Obesity and smoking: can we catch two birds with one tax?

Dragone, Davide; Manaresi, Francesco; Savorelli, Luca Working Paper Obesity and smoking: can we catch two birds with one tax? Quaderni - Working Paper DSE, No. 873 Provided in Cooperation with: University of Bologna, Department of Economics Suggested Citation: Dragone, Davide; Manaresi, Francesco; Savorelli, Luca (2013) : Obesity and smoking: can we catch two birds with one tax?, Quaderni - Working Paper DSE, No. 873, Alma Mater Studiorum - Università di Bologna, Dipartimento di Scienze Economiche (DSE), Bologna, https://doi.org/10.6092/unibo/amsacta/3891 This Version is available at: https://hdl.handle.net/10419/159712 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Davide Dragone Francesco Manaresi Luca Savorelli Quaderni - Working Paper DSE N°873 Obesity and smoking: can we catch two birds with one tax?∗ Davide Dragone†Francesco Manaresi‡Luca Savorelli§ March 26, 2013 Abstract The debate on tobacco taxes and fat taxes often treats smoking and eating as independent behaviors. However, since there exists medical and sociological evidence about the interdependence between eating and smoking choices, antismoking policies may also affect the obesity prevalence and fat taxes could influence smoking behavior. We address this issue from a theoretical standpoint and propose a dynamic rational model where eating and smoking are simultaneous choices that jointly affect body weight and addiction to smoking. Focusing on direct and cross price effects, we compare tobacco taxes and fat taxes and we show that a single policy tool can reduce both smoking and body weight. In particular, fat taxes can be more effective than tobacco taxes at simultaneously fighting obesity and smoking. Keywords: Addiction, Fat Tax, Obesity, Smoking, Tobacco. JEL code: D91, H31, I18. ∗We thank for useful discussion Giacomo Calzolari, Arsen Palestini, Giuseppe Pignataro, Giovanni Prarolo, Paolo Vanin and the participants in the ECHE 2012, PET 2012, 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, and in the seminars at the University of Alicante, Lausanne, Modena and Reggio Emilia, York, St. Andrews, Bologna. Financial support from FarmaFactoring Foundation and from the SoNIC project (FIRB grant no. RBFR084L83) is gratefully acknowledged. The views expressed in this paper are the authors’ own and do not necessarily reflect those of the Bank of Italy. The usual disclaimer applies. †Corresponding author: Davide Dragone, University of Bologna, Dipartimento di Scienze Economiche, Piazza Scaravilli 1, 40126 Bologna, Italy; Phone: +39-051-209-8880, Fax: +39-051-209-8143, E-mail: [email protected]. ‡Bank of Italy, Structural Economic Analysis - Labour Market Division, via Nazionale 91, 00184 Rome, Italy; Phone:+39-06-479-224-26; E-mail: [email protected]. §University of St Andrews, School of Economics & Finance, Castlecliffe, The Scores, St Andrews, Fife KY16 9AR, Scotland, United Kingdom. Phone: +44-1334-462449; e-mail: luca.sa[email protected]. 1 1 Introduction In this paper we propose a dynamic model where eating and smoking are interdependent choices and we show under which conditions a single policy tool suffices to reduce both smoking and obesity. Comparing taxes on tobacco and taxes on food, we show that the latter can be more effective in simultaneously reducing obesity and smoking. This result has important policy implications, as smoking and obesity are two major causes of preventable death. In the United States, almost one out of four deaths is estimated to be due to tobacco smoking or obesity, which also have a significant impact on the health care system, with yearly medical expenses and related costs of about the magnitude of $117 billions for smoking and $190 billions for obesity (Cawley and Meyerhoefer, 2012; Mokdad et al., 2004). Since both produce externalities or, in case of time inconsistent choices, internalities (Chaloupka and Warner, 2000; Evans et al., 1999; Gruber, 2001; Gruber and K˝oszegi, 2001, 2004; Finkelstein et al., 2004), national governments have tried to modify smoking and eating behavior through the introduction of taxes, educational interventions, advertising campaigns, and the provision of assistance and tutoring. The evaluation of the effectiveness of these policies and the debate about the introduction of new ones usually focus on their direct effects. For example, tobacco taxes are considered to be effective if smoking prevalence in the population decreases, and the debate on imposing taxes on energy-dense food (often called fat taxes) concentrates upon their expected effects on obesity rates. This approach can be appropriate when the indirect effects of the policy interventions are negligible. When considering smoking and obesity, however, this appears not to be the case, as suggested by the medical and sociological literature showing that smoking, eating behavior and body weight are interdependent and reciprocally influence each other. Interestingly, in the United States average smoking prevalence has been constantly decreasing in the last forty years (passing from 42% in 1965 to 20% in 2007, CDC, 2010) while, in the same span of time, obesity rate has increased (from 12.8% to over 30%, Flegal et al., 1998, 2012). This evidence has stimulated a lively research agenda which studies whether the observed time-trends in smoking and obesity rates are the causal result of antismoking campaigns, rather than just a suggestive correlation. The economic literature on this issue is relatively recent and so far the empirical findings are mixed. In line with the common wisdom and the medical evidence that nicotine boosts metabolism and reduces appetite, some studies find that a raise in cigarette prices and in excises on tobacco increases average body mass index (BMI) in the population (Chou et al., 2004; Rashad and Grossman, 2004; Rashad et al., 2006; Baum, 2009). Other papers point to the opposite direction, finding that an increase in cigarette prices decreases BMI (Gruber and Frakes, 2006; Courtemanche, 2009; Wehby and Courtemanche, 2012; Dragone et al., 2013), which would instead support the conclusion that smoking and obesity are complements, rather than substitutes. 2 To interpret the empirical results and to guide future policy interventions, a theoretical framework is needed; however, to the best of our knowledge, there is no theoretical model which treats smoking and eating behavior as joint interdependent choices. To address this issue, in this paper we propose a dynamic model for understanding how smoking and eating choices are jointly determined, and to provide novel testable predictions on the impact of taxation on smoking and obesity. We exploit the results from a body of recent medical and sociological literature, and we allow for two different pathways through which smoking, eating behavior and body weight are related: individual preferences and the effect of smoking on metabolism. The model is dynamic because smoking is addictive, and because body weight and addiction to smoking build up over time (Becker and Murphy, 1988; Levy, 2002; Dragone, 2009). This allows to construct a theoretical benchmark featuring both interdependence between goods consumed at different dates, as well as interdependence between different goods consumed at the same date. Using this dynamic framework, we identify which behavior is consistent with a forwardlooking rational agent and show that the demand for smoking can be partially imputed to the demand for weight control. This result rationalizes the empirical finding that smoking initiation is sometimes driven by the desire to reduce appetite and to control body weight and, analogously, that fear of gaining body weight plays an important role in the decision to quit smoking (Moran et al., 2004; Cawley et al., 2004; Cawley and Scholder, 2013). We also show that a person can reach a healthy body weight and be not addicted to smoking, although this is only one of the possible outcomes of the model. In general, less healthy outcomes can emerge, including situations in which a person (optimally) smokes, is overweight and on a diet, or smokes, is underweight and binges. Finally, focusing on a permanent price increase we study the long-run demand for smoking, food consumption and body weight in order to understand the effect of policy actions that affect the price of smoking and of food. By studying the demand for food in a dynamic framework where individuals are concerned about their body weight, we contribute to the debate on the introduction and effectiveness of taxes on targeted types of food. Supported by the United Nations and by the World Health Organization, some countries (notably, Denmark, Hungary, and France) have recently introduced some forms of food taxation, although with controversial outcomes (Mytton et al., 2012). Other countries, such as Ireland, Italy, Peru, the United Kingdom and the United States are actively considering whether introducing fat taxes to reduce obesity rates. Despite the fact that some policy actions have already been implemented, the theoretical literature on the impact of fat taxes on body weight is surprisingly thin. In a recent contribution, Yaniv et al. (2009) study how fat taxes and time constraints can affect obesity due to the simultaneous interdependence between healthy and junk food, and physical exercise. Here we consider a different perspective which focuses on the simultaneous interdependence between eating and smoking choices, as well as on the intertemporal effects of individual behavior 3 on future utility and on the accumulation of body weight and addiction. To the best of our knowledge, such a dynamic theoretical framework is missing in the literature, and this paper is a first step to fill this gap. By emphasizing the role of interdependencies between smoking and eating behavior, we identify the critical conditions that determine whether a tax-based policy intervention may produce undesirable trade-offs such as, e.g., a reduction in smoking prevalence but an increase in obesity. Importantly we highlight the possibility for the policy-maker to ”catch two birds with one tax”, i.e. the possibility for the policy maker to implement a single policy action which curbs both smoking and obesity. This result provides a rationale for those empirical papers emphasizing the role of antismoking policies in the reduction of obesity (Gruber and Frakes, 2006; Courtemanche, 2009; Wehby and Courtemanche, 2012; Dragone et al., 2013), and it opens the way to further research on policies that accomplish multiple goals with a single policy tool. Finally, we show that smoking and eating behavior asymmetrically react to changes in prices. This is due to the fact that the metabolic effect of nicotine impacts on the accumulation of body weight, while food consumption does not affect the accumulation of addiction to smoking. This property implies that the policy implications of taxing tobacco and taxing food can be very different in terms of individual behavior and outcomes. More specifically, we find that fat taxes can be more effective than tobacco excises in simultaneously fighting obesity and smoking. The intuition for this result is that an increase in cigarette prices curbs tobacco consumption, but also reduces the ”dieting” effects of nicotine. As a consequence, body weight decreases only if the reduction in smoking also leads to a strong reduction in food intake that more than compensates for a slower metabolism. By contrast, increasing the price of food reduces food consumption, and consequently body weight, which in turn makes smoking less desirable as a dieting device. The paper is structured as follows. In the next section we review the evidence on the interdependence between smoking and eating behavior, and we present the theoretical literature on the taxation of addictive goods and on fat taxes. In section 3 we introduce the model and we solve it. In section 4 we study the short- and long-run demand functions for smoking and food consumption, and we compare the effects of taxing tobacco or food. Discussion and final considerations are contained in section 5. 2 Literature review Smoking and eating behavior can be interdependent through different avenues. A survey of the literature suggests that smoking may affect body weight through two major non mutually exclusive channels. The first one relies on the evidence that nicotine is an appetite suppressor through the central nervous system (Mineur et al., 2011). This anorexic effect of 4 nicotine would suggest that smoking has a satiating effect on food consumption. This is not a general rule, however, because biological factors interact with individual preferences and social factors. Indeed, smokers tend to crave for smoking more when they are eating than in other situational correlates (Dunbar et al., 2010) and there exists a category of smokers that accounts for about one fourth of the market, the so-called social smokers, who smoke primarily in social contexts, such as in bars, parties, restaurants, celebrations and in presence of others (Debevec and Diamond, 2012; Schane et al., 2009). Contrary to the trend for regular smokers, the proportion of social smokers is rising. Analyzing data from the 1996- 2001 Behavioral and Risk Factor Surveillance System, the U.S. Center for Disease Control finds significant increases in the proportion of nondaily smokers among current smokers in 38 states (CDC, 2003). Social smoking is particularly prevalent among young people. In a 2004 cross-sectional study of college students, Moran et al. (2004) classified 51% of the sample of current smokers as social smokers. Moreover, heavy smokers are more likely to be obese. Despite the anorexic effect of nicotine, this evidence thus suggests that overall complementarity among smoking and eating behavior cannot be excluded (Chiolero et al., 2008), and that the reciprocal reinforcement between smoking and eating behavior is channelled through individual preferences, lifestyle choices and social factors such as peer-pressure and the conviviality dimension of smoking and eating. The second channel of interdependence between smoking and eating behavior is based on the medical evidence that nicotine accelerates metabolism, which in turn increases caloric consumption (Chiolero et al., 2008; Mineur et al., 2011). Consistent with this result, a recurrent finding in the medical literature is that nicotine administration causes reduction in body weight, and that increased body weight results after cessation of administration (Donny et al., 2011). Interestingly, smoking is often reported to be used as a method for weight control: smoking initiation among teenagers is motivated by concerns on body weight (Moran et al., 2004) and, in a similar vein, some people refrain to quit smoking because they fear post-cessation weight gain (Spring et al., 2009; Cawley and Scholder, 2013). A recent study has shown that in the US 46% of girls and 30% of boys smoke to control weight and that the demand for smoking can be partially derived from the demand for weight control (Cawley and Scholder, 2013). The above evidence and the negative correlation over time between smoking and obesity prevalence have inspired the conjecture that, due to the interdependencies between eating and smoking behavior, the obesity epidemic might have been fostered by antismoking policies. Whether this is empirically the case, however, is controversial. Focusing on the effect of increases in the prices of cigarettes, Chou et al. (2004), Rashad and Grossman (2004), Rashad et al. (2006), Baum (2009) show that quitting smoking is associated with increased body weight, while Gruber and Frakes (2006), Courtemanche (2009), Wehby and Courtemanche (2012) arrive at the opposite conclusion. Using detailed clinical data on individual health, 5 smoking, and dietary habits, in a companion paper (Dragone et al., 2013) we show that increasing excise taxes on tobacco decreases body weight and caloric intake and improves the quality of eaten food. The effect of price increases for addictive goods has been addressed from a theoretical stance since the seminal contribution by Becker and Murphy (1988). The main idea of rational addiction is that current preferences for an addictive good can depend on past consumption of that good. Becker and Murphy show that a decision-maker may rationally choose to become addicted by trading-off the intertemporal benefits and costs of consuming the addictive good, and that the demand for the addictive good decreases when its price increases. An important policy implication of Becker and Murphy’s model is that, to reduce the consumption of the addictive good, one should increase its price. This prescription has received much attention both in the policy practice and in the literature, and there exists a large empirical consensus on the aggregate effectiveness of interventions based on increasing the price of addictive goods such as smoking, alcohol and heroin, among others. Similar theoretical predictions are obtained by Gruber and K˝oszegi (2001) in a rational addiction model with time-inconsistent agents, and by Gul and Pesendorfer (2007), who develop a model where consumption of the addictive good is a tempting choice that erodes self-control in future periods. In the theoretical literature on obesity, the role of fat taxes on body weight has not been explicitly addressed, yet. An exception is in Yaniv et al. (2009), who adopt a static approach to show that fat taxes, while reducing junk-food consumption, may encourage the preparation of healthy meals. Since this requires time for cooking and shopping healthy-ingredients, and time is constrained, less time for physical activity remains available and an increase, rather than a decrease, in body weight can result. Even though the literature on fat taxes is scarce, there exists a small, but growing literature which models eating behavior and its dynamic effects on body weight. Rational eating models share many features of rational addiction models: consumers are forward-looking and maximize intertemporal utility taking into account that past choices affect current utility. In the context of eating behavior, food consumption choices affect future body weight, which in turn affects future utility because having an unhealthy body weight reduces the survival probability of the agent (Levy, 2002; Dragone, 2009) or determines health losses (Dragone and Savorelli, 2012). When trading off the current and future consequences of eating behavior, both being overweight and underweight can be rational outcomes, including apparently pathological situations where a person is underweight and yet is on a diet, or is overweight and binges (Dragone and Savorelli, 2012). In the next section we merge these literatures on rational addiction and rational eating considering eating and smoking as simultaneous and interdependent choices. 6 3 A model of rational smoking and eating Consider a representative agent whose utility function U(s, c, q, a, w) depends on smoking s, food consumption c, a composite good q, past smoking experiences a, and body weight w. The utility function U(·) is continuously differentiable, jointly concave, and with negative second order derivatives Ucc, Uss, Uww, Uaa. In the rational addiction model by Becker and Murphy (1988), an addictive good features reinforcement between past and current consumption, and tolerance. Reinforcement implies that the marginal utility of consuming an addictive good increases with past consumption of that good. As a consequence of reinforcement, the more a person is addicted, the more she desires to consume the addictive good. Tolerance means that utility from a given amount of consumption is lower when past consumption is greater. Formally, the reinforcement property requires past smoking to increase the marginal utility of current smoking (Usa >0), and tolerance implies Ua≤0 for a≥0.Beside the interdependence in consumption of the same good at different dates, we are also willing to assume interdependence in consumption of two different goods at the same date. In particular, based on the evidence reviewed in the previous section, we allow for current smoking to affect the marginal utility of food consumption, as indicated by the mixed derivative Ucs.Moreover, we allow for smoking to accelerate metabolism (due to the metabolic effect of nicotine), which contributes to reduce the accumulation of body weight. Hence the evolution of body weight wdepends on past and current eating behavior, as well as on current smoking, so that ˙w(t) = g(c(t), w (t), s (t)) with gc≥0 for c(t)≥0, gw≤0 for w(t)≥0 and gs≥0 for s(t)≥0 (subscripts denote partial derivatives). The variable arepresenting past smoking experiences (addiction to smoking) evolves over time depending on current and past smoking choices, ˙a(t) = f(s(t), a (t)) ,with fs≥0 for s≥0 and fa≤0 for a≥0. Given the initial body weight w0, addiction to smoking a0and wealth b0, the agent must choose the path of food consumption, smoking and consumption of the composite good that satisfies the following intertemporal problem: max s(t),c(t),q(t)ZT 0 e−ρt [U(c(t), s (t), w (t), a (t), q (t))] dt (1) s.t. ˙a(t) = f(s(t), a (t)) (2) ˙w(t) = g(c(t), w (t), s (t)) (3) ˙ b(t) = rb (t) + M−pcc(t)−pss(t)−q(t) (4) a(0) = a0, w (0) = w0, b (0) = b0 c(t)≥0, s (t)≥0, q (t)≥0 w(t)>0, a (t)≥0, where ρ > 0 is the intertemporal discount rate, ris the market interest rate, Mis the 7 4.2 Increasing the price of food In this section we consider the effect of increasing the price of food on smoking, eating behaviour and body weight. The following proposition confirms that the law of demand holds also for food consumption. Proposition 4 When the price of food increases, food consumption decreases both in the short- and in the long-run. Proof. See the Appendix. When considering the cross price effects, the short- and long-run reaction of smoking to changes in the price of consumption mirrors the reactions of food consumption to changes in the price of smoking. Interestingly, as shown in the Proposition below, the response of body weight to the price of smoking is different from the response to the price of food, due to the fact that smoking accelerates individual metabolism and that smoking is addictive. Proposition 5 When the price of food increases: 1. In the short-run smoking decreases if Ucs >0, and increases otherwise; 2. In the long-run •Smoking decreases if Ucs > σ1,and increases otherwise; •Body weight decreases if Ucs < σ3,and increases otherwise; where σ3=−[(2δ+ρ)Usa +Uaa +δ(δ+ρ)Uss]/[δ(δ+ρ)ε]. Proof. See the Appendix. 14 6 - Ucs Usa UnstableUnstable |J|= 0 @ @R 0 σ1σ2 σ3 ∂sss ∂pc↑ ∂wss ∂pc↓ ∂css ∂pc↓ ∂sss ∂pc↓ ∂wss ∂pc↓ ∂css ∂pc↓ ∂sss ∂pc↓ ∂wss ∂pc↑∂css ∂pc↓ Figure 2: Long run effects of an increase in the price of food on smoking, body weight and food consumption. Consider Figure 2, where we represent the cases described by the above Proposition.9 When the satiating effect of smoking on food consumption is large enough (Ucs < σ1), food consumption and body weight are complements in the long-run, while food consumption and smoking are substitutes. Hence in such a case the increase in the price of food is effective in reducing obesity, but the agent optimally substitutes smoking for food, which implies that the policy maker must carefully assess the trade-off between increased smoking and reduced obesity. In the area on the right of the vertical line indicated by σ1, the reduction in food intake is accompanied by a reduction in smoking. The intuitive reason is that the fat tax directly discourages eating, which helps controlling body weight accumulation and reduces the incentives to smoke for losing weight. The intensity of the reduction in smoking depends on the intensity of Usa: the higher the reinforcing effect of past smoking on current smoking, the higher the reduction in current smoking after an increase in the price of food. In the area above the σ3line, the reduction in smoking is large, and the consequent slowing down of metabolism offsets the reduction in food intake. Hence, after an increase in the price 9In Figure 2 we consider the case where stability of the steady state requires |J|>0 and where all thresholds σ1, σ2and σ3are feasible. 15 of food, the agent reduces food intake and smoking, and yet her body weight increases. The area below the σ3line, instead, denotes the case where smoking is not very addictive. Consequently, although smoking is reduced, the effect on individual metabolism is dominated by the reduced food intake. This implies that, after an increase in the price of food, the agent will reduce eating, she will get thinner and she will also reduce smoking. The latter result is interesting for two reasons. First, it highlights a possibility that does not appear to have been fully considered in the debate on eating policies against obesity, namely the possibility of implementing eating policies that contribute to reduce the smoking prevalence. In particular, this result is most relevant for those people who initiate and continue smoking because they are concerned about being overweight, in which case implementing policies that directly impact on food consumption and body weight would also make smoking less attractive. Second, there is an important asymmetry between the response of body weight to an increase in the price of smoking and an increase in the price of food consumption. While in both cases there is the possibility that smoking, food consumption and body weight are complements, when considering the price of food this outcome can occur in a larger set of cases: when smoking reinforces food consumption, when it has a mild satiating effect, and even when preferences for current smoking are independent from current eating. Although it is questionable whether focusing only on body weight and BMI provides enough information on the health condition of the agent, policy makers and institutions such as the World Health Organization are explicitly concerned about fat accumulation as a risk to health, and the corresponding campaigns are aimed at reducing obesity. Hence, identifying different effects on obesity prevalence as a response to different policy tools is of particular interest because it opens to the possibility of comparing the effectiveness of antismoking and antiobesity policies, as we do in next section. 4.3 Taxing tobacco or taxing junk food? In this section we exploit the previously obtained results to compare the effectiveness of antismoking and antiobesity interventions. Our interest is on those policies that either raise the monetary cost of smoking (such as the introduction of excise taxes on tobacco) or the cost of food, everything else equal. Interpreting food consumption as a basket of different types of food, the latter case includes scenarios where taxes are imposed only on specific foods, as it is the case of fat taxes on junk food (energy-dense food, soft drinks etc.), raising the overall price of the basket. Based on the results contained in Propositions 2, 3, 4 and 5, the following holds: Proposition 6 Fat taxes can be more effective than tobacco taxes to simultaneously fight obesity and smoking. 16 The above Proposition highlights the fact that, although it is possible for the policy maker to reduce both obesity and smoking by using either tobacco taxes or fat taxes (provided there exists some interdependence among smoking and food consumption), their effect on body weight is not symmetric. By increasing the price of food, body weight and smoking decrease when current smoking and eating are either reinforcing or independent, or even when there is a mild satiating effect of smoking on eating (graphically, these cases correspond to the area on the right of σ1and below the σ3line, see Figure 2). When increasing the price of smoking, the same result can be obtained only if smoking is sufficiently reinforcing (area on the right of the σ2line). The result in Proposition 6 rests on the observation that the former region includes the latter one, which implies that the set of cases in which fat taxes determine a reduction in both smoking and obesity is (weakly) larger than the set where tobacco taxes accomplish the same goals. The possibility of identifying a policy tool that reduces long-run obesity and smoking in a large range of cases is a relevant result because both smoking and obesity are major issues in the agenda of health authorities, due to the associated health risks (see, for example, WHO, 2000), to the production of externalities (both in terms of health, and in terms of hospitalization costs and medical care), and to the possible existence of internalities created by self-control problems. Since implementing a policy intervention is costly, showing that there exist differences in the effectiveness of policy actions provides information on which intervention is more desirable. In particular, the role of a dynamic framework must be emphasized, as the relative advantages of the two tools emerge from explicit consideration of the interdependence between different goods consumed at the same date, of the interdependence between the same good consumed at different dates, and on the interdependence in the evolution of body weight. In this direction, the above result allows to understand the variables that crucially determine the conditions under which no trade-off between smoking and obesity emerges, and it may provide a useful tool for guiding future policy interventions. 17 5 Conclusions In this paper we have introduced a dynamic model to jointly study the interaction between smoking and eating behavior over time, and to understand the conditions under which taxation aimed at affecting one health-related behavior may have a different scope than expected. We exploited the available medical and sociological evidence to support the assumption that smoking and eating behaviors are interdependent, either in terms of preferences or because they affect individual metabolism, and we have shown the trade-offs that characterize the rational behavior of a forward-looking agent. Consistent with the empirical evidence, we have found that a variety of stable eating and smoking outcomes may emerge, including clusters of unhealthy behaviors leading to being overweight and addicted to smoking, or being underweight and on a diet. By emphasizing the role of interdependencies between different health-related behaviors, we show that targeting single health-related behaviors as if there were no interdependence with other behaviors can have a different scope than expected. This, however, is not necessarily bad news. Although it is possible for antismoking policies (or antiobesity policies) to backfire, there are conditions under which a single policy tool, such as the introduction of excises on tobacco, suffices to induce an overall health improvement by jointly reducing smoking and obesity rates in the population. In the latter case, the policy maker hits ”two birds with one stone”. We further studied whether taxing food provides any comparative advantage with respect to taxing cigarettes. We indeed found that the set of cases in which this two-for-one result is obtainable is larger when increasing the price of food than when increasing the price of smoking. This suggests that taxation of junk food may jointly reduce smoking and obesity prevalence more effectively than tobacco taxation. The intuition for this result is that a decrease in body weight also makes smoking less valuable as a dieting device, while a decrease in smoking slows down metabolism and reduces the efficiency of calorie burning. Nevertheless, our results should be cautiously considered by the policy maker. First, our model may be interpreted as considering a representative agent, but distributional aspects of the population could play a role. The strength of reinforcement for smoking and the degree of interdependence between smoking and eating in preferences may substantially vary across socio-demographic groups. For example, the category of social smokers, which accounts for one fourth of the smoking market, is characterized by a mild addiction to smoking and a reinforcing effect between concurrent smoking and eating. In this case, our results predict that food taxation can be effective at reducing both smoking and body weight, while tobacco taxes may have an adverse effect on body weight. The policy maker could then introduce food taxation only in specific places where the conviviality dimension is more relevant for social smokers (e.g. bars, restaurants, pubs). Second, food taxes and cigarette taxes are 18 both regressive (Philipson and Posner, 2008, Gospodinov and Irvine, 2009, Haavio and Kotakorpi, 2011). We have not discussed here the regressive nature of taxation, nor provided a welfare assessment of the policies. In this respect, the policy maker should take into account the underlying asymmetry between smoking and eating behavior. Food taxation will impact the whole population, including thus normal weight individuals, smokers and non-smokers. Cigarette taxes are effective at curbing smoking consumption among smokers and discouraging smoking initiation, but do not impact non-smokers decisions on eating behavior and may have positive effects on body weight. Our cautionary message is thus that cigarette taxes should not be waived or reduced a priori and that the possibility to address two risk factors with food taxation should be balanced with the greater regressive effects that it may have. The goal of this paper was to study the interaction between smoking, eating behavior and body weight over time, and to understand the conditions under which policies aimed at affecting one health-related behavior may have a different scope than expected. However, future research could extend this model by introducing choices over physical exercise, junk and healthy food, addictiveness of food, availability of information, self-control and timeinconsistency issues, and explicitly modelling social interactions. 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Obesity: preventing and managing the global epidemic. Report of a WHO Consultation. WHO Technical Report Series 894. World Health Organization, Geneva. A Appendix A.1 The solution under bounded rationality Here we study the extreme case in which the agent does not take into account the future consequences of her current eating and smoking choices on future body weight and addiction to smoking. In other words, we consider the case where, at each time t, the agent maximizes (5) given the budget constraint, her current body weight and her current addiction to smoking, but without taking into account (6) and (7). This case is instructive, because it allows to determine the optimal solution of an agent that, due to informational or cognitive constraints, does not consider (or is not able to determine) the rational forward-looking path of choices that would maximize her intertemporal utility. The agent thus takes into account current addiction and body weight when choosing the optimal level of smoking and food consumption, but she ignores that future addiction and body weight will change as a consequence of her current choices. As shown in the main text, this na¨ıve approach is not optimal for a forwardlooking agent, because it does not allow to take into full consideration how the future evolution of addiction and body weight will impact on future utility. Given current body weight and addiction to smoking, the optimal choice of food con- 22 sumption and smoking satisfies the following condition Uc Us =pc ps,(16) which is formally equivalent to the familiar static optimization solution under budget constraint where the marginal rate of substitution between two goods equals the ratio of the corresponding market prices. However, here the solution is not static because the optimal amount of smoking and eating depends on addiction to smoking and body weight. Since addiction and body weight change as a consequence of the choices of the agent, they are going to affect Uc/Usand, consequently, the optimal level of food consumption and smoking that satisfies (16) will change over time. This process stops when (16) holds and ˙w= ˙a= 0. Whether this condition is associated to being over- or underweight, or with being on diet or binging, requires additional specific assumptions. For a forward-looking agent, instead, we have shown that Uc/Us=pc/psresults in steady state if the agent has a healthy body weight and is not addicted to smoking. A.2 Proof of Proposition 1 It is convenient to express the conditions (8)-(11) as a systems of differential equations where only control and state variables appear. Differentiating (8) and (9), replacing (10), (11), and using (8), (9), the following dynamic system results ˙s=1 ψ(AUcs −BUcc) (17) ˙c=1 ψ(BUcs −AUss) (18) ˙a=s−δa (19) ˙w=c−εs −δw. (20) where A= (δ+ρ) (pc−Uc)−Uw,(21) B= (δ+ρ) (ps−Us)−Ua+ ˙aUsa +εUw,(22) ψ=UccUss −U2 cs >0, In steady state, conditions (17)-(20) must be equal to zero. Since ψ > 0 holds by assumption, this implies the following: Uw= (δ+ρ) (pc−Uc) Ua= (δ+ρ) (ps−Us) + εUw δwss =css −εsss δass =sss 23