that of an average nonsmoker, indicating a large gain from smoking cessation. Given the population weights (24.6% smokers and 75.4% nonsmokers), the (weighted) average VSL in our model is 2.546 million US dollars, in line with the empirical literature.⁴³

5.3 Findings

5.3.2 Lifecycle profiles: Quitters versus nonquitters

To compare lifecycle profiles between a quitter and a nonquitter, we consider a quitter as one who stops smoking after treatment at age 37 or 52, under a particular policy, with a nonquitter as the counterfactual case of the same person who did not quit. For illustrative purposes, we focus on two demographic groups: (i) white females with no college degree (the largest group of smokers with work efficiency far below one) and (ii) white males with a college degree (constituting a small share of smokers but with the highest work efficiency). For both groups, we choose the H2 haplotype, which constitutes the largest fraction of smokers in both demographic groups.

Figure 3 plots the lifecycle profiles of the smoking expenditure share and the health investment share, and Figure 4 plots the lifecycle profiles of health capital and total income. Both are for quitting at 37, while we relegate the similar pattern for quitting at 52 to Supplemental Appendix Figures A1–A2. Several observations are in order.

First, while the smoking expenditure share declines over the lifecycle for both groups of smokers, that of the white males with a college degree is much lower than that of the white females with no college degree, because the former group has higher income and higher opportunity cost of smoking than the latter group.

Second, both groups have U-shaped health investment shares, which increase sharply after retirement; smoking cessation reduces the health investment share in the short run while increases it in the long run due to increased life years. Throughout the life time, the health investment share is higher for white males with a college degree than white females with no college degree, since the positive health effect on life expectancy makes health a luxury good relative to consumption.

Third, smoking cessation slows down health deterioration, boosting up health capital by a large margin. While the health capital of white female nonquitters with no college degree and white male nonquitters with a college degree deplete by half at ages 54 and 53, respectively, quitters in both groups are able to prolong the half-life by 8–9 years. At 52, both groups have about 14% higher health capital by quitting.

Fourth, for both groups of smokers, total income reaches the peak 3 years earlier for nonquitters than for quitters. At the respective peak-income ages, white female quitters with no college degree and white male quitters with a college degree have 12.3% and 9.5% higher total income than their nonquitter counterparts. Such gains drop substantially when quitting at 52, to 0.7% and 1.6%, suggesting a larger smoking cessation effect on income enhancement when quitting earlier.

5.4 Sources of welfare gains

We begin by verifying the essentiality of endogenous life expectancy and smoking habits for the working of smoking cessation policies. Our counterfactual exercises indicate that the endogenous life expectancy effect is a necessary driver for health investment: without it, individuals would have not had sufficient incentives to invest in health for higher earnings (i.e., $$ in all circumstances). The detrimental effect of smoking habits on utility is also a necessary driver for quitting under treatment: without it, addicts would have not had sufficient incentives to quit smoking. That is, they are quintessential channels for welfare gains from any smoking cessation policy, which will be included throughout the decomposition analysis below.

There are four additional channels through which the smoking cessation policy may yield welfare gains: (i) a pure income channel (PI) due to subsidy received by each participant net of the out-of-pocket cost to participate the program, which would not affect any decision margins; (ii) a health-productivity channel (HP) resulting from higher labor income due to better health; (iii) a health investment channel (HI) that raises health capital and life expectancy but is accompanied with higher out-of-pocket expenditure; and, (iv) a bequest motive channel (BM) due to greater wealth accumulation induced by better health. Once these channels are considered, the smoking cessation effect on consumption is automatically accounted for, via pure and labor income channels (PI and HP) as well as consumption-health investment and consumption-bequest trade-offs (captured by HI and BM).

To perform counterfactuals, we focus on the quitters in the benchmark policy experiments under policy P and recompute their CE and IE by solving the model with one of the channels above shut down. In particular, the net income effect with policy ($$) is simply a once-and-for-all term at the time of policy implementation ($$): $$ per participant subsidy—per participant program cost. Because by construction the net income effect without policy ($$) is zero, to shut down PI, we set $$ at $$. To shut down HP, we set the labor income path $$ to the no-policy benchmark and set $$ to zero.⁵⁰ To shut down HI, we restore the health investment path under policy $$ to the no-policy benchmark.⁵¹ To shut down BM, we set $$. We compute the contribution of each channel j as: $$ of benchmark—CE of $$. By renormalizing total contribution to 100%, we obtain the following decomposition results: $$, summarized in Table 13.

Overall, the endogenous health investment (HI) is most important, accounting for over 60% of the welfare gain from the smoking cessation policy. This is because HI incorporates not only the policy effects on health capital throughout life but also the consequent impact on life expectancy. The health-productivity (HP) channel is also important, but only when treatment occurs at a young age. On the contrary, bequest motive (BM) is equally important as HP when one takes the treatment and quits at a young age, but its contribution rises at an old age because its lifesaving effect on wealth accumulation to be used by the descendants becomes more prominent when incremental labor income in-flows start to decline. Regardless of the treatment age, the pure income channel (PI) is inconsequential.

5.5 Further discussion

We further conduct three counterfactuals to investigate the roles played by (i) second-hand smoke, (ii) incomplete knowledge about the detrimental health effect of smoking, and (iii) undervaluation of health, in the effectiveness of policy P. In particular, we set, respectively, $$ (absence of second-hand smoke), $$ (complete health knowledge), and $$ (full valuation of health). The results are reported in Supplemental Appendix Table A6.

Second-hand smoke is found to cause lower life year gains from quitting and lower quit rates for old addicts but higher quit rates for young addicts. At both ages, however, welfare gains from smoking cessation policy for quitters are lower. The presence of second-hand smoke would yield a stronger role played by smoking cessation policy for mitigating smoking-induced negative externalities. Thus, it is expected that second-hand smoke can lead to greater cost effectiveness (lower C/E ratios), but our result indicates it is so only when the policy is implemented for young addicts. This latter finding is mainly due to the lower quit rate for the old addicts with second-hand smoke: the old have already reduced smoking before treatment, so the presence of second-hand smoke makes quitting a less important margin; on the contrary, the young smoke more heavily, so quitting becomes more important given the detrimental effect of second-hand smoke.

The presence of incomplete knowledge yields higher life year gains from quitting. Similar to second-hand smoke, it lowers quit rates for old addicts due to weakened incentives for quitting, but higher quit rates for the young who are more vulnerable. Yet, for quitters, the welfare gains from smoking cessation policy are higher for old quitters but lower for young quitters. Because quitting is the main driver quantitatively, cost effectiveness is lower for old smokers in the presence of incomplete knowledge, though more modest than second-hand smoke.

Undervaluation of health always results in smaller life year gains from quitting and lower quit rates, regardless of the treatment age. While it lowers welfare gains of a young quitter, it raises that of an old quitter due to the lesser degree of undervaluation ($$ increases over the lifecycle. Nonetheless, undervaluation of health causes smoking cessation policy less cost effective for both ages. Our results are in line with empirical findings in Adda and Lechene (2013) in which individuals who have poorer nonsmoking related health (and thus tend to undervalue health) are more likely to start smoking and to smoke more cigarettes than those with better nonsmoking related health, and that smoking has a lower effect on mortality for the former group than for the latter group.

One might also wonder whether there is an optimal age for policy intervention? Unfortunately, limited samples in the clinical trials prohibit us from conducting the exercises at all ages. Nonetheless, we may gain further insight by constructing an overlapping group under age 45 (mean age of the 35–54 age group, covering half of the 25–44 age group and half of the 45–64 age group). In Supplemental Appendix Tables A7–A8, we report the counterparts of calibrated figures to Tables 5–6 and Table 12 in the main text. As can be seen, quit rates and equivalent measures often exhibit nonmonotonic patterns over ages 37, 45, and 52, where some patterns are even U-shaped.⁵² Thus, it becomes difficult to pin down a reasonable range for the optimal age of policy intervention.

We conduct two sets of robustness checks, one considering the net deadweight cost of medical treatment and the other considering a lump-sum tax imposed on all agents to finance the government subsidy. A summary of the results is presented in Supplemental Appendix Table A9. In short, we find that such variations do not alter much of our main findings, neither qualitatively nor quantitatively.