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1 Chpter 11 THE ANATOMY OF HEALTH INSURANCE* DAVID M. CUTLER nd RICHARD J. ZECKHAUSER Hrvrd University nd Ntionl Bureu of Economic Reserch Contents Abstrct 564 Keywords Helth insurnce structures in developed ntions Helth insurnce in the United Sttes The principles of insurnce Insurnce with fixed spending Morl hzrd nd principl-gent problems Morl hzrd Evidence on the price elsticity of medicl cre demnd Coinsurnce in prctice Optiml insurnce given morl hzrd Ptients, doctors, nd insurers s principls nd gents Trnsctions costs Reltionships between insurers nd providers Equilibrium tretment decisions in mnged cre Evidence on supply-side pyment nd medicl tretment Optiml mix of demnd- nd supply-side controls Mrkets for helth insurnce: pln choice nd dverse selection Equilibrium with dverse selection - the bsics Equilibri with multiple individuls in risk group Continuous risk groups Evidence on the importnce of bised enrollment Evidence on the importnce of pln mnipultion The trdeoff between competition nd selection Risk djustment Person-specific pricing, contrct length, nd premium uncertinty Insurnce nd helth outcomes 629 *We re grteful to Dn Altmn for reserch ssistnce, to Jon Gruber, Tom McGuire, Joe Newhouse, nd Alexndr Sidorenko for helpful comments, nd to the Ntionl Institutes on Aging for reserch support. Hndbook of Helth Economics, Volume 1, Edited by A.J. Culyer nd J.P. Newhouse 2 Elsevier Science B. V All rights reserved

2 564 D.M. Cutler nd R.J. Zeckhuser 9. Conclusions nd implictions 631 Appendix 634 References 637 Abstrct This rticle describes the ntomy of helth insurnce. It begins by considering the optiml design of helth insurnce policies. Such policies must mke trdeoffs ppropritely between risk shring on the one hnd nd gency problems such s morl hzrd (the incentive of people to seek more cre when they re insured) nd supplier-induced demnd (the incentive of physicins to provide more cre when they re well reimbursed) on the other. Optiml coinsurnce rrngements mke ptients py for cre up to the point where the mrginl gins from less risk shring re just offset by the mrginl benefits from reduced provision of low vlued cre. Empiricl evidence shows tht both morl hzrd nd demnd-inducement re quntittively importnt. Coinsurnce bsed on expenditure is crude control mechnism. Moreover, it plces no direct incentives on physicins, who re responsible for most expenditure decisions. To plce such incentives on physicins is the gol of supply-side cost continment mesures, such s utiliztion review nd cpittion. This gol motivtes the surge in mnged cre in the United Sttes, which unites the functions of insurnce nd provision, nd llows for ctive mngement of the cre tht is delivered. The nlysis then turns to the opertion of helth insurnce mrkets. Economists generlly fvor choice in helth insurnce for the sme resons they fvor choice in other mrkets: choice llows people to opt for the pln tht is best for them nd encourges plns to provide services efficiently. But choice in helth insurnce is mixed blessing becuse of dverse selection - the tendency of the sick to choose more generous insurnce thn the helthy. When sick nd helthy enroll in different plns, plns disproportiontely composed of poor risks hve to chrge more thn they would if they insured n verge mix of people. The resulting high premiums crete two dverse effects: they discourge those who re helthier but would prefer generous cre from enrolling in those plns (becuse the premiums re so high), nd they encourge plns to dopt mesures tht deter the sick from enrolling (to reduce their overll costs). The welfre losses from dverse selection re lrge in prctice. Added to them re further losses from premiums tht vry with observble helth sttus. Becuse insurnce is contrcted for nnully, people re denied vluble form of intertemporl insurnce - the right to buy helth coverge t verge rtes in the future should they get sick tody. As the bility to predict future helth sttus increses, the lck of intertemporl insurnce will become more problemtic. The rticle concludes by relting helth insurnce to the centrl gol of medicl cre expenditures - better helth. Studies to dte re not cler on which pproches to helth insurnce promote helth in the most cost-efficient mnner. Resolving this question is the centrl policy concern in helth economics.

3 Ch. 11: TheAntomy of Helth Insurnce 565 Keywords dverse selection, gency problems, HMOs, indemnity insurnce, intertemporl insurnce, mnged cre, morl hzrd, pooling equilibrium, seprting equilibrium, supplier-induced demnd JEL clssifiction: I1

4 566 D.M. Cutler nd R.J. Zeckhuser Insurnce plys centrl role in the helth cre ren. More thn 8 percent of helth cre expenditures in the United Sttes re pid for by insurnce, either public or privte, with n even greter percentge supported in most other developed ntions. Insurnce thus provides the money tht motivtes nd supports the helth cre system. This pper describes the ntomy of helth insurnce. At the micro level, it detils why individuls seek insurnce, nd the chllenges in structuring insurnce policies. At the mcro level, it explins the role of helth insurnce in the medicl cre sector. The medicl cre trid (Figure 1) depicts tht sector in fundmentl fshion. Insurers medite between individuls 1 nd their providers. Often times, the flow of funds is more roundbout: governments or employers nominlly py insurers, but these costs re then pssed on to individuls, vi incresed txes or lower wges. The insurer intermediry must design policy to py for (nd possibly provide) cre. This is trecherous tsk. Designing helth insurnce policy is not nerly so chllenging technologiclly s, sy, designing personl computer system, but it must still overcome some distinct nd substntil economic obstcles. The most importnt of these obstcles re gency problems. Insurers cnnot get relevnt prties to do wht efficiency requires. Thus, people with generous insurnce spend more on medicl cre thn people with less generous insurnce (morl hzrd), nd providers pid on fee-for-service (piece-rte) bsis my provide more cre due to supplier-induced demnd thn they would if they were not pid per tsk. In sitution where gency reltionships re imperfect, insurnce is necessrily second-best. Insurers must trde off the benefits from more generous insurnce - primrily the reduction in risk it ffords - ginst the costs of more generous insurnce - morl hzrd or supplier-induced demnd. Throughout this chpter, we highlight centrl lessons bout helth insurnce, which re then collected in Tble 1. This clsh between risk shring nd incentives is Lesson 1 bout helth insurnce. Figure 1. The medicl cre trid. Solid lines represent money flows; the dshed line represents service flows. 1 Throughout the pper, to fcilitte exposition, we mostly refer to ptients or insureds s individuls, lthough most helth insurnce is purchsed on behlf of fmilies.

5 Ch. 11: TheAntomyofHelthInsurnce 567 Agency problems in helth cre cn be llevited in two wys. The demnd-side pproch discourges excessive utiliztion by mking people py something when they consume medicl cre. Demnd-side rtioning is epitomized in the trditionl indemnity insurnce pln, which previled in the United Sttes for hlf century. The supply-side pproch discourges utiliztion by monitoring providers crefully, penlizing them if they re profligte, nd giving them finncil incentives to provide only essentil cre. Incresingly, supply-side limittions re fostered by integrting insurnce nd provision. Some HMOs, for exmple, re both insurers nd providers of cre. Integrtion of the insurnce nd provision functions is unique to medicl cre, nd results from the fundmentl difficulties with solely demnd-side rtioning. The integrtion of helth insurnce nd provision of medicl services is Lesson 2 bout helth insurnce. Sections 3 through 5 of the chpter ly out the issues involved in demnd- nd supply-side rtioning. We then move from these micro reltionships to the broder ren of the mrket for helth insurnce. People hve preferences for different types of helth insurnce, nd those preferences should be ccommodted to the extent possible. In ddition, competition in helth insurnce cn encourge production efficiency, driving down overll costs. But competition in helth insurnce produces results unlike competition in other mrkets, for fundmentl reson: the costs of providing insurnce, s opposed to sy computers or food, depend on the chrcteristics of the buyer. People with poor medicl history will benefit more from nd cost more to insure thn those with helthy pst. Thus, the sick will sort themselves into more generous plns thn will the helthy. This process, clled dverse selection, cn substntilly limit the benefits of helth pln choice. Individuls will hve incentives to choose less generous policies over more generous ones (to pool with the helthy insted of the sick) nd insurers will hve incentives to reduce the generosity of their benefits (to ttrct the helthy insted of the sick). Lesson 3 describes the consequences of competition when buyer identity ffects costs. Section 6 discusses dverse selection nd pproches to del with it. The nturl tendency of insurers to chrge the sick greter premiums thn the helthy presents further chllenge to helth insurnce: lck of coverge ginst the longterm risk of becoming sick nd hving higher expected costs in the future. Using the thought experiment of individuls mking choices behind the veil of ignornce, they would choose to insure their risk of becoming sicker thn verge - multi-yer risk - just s individuls in ny yer wish to insure their medicl costs tht yer. Mrkets for multi-yer insurnce do not exist, however, for understndble resons, nd in prctice individuls re left without this insurnce. The kernel of the problem is tht informtion on risk levels becomes vilble before insurnce contrcts re drwn. Lesson 4 is tht erly informtion dries up insurnce mrkets. Long-term insurnce is tken up in Section 7 of the chpter. However effectively helth insurnce controls costs or spreds risks (the focus of most of this chpter), its key gol is to promote helth. In Section 8 we exmine the reltionship between helth insurnce nd helth. Vritions in insurnce generosity hve reltively little impct on helth outcomes mong those with insurnce. This finding is

6 568 D.M. Cutler nd R. J Zeckhuser consistent with the ide tht insurnce generlly restricts cre offering reltively low vlue. But the time frme over which these issues hs been exmined is not lrge. We know less bout the long-run effect of different helth insurnce rrngements on helth thn we should. We mrk the centrlity of helth s opposed merely to finncil trnsfers nd the lck of cler evidence on the reltive benefits of different systems s Lesson 5 bout helth insurnce. At the outset, it is importnt to tke ccount of the distinctive role helth insurnce plys in society. Economists trditionlly mesure vlue by willingness to py, nd the vlue of helth insurnce, or its byproduct medicl cre, is clibrted in dollr terms - the sme s pples or television sets. In much of the world, however, prticulrly outside the United Sttes, medicl cre nd medicl insurnce re treted differently. Medicl cre is often viewed s right, for which mrket-bsed lloction is not pproprite. For some, the right is bsolute; mrkets should ply no role in the lloction of medicl services. More moderte positions ssign government specil responsibility for medicl cre, which leds to government insurnce system or set of subsidies. Rights-oriented sentiments show up even in the United Sttes. The United Sttes subsidizes medicl insurnce directly for poor people nd old people, nd indirectly for the working-ge popultion (through the exclusion of helth insurnce from individul txble income). While some such subsidies my be justified on externlity grounds (when people get medicl cre, they re less likely to spred infectious diseses to others), merit-good rguments, or fiscl externlity rguments (when people re helthier, they ern more, py more in txes, nd receive less in public benefits), we suspect tht right to medicl cre is the more bsic motive. But the rtionle for subsidizing helth insurnce, s opposed to medicl cre, is less cler. The government could promote consumption of medicl cre through direct delivery of services or by subsidizing inputs, without intervening in the medicl insurnce mrket. We thus focus primrily on the economic nlysis of helth insurnce, leving side normtive views bout ccess to bsic medicl services [Hurley (2), Wgstff nd vn Doorsler (2), nd Willims nd Cookson (2)]. We come bck to the ccess issue in the lst section. In this essy, we follow common prlnce by [primrily] using the terms helth cre nd helth insurnce, lthough the terms medicl cre nd medicl cre insurnce might be better descriptors. Helth sttus cnnot be insured. The costs of medicl cre cn be, nd re, lbeit often bering the lbel helth insurnce. We begin in the first section by discussing the provision of helth insurnce round the world nd in the second with review of the principles of insurnce. We then exmine the micro nd mcro issues in helth insurnce. 1. Helth insurnce structures in developed ntions Helth insurnce is common to ll developed countries, but the mechnism for obtining insurnce differs from country to country. In most countries, helth insurnce is

7 Ch. 11: TheAntomyofHelthInsurnce 569 universl; everyone is entitled to coverge nd is required to purchse it. 2 In some ntions, such s Cnd, the finncing is through txtion; people py n income or pyroll tx, nd the proceeds re used by the government to purchse or provide helth insurnce. In other ntions, the finncing is through privte insurnce; individuls or their employers contribute to helth insurnce compnies, which then provide insurnce for the popultion. While the pyment for ny individul my differ in these two systems ( tx-finnced system generlly imposes reltively more on the rich), the implictions for the provision of helth insurnce re generlly slight. Governments in both systems re intimtely involved in determining wht services re covered, the cost shring tht ptients fce, nd the restrictions imposed on providers. The specifics of helth insurnce structures differ significntly cross developed ntions. Countries such s the UK nd Itly finnce helth insurnce through generl txtion nd (t lest historiclly) provide services publicly. 3 Countries such s Cnd nd Germny finnce insurnce publicly but contrct for services through privte providers Helth insurnce in the United Sttes Describing the detiled structures for helth insurnce in different ntions would tke n entire volume. We focus our ttention primrily on the United Sttes. The United Sttes is distinctive mong OECD countries becuse helth insurnce is not universl. 4 Tble 1 shows the sources of helth insurnce in the United Sttes. About one-qurter of the United Sttes popultion is insured through the public sector. The primry public progrms re Medicre, which mostly insures the elderly, long with the disbled nd people with kidney filure; nd Medicid, which insures younger women nd children, the elderly (for services not covered by Medicre such s nursing home cre), nd the blind nd disbled. Other public progrms, primrily for veterns nd dependents of ctive-duty militry personnel, insure nother 1 percent of the popultion. Another 6 percent of the popultion hs privte helth insurnce. Most of this insurnce is provided by employers; less thn 1 percent of the popultion purchses insurnce privtely. The predominnce of employer-provided insurnce results from the fvorble tx tretment of tht method of pyment. Compenstion to employees in the form of wges nd slries is txed through federl nd stte income txes, nd through the federl Socil Security tx. Compenstion pid s helth insurnce, in contrst, goes untxed. Since mrginl tx rtes rnge from 15 to 4 percent for most employees, 5 the 2 In some countries, such s Germny, temporry workers do not receive helth insurnce, but they comprise smll prt of the popultion. All citizens re entitled to insurnce. 3 Countries such s the UK hve moved to more of decentrlized provision system in recent yers. Hospitls hve been set up s privte trusts, for exmple, nd physicins re no longer slried. 4 Since 1996, helth insurnce coverge hs been required in Switzerlnd, but before then it ws subsidized so hevily tht essentilly everyone purchsed it. 5 Income tx rtes cn rnge s high s 4 percent, but the income level t which these rtes re reched re pst the cp on ernings subject to the pyroll tx.

8 57 D.M. Cutler nd R.J. Zeckhuser Tble I Sources of helth insurnce coverge for the United Sttes popultion Source Groups insured Shre of totl Shre of totl popultion (%) pyments (%) Public Medicre Elderly; disbled; end-stge renl disese Medicid Elderly; blind nd disbled; 1 15 poor women nd children Other* Militry personnel nd 1 8 their dependents Privte Employer sponsored Workers nd dependents 56 Nongroup Fmilies 6 Uninsured 16 2 * Other public spending includes non-insurnce costs such s public hospitls, the Veterns Administrtion, etc. Source: Authors' clcultions bsed on dt from Deprtment of Helth nd Humn Services, Ntionl Helth Accounts (medicl spending), nd from Employee Benefit Reserch Institute (insurnce coverge). subsidy to employer-provided insurnce, s opposed to individully-purchsed insurnce, is substntil. The subsidy to employer-provided helth insurnce generlly does not extend, however, to out-of-pocket pyments mde by employees. As result, there re incentives to hve generous insurnce, pid for by employers, with few individul copyments. We return to the effects of this subsidy structure below. The remining 16 percent of the United Sttes popultion is uninsured. The implictions of being uninsured re subject of vigorous debte [Weissmn nd Epstein (1994)]. Some of the uninsured (perhps 4 percent) re eligible for public insurnce (prticulrly Medicid) but hve chosen not to tke up tht insurnce. Presumbly, if these people become sick they will enroll in Medicid. 6 Others will receive "uncompensted" cre if they become sick - they will get emergency cre if they need it, but they will not py for it. The costs of uncompensted cre then get shifted to people with insurnce, for whom pyments mde exceed the cost of services provided. In this sense, the United Sttes hs form of universl insurnce coverge for ctstrophic cre, lthough the ptchwork nture of tht coverge is undoubtedly suboptiml. It lso limits primry nd preventive cre for those without helth insurnce. The lst column of Tble 1 shows the shre of totl pyments tht ech group mkes. As in ny insurnce policy, people my use more or less of the service thn they py 6 Since it is difficult to deny tretment, providers hve strong interest to enroll eligible people in Medicid, so tht they cn receive some pyment for them.

9 Ch. 11: The Antomy of Helth Insurnce 571 for. This is prticulrly true for the uninsured, whose out-of-pocket pyments re much lower thn the cost of services they receive. The tble reports the shre of totl pyments mde by ech group; the shre of services tht is used by ech group will be somewht different. Becuse people insured through the public sector re older nd sicker thn people insured privtely, nd becuse some of the costs of the uninsured re pssed on to the public sector, the public sector ccounts for much more of medicl spending thn its demogrphic shre of insurnce coverge. Close to hlf of medicl spending in the United Sttes is pid for publicly. While this mount is extremely high reltive to most goods nd services in society, it is low by interntionl stndrds for medicl cre. In OECD ntions, governments generlly py for 75 to 9 percent of medicl cre. Whether run publicly or privtely, helth insurnce encounters fundmentl problems tht ny insurer must fce. Adverse selection, though diminished for government since some of its progrms re so hevily subsidized tht the vst mjority choose to prticipte, still exists, nd morl hzrd ffects governments no less thn privte insurers. Thus, when we discuss the optiml design of helth insurnce policies, we do not distinguish between public or privte insurers. We return to public versus privte insurnce issues in the conclusion. 2. The principles of insurnce In this section nd the next three, we discuss the optiml design of helth insurnce policies. Our perspective is tht of n insurer - public or privte - wnting to optimlly insure its enrollees ginst the costs of treting dverse helth outcomes. The vlue of helth insurnce is rooted in the unpredictbility of medicl spending. While individuls know something bout their need for medicl services, the exct mount they will spend on medicl cre is to significnt degree uncertin. Medicl spending is extremely vrible. Tble 2 shows the distribution of medicl spending in the United Sttes in 1987 [Berk nd Monheit (1992)]. The top 1 percent of medicl cre users consume n verge of nerly $5, ech in yer (in 1987 dollrs), nd Tble 2 Distribution of medicl spending, 1987 Shre of distribution Cumultive shre of spending (%) Top 1 percent 3 Top 5 percent 58 Top 1 percent 72 Top 5 percent 98 Totl popultion 1 Source: Berk nd Monheit (1992).

10 572 D.M. Cutler nd R.J. Zeckhuser ccount for 3 percent of medicl spending. The top 1 percent of users ccount for nerly three-qurters of totl medicl spending. The shorter the time period, of course, the greter is the percentge disprity in medicl spending mong individuls. But even looking over severl yers, the skewness of medicl spending is substntil [Roos et l. (1989), Eichner, McClelln, nd Wise (1998)]. In such sitution, insurnce cn significntly spred risks. Risk-verse individuls will wnt to gurd ginst the potentil of requiring substntil mount of medicl cre. One wy to do this is to wit, borrow money for tretment should they get sick, nd then repy the money when well. But borrowing when debilitted is difficult, since the individul my not live long enough or be helthy enough to repy the lon. The borrowing process, moreover, my lso tke more time thn the sick individul hs vilble. A resonble lterntive might be for individuls to sve money when they re helthy to py for medicl cre should they get sick. But some sicknesses re significntly more expensive thn others. The substntil expenses of very severe illness mke sving prior to illness imprcticl s protective mesure. All of us would hve to significntly curtil consumption to sve up for expenses tht would be borne by only few. The nturl solution is to insure ginst the possibility of medicl illness by pooling risks with others in the popultion. Annul consumption would be reduced only by the premium, the verge cost of cre. Risks to helth hve lwys been with us, but helth insurnce is reltively new phenomenon, only becoming economiclly significnt in the postwr er. Fire nd life insurnce were well developed by the end of the 19th century, nd mrine insurnce ws lredy being written in the 12th century. There ws little role for helth insurnce in erlier ers, however, since expensive medicl tretments could ccomplish little for helth. Insurers lso fered they could not control individul use of medicl services if the services were insured. Once effective hospitl cre - n extremely expensive commodity - becme possible, significnt helth insurnce becme desirble nd inevitble Insurnce with fixed spending The simplest insurnce sitution is one where sickness entils fixed cost nd insurnce is priced t its cturil cost. Imgine sitution where initilly identicl individuls re either helthy or sick in period of one yer. There is one disese. People re helthy with probbility 1 - p, in which cse they require no medicl cre. People get sick with probbility p. Let d = or d = 1 indicte whether bsent medicl cre the person is helthy or sick. Tretment of person who is sick requires medicl spending of m. The fter-expenditure helth of sick person is h = H [d, mi]. To simplify exposition, we ssume tht medicl spending restores person to perfect helth, so tht H [1, m] = H[, ]. Before proceeding, we lert the reder to our use of mthemtics. We use mthemtics to derive sttements precisely. We lso endevor to explin ll of our results intuitively. Thus, reders who wish to skip the mthemticl portions of the chpter cn still follow the centrl rguments.

11 Ch. 11: TheAntomyofHelthInsurnce 573 Individuls receive utility, u, which depends on their consumption, x, nd their ftertretment helth, h. Thus we hve u = U (x, h). Assume, for simplicity, tht people hve exogenous income endowments, y; nd tht they cn neither borrow or lend. Thus, n individul's consumption is wht is left over fter pying medicl expenditures, or if insured, his insurnce premium, r. Thus, for uninsured people, x = y when helthy nd x = y - m when sick. For insured people, x = y - r whether helthy or sick. We use the subscripts I nd N to indicte whether the individul is insured or not insured. Let U(x) U(x, H[, ]); i.e., it is the reduced form utility function for consumption given perfect helth. In the bsence of insurnce, n individul's expected utility is given by: VN = (1 - p)u(y, H[O, ]) + pu(y - m, H[1, mi), = (1 - p)u(y) + pu(y - m), where the second equlity follows from the ssumption tht medicl cre restores the person to perfect helth. 7 We ssume tht U hs the stndrd property tht utility is incresing in consumption lbeit t declining rte: U' > nd U" <. We further ssume tht medicl expenditures re worthwhile even if the individul is not insured. Suppose the individul purchses insurnce ginst the risk of being sick. For n insurnce compny to brek even, the fir insurnce premium would hve to be 7r = pm. The insurnce compny collects the premium ech yer nd pys out m when the individul is sick. If n individul chooses this policy, his utility would lwys be: Vi = U(y - r). (2) Using Tylor series expnsion of Eqution (1),8 we cn pproximte tht eqution s: Therefore, VN U(Y - 7r) + U'(U"/2U')r(m - rt). (3) Vlue of Insurnce = (VI - VN)/U'/ (1/2)(-U"/U')r(m - 7r). (4) 7 Assuming tht medicl expenditure is worthwhile, this nlysis ctully requires less stringent condition. The sme eqution would pply if restored helth imposed fixed utility cost, k, reltive to initil perfect helth, so tht U(c, H[O, ]) = U(c, H[1, ml) + k for ll c. 8 The Tylor series is tken bout the level of income net of insurnce premiums. From Eqution (1), VN (1 - p)[u(y - 7r) + U'7r + (1/2)U"r 2 ] + p[u(y - r) - U'(m -7r) + (1/2) U"(m - 7 ) 2 ]. Collecting terms, this simplifies to VN U(y - r) + U'{(1 - p)7 - p(m - r) + (1/2)U"{(1- p)r 2 + p(m - r) 2 }. The term (1 - p)7t - p(m - t) is zero. The term (1- p)7r 2 + p(m -r) 2 cn be expnded s (1 - p)7r 2 + pm 2 2pm7r + pir 2. Since pm = Jr, this simplifies to pm 2-7r 2 = 7r(m - 7r).

12 574 D.M. Cutler nd R.J. Zeckhuser The left hnd side of Eqution (4) is the difference in utility from being uninsured reltive to being insured, scled by mrginl utility to give dollr vlue for removing risk. The right hnd side is the benefit of risk removl. Here, (-U"/ U') is the coefficient of bsolute risk version; it is the degree to which uncertinty bout mrginl utility mkes person worse off. Becuse U" < nd U' >, this term is positive. The term 7r(m - r) represents the extent to which fter-medicl expenditure income vries becuse the person does not hve insurnce. It too is positive. The product of terms on the right hnd side of Eqution (4), therefore, is necessrily positive, implying tht fir insurnce is preferred to being uninsured. The dollr vlue of risk spreding increses with risk version nd with the vribility of medicl spending. The intuition supporting this result is tht risk verse individuls would like to smooth the mrginl utility of income - to trnsfer income from sttes of the world where their mrginl utility is low to sttes of the world when their mrginl utility is high. In the bsence of insurnce, person's mrginl utility of income when helthy is U'(y) nd when sick is U'(y - in). Since mrginl utility flls s income increses, mrginl utility is lower when helthy thn when sick. Trnsferring income from helthy sttes to sick sttes until mrginl utility is equlized mximizes totl utility, ssuming fir insurnce. Helth insurnce crries out this trnsfer, chrging premiums up front nd reimbursing expenditures lter. 9 There is digrmmtic wy to mke the sme point; it is shown in Figure 2. We think of the two sttes of the world - being sick nd being helthy - s if they were two goods. Individuls would like more consumption in ech stte. In the bsence of ny probbility of being sick, people would be ble to consume y in ech stte. Becuse of required medicl spending, however, people cn only consume y - m when sick. This is shown s point E in the figure. 9 The sitution is more complex when medicl spending fils to restore the person to perfect helth, nd the mrginl utility of income is ffected by helth sttus. Suppose tht when sick person still needs medicl spending of m, but tht his fter-expenditure helth remins below wht it would be hd he never got sick; i.e., tht H[l, m] < H[O, O]. Expected utility for people without insurnce is given by VN = (1 - p)u(y, H[O, ]) + pu(y - m, H[1, m]), nd the mrginl utilities of income re Ux (y, H[O, ]) when helthy nd Ux (y - m, H[1, m]) when sick, where the subscripts indicte prtil derivtives. Becuse the mrginl utility of income my be ffected by helth nd helth vries cross sickness sttes, it is not cler how much insurnce the person will wnt. If people ttch little vlue to money when sick - for exmple, if there re few plesurble ctivities they cn engge in - they my not wnt ny helth insurnce t ll. Alterntively, if the vlue of money when sick is prticulrly high, sy becuse ides re needed to crry out the ctivities of dily life, people my wnt more thn full insurnce ginst medicl expenditures. This exmple highlights the difference between medicl cre insurnce nd wht, if we used strict interprettion, would be lbeled helth insurnce. Helth insurnce trnsfers money cross people - generlly from the helthy to the sick. The money cn be used to purchse medicl services the individul otherwise could not fford, or to llow the individul to purchse more of other goods nd services fter medicl cre hs been pid for. But helth insurnce cnnot gurntee tht n individul's helth will be unffected by outside fctors. Insuring one's helth is technologiclly infesible.

13 Ch. 11: The Antomy of Helth Insurnce 575 Dollr 45n y insurnce line y Dollrs when helthy Figure 2. The welfre gins from helth insurnce. The fir odds insurnce line is the individul's implicit budget constrint. It is drwn for the cse where p =.2. The slope of the line is -l/p, or -5.1 The indifference curve for consumption is lso steeply sloped, recognizing tht the sick stte is unlikely to rise. Thus, people re not willing to give up much consumption when helthy to get consumption when sick. A person cn trde consumption when sick for consumption when helthy, t rte given by the insurnce premium. People will choose to purchse some insurnce. If insurnce is priced cturilly firly, individuls will choose to be fully insured - they will hve the sme consumption when sick s when helthy. This optimum is shown s point E' in the figure. People re better off t E' thn they re t E; they hve moved to higher indifference curve. In our simplified world, the optiml insurnce policy is n indemnity policy - it pys fixed mount of money for prticulr condition when the individul is sick. The mount pid equls the cost of the pproprite tretment for the person's disese; if there is more thn one disese, the pyments vry. Since ech disese requires fixed mount of cre - there is no more nor less tht person cn consume - there re no wsted resources in the policy; the indemnity insurnce pln is efficient. Beyond its efficiency properties, the indemnity policy is the simplest helth insurnce policy. In effect, it opertes s contingent clims mrket; people get pid specified mount depending on which contingency occurs [Zeckhuser (197)]. Helth insurnce strted off s qusi-indemnity policy - in most cses pying fixed mount per dy in the hospitl. The first Blue Cross policies, for exmple, were o1 A fir insurnce policy tht chrges $1 ech yer nd pys n mount k when sick is defined by: pk+ 1 =. Thus, k = -p. Some uthors ssume the insurnce pyment is mde only when the person is helthy, in which cse the fir odds policy is defined by: pk' + (1 - p) =, or k'= -(1 - p)/p.

14 576 D.M. Cutler nd R.J. Zeckhuser developed just before nd during the Gret Depression. These policies, run by hospitls, gurnteed certin number of hospitl dys per yer (for exmple, 21 dys) for n nnul premium (for exmple, $5 to $1 in the erly 193s). After World Wr II, life insurnce compnies entered the helth insurnce mrket, driven by the profits of Blue Cross policies nd the expnding demnd for helth insurnce resulting from its fvorble tx tretment. These nscent helth insurers offered indemnity policies s well, limiting their potentil losses by fixing the mximum mount they would py per hospitl dy. 3. Morl hzrd nd principl-gent problems Helth insurnce must ddress severl problems beyond risk spreding. We now turn to some of these chllenges Morl hzrd Morl hzrd refers to the likely mlfesnce of n individul mking purchses tht re prtly or fully pid for by others [Arrow (1965), Puly (1968, 1974), Zeckhuser (197), Spence nd Zeckhuser (1971), Kotowitz (1987)].1 He will overspend; i.e., he will use more services thn he would were he pying for the medicl cre himself. Since insurnce is n rrngement where others py for the lion's shre of one's losses, it cretes morl hzrd to use dditionl medicl resources. The designtion morl hzrd, disquieting term, frequently connotes some morl filure of individuls, but this is not ment to be so. Indeed, Kenneth Arrow (1985) employs the less judgmentl nd more informtive term "hidden ction" for morl hzrd. Morl hzrd is concern becuse it conflicts with risk-spreding gols. Insurnce is vluble becuse it llows people to trnsfer income from when they need it less to when they need it more. But this trnsfer is not perfect becuse people increse their consumption of medicl cre when it is subsidized. This cretes n inherent secondbest problem in designing insurnce policies: insurers must trde off the benefits from spreding more risk ginst the cost of incresed morl hzrd. We formlize this Lesson 1 bout helth insurnce: Lesson 1: Risk spreding versus incentives. Helth insurnce involves fundmentl trdeoff between risk spreding nd pproprite incentives. Incresing the generosity of insurnce spreds risk more brodly but lso leds to incresed losses becuse individuls choose more cre (morl hzrd) nd providers supply more cre (principl-gent problems). 11 The theory of morl hzrd, if not the words, goes bck t lest to Adm Smith: "The directors of such compnies, however, being the mngers rther of other peoples' money thn of their own, it cnnot well be expected, tht they should wtch over it with the sme nxious vigilnce with which the prtners in privte coprtnery frequently wtch over their own... Negligence nd profusion, therefore, must lwys previl, more or less, in the mngement of the ffirs of such compny" [Smith (1776, p. 7)].

15 Ch. 11: TheAntomy of Helth Insurnce 577 Morl hzrd, or hidden ction, emerges in one form in the risks tht individuls choose to tke. People my tke worse cre of themselves when they hve insurnce thn if they do not. If their ctions were redily observed, the insurnce compny would merely not py off were they reckless or negligent. But individul ctions re difficult to observe; they re hidden. The extent of morl hzrd in terms of ctions tht ffect helth my not be lrge for helth insurnce in most instnces, since the uncompensted loss of helth itself is so consequentil.1 2 Thus, it would be surprising if people smoked becuse they knew helth insurnce would cover the costs of lung cncer. Hidden ction lso rises becuse individuls my get tretments they would not py for themselves. Though the ction itself (seeking medicl cre) is not hidden, the motivtion behind it is. 13 Optiml insurnce plns would py for tretment only if the individul would hve chosen the sme tretment hd he borne the full bill. The thought experiment here is whether the person would py for the medicl expenditure in expecttion, before he knew his condition. For exmple, suppose tht person hs income of $25,, nd fces 1 percent probbility he will hve serious illness. If he could commit in dvnce, he would gree to receive $5, of medicl cre when sick in exchnge for $5 premium. If fully insured, however, the individul will choose to consume $6, of cre. The morl hzrd in this exmple is $1, - the dditionl spending beyond the optiml mount of cre he would contrct for in dvnce of being sick. In the terminology of demnd theory, morl hzrd is the substitution effect of people spending more on medicl cre when its price is low, not the income effect of people spending more on medicl cre becuse of insurnce, by efficiently trnsferring resources from the helthy stte to the sick stte, mkes them richer when sicker [De Mez (1983)]. In the exmple considered, sy the individul would hve spent hlf his income, $12,5, on medicl cre in the bsence of insurnce. Insurnce thus rises medicl spending by $47,5, but only frction of this increse is due to morl hzrd. If some fixed m were the known optiml medicl expenditure for ny sick person, insurnce plns would experience no morl hzrd. They could simply py m in medicl expenditures to or for those who re sick. Morl hzrd rises becuse medicl needs re not fully monitorble, nd different people with the sme condition hve different optiml expenditures, t lest s best the insurnce compny cn determine. Suppose tht the optiml medicl expenditure for treting prticulr condition is mi, which vries cross people, indexed by i. The insurnce compny requires the individul to py coinsurnce mount c(m) for medicl cre received. The rest of the cre, m - c(m), is pid by the insurer. In effect, the insurer tkes the individul's medicl expenditure 12 This does not men tht people will not smoke or fithfully tke their medictions. But there is no morl hzrd if their ctions would be the sme if they hd no helth insurnce, i.e., if these helth-hrming behviors re inelstic with respect to cost shring. 13 Morl hzrd lso results from ptients mking less effort to serch for low-cost providers. For exmple, when ptients py but one-fifth of the cost of their drugs, they will hve wek incentives to switch to generic brnds or stry beyond the locl phrmcy.

16 578 D.M. Cutler nd R.J. Zeckhuser to be signl of his true medicl needs; the coinsurnce pyment cretes the necessry costs to hve signling operte. Two polr extremes for the form of c(m) re commonly found. The first is the indemnity policy discussed bove: the insurer pys fixed mount, cll it m*, nd the individul pys c(m) = m - m*. The second is full insurnce: the insurer pys the full costs of medicl cre, regrdless of its cost, nd the individul pys nothing (i.e., c(m) = ). The full insurnce policy removes ll risk from the insured, but engenders greter morl hzrd. To understnd the optiml insurnce policy, consider cse where n indemnity policy is not optiml. Suppose tht rther thn being helthy or sick, the individul hs rnge of potentil illness severities, s, with s distributed with density function f(s). Helth is given s before by h = H[s, m]. The ptient's s will determine the optiml tretment. The insurer cnnot observe s, however. Thus, mking fixed indemnity pyment to nyone sick is not optiml. The ex nte utility function for the insured consumer is: V = u(y - r - c(m(s)), H[s mf m(5) (s), ds, where mr(s) tells how much medicl cre n individul with condition s chooses to receive. We consider first the optiml policy - the mount of medicl services the person would like to contrct for if he could write perfect stte-contingent contrct nd thereby eliminte morl hzrd. When s is observble, the coinsurnce rte depends only on s, hence cn be written s c(s). The individul will choose m*(s) mximum fesible utility: Mx(s) f U(y - - c(s), H[ s) dss,(6) where 17 = f(m(s) - c(s))f(s) ds. The solution to this problem sets Hm UH = E[Ux], (7) where the subscripts denote prtil derivtives nd x = y c(s). The left-hnd side represents the gin in utility from spending nother dollr on medicl cre; it is the product of the effect of medicl cre on helth nd the effect of helth on utility. The right hnd side is weighted verge expecttion of the mrginl utility of consumption in different illness sttes, nmely: E[U,] = f U,(y - - c(s), H[s, m])f(s)ds. (8)

17 Ch. 11: The Antomy of Helth Insurnce 579 Eqution (7) sys tht with the optiml first-best policy, the expected mrginl utility gined from n dditionl dollr of medicl cre in ech stte of the world equls the utility cost of dollr. 14 In the cse where the mrginl utility of income does not depend on the helth stte, 15 imposing coinsurnce pyment in ny helth stte, i.e. vrible c(s), increses the vribility of income nd thus reduces expected utility. The optiml policy for this commonly studied cse in thus no coinsurnce, nd pyment m*(s) tht fully reimburses optiml spending in ech stte. 16 Now consider sitution where severity of illness is not monitorble, hence the optiml policy just discussed cnnot be implemented. At the time the consumer is seeking medicl cre, he lone knows his severity. We ssume the consumer trets the insurnce premium s fixed - nothing he does will rise or lower his insurnce premium tht yer. Further, we ssume for now tht individuls re not penlized in future yers for dditionl medicl spending this yer, becuse expected future chnges in costs re spred eqully over everyone in the group. The cost to the consumer of nother dollr of medicl expenditure will be c'(m).17 The sick consumer will therefore choose medicl cre utiliztion to mximize utility when sick. Thus, he will choose m#(s) s the m which mximizes utility given knowledge of s: Mx(s)U(y -17-c(m), H[s, m]) for ech s. (9) The solution to this problem will depend on the specific s the individul hs relized, nd is given by the first order condition: Hm Uh = c'(m)uzx forechs. (1) The left-hnd side once gin represents the gin in utility from spending nother dollr on medicl cre. The right-hnd side is the utility cost to the individul from spending 14 This ssumes tht these functions re well behved, hence tht locl optim re globl optim. Some medicl expenditures my offer incresing returns over relevnt rnge. For exmple, it my cost $2, to do hert trnsplnt, with $1, ccomplishing much less thn hlf s much. Efficiency then requires the insurnce progrm spend t lest to the minimum verge cost of benefits point, or not t ll. 15 This cse would rise if utility is dditively seprble between income nd helth. 16 If utility does depend on the helth stte, for exmple, if disbled person needs more non-medicl services, then optiml coincurnce will ctully py the individul when disbled. 17 The structure of the insurnce pln my present the insured with rnge of decresing mrginl cost. Sy pln hs deductible of $6 with copyment of 2% beyond tht point, common structure. The insured cn receive $6 of benefits for $6, but $12 of benefits for $72. Sy the individul solves, nd finds $4 expenditure is loclly optiml. He must lso look globlly to the optiml expenditure beyond $6, which my be superior. Recognizing tht using up deductible gets one to rnge of lower costs, gives the insured n interesting dynmic optimiztion progrm where there re two benefits from spending below the deductible: (1) the helth cre itself, nd (2) the incresed potentil for getting to the low-cost rnge [Keeler, Newhouse, nd Phelps (1977)].

18 58 D.M. Cutler nd R.J. Zeckhuser tht dollr; it is the product of the out-of-pocket cost of medicl cre nd the utility loss from losing tht dollr for consumption. Compring Equtions (7) nd (1) shows the loss due to morl hzrd. When c'(m) < 1, s it will be when mrginl spending is in ny wy insured, people will overconsume medicl cre when sick nd thus py more for helth insurnce thn is optiml.l Evidence on the price elsticity of medicl cre demnd How does n individul's demnd for medicl cre respond to his required out-of-pocket expenses? Economists used to differ on this question. Tble 3 detils estimtes of the elsticity of demnd for medicl cre. 19 A substntil literture in the 197s estimted the elsticity of demnd for medicl cre using cross-sectionl dt, or cross-sectionl time series dt. Pre-eminent mong these ppers re Feldstein (1971), Phelps nd Newhouse (1972b), Rosett nd Hung (1973), nd Newhouse nd Phelps (1976). Feldstein (1971) ws the first sttisticlly robust estimte of price elsticities using time-series micro dt, in this cse on hospitls. Feldstein identified the effect of coinsurnce rtes on demnd using stte-vrition in insurnce coverge nd generosity, estimting demnd elsticity of bout -.5. The subsequent ppers use ptient-level dt nd more sophisticted study designs. The elsticities tht emerged from these ppers rnged from s low s -.14 [Phelps nd Newhouse (1972b)] to s high s -1.5 [Rosett nd Hung (1973)]. The impliction of this rnge of elsticity estimtes ws tht morl hzrd ws likely significnt force. This estimtion literture suffered from two mjor difficulties, however. First, the generosity of helth insurnce t either the stte or the individul level might be endogenous. Generous insurnce might boost utiliztion of medicl services, s posited; or lterntely, res where people desire or need more medicl cre my lso be res where people demnd more helth insurnce. One cnnot seprte these two effects sttisticlly without n instrument for the rte of insurnce coverge in n re, but such instruments were not esy to find. Second, the studies typiclly filed to distinguish verge nd mrginl coinsurnce rtes. Usully for dt resons, most of these studies relted medicl spending to the verge coinsurnce rte in n re. But theory predicts tht medicl spending should relte to the mrginl coinsurnce rte. Becuse insurnce policies re non-liner, verge nd mrginl prices my differ substntilly. 2 As result of these problems, s lte s the 197s mny critics still believed tht medicl cre ws determined by "needs" nd no other economic fctors, i.e., tht demnd ws totlly 18 This cn be derived by tking expecttions of both sides of Eqution (1) nd compring to Eqution (7). There is lso risk-bering loss when severity, is not monitorble, s reflected by the term U. in (1) s opposed to E(ux) in (7). 19 Zweifel nd Mnning (2) discuss the elsticity of demnd for medicl cre in more detil. 2 Of course, if individuls re ppropritely forwrd looking, it is the expected mrginl coinsurnce rte t the end of the yer tht should ffect behvior, rther thn the ostensible mrginl coinsurnce rte t the time services re used.

19 Ch. 11: TheAntomy of Helth Insurnce 581 OD,.2 = :g =,X C 7 - o l tv u e, t ~o C. N O _ 6 t6 C o - % 'g' 8 - = ec, c' o - o 8 1 F C) o _O ej., -,. -- C fg t o OC. o,, - t - '- r- CO o _ sm. C C- E o 5 'Zw CO E, >., o-, C C ON ONo P e, ~ ~ ~ OO COO d L4 F4 ~~~~~~~~~~~~~~~~~~~,~ donq

20 582 D.M. Cutler nd R.J. Zeckhuser ) t..~5 O :> * 5s - 7 rr I E- 'o r- * ~ O -h - O c CO o d r 9Z ~ - "Zi, 41 1 C) ). CO.2 -s 1. H E H Y w.fc E Ed o -c o Jo -='Sp ) C. o c5 oi o v o o~. 9 99o O, - C O 9 P C C R. 5 5 o ).5 5 ~ g SH SH.9. t b.9.) 't ) ) 5 3 i - 5.i 5 8~.9r / o 5 - O = N I I I.. E ) r - o 9; ' 5.J ) 9. C. 9 o '. CO> CO o CO CO C 5 t C o O... F _m. 9 5 U o~h ) 9 o 9 o 7 t. I On ~,- ' CO U 'C. ON o - CO C.-. PI. rn ) 9 i E COB - '8 I U R c 8? - ) - CO 9 I O O i m, U 5'9 U ) - CO "-SC 9A5 Z ~2 o - - N A C- C - C V) <C -m, -. - CO 4 ) t, U, cz 3 CL C- r- -C'. z- - ) z ,. cl Or O z I CO,.1 cn 5 Euz. CO<o oo

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