Series ESRI Working Paper Series; No Economic and Social Research Institute.

Transcription

1 Provided by he auhor(s) and Universiy College Dublin Library in accordance wih publisher policies. Please cie he published version when available. Tile Tobacco axes and saring and quiing smoking : does he effec differ by educaion? Auhor(s) Madden, David (David Parick) Publicaion dae 2003 Series ESRI Working Paper Series; No Publisher Economic and Social Research Insiue Link o online version Iem record/more informaion hp:// %20Tobacco%20Taxes%20and%20Saring%20and%20Quii ng%20smoking.pdf hp://hdl.handle.ne/10197/785 Downloaded T16:33:30Z The UCD communiy has made his aricle openly available. Please share how his access benefis you. Your sory maers! (@ucd_oa) Some righs reserved. For more informaion, please see he iem record link above.

2 Tobacco Taxes and Saring and Quiing Smoking: Does he Effec Differ by Educaion? David Madden Working Paper No. 3 Research Programme on Healh Services, Healh Inequaliies and Healh and Social Gain This programme is suppored by he Healh Research Board, and is being carried ou by researchers a he Economic and Social Research Insiue (ESRI), Universiy College Dublin and he Universiy of Ulser. Deparmen of economics, Universiy College Dublin I would like o hank Joe Durkan for use of he Saffron survey and Frank Daly and Jonahan Hore for supplying ax and price daa. I would also like o hank Andrew Jones and Sephen Jenkins for assisance wih programming codes and Joe Durkan and Anhony Murphy for useful discussion. The usual disclaimer applies.

3 Absrac: This paper uses duraion analysis o invesigae he role of obacco axes in saring and quiing smoking. Applying a variey of parameric duraion models, including a spli populaion model, o a sample of Irish women, i finds ha in general obacco axes do influence saring and quiing smoking in he expeced direcion. I also finds ha he effec for saring differs by educaion bu in a non-monoonic way, wih he greaes effec for women wih inermediae levels of educaion. The resuls for quiing sugges he greaes effec for women wih he lowes level of educaion. These resuls are no changed when accoun is aken of unobserved heerogeneiy. JEL Codes: I18, D12, C41. Keywords: Duraion, Spli Populaion, Smoking. 2

4 Tobacco Taxes and Saring and Quiing Smoking: Does he Effec Differ by Educaion? 1. Inroducion There is ample medical evidence indicaing he adverse effecs of obacco consumpion upon healh (see Madden, 2001a, for a recen summary). Recen Governmen publicaions in Ireland have suggesed he long-erm goal of a obaccofree sociey. As he accompanying leer o a recen Governmen repor saed: here is a common objecive of seeking he mos effecive measures possible o dramaically reduce he level of smoking in our sociey and above all o preven our children from saring o smoke (Mooney, 2000). I follows ha idenifying he facors behind he decision o smoke and he decision o qui is crucial in erms of formulaing policy. In a recen paper Madden (2001a) examined he facors influencing paricipaion in smoking, he amoun smoked and facors influencing quiing for a sample of Irish women. However, one facor absen from ha work was he influence of a crucially imporan ool of governmen policy in is drive owards a obacco-free sociey, he rae of axaion on obacco and obacco producs. The daa in Madden (2001a) was a single cross-secion of Irish women and he absence of any variaion in ax or price mean ha i was impossible o infer he effec of hese variables on smoking behaviour. The daase however did include some rerospecive daa on he year of quiing smoking (for hose women who qui) and also he number of years smoking (from which could be inferred he year of saring smoking). Using his daa, and incorporaing he relevan ax rae for he year in quesion, i is possible o consruc a longiudinal daa se wih he ax rae as a ime-varying covariae. Given his background, his paper has wo principal aims. Firs, i examines he effec of obacco axes on saring and quiing smoking, applying duraion analysis o a sample of Irish women. Secondly, i explores he exen o which such a ax effec differs by educaional background. 1 For duraion modelling in he case of saring we use he spli-populaion duraion model of Schmid and Wie (1989), Douglas and Harihan (1994) and Foser and 1 Noe ha we are no rying o esimae wha he opimal ax on obacco should be. For a recen discussion in he Irish case, see Madden (2002). 3

5 Jones (2000) while for quiing we follow he approach of Tauras and Chaloupka (1999) and Foser and Jones (2000) in applying sandard parameric models. The remainder of he paper is as follows: in secion 2 we briefly discuss some of he exising lieraure and in secion 3 we ouline a simple model of saring and quiing smoking. In secion 4 we discuss our daa and describe and presen resuls from our empirical model while secion 5 provides concluding commens. 2. Review of Lieraure 2 I was believed a one ime ha cigaree smoking and oher addicive behaviour was no raional and so no suiable for convenional economic analysis (e.g. Schelling, 1984). There is now however a subsanial body of lieraure o esify ha he demand for cigarees clearly responds o changes in prices and oher facors. Early sudies of cigaree demand employed aggregae ime-series daa and produced esimaes of he price elasiciy of demand in he region of 0.4. One disadvanage of hese sudies was ha hey were unable o disinguish beween he elasiciy of cigaree demand condiional upon smoking and he elasiciy of paricipaion. Laer sudies used he ype of individual level daa employed in his sudy. These sudies are able o consider separaely he effec of price on he probabiliy of smoking and on average consumpion of smokers. Furhermore, sudies on he probabiliy of smoking can be divided ino hose which view saring and quiing as binary evens wihin a discree choice framework and hose which use duraion analysis. For an example of an applicaion of he former approach o he daase used in his paper see Madden (2001a). However his paper only examined a single cross-secion and so could no incorporae ime series variaion in price or ax daa. As we will see below i is possible o expand his framework and exend he binary choice framework o include he effecs of axes/prices. 3 Sudies which have examined smoking iniiaion in a discree choice framework have ypically esimaed elasiciies of paricipaion wih respec o ax in he region of 0.5 o 1.0 wih an apparen inverse relaionship beween age and smoking elasiciy (for a summary see Chaloupka and Warner, 1999). There are fewer applicaions of duraion analysis. Douglas and Harihan (1994) use a spli populaion model o 2 The firs par of his secion draws upon he excellen survey by Chaloupka and Warner (1999). 3 In a companion paper o he curren one, Madden (2001b) esimaes he effec of axes using a discree choice approach. 4

6 analyse saring smoking. They find no evidence of a saisically significan price effec. Douglas (1998) analysed he hazards of saring and quiing, once again using a spli populaion model, bu his ime wih an ordered probi, which disinguishes beween hose who never sar smoking, hose who sar and qui and hose who sar bu do no qui. The delay before saring and quiing are modelled using a loglogisic and Weibull specificaion respecively. The price of cigarees is included as a ime-varying covariae. The price of cigarees has no significan effec upon he hazard of saring smoking bu he number of years an individual smokes has an approximaely uniary elasiciy wih respec o price. Forser and Jones (2000) analyse rerospecive UK daa wih a spli populaion model for saring smoking and a variey of parameric duraion models for quiing. They find a ax elasiciy of he age of saring smoking of for men and for women. The esimaes of he ax elasiciy of quiing are 0.6 for men and 0.46 for women. They also include a variey of specificaion ess and find heir esimaes o be quie robus. Finally, Lopez-Nicolas (2002) analyses Spanish daa, once again using a spli-populaion model, and finds elasiciies of delay wih respec o saring of 0.07 and elasiciies of duraion before quiing of 1.3 o 1.5. One feaure of he above duraion sudies is ha, while hey include measures of educaion or income as covariaes, hey do no inerac such variables wih he ax, hus consraining he ax/price response o be idenical across he disribuion of educaion/income. This is despie evidence from cross-secion sudies ha such a response does differ according o socio-economic characerisics such as income and educaion. For example, Evans e al. (1999) noe ha in he US higher-income individuals are less responsive o ax changes han ohers. Townsend e al (1994), using UK daa, found ha men and women in lower socio-economic groups are more responsive han are hose in higher socio-economic groups o changes in he price of cigarees and less o healh publiciy. Borren and Suon (1992) find evidence of an inverse-u relaionship in erms of price responsiveness, wih a higher elasiciy for middle-income men compared o lower and higher-income men. Their evidence for women, while less clearcu, appears o indicae ha elasiciy declines as income increases. We explicily invesigae his issue in his paper by including ineracion erms which permi he effec of axes o differ across he educaion specrum. We complee his secion by briefly reviewing he exising Irish sudies on obacco consumpion. A variey of models of obacco consumpion have been esimaed 5

7 mosly using aggregae ime-series daa for Ireland daing from O Riordan (1969) o Madden (1993). 4 These sudies have produced broadly comparable resuls wih a median esimae for he price elasiciy of obacco in he region of 0.5, which is in line wih resuls from elsewhere in he world. The use of aggregae ime-series daa precludes disinguishing beween he effec of price on he probabiliy of smoking and on he demand for cigarees condiional on smoking. Conniffe (1995) remedies his o some exen by combining analysis of aggregae ime-series daa wih daa on he proporion of he oal populaion who are smokers. He found ha he proporion of he populaion smoking is unaffeced by price (or income) bu exhibis a downward rend relaed o healh concerns. Consumpion by smokers does no exhibi such a downward rend bu appears o have a significan price elasiciy of around 0.3. We now urn o ouline he simple model of saring and quiing smoking which underlies our analysis. 3. A Model of Saring and Quiing Smoking In his secion we ouline a simple heoreical model which underlies our empirical approach. The model draws on he exposiion of Douglas and Harihan (1994). Suppose each individual has a concave uiliy funcion a ime U = U( C, Y, S, L ) where C is he level of consumpion of he addicive good whose price is P, Y is consumpion of a non-addicive numeraire good whose price is uniy, S is he sock of accumulaed addicion capial and L represens oher demographic/life cycle variables which may affec uiliy. The sock of addicive capial S depreciaes a rae γ bu i is replenished by curren consumpion of he addicive good C so ha S + 1 = (1 γ ) S + C. Since he individual sars off wih zero unis of consumpion S = 0 0. Assume ha each individual is infiniely lived, hen discouned remaining lifeime uiliy a ime, V is given by 1 V = U i (1+ ρ) i= i 4 The excepion was O Riordan (1969) who used daa from he Tobacco Research Council. 6

8 where ρis he rae of ime preference. wealh The lifeime budge consrain is deermined by he presen value of lifeime A, he presen value of lifeime expendiure on he numeraire good Y and he presen value of lifeime expendiure on he addicive good C a prices P. We make he simplifying assumpion ha lifeime earnings are no affeced by he sock of addicion. 5 where The budge consrain for he individual a ime is i= (1 1 I i ( Y + P C ) = r (1 + r ) i i i i + ) i = I i is income a ime i and r is he rae of ineres. We can now look a he decisions o sar and qui smoking. Dealing wih saring firs, a raional individual will begin smoking if he marginal benefi of he firs cigaree exceeds is marginal cos i.e. MB C i ( C, Y, L S 0) > MC ( C, Y, L S = 0) A = C where MBC is he marginal discouned remaining lifeime benefi of cigaree consumpion while MC C is he marginal discouned remaining lifeime cos. I seems likely ha some of he variables affecing marginal cos and benefi will have a sochasic componen. For example, hey could boh be affeced by he occurrence of respiraory illnesses which would reduce he appeal of smoking or hey could be influenced by he number of smokers in he poenial smoker s peer group. So he above condiion could be re-specified along he lines: MB + ε > MC + µ * * * where MB E{ MB ( C, Y, L S = 0)} and MC E{ MC ( C, Y, L S = 0)}. C * = C Thus he probabiliy of saring smoking a ime given ha an individual has no sared smoking in a previous period is Pr{ C 0 S = 0} = Pr{ MB ( C, Y, L S = 0) > MC (( C, Y, L S = 0)} > C C * * = Pr{ ε µ > MC MB }. * * = H( MC MB ) = H( ) 5 There is some conroversy as o he effec of he consumpion of addicive goods on wages. Clearly ill-healh (arising from smoking) could affec earnings via los hours and here is also evidence ha moderae alcohol consumpion has a posiive effec upon wages bu ha obacco use reduces wages. See Auld (2000) for a recen discussion. 7

9 where H( ) is a hazard funcion based on he disribuion F( T ) = Pr{ T}. H ( ) will be decreasing in * * MB Sar Smoking a MC. In his case he hazard funcion is he condiional probabiliy ha a person will smoke in period given ha he has no smoked up o and including period -1. The analysis of quiing is very similar, excep of course ha marginal cos and benefi are now condiional upon a sock of accumulaed addicive capial. A person will qui in period T if he following condiion holds: MC C ( C, Y, L T 1 = τ S T 1 > 0) > MBC ( C, Y, L S = τ > 0) T 1 S = τ where > 0 reflecs he sock of accumulaed addicive capial up o period T and he person sared smoking in period ô. Noe ha his assumes a single spell of smoking we do no allow for muliple spells of smoking, no smoking, smoking again ec. Then, following he analysis above, he probabiliy ha someone will qui smoking in period T, given ha hey were smoking in period T-1 is Pr{ C T T 1 * * 1 T < MC T MBT = 0 C T > 0, S > 0} = Pr{ εt µ = τ } In his case H (T ) is increasing in * * = H( MC MB ) H( T ). T T = MC. * * T MB T 4. Daa and Empirical Model In his secion we discuss our daa and he empirical model adoped. Our daa comes from a survey known as he Saffron Survey which was carried ou in 1998 by he Cenre for Healh Economics a Universiy College Dublin. The Saffron Survey s aim was o survey women s knowledge, undersanding and awareness of heir lifeime healh needs. Much of he focus of he survey was on he issue of hormone replacemen herapy 6 bu oher informaion regarding healh, lifesyle choices and demographics was also colleced. For our purposes in his paper he relevan quesions regarding smoking were as follows: Do you currenly smoke?. People who answered yes o his quesion were hen asked For approximaely how many years have you smoked?. People who replied ha hey did no currenly smoke were asked had hey ever smoked and if hey answered yes o his quesion hey oo were 6 See Thompson (2000). 8

10 asked for approximaely how many years hey had smoked, and in wha year hey had sopped smoking. From he answers o hese quesions i is possible o calculae he years people sared (and sopped if applicable) smoking. The grea advanage of his ype of informaion is ha i is possible o examine he effec of he ax rae in each given year on he probabiliy of saring/quiing smoking. Before he formal analysis i is useful o look a some summary informaion on our sample. The original sample size for he Saffron survey was However, since we only have ax and price daa going back as far as 1960, we have dropped all women who were aged 10 or more in We are effecively assuming ha subjecs were a risk of saring smoking from he age of en. Our daa suggess ha his is a reasonable assumpion since he number of subjecs who repored saring smoking before en was miniscule. Thus we only have women who were born afer 1950, leaving us wih a oal sample of jus over 700. Of hese, abou half have smoked a some sage of heir lives and abou 35 per cen were smoking a ime of inerview. In able 1 we give summary saisics (wih sandard errors in brackes) for a number of key variables for he various subgroups in our sample. There is relaively lile difference across he groups by age excep for ex-smokers who end o be older. As migh be expeced his group also ends o have worse healh (which perhaps promped hem o qui smoking). They also show a higher proporion of married, which may reflec people giving up smoking on geing married. Probably he bigges difference across he columns is o be observed in educaional aainmen. 7 Of he oal populaion (including smokers) over 60 per cen have obained Leaving Cer or higher, bu of hose who have ever smoked only abou 47 per cen have. This drops o abou 44 per cen when we examine hose people sill smoking in Thus geing beyond Junior Cer appears o no only lower he chances of saring smoking, bu also increases he chances of quiing if you do sar o smoke. As explained above, he Saffron survey was a cross-secion survey carried ou in However, we are exploiing he rerospecive informaion which enables us o examine he impac of a ime-varying covariae such as ax or price on he decision o sar/qui smoking. One issue which mus firs be discussed in he choice of ax/price. 7 The defaul caegory for educaion is Primary Cer indicaing ha formal schooling ended a approximaely he age of 12. Junior Cer indicaes formal schooling ceased a approximaely 16, while Leaving Cer indicaes schooling ended a approximaely 18. 9

11 The choice of such a variable is moivaed by he heory of consumer demand which suggess ha he quaniy consumed (or in his case he decision o consume) will be influenced by a number of facors, including he consumer price (which in urn is influenced by he ax on obacco). The ax elemen in he reail price of a packe of cigarees has wo componens, excise duy and value-added ax (VAT). In Ireland here is a specific and an ad valorem excise duy as well as VAT. Thus he specific excise duy is added o he producer price and he ad valorem excise duy and VAT is hen applied a he appropriae rae o obain he reail price. While he reail price is hus influenced by wo ax insrumens (he rae of excise duy and VAT) i is arguable ha only excise duy can be regarded as a specific ax insrumen o address smoking, since any increase in he rae of VAT will also cause he prices of many oher goods o rise. To engineer a rise in he relaive price of obacco, a rise in excise duy is appropriae. Unforunaely he daa supplied o us by he Revenue Commissioners does no break down he ax componen ino excise and VAT for he period up o Thus we have aken he oal ax componen of he reail price and deflaed i by he personal consumpion deflaor o arrive a a real ax on obacco. This sideseps he need for such a breakdown since any excise ax increase in excess of overall inflaion will appear as an increase in he real ax whereas increases in VAT will also be refleced in increases in he overall price level and hus conribue less o any increase in he real ax. We hus have a choice beween using he real ax conen or he consumer price as he relevan ime-varying covariae. I can be argued ha from he poin of view of he decision which he consumer makes re saring or quiing i is he consumer price which is relevan. On he oher hand, from he poin of view of governmen i is he ax conen which is he policy variable. However, from a pracical poin of view, he choice beween hem is largely irrelevan. As figure 1 below shows, he wo series move prey much in andem and he correlaion coefficien beween hem is We now urn o discuss he more formal analysis of saring and quiing, dealing wih saring firs. 4.1 Saring Smoking To analyse he decisions o sar/qui smoking, we employ duraion analysis, wih he exra proviso ha when examining he decision o sar smoking we employ a spli 10

12 populaion model. When modelling he decision o smoke, we include as one of our covariaes he ax rae for he year in quesion. Thus say we observe woman A, aged 40 in 1998 (he year of he survey) who commenced smoking aged 20 (i.e. in 1978). We assume people are a risk of saring smoking from he age of en (1968 in he case of woman A). Thus we will have en observaions on woman A where she does no smoke, followed by he ransiion in year 11 where she does smoke. Each observaion for each year for his woman (up o when she sars smoking) is regarded as a separae observaion. Thus he observaion for 1968 for woman A has a duraion of one, wih he ax rae for 1968 as one of he covariaes and is regarded as righcensored. The observaion for 1969 for woman A has a duraion of 2, is sill righcensored and has he ax rae for 1969 as a covariae. This coninues up o he observaion for 1978 where here is a failure or ransiion o smoking. Consider now he case of woman B wih he same age as woman A bu who has no sared smoking by In his case here are hiry observaions for woman B, all of hem righ-censored. No failure or ransiion o smoking is observed. Sandard duraion models assume ha failure will evenually ake place. Thus even if he las observaion for an individual is righ-censored (i.e. in our case hey have no sared smoking by 1998) i is assumed ha a some sage hey will sar smoking. If, say, we were rying o model he duraion of a ligh bulb hen his assumpion is realisic. A some sage he ligh bulb will fail. Bu he assumpion is no realisic for he case of saring smoking, since a subsanial prporion of he populaion never smoke a any sage of heir lives. In his case a spli populaion model is appropriae where he likelihood of each observaion is weighed by he probabiliy ha he individual will ever sar o smoke and so he duraion analysis is applied only o hose individuals prediced o sar smoking. We also esimae log-logisic duraion models where he populaion is no spli. We esimae hen for he populaion as a whole and also for he populaion of smokers only. Before discussing he appropriae parameric duraion model we firs presen he plo of he empirical hazard funcion below. This is paricularly useful when choosing a parameric hazard funcion. We use he lifeable esimae of he hazard funcion (wih confidence inervals as shown) and his is qualiaively very similar o he Kaplan-Meier esimae of he empirical hazard. 11

13 .1 azard seqvar Hazard Funcion, Saring Daa (lable) This figure shows ha he hazard increases a firs and hen decreases. I reaches is peak when he ime period equals seven, which corresponds o age seveneen since we assume subjecs are a risk of smoking from age en. There is anoher local peak a age weny-one and hen a fairly sharp decrease. Wha his suggess is ha a monoonic hazard funcion is no appropriae for his daase. A hazard funcion which a firs increases and hen decreases seems mos appropriae, suggesing he log-logisic model is worh rying. For he smokers in our sample we infer he age of saring as oulined above and he duraion daa can be viewed as a complee spell. The sample, of course, also conains individuals who are no observed o have sared smoking. A parameric duraion model would inerpre hese individuals as incomplee spells and assume ha hey will evenually fail and sar smoking. They are viewed as righ-censored a he ime of he survey. As explained above his does no appear reasonable when dealing wih smoking and consequenly Douglas and Harihan (1994) in heir analysis of US daa and Foser and Jones (2000) in heir analysis of UK daa have argued ha a spli populaion model be used. In his model duraion analysis is applied only o hose individuals who are prediced o evenually sar smoking. Following Foser and Jones (2000) suppose we define s = 1 for an individual who will evenually sar smoking and modelling evenual failure (i.e. saring smoking) using a probi specificaion we have where Pr( s = 1) = Φ( α z ) and Pr( s = 0) = 1 Φ( α z ) i z i is a vecor of ime invarian covariaes, Φ is he cumulaive densiy funcion for he sandard normal disribuion and α is a parameer vecor. Thus he i 12

14 probabiliy of saring smoking a a given ime is defined condiional upon evenually saring. Given he plo of he empirical hazard funcion above he mos appropriae parameric duraion model is he log-logisic. The probabiliy densiy funcion f (.) and he survival funcion S (.) of he log-logisic disribuion for hose individuals who evenually sar smoking are f ( s = 1; x S( s = 1; x i ( )) i ( )) 1 γ λ 1 1 γ γ[1+ ( λ ) ( λ ) where λ = exp( βx i ( )), x i () is a vecor of ime varian and ime-invarian covariaes and γ is a scale parameer. Then he conribuion o he log-likelihood funcion for he spli populaion model becomes, for individual i: c i ln[ Φ( α zi ) f ( s = 1; x i ( ))] + (1 c i )ln[1 Φ( α z i ) + Φ( α z i ) S( s = 1 γ 1 γ ] 2 1; x i ( ))] For hose who are observed as smokers in he sample, c = 1 and heir conribuion o he likelihood funcion is simply he log of he probabiliy of being a smoker Φ α z ) i ( i imes he probabiliy densiy funcion of saring a he observed saring age, f (.). For hose who are observed as no saring ( c = 0 ), he conribuion is he log of he probabiliy of never saring Φ( α z ) plus he probabiliy of saring afer he age 1 i observed a he ime of he survey, Φ ( α z i ) S(.). i In able 2 we presen esimaes of he above spli populaion model and in ables 3 and 4 we presen esimaes of he log-logisic model where he populaion is no spli. In ables 3 and 4 we apply he log-logisic model o he whole sample and also o he sample of smokers only. We include boh ime-varying and non-imevarying covariaes in hese models. Educaion is frequenly regarded as an imporan deerminan of healh and smoking habis (see Meara, 2000) and we include caegorical variables for Junior Cerificae, Leaving Cerificae and hird level. The defaul caegory is Primary Educaion whereby formal schooling ends a abou welve years of age. 13

15 The mechanism whereby educaion affecs smoking behaviour is unclear. I may indicae ha more educaed people simply have more informaion regarding he effecs of smoking upon healh. I may also indicae ha more educaed people are beer able o process or ac upon informaion on regarding he healh effecs of smoking. Finally i may reflec he presence of a hird variable whereby which simulaneously influences aiudes owards boh educaion and smoking/healh. Thus individuals wih a low discoun rae (i.e. hey are more fuure-oriened ) will inves in boh heir healh capial (by refraining from aciviies such as smoking) and heir human capial. In he absence of reliable measures of such discoun raes i is difficul o disinguish beween hese differen mechanisms bu i is likely ha all hree (and perhaps ohers) are a work. 8 However, in an aemp o disinguish beween hese influences o some degree, we include a variable which we label healh knowledge. As menioned above, he Saffron survey colleced a variey of informaion regarding he healh habis and needs of women. Owing o is concenraion on hormone replacemen herapy, a number of quesions were asked regarding healh knowledge in his area. As our measure of healh knowledge we include a dummy variable which measures he response o he quesion Have you ever heard of oseoporosis?. 9 Clearly his quesion refers o a dimension of healh which differs from smoking, bu we do no believe i is unreasonable o expec ha knowledge regarding oseoporosis may be correlaed wih oher aspecs of healh knowledge, including he healh effecs of smoking. To allow for he possibiliy of a secular drif in smoking habis over ime, perhaps relaed o increased healh awareness or general public inolerance owards smoking we also include a ime rend. Given ha all he variaion in ax raes is aribuable o variaion across calendar years here may be an idenificaion problem in separaing he ime rend and ax effecs. Following Foser and Jones (2000) we include a higher-order polynomial in ime, which allows for a smooh bu flexible 8 For a discussion on he relaive imporance of hese mechanisms for he link beween smoking, healh and socio-economic saus, see Meara (2001). 9 While knowledge abou oseoporosis may appear o be a narrow definiion of healh knowledge, i may be a suiable measure for our sample. Typically oseoporosis is more common amongs older women. Given ha our sample are all aged 48 or less, his reduces he chances ha knowledge regarding i comes from direc experience bu insead comes from being generally well-informed on healh issues. Also since smoking increases he risk facor for oseoporosis i may be a good proxy for healh knowledge specifically relaed o smoking. 14

16 ime rend. Finally, we also include a cohor dummy, which akes on a value of one if he individual is aged 33 or less and a dummy variable for marial saus. Before discussing he resuls i is imporan o poin ou ha while educaional achievemen and marial saus are facors which clearly will vary over a woman s lifeime, we are no reaing hem as ime-varying covariaes in his analysis. We do no have informaion on age of marriage nor on age of compleion of educaion. Thus even hough a women may be classified as married she will no have been married for a leas par of he ime during which her smoking behaviour is analysed (e.g. during her early eens). However, if educaion and/or marial saus is correlaed wih some more fundamenal aribue such as an individual s underlying rae of ime preference hen he use of ulimae educaional/marial saus is jusified, o a degree a leas. Bearing in mind he evidence cied above ha ax responsiveness may differ by educaion or socio-economic characerisics we also include specificaions wih ineracion erms which aemp o capure such an effec. 4.2 Unobserved Heerogeneiy or Fraily The specificaions we have oulined above, plus he included covariaes may sill no explain all he variabiliy in observed ime o failure. The excess unexplained variabiliy, or overdispersion, may be caused by misspecificaion or omied covariaes. In survival analysis his is known as fraily since he model is unable o explain fully why subjecs wih shorer ime o failure are more frail han ohers. A fraily model aemps o measure his overdispersion by modelling i as resuling from a laen muliplicaive effec on he hazard funcion. Thus given a hazard funcion h () he hazard becomes α h(). Fraily may also be shared in he sense ha he subjecs in a given group may experience he same unobserved heerogeneiy e.g. he group may represen a family, or, as is he case here, a single subjec for which muliple episodes are observed. Recall ha in he case of fraily he hazard funcion becomes α h(). For purposes of idenifiabiliy i is usually assumed ha α is disribued wih mean one and variance θ. The issue hen becomes he esimaion of he addiional fraily variance, θ. Probably he wo mos common parameric choices for g (α), he probabiliy densiy funcion for α, are he gamma and he inverse gaussian. While he associaed 15

17 hazard funcion for he wo disribuions are quie alike here is one imporan disincion. Suppose we have wo individuals wih common fraily. Condiional on (2) (1) he given fraily heir respecive hazards are proporional wih, say, h ( ) / h = c. (2) 1 Marginally however, for gamma frailies he hazard raio h θ ( ) / hθ ( ) = c a = 0, bu diminishes wih ime so ha in he limi he raio becomes uniy. For he inverse-gaussian once again suppose ha (2) 1 h θ ( ) / hθ ( ) = c a = 0. However, in his case he limi of his raio is no uniy bu effec does no diminish compleely over ime. 1/ 2 c so ha he fraily 4.3 Saring Smoking: Resuls and Discussion We firs of all discuss he resuls in ables 2, he spli-populaion model and able 3, he log-logisic model applied o smokers only (hus here are no righcensored observaions). The resuls from he probi for becoming a smoker show he expeced negaive effec for Leaving Cer (and o a lesser exen for hird level educaion) compared o he defaul caegory of primary educaion only. Wha is also of ineres is he posiive coefficien on Junior Cer indicaing a non-monoonic effec of educaion on he probabiliy of becoming a smoker. The resuls also show ha marriage has a negaive effec while younger cohors are more likely o become smokers. Turning now o he duraion par of he spli populaion model, when no ineracion erms beween ax and educaion are used, he coefficien on ax is in he expeced direcion (i.e. posiive, indicaing ha higher axes delay he period before saring), bu is no significan. When he ineracion erms are used, he coefficien on ax alone is negaive bu even less well-deermined ha when no ineracions erms are used. The ineracion erm wih Junior Cer is saisically significan however, albei a only he 10% level. The ineracion erm wih Leaving Cer is similar in magniude and very near convenional significance levels, while he ineracion erm wih hird level is smaller and insignifican. Thus ax has no significan effec on duraion for he defaul group, followed by a posiive bu declining effec on duraion for subsequen educaion groups. This appears o sugges ha he ax elasiciy is non-monoonic bu declines wih educaion afer Junior Cer. This is parly in line 16

18 wih he Townsend e al. and Borren and Suon findings bu, given he significance levels of he coefficiens, hese resuls are enaive raher han conclusive. Turning now o he duraion model for smokers only in able 3, we see ha in general, he coefficiens are beer deermined. In he model wihou he ineracion erms, he coefficien on ax is similar o ha in he spli populaion model, and his ime i is saisically significan. Perhaps surprisingly, educaion has lile or no effec. This broadly carries hrough o he model wih ineracion erms. Even hough he coefficien on hird level educaion is posiive and significan, he overall effec of hird level educaion is given by his coefficien plus he produc of he coefficien on he ineracion erm beween ax and hird level educaion and he average value of ax. Since i is he log of ax which is used, his second erm will be negaive, hus offseing o some degree he posiive effec of hird level educaion on duraion. Similarly, he effec of ax for each educaional group is given by he sum of he overall coefficien for ax and he ineracion coefficien. In his respec we see enaive evidence once again of an inverse-u effec wih he greaes impac of ax upon hose wih Junior Cer educaion. In able 4 we presen evidence for he log-logisic model, his ime applied o he populaion as a whole i.e. here are some righ-censored observaions. We also include he fraily models here, given ha he p-values for he LR es for fraily indicaes is presence. 10 For he models wihou ineracion erms, he coefficien on ax is in he expeced direcion and for he model wihou fraily and he model wih inverse gauss fraily he coefficiens are significan (and similar in magniude). The resuls when ineracion erms are used are similar across models and once again indicae non-monooniciy bu ineresingly he greaes effec of ax is now seen for hose wih Leaving Cer raher han Junior Cer. Summarising he resuls from ables 2-4 i seems fair o say ha ax does appear o have an effec on duraion before quiing and ha here is evidence of nonmonooniciy in is effec across educaion. While he resuls from each individual regression is enaive, he uniformiy across regressions is noable. When using a parameric duraion model i is imporan o deermine wheher he daa suppor he paricular parameric form of he hazard funcion. Probably he mos frequenly employed mehod is o use he model based esimae of he 10 The presence of fraily was decisively rejeced for he models run on smokers only. Hence we do no include hem. They are available on reques. 17

19 cumulaive hazard funcion o form wha is known as he Cox-Snell (1968) residuals. The Cox-Snell residual for subjec j a ime is defined as Hˆ ( ) = lnsˆ ( ), he esimaed cumulaive hazard funcion obained from he fied model, given ha S ˆ ( ) is he esimaed survival funcion. Cox and Snell argued ha if we have n j j subjecs hen if he correc model has been fied o he daa, hese residuals are n observaions from an exponenial disribuion wih uni mean. Thus a plo of he model-based cumulaive hazard agains he cumulaive hazard funcion obained from a nonparameric or empirical esimaor should yield a sraigh line wih slope equal o one if he parameric model is correc. Below we show such a plo for he log-logisic model for saring smoking for smokers only and hen for he oal populaion (for breviy we include only he specificaions wih he ineracion erms wih educaion. The plos for he oher specificaions are available on reques). j j j j j Cox-Snell Residuals, Log-logisic model, smokers only H cum. Cox-Snell residual cum. Cox-Snell residual Cox-Snell Residuals, Log-logisic model, smokers and non-smokers 18

20 H cum. Cox-Snell residual cum. Cox-Snell residual In evaluaing hese plos care mus be aken regarding he scale of he axes. For he case of smokers only, he residuals deviae from he 45 degree line afer he esimaed cumulaive hazard akes a value of around 1.3 indicaing a limied degree of misspecificaion. For he whole populaion his deviaion is observed when he cumulaive hazard is around 0.9, suggesing a greaer degree of misspecificaion for his model. 4.4 Quiing Smoking: Resuls and Discussion For he case of quiing smoking he analysis is in many ways he mirror image of he analysis repored above. In his case he ransiion, or failure, is he ac of quiing smoking. Thus a person who has smoked for say 10 years and hen quis represens en observaions, where he duraion variable increases by one each year. Each year up o he poin of quiing is regarded as righ-censored and hen he quiing year is he ransiion year. A person who say sars smoking in 1988 and has no qui by 1998 (he year of he survey) is simply reaed as having en righ-censored observaions. We do no employ he spli-populaion model for quiing since i seems more reasonable o assume ha from a populaion of smokers, all, or a leas a majoriy of hem, will qui or would evenually qui if hey could be observed for long enough, han o assume ha from a populaion of non-smokers, all will evenually sar smoking. Below we show he plo of he empirical hazard funcion for quiing, once again using he lifeable esimae wih confidence inervals. 19

21 .2.15 Hazard seqvar Hazard Funcion, Quiing Daa (lable) Apar from he spikes a en and weny years here is relaively lile evidence of an increasing or decreasing hazard. This suggess ha amongs parameric duraion models, he exponenial or Weibull migh be an appropriae choice. The survival funcion for he exponenial model (in acceleraed failure ime forma) is: S( ) = exp( λ ) where λj = exp( x j β) and x j and β represen a vecor of covariaes and regression coefficiens respecively. The corresponding funcions for p he Weibull model are S( ) = exp( ( λ ) ) where λ j = exp( x j β/ p) and x j and β are as before. Clearly he exponenial model is a special case of he Weibull model, where p = 1. We also include esimaes from he generalised gamma model. This is an exremely flexible model which ness boh he exponenial and Weibull model. Is z survival funcion is S( ) = 1 I( κ exp( )) where I is he incomplee gamma κ funcion and ln λ z = σ while κ = 1 and σ = 1 gives he exponenial disribuion.. When κ = 1 his reduces o he Weibull disribuion, Table 5 gives he resuls for he exponenial and gamma models while able 6 gives resuls for he Weibull model where we have also included fraily models (wih he resuls presened in acceleraed ime forma). 11 Noe ha in erms of inuiion, we expec coefficiens o be of opposie sign o he saring models, since here we are esimaing he effec of variables on he delay before quiing. Looking a he models firs of all wihou ineracion effecs, we noe ha in all cases he coefficien on ax 11 The null hypohesis of no fraily was no rejeced for he gamma and exponenial models 20

22 has he expeced negaive sign i.e. higher ax reduces he delay before quiing. The magniude of he coefficien is also very similar across models bu in no case is i saisically significan. When he ineracion erm is included he coefficien on ax increases in absolue size and becomes saisically significan for he non-fraily specificaions. The coefficiens on he ineracion erms are only significan for Junior Cer for he gamma and Weibull models. Given ha he ineracion erm for Leaving Cer lies below ha for Junior Cer and hird level for all specificaions (even hough i is no saisically significan) his is enaive evidence of an even more complex relaionship beween ax elasiciy and educaion, whereby he effec is sronges for hose wih he leas educaion, nex sronges for hose wih Leaving Cer, hen hird level and finally weakes for hose wih Junior Cer. No only is his a more complex relaionship beween ax elasiciy and educaion, i is also a odds wih some of he evidence for saring which indicaed he sronges ax effec for hose wih Junior Cer. Since he parameric models are nesed i is possible o check heir validiy agains each oher, which is carried ou in able 7. In all cases of he es for ó=1 i.e. beween Weibull and exponenial, he null is rejeced, indicaing he Weibull is o be preferred over he exponenial. For he es ê=1. i.e. beween gamma and Weibull, he null is rejeced for he case wih ineracion erms, indicaing a choice of gamma over Weibull, while i is no rejeced when ineracion erms are no included. We also presen values of he Aikake informaion crierion, whereby AIC=-2 log likelihood +2(c+p+1) where c is he number of model covariaes and p he number of model specific ancillary parameers. The model wih he lowes AIC is o be preferred. We see ha in erms of AIC he exponenial model has values well in excess of he gamma or Weibull, bu here is very lile o choose beween he Weibull and gamma specificaions. The esimaed coefficiens for hese models are also quie similar in sign and magniude. We also noe ha all models have a Ramsey RESET p-value in excess of 0.8. Wha abou he Cox-Snell residuals? Below we presen Cox-Snell residual and once again for he sake of breviy we presen only he residuals where he ineracion erms are included (he residuals for he models wihou ineracion erms are available on reques). 21

23 Cox-Snell Residuals for Gamma Model H cum. Cox-Snell residual cum. Cox-Snell residual Cox-Snell Residuals for Weibull Model H cum. Cox-Snell residual cum. Cox-Snell residual Cox-Snell Residuals for Exponenial Model 22

24 H cum. Cox-Snell residual cum. Cox-Snell residual Casual eyeballing of hese plos suggess he greaes degree of misspecificaion for he exponenial model wih relaively lile o choose beween he gamma and Weibull models, hough perhaps he gamma model is o be marginally preferred. This is enirely consisen wih he resuls from able Discussion and Conclusion This paper has examined he facors influencing saring and quiing smoking for a sample of Irish women using duraion analysis. The innovaion in he paper is ha rerospecive daa in he sample allows for he inclusion of he real ax on obacco as a ime-varying covariae, hus permiing analysis of he effeciveness of a major policy variable in erms of combaing smoking. The inclusion of ineracion erms wih educaion also permis analysis of how he effeciveness of axaion differs according o educaion. The evidence presened here is mixed. In erms of saring smoking, here is evidence of an inverse-u effec, wih he sronges effec of axaion on hose wih inermediae levels of educaion and weaker effecs for hose wih he mos and he leas educaion. I has o be sressed however, ha his evidence is relaively enaive given he calculaed significance levels. There is also some evidence of misspecificaion in he diagnosics. The evidence for quiing suggess an even more complex relaionship beween educaion and he effeciveness of axaion. Tax seems o be mos effecive in erms of encouraging quiing for hose wih he leas educaion. I is also effecive for hose who complee second level educaion, less so for hose who complee hird level 23

25 educaion and leas effecive of all for hose wih an inermediae level of educaion (i.e. hose who leave school a around ages 15-16). Overall, he resuls in his paper are probably more suggesive han definiive in erms of he role of obacco axes in influencing saring and quiing. I should also be borne in mind ha he resuls here apply only o a sample of women aged 48 or under. However, given he wealh of resuls from oher counries and ime periods regarding he effec of axes and prices on obacco consumpion, i is clear ha obacco axaion is likely o remain a major insrumen in public policy o discourage smoking. 24

26 References Akaike, H., (1974): A New Look a he Saisical Model Idenificaion, IEEE Transacion and Auomaic Conrol, Vol. 19, pp Auld, C., (2000): Smoking, Drinking and Income, Universiy of Calgary, mimeo. Borren, P., and M. Suon (1992): Are Increases in Cigaree Taxaion Regressive?, Healh Economics, Vol. 1, No. 4, pp Chaloupka, F., and K. Warner (1999): The Economics of Smoking, NBER Working Paper, W7047. Cox, D. R., and E.J. Snell (1968): A General Definiion of Residuals (wih discussion), Journal of he Royal Saisical Sociey, Vol. 30, pp Douglas, S., (1998): The Duraion of he Smoking Habi, Economic Inquiry, Vol. 36, pp , and G. Harihan (1994): The Hazard of Saring Smoking: Esimaes from a Spli Populaion Model, Journal of Healh Economics, Vol. 13, pp Evans, W.N., J. Ringel and D. Sech (1999): Tobacco Taxes and Public Policy o Discourage Smoking, in Tax Policy and he Economy (ed. J. Poerba). NBER. MIT Press. Forser M., and A. Jones (2000): The Role of Tobacco Taxes in Saring and Quiing Smoking: Duraion Analysis of Briish Daa, forhcoming in JRSS Series A: Saisics in Sociey. López Nicolás, A., (2002): How Imporan are Tobacco Prices in he Propensiy o Sar and Qui Smoking? An Analysis of Smoking Hisories from he Spanish Naional Healh Survey, Healh Economics, Vol. 11, No. 6, pp Madden, D., (2001a): Smoke and Srong Whiskey: Facors Influencing Female Smoking and Drinking in Ireland, mimeo (2001b): Do Tobacco Taxes Influence Saring and Quiing Smoking: A Discree Choice Approach, mimeo (2002): Seing he Appropriae Tax on Cigarees in Ireland, in Budge Perspecives 2003 (eds. T. Callan, D. Madden and D. McCoy). Economic and Social Research Insiue, Dublin, Meara, E (2001): Why is Healh Relaed o Socioeconomic Saus?, NBER Working Paper, W8231. Mooney T. (2000): Towards a Tobacco Free Sociey : Repor of he Tobacco Free Policy Review Group. Dublin : Deparmen of Healh and Children. 25

27 Schelling, T., (1984): Self-command in pracice, in policy and in a heory of raional choice, American Economic Review, Vol. 74, pp Schmid, P and A. Wie (1989): Predicing Criminal Recidivism using Spli Populaion Survival Times, Journal of Economerics, Vol. 40, pp Tauras, J. and F. Chaloupka (1999): Deerminans of Smoking Cessaion: an Analysis of Young Adul men and Women, NBER Working Paper, W7262. Thompson, J., (2000): Economic Aspecs of Women s Healh wih regard o Hormone Replacemen Therapy in Ireland, unpublished MA hesis, Economics Deparmen, Universiy College Dublin. Torelli, N., and U. Trivellao (1993): Modelling Inaccuracies in Job-Search Duraion Daa, Journal of Economerics, Vol. 59, pp Townsend, J., P. Roderick and J. Cooper (1994): Cigaree Smoking by Socioeconomic Group, Sex and Age: Effecs of Price, Income and Healh Publiciy, Briish Medical Journal, Vol. 309, pp

28 Variable Toal (N=703) Age ( ) Table 1: Summary Saisics for Sample Ever Smoked (N=348) ( ) Smokers (N=246) ( ) Ex-Smokers (N=102) ( ) Age Sared Smoking ( ) ( ) ( ) Healh Problem ( ) ( ) ( ) ( ) Single ( ) ( ) ( ) ( ) Married ( ) ( ) ( ) ( ) Widowed ( ) ( ) ( ) Separaed ( ) ( ) ( ) ( ) Primary Educaion ( ) ( ) ( ) ( ) Junior Cer ( ) ( ) ( ) ( ) Leaving Cer ( ) ( ) ( ) ( ) Third Level ( ) ( ) ( ) ( ) Working ( ) ( ) ( ) ( ) Cigarees per Day ( ) ( ) ( ) 27

29 Table 2: Spli Populaion Duraion Model for Saring Smoking (N=11733) Duraion Probi Duraion Probi Junior Cer (0.168) (0.090)** (0.330) (0.092)** Leaving Cer (0.178) (0.089)*** (0.346) (0.090)*** Third Level (0.207) (0.103) (0.383) (0.105)* Ln (Tax) (0.391) (0.728) Cohor (0.267) (0.065)*** (0.296) (0.067)*** Healh Knowledge (0.144) (0.079) (0.155) (0.080) Married (0.123) (0.063)* (0.131) (0.065)* Tax*Junior Cer (0.728)* Tax*Leaving Cer (0.763) Tax*Third Level (0.793) Time (0.077) (0.083) Time^2/ (0.470) (0.499) Time^3/ (0.085) (0.090) Consan (0.386)*** (0.100)*** (0.448)*** (0.102)*** Gamma (0.032)*** (0.035)*** Sandard errors in parenheses * significan a 10%; ** significan a 5%; *** significan a 1% 28

30 Table 3: Log-Logisic Duraion Model for Saring Smoking, Smokers Only (N=3202) Junior Cer (0.114) (0.200) Leaving Cer (0.120) (0.213) Third Level (0.122) (0.217)** Ln (Tax) (0.293)* (0.472) Cohor (0.138) (0.140) Healh Know (0.092)** (0.096)** Married (0.071) (0.072) Tax*Junior (0.441)** Tax*Leaving (0.491)* Tax*3 rd Level (0.467)* Time (0.062) (0.063) Time^2/ (0.329) (0.335) Time^3/ (0.053) (0.054) Consan (0.324)*** (0.336)*** Gamma (0.022)*** (0.022)*** Observaions Sandard errors in parenheses * significan a 10%; ** significan a 5%; *** significan a 1% 29