Optimal taxation of sin goods: an analytical review

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Maria Alessandra Antonelli Sapienza University of Rome, Italy

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Angelo Castaldo Sapienza University of Rome, Italy

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Valeria De Bonis Sapienza University of Rome, Italy

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Alessandro Gandolfo University of Pisa, Italy

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We present an analytical literature review on optimal sin taxes. After identifying the distinctive features of sin goods, we develop a simple, encompassing model of the taxation of sin goods that allows for treating the main models found in the literature as subcases. We derive the optimal sin tax rates, while also considering the subsidisation of healthy goods. We then discuss the Pareto-improvement result obtained in the theoretical literature, confronting it with the debate on the regressivity of this kind of taxation. We highlight the crucial role of the interaction of tastes, self-control problems and poverty when deriving policy conclusions from theoretical models.

Abstract

We present an analytical literature review on optimal sin taxes. After identifying the distinctive features of sin goods, we develop a simple, encompassing model of the taxation of sin goods that allows for treating the main models found in the literature as subcases. We derive the optimal sin tax rates, while also considering the subsidisation of healthy goods. We then discuss the Pareto-improvement result obtained in the theoretical literature, confronting it with the debate on the regressivity of this kind of taxation. We highlight the crucial role of the interaction of tastes, self-control problems and poverty when deriving policy conclusions from theoretical models.

Introduction

The increase in the global burden of non-communicable diseases (cardiovascular and coronary heart diseases, diabetes, and some types of cancer) has stressed the role of diet and prevention (World Health Organization, 2016). Thus, excessive consumption of unhealthy commodities, such as food and beverages that are rich in salt, fat and sugar, has been added to traditional vices, such as the abuse of alcohol, tobacco, drugs and gambling – the so-called ‘sin goods’ (Hines, 2007; Allcott et al, 2019a) – renewing old questions on the scope for government intervention to discourage their consumption.

This article presents an analytical review of the literature on optimal sin taxes. Sin goods share with demerit goods (Musgrave, 1957, 1958; Scitovski, 1992) the contrast to certain community preferences, in that an increasing social value is now given to health. There is, however, a feature that distinguishes sin goods from demerit goods: overconsumption of sin goods may be a mistake from the individual point of view too, in that consumers themselves regret it afterwards (see, for instance, Cremer et al, 2012). This is because people may not (fully) take into account the damage to their own health deriving from the consumption decision.

Making an error is thus equivalent to imposing an externality upon oneself, often referred to as an ‘internality’ (Herrnstein et al, 1993). Public intervention thus overcomes a difficulty in implementing consumer sovereignty, rather than treading upon it. This feature also distinguishes the category of sin goods from that of externalities (even if their consumption is often associated with costly external effects) (on the externalities stemming from the consumption of sin goods, see, among others, Manning et al, 1989; Crawford et al, 2010, Wang et al, 2020). The mistake is typically ascribed to self-control problems, deriving from time inconsistency. This stems from: myopia, that is, a short-term propensity that individuals regret afterwards (O’Donoghue and Rabin, 2006); emotional factors, such as a transitory feeling of deprivation (Hoch and Loewenstein, 1991); or a perceived wedge between self-interest and behaviour because of the operation of visceral factors (Loewenstein, 1996) turned on by cues (Laibson, 2001; Bernheim and Rangel, 2004). As a result – and from a strictly economic point of view – individuals have present-focused preferences (Ericson and Laibson, 2018) affecting the level of consumption of sin goods to the detriment of healthy goods (Kalamov and Runkel, 2020).

Fiscal policy can target overconsumption, typically by changing the relative price of sin goods via taxation. In recent years, for instance, a wide debate has accompanied the introduction of new taxes on unhealthy items, such as sugary drinks, saturated fats, confectionery, chocolate and ice creams. In 2019, 75 countries had a tax on sugar-sweetened beverages; there were 53 in 2017.1 In France, they amounted to 1.67 per cent of total consumption tax revenues in 2018.2

However, this class of taxes, as well as the traditional ones on alcohol and tobacco (Crawford et al, 2010), are often criticised, both as an expression of paternalism in government intervention and because of their regressive impact. Among the critics, public choice scholars have stressed how the political process of tax policymaking involves welfare losses, especially through rent-seeking behaviour. To minimise these costs, one should opt for a structure of uniform excise tax rates and the application of the benefit principle (see, among others, Holcombe, 1998; Leeson and Thompson, 2021). As for the taxation of sin goods, while literature contributions recognise the possibility of benefits from consumption reduction, they point at several factors producing costs that might outweigh them. Among these, there are: welfare costs from lobbying against sin taxes; substitution effects towards other equally harmful but less-taxed goods; regressivity costs, since sin taxes fall most heavily on poor consumers; and a use of revenues not addressing the negative effects of the consumption of sin goods (Hoffer and Nesbit, 2018; Leeson and Thompson, 2021).

Within this framework, the literature provides different perspectives of analysis. Recent literature analyses the relationships between sin taxes, public regulation and the market power of operating firms. Miravete et al (2018) show that changes in tax rates for alcoholic beverages are compensated by opposite change of prices by firms operating in non-competitive settings, with consequent small effects on consumption and tax revenues. The ability of firms to adopt strategic price behaviour in response to changes in tax policy affects the relationship between tax rates and tax revenues, thus flattening the Laffer curve. In the same line of research, Hollenbeck and Uetake (2021) point at imperfect competition and the market power of firms operating in legal markets for sin goods, highlighting the role played as regards tax incidence, tax revenue and marijuana consumption in Washington state. They find that marijuana is not overtaxed and that sin taxes are primarily borne by consumers.

Another branch of the literature highlights the effects of social norms on marketing strategies (Kotler and Levy, 1971; Prevel Katsanis, 1994; Craig Smith and Cooper-Martin, 1997; Davidson, 2002, 2003; Harrison and Kacperczyk, 2009; Kim and Venkatachalam, 2011; Christensen and Nafziger, 2016; Grougiou et al, 2016; Kang et al, 2016; Cahan et al, 2017). A set of contributions mainly focuses on consumers’ behaviour, stressing psychological elements (Strotz, 1955; O’Donoghue and Rabin, 1999a, 2001). By identifying different types of consumers according to the weight given to various elements – such as rationality, addiction, emotional factors, self-control and commitment – this literature defines different levels of paternalistic public intervention as cautious paternalism (O’Donoghue and Rabin, 1999c), asymmetric paternalism (Camerer et al, 2003) and libertarian paternalism (Thaler and Sunstein, 2003). These analyses suggest that moderate public intervention policies significantly affect consumers with self-control problems, while having little effect on others.

A complementary branch of the economic literature analyses the instruments of public intervention. Most of the analyses concern the optimal taxation of sin goods, while public policies – such as education and the diffusion of information – designed to make consumers more aware of the damage of the consumption of sin goods on health receive less attention.

Moreover, in the context of economic analysis, the problem of sin goods is analysed both empirically and theoretically. In this article, we follow a theoretical approach. Theoretical analyses of the taxation of sin goods adopt a variety of models that differ from each other in the analytical form of the utility function reflecting consumers’ preferences and attitudes towards sin goods. Therefore, each model is contingent on its particular assumptions, which also reflect psychological, behavioural, philosophical and economic elements.

Against this background, this article presents an analytical review, not present in the literature, of the theoretical models on the taxation of sin goods. The purpose of this review is to propose a unifying framework through an encompassing model that allows for treating the main models found in the literature as subcases (see the second, third, fourth and fifth sections). This approach can be useful in producing a summarised vision of a heterogeneous and complex literature in order to evaluate the efficiency and the distributive effects of sin taxes (see the sixth section). The seventh section concludes the article.

The theoretical framework for the taxation of sin goods: an overview

Mainstream economics takes consumer sovereignty as the reference point of welfare evaluation. Thus, if well-informed individuals choose their consumption levels of sin goods rationally, a corrective public intervention can be justified only if consumption exerts externalities on others (Wang et al, 2020). Actually, excise taxes on tobacco and alcohol have traditionally been justified on this ground. Crawford et al (2010) review the estimates of the amount of the externalities generated by the consumption of these two products, finding that they are quite low for smoking, while they are quite high for drinking. Despite this, at least in developed countries, excise taxes are relatively higher than the corresponding externality estimates for tobacco, while the opposite is true for excise taxes on alcohol. This divergence has been interpreted as an indication of the inadequacy of standard utility models in explaining the choice of consuming – and taxing – sin goods given their typically addictive nature and the relevant negative effects of consumption on consumers’ health.

A good is potentially addictive if increases in past consumption raise current consumption (complementarity between future and present consumption, as in learning-by-doing set-ups). Some addictive goods have a negative impact on future utility (and earnings). The shadow price of the addictive good is thus equal to the sum of its market price and the money value of these future costs. Individuals might recognise these detrimental effects and still rationally choose to consume an addictive good if the resulting increase in utility is higher than the related cost (Becker and Murphy, 1988). Addiction is thus rational in the sense that there is forward-looking maximisation with stable preferences, that is, individuals maximise utility consistently over time.

The effect of past consumption on the utility of current consumption implies that tastes are no longer fixed. This is the core of the idea of habit formation proposed by Duesenberry (1952). Habit formation does not contrast with rationality if individuals can correctly predict the effect of current consumption on future tastes. However, are people able to do it? Experimental evidence, starting with Loewenstein and Adler (1995), seems to contradict this. In addition, even if individuals were able to correctly optimise their utility function, one wonders whether they would be able to carry out their plans. For this second aspect too, there is some contrary laboratory evidence (Ainlie and Haslam, 1992).

On these premises, the literature has developed alternative models that share a common feature: the existence of self-control problems that, at the theoretical level, stem from deviations from the standard discounted utility model, dating back to Samuelson (1937). One can divide these models into two broad categories. The first one identifies the mistake in the time inconsistency of individual behaviour. In these models, the discount function is non-exponential, which implies time-inconsistent preferences. In particular, hyperbolic discounting is assumed, with a declining rate of time preference. Therefore, once people reach future periods, they will make choices that are more impatient than what is preferred according to today’s tastes. The second category, instead, considers deviations from the standard model that consist in additional elements of the instantaneous utility function. In particular, these allow either for fluctuations in tastes due to visceral influences/cues, or for reference-dependent utility. The effect is an increase in the utility of immediate consumption of the sin good. In connection with visceral cues, there are also models that allow for an effect on utility from not-chosen alternatives (temptation utility), which represent a more radical departure from the standard discounted utility model. The role of all these factors is more relevant in the case of habit formation, even if not dependent on addiction itself.

To discuss this literature, we adopt a simple, encompassing model that allows for both hyperbolic discounting and increased utility of current sin good consumption because of transitory emotional factors or a bias in the prediction of tastes. In doing so, we start with the general approach of O’Donoghue and Rabin (1999a). In the following analysis, parameters modifying the utility and cost of the sin good represent deviations from the standard utility model.

A basic model

Let us first consider the behaviour of a single (representative) consumer. In the standard intertemporal utility-maximisation framework, individuals discount the future exponentially, that is, if d is the one-period discount factor, they discount n periods forward at a rate of dn:
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where u is the instantaneous utility function.

The first deviation we allow for is the introduction of a second parameter, b; a preference for immediate gratification corresponds to a value of b < 1, while b = 1 corresponds to the standard model:
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Thus, while the relative discount rate between two future periods is 1, that between today and tomorrow is less than 1, which implies impatience as for present consumption. This implies time inconsistency: when the future actually arrives, the individual will consume more than what is optimal from today’s point of view. For simplicity, we assume d = 1 throughout the article.

The second deviation from the standard model concerns the instantaneous utility function. We allow for the operation of an increase in today’s utility from sin good consumption deriving from visceral factors. These are introduced by the parameter e; a value of e > 0 might capture emotions triggered by the operation of cues (assuming that the cue is operative in any period, we have es > 0 if t = s and es = 0 if t > s).

We adopt a log-linear utility function:
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where x is a sin good, y is a standard good and z is the numeraire, with ac. Consumption of the sin good implies not only an increase in utility in the present, but also (health) costs in the future, which, for simplicity, occur only in the period following consumption. Benefits and costs of period t consumption are additively separable from consumption in any other period. Thus, in each period, the individual maximises:
(1)
subject to the individual budget constraint:
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where H is the individual endowment of the numeraire good.

Expenditure on x will be, while expenditure on y will be g. Thus, individual demand will be:
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In the literature that we illustrate later, the two deviations from the standard model, that is, b < 1 and e > 0, are considered to be mistakes deriving from self-control problems. Thus, individual choices differ from optimal ones, derived from the following maximand3:
(2)
Optimal quantities demanded will then be:
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By comparing the levels of quantity demanded for the sin good, one can note that if e > 0 and/or b < 1, , that is, there is overconsumption of the sin good.

We now review the models that adopt a hyperbolic utility function, on the one hand, and those modifying the instantaneous utility function, on the other, as special cases of this encompassing framework.

Hyperbolic discounting

Let us consider the case in which the only deviation from the standard model is represented by a value of b < 1, with e = 0, which we call Case 1. The parameter reflects a short-term propensity that the individual will regret thereafter. This is the standard model in this strand of the literature (see, in particular, O’Donoghue and Rabin, 2003, 2006). Equation 1 becomes:
(1’)
Thus, the parameter b induces an undervaluation of future costs associated with present consumption of the sin good. Quantities demanded become4:
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The deviation from the standard model is thus intertemporal inconsistency. In a path-breaking article on intertemporal inconsistency, Strotz (1955) considers exponential discounting as just a particular case of discounting. He argues that individuals reconsider plans as time goes on. Since the discount function is shifted, the solutions of the utility-maximisation problem can be different. Actually, they remain the same only if all future periods are discounted at a constant rate (exponential discounting). In other words, the relative importance of period t and period t + 1 is the same at t – 1 and t. In all other cases, individuals constantly repudiate their plans, as preferences in the future differ from today’s preferences.

Strotz (1955: 177, 179) also raises a concern for discount functions that overvalue ‘the more proximate satisfaction relative to the more distant ones’, especially if these are ‘gained at the expense of still-more-future cost’. This applies, among other situations, to the consumption of sin goods.

Laibson (1997) explicitly considers a hyperbolic utility function, which displays a declining discount rate between time t and time t + 1 but a constant discount rate thereafter. Declining discount rates are connected to self-control problems (Loewenstein and Prelec, 1992). O’Donoghue and Rabin (1999a, 2001) argue that the present-biased preferences implied by hyperbolic discounting produce the procrastination of actions involving immediate costs and the preproperation of actions involving immediate rewards. Individuals might be sophisticated, that is, aware of this self-control problem, or naive, that is, think that they will have the same preferences in the future as in the present.5 Individuals willing to ensure that they will do tomorrow what is best from today’s point of view can adopt a pre-commitment strategy, eliminating options that, though being inferior today, might be preferred in the future.

Hyperbolic preferences have been used to explain actual economic behaviour in several types of decisions, beginning with consumption-saving choices. O’Donoghue and Rabin (1999b), Carrillo (1999) and Gruber and Koszegi (2001) have started a strand of literature that applies it to the consumption of addictive goods. In particular, Gruber and Koszegi (2001, 2004) incorporate hyperbolic discounting into Becker and Murphy’s (1988) model, with sophisticated individuals wishing to consume less in the future than what they will actually manage to do. Since people do not act in their best interest, consumer sovereignty is no longer an argument against government intervention if externalities are not present. In particular, they show that the discounted utility of a sophisticated consumer can rise with the imposition of a tax, as this works as a commitment device that agents cannot implement by themselves.

O’Donoghue and Rabin (2006) consider sin goods that are not addictive. Actually, the fundamental feature of addictive behaviour is the dependence of the utility of present consumption on the level of past consumption. This characteristic is not a necessary feature of a sin good. Its essential characteristic is overconsumption, regretted afterwards because of the consequent health costs. Hyperbolic preferences deliver this feature, as they generate a short-term propensity that people regret afterwards. Thus, individuals do not maximise their own welfare. The existence of such mistakes is a common issue in the behavioural economics literature (see, for instance, Kahneman, 1994). The basic model can illustrate the role of taxation in the lack of addiction. Let us assume that the government maximises the individual’s ‘long-run’ utility (Equation 2). Thus, it considers time inconsistency an error that it can correct through taxation. We consider two cases, a tax on the sin good only that is returned to consumers by a lump-sum subsidy, and a Ramsey optimal taxation framework. For simplicity, in what follows we normalised to unity pre-tax prices.

Sin taxation and lump-sum subsidy

Let us consider the case of the government wishing to tax the sin good just to correct for the distortion in individual choice. It therefore maximises Equation 2 subject to the budget constraint:
(3)
where S is a lump-sum subsidy that returns the amount of the numeraire subtracted via taxation to the consumer. The tax distorts the price of the sin good, which becomes. The individual budget constraint is:
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Quantities demanded become:
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To obtain the first best, the tax rate needs to be chosen so that coincides with ; setting and solving for , one gets the expression for the optimal sin tax:
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The rationale for the tax is a Pigouvian correction for the internality: with b = 1, the optimal tax rate would be zero. The result can be extended to the case of heterogeneous individuals. For adherence to the real context, we consider a situation in which the government cannot make use of personalised taxes and transfers.6 To concentrate on the role of intertemporal inconsistency, we assume that individuals differ only in the value of the parameter b, which is a random variable with support b [0,1] and density function f(b). Therefore, b induces a probability distribution on x, meaning that the quantity demanded depends both on the price and on the individual value of the parameter b. Let us assume that the policymaker maximises a utilitarian welfare function, attaching an equal weight to each individual. The maximand function is:
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Maximising with respect to to obtain (given that px = 1 + tx; note that only the term is involved) yields:
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Substituting from the first-order condition of the individual maximisation , one gets:
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with E(1 – b) representing the average intertemporal distortion, which replaces the individual parameter value of the representative individual case. O’Donoghue and Rabin (2006) argue that with uniform tax and transfers, taxation of the sin good distorts consumption choices and redistributes income from people that consume a greater amount of the sin good to people that consume a lower one. With taste heterogeneity, even with the lack of self-control problems, taxation only creates a second-order loss, while transfers create first-order effects from income redistribution. If some individuals have self-control problems, they benefit because taxes counteract overconsumption, while rational consumers receive income: a Pareto improvement is possible in this context.7 These results hinge on the assumption that rational individuals consume less than irrational ones. However, if individuals differ both in the standard parameters (a, c, g) and in the error parameter b, deviations from b = 1 cannot be detected on the basis of the amount consumed, except in the a = c case, with time-consistent individuals not consuming the sin good at all.

Haavio and Kotakorpi (2011) analyse the determination of sin taxes under majority voting. With hyperbolic consumers, the equilibrium tax will generally be lower than the socially optimal level. This is because the median voter does not take into account that the positive welfare effect of taxation on hyperbolic consumers exceeds the negative impact on rational consumers. The result hinges upon the hypothesis that the demand of irrational consumers, characterised by a high consumption level, is more price elastic than that of rational consumers, with a low consumption level.8

A Ramsey optimal taxation framework

In a Ramsey optimal taxation framework, the government maximises Equation 2 subject to the budget constraint:
(3a)
Taxes distort prices, which become:
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Quantities demanded become:
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The government maximises Equation 2 subject to Equation 3a, from which we derive optimal taxes. Substituting quantities demanded into Equation 2 and 3a, the maximand becomes:
(2b)
Since is independent of taxes, the government chooses tax rates to max:
(2b’)
subject to:
(3a’)
Equation 3a’ implicitly defines a function . Differentiating Equation 3a’ yields:
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(4)
Taking the first-order condition of Equation 2b’ with respect to and using Equation 4:
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(5)
Using Equations 5 and 3a’, one gets:
(6)
(7)

The tax rate for the sin goods displays Sandmo’s (1975) additivity property, also obtained by Wang et al (2020) in the specific context of the taxation of sin goods. The first term of the right-hand side of Equation 6 relates to the government revenue constraint, while the second one is the Pigouvian component. If , the revenue requirement is exactly covered by the first-best correction; with , instead, the second-best revenue requirement is binding. As for the tax rate on y, the right-hand side of Equation 7 only displays the second-best revenue requirement component.

If the individual were rational, that is, with b = 1, the tax rates on the two goods would be the same given that they have the same price elasticity; otherwise, the sin good is taxed more than the other good, as the government wishes to correct the consumer’s mistake. If the government does not aim at raising revenues, that is, with R = 0, tax revenues from the corrective tax can only be distributed back through a distortionary subsidy on good y; thus, if y were a ‘healthy’ good, taxing the sin good implies subsidising the healthy one. In a framework with heterogeneous individuals, if the government cannot use personalised instruments, the preceding expressions hold with the parameter b replaced by its average value, as outlined earlier. In such a context, O’Donoghue and Rabin (2003) argue that increasing taxes on unhealthy goods (and lowering taxes on healthy or neutral ones) has second-order negative effects on rational consumers, though possibly high first-order effects on irrational ones, given that they correct for overconsumption of the sin good.9

The public choice literature, however, has criticised the effective possibility of applying the Ramsey rule once the political aspects of the design of taxation are taken into account. Given that tax rates are set according to the political power of interest groups, the tax structure will not follow the Ramsey rule, and the existence of different rates of excise taxation will induce political costs because of rent-seeking behaviour (Holcombe, 1998). This applies both to excise taxation in general and to sin goods in particular (Hoffer and Nesbit, 2018; Leeson and Thompson, 2021). A differential treatment of sin goods might therefore end up in a welfare loss, rather than in a welfare improvement.

An extension: effects of investment in healthy activities

The negative effect on health not fully anticipated and regretted afterwards is the distinctive feature of sin goods. Thus, the literature has added investment in health to the basic framework of analysis. The role of investment in health has been studied by, among others, Grossman (1972), Goulao and Pérez-Barahona (2014) and Wang et al (2017, 2020). With direct reference to the taxation of sin goods, Cremer et al (2012) consider a two-period framework in which individuals can invest in health care in the second period to counteract the negative effect of first-period sin-good consumption. They distinguish between people with ‘dual selves’, who actually recognise their error in time to correct it by the choice of the amount of health expenditure, and people who do not (or not before having chosen the amount of consumption of health services). Optimal tax rates depend on a Pigouvian, corrective component and a redistributive one. They find that for both types of people, the sin tax is lower if wealthier individuals are less myopic. In the case of dual selves, the sin tax is higher and the health subsidy is lower the higher their impact on savings.

Wang et al (2017) suggest that taxes on sin goods might be ineffective in improving health if they also determine a decrease in investment in health. Therefore, sin taxation should be accompanied by other instruments, such as subsidies for health investments or reductions in the income tax. To account for this issue, we consider an extension of the hyperbolic model, introducing the opposite of a sin good; let us call it a ‘healthy good’. Its consumption not only increases current utility, but also exerts a positive effect with a one-period lag. With a hyperbolic discount function, this positive effect will be undervalued, as with the negative one from sin-good consumption. To consider this case, let us extend our basic model and consider y a healthy good. The instantaneous utility function becomes:
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In each period, the (representative) consumer maximises:
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while optimal behaviour (that is, b = 1) would entail maximising:
(2’)
Quantities demanded will be:
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which differ from those that would obtain under optimal behaviour:
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In particular, myopia implies not only an overconsumption of the sin good, as before, but also an underconsumption of the healthy one (). We assume again that the government maximises Equation 2’ in a Ramsey optimal taxation framework. The budget constraint will thus again be Equation 3a, which, after substituting in from the individual maximisation first-order conditions, becomes:
(3b)
Following the same procedure as before, we derive the optimal tax rates:
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with the sin good being taxed and the healthy good being subsidised. Assuming, for simplicity, c = h, the optimal tax rates become10:
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With no revenue requirements, that is, , the first-best corrective tax on good x yields an amount of revenues that exactly matches the amount of the Pigouvian corrective subsidy on y. Instead, if , the second-best corrective tax is binding.

Time inconsistency and government intervention: some reflections

The hyperbolic utility function appears appealing; beside the discount rate, it gives a higher weight to consumption in the only period in which we are certainly alive, that is, today. It also delivers the individual’s regret that supports a corrective public intervention without impairing the consumer’s sovereignty. One can, however, argue that time inconsistency might be found with respect to consumption choices over some goods only. Actually, while the standard model considers one single discount rate, a large body of empirical literature shows that discount rates are inconsistent across different goods. Frederick et al (2002) review this literature and argue that time preference should be studied through a composite approach, as it was in the economic literature of the early 20th century.

However, if the time-inconsistency parameter b applies to some goods only, the same results could be obtained if the parameter b referred to a valuation of the future damage to health (or a value attached to health) that is lower than the ‘correct’ one, rather than to myopic behaviour. With a standard intertemporal utility function:
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and an instantaneous utility function of the following form:
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the individual maximand is Equation 1’, as in the hyperbolic consumer case. Under this perspective, hyperbolic discounting and underestimation of future damages to health are equivalent, but regret for not sticking to plans is no longer a justification for government intervention. Government intervention is instead triggered by a different evaluation of these damages or, equivalently, a different evaluation of the value of health from the individual one. This brings us back to demerit-goods arguments. The practical reference point for government intervention becomes quantity consumed, and therefore expected effects on health themselves, regardless of the extent of self-control problems. A different evaluation of marginal harm from consuming the sin good (higher for the government than for the individual), rather than a correction for time inconsistency, is, then, the factor that triggers government intervention.

Enriched specifications of the instantaneous utility function

Let us now consider the case in which the only deviation from the standard model is represented by a value of e > 0, with b = 1, which we call Case 2. The parameter reflects an overvaluation of present consumption of the sin good that stems from transitory or unpredicted changes in tastes; this case of the model comprehends several approaches that deviate from the standard utility model as regards the configuration of the instantaneous utility function. We divide them into two classes: (1) models in which the short-term propensity to consume derives from visceral factors; and (2) habit-formation (addiction) models with bias in the prediction of tastes.

Visceral factors

An alternative to the explanation of time-inconsistent behaviour provided by the hypothesis of hyperbolic discounting is a short-term increase in the propensity to consume the sin good brought about by visceral factors (see, for instance, Loewenstein, 2000). This term refers to emotional influences, such as craving, thirst, hunger, fear and pain. They can induce a transitory alteration in tastes, while the permanent evaluation of the good remains the same. Visceral influences differ from tastes in several respects (Loewenstein, 1996). They fall back on different neuropsychological mechanisms (chemical regulations, while tastes draw on information stored in memory) and change more rapidly than tastes. In addition, these changes depend on external circumstances, and even if the consumption level remains constant, they have direct hedonic consequences (which are negative in the examples mentioned earlier). Although visceral influences share with hyperbolic discounting the consumer’s focus on the present, they are turned on not only by the time factor, but also by other forms of ‘proximity’ to the good, or cues (for example, spatial proximity, smell, sounds and so on). The operation of these different types of cues allows for confining inconsistent behaviour to some types of goods (and environmental circumstances) only, while hyperbolic discounting refers to all goods. Laibson (2001) and Bernheim and Rangel (2004) analyse the role of cues in addictive behaviour in order to provide a ‘biological micro-foundation’ to Becker and Murphy’s (1988) model. Laibson (2001) assumes that addiction effects are activated by the presence of cues associated with past consumption of the addictive good. Therefore, a current cue is complementary with current consumption if that cue has been associated with consumption in the past. The operation of visceral factors, however, introduces time inconsistency in behaviour, thus invalidating the rationality assumptions of Becker and Murphy’s (1988) model. Again, it is possible to distinguish between sophisticated and naive consumers. Laibson (2001) shows that those individuals who perceive a wedge between behaviour and self-interest will be willing to follow a ‘pseudo-commitment’ strategy, that is, to devote resources to reduce their future choice set. Thus, differently from consumers in Becker and Murphy’s (1988) model, who find it optimal to remain addicted, given that the level of past consumption is given, consumers can manipulate cues and resist consumption. Moreover, if individuals are willing but unable to manage cues, public intervention can be beneficial (Bernheim and Rangel, 2004). Of course, attempts to resist consumption show that this is somehow unwanted: use is a mistake, that is, a pathological divergence between choice and preference.

Another class of models that belong to the broader category of ‘visceral factors’ are those with reference-dependent utility (Hoch and Loewenstein, 1991; Tversky and Kahnemann, 1991). These models adopt the prospect theory (Kahneman and Tversky, 1979) assumption that outcomes are evaluated over a value function defined over departure from a reference point, which might depend, for instance, on past consumption. A shift in the reference point can bring about a sudden and transitory change in tastes. This induces a state of deprivation that operates as a cue, increasing ‘long-run’ utility through relief from deprivation. Again, pre-commitment is a way of manipulating the reference point and resist overconsumption. All these models try to bridge the gap between rational and emotional motives, as with Holbrook et al (1990), an attempt dating back to Abelson (1963) and Hirschmann (1977).11

Habit formation (addiction) with bias in the prediction of tastes

A value of e > 0 can also derive from addiction; as exposed earlier, the basic feature of addiction is the increase in utility of the addictive good because of past consumption (e > 0 if xt – 1 > 0). This is a particular case of the endowment effect, that is, the tendency of people to value a good more highly once they possess it than they would do if they did not. There is nothing irrational in this change in tastes taken by itself, as addiction is not in Becker and Murphy’s (1988) model. Some authors, however, question whether people are able to foresee the effects of their current behaviour on their own future tastes (Thaler, 1980; Kahnemann et al, 1990; Loewenstein and Adler, 1995). Their experimental evidence indicates a downward bias in the prediction of the effects of the magnitude of the endowment effect.12 Thus, (over)consuming today is again a mistake, which the additional parameter e of our simple model can account for. Addictive behaviour becomes irrational not because of the undervaluation of future costs, but because of the error in predicting the increase in the desire for the good (Loewenstein et al, 2003; Chen et al, 2019). All these approaches imply an overvaluation of present consumption, that we apply to our sin good x by adding the parameter e to the standard parameter a. With b = 1 and e > 0, Equation 1 becomes:
(1’)
Quantities demanded become:
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The deviation from the standard model is thus an overvaluation of present consumption of the sin good. Let us assume that the government maximises the individual’s utility as devoid from the effects of self-control problems (Equation 2), thus considering the parameter e as an error that can be corrected through taxation. Let us consider, for the sake of brevity, a Ramsey optimal taxation framework only. Taxes distort prices and quantities demanded become:
article image
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Substituting quantities demanded into Equation 1’, the government’s maximand function becomes:
(2c)
Since is independent of taxes, the government chooses tax rates to max the following equation:
(2c’)
subject to:
article image
Following the same procedure used earlier, we derive the optimal tax rates:
article image
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Again, x is taxed, while y is subsidised. In a context with heterogeneous individuals, differing both in the standard parameters (a, c, g) and in the error parameter e, deviations from e = 0 cannot be detected on the basis of the amount consumed, except in the a = c case, with non-emotional individuals not consuming the sin good at all.

Efficiency and the distributive effects of taxation

The literature on the taxation of sin goods reviewed earlier finds that sin taxes under some conditions can result in a Pareto improvement (for the case of a sin tax returned to consumers by means of a lump-sum subsidy, see, for instance, O’Donoghue and Rabin, 2006).13 There are two such conditions: first, rational individuals consume a smaller amount of the sin good than irrational ones; and, second, irrational individuals’ consumption is price elastic. Thus, on the one hand, taxation of the sin good redistributes income from irrational to rational individuals, while irrational individuals benefit because the tax counteracts overconsumption.

However, if individuals differ both in the error parameter and in tastes, the first hypothesis does not necessarily hold. Heavy consumers of the sin good could be rational individuals with a strong taste for it, and they could suffer both through the distortion and through the redistribution effect.

As for the second assumption, the extent of the correction effect benefiting irrational consumers depends on the price elasticity of demand: it will be high if price elasticity is high (unless people can turn to other unhealthy but untaxed substitutes)14 and low if price elasticity is low. Within the theoretical frameworks analysed earlier, if the mistake derives from the influence of visceral factors, it is plausible to assume that elasticity is low. In this case, a greater effect on quantities consumed might be achieved with different forms of intervention, such as advertising and marketing restrictions, or the introduction of counter-cues (Hoch and Loewenstein, 1991).

A connected issue, central in the political debate on sin taxes, stems from their potentially regressive impact: if poor individuals consume sin goods more (for related evidence, see, among others, Gruber and Koszegi, 2004; Goldin and Homoroff, 2013; Allcott et al, 2019a, 2019b), the positive correction effect of taxation would entail a regressivity cost. From a theoretical point of view, Becker and Murphy (1988) find a relationship between the consumption of addictive goods and income through the effect on labour productivity. The same arguments can, in principle, be applied to sin goods given that their consumption has a negative impact on health and therefore on productivity. Thus, if consumption of the sin good reduces relatively more the productivity of skilled jobs, that is, if it has larger effects on higher earnings, the good becomes an inferior one. Becker and Murphy (1988) apply the result to developments in tobacco consumption, which has witnessed an increase of the share of low-income consumers. They explain this with the spreading of information on the costs deriving from smoking, which has lowered its income elasticity, making it an inferior good.

The fact that poor consumers pay more for sin taxes out of their income than rich ones is not a sufficient element to assess the overall impact of the measure; one should also consider the use of their revenues. For instance, Lockwood and Taubinsky (2017) consider the options of ‘recycling’ resources to increase the progressivity of the income tax or for expenditure programmes that benefit the poor; they argue that they will be effective if the consumption of sin goods depends on income elasticity, rather than on tastes. Cremer et al (2012) and Wang et al (2017) propose subsidies for health investment.

Moreover, the benefit from the increase in welfare deriving from the Pigouvian tax should also be considered. With respect to this, one can note that the link between income level and the consumption of sin goods also has implications for the extent of price elasticity and, therefore, the corrective impact of taxation. According to Corlette and Hague’s (1953) rule, low price elasticity of the demand for sin goods should be expected if these are complements to leisure. According to some survey studies, activities undertaken during free time significantly vary with income level. In particular, rich people are found to devote time to playing sports and attending performing-arts events, while poor ones devote time to watching television.15 It seems plausible that the former amusements are less complementary to the consumption of sin goods than the latter are. Of course, a low elasticity implies a low change in quantity and, therefore, a relatively low corrective effect.

This is true if poor consumers disproportionately consume sin goods not just because of a stronger taste for it, but because their choices are more biased by self-control problems. Psychologists have actually found that poverty reduces self-control by impeding cognitive functions (Mani et al, 2013) and inducing an orientation towards immediate needs (Lamm et al, 1976). Moreover, self-control is something that people learn. With reference to discount functions, Strotz (1955) argues that, besides pre-commitment, a strategy to avoid always repudiating plans is to substitute the exponential discount function for our natural one, which is possibly hyperbolic. This usually happens because people are taught to plan consistently from their early years.16 Analogous considerations may apply to the ability to refrain from emotional, impulsive choices, as in the case of the self-control problem stemming from visceral influences. In this respect, one should notice that financial poverty usually accompanies time poverty (Harvey and Mukhopadhyay, 2007), leaving less time for parents to teach children.17

Therefore, if poor consumers are those that exhibit an overconsumption of sin goods because of more pronounced self-control problems, investing revenues in educational services, such as pre-school programmes, might increase the overall corrective effect of the taxation of sin goods and help overcome regressivity costs.

Conclusions

The recognised social value of health has been increasing over time, so that unhealthy goods have entered the list of demerit goods, involving a justification for taxation, since their consumption, though in line with individual tastes, contrasts with community values. However, the economic literature has developed a new category of goods, that is, the sin goods, distinguished from traditional merit goods. Moreover, it has developed optimal taxation models that deliver, under some conditions, the result of a Pareto improvement by combining the taxation of sin goods and redistributive transfers. There are a few implications that can be drawn from our review of the literature on the optimal taxation of sin goods.

First, the origin of the self-control problem can be used to distinguish among the different literature models. Sin goods combine the damage to health with a self-control problem: individuals themselves thus regret their overconsumption afterwards. Regret stems from a divergence between short-run and long run utility, generating behavioural errors because of impatience. Existing contributions can thus be divided into two categories, according to the source of impatience: individuals discount the feature hyperbolically or act under the influence of emotional, rather than rational, factors. All these factors imply a change in individual tastes, which does not constitute a mistake by itself, unless connected to a self-control problem.

Second, the line dividing the concept of sin goods from that of merit goods is quite subtle. In these situations, government intervention is considered justified not on merit-goods arguments, but as a way to implement consumer sovereignty, impaired by individuals’ errors. This argument implies that individuals perceive the wedge between self-interest and behaviour. This is definitely true for sophisticated individuals who are unable to resist overconsumption. In this case, government intervention, for instance, taxation of the sin good, is a substitute for the inability of consumers to adopt commitment strategies. However, what about individuals who do not regret – still or ever – their consumption choices? In this case, it seems that the justifications for taxation or other forms of intervention fall back on merit-goods arguments.

Third, the taxation of sin goods can increase efficiency if the demand for the sin good is price elastic and rational individuals consume less than irrational ones. Of course, the very existence of a Pareto improvement rests on the assumption that consumption choices are biased by a mistake. Therefore, the corrective effect of taxation works through the increase in the price of the sin good and its effect on the quantity demanded. Consequently, it depends on the degree of the price elasticity of demand: the lower the elasticity, the lower the Pigouvian improvement. There are some reasons why the price elasticity of the demand for sin goods might be low: overconsumption could stem from visceral factors or sin goods could be complementary to leisure. Moreover, in a context with heterogeneous individuals, with some making biased choices and others behaving rationally, the correction that benefits the former should be compared with the distortion in the choices of the latter. The literature on the optimal taxation of sin goods obtains the result that sin taxes might result in a Pareto improvement if they are combined with redistributive transfers. If the revenues of (linear) sin taxes are accompanied by lump-sum subsidies, irrational individuals eventually benefit from the correction, even if the amount of taxes paid exceeds the subsidy received, and rational ones benefit from the subsidy, which exceeds the income and substitution effects of the tax. Thus, the result obtains if two assumptions hold: first, the demand for the sin good is price elastic; and, second, rational individuals consume less than irrational ones. The second assumption depends on the interplay between tastes and mistakes, as argued earlier.

Fourth, the question of whether the potential increase in efficiency might be shared among all members of society remains open. In other words, there is a trade-off between efficiency improvements and regressivity costs. Our analysis shows that the regressivity issue is linked to the theoretical result that poor people disproportionately consume sin goods, whether because of tastes or error. Theoretical models actually find that unhealthy goods are likely to be inferior, while empirical research shows that poor people consume sin goods relatively more than rich ones and that poverty favours present-oriented choices, thus increasing the likelihood of inconsistent behaviour. Moreover, sin goods are complements of leisure activities on which poor people widely spend their time, which implies a low price elasticity of their demand for the sin goods. Thus, the increase in utility because of the correction effect of taxation risks being outweighed by the regressivity cost.

Finally, an important factor in balancing the two effects is the destination of revenues from taxation. Besides traditional measures, such as increases in the progressivity of income tax or subsidies targeted at the poor, investment in education programmes can provide a way not only to offset the regressive impact of the tax, but also to strengthen its error-correction effect. This is because, as argued earlier, educational poverty might be a cause of self-control problems. In summary, the main implication of our literature review, therefore, is that the interplay of tastes, self-control problems and poverty is crucial when deriving policy conclusions from the theoretical models.

Notes

2

For data, see Eurostat-National Tax Lists 2018-2019; country notes available at https://ec.europa.eu/eurostat/cache/metadata/en/gov_10a_taxag_esms.htm

3

While Equation 1 is the objective function in each period in the recursive, time-consistent formulation, Equation 2 is the objective function in each of the future periods t, when the decision is taken at t – 1 but ignores the present choice at t – 1. This is the formulation under commitment.

4

The demand for the sin good is elastic with respect to the parameter b if b > a2c.

5

For laboratory evidence on sophistication and naivety (and on ‘dual selves’), see Della Vigna (2009).

6

If they were available, first-best efficiency could be achieved. The same result would be obtained with alternative personalised instruments, in particular, sin licences (O’Donoghue and Rabin, 2003; Haavio and Kotakorpi, 2016).

7

Immordino et al (2015) extend O’Donoghue and Rabin’s (2006) framework to the case of inefficient taxation. In our model, this case would correspond to a value of the lump-sum subsidy that falls short of revenues by the measure of the inefficiency parameter, that is, S = µtxx, with µ < 1 representing the inefficiency parameter.

8

For a discussion of this hypothesis, see the fourth section.

9

For an analysis of the subsidisation of healthy food, see Cheng and Chu (2018). Yaniv et al (2009) find that a subsidy for healthy food might increase obesity (because preparing healthy food subtracts time from physical activities), while a tax on unhealthy food decreases it.

10

For the derivation of the optimal tax rates with heterogeneous individuals, see the Appendix.

11

An alternative to preference changes is given by temptation-utility models (Gul and Pesendorfer, 2001), which extend the utility function to include temptation, so that well-being also depends on alternatives that are actually not chosen. Temptation is an option that the agent would prefer not to have and that decreases utility either by distorting choice or by requiring costly self-control. Thus, even if the consumer resists it, its existence is enough to lower utility. Temptation is a rationale to engage in pre-commitment. If this is not available, agents may consume the sin good compulsively.

12

The problem might arise in other contexts of changing tastes (changes in visceral influences or in reference points).

13

Camerer et al (2003) argue that the sum of consumer and producer surplus increases with policies that help consumers not to make errors, even if firms may benefit from exploiting them.

14

This suggests that sin taxes should apply to all goods with similar unhealthy characteristics and self-control problems – which is not easy, in practice, especially when it comes to foods and beverages. The possible substitution effects in favour of goods that are just as harmful as those being taxed, as well as the possibility that taxation will feed illegal trafficking, is stressed in the public choice literature on the taxation of sin goods (see, for instance, Leeson and Thompson, 2021).

15

See, for instance, the American Time Use Survey (available at: https://bls.gov/tus/). This is not only due to differences in prices; poor people also walk or run less than richer ones, possibly because they often live in unsafe areas.

16

‘Children are known to discount the future most precipitously and the “virtue” of frugality is something to be instilled when building “character”. True discount functions become sublimated by parental teaching and social pressure, and the inconsistency problem … becomes lost from sight’ (Strotz, 1955: 177).

17

These arguments apply not only to rationality, but also to sophistication. For a tailoring of policies to the degree of sophistication, see Frederick et al (2002).

Funding

Sapienza University of Rome supported this work (Protocol Number: RM1181643668A041).

Acknowledgements

We thank the referees for their very helpful comments and suggestions.

Conflict of interest

The authors declare that there is no conflict of interest.

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  • Wang, J., Marsiliani, L. and Renstrom, T. (2020) Optimal sin taxes in the presence of income taxes and health care, Economics Letters, 186: 108767. doi: 10.1016/j.econlet.2019.108767

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Appendix: optimal tax rates on the sin and the healthy goods with heterogeneous individuals

To concentrate on the role of intertemporal inconsistency, we assume that individuals differ in the value of the parameter b only, which is a random variable with density f(b) and support b [0,1]. We assume that the policymaker maximises a utilitarian utility function, attaching an equal weight to each individual. The maximand will then be the expectation of individual welfare:
article image
Taking some constants and deterministic variables out of the integral, we can write it as:
article image
Substituting in the budget constraint R = txx + tyy the individual first-order conditions and , we have:
(1A)
which can be rewritten as:
article image
To simplify, we pose and . The budget constraint becomes:
article image
Taking the total differential, we get:
(2A)
Taking Equation 1A and calculating the first-order condition with respect to :
article image
Substituting from Equation 2A for , we have:
article image
which yields:
article image
By using this expression and the government budget constraint, we can derive the expressions for the optimal tax rates:
(3A)
(4A)
Substituting from Equation 3A for and into Equation 4A, we have:
article image
and, simplifying:
(5A)
or, in extensive form:
(5A’)
Substituting for from Equation 5A in Equation 3A, we obtain:
article image
from which we can derive the optimal tax rate:
(6A’)

From Equation (5A’), we note that for R = 0, , that is, with individuals who underestimate the damage of the sin good. Likewise, from Equation 6A’, with R = 0.

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    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Wang, J., Marsiliani, L. and Renstrom, T. (2017) Tax Reform, Unhealthy Commodities and Endogenous Health, Working Paper No. 2017_12, Durham: University Business School.

    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
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