Elsevier

Journal of Health Economics

Volume 62, November 2018, Pages 1-12
Journal of Health Economics

Smoking kills: An economic theory of addiction, health deficit accumulation, and longevity

https://doi.org/10.1016/j.jhealeco.2018.09.001Get rights and content

Abstract

In this paper I unify the economic theories of addiction and health deficit accumulation and develop a life cycle theory in which individuals take into account the fact that the consumption of addictive goods reduces their health and longevity. I distinguish two types of addiction: sophisticated and naive. Individuals with sophisticated addiction perfectly control their addiction. Individuals with naive addiction, though otherwise rational and forward looking, fail to fully understand how their addiction develops. I argue that the life cycle consumption pattern predicted for naive addiction is more suitable for motivating empirically observable patterns of addictive goods consumption. I take the case of smoking as unhealthy behavior, calibrate the model with U.S. data, and apply it in order to investigate the life cycle patterns of smoking and quitting smoking and the socioeconomic gradients of unhealthy consumption and longevity.

Introduction

In this paper I unify the economic theories of addiction and health deficit accumulation in order to provide a life cycle theory of addiction that can be calibrated with real data. The model is then used to motivate some stylized facts of smoking and its impact on health and longevity. Smoking is used as a prime example of unhealthy consumption not only because of data availability but also because it is well known that smoking affects health and potentially causes premature death. Cigarette smoking harms nearly every organ in the body, causes many diseases, and reduces the health of smokers in general. In the U.S. and many other developed countries smoking is the leading preventable cause of death (HHS, 2014, WHO, 2016). “Smoking kills” warns the advertisement on cigarette packages. It is thus likely that even uneducated and myopic individuals know that smoking reduces their life expectancy. In any case, we expect individuals with rational expectations to take into account the fact that smoking affects their health and longevity.

The classic economic explanation of addictive behavior is Becker and Murphy's (1988) theory of rational addiction (TORA). It is perhaps fair to say that it is the canonical economic theory of addiction to date (Cawley and Ruhm, 2012).1 According to TORA, addiction is conceptualized as habit formation with three characteristic effects of unhealthy consumption on utility (reinforcement, tolerance, and withdrawal). Most importantly, as already mentioned in the opening quote, TORA assumes that individuals live forever such that harmful addiction, by assumption, cannot affect individual longevity. The negative effects of addiction on health can be represented indirectly as negative effects on utility but the impact of smoking on premature death through deteriorating health cannot be taken into account.

Considering life as continuing infinitely could be harmless if the assumption were non-crucial and indeed made just for simplicity (as perhaps in some representative agents models in macroeconomics). In the context of addiction, however, it turns out that the assumption is crucial. Replacing the span of life from infinite to finite fundamentally changes the predictions derived from the model. This important point has recently been made by Laporte et al. (2017). The reason is that the optimal life cycle trajectory no longer converges towards a steady state when life is finite, a feature which invalidates the predictions made under the steady state assumption of TORA. Without further knowledge of initial conditions, the optimal life cycle trajectory motivates any autocorrelation of addictive consumption and is therefore hard to test empirically.

In contrast to the destructive study of Laporte et al. (2017), this paper aims to be more constructive and proposes a model of addiction in which individuals take into account the fact that their life span is finite and negatively influenced by the consumption of addictive substances. The theory of addiction will be integrated into a model of health deficit accumulation where, in contrast to TORA, there exists no steady state and life ends when sufficiently many health deficits have been accumulated (Dalgaard and Strulik, 2014). New testable predictions are derived from observing the life cycle trajectories of a calibrated model.

When unhealthy consumption affects longevity, the assumption of fully rational behavior is hard to square with the observable life cycle consumption patterns of important addictive goods, like cigarettes. In this case, the model predicts that the greatest increase in unhealthy consumption should be observed among the elderly. This prediction, which will be formally derived below, is easy to understand intuitively. When unhealthy consumption starts or increases in old age, there is little time left to get hooked, i.e., in TORA-language, to built up addictive capital. Under the reasonable assumption of tolerance, i.e. the feature that utility decreases in the stock of addictive capital, it makes sense to postpone addiction to old age and indulge in the most unhealthy goods shortly before death.

Postponing an increase in unhealthy consumption until shortly before death may adequately describe some hard drugs like heroine. Smoking and drinking, however, follow a different life cycle pattern: they tend to decrease in old age (Cawley and Ruhm, 2012). Holford et al. (2014) constructed a lifetime smoking history for cohorts of U.S. Americans and showed that smoking prevalence as well as smoking intensity reaches a peak at mid age of cohorts, on average around age 40. Later born cohorts tend to reach peak prevalence and peak intensity at an earlier age and at a lower level. Many individuals stop smoking in mid or old age and the share of smokers is lowest among the elderly. Health concerns and the concern that smoking affects death are the major reasons for quitting (Newport, 2013).

In order to reconcile the model's prediction with the stylized facts, I distinguish between sophisticated and naive addiction. Individuals with sophisticated addiction are fully rational in the Becker–Murphy (1988) sense. That is, taking into account how unhealthy consumption affects their addiction, they consume (drink, smoke) the most in old age and shortly before they die. Individuals with naive addiction fail to understand how unhealthy consumption affects their addiction (their stock of addictive capital). This small change in behavior allows for more flexibility of the life time addiction trajectory. Formally, this flexibility is achieved by eliminating the transversality condition for addictive capital (as derived in detail below). I then show that the model calibrated for naive addiction and smoking as unhealthy consumption predicts that individuals reduce or abandon unhealthy consumption in mid age or old age.

Naive addiction does not mean that individuals are myopic. On the contrary, individuals with naive addiction know that they are addicted, are planning ahead in the Becker–Murphy (1988) sense, and take into account that unhealthy consumption affects their health and longevity. They only fail to understand how unhealthy behavior affects their addiction. This mild form of bounded rationality can be easily motivated by the fact that even medical scientists do not fully understand how addiction “works” (for a survey, see Hyman et al., 2006). The focus on naive addiction does not preclude that other more severe forms of bounded rationality, which are not addressed in this paper, as e.g. time inconsistent decision making (Gruber and Koszegi, 2001, Khwaja et al., 2007) or self-control problems (Strulik, 2018b), contribute to the understanding of addiction as well. Here, I am interested in a minimally-invasive modification of TORA that helps to reconcile the model's prediction with some stylized facts of addiction and unhealthy consumption when it is taken into account that the length of life is finite and endogenous.2

Because individuals are planning ahead under naive addiction as well as under sophisticated addiction, an anticipated future price change of unhealthy goods elicits a change in consumption today as in conventional TORA. The triggered change of behavior, however, differs fundamentally. Given an infinite life, standard TORA predicts that individuals reduce consumption today in anticipation of a future price increase. In contrast, if life is finite and malleable by unhealthy consumption, young individuals are predicted to consume more today and reduce their consumption only after the price change takes effect.

Another distinguishing feature of the model is that it motivates a socioeconomic gradient for unhealthy behavior (Contoyannis and Jones, 2004, Balia and Jones, 2008). In particular, when calibrated for smoking, the model predicts that rich individuals smoke less, quit earlier, and are less likely to start smoking. The reason is that lifetime is endogenous, which provides a trade-off for intertemporal consumption (see Hall and Jones, 2007; Dalgaard and Strulik, 2014): more income could be used to consume more at each point in time or to consume more over a longer life. Rich individuals already consume a lot at any point of time and face a low marginal utility from even higher consumption. They are thus more interested in extending consumption over time and in order to reach this goal, they are more willing to make sacrifices in the form of more health expenditure and less indulgence in unhealthy consumption.

The impact of addiction on health in a life cycle model is also investigated by Carbone et al. (2005) and Jones et al. (2014). These studies integrate addiction into the health capital model (based on Grossman, 1972). The health capital model, however, is less suitable for discussing the issue of addiction and longevity since it implies convergence towards a steady state of constant health and infinite life. The reason for this is that health capital is assumed to depreciate at a given (potential age-specific) rate d(t) such that individuals with health capital H(t) lose health d(t)H(t) through health depreciation. The health capital model thus assumes that among two people of the same age t, the one in worse health, i.e. with less health capital H(t), loses less health in the next period. In other words, the pace of aging declines as people get older, a feature that supports convergence towards a steady state of constant health. Other undesirable implications of the health capital model are the prediction that health expenditure declines in old age and that health shocks in early life are depreciated away as individual age, i.e. its incompatibility with the fetal origins hypothesis.3

The studies of Carbone et al. (2005) and Jones et al. (2014) assume that individuals take into account how their addiction evolves. In the language of the present paper, they focus on sophisticated addiction. The problem of increasing unhealthy consumption in old age, however, has remained unnoticed. In the case of Jones et al., this is because the analysis stops after showing the first order conditions. The transversality conditions are never applied and the optimal life cycle trajectory is not identified. Carbone et al. apply the transversality conditions that hold for an infinite time horizon. In the context of the Grossman model, this procedure is, in principle, justified because a steady state of constant health exists.4 Carbone et al. use the model for quantitative analysis and predict, as an implication of the health capital approach, that health care spending declines in old age.

In this paper, I integrate addiction into the health deficit model (based on Dalgaard and Strulik, 2014). The health deficit model has a foundation in gerontology and predicts that unhealthy people age faster and that the pace of aging increases as people get older. Most importantly, in contrast to health capital, which is a latent variable (and unknown in medical science), health deficits are easily measured by a straightforward metric, the frailty index (Mitnitski et al., 2002a, Mitnitski et al., 2002b, Mitnitski et al., 2005, Rockwood and Mitnitski, 2007, Harttgen et al., 2013). This allows for a calibration of the model with real data such that the model can be used to quantitatively address life time health issues of addiction.5

The paper is organized as follows. In the next section, I set up the model of addiction and health deficit accumulation and discuss the cases of naive and sophisticated addiction. In Section 3, I calibrate the model for an average American using smoking as unhealthy behavior. In Section 4, I explore the life cycle patterns of unhealthy consumption and their comparative dynamics. I derive impulse responses to anticipated future price increases and investigate the income gradient of smoking. I discuss the case of undesired addiction and how individuals of different socioeconomic status manage to stop smoking. Finally, I consider whole populations and feed a distribution for the (genetic) susceptibility to addiction into the model and explore the predicted age and income patterns of quitting smoking. Section 5 concludes.

Section snippets

Addiction

Consider an individual who derives utility from consuming health-neutral goods c and unhealthy goods u. Moreover, the past stock of unhealthy consumption z, as a measure of consumption habits, affects utility as well. A utility function that is parsimonious and simultaneously sufficiently rich to allow for a comprehensive discussion of addictive behavior is given by (1).U(c,u,z)=c+(ϕ+αz)u1σ11σβ2z2,in which σ determines the elasticity of intertemporal substitution in consumption and ϕ, α, β

Calibration

As in Dalgaard and Strulik (2014), we consider a 20-year-old male U.S. American in the year 2000 who has a life expectancy of 55.5 years (dies at age 75.5; NVSS, 2012). The individual earns an annual labor income of $ 35,320 (BLS, 2011) until age 65, and afterwards, a pension of 0.45 · 35, 320 (with net replacement 0.45 according to OECD, 2016). The individual spends about 13 percent of his lifetime income on health (the health expenditure share of GDP in the U.S. in the year 2000; World Bank,

Results

Fig. 2 shows the optimal life cycle trajectories for u, z, and h, as well as the implied health deficit trajectory D for the Reference American with naive addiction (Ψ = 0). Smoking as well as addictive capital increase in young age and then decline to almost zero from age 60 onwards. The smoking trajectory replicates the stylized life cycle pattern of smoking observed by Holford et al. (2014) reasonably well. The habit stock follows the trajectory of unhealthy consumption with a delay of a

Conclusion

In this paper I proposed a refinement of the theory of addiction in the context of the health deficit model. Unhealthy consumption affects health and longevity and this fact is taken into account by individuals contemplating the consumption of addictive goods. I showed that the feature of finite life changes the prediction for unhealthy consumption over the course of life. When individuals understand how their addiction develops (sophisticated addiction), the bulk of their unhealthy consumption

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