The Aggregate Demand for Private Health Insurance Coverage in the U.S.

Transcription

1 Universiy of Connecicu Economics Working Papers Deparmen of Economics The Aggregae Demand for Privae Healh Insurance Coverage in he U.S. Carmelo Giaccoo Universiy of Connecicu Rexford E. Sanerre Universiy of Connecicu Francis W. Ahking Universiy of Connecicu Follow his and addiional works a: hp://digialcommons.uconn.edu/econ_wpapers Recommended Ciaion Giaccoo, Carmelo; Sanerre, Rexford E.; and Ahking, Francis W., "The Aggregae Demand for Privae Healh Insurance Coverage in he U.S." (2005). Economics Working Papers. Paper hp://digialcommons.uconn.edu/econ_wpapers/ This is brough o you for free and open access by he Deparmen of Economics a DigialCommons@UConn. I has been acceped for inclusion in Economics Working Papers by an auhorized adminisraor of DigialCommons@UConn. For more informaion, please conac digialcommons@uconn.edu.

2 Deparmen of Economics Working Paper Series The Aggregae Demand for Privae Healh Insurance Coverage in he U.S. Carmelo Giaccoo Universiy of Connecicu Rexford E. Sanerre Universiy of Connecicu Francis W. Ahking Universiy of Connecicu Working Paper Ocober Mansfield Road, Uni 1063 Sorrs, CT Phone: (860) Fax: (860) hp:// This working paper is indexed on RePEc, hp://repec.org/

3 Absrac This paper esimaes he aggregae demand for privae healh insurance coverage in he U.S. using an error-correcion model and by recognizing ha people are wihou privae healh insurance for volunary, srucural, fricional, and cyclical reasons and because of public alernaives. Insurance coverage is measured boh by he percenage of he populaion enrolled in privae healh insurance plans and he compleeness of he insurance coverage. Annual daa for he period are used and boh shor and long run price and income elasiciies of demand are esimaed. The empirical findings indicae ha boh privae insurance enrollmen and compleeness are relaively inelasic wih respec o changes in price and income in he shor and long run. Moreover, privae healh insurance enrollmen is found o be inversely relaed o he povery rae, paricularly in he shor-run. Finally, our resuls sugges ha an increase in he number cyclically uninsured generaes less of a welfare loss han an increase in he srucurally uninsured. Journal of Economic Lieraure Classificaion: I10 We have received many helpful commens from Mark Pauly, Barbara Beliveau, Dave Gulley, John Harding, Saff Johnson, Seve Miller, Tom O.Brien, and John Vernon. We also hank wo anonymous referees of his journal for helpful commens on an earlier version of his paper. All remaining errors are our responsibiliy.

4 I. Inroducion On a yearly basis, abou 14 o 16 percen of he U.S. populaion ends o be uninsured (DeNavas-Wal, Procor, and Lee, 2005). Many of he involunarily uninsured face he sharp psychological sing from he financial insecuriy ha can resul from an unexpeced medical occurrence. In addiion, uninsured individuals are more likely o find hemselves in he emergency room of a hospial, someimes afer i is oo lae for proper medical reamen, wih heir resuling poorer healh and shorer lives causing sizeable social coss. Indeed, Miller e al. (2004) esimae a lower bound dollar value of he healh forgone because of uninsurance in he U.S. a $65 o $130 billion per year. Thus, reducing he uninsured populaion seems a legiimae social goal and idenifying why some people are wihou privae healh insurance coverage becomes a valuable endeavor for public policy purposes. Logic suggess ha people are wihou privae healh insurance for a variey of reasons. Firs, in a privae healh insurance sysem, some people aler heir purchasing of healh insurance in response o changing economic circumsances such as he price of insurance or heir income jus like hey change heir demands for oher goods and services. Tha is, some people may choose o be wihou privae healh insurance coverage or may choose only minimal coverage. For example, an individual may decide o self-insure because she expecs o gain lile from marke provided healh insurance as a resul of is high price relaive o expeced medical benefis paid ou. In his case healh insurance is a negaive ne presen value invesmen, hence i is raional no o buy insurance. Bu some people may be wihou privae healh insurance coverage for reasons oher han is volunary naure. By borrowing from he differen classificaions for unemploymen offered by labor economiss, hree caegories of uninsurance can be specified, alhough admiedly hese 2

5 classificaions are no muually exclusive in he conex of uninsurance. Firs, some people may lack privae healh insurance coverage during a paricular ime period because hey become fricionally uninsured. Fricional uninsurance considers ha some people erminae one job ha offered healh insurance and are searching for anoher job. In fac, COBRA of 1985 was developed expressly wih fricional uninsurance in mind by requiring employers wih more han 20 workers o allow former employees and heir dependens he opion o reain heir healh insurance coverage for up o 18 monhs afer erminaing employmen. However, given ha his Ac requires he fricionally uninsured o pay he full premiums and an adminisraive fee of 2 percen, only abou 20 percen of hose eligible exend heir healh insurance under COBRA while in-beween jobs (Madrian, 1998). Fricional uninsurance also occurs when people are emporarily wihou privae healh insurance because of a mismach of informaion. Because of imperfec informaion, consumers ake ime o shop around for he righ insurers while healh insurers search for he righ cusomers. I sands o reason ha insurance agens and brokers can impac he number of individuals fricionally uninsured and he duraion of fricional uninsurance by providing imely and reliable informaion (Conwell, 2002). Wihin he conex of fricional uninsurance, Swarz, Marcoe, and McBride (1993) find ha monhly family income, educaional aainmen, and indusry of employmen in he monh prior o losing healh insurance are he characerisics wih he greaes impac on he duraion of a spell wihou healh insurance. Second, he srucurally uninsured comprise anoher caegory of hose wihou privae healh insurance. Included in he srucurally uninsured caegory are hose individuals who are wihou healh insurance on a long-run basis because of chronic illnesses, pre-exising condiions, employmen ha does no offer healh insurance coverage, and/or insufficien income. Finally, hose 3

6 individuals cyclically uninsured make up he las caegory of uninsurance. Cyclical uninsurance perains o hose individuals (and heir families) who change insurance saus as hey drif in and ou of jobs offering group healh insurance benefis as he macro-economy normally expands and conracs in he shor-erm. Cyclically uninsured individuals end o possess low-skills and may flucuae beween working in small and large firms over he course of he business cycle. Oher han volunary, fricional, srucural, and cyclical uninsurance, he exisence of public healh insurance alernaives may provide anoher explanaion for he flucuaions in he percenage of he populaion covered by privae healh insurance. Boh Medicare and Medicaid were enaced in Since ha ime, eligibiliy in boh programs has expanded. Thus he creaion and expansion of hese wo public programs may have influenced he number of individuals wih privae healh insurance coverage. In sum, a any poin in ime, some people may no be covered by privae healh insurance because of is volunary naure, public healh insurance alernaives, or heir saus of being fricionally, srucurally, or cyclically uninsured. Obviously, he mix of people lacking privae healh insurance for hese specific reasons will change over ime in response o varying marke condiions and personal circumsances. No surprisingly, various sudies have aemped empirically o sor ou he differen reasons why people remain wihou privae healh insurance coverage. Mos of he sudies focus on he volunary naure of privae healh insurance and have esimaed he demand for employer-provided healh insurance a he micro level o gauge is sensiiviy o variaions in price and income. These sudies end o agree ha he demand for healh insurance is relaively inelasic wih respec o changes in boh price and income (e.g., Taylor and Wilensky, 1983; Marguis and Long, 1995; and Liu and Chrisianson, 1998). Recenly, a couple of 4

7 sudies have quesioned he impac of macroeconomic forces on cyclical uninsurance using micro daa ses. Culer (2002) finds ha employer-sponsored healh insurance fell during he boom of he 1990s primarily because fewer employees ook up coverage when i was offered. His esimaes sugges ha increased coss o employees explain he enire reducion in ake-up raes during he 1990s. Cawley and Simon (2003) find ha he probabiliy of any insurance is inversely relaed o sae unemploymen and direcly relaed o sae GDP. The evidence in heir sudy, however, does no suppor he predicion of a negaive impac of a naional recession on healh insurance coverage raes. In fac, some of heir findings indicae a direc and saisically significan relaionship beween he exisence of a naional recession and he insurance rae. While hese sudies have provided valuable insighs abou he forces shaping he demand for privae healh insurance, he available empirical evidence is incomplee for several reasons. Firs, he exising empirical lieraure is mosly based on a saic analysis of cross-secional micro-level daa. In some cases, e.g., Culer (2002) and Cawley and Simon (2003), he panel daa include repeaed measuremens over en o fifeen years. Bu he ime period is oo shor o allow a horough invesigaion of he economic forces ha cause he level of privae healh insurance o rise and fall over ime. Second, in he presence of sochasic non-saionary rends commonly found in variables such as he percen wih privae healh insurance, sandard saisics such as -saisic, R 2, and Durbin-Wason may lead o erroneous conclusions. While hese saisics are properly specified for cross-secional daa, i is well known ha ime series require a differen economeric mehodology for proper inference. For example, i is possible ha some observed significan correlaions over ime may be simply due o he phenomenon of spurious regression (Granger and Newbold, 1974). Third, he empirical models in previous sudies implicily assume ha he esimaes represen long- 5

8 run equilibrium, where people are conen wih being wih or wihou healh insurance or wih a cerain amoun of insurance coverage. However, shor run disequilibrium siuaions are likely o occur as decision-makers balance he cos of being away from heir preferred posiions and he cos imposed by he adjusmen process iself. Consequenly, hese previous sudies may have failed o capure some imporan informaion abou he shor run dynamics characerizing he decision o purchase privae healh insurance. To capure boh long run and shor run dynamics, his paper esimaes he aggregae demand for healh insurance in he U.S. using an error correcion model. 1 The error correcion model incorporaes a dynamic adjusmen process in response o emporary and permanen shocks o privae healh insurance enrollmens. In addiion, he model incorporaes he cos of being away from a long run aggregae equilibrium level of privae insurance. This equilibrium level should be dependen on macroeconomic facors such as GNP, naional ax policy, growh of jobs in service secor, ec. Thus, boh shor run and long run demand elasiciy esimaes can be derived. This sudy explois a previously overlooked naional daa series on privae healh insurance coverage in he U.S. and considers he volunary naure of privae healh insurance as well as is fricional, srucural, and cyclical aspecs. In he nex secion, he daa on privae healh insurance coverage are described more fully and racked over ime. Secion III inroduces he basic demand model and discusses he daa used in he empirical es while secion IV develops an error correcion model o explain variaions in he privae healh insurance coverage rae. Secion V provides concluding commens and policy implicaions. II. Time Series Daa on Privae Healh Insurance Coverage Raes in he U.S. The Healh Insurance Associaion of America (HIAA) independenly gahered and issued 6

9 informaion on he healh insurance enrollmen of he U.S. populaion since he 1940s bu heir daa collecion apparenly ended in he mid-1990s. Now HIAA simply repors Census daa in heir annual guide. The U.S. Census Bureau began sysemaically collecing and reporing daa on he healh insurance saus of he U.S. populaion since he mid-1980s. By combining hese wo series, he percenage of he populaion enrolled in privae healh insurance can be viewed over ime. Combining he wo daa series does no seem o be problemaic as hey are fairly close over eigh overlapping years wih privae healh insurance enrollmen figures differing by only 0.5 percen, on average. Since mos of our daa are from he period 1960 o 1999, we focus exclusively on ha period in he ensuing discussion. According o he naional daa repored by he HIAA and Census Bureau, enrollmen in privae healh insurance has varied considerably over ime. For example, Figure 1 illusraes ha enrollmen in privae healh insurance plans as a percenage of he populaion sood a nearly 66 percen in 1960, increasing a abou 1 percenage poin per year o roughly 76 percen of he populaion by From 1970 o 1980, enrollmen in privae healh insurance coninued o expand bu he rae of growh slowed o less han one-half of a percenage poin per year oaling 81 percen of he US populaion in The daa furher show ha enrollmen in privae healh insurance peaked in he lae 1970s and early 1980s. Afer ha poin, he privae healh insurance coverage rae coninued o fall hroughou he res of he 1980s and mos of he 1990s. Only afer 1997 did he downrend in he percenage of he US populaion covered by privae healh insurance begin o increase once again. Ineresingly, he percenage of he U.S. populaion covered by privae healh insurance increased by only a mere 5 percenage poins over he enire 40 year period. 7

10 The Cener for Medicare and Medicaid Services publishes yearly daa ha can be used o calculae he fracion of consumer expendiures on personal healh care iems ha is reimbursed by privae insurance companies. These annual figures rack he compleeness of healh insurance coverage over ime and are repored in Figure 2 also for he period from 1960 o Noice ha privae healh insurance covered less han 30 percen of personal healh care in 1960 bu rose o nearly 70 percen by Also noice ha he growh in he compleeness of healh insurance coverage slowed briefly during he mid-1970s, mid-1980s, and lae 1990s. Overall, he ime series daa on privae healh insurance enrollmen and he compleeness of coverage do no display he ypical paern of a saionary process (consan uncondiional mean and variance). To our surprise, boh series look more like (near) random walks wihou drif; he enrollmen series crossing is mean value (74 percen) only wice: firs in 1968 and again in 1988, and he compleeness series crossing is mean value (0.51) only once. If privae healh insurance coverage can be modeled as a nonsaionary variable, he implicaion is raher sarling: a shock o he process will no die ou -- even in he long run. For example, suppose a negaive shock during a recession causes he loss of a cerain number of high qualiy jobs (i.e., jobs wih medical coverage), and if hese jobs are los permanenly, hen he shock o he coverage rae will also be permanen. I follows ha some imporan informaion migh be gained by modeling boh he shor run dynamics and long run behavior of he privae healh insurance coverage rae. Consequenly, in his paper, we empirically invesigae wheher he privae healh insurance enrollmen and compleeness raes can be modeled as non-saionary variables and wheher hese raes are coinegraed wih a se of underlying facors such as real per capia income, price of privae healh insurance, union membership, ec. The empirical analysis is couched in erms of an aggregae demand for privae 8

11 healh insurance. The coinegraion regression models and he concomian error correcion represenaions allow us o examine empirically boh he long run and shor-run dynamic properies of he aggregae demand for privae healh insurance. In he nex secion, he long run equaion for he aggregae demand for privae healh insurance is specified and he specific variables and daa used in he empirical es are discussed. III. Modeling he Aggregae Demand for Privae Healh Insurance Sandard uiliy heory suggess ha he quaniy demanded of healh insurance, Y, can be wrien as a funcion of he user price of healh insurance, P, income, I, and a vecor of oher facors, Z or (wih ime subscrips suppressed): Y β + β P + β I + Z. (1) = β 3 Suppose all of he variables are expressed as logarihms, he slope parameers can be reaed as elasiicies. Thus, β 1 and β 2 represen, respecively, he price and income elasiciies of he demand for privae healh insurance. Equaion (1) represens a saic demand funcion devoid of a ime dimension. I is well known, however, ha demand heory offers lile guide as o he dynamic adjusmen process when he marke is emporarily ou of equilibrium. In he nex wo subsecions, we discuss a number of economeric issues ha arise when we esimae a dynamic version of he demand model (secion III.A) and he daa specificaions (secion III.B). III.A Economeric Specificaion Issues Firs, as menioned above, equaion (1) is a simple represenaion of a long run seady-sae equilibrium aggregae demand funcion. However, in he shor run, user price (P) or income (I) may no adjus quickly enough o clear he marke; hence he equaliy may no hold exacly. The error 9

12 correcion model is a formal mehodology o characerize he adjusmen process ha allows deviaions from equilibrium in he shor run bu no he long run. Second, i is likely ha an expeced change in curren (or fuure) employmen or income level will impose ransiion coss on individuals. These coss imply ha demand for healh insurance will depend no only on he curren values of P and I bu also on raional forecass of hese variables. Hence, lagged variables should be an inegral par of equaion (1) o he exen ha pas values are useful in predicing fuure values. Third, microeconomic heory offers lile guide as o wha facors -- besides price and income, migh influence he demand for healh insurance. One possible way o selec he elemens of Z is o consider employmen relaed characerisics of individuals, such as, for example, is he person employed or unemployed? Does he or she belong o a union? Is he person employed in he service indusry? If hese characerisics are measured as zero-one dummy variables, hen he inercep in Equaion (1) becomes β+z j where he subscrip applies o he jh economic agen a each poin in ime ; hence he inercep in he demand equaion will vary across individuals. An advanage of his approach is ha while price and income elasiciies (β 1 and β 2 ) are sill consan, a varying inercep capures how differen characerisics migh influence healh insurance demand. Ideally, he empirical analysis should be based on a sample of repeaed measures of demand for he same group of individuals over a long period of ime. While cross-secional daa are readily available, he ime-span of hese daa ypically covers only a dozen years or less. One poenial soluion ha will enable us o analyze he demand for healh insurance over a much longer period of ime is o aggregae daa cross-secionally, and divide by he number of economic agens during each period o obain a ime series of per-capia demand. Furher, employmen characerisics are 10

13 proxied by percen employed in service indusries, union membership rae, unemploymen rae, ec. A relaed economeric problem is wheher he coefficiens of he demand equaion are likely o remain consan for observaions gahered over a long period of ime. The inclusion of he conrol Z variables offers a simple mechanism o accoun for poenial srucural shifs. III.B Daa Specificaion Issues In he empirical analysis below, all variables are ransformed by aking he naural logarihm so ha he esimaed parameers measure elasiciies. The quaniy demanded of healh insurance is measured in wo ways: he percenage of he populaion wih privae healh insurance as depiced in Figure 1 (henceforh denoed as LPRIVATE ), and he compleeness of he healh insurance coverage ( LCOVERAGE ), measured as he fracion of consumer personal healh care spending reimbursed by insurance, as shown in Figure 2. Following he economics of healh insurance lieraure, he user price of privae healh insurance ( LPRICE ) is specified as ln(( 1 e * r) * LF). As specified, he user price depends on he marginal ax rae on wage income, r, he fracion of healh insurance premiums exemped from axaion, e, and he loading fee, LF, expressed as premiums divided by medical benefis paid ou. Theory suggess ha he user price of healh insurance falls wih a higher marginal ax rae and exemp fracion bu rises wih a greaer loading fee. The user price of healh insurance is expeced o have an inverse relaionship wih our wo measures of he quaniy demanded of healh insurance. For empirical purposes, he marginal ax rae on wage income is measured solely by he annual average marginal federal ax rae. Daa for he yearly average social securiy ax rae and average sae income ax rae, which also should be included in he measuremen of he marginal ax rae on wage income, are unavailable for he enire period from 1960 o 1999, unforunaely. The 11

14 fracion of premiums exemped from axaion, e, is proxied by one minus he fracion of he workforce ha own heir own businesses. Up unil 2003, he self-employed were unable o ake a 100 percen exempion for healh insurance premiums. 3 Per capia real disposable income ( LINCOME ) represens income in he empirical analysis. A direc relaion is expeced beween per capia real disposable income and boh LPRIVATE and LCOVERAGE, given ha mos sudies have found ha privae healh insurance represens a normal good (Sanerre and Neun, 2004). Included among he Z vecor of independen variables are he federal povery rae ( LPOVERTY ), he percenage of naional employmen in service indusries ( LSERVICE ), he naional unemploymen rae ( LU ), he labor unionizaion rae ( LUNION ), he percenage of he populaion covered by Medicare ( LMCARE ), and he percenage of he populaion covered by Medicaid ( LMAID ) (only in he LPRIVATE equaion). The federal povery rae and percenage of naional employmen in service indusries, conrol for he likelihood of srucural uninsurance. In he absence of public programs, poor households lack he wherewihal o purchase healh insurance. In addiion, shifing employmen paerns among indusries are beyond he conrol of individuals in he labor marke and can ulimaely influence long-erm paerns of uninsurance. 4 More precisely, Long and Rodgers (1995) noe ha employmen paerns have shifed from manufacuring where radiionally healh insurance has been rouinely sponsored by employers o he service indusries where employer-sponsored healh insurance has no been as widespread. An inverse relaion is expeced beween boh he federal povery rae and he percenage of economy-wide employmen in he service secor and he percenage of he populaion wih privae healh insurance. We also expec ha povery will be inversely relaed wih he 12

15 compleeness of he healh insurance coverage because of he inabiliy o pay bu hold no priors for he relaionship beween service secor employmen and insurance compleeness. The percenage of he labor force belonging o a union is inended o capure he degree of fricional uninsurance. Long and Sco (1982) argue ha unions provide informaion abou he availabiliy and imporance of employer-sponsored healh insurance benefis o workers. Alernaively, union jobs are good jobs wih rens ha ake he form of benefis. For hese wo reasons, he number of individuals wih privae healh insurance should be greaer when a larger percenage of he workforce belongs o a union, ceeris paribus. The unemploymen rae, as a reflecion of cyclical uninsurance, is expeced o be inversely relaed o he percenage wih privae healh insurance coverage. We also expec a direc relaionship beween union membership and he compleeness of healh insurance coverage bu hold no priors for he relaionship beween he laer variable and he unemploymen rae. The availabiliy of public healh insurance may affec he demand for privae healh insurance coverage so he percenage of individuals covered by he Medicare and Medicaid programs are also specified in he esimaion equaion. The precise relaion beween Medicare enrollmen and he percen of he populaion wih privae healh insurance is heoreically unclear. On he one hand, elderly individuals are required o enroll in Par A of Medicare. This requiremen ends o reduce he number of individuals wih privae healh insurance. However, Medicare enrollees ofen purchase Medigap, as a privae insurance complemen o heir public insurance, because i covers medical expenses no reimbursed by Medicare. Also for some individuals, Medicare represens he secondary payer because hey are also covered by employer-sponsored healh insurance. Thus, he ne impac of a growing percenage of he populaion covered by 13

16 Medicare on he percenage of he populaion wih privae healh insurance and he compleeness of healh insurance coverage is heoreically unclear. The heoreical relaionship beween enrollmen in he Medicaid program and privae insurance is less ambiguous. The hypohesis is ha he Medicaid program crowds-ou privae healh insurance (Culer and Gruber, 1996). Thus an inverse relaionship is anicipaed beween he percenage of he populaion enrolled in Medicaid and he percenage of he populaion wih privae healh insurance. The percenage of he populaion covered by Medicaid is no expeced o have any effec in he insurance compleeness equaion, however, because he wo variables are unrelaed since Medicaid subsiues compleely for privae healh care expendiures and no balance billing is allowed. Daa for Medicaid enrollmen is measured as person-year equivalens as repored in Klemm (2000). In sum, he quaniy demanded of privae healh insurance, as capured by boh enrollmen and compleeness of insurance coverage, should be found inversely relaed o price and direcly relaed o income in he empirical analysis. Moreover, an inverse relaionship is anicipaed beween enrollmen in privae healh insurance plans and he federal povery rae, he naional percenage of employmen in service indusries, he unemploymen rae, and he Medicaid coverage rae. Greaer unionizaion should be associaed wih increased paricipaion in privae healh insurance plans. The relaionship beween Medicare and privae healh insurance coverage rae is unclear heoreically. In addiion, he compleeness of insurance coverage is expeced o be inversely relaed o he povery rae, direcly relaed o income and union membership rae, and we have no prior expecaion as o is relaionship o percenage of employmen in he service indusries or he unemploymen rae. Appendix A conains he definiion of our variable names, heir sources, he mean, sandard 14

17 deviaion, minimum and maximum value of each of hese variables. Sample daa are annual observaion from 1960 o 1999, excep for Medicare and Medicaid which did no exis prior o Noe ha because all our variables are found o be non-saionary (see Secion IV.A below), he saisics on he mean and sandard deviaion are inended only o provide summary descripion of he ime series variables for he sample period, and do no represen saisical populaion measures. Finally, as menioned earlier, before any acual economeric analysis is carried ou, we ransform all he variables by aking he naural logarihm of hese variables. This allows us o inerpre he esimaed coefficiens as elasiciies. IV. IV.A Empirical Analysis of he Aggregae Demand for Privae Healh Insurance Uni Roo Tess We begin our empirical analysis by firs examining he ime series properies of our daa. We firs plo and also calculae he auocorrelaion and parial auocorrelaion funcions of he level and firs-difference of he daa. Preliminary analysis srongly suggess ha he daa are nonsaionary. As Granger and Newbold (1974) observed many years ago, nonsaionariy may be he rule raher han he excepion for macroeconomic ime series daa. Moreover, regression wih nonsaionary variables may lead o spurious regression resuls. There are, however, several empirical mehodologies ha have been developed for regression wih nonsaionary variables. The mos popular being he coinegraion ess of Engle and Granger (1987) and Johansen (1988). Coinegraion es, however, requires ha he ime series variables are inegraed processes of he same order. For example, an inegraed process of order d 1, denoe as I (d) conains d uni roos. Accordingly, we sar wih he augmened Dickey-Fuller (ADF) es for one uni roo. The ADF regression ha we use is: 5 15

18 X = a0 + a X 1 + φ + ε, (2) 1 k i= 1 i X i where is he firs difference operaor, and ε is a covariance saionary zero mean process. The null hypohesis for he presence of a uni roo corresponds o a = 1 0. We use he BIC mehod o choose he lag lengh k, allowing for a maximum of k = 6. We also iniially include a linear ime rend in Equaion (2) o allow for he possibiliy ha he nonsaionariy may be he resul of a deerminisic rend. The individual -saisic on he coefficien 2 of he ime rend is never saisically significanly differen from zero, however, and a χ es on he join hypohesis of a uni roo and he absence of a linear ime rend is no rejeced in all cases. For hese reasons, we omi a linear ime rend from our repored ADF regressions. Table 1 displays he resuls of our uni roo ess where we repor he value of k, he esimaed value of a 1 and is corresponding -saisic, and he Ljung-Box Q-saisic, which is a 2 pormaneau es for serial correlaion in he residuals. The Q-saisic is disribued as χ, and we calculae he Q-saisic over welve lags, wih he degrees of freedom indicaed in parenheses nex o he saisic. The criical values for he -saisic are no sandard bu may be found in Fuller (1976), and he 5% criical value is 2.94 for our sample size. As can be seen, we canno rejec he null hypohesis of a uni roo for any of our en variables. Moreover, he Q-saisics sugges ha he hypohesis of serially uncorrelaed residuals is no rejeced a he 5% significan level in all cases excep for LSERVICE, which is no rejeced a he 1% significan level. The Q-saisic for LSERVICE is dominaed by a few relaively large coefficiens, especially a lags 2, 7, and 9, and adding addiional lags o he ADF regression for his variable did no improve he Q-saisic significanly. Since here is no obvious explanaion for he correlaions a hese lags, we conclude 16

19 ha hey are mos likely spurious. Based on hese resuls, we enaively conclude ha all our variables conain a leas one uni roo. We es nex for a second uni roo. The esing procedure follows exacly ha of our es for one uni roo, excep ha all variables used in Equaion (2) are differenced a second ime. The lag lengh is once again chosen using BIC. As we can see from Table 1, he null hypohesis of a second uni roo is uniformly rejeced a he 5% significan level. Noe, however, he Q-saisic for LU is no rejeced only a he 1% significan level, and a 0.5% level of significance for LSERVICE. Once again, he Q-saisics for hese wo variables are dominaed by a few relaively large coefficiens a relaively high order lags, suggesing again ha hey are mos likely spurious. Moreover, an examinaion of he plos, auocorrelaion and parial auocorrelaion funcions of he firs difference of hese wo variables did no reveal srong evidence of a second uni roo. Based on he resuls in Table 1, we conclude ha all our variables could be adequaely represened by a firs-order inegraed process, i.e., I(1) process. Of course, he uni roo hypohesis canno be sricly correc because many or our variables are expressed as percenages, and are bounded beween zero and one. In conras, a sochasic process characerized by a uni roo has infinie variabiliy. Bu as Hall, Anderson and Granger (1992) poin ou; he uni roo hypohesis is a reasonable working assumpion for he purpose of model building. IV.B Error Correcion Represenaion and Coinegraion The uni roo ess of he las secion uniformly rejec he saionariy hypohesis. I seems naural, herefore, o explore he possibiliy of a co-inegraing relaionship beween he quaniy demanded of privae healh insurance and is deerminans. Tha is, we may use he Granger Represenaion Theorem (Engle and Granger, 1987) o esablish wheher a long-run saionary 17

20 equilibrium exiss for LPRIVATE and LCOVERAGE wih heir economic and conrol variables. Saionary long run equilibrium may exis as a consequence of economic agens behaving as if hey minimize a cerain quadraic muliperiod loss funcion. Specifically, define Y s * as he long-run equilibrium demand during period s. 6 We assume ha, in he aggregae, economic agens behave as if he acual level of Y s is se o minimize a weighed average of he adjusmen cos (Y s - Y s-1 ) over a single period, and he disequilibrium cos (Y s - Y s *) for all fuure ime periods. We may associae he period-o-period adjusmen coss wih uiliy loss incurred by individuals experiencing fricional or cyclical uninsurance. Deviaions from long run equilibrium, on he oher hand, may reflec uiliy loss caused by srucural uninsurance. The loss funcion is given by: 7 2 [(1- w) ( - ) + w ( Y +i -Y +i- ) ] i * 2 L = E ρ Y + i Y + i 1 (3) i=0 where E is he expeced value operaor condiional on informaion available in he curren period ; ρ is a fixed discoun facor; (1 - w) and w are he relaive weighs associaed wih heir respecive adjusmen coss. We hypohesize ha he opimal value Y s * may be represened by a linear funcion of he X vecor, which conains boh economic and conrol variables: Y * = ' γ + ε, where ε s is a random s X s disurbance erm o accoun for he effec of oher marke forces. I can be shown ha he opimal soluion, known as he Euler equaion, is given by: s Y β = η (4) ' X i ' where η = λ 1 + (1 λ) E Y ( ρλ) X +i β + (1 λ)(1 ρλ) ε, β = ( 1 λ) γ, and λ, one of he i=1 18

21 wo roos from he Euler equaion, is assumed o be less han one o achieve convergence. Thus, he difference beween he curren level of demand and a linear combinaion of he variables in X depends on he presen value of he firs difference of he fuure values of he variables in X. Moreover, he difference will be saionary if one of he roos o he Euler Equaion is close o zero. 8 1 I can be shown ha he roo λ saisfies he quadraic equaion 2 1+ ρw λ ( ) λ + 1 = 0 ρ ρw (see Nickel, 1985). For values of he discoun facor ρ in he neighborhood of 0.95, λ close o zero implies a small weigh on he cos of adjusmen; in he aggregae, economic agens pu more emphasis on he cos associaed wih being away from he desired level of privae insurance. Alernaively, λ close o one implies more concern wih shor-erm adjusmen coss. If he error erm η is covariance saionary, hen Y and he vecor X are coinegraed wih coinegraing vecor (1, -β). The imporance of his resul is wofold: firs, since he variables are coinegraed we can be sure ha he esimaed resuls are no due o spurious regression; and second, in he long run he same forces ha shape he level of oher macro economic variables in he vecor X also drive he behavior of aggregae demand. Given he relaively large number of variables and he relaively small sample size ha we have, we suffer from he curse of dimensionaliy if we use a popular coinegraion es such as Johansen s (1988) maximum likelihood approach. Tha is, as demonsraed in Hansen (1990), here is a dramaic reducion in he power of he es as he size of he sysem increases, rendering a es such as Johansen s fairly ineffecive for our siuaion. Insead, we use he es developed by Hansen (1990) o es he coinegraion hypohesis; is main advanage is ha he asympoic disribuion of he -saisic does no depend on he number of regressors. 9 To implemen Hansen s es, we assume ha he error erm in he coinegraing regression, 19

22 η, in Equaion (4), follows an auoregressive process wih auocorrelaion coefficien θ. In he firs sage, we use he mehods of Cochran-Orcu o esimae he parameers of Equaion (4) including θ. In he second sage, we semi-difference he daa: Y = Y θ Y 1 and X = X θ X 1 and re-esimae a ransformed equaion (4), i.e., Yˆ ' X ˆ ˆ ˆ ˆ β = ˆ η. This procedure may be repeaed a number of imes o ˆ ˆ insure convergence of θˆ. Because Hansen has shown ha here is a size bias in he esimaion of θ in finie sample, we use a bias adjusmen suggesed by Hansen. We firs obain an iniial esimae of θ, we nex define ˆ ~ θ = θ + c / T, whereθ ~ is he iniial esimae of θ, T is he sample size, and following Hansen, we use c =10. We hen semi-difference he daa usingθˆ and follow he procedure as described above unil he final ieraion whereθ is used wihou he bias adjusmen. The esimaed residuals ηˆ may hen be esed for he presence of a uni roo using equaion (2). For our sample, 10 we found θˆ = and he ADF uni-roo es saisic on ηˆ is for he LPRIVATE equaion. Similarly, for he LCOVERAGE equaion, θˆ = and he ADF uni-roo es saisic on ηˆ is Thus, he evidence leads o a rejecion of he uni roo hypohesis a beer han he 1% level; we conclude ha he error erm in equaion (4) follows a saionary process. The economic implicaion of hese resuls is ha here exiss an equilibrium relaionship beween aggregae demand (boh specificaions) and he user price, real income, and he remaining conrol variables. Moreover, he regression coefficiens may be inerpreed as long-run demand elasiciies. Table 2 repors he esimaed coefficiens and heir sandard errors. Noe however, alhough he coefficiens are unbiased, consisen and converge quickly, hey are no efficien, since he residuals are auocorrelaed. Accordingly, we follow he pracice in he lieraure and discuss he resuls in Table 2 in erms of sign and magniude, raher han in erms of saisical significance. 20

23 According o he resuls for he LPRIVATE equaion, user price elasiciy is whereas income elasiciy is 0.151, hus boh coefficien esimaes have heir anicipaed signs. Similarly, he resuls for he LCOVERAGE equaion indicae ha he user price and income elasiciies are and 0.353, respecively. Despie he use of macro-level daa, he esimaed elasiciies compare very closely o previous esimaes ranging beween and for price elasiciy and beween 0.01 and 0.15 for income elasiciy from sudies using micro-level daa (Sanerre and Neun, 2004). The resuls for he conrol variables are equally ineresing. The sronges effecs, in erms of elasiciies, come from LSERVICE and LUNION : and 0.254, for he LPRIVATE equaion and and for he LCOVERAGE equaion, respecively. Variables such as LU, LMCARE, and LMAID do no appear o have imporan long run effec on he demand for privae healh insurance, while LPOVERTY appears o be marginally imporan and has he expeced sign for he LPRIVATE equaion only. Ineresingly, excep for LPRICE, LINCOME, and LUNION, he various coefficiens on he same variables in he wo equaions end o differ wih respec o heir signs. Two reasons may accoun for hese observed differences. Firs, being poor or working in a service indusry, for example, may affec he likelihood of someone being uninsured, bu once insured hese same condiions migh have lile or an opposie impac on how much insurance he person purchases. 11 For example, unlike workers in he manufacuring indusry, service secor workers end o have less opporuniy o purchase healh insurance hrough heir employers such ha he coefficien esimae on he LSERVIVCE variable is likely o be negaive in he LPRIVATE equaion. However, a greaer percenage of service secor workers may be female, and females end o consume more healh care services han males. Therefore, once insured, service secor workers may end o demand more complee healh insurance producs such ha he coefficien esimae on he LSERVICE variable is 21

24 posiive in he LCOVERAGE equaion. Second, he wo ses of resuls may differ because possessing insurance may be more abou access o medical care han abou risk aversion (Nyman, 2003). Nyman argues ha healh insurance solves an affordabiliy problem and allows financial access o medical care ha some people could no oherwise afford because of heir low ne worh relaive o he coss of many medical procedures. If so, he LPRIVATE equaion may be capuring he access value of possessing healh insurance by idenifying he number of people wih a leas caasrophic coverage, whereas, he LCOVERAGE equaion may reflec he risk aversion feaure of healh insurance by idenifying he exensiveness of he coverage. Thus, he same explanaory variables may have differen impacs on he dependen variables in he wo regression equaions. IV.C Long Run Equilibrium Relaionship and he Error Correcion Model The analysis of he previous secion shows ha boh he LPRIVATE and he LCOVERAGE equaions are coinegraed. Engle and Granger (1987) show ha a se of coinegraed variables has an error correcion model (ECM) represenaion. The ECM follows direcly from Equaion (4), assuming ha each of he independen variables follows a random walk: where ˆ η 1 is he error correcion erm. Y = ( λ 1) ˆ η + X α + ζ, (5) 1 The empirical resuls associaed wih he ECM are displayed in Table 3. Before discussing he resuls, we noe ha checks for serial correlaion, heeroscedasiciy (agains an ARCH alernaive), and parameer consancy (wih a breakpoin in he year COBRA was passed ino law), all urn ou o be saisically insignifican for boh demand equaions. Also, we noe ha he adjused 2 R is fairly large for a growh rae model: 50% and 72%, respecively, for he LPRIVATE ' 22

25 and LCOVERAGE equaions. The esimaed coefficien for ˆ η 1 is wih a -saisic of (p-value = 0.002) for he LPRIVATE equaion, and wih a -saisic of (p-value = 0.000) for he LCOVERAGE equaion. Hence, he esimaed coefficiens saisfy boh heoreical requiremens: less han one in absolue value, negaive and saisically differen from zero. Moreover, he magniude implies a sizable feedback effec. For example, for he LPRIVATE equaion, 88 percen of a uni equilibrium error in he previous period is reversed in he curren period. Hence, he percen of individuals wih privae insurance adaps fairly quickly o variaions in is long run equilibrium. In some sense his is good news for policy makers who wish o impac he equilibrium level of he srucurally uninsured, especially if some variables such as he povery rae are highly sensiive o policy adjusmens. The implied value of λ, he roo from he Euler equaion, is for he LPRIVATE equaion, and for he LCOVERAGE equaion. The implicaion is ha, in he aggregae, people consciously consider more he cos of disequilibrium han he period-o-period adjusmen cos. In oher words, ransiioning beween shor spells wih or wihou privae healh insurance generaes less disuiliy han long periods wihou insurance. Alernaively saed, he welfare loss creaed by a drop in he percen of privae healh insurance caused by changes in he number of fricionally or cyclically uninsured is smaller han he welfare loss due a change in he number of srucurally uninsured. Table 3 shows shor-run elasiciy esimaes for he various deerminans of he aggregae demand for privae healh insurance. 12 According o he esimaes, he aggregae demand for privae healh insurance, boh in erms of enrollmen and compleeness of coverage, is relaively inelasic in 23

26 he shor run wih respec o user price. Specifically, he elasiciy esimae on user price implies ha a 10 percen increase in price is associaed wih a 2.3 percen decrease in he percenage of he populaion wih privae healh insurance and a 1.8 percen reducion in he compleeness of healh insurance coverage in he shor-run. The income elasiciy of demand for privae healh insurance enrollmen is posiive, as expeced, and saisically significan a beer han he 5 percen level for a one-ailed es. According o is esimae, a en percen increase in income is associaed wih a 3.6 percen increase in he percenage of he populaion covered by privae healh insurance. The only surprising resul obained is he negaive income elasiciy of demand esimae in he compleeness equaion. Recall ha a posiive income elasiciy esimae was anicipaed. However, his expecaion of a direc relaionship was based on prior research focusing on he impac ha income has on he purchasing of healh insurance wih lile regard o he compleeness of he coverage. Thus, from a heoreical perspecive, we canno rule ou an inverse relaionship beween income and he compleeness of healh insurance. For example, he degree of insurance compleeness may decline wih income, a leas afer some poin, because higher income households can avoid some of he expense load behind insurance by self-insuring o a greaer exen and paying a greaer amoun as ou-of-pocke expenses when an illness akes place. However, given ha he coefficien esimae on income is only marginally saisically significan, i would be impruden of us o generalize our findings beyond his paricular sample. Resuls for he oher variables also meri some discussion. Firs, as anicipaed, he empirical resuls sugges ha he privae healh insurance coverage rae and povery rae move in opposie direcions in he shor-run. More specifically, he elasiciy esimae suggess ha a 10 percen 24

27 decline in he povery rae is associaed wih a 1.2 percen increase in he percen enrolled in privae healh insurance plans. Similarly, a 10 percen decline in he povery rae is associaed wih a 1.1 percen increase in he compleeness of healh insurance coverage. Second, he resuls indicae ha variables oher han price, level of income, and he disribuion of income, represened by he povery rae, have no shor-run impac on he demand for healh insurance or he compleeness of coverage. This finding is no oo surprising given ha mos of hese variables, like he percenage of workers in he service secor and union membership rae, end o change very slowly over ime and herefore have more of a long-erm han shor run impac on healh insurance coverage saus. V. Conclusion In his paper we examine he long run behavior and shor run dynamics of he aggregae demand for privae healh insurance wihin a coinegraion and an error correcion model framework. The error correcion model considers ha people incremenally balance he benefis of an adjusmen owards heir desired objecive wih he coss of making he adjusmen. Jus like he demand for oher goods and services, he empirical findings in his paper indicae ha he aggregae demand for privae healh insurance is relaed o price, income, and oher facors in a fairly predicable manner. Individuals weigh he cos of adjusing heir healh insurance purchase relaive o he disequilibrium cos of being away from heir preferred quaniy of healh insurance a a poin in ime. A he margin, i appears ha disequilibrium coss impose greaer disuiliy han shor-run spells in-beween insured and uninsured saus. In his paper we also advance he argumen ha people are uninsured for volunary reasons as well as for involunary reasons reflecing srucural, fricional, and cyclical circumsances. In fac, he original Medicare Ac, and especially Medicare s expansion in 1973 o individuals wih cerain 25

28 disabiliies, may have been enaced wih srucural uninsurance in mind. As menioned previously, COBRA of 1985 was direced a fricional uninsurance. In addiion, many analyss believe ha individual healh insurance plans may grow in he fuure as informaion on he Inerne reduces he ime involved in searching ou a healh insurance company. I follows ha any serious public or privae iniiaives o increase privae healh insurance coverage hrough volunary means, boh in erms of enrollmen and compleeness, should consider he various reasons why people remain uninsured. Tha is, we canno expec one remedy o cure all of he causes for uninsurance. Thus, a variey of public and privae approaches may be necessary o reduce uninsurance in a primarily volunary healh insurance sysem. Our empirical findings srongly confirm resuls from prior micro-level sudies regarding he price and income elasiciies of he demand for healh insurance. Despie he aggregae naure of our daa and he error correcion modeling, we find ha he demand for privae healh insurance appears o be relaively insensiive o changes in user price and consumer income in boh he shor and long run and wih respec o boh enrollmen in privae healh plans and he compleeness of healh insurance coverage. The relaive insensiiviy of demand o changes in user price may mean ha incremenal subsidizaion programs may have lile impac on he purchasing and compleeness of privae healh insurance coverage a he aggregae level. Moreover, unlike many oher ypes of social problems like infan moraliy, environmenal condiions, and workplace safey, he relaively small income elasiciies of demand may imply ha we canno expec privae healh insurance coverage o naurally improve wih a higher sandard of living in he U.S. Thus, jus like social securiy and auomobile liabiliy insurance are required for mos workers and drivers, i may be necessary o 26

29 mandae healh insurance coverage if sociey one day reaches he conclusion ha he benefis of universal healh insurance coverage ouweighs is coss. Finally, alhough we obain reasonable resuls wih our empirical procedures, we are unable o esimae our equaions wihin a sysem framework because of our limied sample size and he relaively large number of variables involved. Thus, we are unable o address he quesion of muliple coinegraion. This is a shorcoming of his sudy, which hopefully will be addressed in fuure sudies. 27

30 References Blair, R.D., and R.J. Vogel, (1978), A Survivor Analysis of Commercial Healh Insurers, Journal of Business 51 (July), pp Cawley, J., and K.I. Simon, (2003), The Impac of Macroeconomic Condiions on he Healh Insurance Coverage of Americans, in Froniers in Healh Policy Research, Volume 6, edied by David Culer and Alan M. Garber. (Naional Bureau of Economic Research: Cambridge, MA). Conwell, L.J., (2002), The Role of Healh Insurance Brokers, Issue Brief #57, Cener for Sudying Healh Sysem Change, Washingon, D.C., Ocober. Culer, D. M., (2002), Employee Coss and he Decline in Healh Insurance Coverage, NBER Working Paper Series #9036 (July). Culer, D. M., and J. Gruber, (1996), Does Public Insurance Crowd Ou Privae Insurance? Quarerly Journal of Economics, 111 (May), pp DeNavas-Wal, C., B. D. Procor, and C. H. Lee, (2005), Income, Povery, and Healh Insurance Coverage in he Unied Saes: 2004, U.S. Census Bureau, Curren Populaion Repors, P60-229, U.S. G.P.O., Washingon, D.C. Engle, R., and C. Granger, (1987), Coinegraion and Error Correcion Represenaion, Esimaion and Tesing, Economerica, 55, Feenberg, D., and E. Cous, (1993), An Inroducion o he Taxsim Model, Journal of Policy Analysis and Managemen, (winer), pp Fuller, W., (1976), Inroducion o Saisical Time Series, New York: Wiley. Granger, C., (1986), Developmens in he Sudy of Coinegraed Economic Variables, Oxford Bullein of Economics and Saisics, 48, Granger, C., and P. Newbold, (1974), Spurious Regressions in Economerics, Journal of Economerics, 2, Gregory, A., (1994), Tesing for Coinegraion in Linear Quadraic Models, Journal of Business and Economic Saisics, 12, Hall, A., Anderson, H., and C. Granger, (1992), A Coinegraion Analysis of Treasury Bill Yields, Review of Economics and Saisics, Hansen, B., (1990), A Powerful, Simple Tes for Coinegraion Using Cochrane-Orcu, Working Paper 260, Universiy of Rocheser, Dep. of Economics. 28