Anti-smoking Policies and Smoker Well-Being : Evidence From Britain ∗

Anti-smoking policies can in theory make smokers better o , by helping smokers with time-inconsistent preferences commit to giving up or reducing the amount they smoke. We use almost 20 years of British individual-level panel data to explore the impact on self-reported psychological well-being of two policy interventions: large real-terms increases in tobacco excise taxes and bans on smoking in public places. We use a di erence-in-di erences approach to compare the e ects on well-being for smokers and nonsmokers. Smoking behaviour is likely to be in uenced by policy interventions, leading to a selection problem if outcomes are compared across current smokers and non-smokers. We consider di erent ways of grouping individuals into `treatment'and `control' groups based on demographic characteristics and observed smoking histories. We nd fairly robust evidence that increases in tobacco taxes raise the relative well-being of likely smokers. Exploiting regional variation in the timing of the smoking ban across British regions, we also nd some evidence that it raised smoker well-being, though the e ect is not robust to the measure of well-being. The economic signi cance of the e ects also appears to be quite modest. Our ndings therefore give cautious support to the view that such interventions are at least partly justi able because of the bene ts they have for smokers themselves. JEL: D03, D12, H23, H31


Introduction
It has long been recognised that policies to reduce smoking behaviour can be justied by the negative externalities associated with smoking. 1 Costs including passive smoking and the net cost to public healthcare are borne by wider society but not the smoker, leading to excessively high levels of smoking from a socially optimal perspective. Policies such as tobacco excise taxes which raise the cost of smoking can therefore improve overall social welfare, though are usually assumed to make smokers individually worse o. However, recent insights from behavioural economics suggest that smokers themselves may benet from anti-smoking interventions. In particular, when smokers are time inconsistent, they may not be acting in their own best interests in making their smoking decisions. They make plans to give up smoking in the future but are unable to act on them when the future comes and they are faced with the immediate decision to smoke again. 2 In such cases, anti-smoking policies could help smokers commit to giving up, meaning the policies could be further rationalised by the commitment benets they confer on smokers.
It is hard to determine straightforwardly whether or not there is such a rationale for intervention. Empirical predictions about how smoking behaviour responds to price increases (now or expected in the future), for example, are the same whether or not smokers are assumed to be time inconsistent. A small emerging literature, beginning with Gruber and Mullainathan (2005), has started to look at how the self-reported well-being of smokers responds to policy reforms. Assuming that self-reported well-being is informative about individual welfare, evidence that smokers are made relatively better-o when anti-smoking reforms are enacted would be suggestive of time inconsistency. The key methodological challenge of this literature is to overcome the fact that smoking behaviour is in itself partly determined by policy reforms.
This paper contributes to this emerging literature in a number of ways. Most signicantly, we make use of a long individual-level panel dataset which includes information on smoking behaviour alongside selfreported well-being. Previous studies looking into the same question have made use of cross-sectional data, relying on a modelled propensity to smoke (assumed exogenous to policy changes) to identify the impact on well-being. Using panel data allows us to make use of individuals' own smoking histories to construct treatment groups of people likely to benet from the commitment value of anti-smoking policies, but where treatment status is not itself determined by policy changes. We also explore the dierential impact of the policies across education groups. If low education (a proxy for low lifetime income) people are more prone to time-inconsistency, they may see greater welfare benets from anti-smoking policies. This has implications for the distributional eects of such policies.
We look at the eect both of tobacco excise taxes and bans on smoking in public places. Bans have 1 A summary of the evidence on the magnitude of smoking-related externalities is in Crawford et al. (2010). 2 Around two thirds of adult smokers in England say they would like to give up (NHS Information Centre, 2012). been implemented in a number of OECD countries in recent years, as anti-smoking policies move beyond price-based incentives toward more direct regulation of smoker behaviour. We exploit time-specic variation in cigarette taxation and regional variation in when smoking bans were implemented to identify the impact of these measures on smoker well-being. Our study provides the rst evidence on this issue for Britain, which has been active both in implementing bans on smoking and in raising tobacco taxes. As at July 2011, British excise taxes on cigarettes were the second-highest (behind Ireland) in the EU.
To preview briey our key results: we nd evidence that higher real tobacco taxes increase the relative well-being of likely smokers, suggestive of time inconsistency in smoker behaviour. This result is broadly robust to dierent denitions of treatment groups and measures of well-being. We nd similar evidence that bans on smoking in public places raise smoker well-being, though this result is more sensitive to the measure of well-being. We do not nd any dierential eects across education groups.
The rest of the paper proceeds as follows. Section 2 recaps the recent evolution of UK tobacco taxes and bans on smoking in public places, our main policies of interest. Section 3 then describes the main economic and conceptual ideas around smoker behaviour and the implications of anti-smoking policies for smoker welfare. Section 4 develops the empirical strategy and describes the data used for the analysis. Section 5 describes the main results, and Section 6 concludes.  3 Other tobacco products generally face specic taxes by weight. Rates can be found at http://www.hmrc.gov.uk/rates/tobacco-duty.htm. 4 Series CZMP at http://www.ons.gov.uk/ons/datasets-and-tables/data-selector.html?table-id=3.1&dataset=mm23. Source: ONS data on prices (series CZMP, Consumer Price Indices). UKtradeinfo data on taxes (www.uktradeinfo.com). Converted to June 2012 prices using the all-items Retail Prices Index.
Real tax rates more than doubled over the period. Between 1993 and 2000, there was an explicit`escalator' policy to increase the specic tax in real terms, by 3% above ination at rst and then, from July 1997, by 5%. Over this period, real tobacco taxes increased by around 64% from ¿2. 32  Smokers may also respond by purchasing illicit tobacco (e.g. from low-tax jurisdictions by people living near borders, or through increased organised smuggling). Stehr (2005) uses US data and nds cigarette purchases repond more than cigarette consumption to tax changes, ascribing much of the dierence to evasion.
Price is not the only determinant of evasion, which will also depend on resources devoted to enforcement. 3 Economic models of smoker behaviour and welfare implications of policy interventions The workhorse economic model of smoking has been the`rational addiction' framework (Becker and Murphy, 1988). Consumption of an addictive good like tobacco builds up a`stock' of addiction. Utility in each period depends not only on current consumpion of tobacco and other goods, but also the accumulated addiction stock (reecting for example the health costs of smoking). This introduces a non-separability in preferences across periods, such that current smoking will be inuenced by expectations of future tobacco prices. Addiction is characterised by`adjacent complementarity': the higher the addiction stock, the higher the marginal utility from smoking. Consumers pick a path for current and future consumption of tobacco and the non-addictive good, taking into account how current decisions aect future utility. In the absence of any unexpected shocks, they will follow through that plan. A key implication of the rational addiction framework is that increases of the cost of smoking (such as higher tobacco taxes or public smoking bans) will reduce smokers' well-being.
The rational addiction model has been extended in a number of ways to account for smokers expressing regret about their smoking behaviour or failing to give up when they express a preference to do so, whilst maintaining the basic assumption that smoking decisions are the result of utility maximising behaviour.
For example, if consumers make boundedly rational decisions with informational uncertainty about their tendency to become addicted (Orphanides and Zervos, 1995), then taking up smoking might look optimal given some perceived risk of addiction which later turns out to be wrong, but continued smoking is then optimal given the addiction stock which has been built up. There is some empirical evidence that young with limited foresight: consumers may make smoking choices only considering some proportion of the future rather than the whole lifetime. In this framework it is possible that the lifetime optimal choice would be not to smoke but the limited foresight optimal choice is to smoke. They show that if the foresight horizon 5 It is also possible that people may misperceive the health risks of smoking which would cause them to come to regret their decisions as and when their information changed. Sloan and Platt (2011), though, suggest that if anything young people tend to overestimate the risk of health harms from smoking. increases with age (perhaps reecting increased learning or maturity), older people will give up or, in some cases, cycle between smoking and not smoking.
Whilst these ideas suggest why people come to regret past decisions or change their behaviour in the light of new information or experience, they do not clearly explain why people say they plan to give up but fail to do so. 6 Another development of the theory has considered that people suer from a time inconsistency problem. The rational addiction framework assumes that there is a constant discount rate: from today's perspective, utility in two periods is discounted twice as much as utility next period. If, instead, people discount the immediate future more heavily relative to the far-distant future, then it is possible that a plan to quit looks optimal from today's perspective but is no longer optimal when the time comes to follow that plan through. As a result, the passage of time alone is enough to change behaviour, hence the expression`time The hyperbolic discounting model of Laibson (1997) builds this change in discount factors into standard models of people making inter-temporal choices. O'Donoghue and Rabin (1999) look at this in the context of procrastination over whether or not to carry out a discrete action such as giving up smoking. Gruber and K®szegi (2000Gruber and K®szegi ( , 2001Gruber and K®szegi ( , 2004 build hyperbolic discounting into the rational addiction framework to think about continuous choices over cigarette consumption. Their model forms the basis for our empirical approach -we outline the main points below but full details of the derivation and proofs can be found in their papers.
Consumers allocate income across two goods in each period t, addictive tobacco a t and a non-addictive consumption good c t . Utility is assumed to be additively separable in the two goods. Consuming the addictive good builds up an addiction stock S t which depreciates at a constant rate 0 < d < 1 in each period. Utility from consuming the addictive good depends on the accumulated stock as well as the current consumption.
Thus the utility function takes the form: Addiction in this model arises when v aS > 0, that is, the marginal utility of current tobacco consumption increases in the addiction stock. The harmful health consequences of tobacco can be modelled by assuming 6 Assuming of couse that a stated preference to give up is genuine and does not reect a bias of survey respondents to givè socially acceptable' answers. Under quadratic utility, the subutility functions can be written as: with α a , α c , α aS > 0 and α aa , α SS , α S < 0. Tobacco is sold at a price p in each period, and the non-addictive good is sold at a normalised price of 1. Consumption of the non addictive good is therefore given as residual Consumers maximise discounted current and future utility. Utility over T periods is given as: with β, δ ∈ (0, 1). Hyperbolic discounting in this model arises because from the period t perspective, utility in the next period t + 1 is discounted by βδ whereas utility between periods t + 1 and t + 2 (or any two future consecutive periods) is discounted only by δ. In other words, the immediate future is more heavily discounted than the distant future. In the next period, the discount rate between t + 1 and t + 2 will then change to βδ.
Consumers are assumed to be aware that their discount rates are time-varying in this way. It is also assumed that from a welfare perspective, what matters for consumers are their long-run preferences (i.e. ignoring the additional immediate discount factor β). 7 The question is then how an increase in the price of tobacco aects consumer welfare. Since (conditional on income) utility will depend on the price of tobacco and the addiction stock in this model, from today's perspective, the expression of interest is: Gruber and K®szegi (2004) show using an iterative procedure that the derivative of discounted utility with respect to the price of tobacco is given by: The rst term is the standard result where there is no time inconsistency: higher tobacco prices reduce utility by increasing the cost of smoking. The second term is the commitment benet of higher prices. In each period, consumers smoke by more than they would`like' on the basis of their long-term preferences because the immediate future is more heavily discounted. Higher prices induce a consumption response ∂aj ∂p < 0 which helps time-inconsistent consumers to act more in line with their long-run preferences. The whole second expression is positive: that is, the utility cost of higher prices is mitigated by the self control benet.
To reiterate: the important implication of building time inconsistency into the addiction framework is that increases in the cost of addictive goods (such as tobacco) need not reduce individual welfare. With time inconsistency, higher costs provide a`commitment' benet to smokers, reducing future consumption towards levels that would be optimal in a time consistent model. 8 Gruber and K®szegi (2004) carry out a calibration exercise to show that higher prices are particularly likely to be welfare-improving when the hyperbolic discount factor is low (that is, when people are very impatient over the immediate future). This suggests that increases in tobacco tax rates can make smokers better o, giving a rationale for smoking taxes even without negative externalities. A similar argument can be made for other policies which raise the cost of smoking, such as bans on smoking in public places.
If we can interpret measures of self-reported well-being in surveys as a measure of individual welfare (or at least assume that they are positively correlated with welfare), then this model implies that when smokers are very time-inconsistent their reported well-being will rise when smoking costs increase, whereas non-smokers will be unaected.
9 This forms the basis of our empirical strategy outlined in the next section. 8 As noted in Gruber and Mullainathan (2005), other`behavioural' models besides time inconsistency can generate a demand for commitment. Bernheim and Rangel (2004) discuss`cue-based' consumption models, where consumption decisions depend on particular environmental signals (such as intending not to smoke but being inuenced to do so when in the company of other smokers). Smokers who are aware of this would demand mechanisms that help them avoid those cues. The model of Pesendorfer (2001, 2007) considers the`self-control' costs that people face to avoid`temptation' -think of the willpower eort needed not to smoke when cigarettes are easily available -and so demand mechanisms that reduce self-control costs. In both cases, simple versions of these models imply that higher prices make smokers worse-o because consumption in the presence of a cue or the temptation value placed on smoking is essentially unresponsive to price. However, allowing cue-based demand or temptation utility to vary with price can restore the interpretation that smoker welfare improves when the costs of smoking rise. 9 Larsen and Fredrickson (1999) and Stutzer and Frey (2010) summarise evidence on the relationship between survey-based measures of happiness and other indicators of well-being (including observer-reports of happiness and economic indicators). There are of course reasons why non-smokers may be impacted by higher tobacco taxes as well. Reduced smoking rates may have positive benets for non-smokers in the presence of negative externalities, for example. The use of increased tobacco tax revenues to fund public spending or reduce other taxes may also benet non-smokers. However it might be expected that these gains are second-order in magnitude relative to the direct gains for time-inconsistent smokers.

Empirical strategy
We carry out a reduced-form analysis of the impact of anti-smoking policy interventions (increases in cigarette excise taxes and bans on smoking in public places) on self-reported individual measures of well-being. In particular, we compare whether these policies have a dierential impact on the well-being of the people most likely to benet from the commitment value they generate: smokers or groups of people who, on the basis of their observable characteristics or past smoking behaviour, are likely smokers. We exploit time-varying real excise taxes and time-and location-varying bans on smoking alongside detailed long-term panel data reporting happiness and smoking measures for a large sample of British adults to conduct our analysis. The data are described in more detail in Section 4.2.
We draw on a number of recent studies, most notably the pioneering work of Gruber and Mullainathan (2005). Using US and Canadian data, they nd evidence that higher real cigarette excise taxes signicantly reduce the tendency of likely smokers to report being unhappy relative to those unlikely to smoke. Their Other studies have provided empirical support that smokers support anti-smoking policies. Hersch (2005) uses US data to look at support for restrictions on smoking in six dierent types of public place among current smokers, distinguishing those who say they want to quit (who may therefore reveal themselves to be suering from time inconsistency) from those who do not. The results show stronger support for the bans amongst those who want to give up. Interestingly, the support is even stronger for those who have tried and failed to quit than those who are planning to try for the rst time. They suggest this is evidence that those who have failed before have higher quit costs (such as the pain of withdrawal or diculty in obtaining support for giving up elsewhere) and so would place even greater value on the policies. Kan (2007) nds evidence in Taiwanese data that smokers who want to quit express more support for higher tobacco taxes and smoking bans in public places or at work. Badillo Amador and López Nicolás (2011) nd similar results in Spanish data.

Cigarette excise taxes
In looking at the impact of tobacco excise taxes, we compare how they aect the self-reported well-being of likely smokers relative to non-smokers. The basic estimating equation takes the form: where H it is a measure of well-being (i indexing individuals and t indexing the time (year and month) in which the individual is observed), T t is the ination-adjusted tobacco tax rate, S it is a variable indicating smoker status and X it is a vector of individual-specic observable characteristics that could aect well-being.
We detail the set of covariates in Section 4.2. Because we use panel data, we cluster the standard errors at the individual level to account for any correlation in the error structure within individuals over time. The parameter of interest is ξ which measures the dierential impact of real excise taxes on the well-being of smokers relative to non-smokers. A positive coecient would be suggestive of the commitment benets from higher taxation seen in time inconsistency models of smoker behaviour.
Simply using current smoker status as the measure of S it in the model may lead to problems since smoking behaviour today will be endogenous to current tax rates. This leads to a selection eect: if those who continue to smoke following a tax rise have lower happiness than those who quit, this will bias downward the coecient ξ.
We consider a number of approaches to deal with this. The rst closely follows that of Gruber and Mullainathan (2005). In place of current smoking status, they use a modelled estimate of an individual's propensity to smoke based on observable characteristics, where smoking propensity is not a function of current smoking tax rates. Using the rst wave of data (from 1991) we estimate a probit model of the propensity to smoke where the dependent variable is a dummy variable for current smoker status and the independent variables are the same covariates used in the happiness equation. 10 We use the parameter estimates to predict the likelihood that individuals observed in each year would have been smokers had they been observed with those covariates in the 1991 sample. This propensity P 91 it is then used in place of S it in the well-being equation.
11 There are two small dierences between the Gruber and Mullainathan (2005) approach and our 10 The model results from this probit are detailed in the Appendix. Controlling for other observables, women are less likely to smoke than men. People in poorer households and with lower educational attainment are more likely to smoke, as are those who are unemployed. Divorced, widowed or co-habiting people are more likely to smoke than married people. Private and social renters are more likely to smoke than other tenure types. Those with breathing problems are more likely to be smokers. 11 Note that as discussed in Gruber and Mullainathan (2005), we do not use P 91 it as an instrument forS it ; rather, it directly replaces it as the object of interest in the estimating equation. Further, as we use the same covariates in the happiness equation and the rst stage probit equation, identication of the θ parameter in the happiness equation is rather tenuous, driven largely by the fact that the propensity score is modelled non-linearly whereas the parameters enter linearly into the happiness equation. However, these covariates in the happiness equation are not really of direct interest and serve merely as controls: the key parameter of interest is ξ which is identied by the interaction of smoking propensity with real tax rates. rst method. First, we model the propensity only using the rst year of data rather than estimating separate propensity models for each year of data. The idea is that modelled propensity to have been a smoker in 1991 is exogenous to tax rates in later years. Second, we account for the fact that we use a two-step method and use bootstrapping techniques to calculate standard errors in the happiness equation. Not doing this gives misleadingly small standard errors which could give rise to spurious signicance of the key terms of interest.
The fact we are using a long panel dataset of individual smoking and happiness data allows us to consider two further approaches. Rather than modelling the likelihood that individuals are smokers, we are able to draw on each individual's own smoking history to assign them to a`treatment' group who would benet from the commitment value of higher taxation under time inconsistency and`control' group who would not.
First, we dene those who are smokers in the initial 1991 wave of data as treated and track how their wellbeing responds to changes in cigarette excise taxes relative to those who were not smokers in 1991. Second, we dene those who are ever observed to smoke over the entire data period (1991 to 2008) as treated and those who never smoke as controls. Clearly, those who smoked in 1991 are a subset of those who are ever observed to smoke over the whole period. It may be that some of those who were not smoking in 1991 but later took it up were also at risk of starting in earlier years and so would also have valued the commitment benet of taxation. Rather than estimating a propensity weight, these approaches essentially boil down to a straightforward dierence-in-dierences model where treatment status is exogenous to policy reforms. 12 One particular implication of the economic model is that likely smokers who exhibit a greater degree of time inconsistency will see the largest welfare gains from increased taxes, since they will value the commitment mechanism more highly. There is relatively little evidence on whether time inconsistency varies directly with observable individual characteristics. Paserman (2008) nds unemployed workers previously on low incomes exhibit more time inconsistency than those previously on high incomes. Choi et al. (2011) nd evidence that better-o consumers make decisions consistent with economic rationality, but do not test time-consistency directly. We investigate the issue by exploring whether there is any dierential in the relative impact of taxes on self-reported happiness for smokers in dierent education groups, where education is assumed to reect dierences in permanent income across households. This involves further interacting the policy and smoker status interaction with an educational attainment dummy for those who achieved post-compulsory qualications. Finding larger eects for low education individuals could be suggestive evidence that time 12 We considered other approaches to determining treatment status. For example, in 1999 individuals were asked about their smoking histories over their whole life and we could have classied anyone who had ever smoked as treated. However, around two-thirds of people had smoked at some point, and we found little dierence between modelled smoking propensity across treatment and control individuals using this denition. It was also unclear that experimental youth smoking would be a good determinant of whether or not people suered from time inconsistency problems as a later adult non-smoker. We also could have used any past smoking behaviour as a current treatment indicator, such as smoker status in the previous year, rather than smoker status in the rst wave. However, the assumption that smoking status a year ago is exogenous to current policy changes is perhaps less credible than assuming exogeneity of initial smoker status to current policy, particularly where people may have had reasonable expectations about how policy would change in the near future either during the tobacco tax escalator or around the time that smoking bans were being introduced in dierent regions. inconsistency problems are larger for poorer people.

Bans on smoking in public places
We adopt a similar approach to assessing the well-being eect of the ban on smoking in public places. We exploit regional variation in the timing of the smoking ban. We restrict our sample to those who are dened as likely smokers, and compare changes in smoker well-being for those living in Scotland to those living in England and Wales in the period following the ban being implemented in Scotland. Again this is a straightforward dierence-in-dierences estimation where the sample is restricted to individuals likely to benet from the commitment value of the ban, and`treatment' is now dened across regions rather than people.
We dene groups of likely smokers using individual observed smoking histories in a similar way as described above. 13 First we take smoking status in the rst year in which individuals are observed. In the analysis of the smoking ban, we begin in 1999 (rather than in 1991 as for the tax analysis) in order to make use of regional booster samples in the data which signicantly increase the Scottish sample size. Second we take smoking status over the whole data period beginning from 1999 and dene likely smokers as those who smoked at any time. As above, treatment status should be exogneous to the policy reforms.
The estimating equation is of the form: where SCOT it is a dummy variable for individuals living in Scotland, and P OST it is a dummy for someone observed in March 2006 or later, following the ban being introduced in Scotland. The coecient on the interaction term ξ then represents the relative impact on well-being for a`smoker' living in Scotland following the ban there compared to one living in England or Wales before the ban was extended to the rest of Britain.

Data
Our data come from the rst eighteen waves of the British Household Panel Survey (BHPS), which covers the period September 1991 to April 2009. The BHPS is annual survey that initially sampled around 5,500 households (10,000 individuals) in 1991. The survey attempts to follow the same individuals and their natural descendents through successive waves, even if they move home. All adult members (age 16+) of the sample households are interviewed each year, including adults that move into the household after the start of the 13 Note that we do not use a propensity score approach in this part of the analysis. We could model smoking likelihood and take some arbitrary cut o value to dene those`likely' smokers over whom to make regional comparisons in well-being, but it is not clear what the appropriate cut-o to take would be. survey and children that reach adulthood. Most interviews (around 97%) take place between September and November each year, though a small number take place between December and May. The survey initially only covered England, Scotland and Wales. Booster samples of around 1,500 households each from Scotland and Wales were added in 1999 to allow regional-level analysis.
14 Information on individual and household socio-economic characteristics is collected each year, along with physical and mental health status and current smoking behaviour.
The survey asks several questions on individuals' subjective well-being. However, the only questions that have been asked consistently across waves are the General Health Questionnaire (GHQ) questions of Goldberg Values for each question are then simply added up to give a total score between 0 and 36, with higher values representing greater distress. Answers to these questions are recorded by the respondents on a self-completion questionnaire and are not interviewer-delivered.
We draw on the GHQ measure in two ways to dene the dependent variable in the well-being equation.
First, we use the total GHQ score and estimate the well-being model using simple OLS. Second, we select one of the twelve questions which make up the GHQ: have you recently been feeling reasonably happy, all things considered? Respondents can answer more so than usual, the same as usual, less so than usual or much less than usual. We generate three dummy variables for happier than usual, the same as usual and less happy than usual (the latter includes those reporting much less which is relatively rarely observed), and then estimate three separate linear probability models for each outcome.

16
Note that the GHQ specically asks respondents to consider their feelings relative to`usual'. There may be some concern about this. If time-inconsistent smokers felt their`usual' happiness rise following antismoking policy interventions, we may not pick this up with the questions as phrased. However, what would be particularly hard to account for outside of a time inconsistency framework is a short-term increase in happiness following an anti-smoking intervention, which is precisely what this sort of question would capture. 14 A sample of around 2,000 housheolds from Northern Ireland was included from the 11th wave (2001) to allow UK-wide analysis; because the region is not covered across all waves we exclude Northern Ireland observations from all our results. Further details of the BHPS can be found at https://www.iser.essex.ac.uk/bhps. Note that from 2009 onwards, the BHPS sample has been subsumed into the wider survey Understanding Society which has much larger sample sizes. The rst wave of Understanding Society to incorporate the BHPS sample was in 2010. However, information on smoking is not routinely collected in Understanding Society; rather smoking history information will be gathered every three years. This means it has not been possible to extend the analysis beyond 2008. 15 A seven point measure of life general life satisfaction is only available from 1996 to 2000 and 2002 to 2008, and so misses a large period during which real-terms cigarette excise taxes were rising rapidly (see Figure 1). 16 This follows Ai and Norton (2003) who warn of the diculty of interpreting interaction terms in non-linear models. However, results using probit methods are qualitatively similar and are available on request. Fewer than 1% of observations in all cases had predicted probabilities outside the 0-1 range.
Within the standard rational addiction model, for example, smokers could be happier (have higher utility) if they did not smoke than if they did, but given their accumulated addiction stock and the short-term costs of quitting the optimal decision is to continue to smoke. Higher taxes may help smokers to give up, and eventually attain a higher baseline happiness level, but we would expect the short-term eect on happiness to be negative whilst the costs of quitting are endured. If we nd evidence that anti-smoking measures make likely smokers happier than usual this could be even more persuasive evidence for time inconsistency if we interpret it as a short-term gain to happiness. Note too that we are not the rst to use the GHQ as a straightforward happiness measure (see for example Oswald, 1997;Clark and Oswald, 2002), or as a measure of happiness relating to smoking behaviour in the BHPS: Moore (2009) nds that increases in smoking behaviour are correlated with reduced happiness using the same GHQ happiness question.
We include a number of covariates in the model which we might expect to inuence well-being. This includes real net equivalised annual household income, based on the income derivations for the BHPS provided by Bardasi et al. (2012). Rather than using absolute income, we construct within-wave income deciles to allow for the possibility that well-being is aected by relative income position rather than absolute income, and to allow for non-linear relationships between income and well-being.
17 Individual-level covariates include age (and age squared), gender, the presence and number of children of dierent age groups in the household, highest educational attainment, employment status, marital status, housing tenure type, and a number of physical and mental health problems as recorded by the individual in the self-completion questionnaire. Clark and Etilé (2002) note that deterioration in health is correlated with quitting smoking. Health outcomes are therefore likely to be related both to smoking status and self-reported well-being, suggesting that excluding them could bias our results.
The BHPS data are supplemented with real-terms smoking excise duties as described in Section 2 above.
These are merged into the BHPS data at a monthly level, expressed in June 2012 prices based on the all-items RPI measure of the price level.

Sample selection
As described in Section 4.1.1, we consider three main approaches to explore the relationship between antismoking policies and the relative well-being of likely smokers. Here we outline the samples selected from the data for the dierent approaches. 17 Clark and Oswald (2002) discuss absolute versus positional measures of income as determinants of well-being.
All of our analysis of excise taxes is restricted to the`original' BHPS sample (individuals who were interviewed in the initial 1991 wave). We start with a naive analysis using current smoker status; here our only restriction on the sample is to include individuals who are observed in 1991 and have non-missing smoker information in a given year.
For the model using smoking propensity in place of smoker status, we also restrict the sample to individuals observed in 1991. This is largely because we bootstrap the estimates to account for the two-stage nature of For the model using 1991 smoking status as a treatment indicator, it is obvious that we need to restrict the sample to those individuals observed in that year with non-missing smoking status. Conditional on that we do not make any other sample selection. This means that we can include observations in later years where smoking status is missing (unlike the naive model) since the treatment indicator has been dened for that observation.
For the model using observed smoking status over the period 1991 to 2008 as a treatment indicator, we condition on the individual reporting their smoking status in at least 15 waves (including 1991). 18 If they ever report a positive response to current smoking behaviour we classify them as treated individuals in all years, otherwise they are classed as controls. Essentially we are willing to assume that someone who reports being a non-smoker in at least 15 separate years is unlikely to be a smoker in the years in which their smoking status is not observed. Since this is the only specication that conditions on smoking status being observed a given number of times the sample sizes for this specication are substantially lower than the others (see Table 1).

19
Across all specications, we further condition on individuals having a full set of right-hand side control variables without missing values. We also exclude proxy respondents.

Bans on smoking in public places
Our analysis of smoking bans relies explicitly on regional variation in when bans are introduced. Since the original BHPS sample contains relatively small numbers of Scottish observations, relying on this sample alone 18 Conditioning on observing individuals in 1991 excludes new entrants to the survey whose smoking status may be depend on tax rates in the years they join. 19 This selection does not appear to materially aect things: our empirical ndings are not sensitive to using this more restricted sample with the other approaches. makes it much less likely that we would pick up any dierential eect on well-being across regions. Thus for this analysis make use of the regional booster samples. Since these were introduced in 1999, we start our analysis in that year. All of our analysis for the smoking ban ends before the ban is extended to England and Wales in 2007. Since our smoking ban models use region as a treatment indicator and are restricted to`smokers' from a subset of the whole data period, the sample sizes are much smaller than the tax-based models, even though we make use of the regional boosters.
As noted, we do not use a propensity model for the smoking ban analysis, since our interest is in regional with no more than two missing observations over that period. Table 1 shows the number of individuals and number of observations for each specication following these various selection criteria.

Descriptive statistics: smoking and happiness
Smoking rates in the BHPS sample have fallen over time. 20 Overall smoking prevalence fell from 29% in the 1991 survey to 20% in the 2008 survey.
Males have remained slightly more likely to smoke than females, though both have seen similar declines in participation over time. These gures and trends are very close to those reported in ocial smoking statistics based on data from the General Lifestyle Survey (Dunstan, 2012). Males are also more likely to smoke than females conditional on educational attainment. Whilst those with post-compulsory education are considerably less likely to smoke than those without, there has been a strikingly dierent trend over time in smoking rates by education. For those with low education, smoking rates have declined fairly consistently over the whole period. By contrast, for those with higher education, prevalence actually rose in the mid 1990s before falling back in the 2000s. 20 These gures are based on the full samples in each year rather than the selected samples for our empirical specication. This includes regional booster samples where available. All gures are weighted to national totals.  1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 1991 1992 1993 1994 1995 1996 1997 1998 1999  There appears to be a negative correlation between smoking and self-reported well-being. Figure 3 shows the average GHQ score (between 0 and 36) by current smoker status and survey year where higher values reect lower well-being. Across all waves, smokers report on average a GHQ score of 11.8 and non-smokers a score of 10.9. For both groups there has been a slight upward trend over time in the average score, though the recent trend is stronger for smokers such that the gap has widened in the most recent years having narrowed in the later 1990s. Of course, as is clear from Figure 2, compositional changes over time in those who are smokers mean we cannot draw clear conclusions from these trends alone about how anti-smoking policies have aected the relative well-being of smokers. Hence we turn to our empirical results.

5.1
Cigarette excise taxes Table 2 shows the proportion of individuals classied as current smokers and as treatment and control groups under the two specications which use smoking histories to dene those who may benet from higher excise taxes as a commitment device. It also shows the average smoking propensity score from the probit model of smoking status using the 1991 sample for the treatment and control groups and for current smokers. The table shows that the average propensity score is higher for individuals observed smoking in any given year than those observed not smoking, though the dierence is not huge (0.35 compared to 0.24). 35% of the sample were seen smoking at one point in our sample and are included in our ever smoked group.
Interestingly, only 16% of those observed not smoking in any given year are seen smoking on some other occasion, suggesting that most non-smokers are essentially never smokers. 29% of the sample were seen smoking in the rst year of data in 1991.
All of the well-being equations include year dummies, 21 the smoker status variable (the treatment/control indicator or the propensity score) and its interaction with the real excise tax rate (measured in pounds per pack of 20 cigarettes), and the same set of covariates as the smoking propensity model. As discussed earlier, these covariates serve merely as controls in the model. For reasons of space we do not therefore present the full model results, and instead present the key results of interest. Full results are available on request. Table 3 shows results from an OLS specication where the overall GHQ score (on the 0-36 scale) is the dependent variable. Recall that higher GHQ scores reect lower well-being; as a result, if higher excise taxes were associated with an increase in the relative well-being of the smoker groups we would expect a negative coecient on the interaction term. Each column shows a dierent specication of the denition of the`smoker' variable as outlined above. Column (1) shows a naive specication using current smoker status, likely to be endogenous to the current tax rate. Column (2) replaces current status with the propensity score based on the 1991 smoker probit. Column (3) replaces current smoker status with a treatment indicator set to 1 for those who were smokers at any time between 1991 and 2008. Column (4) sets the treatment indicator to 1 for those who smoked in 1991.  have average GHQ scores around 0.8 to 0.9 points higher than non-smokers. It is hard to compare that to the 21 We do not control specically for month -whilst we may expect seasonal variation in reported well-being, recall that almost all the interviews in the BHPS take place between September and November in a given year.
propensity score specication (column 2) since here the`smoker' variable is just the propensity score in the range 0 to 1. Taking the average observed propensity score for current smokers in the sample (0.36) compared to the average propensity score for non-smokers (0.25) and multiplying the dierence by the coecient gives that an average smoker in this specication has a GHQ score around 0.5 points higher than an average non-smoker.
Increases in real cigarette taxes also tend to raise GHQ scores (reduce well-being): a ¿1 tax rise is assocated with an average increase of around 1 to 1.2 points in the GHQ score, though this is not statistically signicant in all specications.
The interaction terms are consistently negative, though the statistical signicance varies across specications, being strongly signicant for the treatment/control models but not signicant in the propensity score model. These results lend some support to the view that a treatment group of smokers sees their well-being rise relative to a control group of non-smokers as taxes increase (though note that the overall eect of higher taxes on`smoker' well-being given by the sum of the tax and interaction terms is still negative). Taking the treatment/control specications, for example, a ¿1 rise in taxes would be associated with a relative fall in the GHQ score of smokers of around 0.2 points. This compares to an average GHQ score for the sample of 11.1 and a standard deviation of 5.3.
As discussed in Section 4.1, an open empirical question is whether poorer consumers exhibit a greater degree of time inconsistency. If so, one implication is that low education smokers (where low education is a proxy for low lifetime income) would see the largest benets from the commitment value of higher taxation. Table 4 repeats the analysis, further interacting the smoker status and tax interaction with three educational attainment groups (post-compulsory, compulsory only and no formal qualications). The interaction terms are all negative, though vary across specications in terms of stastistical signicance. The results point in the direction that those with compulsory education see larger benets from higher taxes than those with post-compulsory education, but also larger benets than those with no formal qualications. However it is possible that the`no qualication' group also tend to be older, possibly conating age and education eects.
Further, the degree of statistical signicance of the dierences across education groups is limited: F-tests fail to reject the null hypothesis that all the interaction coecients are the same except in the specication dening treatment status based on observed smoking behaviour between 1991 and 2008 (column 3). Thus there is relatively little compelling evidence for greater time inconsistency among the lifetime poor from these results.  (2) are based on 1,000 bootstrap replications. * p < 0.10 , ** p < 0.05 , *** p < 0.01 The results so far have focused on the broad GHQ measure derived from twelve separate questions relating to current well-being. As we discussed previously, the single sub-question which forms part of the overall GHQ asking about current happiness relative to usual may provide a more concrete test of the rational addiction model. We run separate linear probability models for those responding being more happy than usual (Table 5), the same as usual (Table 6) or less happy or much less happy than usual (Table 6). 22 We would expect the interaction term to be positive in Table 5 and negative in Table 7; it is not clear whether we would expect any obvious interaction eect in Table 6: likely smokers may move into or out of this group if they are less likely to be unhappy but more likely to be happy.
The results broadly follow this pattern, though there are interesting dierences across specications when compared to the results based on the overall GHQ measure. Most notably, we nd fairly consistent evidence that likely smokers are relatively less likely to report being unhappier than usual when real taxes rise. However, this result is more strongly signicant in the propensity specication, and only weakly signicant in the specication based on 1991 smoking status. This is the opposite pattern of signicance to the GHQ results. A similar picture emerges looking at the probability of being more happy than usual: the interaction coecients are signicantly positive for the propensity specication, but only weakly positive for the specications based on smoking histories. We nd no evidence at all for any eect on the relative likelihood of reporting being as happy as usual. 22 Note that the most consistent signicant ndings reported by Gruber and Mullainathan (2005) were a reduced probability that likely smokers reported being unhappy.  (2) are based on 1,000 bootstrap replications. * p < 0.10 , ** p < 0.05 , *** p < 0.01 Clustered (on the individual) standard errors in parentheses. Standard errors in Column (2) are based on 1,000 bootstrap replications. * p < 0.10 , ** p < 0.05 , *** p < 0.01 Clustered (on the individual) standard errors in parentheses. Standard errors in Column (2) are based on 1,000 bootstrap replications. * p < 0.10 , ** p < 0.05 , *** p < 0.01 In summary, the results based on the single happiness question point in the same direction as the results based on the overall GHQ measure: likely smokers appear to be made relatively better o from higher real excise taxes. Taxes had a negative and signicant eect on the relative distress of likely smokers for two out of three of the treatment groups at the 5% level; in the third case the sign of the eect was also negative. For all specications, treatment groups were more likely to report being happier than usual and less likely to report being unhappier than usual with at least 10% signicance. Although the magnitude of the interaction term is quite low relative to the mean or standard deviation of happiness measures, the fact that they all point consistently in the same direction is noteworthy, and goes against the prediction of the rational addiction model. We nd only very weak evidence that the eect is greater for low education individuals in the treatment group.

Ban on smoking in public places
For the analysis of regional variation in the timing of the smoking ban, the sample is restricted to those As always with dierence-in-dierence studies, we make the common trend assumption. This means that changes in likely smoker well-being in England and Wales would be a good predictor of changes in Scotland absent the smoking ban having been implemented there. Figure 4 shows trends in the average GHQ score by region (Scotland versus England and Wales) and year among those who smoked in 1999. The trends are broadly similar: at or declining GHQ scores in both regions up to around 2003 with some evidence of increasing scores (reduced well-being) since then. The striking dierence is 1999 to 2000 when there was a large increase in the GHQ score in England and Wales not seen in Scotland. While we nd no signcant eects of the ban on the relative probability of a smoker being more, less, or no more happy than usual, we do nd signicant eects of the ban on the overall GHQ score of those who were seen smoking in 1999. According to the results in column 4, the smoking ban appears to have improved well-being for likely smokers in Scotland by around 0.5 points relative to likely smokers in England and Wales, but was associated with a weakly signicant reduction in overall well-being of around 0.9 points for likely smokers as a whole. This is similar to the ndings for taxation when looking at the GHQ score outcome: higher real taxes were associated with an overall reduction in well-being but the reduction was smaller for likely smokers. Here, the ban reduced the overall well-being of smokers but had a smaller impact in Scotland (where it was eective) than in England and Wales (where it was not). Clustered (on the individual) standard errors in parentheses. Note the sample is restricted to those who smoked in 1999. * p < 0.10 , ** p < 0.05 , *** p < 0.01

Discussion
Our results lend some support to the view that anti-smoking policies raise the relative well-being of likely smokers, as suggested by models of time inconsistency in which smokers value the commitment benets of such policies. Using dierent methods to classify individuals as likely smokers, we nd consistent evidence that higher real-terms cigarette excise taxes raise the relative self-reported well-being of smokers. This holds for two dierent measures of well-being: an index of distress and a specic question on current happiness relative to usual. That the results hold across dierent specications and dierent outcome variables, and correspond to those from the US and Canada of Gruber and Mullainathan (2005) using data from another country, is suggestive that this eect is quite empirically robust. However, it is notable that the statistical signicance of the eect is somewhat sensitive to the particular method chosen to dene likely smokers, and that the pattern of signicance across methodologies also varies for dierent measures of well-being. The size of the relative increase in well-being for likely smokers is also quite small compared to the mean or standard deviation of observed responses.
We nd some positive eect of the ban on smoking in public places on the well-being of Scottish smokers relative to those in England and Wales during the short period in which it was only in operation in Scotland, though the eect is not robust to the outcome measure of well-being chosen.
We relate well-being measures to contemporaneous smoking policies. It is possible that forward-looking smokers will react to taxes or bans on smoking when they are announced rather than when they are implemented. 23 In the UK, the smoking tax escalator announced an intention to raise real excise taxes by 3% per year in November 1993. Assuming that smokers believed the plans would be carried through, in principle most of the real tax rises in the 1990s should have been completely anticipated by smokers. The escalator was raised to 5% in July 1997 which might suggest a further`shock' for likely smokers who had anticipated a 3% rise. This could be investigated by looking for year-specic variation in the relative well-being eects.
Similarly, whilst the ban on smoking was only in place in Scotland in 2007, smokers in England and Wales could have anticipated bans based on legislation passing through national parliaments at the time. Forwardlooking time-inconsistent smokers might therefore have already adjusted to an expected future ban even before its implementation. However even if at least some future policy reforms were anticipated, this does not undermine our central nding that they appear to have had a small but positive eect on the relative well-being of groups of likely smokers.
A related point thinking about wider inuences on smoker well-being is to consider whether there were other changes in anti-smoking policies at the same time as tax changes or the smoking ban. If so, without explicitly measuring and controlling for other policy changes, we might attribute some of their impact on relative smoker well-being to our policies of interest. It is common to see policies packaged together as part of a wider anti-smoking strategy. 24 However, there is no clear evidence that other signicant anti-smoking 23 As noted in Gruber and K®szegi (2000Gruber and K®szegi ( , 2001Gruber and K®szegi ( , 2004, time inconsistency is still compatible with consumers being forwardlooking. 24 For example, the 1998 White Paper Smoking Kills looked at measures including advertising restrictions and clamping down on smuggling. reforms were introduced at the same time as the main increase in real excise taxes in the 1990s under the duty escalator. Cigarette advertising had been banned on UK television since 1965, and advertising in other media was progressively banned between 2003 and 2005 as part of the Tobacco Advertising and Promotions Act 2002, following the end of the escalator period. Health warnings on cigarette packets were introduced compulsorily in July 1991, before the excise escalator, and increased in prominence and visibility from 2002, after the escalator had ended. The legal purchase age for cigarettes was also raised after the escalator period, in October 2007. An alternative explanation for our results is that taxes aect the well-being of smokers through their eects on the illicit (untaxed) market for tobacco. As noted above, illicit tobacco appeared to command a relatively high share of the market in the 1990s when tax rates were increasing rapidly. If tax increases lead to a rise in the availability of illicit tobacco, this could actually reduce the cost of smoking and make smokers better o even under a time consistent framework. This would undermine the power of our test to discriminate between time inconsistentcy and rational addiction. Note, though, that for this to hold would require the cost of obtaining tobacco to fall when the tax rate went up, where the cost of illicit tobacco includes not only the purchase price but also the costs of obtaining it (which may include the hassle of dealing with illicit sellers and any moral costs). In general, we might expect that people turning to illicit tobacco might be paying more than they had paid for tobacco before the tax increase, just less than the cost of obtaining licit (duty-paid) tobacco following the tax rise. However, it is possible that the cost of smoking fell as a result of tax increases if, for instance, the growth in the size of the illicit market allowed tobacco smugglers to benet from economies of scale, or if more widespread use of illict tobacco reduced any social stigma or moral costs from consuming it. It is of course hard to determine whether these sorts of eects exist or how important they are without data on who smokes illicit tobacco and how the price of licit and illicit products changed over this period.
A nal potential concern is attrition from our panel. Attrition may be inuenced by both happiness and smoking behaviour, and if there is any interaction between these eects it could bias our results (for example, if relatively unhappy smokers are more likely to die or attrit from the sample for other reasons, then we may see an upward trend in the relative happiness of smokers which correlates with the trend in real excise taxes). To check the robustness of our results to problems of attrition, we repeat our analysis from Table 3  observed in all years of data. This reduces our sample sizes substantially: for example, using 1991 smoking status to classify treated individuals, the number of observations falls by around 45% and the number of individuals by around 64%. Using the GHQ index measure of well-being, we still nd negative interaction eects between smoker status and the real excise tax for both specications (-0.17 and -0.09 respectively), with the former signicant at the 5% level but the latter no longer statistically signicant. Thus we continue to nd the negative interaction term, but we have much less precise estimates. It is possible that an attrition bias explains some part of our nding, but at least for some specications the result appears robust to a sample where attrition is ruled out -even when that also entails a substantial reduction in sample size.

Conclusions
When people suer from time inconsistency problems that lead them to over-consume harmful products, policies that restrict their behaviour can in principle make them individually better o. We nd quite strong evidence of such an eect of tobacco taxes using British panel data recording smoking status and self-reported measures of well-being over a long period. There is also weaker evidence of a similar eect for a ban on smoking in public places introduced in Scotland. We nd little compelling evidence that the relative eect is larger for poorer households as measured by educational attainment. The size of the eect appears to be fairly modest, but is robust to dierent treatment indicators and measures of well-being, and points in the opposite direction to the predictions of standard theory.
From a policy perspective, our ndings suggest a possible`internality' rationale for tobacco taxation as well as the more usual externality rationale. This could suggest that optimal tobacco excise taxes exceed those which would be justied by estimates of the marginal external cost imposed on others, though we are unable to quantify the size of the internality on the basis of our results. Drawing on a theoretical framework, Gruber and K®szegi (2001) estimated the internality-correcting tax could be around $1 per pack of cigarettes compared to an excise tax at the time of around 65 cents. They also argued that if poorer individuals were more likely to suer from time inconsistency, increases in taxes could be progressive in terms of the welfare impact. However we nd no signicant evidence that this is the case: tax do not appear to have a larger relative eect on the well-being of poorer (low education) smokers than richer (high education) smokers.
Appendix: Propensity to smoke results