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‘A pack a day for 20 years’: smoking and cigarettepack sizesLisa Farrell a , Tim R. L. Fry a & Mark N. Harris ba School of Economics, Finance and Marketing , Royal Melbourne Institute of Technology ,Melbourne, Australiab Department of Econometrics and Business Statistics , Monash University , Melbourne,AustraliaPublished online: 30 Sep 2010.

To cite this article: Lisa Farrell , Tim R. L. Fry & Mark N. Harris (2011) ‘A pack a day for 20 years’: smoking and cigarettepack sizes, Applied Economics, 43:21, 2833-2842, DOI: 10.1080/00036840903389838

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Applied Economics, 2011, 43, 2833–2842

‘A pack a day for 20 years’: smoking

and cigarette pack sizes

Lisa Farrella,*, Tim R. L. Frya and Mark N. Harrisb

aSchool of Economics, Finance and Marketing, Royal Melbourne Institute

of Technology, Melbourne, AustraliabDepartment of Econometrics and Business Statistics, Monash University,

Melbourne, Australia

This study focuses on the determinants of cigarette consumption. In

particular, the impact of cigarette pack sizes on the typical daily

consumption of smokers is investigated. Results are presented from a

new multi-modal count data model which allows for ‘pack-effects’ in daily

consumption levels. Our results suggest that smokers regulate their

consumption in accordance with the variety of pack sizes that are available

to them.

I. Introduction and Background

It has long been acknowledged that there are signif-

icant health risks associated with cigarette consump-

tion. Yet, around 46 million adults in the US and

12 million in the UK smoke. Large amounts of public

expenditures are directed towards health education

programs aimed at reducing participation rates. In

the US, smoking causes roughly 400 000 deaths per

year at an estimated cost of more than $75 billion.

The addictive nature of tobacco makes policies aimed

at reducing cigarette consumption a particularly

difficult process.The focus of this study is the relationship between

consumption and cigarette pack sizes. Whilst much

analysis has been undertaken into the factors that

determine the decision to start and stop smoking, less

has been done on the factors that determine the level

of smoking for smokers. Market research has

concentrated on the impact of the elements of

marketing mix on consumption levels, but there

appears to be no research on the impact of pack

sizes on daily consumption patterns. This is impor-

tant as, given the addictive nature of tobacco, many

smokers may try to regulate their consumption via

the number of packets that they smoke in a given time

period.Whilst governments do closely regulate the sale

of tobacco, few have experimented with pack size

regulation. Most governments dictate the smallest

pack size that can be sold (and legislate against selling

cigarettes individually), and it is the choice of the

manufacturers with regard to what pack size varieties

to offer (influenced, in part, by tradition and excise

duty). The current legislation is designed mainly to

prevent children from smoking. In England (where

this study is focused), it is illegal to sell cigarettes

individually and the smallest pack size allowed to be

sold is 10 cigarettes. Purchasing cigarettes in packs

raises the cost of smoking to a level outside of a

child’s income range. However, there is much debate

regarding the effectiveness of this legislation. Studies

have shown that the price elasticity for cigarettes by

youths is more inelastic than that of older smokers – a

result of brand loyalty by young smokers (Harris and

Chan, 1999). The tax system in England is indifferent

to pack sizes. Taxes are levied as a tax per 1000

cigarettes sold, and an additional ad valorem tax per

pack sold. These (relatively high) taxes are designed

to raise prices, so discouraging consumption.

*Corresponding author. E-mail: lisa.farrell@rmit.edu.au

Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online � 2011 Taylor & Francis 2833http://www.informaworld.com

DOI: 10.1080/00036840903389838

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However, there is much debate in the literatureregarding the relative merits/success of regulationversus taxation as a means of reducing and prevent-ing cigarette consumption (Wasserman et al., 1991).

Given the addictive nature of cigarettes, manysmokers try to regulate their consumption in orderto ‘control’ their addiction. Indeed, it is likely thatsmokers will do this by regulating their consumptionaccording to the number of packets of cigarettes thatthey smoke in a given period. The idea that the packsize is an important determinant of consumptionbehaviour has been acknowledged in the marketingliterature since the work of Ehrenberg and hiscolleagues in the 1960s and 1970s (see, e.g.Ehrenberg, 2000). The fact that cigarettes cannot bebought individually, reinforces this. If smokers areconstrained to purchase cigarettes in given quantities,it is natural to expect their consumption to reflectthese quantity constraints. This is consistent with theideas in Ehrenberg (2000), who claims that, for a widerange of products, the number of packs bought ona given purchase occasion appear to be constant andthe purchase interval (time between purchase occa-sions) tends to be the same, regardless of the size ofthe pack. Thus, if a consumer wishes to regulateconsumption, he/she may do so by his/her choice ofpack size rather than by changing the frequency ofpurchase. This literature suggests that people havea standard shopping list and should they wish tochange their consumption patterns, they adjust thequantities they purchase rather than the frequency ofpurchase. In essence, there are menu costs. Droppingitems on and off the shopping list increases the risk ofaccidentally not purchasing a needed item. Quantityreduction, however, eradicates this risk. Thus, smo-kers wishing to cut back their cigarette consumptionwill switch to purchasing smaller packs. Hence, thevariety of pack sizes available will impact on the levelof consumption.

This article contributes to this debate by hypothe-sizing that the variety of pack sizes available toconsumers significantly impacts upon the number ofcigarettes an individual smokes in a given period.Thus, one policy to aid smokers reduce their con-sumption is to allow the sale of cigarettes in smallpacks (in contrast to the existing regulation).

II. The Data

The data is drawn from the Health EducationMonitoring Survey (HEMS) conducted by theOffice of National Statistics (ONS) in the UK.The HEMS is an individual-based nationally

representative annual survey that covers the adultpopulation aged 16–74 years living in England. Itsmain purpose is to provide information on respon-dents’ knowledge of health-related issues. In partic-ular, for the purposes of this study, informationis collected on individual characteristics, socio-demographic characteristics, alcohol consumption,physical activity and, finally, the number of cigarettestypically consumed per day. Data from the 1998survey is used. A major innovation in this survey yearwas to investigate the effect of major life-events onhealth-related behaviour and health. Thus the 1998HEMS is one of the very few studies that containboth detailed information on the count of cigarettesconsumed (as opposed to expenditure on cigarettes)and on major life events.

The distribution of typical daily (weekday) con-sumption of the number of cigarettes can be seen inFig. 1. It is immediately obvious that there is a largeconcentration of individuals who do not smoke ona typical weekday. Indeed, some 74% of our samplerecords zero cigarette consumption. Some of theseobservations will also correspond to social smokers,i.e. those who may not smoke during the week, butwhom might smoke occasionally on a weekend. It willbe important in the statistical analysis to allow for thefact that there are two types of individuals in our dataset who may record a zero count.

The observations are clearly not evenly distributedacross all the possible counts, there are spikes(multiple modes) in the distribution (for those whodo smoke) at 5, 10, 15 and 20 cigarettes per weekday(Fig. 2). Importantly, the counts of 10 and 20correspond to the packet sizes that cigarettes aresold in (in England). Moreover, the remaining spikescorrespond to half a pack and one and a half packsper day. This suggests that individuals are indeedregulating their cigarette consumption by countingthe number of packets they smoke in a given timeperiod, rather than counting the number of cigarettesdirectly. For example, everyone has heard of thetriumphant smoker who is trying to quit, proudly

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Cigarettes

Indi

vidu

als

Fig. 1. Unconditional distribution of typical weekdaycigarette consumption

2834 L. Farrell et al.

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announcing that ‘he has cut back from one pack aday to half a pack a day’. Such pack counting isconsistent with the observed pattern of cigaretteconsumption shown in the raw data.

Tables 1 and 2 provide some simple sampledescriptive statistics of the raw data (the variable

descriptions and motivations for their inclusion in the

model will be discussed in Section III). Table 1presents sample means for the variables used in thisanalysis. The sample consists of 5766 individuals, of

whom 1491 smoke. The average consumption is 3.48cigarettes per weekday (13.46 cigarettes per weekday,conditional upon participation).

Table 2 shows the conditional means for smokers

and nonsmokers of the variables, which one mightexpect to be determinants for the participationdecision. It is clear that there are significant

differences in the demographics of smokers andnonsmokers. Importantly, the conditional means are

statistically significantly different between smokersand nonsmokers for all of the socioeconomic statusvariables. Section IV presents the results of a more

rigorous multivariate analysis.

III. Statistical Framework

The econometric model

Given our preliminary investigation of the data, it isclear that we need an econometric estimator capable

of modelling a multi-modal count data process,although no such model currently exists in theliterature. Given that the data to be modelled is

that of an integer count, the literature would suggestthat an appropriate statistical model might be the

Poisson regression model. The Poisson regressionmodel is, in many respects, a restrictive specification.In particular, it is not able to cope with an abundance

of observed zeros in the data to be modelled. Thedata here has 74% of the observations recorded aszero. This preponderance of zeros is inconsistent with

the Poisson regression specification and tends to leadto an underestimation of the expected value of the

count process and potentially spurious evidence ofover-dispersion.

To overcome the problems caused by the abun-dance of zeros often encountered in empirical counts,

several researchers (see, e.g. Mullahey, 1986, 1997;Heilbron, 1989; Lambert, 1992; Greene, 1994;Pohlmeier and Ulrich, 1995) have suggested models

that ‘inflate’ or ‘augment’ the Poisson process. Thesemodels account for the zeros that are additional tothose expected from a simple Poisson process. The

models are variously termed as Zero Inflated Poisson(ZIP) or Zero Augmented Poisson (ZAP) models. In

essence, what these models do is – add an additionalbinary statistical process to the assumed datagenerating process. This binary model allows for

0

50

100

150

200

250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Cigarettes

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Fig. 2. Conditional distribution of typical weekday cigarette

consumption

Table 1. Sample descriptive statistics

Variable Sample means SD

Number of observations 5766Number of cigarettes 3.481 (6.72)Standard demographicsAge/10 4.939 (1.90)Male 0.441 (0.50)Secondary education 0.377 (0.48)Post-secondary education 0.329 (0.47)Single 0.429 (0.50)Non-White 0.046 (0.21)Presence of children 0.293 (0.46)Income and employmentIncome 5000–9999 0.203 (0.40)Income 10 000–14 999 0.128 (0.33)Income 15 000–19 999 0.115 (0.32)Income 20 000–29 999 0.161 (0.37)Income 30 000þ 0.198 (0.40)Employed 0.580 (0.49)Major life eventsSad 0.095 (0.29)Happy 0.089 (0.29)Life style factorsPhysical activity 0.553 (0.50)Heavy drinking 0.221 (0.41)Activity and drink interaction 0.144 (0.35)Health statusStress levels 2.840 (0.49)Long-term illness 0.413 (0.49)Socioeconomic statusDeprivation index �0.278 (2.76)Renting 0.300 (0.46)Living in the South 0.495 (0.50)

Note: Omitted categories are: female, no formal qualifica-tions, married/widowed/divorced, White, no children, nolong-term illness, home owner and living in the north ofEngland.

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zero observations to occur separately from thePoisson count process ones.

In these models, the zero observation may be adrawing from a choice set that comprises the singleoutcome zero, or zero from a Poisson process. TheZIP model therefore implies that the probability ofthe occurrence of a zero observation has twocomponents: one from the binary process and theother from the Poisson process. This inflates theprobability of a zero from that obtained from asimple Poisson process. There is agreement in theliterature that this binary process is an over-simplification and should be specified as a binarylogit (or probit) that allows the probability of a zeroto depend upon observed characteristics.

Using a binary logit or probit is particularlyattractive as it allows nonparticipation (zero cigar-ettes) to depend upon individual characteristics.Further, in the context of cigarette consumption,a zero observation can be generated either from anonparticipant or from a participant who recordsa zero for typical weekday consumption. The latter,for instance, may be an infrequent smoker, who ona typical work day does not smoke, but who maysmoke on an atypical workday. Alternatively, he/shemay smoke at weekends only.

Whilst the parameterized ZIP model can allow forthe abundance of zero observations in the data to bemodelled, it is unable to deal with multi-modal data.In the case of our application, these multiple modesare represented by the extra spikes in the observeddata at values such as 5, 10, 15, 20 and 21þ. It wasargued earlier (Section II) that individuals mightchoose to regulate their consumption through

multiples of pack sizes. Additionally, a by-productof the question asked for survey respondents is thatthey might mentally round their responses to themultiples of five (digit preference). Thus individualsare drawn to certain outcomes, and there is an‘attraction’ to multiples of pack sizes.

To address the presence of multiple modes in countdata it is noted that the idea behind the ZIPformulation is the same as that in Manski (1977),where in the discrete choice context it is argued thatthere are two distinct probabilistic processes at work:a ‘choice set generation’ and a ‘choice decision’.Individuals are faced with a choice set generated fromone probabilistic process and choose their preferredoutcome from that set. In the ZIP models individualschoose to be participants or not, and if they parti-cipate their consumption follows a Poisson process.

An obvious extension of the parameterized ZIPtherefore is to extend the first component to amultinomial process, where individuals might benonparticipants, be drawn to multiples of pack sizesor participate and choose ‘freely’ according to aPoisson process. The outcomes in the choice setgeneration process in this application are: nonparti-cipation; ‘attraction’ to: 5, 10, 15 and 20 cigarettes;heavy consumption and participation with ‘free’choice. This can be represented by a multinomialindicator

d ¼

0 if nonparticipant

0 if ‘attraction to 5’

..

.

6 if participant is ‘free’

8>>>><>>>>:

Table 2. Sample conditional descriptive statistics

Variable Sample means SD Nonsmokers SD Smokers SD

Number of observations 5766 4275 1491Number of cigarettes 3.481 (6.72) 0.000 (0.00) 13.463 (6.35)*Standard demographicsAge/10 4.939 (1.90) 5.154 (1.92) 4.323 (1.70)*Male 0.441 (0.50) 0.435 (0.50) 0.458 (0.50)Secondary education 0.377 (0.48) 0.368 (0.48) 0.402 (0.49)*Post-secondary education 0.329 (0.47) 0.353 (0.48) 0.258 (0.44)*Single 0.429 (0.50) 0.404 (0.49) 0.502 (0.50)*Non-White 0.046 (0.21) 0.051 (0.22) 0.034 (0.18)*Presence of children 0.293 (0.46) 0.272 (0.45) 0.354 (0.48)*Health statusLong-term illness 0.413 (0.49) 0.408 (0.49) 0.429 (0.50)Socioeconomic statusDeprivation index �0.278 (2.76) �0.507 (2.68) 0.378 (2.86)*Renting 0.300 (0.46) 0.247 (0.43) 0.450 (0.50)*Living in the South 0.495 (0.50) 0.505 (0.50) 0.466 (0.50)*

Notes: * Indicates a statistically significant difference at the 5% level between the means for smokers relative to nonsmokers.Omitted categories are: female, no formal qualifications, married/widowed/divorced, White, no children, no long-term illness,home owner and living in the North of England.

2836 L. Farrell et al.

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As in the ZIP model, the probabilities of the

observed outcomes are a mixture of those from the

multinomial process and the Poisson process. These

are given by

PrðY¼ 0jxÞ ¼ Prðd¼ 0Þ þ ½Prðd¼ 6Þ � expð��Þ�

PrðY¼ 5jxÞ ¼ Prðd¼ 1Þ þ Prðd¼ 6Þ �expð��Þ�5

5!

� �

PrðY¼ 10jxÞ ¼ Prðd¼ 2Þ þ Prðd¼ 6Þ �expð��Þ�10

10!

� �

..

.

PrðY¼ 21jxÞ ¼ Prðd¼ 5Þ þ Prðd¼ 6Þ �expð��Þ�21

21!

� �

PrðY¼ yjxÞ ¼ Prðd¼ 6Þ �expð��Þ�y

y!,

y 6¼ 0, 5, 10,15, 20, 21þ

where �¼ exp(x0/�).To complete the specification, it is necessary to

define the multinomial (choice set) probabilities. The

above arguments suggest that the nonparticipation

outcome is likely to depend upon certain individual

characteristics (z). However, there is no clear ratio-

nale for attraction to outcomes (5, 10, 15, 20 and

21þ) to depend upon such characteristics. They might

be the result of either consumption regulation or digit

preferences.1 Thus the full multinomial model is

parameterized as

Prðd¼ 0jzÞ ¼expðz0�Þ

1þðexpðz0�Þþ �5þ �10þ �15þ �20þ �21Þ

Prðd¼ 1jzÞ ¼�5

1þðexpðz0�Þþ �5þ �10þ �15þ �20þ �21Þ

Prðd¼ 2jzÞ ¼�10

1þðexpðz0�Þþ �5þ �10þ �15þ �20þ �21Þ

..

.

Prðd¼ 6jzÞ ¼1

1þðexpðz0�Þþ �5þ �10þ �15þ �20þ �21Þ

Once the full set of probabilities has been specified,

and given an independent and identically distributed

(i.i.d.) sample from the population (i¼ 1, . . . ,N), the

parameters of the model (�) can be consistently and

efficiently estimated using the maximum likelihoodcriteria. The log-likelihood function is

‘ ð�Þ ¼XJj¼1

XNi¼1

hij ln½PrðYi ¼ yijx, zÞ�

where the indicator function hij is

hij ¼1 if individual i chooses count j0 otherwise

�

Thus we have derived an estimator capable ofmodelling multi-modal count data, and whilst it isapplied here to the modelling of cigarette consump-tion, its use is not specific to this application. Theestimator could be employed to model any integerdata which is characterized by more than one modein the count distribution. Moreover, the estimator issufficiently flexible to allow the user to determineif any particular mode should or should not beparameterized. Thus one can estimate unparameter-ized, fully parameterized and partially parameterizedspecifications.

Model specification

Two distinct sets of covariates are required: x

determine the amount (level) of cigarette consump-tion and form the structural equation, and ‘partici-pation’ variables, z, form the first hurdle equation.The latter help to identify nonsmokers from infre-quent smokers within those observations recordedas a zero count.

Participation. It is possible to conceive of threebroad groups of variables that are likely to affect theprobability of smoking participation: standard demo-graphics, health status indicators and socioeconomicfactors. These are dealt within turn below.

We begin by looking at standard demographics.Evidence suggests that most smokers start smoking ata relatively early age (teenage years), older non-smokers are less likely to start smoking and oldersmokers are more likely to (at least to attempt to)quit. The more educated, being more aware of thehealth risks involved, will be less likely to participate.Although there is debate in the literature whether thenegative relationship between education and smokingpicks up better health knowledge and understandingof the associated risks or if it proxies lower discountrates of the better educated (Sander, 1995).

1One might hypothesize, given the literature on frequencies of purchase, that ‘shopping habits’ would be the type of variablesthat might be employed to characterize the higher �s; however, the dataset affords us no such variables with which to test thishypothesis.

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Gender plays a role in the selection into smoking withmales being more likely to participate. There is alsoevidence that minority groups generally have higherparticipation rates (perhaps due to cultural reasons).Hersch (1996) finds that Whites choose safer pro-ducts to consume, where smoking is defined as a riskyconsumption decision. Marital status is also included,although its effect is somewhat ambiguous a priori(e.g. there may be contagion effects if both partnerssmoke, or both do not). Jones (1994) finds evidencethat the presence of other smokers in the householdhas a significant influence on the decision to start andstop smoking. The data does not allow us to observethis interaction in such detail, but controls for thepresence of a partner are included. The presence ofchildren is also expected to exert a negative effect onparticipation owing to the effects of passive smoking.Blaylock and Blisard (1992) report that as the numberof children in the household increases, the probabilityof smoking participation decreases. Regarding healthstatus indicators, respondents are asked whether theysuffer from any long-standing illness, disability orinfirmity. The general health implications of theseconditions should ensure that they are negativelyassociated with smoking participation.2 Evidenceshows that those who suffer worsened health whilstsmoking are more likely to quit (Jones, 2002).

The variables unique to the participation equationrelate to the individual’s socioeconomic position.Smoking participation rates tend to be much higheramongst the lower social class classifications. Theproxies used for this are: a ‘deprivation index’(running from affluent to deprived), residence inrented or socially provided accommodation and theregion of residence (North and South).

The level of consumption. Factors relating to thestructural equation inform on the level of cigaretteconsumption and can be grouped under three mainheadings: standard demographics, major life eventsand lifestyle and health factors.

Regarding demographics, evidence suggests thatmen smoke more than women, so gender is alsoincluded here. The possibility that the age–consump-tion profile will be ‘n-shaped’ is allowed for byincluding a quadratic in age. Wasserman et al.(1991) report that the married smoke more, suggestinghousehold contagion effects and also that, conditionalon smoking, Whites smoke more than non-Whites.Income is included for standard demand schedulereasons. Blaylock and Blisard (1992) show that

income has no effect on participation, but is signifi-cant in determining consumption. The observed countof cigarettes smoked relates to the weekday consump-tion, and therefore it is necessary to control forwhether or not a person is employed and likely to be ina workplace environment on a typical weekday. Giventhat this may have an impact on their freedom tosmoke, or indeed lead to peer pressure to smoke more/less.

The data is unique in containing informationregarding any major life events that the individualsmay have experienced in the 12 months prior to thesurvey. These life events have been included in ouranalysis through the inclusion of two variables:‘happy’ and ‘sad’. Happy records if the individualsstate they have experienced a happy life event (such asmarriage or a birth in the family). Sad records if theindividual has experienced a negative life event suchas the death of a close relative or friend, personalexperience of theft, a mugging or other crime. Onewould expect that such events are unlikely to causean individual to start smoking. However, for thoseindividuals who do smoke, a priori one would expectnegative life events to be associated with higherconsumption, whereas positive life events will beassociated with lower consumption. The assumptionhere is that for nonsmokers a major life event isunlikely to cause them to start smoking, but for thosewho do smoke such life events are likely to impact onthe level of consumption.

In terms of lifestyle indicators, the data contains an‘activity’ variable, defined as whether the individualhas undertaken any physical activity in the lastmonth. This is a very broad measure (55% of thesample had done so). This indicator is likely to benegatively associated with the level of cigaretteconsumption. Given the complementarily of smokingand drinking, a ‘heavy drinker’ indicator is alsoincluded in the Poisson process. The indicator isdefined as consumption of more than the recom-mended daily intake of alcohol. Given the very broadnature in which these two variables have beendefined, it is unlikely that they will be able to helpidentify participation effects. However, they may besignificant indicators of heavy cigarette consumption.It is unlikely that those who smoke heavily willparticipate in exercise, and it is likely that given thecomplementarily between smoking and alcohol con-sumption, heavy smokers may be more prone todrink higher than the medically recommended intake.There is significant evidence from the literature

2Whilst the survey does contain questions relating to the respondents’ current health status, this variable is not included inour model as it is clearly endogenous to current smoking behaviour. However, a question relating to long-term illness isincluded, as this will affect smoking behaviour, but is also less endogenous to current cigarette consumption.

2838 L. Farrell et al.

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investigating health production functions that thesebehaviours are correlated. Individuals are seen todevelop healthy or unhealthy lifestyles, and thereforeobservation of their lifestyle choices for alcoholconsumption and exercise activity is likely to be agood indicator of their smoking-related decisions(Kenkel, 1995). An interaction term of these twovariables is also included and is designed to pick upthe potential bias that may occur in the coefficientsfor activity and alcohol consumption caused by thepresence of social sports players who engage inphysical activity and also consume alcohol. It is aninteresting line of enquiry to investigate if these socialsports players also smoke.

In relation to health status, the long-term illnessindicator is also included for the Poisson process forthe reasons as outlined above. There is also a self-reported measure of the respondent’s overall levelof stress. For smokers, increased levels of stress arelikely to be associated with higher consumptionlevels, although this is unlikely to affect the partic-ipation decision.

Note that all of the negative effects (in bothprocesses) are likely to be smaller in absolute termsthan the positive ones, due to the addictive nature oftobacco. It is easier to start smoking than to stop, andit is easier to increase consumption rather than toreduce it (all other things equal).

IV. Results

The full set of results are reported in Table 3 andconfirm the key findings from the existing literaturein terms of the impact of the covariates included. Thefirst hurdle, or participation decision, appears to beextremely well-modelled given the strong significanceof all of the parameters. Indeed, all of the parameters,bar the constant and the dummy variable for post-secondary qualifications, are significant at the 5%level. Of the standard demographics, both males andnon-Whites are more likely to be participants(recalling that a negative coefficient here reduces�0). The more educated individuals are less likely tosmoke, as are singles. As individuals age, smokingparticipation rates decrease, as older individuals arelikely to become more health aware. The familycomposition variables show that being singleincreases the probability of not smoking as does thepresence of children in the household. The healthstatus factor of having a serious long-term illnesssignificantly increases the probability of nonpartici-pation. Finally, with regard to the participationequation and socioeconomic status, smoking

Table 3. Estimation results

Coefficient SE

Structural parametersConstant 1.285 (0.19)**Standard demographicsAge/10 0.347 (0.08)**

Age2/1000 �0.346 (0.09)**Male 0.106 (0.05)**Secondary leveleducation

0.214 (0.06)**

Post-secondarylevel education

�0.001 (0.07)

Single �0.091 (0.05)*Non-White �0.091 (0.05)**Money and employmentIncome 5000–9999 0.200 (0.06)**Income 10 000–14 999 �0.186 (0.08)**Income 15 000–19 999 0.022 (0.08)Income 20 000–29 999 �0.376 (0.09)**Income 30 000þ �0.455 (0.09)**Employed 0.068 (0.06)Major life eventsSad 0.132 (0.10)Happy �0.098 (0.10)Life-style factorsPhysical activity �0.220 (0.06)**Heavy drinking 0.298 (0.09)**Activity�Heavy drink �0.145 (0.12)Health statusStress levels 0.005 (0.03)Long-term illness �0.065 (0.05)First hurdle parametersConstant �0.065 (0.06)Standard demographicsMale �0.118 (0.01)**ln(age) 0.555 (0.03)**Single 0.411 (0.07)**Secondary education 0.779 (0.08)**Post-secondaryeducation

�0.081 (0.07)

Non-White �0.531 (0.07)**Children 1.408 (0.21)**Health statusLong-term illness 0.533 (0.02)**Socioeconomic statusDeprivation index �0.291 (0.07)**Renting �0.505 (0.07)**Living in the South �1.819 (0.13)**� Coefficients�5 �1.674 (0.03)**�10 �0.773 (0.08)**�15 �0.867 (0.03)**�20 �0.952 (0.08)**�21 �1.075 (0.03)**

Log-likelihood �6910No. observations 5766

Notes: SEs in parentheses. Omitted categories are: female,no formal qualifications, married/widowed/divorced,White, no children, no long-term illness, home owner andliving in the North of England.* and ** indicate significance at 5% and 10% levels,respectively.

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participation clearly increases with reduced socialstanding and poorer living environments.

With regard to the conditional count process, theage–consumption profile is distinctly ‘n-shaped’.Males and the lower educated smoke more, condi-tional on participation, whilst non-Whites smoke less.Regarding marital status, the model shows that singlepeople smoke less. One feasible explanation is thathousehold contagion exists if one partner smokesthen the other partner will find it hard to quit. Forsmokers, stress increases the typical daily consump-tion, as does the occurrence of sad events. On theother hand, happy events decrease typical dailyconsumption (although as predicted smokers respondmore strongly to factors that increase consumptionas opposed to reducing consumption). However, thestatistical significance of this group of variables issurprisingly low. It seems that stress-related factorsimpact little on the levels of consumption.

The consumption–income profile is somewhaterratic, but it can be seen that the highest twoincome categories smoke less than the lowest incomegroup. Employment does not appear to significantlyaffect cigarette consumption. In terms of conditionalconsumption and lifestyle factors, the complemen-tarity of drinking and smoking is clearly evident,probably as a result of social scripts.3 Thoseindividuals who participate in any kind of (broadlydefined) physical activity tend to have lower cigaretteconsumption. In essence, lifestyle factors work wellto identify those heavy smokers with particularlyunhealthy lifestyles.

Most importantly, in terms of our central hypoth-esis, the pack-size effects are all strongly significant.4

The largest effect is afforded by 10, then 15, 20, 21and five. As noted above, the count of 10 correspondsto one of the pack-sizes available in England. Manysmokers are clearly regulating their consumption to‘a small pack a day’. Alternatively, this correspondsto a standard pack (of 20), every other day.

Model evaluation and predictions

In Fig. 3, observed sample proportions are plottedalongside probabilities (evaluated at covariate samplemeans) of our model; the ZAP and the Poissonmodels. This is the discrete choice analogue of theactual versus predicted plot of more traditional linearmodels. Ignoring the concentration of observationsat zero, clearly leads to misspecified models and

erroneous inference as is evidenced by the poor

results of the standard count data model (Poisson).Augmenting the standard count data model to

account for the preponderance of zeros improves the

performance somewhat. However, in effectively

ignoring the zeros in the count process, the condi-

tional mean of the Poisson component of the ZAP

model is biased towards the larger counts. Thus, this

model is unduly influenced by the modal points in

the distribution at larger counts (those spikes corre-

sponding to pack sizes and digit preferenced

outcomes).Finally, our new model clearly outperforms the

other statistical models. The participation/nonparti-

cipation choice is modelled well and almost exactly

replicates the observed sample proportions.

Moreover, the model clearly picks up the increased

probabilities at the observed modes in the distribu-

tion. Specifically, the model proposed here excels in

its ability to replicate the probability mass of

observations at pack sizes and provides a much

clearer understanding of the drivers of typical ciga-

rette consumption.Using the estimated parameters, it is interesting to

ask what level of cigarette consumption the model

predicts for a number of individuals with differing

characteristics. In particular, a few stylized sets of

characteristics will be analysed. In the first instance

a typical nonsmoker is considered and second, an

individual with the characteristics of a heavy smoker

is profiled. These are illustrated in Fig. 4.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2 50 1 3 4 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Cigarettes

Prob

abili

ty

SampleParameterized Dogit PoissonZAPPoisson

Fig. 3. Sample proportions and predicted counts fordifferent models

3 Psychologists refer to cigarette consumption as part of a script, where a script is a set of inter-locking consumption patternswhich have a re-enforcing quality. For many smokers the script involves tobacco and alcohol, but it might equally be the‘slow’ cigarette after a meal.4 Experimentation with a specification that included a � for all the possible counts was conducted, but this specification wasfound to ‘over fit’ the data.

2840 L. Farrell et al.

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The model predicts that the probability of smokingzero cigarettes a day for a nonsmoker is, notsurprisingly, very high. For a typical smoker thereis effectively zero probability of nonparticipation.Maximum probability occurs at 15 cigarettes closelyfollowed by counts of 10, 20 and 21 plus cigarettesper weekday. There is also significant mass at thelarger levels of consumption. In addition to estimat-ing the predicted probabilities of the various countoutcomes, the model can also be used to estimateexpected values of counts for stylized individuals. Foran average person in the data set (i.e. setting allvariables to sample means) the expected numberof cigarettes smoked per weekday is three.5 For anindividual with the characteristics of a nonsmokerthis expectation falls to zero cigarettes per day. Fora typical smoker the expected number of cigarettessmoked per day is 10. This is the quantity containedin the smallest pack size available to smokers inEngland. The model predicts an expected value forsmokers consistent with the hypothesis of pack sizeconsumption regulation.

V. Conclusions

The article presents a new model capable of model-ling count data processes where there are multiplemodes in the distribution at particular counts. In thecontext of the application presented here, the focusis on the importance of pack sizes on cigaretteconsumption. Given the addictive nature of tobacco,in an attempt to control their addiction, manysmokers may monitor, or regulate, their consump-tion. Evidence is presented here that smokers regulatetheir consumption in accordance with the size of

packets that are available. That is, daily consumptionpatterns reflect the available pack sizes. Suchdiscreteness in the quantities in which cigarettes canbe purchased correspond to spikes in daily consump-tion of cigarettes. It is perhaps not surprising to findthat smokers count their consumption in terms of thenumber of packs smoked in a given period, since theycan only purchase cigarettes in packs. This hypothesisis confirmed by the estimation results, which suggestthat the (expected) number of cigarettes smoked bya typical smoker is 10 per day – equivalent to theamount contained in the smallest packet thatconsumers can purchase in England.

The results presented here suggest that govern-ments wishing to reduce cigarette consumption cando so by allowing cigarettes to be sold in smallerpackets, and by increasing the variety of pack sizesavailable to consumers. Alternatively, cigarette man-ufacturers could potentially increase sales by restrict-ing the sale of cigarettes to large pack sizes. However,these are only tentative policy recommendations.To test this hypothesis further we would need toobserve individual’s consumption patterns over aperiod when the pack sizes available to consumersare changed. We are not aware of any data thatcorresponds to such a natural experiment.

Acknowledgements

Mark Harris wishes to acknowledge financial supportfrom Monash University.

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0.0

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1.0

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