Kicking the habit is hard: A hybrid choice model investigation into the role of addiction in smoking behavior.

Use of choice models is growing rapidly in tobacco research. These models are being used to answer key policy questions. However, certain aspects of smokers' choice behavior are not well understood. One such feature is addiction. Here, we address this issue by modeling data from a choice experiment on the US smokers. We model addiction using a latent variable. We use this latent variable to understand the relationship between choices and addiction, giving attention to nicotine levels. We find that more addicted smokers have stronger preferences for cigarettes and are unwilling to switch to e-cigarettes. Addicted smokers value nicotine in tobacco products to a much greater extent than those that are less addicted. Lastly, we forecast short-term responses to lowering nicotine levels in cigarettes. The results suggest that current nicotine-focused policies could be effective at encouraging addicted smokers to less harmful products and lead to substantial public health gains.

2004; Strong et al., 2017 for latent variables to measure addiction in tobacco); while we are not the first to take a latent variable approach to measuring addiction, we are the first to use it in a hybrid choice framework to analyze smoking choices. Figure 1 is a schematic of the modeling framework. Within the system, the latent variable is used to explain observed variables, such as indicators of addiction. Thus, these variables do not enter the choice model directly, avoiding possible endogeneity issues. Moreover, this framework can accommodate any number and form (i.e., the nature of the data) of indicator, using all the available information. The latent variable is then used in the utility function in place of the indicators (which would be a more traditional approach). Because there is only a single addiction variable, having to specify a large number of parameters directly in the utility function is thus also avoided. Of course, additional parameters are required for the measurement model components that are used to explain the values observed for the indicators.
The experience-conditioned choice models Hensher, Balbontin, & Greene, 2019;Hensher & Ho, 2016) are based on the notion that preferences and choice behaviors are in part a function of a given individual's prior experience with a given product or service. In the context of smoking, this implies a behavioral assumption that tobacco product choices are to some extent determined by the past use of tobacco products. This is highly appealing because the idea is applicable to both the addiction to nicotine and formation of habits that are associated with longer term, habitual tobacco product use (Wehbe et al., 2018). For this reason, we test addiction-conditioning in our model 1 .
Developing this model allows us to overcome a set of difficult empirical issues and specify a behaviorally appealing model of short-term smoking choices. This model embodies a more sophisticated depiction of smokers' cognitive decisionmaking processes than in previous work. We use this model to study the relationship between addiction and choice behavior, examine smokers' willingness to pay (WTP) for nicotine in tobacco products, and predict the impact of lowering nicotine in cigarettes (which has recently been proposed by the US government). With this, policymakers are better informed in key issues around smoking and addiction. The remainder of the paper is set out as follows. In section 2, we set out the model and its features. In section 3, the results from the model are presented. Section 4 summarizes and discusses.

| Experiment and data
Data are taken from a labeled smoking choice experiment in which 1531 adult smokers chose between cigarettes, e-cigarettes and an opt-out option 2 , labeled "none of these" ; see Figure 2 for a sample choice scenario). Products were described by four attributes: nicotine, flavor, health harms, and price. These attributes and levels were defined according to literature reviews, pilot studies, consultation with subject matter experts, and according to policies that the Food and Drug Administration (FDA) could implement. Restrictions on attribute levels were made to make the experiment more realistic, for example, fruit and sweet flavored cigarettes are not available on the market, so we did not allow them in the experiment; attribute level balance was maintained in the design as far as possible by the design software, Ngene (Choice Metrics, 2018). Table 1 shows the products, attributes, and levels. The design was Bayesian D-optimal, using priors obtained from a pilot study of 87 respondents. The design was based on the main effects only (i.e., without interactions). Individuals each answered 12 choice sets, which balances concerns of learning and respondent fatigue (Hess, Hensher, & Daly, 2012). A total of 36 choice sets were divided into three blocks, and respondents were randomized to each block in the ratio 1:1:1. Choice sets were presented in the same order within blocks. Sampling was based on quotas, defined using the Behavioral Risk Factor Surveillance System data in 2013/14, based on gender, age, education, and region, to make the sample representative of the US smokers. Table 2 shows the descriptive statistics for individuals in the sample. The sample size was sufficient to ensure statistical power for the main parameters and is larger than most discrete choice experiments in health (de Bekker-Grob, Donkers, Jonker, & Stolk, 2015). Data quality measures, including minimum time thresholds, forced responses, attention checks, cheap talk, duplicate ID checks, and practice choice scenarios for respondents, were taken to promote data quality. Failure of any of these checks resulted in respondents being ejected from the survey.
A survey was collected alongside the experiment. In this survey, sociodemographic information on respondents was collected. We also collected revealed preference data on respondents' tobacco behaviors. This data include product use and products' attributes such as prices and flavors. For addiction, a number of indicators of addiction were collected. These were daily smoking, number of cigarettes smoked per day, time before first cigarette of the day is smoked, time since last having smoked a cigarette that day, time since last having smoked a cigarette in the last few days/weeks, the BUCKELL ET AL. number of quit attempts in the past year, e-cigarette use, frequency of e-cigarette use, and current urge to smoke (i.e., craving). These measures include those which may be considered outcomes such as cigarettes per day versus symptoms such as craving (cf. Bold et al., 2018;Strong et al., 2017).
Summary statistics for these measures are shown in Table 2.

| Choice models
In a standard random utility model, the utility U nit that individual n derives from product i in choice t comprises a systematic component, V nit , and a remaining error term, ε nit that follows an iid type I extreme value distribution, such that: F I G U R E 1 Schematic of hybrid choice model for addiction. Square boxes are observed variables; ellipses are unobserved variables. NB, "Tobacco Products and Attributes", particularly nicotine, could of course impact on addiction. But these will be longer-term effects, rather than short-term choices. In this setup, the attributes impact on short-term choices via utility; longer term effects impact on addiction and addiction, in turn, influences utility and choices.
F I G U R E 2 Sample choice scenario. Four options were presented to each respondent in each choice set, along with an opt-out option, "none of these" The systematic component incorporates two parts, with: where δ ni is a constant capturing product-specific preferences for alternative i, where this includes cigarettes, e-cigarette, and the opt-out. β n is a vector of estimated sensitivities capturing the impact of changes in explanatory variables x nit , where this includes nicotine, flavor, health harm, and price. Both δ ni and β n are person-specific, where the former is also different across alternatives. We next allow for deterministic and random heterogeneity across individuals in the values of both δ ni and β n , both directly, and through the latent addiction variable. In particular, we have: and for the coefficient associated with attribute x ni k t : In this specification, μ δ i and μ β k capture mean values in the sample population for δ ni and β nk ; λ δ i and λ β k capture shifts in their values as a function of sociodemographic characteristics, z n ; σ δ i and σ β k capture random heterogeneity, where ξ nδ i and ξ nβ k follow standard normal distributions across individual respondents; and τ δ i and τ β k capture the impact of the latent addiction variable, α n , a point we return to below.
For the price sensitivity, we relax the oft-assumed constant marginal utility of income imposed in many health choice models (Reed Johnson, Mohamed, Özdemir, Marshall, & Phillips, 2011). Preferences for the cost attribute p, are treated as: This drops the random heterogeneity and impact of the latent addiction variable, but adds in an income effect where η is an estimated income elasticity, income n is a given individual's income and income is the sample median.
As per Figure 1, the latent variable for addiction is regressed on individual characteristics in the structural equation: where z n is individual characteristics, γ captures the relationship between addiction and observed individual characteristics, and ξ n is unobserved individual addiction heterogeneity, which follows a standard normal distribution. In our specification, we allow for an impact of the latent addiction variable on the constants for the different alternatives as well as the parameters associated with individual attributes. This in essence means that our model is a standard hybrid choice model, albeit one where the latent variable relates to experience/addiction. We did test a model in which the entire utility function was addiction-conditioned, as in the original Hensher and Ho (2016) work, but this led to inferior results, largely as a function of the conditioning exerting itself on all sensitivities in the same direction, whether they relate to desirable or undesirable components.
With the elements of the utility function defined, we move to the specification of the choice model, which, given the assumption on the error term, takes the classic multinomial logit form: where P C n is the probability of the observed sequence of choices for individual n, where i * refers to the chosen alternative. Next, we examine the relationship between the latent variable for addiction, α n , and the indicator measures of addiction. The data for the indicator measures take three broad forms. For each, its probability is modeled in a series of measurement equations. For the two binary variables (daily smoking, e-cigarette use), such as whether the individual smokes every day or not, a logit model is used: where δ k are constant terms to be estimated, and ζ k are estimated parameters capturing the relationship between the latent variable for addiction and the indicator at hand, I k n , where the exponent I k n ¼ ¼1 ensures that the appropriate numerator is used depending on the observed value for I k n . For five ordered variables (frequency of e-cigarette use, time before first cigarette of the day is smoked, time since last having smoked a cigarette that day, time since last having smoked a cigarette in the last few days/weeks, and the number of quit attempts in the past year), an ordered logit model is used (Greene & Hensher, 2010): where τ k;s are estimated threshold parameters for threshold s of categorical indicator I k n , and ζ k are estimated parameters capturing the relationship between the latent variable for addiction and the indicator at hand.
Finally, for two continuous variables (number of cigarettes smoked per day and current urge to smoke), a linear model is used: where demeaning the variables, as shown by subtracting I k , avoids the need to estimate a constant (Daly et al., 2012b). The variance of the error, σ 2 k , is estimated along with other parameters. ζ k are estimated parameters capturing the relationship between the latent variable for addiction and the indicator at hand.
Finally, each of the model components are combined into a single likelihood function and jointly estimated: We integrate over the parameter mixing distributions and latent variable, where maximum simulated likelihood is used for estimation (Train, 2009). Because we have more than 5 dimensions, standard Halton draws are rejected in favor of 1500 modified Latin hypercube sampling draws per random component and per individual, due to correlation concerns (cf. Bhat, 2003;Hess, Train, & Polak, 2006). Sobol draws would have also been a useful alternative to Halton draws (Czaikowski & Budziński, 2019); the main point is to avoid using Halton draws. Given the known complexities of likelihood functions with mixing distributions, we use an algorithm for searching for starting values, based on Bierlaire, Thémans, and Zuerey (2009) 3 , to aid in finding a global optimum. All models are estimated using Apollo (Hess & Palma, 2019).
We optimized the specification with several rounds of removing interaction terms that were not statistically significant and updating the starting values. We followed the choice modeling literature in the choice of normalization for alternative-specific constants and categorical variables by deliberately over-specifying the model (attempting to estimate all parameters) and then omitting those with the lowest variance (Walker, 2001). On the basis of this, we normalized to zero the constant for the opt-out, the impact of the addiction latent variable on cigarettes, the low level of nicotine, and the impact of the latent variable on high nicotine.
Finally, because we are using the model for forecasting, it is crucial to calibrate the model constants and the scale of utility. We follow the approach of Buckell and Hess (2019). More specifically, the Alternative-specific constants are calibrated post-estimation using national data on tobacco product market shares. This aligns the base choice shares in our model to real-world market shares of the products. We also adopt the partial calibration developed in that paper; that is, the choice share of the opt-out in the uncalibrated model is retained and then the cigarette and e-cigarette choice shares are calibrated according to revealed preference (RP) market shares. This avoids ascribing a specific behavioral interpretation to the opt-out (due to its framing, it could confer several behaviors). For calibrating the scale of utility, we use RP data on respondents collected in the survey and build a RP choice model equivalent of Equation (8). We estimate a common price coefficient in model (8) and its RP equivalent, and estimate an additional SP scale parameter, μ SP . This aligns the scale of the SP model to that of the RP model. Terming the choice probability in model (8) P c;SP and its RP equivalent P c;RP , the log-likelihood becomes:

| Limitations
Our methods are subject to a set of limitations. First, we are limited by the set of indicator measures that we collected. However, those that we do use cover important aspects of addiction: we have measures for cigarettes and e-cigarettes; we have longer and shorter term measures of addiction; we include measures of symptoms (craving) as well as outcome measures (cigarettes per day). While it is common practice to run factor analyses prior to estimating latent variables, we discarded this preliminary exercise in this case. The factor analysis suggested that there were three latent variables. However, the directions of indicator variables across these latent variables were highly implausible. Moreover, attempting to estimate three separate latent variables would have added considerable complexity to the exercise and exposition. And, in fact, the one that we did estimate resulted in plausible directions of coefficients and implied choice behaviors. Using a single latent factor from a factor analysis was similarly done in Shiffman et al. (2004). And other studies that conducted factor analysis yielded a single underlying driver of addiction (Strong et al., 2017). For these reasons, we kept to a single latent variable. As with all hybrid choice models, the latent variable should not be used in forecasts, due to the fact that it is only a cross-sectional measure (Chorus & Kroesen, 2014). Another limitation is the framing of the opt-out as "none of these". This could denote several different behaviors of respondents and ultimately we cannot observe precisely what these meant. However, we note that among smokers, other behaviors such as noncigarette/none-cigarette use-which are likely responses when choosing the opt-out here-are much less popular among smokers, which is in keeping with what we find here. But this is at best speculation, and its interpretation is not clear. It is for this reason that we applied the partial calibration (Buckell & Hess, 2019), to avoid this issue impacting on forecasts and to allow for an open interpretation on the opt-out coefficient. It is also not an issue specific to our study. As we have previously suggested, it may be possible to allow different opt-out options with different labels, for example "I would rather try to quit" or "a cigar" to aid interpretation (Buckell & Hess, 2019). It would also be possible to use post-experimental questions to help interpret these choices (Reed Johnson et al., 2013). Finally, we were limited by processing power to using 1500 Halton draws in estimation. While this is in excess of many other studies in health, we note recent research which suggests this may be too few draws (Czaikowski & Budziński, 2019). Using 1500 draws was the maximum feasible number of draws permissible with the processing power available. This is likely to be common in applications where researchers do not have access to high-performance computing. In preliminary analyses, we used 500 draws. When we moved to 1500 draws, we did not see any notable difference in parameter estimates. So while we would have preferred more draws, we do not see 1500 as problematic. Table 3 shows the results from the measurement equations and the structural equation. This is informative in understanding the nature of addiction captured in the model. By studying the ζ parameters, we note that higher values of the latent variable are associated with a lower chance of being a daily smoker; smoking fewer cigarettes per day; a longer time in the morning before smoking their first cigarette; a longer time since last having smoked a cigarette that day; a longer time since last having smoked a cigarette in the last few days/weeks; more quit attempts in the past year; a higher probability of being an e-cigarette user; no increase in the frequency of e-cigarette use (not statistically significant); and reporting a lower level of current craving. Taken together, these results suggest that a higher value for the latent variable is associated with lower levels of addiction to cigarettes and nicotine (or, equivalently, lower values of the latent variable are associated with higher levels of addiction to cigarettes and nicotine). This is due to, first, the lower levels of cigarette use and addiction. But it is of course possible that more addicted smokers could just be switching away from cigarettes to e-cigarettes. In this case, we would expect to see very little change in reported craving and increased frequency of use of e-cigarettes. However, we see the opposite: no increase in the frequency of e-cigarette use and lower reported craving. Moreover, higher values for the latent variable are associated with more past year quit attempts, which again is a sign of lower addiction. For these reasons, we interpret the latent variable as capturing reduced addiction to cigarettes and nicotine, where lower values signify higher levels of addiction. We then move to the structural equation to examine how individual characteristics of vary with addiction.

| Measurement equations and structural equation
In the structural equation, individual characteristics are used to explain the latent variable. Higher values of the latent variable (i.e., less addicted) are associated with younger individuals (more likely to be younger and less likely to be older); higher education; higher income (less likely to be associated with lower income); nonwhite race/ethnicity (positive values for Hispanic, Black, and Asian); and lower probability that a family member smokes.
This in keeping with what we would expect to see: these demographic patterns are opposite to those of smokers, which would fit with the idea of higher values for the latent variable capturing lower levels of addiction (Wang et al., 2018; though note that the definition of smokers varies between this study and that of Wang et al.; and that we are measuring addiction, whereas Wang et al., 2018 study current use.)

| Utility function and impact of addiction latent variable
Estimates of the utility function are presented in Table 4. All else being equal, the alternative-specific constants indicate that cigarettes are preferred to the opt-out; and e-cigarettes are preferred to the opt-out. Unobserved preferences for cigarettes (relative to the opt-out) vary considerably around the mean, as reflected by the large and significant standard deviation. No preference heterogeneity for cigarettes across sociodemographic characteristics was found. Preferences BUCKELL ET AL.
-9 for e-cigarettes (relative to the opt-out) varied in both unobserved ways (statistically significant estimated standard deviations) and according to age (older adults) as captured by the associated interaction terms of preferences and that characteristic.
For nicotine, medium level is preferred to all other levels (highest relative utility among the mean coefficients). Preferences for nicotine levels vary deterministically across some characteristics, but not all (i.e., associated interaction terms of nicotine levels and sociodemographic characteristics) and random ways for no nicotine and high nicotine (statistically significant estimated standard deviations). Our results indicate that female smokers prefer high and medium nicotine products, reflecting an overall preference for higher levels of nicotine in tobacco products. Older smokers chose high-nicotine products less often, reflecting an aversion to higher levels of nicotine in tobacco products; and e-cigarettes less often. Younger smokers chose high-nicotine products more often. Unmarried smokers had preferences for medium and high-nicotine products. (nota bene of course these preferences are only part of the overall picturecharacteristics are related to the latent variable, which also impacts on product and nicotine preferences.) Price sensitivity, as expected, is negative. The income elasticity estimate implies that price sensitivities decline as income increases. In other words, as income increases, individuals are less sensitive to price changes. Tobacco is preferred to all other flavors. And healthier products are preferred to more harmful products, shown by stronger preferences for fewer life years lost.
Next, we move to the impact of the latent variable. From the interactions of the latent variable and product constant terms, lower addiction (higher values for the latent variable) is associated with increased preferences for e-cigarettes. Oppositely, this implies that those that are more addicted prefer cigarettes. With reduced addiction, the lower levels of nicotine are preferred to high nicotine; or, oppositely, more addicted smokers prefer higher levels of nicotine in cigarettes-and progressively so with higher levels of addiction, as captured by the monotonicity in the interactions of nicotine levels and the latent variable. Notes: In the structural equation, the parameters are the estimated gammas as in Equation (6). In the measurement equations, the zeta parameters are each taken from separate measurement equations, as in (9)-(11). Table 5 shows the estimated WTP (or WTA, in the case of negative values) for the attributes in the utility function using the standard approach (Hensher et al., 2015). These reflect the dollar value per 20 pack (or e-cigarette equivalent) that

Addiction-utility function interactions
Tau � E-cigarette 0.26 2.01 Tau � No and low nicotine 0.37 3.88 Tau � medium nicotine 0.14 3.55 Note: lambda income is the income elasticity; its coefficient reflects that those on higher incomes are less responsive to price variation as economic theory predicts.
Abbreviations: ASC, Alternative-specific constant (mean of the mixing distribution); s.d., standard deviation of the mixing distribution; mu_SP, scale parameter for SP relative to RP (t-ratio vs. 1 ¼ meaning that differences in scale between SP and RP were not statistically significant, which follows from the coefficient being close to 1). BUCKELL ET AL. -11 individuals are willing to pay (must be compensated for, WTA) for that level of the attribute, relative to the omitted category, so as to remain indifferent (equal utility) between two products with these differing levels. For health harm, smokers, on average, are willing to pay $8.64 extra on a packet of 20 cigarettes to reduce the health risk from losing 10 years of life to losing 2 years of life. For flavors, smokers, on average, must be compensated to move to nontobacco flavored tobacco products to attain the same level of utility as for tobacco products. This differs across flavors. For menthol, WTA is $4.31; for fruit, WTA is $1.79; and for sweet, WTA is $2.32. For nicotine, WTP/WTA is more modest on average than for other attributes (note nicotine valuations are also related to addiction, since the latent variable is interacted with these attributes in the utility function). Smokers express WTA for all levels of nicotine; that is, smokers must be compensated to achieve the same utility for moving from medium nicotine strength in tobacco products to any other strength of nicotine in tobacco products. More specifically, WTA at the mean for no nicotine is $0.57; for medium nicotine is $0.68; and for high nicotine is $0 since the estimated coefficient was 0.
From a policy perspective, it is of interest to examine how WTP/WTA for nicotine varies as a function of addiction 4 . The results indicate that key heterogeneity in WTP/WTA for nicotine by addiction is masked by analysis at the sample level. In Figure 3, how WTP/WTA for the levels of nicotine varies as a function of addiction is shown. We have used no nicotine as the reference category for these analyses (which is possible following from the fact that all of the coefficients are based on relative preferences). We have also reversed the scale of the latent variable so that increasing addiction is shown along the x-axis (for ease of reading). We see that increasing addiction is associated with higher WTP for nicotine in tobacco products (positive correlations for each of the attributes). We also see that WTP increases monotonically for higher levels of nicotine (steeper gradients across levels). In some cases, the value of WTP/WTA is in excess of average the price of a packet of 20 cigarettes (around $8), underlining the importance of nicotine to smokers.

| Forecasting of lowering levels of nicotine in cigarettes
A key policy issue is the extent to which smokers would switch away from cigarettes if nicotine levels were reduced in cigarettes. Table 6 shows two models' forecasts of lowering nicotine in cigarettes 5 . Our preferred specification is the calibrated model. Here, we see that the model predicts that lowering nicotine levels in cigarettes would result in around a 3% decline in the choice share of cigarettes; and 4% and 11% increases, respectively, in choice shares for e-cigarettes and the opt-out option. The table also indicates that smokers are slightly less responsive to the reduction in nicotine levels than dual users, because the reduction in cigarette choice share for smokers is less than that for dual users. However, this difference is fairly modest and smokers appear at least somewhat responsive to the lowering of nicotine. Of course, these should be considered as short-term responses in demand; longer term forecasts are not possible with these data. Table 7 shows the diagnostic information. The log-likelihood of the joint estimation is shown, along with, for comparison, the log-likelihood of a model where all products are chosen equally (i.e., no information on choices) and the loglikelihood of a model with only the experimental choice shares (Mokhtarian, 2016). Measures of fit, Akaike information criteria and Bayesian information criteria are presented along with the total number of estimated parameters, 76.

| DISCUSSION AND CONCLUSIONS
In this study, we developed a model to evaluate the role of addiction in smokers' choice behavior. The hybrid choice model seeks to better understand smokers' decision-making by allowing addiction to flexibly impact on smokers' choices. This framework allows us to overcome a set of empirical issues that present in trying to measure addiction and to incorporate addiction in choice models in a traditional manner. We used the model to estimate preferences, WTP for nicotine in cigarettes, and to predict the impact of lowering nicotine levels in cigarettes in the United States.
We find that the latent variable captures addiction, with higher values explaining lower levels of addiction and lower values capturing higher levels of addiction. Higher levels of addiction are associated with increased use of cigarettes (including more cigarettes smoked per day), lower use for e-cigarettes, fewer quit attempts, and higher levels of reported craving. This addiction was associated with sociodemographic characteristics in a way that corresponds to known, observed patterns of cigarette use nationwide. Note: Standard errors are computed using the delta method (see Daly, Hess, & de Jong, 2012).

F I G U R E 3
Willingness to pay/willingness to accept (WTP/WTA) for nicotine as a function of addiction. (left) WTP/WTA for low nicotine (reference: no nicotine) as a function of addiction; (middle) WTP/WTA for medium nicotine (reference: no nicotine) as a function of addiction; and (right) WTP/WTA for high nicotine (reference: no nicotine) as a function of addiction. Addiction is defined as the latent variable (for ease of interpretation we have reversed the scale so that higher score on the latent variable denotes higher addiction). Each point is taken from a draw from the mixing distributions of the parameters and latent variable. NB -WTP for low versus no nicotine will be zero given the parameter restrictions on the model; we show the relationship as there is important random heterogeneity that remains, as can be seen. Overall, WTP increases with addiction for the same level of the attribute (positive correlation) and increases monotonically with increasing levels (progressively steeper gradients). Notes: 95% confidence intervals are listed in parentheses beneath the product forecasts. Calibration follows previous work (Buckell & Hess, 2019). In the table, smokes only refer to those in the sample that report no e-cigarette use; dual user refers to those in the sample that report e-cigarette use.
In terms of the impact of addiction on stated choices, we find that addiction drives preferences for cigarettes, and away from e-cigarettes. Those that are more addicted prefer higher levels of nicotine in tobacco products.
Analysis of WTP indicates that, on average, smokers prefer medium levels of nicotine, and on average are willing to pay or must be compensated in the range of $0.42-0.57 per 20 pack to be equally satisfied with levels of nicotine other than "low", which was the reference in our model. However, these valuations vary considerably across respondents when the range of addiction is taken into account. More addicted smokers exhibit utility for higher levels of nicotine in tobacco products where WTP is, in some cases, in excess of the price of a packet of 20 cigarettes; less addicted smokers value lower levels of nicotine in tobacco products where WTA is, in some cases, in excess of the price of a packet of 20 cigarettes.
Our results suggest that the short-run response to the FDA's proposed lowering of nicotine in cigarettes would result in a slight shift away from cigarettes; roughly 3% of its choice share. Shifts in choice shares would be toward both e-cigarettes (4% increase in its choice share); and a 11% increase in the choice share of the opt-out-either cessation behavior or alternative tobacco products (depending on one's interpretation of the opt-out in the experiment-we have previously interpreted as the former based on higher choices of the opt-out option among those that attempted to quit in the past year; see . These results are likely to have significant meaning for policy. In the United States, the FDA has set out its regulatory agenda, the centerpiece of which is reducing the level of nicotine in cigarettes (FDA, 2019). Therefore, these findings are likely to be of direct relevance to current policymaking. The results suggest that this policy is likely to be effective at shifting smokers' choices away from cigarettes; though with limited impact in the short run (NB-we can make no determination on the medium-to long-term impacts of this policy). While there seems to be more of a response to this policy from the dual users, smokers, too, showed some switching away from cigarettes. Since the smokers are most likely at harm, this is encouraging for the public health implications of this policy.
These results are important because, from a behavioral and policy perspective, we have greater insight into smokers' decision-making processes with respect to nicotine preferences and product choices. Our basic utility function parameter estimates are in keeping with previous results elsewhere in the literature (Pesko, Kenkel, Wang, & Hughes, 2016;Marti et al., 2019;Shang, Huang, Chaloupka, & Emery, 2018). Here, where measured, the preference estimates for nicotine are typically lower than other attributes. However, these studies do not explicitly study the impact of addiction. And now that we do, the results appear to be markedly different. Thus, the key point is that, even when nicotine is used in choice experiments, the behavior of smokers toward products and nicotine is likely to be underestimated if addiction is not explicitly modeled.

ACKNOWLEDGMENTS
Research reported in this publication was supported by grant number P50DA036151 from the National Institute on Drug Abuse (NIDA) and FDA Center for Tobacco Products (CTP). The content is solely the responsibility of the author(s) and does not necessarily represent the official views of the National Institutes of Health or the Food and Drug Administration. Stephane Hess acknowledges support by the European Research Council through the

Estimated parameters 76
Notes: LL (0), log-likelihood where parameters are zero, that is there is no information on preferences and the choices of all products are equally likely. LL (choice share), log-likelihood with only product constants, that is recovering the experimental choices shares.