A Dynamic Model of Demand for Private Health Insurance in Ireland

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1 DISCUSSION PAPER SERIES IZA DP No A Dynamc Model of Demand for Prvate Health Insurance n Ireland Clare Fnn Colm Harmon November 2006 Forschungsnstut zur Zukunft der Arbe Instute for the Study of Labor

2 A Dynamc Model of Demand for Prvate Health Insurance n Ireland Clare Fnn Unversy College Dubln Colm Harmon Unversy College Dubln and IZA Bonn Dscusson Paper No November 2006 IZA P.O. Box Bonn Germany Phone: Fax: E-mal: Any opnons expressed here are those of the author(s) and not those of the nstute. Research dssemnated by IZA may nclude vews on polcy, but the nstute self takes no nstutonal polcy posons. The Instute for the Study of Labor (IZA) n Bonn s a local and vrtual nternatonal research center and a place of communcaton between scence, polcs and busness. IZA s an ndependent nonprof company supported by Deutsche Post World Net. The center s assocated wh the Unversy of Bonn and offers a stmulatng research envronment through s research networks, research support, and vsors and doctoral programs. IZA engages n () orgnal and nternatonally competve research n all felds of labor economcs, () development of polcy concepts, and () dssemnaton of research results and concepts to the nterested publc. IZA Dscusson Papers often represent prelmnary work and are crculated to encourage dscusson. Caton of such a paper should account for s provsonal character. A revsed verson may be avalable drectly from the author.

3 IZA Dscusson Paper No November 2006 ABSTRACT A Dynamc Model of Demand for Prvate Health Insurance n Ireland * The Irsh health care system offers a tax fnanced, unversal entlement to publc care at a nomnal user fee, nonetheless 50% of the Irsh populaton purchase prvate health nsurance. Ths paper emprcally models the propensy to nsure as a functon of ndvdual and household characterstcs usng panel data analyss and compares three alternate approaches; a statc, chamberlan-mundlak and dynamc specfcaton. Usng panel data from 1994 to 2000, we consder whether propensy to nsure s n fact a functon of heterogeney or of state dependence. A range of ndvdual and household characterstcs s shown to nfluence propensy to nsure. Overall the posve effect of educaton and ncome and the negatve effect of poor health status reman robust across three specfcatons. In movng toward a dynamc specfcaton, we show that persstence s a hghly sgnfcant determnant of demand for prvate health nsurance and also that reduces the sze of the coeffcents on the regressors. The latter pont hghlghts that whle educaton, ncome and, to a lesser extent, health status have very large effects on probably of nsurng, these effects are overestmated where no attempt s made to control for unobserved heterogeney or state dependence. JEL Classfcaton: G22, I10, D01 Keywords: health nsurance, dynamcs, panel, unobserved heterogeney, state dependence Correspondng author: Clare Fnn UCD Geary Instute Unversy College Dubln Belfeld Dubln 4 Ireland E-mal: * We would lke to acknowledge fundng from the Irsh Research Councl for the Humanes and Socal Scences, the Endeavour Australa Postgraduate and Post-doctoral Research Fellowshp Programme and PRTLI-HEA, as well as the hospaly of the Centre for Health Economcs and Research Evaluaton (CHERE), UTS and the Department of Economcs at Unversy of Melbourne; We are grateful to Dense Doron, Lsa Farrell, Tmothy Fry, Jane Hall, Namh Hardman, Bran Nolan, Carol Propper, Elzabeth Savage, Mchael Shelds and semnar partcpants at Royal Melbourne Instute of Technology, CAER 3 rd Summer Workshop n Health Economcs, the Geary Semnar Seres and members of the UCD-ESRI HRB Health Economcs and Health Gan Programme for helpful comments, as well as the organsers and partcpants of the Mare Cure Tranng Course n Health Economcs 2006, York.

4 1. Introducton Although the Irsh health care system offers a tax fnanced, unversal entlement to publc care at a nomnal user fee, nearly 50% of the Irsh populaton have prvate health nsurance. Whle orgnally establshed n the late 1950 s to provde cover for the top 15% of earners (those nally excluded from the nomnal fee, publc health sector entlement) the proporton of the populaton choosng prvate health nsurance contnues to grow. Irsh health polcy actvely supports the prvate health sector, whch benefs from a number of cross-subsdes, both drect and ndrect, from publc fnances. Ths paper s motvated therefore by two concerns. Frstly what are the socoeconomc and households characterstcs of those who buy? Secondly, what role does polcy play? Most governments espouse equy of access as a goal of health systems, ndeed the WHO use equy n fnancng & accessbly as crera by whch health system performance s judged, from a equy perspectve then could polcy be contrbutng to nequales n access and qualy of healthcare? Tax relef on prvate health nsurance s justfed on the grounds that allows those wh chronc health condons to benef from nsurance at a reasonable cost (Department of Health and Chldren 1999). However, ths polcy reduces the cost of nsurance to everyone, not just the chroncally ll. There s evdence to suggest that the Irsh nsurance system does not suffer from adverse selecton. In fact would seem that those wh poor health status are less lkely to be nsured than those wh good health 1. Ths suggests that tax relef may not be havng the desred effect. Posng the queston, are the systems structures, as they pertan 1 See Doron, Jones and Savage for a fuller dscusson of the relatonshp between SAHS and the purchase pf prvate health nsurance. 2

5 to, adequately protectng some of the more vulnerable, less healthy segments of the populaton? Only a small lerature pertanng to the Irsh nsurance system exsts (Nolan and Wley 2000; Harmon and Nolan 2001; Watson and Wllams 2001). Only one Harmon & Nolan (2001) models the effects of ndvdual and household characterstcs on propensy to nsure focusng on a cross-secton analyss of propensy to nsure n A number of ndvdual and household characterstcs are shown to nfluence the nsurance decson. In lght of the avalably of new data & ndeed of the huge economc growth experenced n Ireland throughout the latter half the 1990 s nto the 2000, ths paper ams to expand on ths exstng work wh a more detaled panel data analyss. The method of estmaton as allowed us explo the panel nature of the data whle attemptng to control for unobserved ndvdual specfc effects. It has also faclated the ncluson of a lagged dependent varable to consder the possble role of state dependence, that s persstence perhaps due to changng preferences or costs assocated wh the nsurance state. Drawng on lerature relatng to utly and nsurance, a theoretcal framework supportng an emprcal nvestgaton of the effect of ndvdual and household characterstcs on the propensy to nsure s provded. Whle patterns of assocaton are evdent emprcally, the extent to whch they are functon of observed heterogeney or state dependence reman unclear. The robustness of certan ndvdual and household effects to the ncluson of a lagged dependent varable s therefore of nterest. The paper proceeds as follows. As the bass for the emprcal nvestgaton, a theoretcal framework s establshed n Secton 2. Secton 3 s a short overvew of the Irsh health 3

6 and nsurance system. Data and prelmnary statstcs are descrbed n Secton 4. Secton 5 focuses on estmaton. Whle results and conclusons are reported n Secton Theoretcal framework: Utly theory and Insurance The decson to nsure has been wdely consdered n theoretcal lerature pertanng to nsurance n general and, more specfcally, to health nsurance (Arrow 1963; Feldsten 1973; Van De Ven and Van Praag 1981; Propper 1989; Besley 1991; Hopkns and Kdd 1996; Besley, Hall et al. 1998; Besley, Hall et al. 1999). The decson to nsure s one of a dscrete choce, to purchase prvate health nsurance or not. A comparson of expected utly under nsurance to expected utly under no nsurance wll nform the nsurance decson (Besley, Hall et al. 1999; Propper 2000). It s antcpated that expected utly gan or loss from the decson to nsure wll be a functon of determnants pertanng to materal well-beng (ncome, educaton, age, famly characterstcs) and medcal need (age, sex, famly characterstcs, health status) (Van De Ven and Van Praag 1981; Propper 1989; Hopkns and Kdd 1996; Besley, Hall et al. 1999). The mpact of materal well-beng and medcal need on the propensy to demand prvate health nsurance s therefore of nterest. To expand on ths n a less formal dscusson, the utly of havng prvate health nsurance (or not) s nfluenced by expected medcal consumpton or probably of sckness. Medcal need s assocated wh uncertanty and as Arrow notes demand for medcal servces s rregular and unpredctable and affords satsfacton only n the event of llness (Arrow 1963). In lne wh ths Propper (1989) observes, health nsurance can only be used n states of ll health. The utly of prvate health nsurance 4

7 when sck therefore s greater than when well 2. Certan ndvdual and household characterstcs are assocated wh a hgher or lower rsk of medcal need, or to put n another way, wh a hgher or lower rsk vulnerably (Hopkns and Kdd 1996). Supported by the theory of adverse selecton, s expected that those wh hgh-rsk vulnerably are more lkely to nsure. Thus we mght expect that those wh poor health status or a chronc condon the elderly (due to decreasng health), the presence of chldren (due to hgher expected medcal consumpton) and females (due to expected future consumpton related to chldbrth) wll all have a posve effect on demand for prvate health nsurance. Spltng rsk vulnerably nto drect and ndrect rsk vulnerably faclates some further consderaton of the ssues n the context of the Irsh nsurance system. Drect rsk vulnerably refers to varables drectly assocated wh medcal need such as past or present health status/healthcare consumpton 3. On the other hand, ndrect rsk vulnerably s assocated wh characterstcs that do not reflect past or present health status but are ndrectly assocated wh medcal need, as such, those wh hgh ndrect rsk vulnerably have a hgher expectaton of medcal need (e.g as suggested earler, older people, females and those wh chldren). Under communy ratng, as exsts n the Irsh system, there s no dfferentaton n premum prce based on rsk. We would expect therefore that those wh hgh ndrect rsk vulnerably (gven that there s no fnancal penaltes for ther ncreased rsk) would be more lkely to nsure. On the other hand, although those wh hgh drect rsk vulnerably (poor past or present health) are not prohbed from nsurng or ndeed 2 Ignorng that gven the state of uncertanty about states of health there may be some utly n beng nsured, partcularly for the rsk adverse 3 For example, low drect rsk vulnerably descrbes good health status whereas hgh drect rsk vulnerably descrbes poor health status or a chronc condon 5

8 charged hgher prema under communy ratng, under a pre-exstng condon clause any health condons experenced pror to the purchase of nsurance are excluded from the terms of the cover for a perod of fve years. Thus the utly of prvate nsurance take-up s less for those who already have specfc health problems as they wll have to wa a consderable perod of tme before they can use. In essence mght be suggested that the nsurance system creates an ncentve for those wh hgh ndrect rsk vulnerably and a dsncentve for those wh hgh drect rsk vulnerably (those who already suffer from specfc medcal condons) to nsure. Thus whle factors such as age, the presence of chldren and females are all expected to have a posve effect on demand for prvate health nsurance, s antcpated, at least n an Irsh context, that poor health status mght be assocated wh a lower propensy to nsure. There s evdence of selecton nto nsurance by ncome (Van De Ven and Van Praag 1981; Propper 1989; Besley, Hall et al. 1999). Income can determne the probably of purchasng prvate nsurance n two ways. The frst s the ntuve expectaton that the hgher the ncome the less the opportuny cost assocated wh the purchase of prvate health nsurance n pure monetary terms (Hopkns and Kdd 1996). The second relates to the opportuny cost of tme. Wh respect to the latter, Propper (1989) notes that one of the costs assocated wh the publc sector s the cost of wang (Propper 1989). To elaborate on ths cost n the context of loss of tme, s noted that the cost of wang s the opportuny cost of healthy tme. It s assumed for those on a wang lst, stock of health s at less than s usual capacy. Therefore llness reduces the amount of healthy tme avalable. The opportuny cost of healthy tme, accordng to Propper (1989) s a functon of ncome, source of ncome and the extent to whch 6

9 ndvduals re-allocate ther use of tme. Both Hopkns and Kdd (1996) and Propper (1989) recognse that those wh a greater constrant on uses of tme have a hgher the opportuny cost and conclude that the value of tme s probably hgher for those who are employed rather than unemployed or not n the labour force, and those on hgher ncomes rather than lower ncomes (Hopkns and Kdd 1996) 4. Besley et al (1998) also focus on the tme loss assocated wh the publc sector wa; they show a posve relatonshp between publc sector wang tme and prvate nsurance take-up. Despe such evdence, Feldsten (1973) notes, wh respect to the US, that ncome mght negatvely affect the decson to nsure, remarkng for a gven probably dstrbuton of health expenses, hgher ncomes tends to make famles more wllng to assume rsk whch n turn reduces ther demand for prvate nsurance and concludes therefore n relaton hs research that the effect of ncome s ndetermnate. He notes that ths nsgnfcant ncome effect may represent a balancng of posve and negatve ncome effects (Feldsten 1973). Hopkns also nvestgated ths possbly and found ths not to be the case n an Australan context. Educaton may mpact drectly on the nsurance decson va s role n health decson-makng (Hopkns and Kdd 1996). Ths explanaton follows from the assumpton that educaton ncreases the effcency of producton of health (Grossman 1972). In short, those who are better educated may not only have greater knowledge and understandng of health nformaton, but are also capable of makng better health- 4 Ths s supported by the theory of household producton as noted by Becker, G. (1965). "A Theory of the Allocaton of Tme." The Economc Journal Vol. LXXV(No. 299): , who recognses that tme use s affected by fnancal resource, and thus that the extent to whch a tme constrant bnd s n the end an ncreasng functon of the opportuny cost of tme of an ndvdual and other members of hs/her household. The explc predcton s that otherwse dentcal people who s ncome are greater wll feel more rushed for tme (Hamermesh 2004). Ths hypothess s emprcally supported by Hamermesh (2004), they fnd that those wh hgher ncomes are more stressed for tme, and conclude that people wh a hgher value of tme are more stressed for tme, not only because they may work more, but because the command that they possess over goods makes them busy spendng ther ncomes Hamermesh, D. (2004). "Subjectve Outcomes n Economcs." Southern Economc Journal Vol

10 related decsons or formulatng better mxtures of health nputs, of whch nsurance mght be one. Ths mght be one explanaton as to why educaton s an mportant correlate of good health (Grossman 1999). Hopkns and Kdd (1996) and Van Praag (1981) both dentfy educaton and ncome as varables that mpact on materal wellbeng. Indeed those wh hgher educaton are also assocated wh beng more future orentated. Becker and Mullgan (1997) argue causaly between schoolng and tmepreference, that s, schoolng causes tme-preference for the future to rse. As such educaton fosters hgher future tme preference among ndvduals and by nducng nvestments that lower the rate of tme preference for the present (n ths case, prvate health nsurance), they may potentally mprove ther future health. Ths leads to an expectaton that those wh a hgher future tme-preference may forgo ncome now n favour of better qualy and faster access to health servces (n the prvate sector) n the future. Age and famly characterstcs, are also assocated wh materal well-beng through ther mpact on both stock of wealth. Age may act as an mportant determnant of propensy to nsure not only because s a varable assocated wh hgh ndrect rsk vulnerably and thus ncreased expected medcal consumpton but also because s also assocated wh ncreased stock of wealth. Stock of wealth generally ncreases as ndvduals/famles get older and as both Van De Ven (1981) and Hopkns and Kdd (1996) note younger ndvduals and famles are generally less well off. Specfc famly characterstcs, relatng to both famly sze and makeup, may nfluence medcal need and materal welfare. The composon of the famly un may mpact on the decson makers attude to rsk (Hopkns and Kdd 1996)- for example, presence of a spouse/and or chldren may make an ndvdual less lkely to assume rsk. In addon, 8

11 also noted by Propper (1989) (Propper 1989) and Ngu et al (Ngu and Burrows 1990) that the health of one famly member may affect the utly of other famly members, leadng them to conclude that famly composon may be a determnant of the decson to nsure. On the other hand the presence of more famly members, partcularly dependents, may lead to a lower famly wealth stock and hence lower the propensy to nsure. In emprcal lerature maral status tends to be posvely assocated and dependent chldren negatvely assocated wh the propensy to nsure (Propper 1989; Hopkns and Kdd 1996; Harmon and Nolan 2001). 3. Overvew of Irsh health and health nsurance system The Irsh health care system s an amalgam of publc and prvate provson and fnancng. Its charactersaton as a tax fnanced, unversal publc health system s somewhat msleadng as devates from ths model n a number of mportant ways. For those who qualfy for a means-tested medcal card, approxmately 30% of the populaton, general practoner servces, publc out and npatent hospal servces, and prescrbed medcaton are all provded free of charge. For the remander of the populaton, GP servces are charged to the user on a fee-per-vs bass, publc out and npatent hospal servces are heavly subsdsed by the state and provded at a nomnal user fee. Prescrbed medcaton s pad for by the user up to a maxmum monthly amount, the excess s then pad for by the state. Another dstnctve feature of the Irsh health system s the hgh proporton of the populaton wh prvate health nsurance, ths despe the exstence of a prmarly tax-fnanced, unversal publc alternatve. The prvate health nsurance system n Ireland was establshed n 1957, provded by a state-backed, non-prof, monopoly nsurer, VHI, was desgned to cater for the 9

12 top 15% of earners who, at the tme, were excluded from an entlement to free or subsdsed publc health servces. In 1987 nomnal charges for outpatent and npatent hospal care were ntroduced by the state, ths was followed n the early 1990 s wh an extenson of publc healthcare entlement to the whole populaton. Snce s ncepton prvate health nsurance n Ireland has operated under communy ratng. Income tax relef on prema has also been a sgnfcant feature of the system; however tax relef prevously pad at the top-rate tax rate pad was reduced to the standard tax rate n the md 1990 s. Under the 1994 Health Insurance Act (Nolan & Wley, 2000) the nsurance market was opened to competon, however communy ratng was retaned and n addon, rsk equalsaton was provded for. Whle theoretcally came nto effect n January 2003, ths has been postponed and contnues to be an ssue of contenton between the two man nsurers, VHI and BUPA, and the government. In 1996 BUPA entered the market and more recently, n 2004, a newly formed health nsurance company, Vvas. VHI, however, retans a sgnfcant market share, 82% to BUPA s 13% (HIA 2003).Wh s orgns to offer hospal cover to those not entled to publc care, prvate health nsurance has manly developed to provde cover for acute hospal care and typcally covers all or most npatent hospal expenses. Prvate outpatent hospal appontments are pad by the user on a pay-per-vs bass, as are GP servces. There remans a hgh deductble on both these servces; therefore nsurance makes a neglgble, f any, fnancal contrbuton to them. 5 In short, prvate health nsurance cover n Ireland s synonymous wh acute hospal npatent care; cover rarely extends 5 Recently both nsurers have begun to offer polces that make some contrbuton to GP, outpatent and other prmary care costs but ther mpact on the market thus far has been neglgble. Also s mportant to note that our data set precedes the avalably of ths type of nsurance polcy. 10

13 beyond the costs assocated wh an acute hospal stay. Although the Irsh health nsurance system s one orgnally desgned to cater for a small proporton of the populaton, there has been a steady and substantal rse n the numbers prvately nsured snce the 1950 s and currently close to 50% of the populaton are nsured. Ths relatvely hgh demand for prvate health nsurance s perhaps not altogether surprsng gven that Irsh health polcy actvely supports the prvate health sector n a number of ways. It s government polcy to contnue to faclate arrangements for prvate healthcare as the cost would otherwse fall on the state (Department of Health and Chldren 1999) A central tenet of the argument supportng ths polcy s not just the cost-savng to the publc system when patents seek treatment n the prvate sector (thereby forgong ther publc entlements and n theory, freeng up of resources n the publc sector for those that reman) but also the transfer of drect revenue to the publc system from the prvate (va nsurance payments, for example). However there s no research assessng the scale of these purported benefs to the publc system (Nolan 2004). It s clear that prvate health nsurance n Ireland s provded at below the true economc cost (Department of Health and Chldren 1999) and n turn, nsurance companes are not charged the full economc cost for prvate patents n publc hospals. 6 In addon to ths there are a number of other more ndrect ways n whch the publc system supports the prvate sector; va tax relef on nsurance purchase at 20%, tax breaks for prvate hospals, a 20:80 publc-prvate bed desgnaton whch s not strctly adhered to 7, a consultant contract whch does not 6 Although attempt to measure the extent of cross-subsdy n monetary terms has been under taken by Nolan and Wley (2001), ths work concentrates manly on areas of drect subsdy e.g. the dfference between what the actual hotel cost of a prvate patent and that charged to the nsurer. 7 Nolan & Wley (2001) note whle there s substantal crossover of prvate patents to publc beds the flow n the oppose drecton s much smaller. 11

14 specfy the extent of tme to publc patents 8 plus rembursement rules that favour the prvate patent. 9. Furthermore, no fees are charged for use of publc hospal equpment & premses when treatng prvate patents. Fnally, more generally acknowledged problems wh prvate medcne are also recognsed. The publc system absorbs cost of professonal tranng, publc hospal development & ndeed, accdent and emergency costs. Hence there seems to exst a szeable resource transfer from publc to prvate 4. Data & Prelmnary Statstcs In explorng the demand for prvate health nsurance n Ireland the Lvng n Ireland Survey s used. Ths s the frst to eghth wave of the Irsh verson of the European Communy Household Panel (ECHP). As ths s a household panel ndvduals from the same household could not be consdered ndependent. Therefore we use a subset of the sample and focus on the household reference person (HRP) as dentfed by the survey 10. Detaled nformaton categorsng ndvduals by nsurance source s avalable. However followng Besley et al (1999), who argue that provded ndvduals face the same costs n purchasng nsurance, eher out of pocket or lower wages, s consdered legmate not to dfferentate between them (Besley, Hall et al. 1999). The econometrc analyss requres consecutve observatons for the ncluson of lagged nsurance and a common date of entry (to the panel) for nal condons. Hence the panel s unbalanced wh absorbng attron. That s, ndvduals reman n the 8 Whle the type-2 consultant contract desgnates a 33-hour week to the publc sector, does not specfy the extent of ther tme commment to publc patents. In practce, publc patents are typcally left to be tended to by nonconsultant hospal doctors (the salary of whom s also pad by from publc health sector fnances), faclatng specalsts wh ths type of contract to concentrate on ther prvate patents. The Health Servce Executve however has recently deemed ths type two contract untenable n the future. 9 In addon to ths, the manner of consultant rembursement ads the preferental treatment of prvately fnanced patents. Although salared for publc, specalsts are pad on a fee per vs for prvate. As observed by Street and Duckett (1996) publc health systems have done ltle to alter the underlyng ncentves whereby those wh the greatest control over the condons of supply are rewarded rather than penalsed for mantanng wang lsts. 10 An alternatve approach mght be to examne the nsurance decson n the context of the famly un as suggested by Propper (1989) 12

15 sample at subsequent waves untl they have mssng nformaton on nsurance status or are not ntervewed at partcular wave, and drop out due to attron, ndvduals may ex the sample but no new ndvduals are added and ndvduals wh mssng data n 1994 are excluded. An examnaton of the characterstcs of those n our sample wh and whout prvate health nsurance provdes some nterestng nsghts 11. There exsts a clear dspary wh respect to percentage nsured across both educatonal and ncome levels, suggestng that the selecton nto nsurance by both those wh hgher ncomes and better educaton s substantal. Only 20% of those wh prmary educaton have prvate health nsurance, whle 86% of those who completed thrd level are nsured. Smlarly, of those n the lowest ncome quartle only 16% were nsured compared wh 59% of those n the hghest. Ths renforces the expectaton that propensy to nsure s assocated wh both educaton and ncome. ABOUT HERE- Table 1: percentage nsured Self-reported health status also regsters a notable dfference n percentage nsured. Those wh good health status are almost twce as lkely to be nsured (49%) compared wh those wh poor health status (23%). Ths does not seem to support the exstence of adverse selecton. Also worthy of note, those marred or wh partners have a hgher percentage nsured than those who are never marred or whout partners. Fnally the year old age group has the hghest percentage nsured. 11 The percentages reported here are from the HRP sample, however almost dentcal results are found for the full sample. See Appendx for a comparson of HRP and full sample descrptve statstcs. 13

16 ABOUT HERE- Table 2: Varable means A comparson of varable means for both the full and HRP sample shows that the HRP sample s a ltle less educated, older, less lkely to be eher sngle (unmarred) or whout a partner and wh slghtly poorer health status. In the full sample at wave 1 n % of the nal sample were nsured. The percentage nsured contnues to grow reachng over 48% by 2001, reflectng approxmately the proporton nsured n the populaton (Nolan and Wley, 2001). Ths also reflects closely the percentage of the populaton nsured n the sample of household representatve person used here. Furthermore an examnaton of transonal probables suggests consderable persstence n the nsured state. The frst row (Table 3) (for both samples) shows the probably of beng nsured n tme t condonal on beng nsured n t-1. Whle the second row represents the probably of beng nsured n tme t condonal on beng unnsured n tme t-1. The results suggest that havng nsurance n year t-1 s a good ndcator of whether you wll nsure n year t. ABOUT HERE- Table 3: ncdence and persstence 5. Statstcal framework In ths secton we model the decson to nsure n a lmed dependent varable framework. Usng a bnary ndcator, the ndependent varable,, represents the nsurance state of ndvdual n tme t, takng the value of 1 f the ndvdual nsures I and 0 otherwse. As such, I 1 ( * I > 0) = where 1(.) s the ndcator functon takng a 14

17 value of uny f the expresson n parenthess s true and zero otherwse. The basc model s specfed as: I * = β + βx + ν, where =1,2.N, t=1,2 7. (1) o A vector of ndvdual and household characterstcs as ndcated by X. The represents the compose error, s composed of unobserved heterogeney or unobserved tme fxed effects a and the dosyncratc error term u. ν v = a + u, (2) To control for ndvdual specfc unobserved effects, an unobserved effects bnary response model was consdered. In specfcatons (3) and (4) a represents the unobserved ndvdual specfc effect. Under random effects (3) we assume that a and u are normally dstrbuted and ndependent of X. * I = β + β X + a + u, where =1,2, 3.N; t=1, 2,3.N (3) 0 It s also assumed that there s no seral correlaton n and the X. Independence between the, are necessary for consstent results. If the assumptons for RE hold then random effects model s the most effcent and thus the preferred estmator. u a 15

18 If s assumed that the unobserved ndvdual effects are correlated wh the a X then a fxed effect specfcaton s approprate. Under the fxed effect specfcaton correlaton between the a and one or more of the X s assumed. * I = β X + a + u, where =1, 2,3.N; t=1, 2,3.N (4) Followng from ths, a Hausman test to determne random or fxed effects usng log rejects a random effects specfcaton (3) and suggests a legmate concern about unobserved effects. However, whle a fxed effects specfcaton would allow us control for unobserved effects correlated wh the explanatory varables, there s a problem wh usng a fxed effects specfcaton n ths nstance; drops tme nvarant effects, both observed and unobserved, from the model. Thus tells us nothng about varables that do not vary over tme, many of whch are varables of nterest, such as educaton. As such, f our am s to examne the ndvdual and household effects, a model that tells us ltle about tme-nvarant effects s not deal. Ths prompted us to take another approach. To control for unobserved ndvdual effects whle also ncludng explanatory varables such as educaton (whch for the most part s not expected to change over tme) we ntroduce a thrd specfcaton (5), ths takes the form of Mundlak-Chamberlan s Random Effects Model. Ths approach, dealng wh ndvdual effects correlated wh the regressors, specfes the E ( X a ) (Chamberlan 1984). A specal case, assocated wh earler work by (Mundlak 1978), uses the whn-ndvdual means of the regressors. If the assumpton of ndependence between the a and X s volated the results wll be nconsstent. We relax the 16

19 assumpton that a s ndependent of the X and attempt to control for ndvdual specfc unobserved effects correlated wh the X wh the ncluson of x, hence modelng the dependence between the a and X. Typcally ths has taken the form of a vector of tme means of tme-varyng varables, the assumpton beng that the regresson functon of the a s lnear n the tme means of tme-varyng varables (Propper and Burchardt 1999; Arulampalam, Booth et al. 2000; Propper 2000). In ths case we use only ncome as ths varable s expected to do reasonably well at capturng unobserved personaly tras assocated wh the decson to nsure, lke taste for qualy etc. In specfcaton (5), x and a represent unobserved ndvdual heterogeney. The x s the part of the unobserved ndvdual heterogeney correlated wh the X whch we attempt to model and the effects specfcaton. a n now not correlated as n a normal random * I = β + β X + x + a + u, where =1, 2,3.N; t=1, 2,3.N (5) 0 Whle certan observable characterstcs are shown to nfluence propensy to nsure, demand for prvate nsurance may persst for other reasons. Unobserved heterogeney, such as attude to rsk or taste for qualy, mght affect demand for nsurance, so mght state dependence. The latter refers to a causal relatonshp between past and current nsurance status. In short, an ndvdual unnsured n year t-1 wll behave dfferently n year t to an otherwse dentcal ndvdual nsured n year t-1. Ths mght result from an ndvdual changng preferences due to past experence of prvate nsurance or as noted by Propper (2000) from the cost of nformaton assocated wh changng nsurance 17

20 status. Descrptve statstcs gve ndcatons of very hgh nsurance persstence. To faclate examnaton of the effect of havng nsurance n year t-1 on propensy to nsure n year t and thereby consder the effect of persstence, a dynamc random effects prob model, (ncludng lagged dependent varable and correcton term whle also controllng for unobserved heterogeney) s consdered (Orme 1996; Arulampalam, Booth et al. 2000; Propper 2000). The model s specfed as follows. * β o + βx + ρi, t 1 + a1 I = X + δe + a + u, where =1,2,.N; t=2,3.n (6) As before * I represents the nsurance state of ndvdual n tme t. A vector of contemporaneous ndvdual and household characterstcs as ndcated by. The represents unobserved ndvdual heterogeney and the dosyncratc error term. X u a I s a lagged dependent varable representng the nsurance state n the prevous, t 1 year. The x s mean ncome, the tme-varyng explanatory varable, of ndvdual over tme and s ncluded to pck-up possble correlaton between the tme-varyng regressors and any unobservable heterogeny (followng Chamberlan (1984), Mundlak (1978) and outlned n Arulampalam, Booth et al (2000), Propper (2000)), allows us to model the dependence between the a and the X by assumng the regresson functon s lnear n the means of the tme varyng covarates, n ths case ncome. δ e sgnfes the nal condon correcton term. The a represents unobserved ndvdual heterogeney; s the ndvdual specfc and tme-nvarant random component. 18

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