The Macroeconomics of Universal Health Insurance Vouchers (Preliminary and Incomplete)

Transcription

1 The Macroeconomics of Universal Health Insurance Vouchers (Preliminary and Incomplete) uergenung Towson University ChungTran University of New South Wales 9th April 2009 Abstract We investigate a government financed voucher program that allows all Americans to buy health insurance in the private insurance market. We investigate whether health insurance vouchers are able to increase the number of people with health insurance and decrease aggregate health care spending that threatens the solvency of Medicare and Medicaid. We develop a multi-generation dynamic general equilibrium model with endogenous health spending and endogenous health insurance choice and calibrate the model to U.S. data. We then conduct a counterfactual policy experiment and introduce universal health insurance vouchers into this economy. Our analysis suggests that the decrease in health care expendiure as fraction of GDP is primarily due to a general equilibrium savings effect. This effect is caused by increased sales taxes that are needed to finance the health insurance vouchers. Decreased moral hazard due to replacing Medicare with private health insurance plays a minor role. In our model, universal health insurance vouchers transform an economy with high aggregate consumption rates, high health expenditure rates by old agents, and low aggregate savings rates into an economy with lower aggregate consumption rates, lower health expenditure rates by the old, higher health expenditure by the young, and higher aggregate savings rates. Health vouchers therefore seem promising in being able to sustainably finance health care expenditures while providing full health insurance coverage to the entire U.S. population. EL:H5, I8,I38 Keywords: Health Insurance Vouchers, Vouchers, Consumer Driven Health Care Plans, Health Insurance, Privatization of Medicare, General Equilibrium Health Uncertainty Model, Numerical Simulation of Health Care Reform Correspondingauthor: uergenung,towsonuniversity,u.s.a. Tel.: (82) , jjung@towson.edu SchoolofEconomics,UniversityofNewSouthWales,Sydney,Australia. Contact: chung.tran@unsw.edu.au

2 Introduction Adverse selection and moral hazard prevent insurance markets from working effectively. Government interventions in health insurance markets and health care markets can potentially ameliorate the situation but can also introduce distortions and decrease competition. Low health insurance coverage rates and high aggregate health spending that threaten the solvency of Medicare and Medicaid are direct consequences of a malfunctioning health care system. Many researchers have therefore pointed out the need for a substantial reform of the U.S. health care system. One of these proposals discusses a universal health insurance voucher system that would distribute government vouchers to U.S. households which can be used to buy private health insurance. The size of the voucher would depend on the health status of the individual. Systems of universal health insurance vouchers have recently been discussed in Kotlikoff (2007) and Emanuel and Fuchs(2007). These authors argue that universal health insurance vouchers can curb aggregate health spending in the U.S. and achieve universal coverage simultaneously. The success of the health insurance voucher program will depend on the design of the voucher system and how households and private insurance companies respond to this intervention. Theoretically, it is unclear whether health insurance vouchers administered by the government would ultimately improve private health insurance markets or completely damage them. Itisalsounclearatthispointwhatsuchasystemwouldcostandwhetheritwillreally be able to reign in aggregate health expenditures. The following are the main issues arising from a universal health voucher program. First, a health voucher system may worsen moral hazard in private health insurance markets. Private spending on medical services may end up increasing as private agents react (optimally) to the new risk-sharing mechanism. Previously uninsured households would increase their health spending after buying insurance with health vouchers, whereas households who were previously insured may still not curb their spending by simply buying additional health insurance. Consequently, the reform may increase coverage but fail to decrease aggregate health care expenditures even when the government indexes spending on a health voucher program to a fixed health-spending to GDP ratio. Second, a poorly designed health voucher system could severely damage private health insurance markets. If the voucher amounts are too low because the rating system of the government underestimates the expected health expenditures of the patients, then participating private health insurance companies will make losses and will be driven out of the voucher market. Private health insurance companies would then only insure subpopulations and only accept certain risk types (e.g. voucher sizes) where the government managed to accurately price the expected health expenditures. Some patients would then not beabletousetheirvouchersintheprivatemarketinwhichcasethegovernmentwouldhave to insure them directly. This could create unfair competition for private health insurers and further reduce their market share. Finally, vouchers might not be a better replacement for Medicare and Medicaid. The main argument for vouchers is that currently Medicare/Medicaid costs are exploding and the programs in their current form are unsustainable. A voucher system would freeze medical expenditures at a fixed percentage of GDP. This effectively shifts the burden over to private insurance companies who would now try to contain the cost explosion by pressuring health care providers. This will only work if the vouchers are large enough in order to keep the insurance companies solvent so that they keep participating in the system. If costsincreasefromtheproviderside,theneitherthesizeofthevouchershastoincreaseorthe insurance companies must be allowed to ration care(e.g. reduce the services offered in the base insurancepackagethatiscoveredbythevoucher). Ifthatisnotthecase,theninsurancecompanieswillgobankruptordropoutofthevouchermarket. Inthelatercase,thegovernment 2

3 hastostepinandbecomethesoleproviderofbaseinsuranceifitwantstomaintainuniversal coverage. However, this brings us back to the problem that Medicare/Medicaid faces today. The universal health voucher program(i) fundamentally affects consumption, savings and health spending, (ii) has impacts on the entire health care system and (iii) makes up a significant share of the government budget. We therefore think that a macroeconomic analysis, using a state of the art dynamic general equilibrium framework, is necessary to capture most of these effects. None of these effects of a universal health voucher programs have been analyzed thoroughly in the literature. In this paper we therefore investigate whether a health insurance voucher program could solve the problems of under-coverage in health insurance markets and cost explosions in public health care programs like Medicare/Medicaid. We argue that it is critical to understand how households and private insurance companies rationally respond to the government s intervention in order to determine whether health insurance vouchers could be a successful instrument for U.S. health care reform. For the purpose of our analysis we develop a general equilibrium overlapping generations model with health production. Departing from standard models we introduce the following features into our model: (i) endogenous health(capital) production and endogenous health care spending; (ii) endogenous health insurance choice; and (iii) the basics of a health insurance voucher program. We calibrate the model to U.S. data. Preliminary results suggest that the reform increases coverage and decreases the share of GDP spent on health care. Our results also indicate that as private agents react(optimally) to the new risk-sharing mechanism the universal health insurance voucher system adds to moral hazard in private health insurance markets and results in increased spending on medical services. However, as this happens simultaneously with an increase in the savings rate, the model predictsadropofmedicalspendingasshareofgdpduetogrowtheffects. Ourresultshighlight the importance of modelling health insurance, medical spending, and general equilibrium effects together in order to comprehensively analyze universal health insurance vouchers. We see some potential in vouchers being able to transform an economy with high aggregate consumption rates, high health expenditure rates by old agents, and low aggregate savings rates into an economy with lower aggregate consumption rates, lower health expenditure rates by the old, higher health expenditure by the young, and higher aggregate savings rates. Health vouchers therefore seem to be able to generate sustainable health expenditures by providing full health insurance coverage. This effect, however, is not driven by increases in government control over the size of the voucher program (this is endogenous in our model) but mainly by general equilibrium effects on savings and consumption. The latter effects are caused by increased sales taxes that are needed to finance the health insurance vouchers. Interesting alternative experiments with this model could analyze alternative financing schemes for health insurance vouchers (income tax, capital tax) as well as comparisons with an economy where the government provides insurance directly. The paper is structured as follows. The next section discusses recent proposals of universal health insurance voucher systems. Section 3 introduces the model. In section 4 we present the calibration of the model. Section 5 contains the results of our policy experiment and section 6 concludes. The Appendix contains all tables and figures and derivations of the welfare measures used in this paper. 2 Health insurance vouchers Universal health voucher systems share the following features: (i) Universal coverage via health vouchers that are offered annually to every American, (ii) individuals with higher expected 3

4 health care costs receive bigger vouchers,(iii) participants buy health insurance from private insurance companies and can switch plans every year,(iv) the government defines a basket of basic health services that every participating health plan has to cover,(v) insurance companies compete for patients health vouchers, (vi) the annual budget for health vouchers is fixed by the government as a share of GDP, and(vii) Medicare, Medicaid, and employer-based health insurancetaxbreaksareeliminated. The plan works as follows: Each year an individual receives a voucher to purchase insurance coverage(from private insurance companies) for the next year. The size of the voucher is based on the individual s current medical condition. A sick person would receive a large voucher so that insurance companies would like to have her as customers as well and the adverse selection problem prevalent in the current market for health insurance is mitigated. The government would determine the current medical condition of an individual using an experience rating system which would be revised on a yearly basis. The experience rating system would provide an estimate for the expected health care expenditure for the next year. The voucher plan would be progressive as the poor, and therefore more prone to illness, would receive larger vouchers. Current tax deductibility of employer provided health insurance, a subsidy to relatively wealthier households, would be discontinued. All medical information would be transmitted electronically to the government as basis for the experience rating. Confidence of this information would be strictly maintained as it is currently done for Medicare patients. Theinsurerwouldofcourselearnthemagnitudeofthevoucherandwouldbeable to infer the type of the patient. This is currently not possible in private health insurance markets and triggers the adverse selection problem. The insurer would be required to keep this information confidential. The government establishes the values of the vouchers each year and can effectively control the size of its expenditure(in terms of GDP). Benefits would then rise asthesamegrowthrateasgdpandnotoutgrowgdpasitiscurrentlythecase. All insurers participating in the voucher system would have to cover the governmentdetermined set of basic benefits, including prescription drug coverage and nursing home care. The government would therefore be rationing health care, or at least the healthcare that it is willing to pay for. Insurers could offer supplemental insurance that would cover services that are not covered under the basic policy (e.g. private hospital beds, etc.). In order to alleviate a possible adverse selection problem with additional insurance, the plan would only allow additional insurance from the primary health insurer who can infer the health of the client from the health voucher. Insurers can still include deductibles and copayments in their policies whichwouldlimittheuseofhealthcareandreducemoralhazard. Theinsurercanalsoinclude rewards for healthy behavior. An open question is whether any additional funds would be required to finance the voucher system. Emanuel andfuchs(2007) and Kotlikoff(2007)proposearetail sales tax oravat tax in case such additional funds should be necessary. Currently it is not known how much Kotlikoff (2007)attributes theidea toeconomistspeterferraraattheinstitute forpolicy Innovation and ohn Goodman, president of the National Center for Policy Analysis. An earlier contribution suggesting the use of vouchers to reform Medicare is Butler, Moffit and Liu (995). A World Bank publication, WorldBank (2005), provides a summary of the mechanics of health care vouchers. The system proposed by Kotlikoff(2007) is termed the Medical Security System(MSS) and the system proposed by Emanuel and Fuchs(2007) is referred to as Universal Healthcare Vouchers(UHV). The main differences between the MMS and the UHV are that. UHVdotheexperienceratingattheleveloftheinsurerorHMO,whichstillleavessomeoftheadverse selection problems in the system. 2. UHV would maintain Medicare, which according to Kotlikoff(2007) is not a viable option, since Medicare will bankrupt the system eventually. 4

5 extra funding would be needed. 3 Themodel 2 3. Demographics Weuseanoverlappinggenerationsframework. Agentsworkfor periodsandthenretirefor periods. Ineachperiodthereisanexogenoussurvivalprobabilityofcohortjwhichwe denoteπ j. Agents die for sure after periods. Deceased agents leave anaccidental bequest that is taxed and redistributed equally to all agents alive. The population grows exogenously atanannualnetraten.weassumestabledemographicpatterns, sothatsimilartohuggett (996), agej agents makeupaconstantfraction µ j of theentirepopulationatany pointin time. Therelativesizesofthecohortsaliveµ j isrecursivelydefinedas µ j = π j µ (+n) years j, where years denotes the number of years modeled. The relative size of cohorts dying in each period(conditional on survival up to the previous period) can be defined similarly as 3.2 Preferences µ j = π j µ (+n) years j. Households value consumption c and services s derived from health h. We assume a linear technology, s = g(h) = h, that transfers health capital from the current period into health services in the current period. Household preferences are described by a utility function u(c, s) whereu:r 2 RisC 2 andsatisfiesthestandardinadaconditions. 3.3 Technology and firms Inthiseconomy,thereisacontinuumofidenticalfirmsthatusephysicalcapitalKandhuman capitalltoproduceonetypeoffinalgood. Thefinalgoodcanbeusedasaconsumptiongoodc and medical services m. We do not model the production of medical services m separately. The priceofconsumptiongoodsisnormalizedtooneandthepriceofmedicalservicesisdenotedp m. Eachunitofconsumptiongoodcanbetradedfor p m unitsofmedicalservices. Firmschoose physical capital K and human capital L to solve the following profit maximization problem max {F(K,L) qk wl}, () {K, L} taking the rental rate of capital q and the wage rate w as given. Capital depreciates every periodatrateδ. 2 In the current version of the model we abstract from modelling competition in health insurance markets. Our model is therefore not able to capture potential efficiency gains of the voucher system due to increased competition in private health insurance markets. Second, we also do not model the effects of private insurance companies monitoring health care providers and potential gains from increased monitoring due to vouchers. 5

6 3.4 Production of health and the human capital profile Allmedicalcareisusedtoproducenewunitsofhealth. WefollowGrossman(972b)anduse the following accumulation process for health capital h j =i(m j )+ δ j h j +ε j, (2) where h j denotes the current health status (or health capital), function i(m j ) denotes the period health investment function that produces new health with inputs of medical services m j,ε j isanexogenoushealthshock. Health capital depreciates at rate δ j which is a function of the health status at the beginning of the period. This partly captures the immediacy of health expenditures. The longertheagentwaitsto treat ahealthshockwithnewspendingonmedicalcare,themore health is allowed to depreciate, and the higher the health depreciation rate becomes. Finally, anexogenoushealthshockε j followsamarkovprocesswithtransitionmatrixp. Transition probabilitiesfromonestatetothenextdependonthepasthealthshockε j sothatanelement oftransitionmatrixp j isdefinedas P(ε j,ε j )=Pr(ε j ε j ). Notethatweonlymodeldiscretionaryhealthexpendituresm j inthispapersothatincome will have a strong effect on endogenous total medical expenses. Our setup assumes that given the same magnitude of health shock ε j, a richer individual will outspend a poor individual. This may be realistic in some circumstances, however, a large fraction of health expenditures in the U.S. are probably non-discretionary (e.g. health expenditures caused by catastrophic health events that require surgery etc.). In such cases a poor individual could still incur large healthcarecosts. Wedonotcoverthiscaseinthecurrentmodel. Effectivehumancapitale(j,h j )isafunctionofageandhealthcapitalatthebeginning of the period. 3.5 Health insurance markets We restrict the availability of private health insurance to working agents only. We assume that insurance is employer provided so there is no private insurance markets for retirees. In addition, we assume that health insurance companies can screen the worker by age but not by healthstatus. 3 Privatehealthinsurancehaveadeductibleρandcopaymentrateγandcanbe boughtatapremiump j. Thesepremiumsaretaxdeductible. We do not distinguish between group insurance(employer provided) and individual insurance(bought by individuals in the private insurance market). We therefore combine elements of group insurance(e.g. tax deductibility of premium payments) with elements from the individual insurance market(e.g. screening by age) in order to make a statement about the entire private insurance market. Wecaninterpretthemodelasiftheemployeecanchoosetoworkforthreedifferenttypes of employers. Employer one is offering a low deductible health insurance via an insurance company, employer two is offering a high deductible health insurance via a different insurance 3 Weareawarethatemployersarenotallowedtodiscriminateaccordingtohealthstatusoragewhenoffering health insurance. However, we think this is still an acceptable assumption. Between 2000 and 2002, older workers experienced rising unemployment rates that were greater in relative magnitude than those for younger workers over the same period(six(2003)). This suggests that older worker are more likely to lose their employer provided health insurance. They are then forced to buy insurance in the individual market, where they have to pay higher premiums because of their age. 6

7 company, and employer type three offers no health insurance. The tax deductible health insurance premium that enters the workers budget constraint together with the wage income can then be interpreted as the effective wage income. As a consequence, an employee with a health insurance package receives a lower effective wage than an employee working a job without health insurance. Since we do not model employer matching, we abstract from these details and simply claim that the employee can make the employment and insurance type choice. This alsoallowsustoonlyhaveonerepresentativefirmthatpaysonewagerate. Employeesthen decide on their efficiency wage by deciding which insurance they want to have. Inordertobeinsuredagainstahealthshock,agentshavetobuyinsuranceoneperiodprior totherealizationoftheirhealthshock. Agentsintheirfirstperiodoflifearethusnotcovered byanyinsurance. Wedistinguishbetweentwopossibleinsurancestates,in j ={,2},where in j =isthestateofhavingnoinsuranceandin j =2indicatesthattheagenthashealth insurance in period j. The working household s out of pocket health expenditure is therefore denoted as { o(m j )= p m,noins m min[p m,ins m j,γ+ρ(p m,ins m j γ)] ifin j =, ifin j =2, whereγ is the deductibleand ρisthecoinsurancerate. where p m,ins isthe relativepriceof health expenditurespaidby insuredworkersand p m,noins isthe price of healthexpenditures paidby uninsuredworkers. Anuninsured workerpays ahigherpricep m,noins >p m,ins. The copaymentrateγ isthefractionthehouseholdpaysaftertheinsurancecompanypays( γ) of the post deductible amount p m,ins m j ρ. Since households have to buy insurance before health shocks are revealed we assume that working households in their last period j = already decide to buy into Medicare. Insurance companies satisfy their budget constraint within each period and we allow for cross subsidizing across generations. The constraint is (+ω) + [ ] µ j=2 j I {inj (x j )=}( γ)max(0,p m,ins m j (x j ) ρ) dλ(x j ) (3) = I {inj+ (x j )=}p j dλ(x j ) j= µ j whereωisamarkupfactorthatdeterminestheprofitoftheinsurancecompany,i {inj+ (x j )=} is an indicator function equal to unity whenever agents bought the health insurance policy. Since agents have to buy their insurance one period prior to the realization of the health shock, first period agents are not insured. Profits are redistributed in equal amounts to all surviving agents. Alternatively, we could discard the profits ( thrown in the ocean ) in which case we could think of them as loading costs (fixed costs) associated with running private insurance companies. In the model with health vouchers, insurance companies are allowed to charge idiosyncratic premiumsthatareequaltotheexpectedhealthspendingoftheagentinthenextperiod. This premiumcanbewrittenasafunctionoftheagentstatevectorx j, p j (x j )=π j E[( γ)max(0,p m,ins m j+ (x j+ ) ρ)]. Sincepremiumsp j arepaidforbyvouchersfromthegovernmentandthesizeofthevouchers isequaltotheexpectedfuturehealthexpenditureoftheagent,ithastoholdthat p j (x j )=v(x j ). 7

8 Again, insurance companies satisfy their budget constraint within each period. We allow for cross subsidizing across generations. (+ω) µ j= j [( γ)max(0,p m,ins m j (x j ) ρ)]dλ(x j ) (4) = v j (x j )dλ(x j ), and j= µ j whereω isamarkupfactorthatdeterminestheprofitoftheinsurancecompany. Weimpose that insurance companies do not save! They make zero profit in equilibrium. 3.6 Government The government taxes workers income(wages, interest income, interest on bequests) at a progressivetaxrate τ(ỹ j )whichisafunctionoftaxableincomeỹandfinancesthesocialinsurance program T SI as well as government consumption G. The government budget is balanced so that G+ µ j= j Tj SI (x j )dλ(x j )+ µ j= j v(h j (x j ))dλ(x j ) (5) = Tax j (x j )dλ(x j )+ τ C c(x j )dλ(x j ). j= µ j j= µ j Government spending G plays no further role ( thrown in the ocean ). Accidental bequests are redistributed in a lump-sum fashion to all households µ j= j T Beq j (x j )dλ(x j )= µ j=j j a j (x j )dλ(x j ), (6) where µ j denotesthedeceasedmassofagentsagedjintimet.anequivalentnotationapplies forthesurvivingpopulationofworkersandretireesdenotedµ j. The Social Security program is self-financing µ j= + j Tj Soc (x j )dλ(x j ) (7) = 0.5τ Soc we j (x j )+0.5τ Soc( w ) j (x j ) {inj (x j )=}p j {inj (x j )=2}p j dλ(x j ). j= µ j In the benchmark model, the government runs a Medicare program for retirees. After retirementallagentsarecoveredbymedicare. Medicarethenpaysafixedfraction ( γ Med) of the health expenditures that exceed the amount of the deductible ρ Med. The total out of pocket expenditures of a retiree are [ o R (m j )=min p m,ins m j,γ Med +ρ Med( p m,ins m j γ Med)], ifj> +, wherep m,med isthepriceofhealthservicesthatretireeswithmedicarehavetopay. Weassume that old agents j > + do not purchase private health insurance and that their health costs are covered by Medicare and their own resources plus social insurance(e.g. Medicaid) if 8

9 applicable. 4 TheMedicareprogramisself-financing µ j= + j Tj Med (x j )dλ(x j ) = 0.5τ Med we j (x j )+0.5τ Med( w ) j (x j ) {inj (x j )=}p j {inj (x j )=2}p j dλ(x j ). j= µ j In our alternative regime, Medicare is eliminated and government runs a health insurance voucher program, instead. Households receive a health voucher each period that they can use to buy their basic health insurance coverage. The amount of the voucher depends on the discounted(and mortality adjusted) expected health expenditure of the agent in the next period. Wecanthereforewritethesizeofthevoucherforeachagentasafunctionoftheagent statevectorx j v(x j )=π j E[( ρ)max(0, p m,ins m j+ (x j+ ) γ)]. Vouchersarefinancedbyasalestaxτ C onfinalgoodsconsumption. Notethatinthebenchmark model there is no voucher program. 3.7 Households Agejyearoldagentsentertheperiodwithstatevectorx j =(a j,h j,ε j ),wherea j isthe capitalstockatthebeginningoftheperiod,h j isthehealthstateatbeginningoftheperiod, andε {ε,...,ε k }isoneofkpossiblenegativehealthshockswhere0 ε >ε 2 >...,ε k.the statevectorofahouseholdofagej isdefinedas x j = { (a j,h j,in j,ε j ) R + R + {,2} R =D. Foreachx j D(x j )letλ(x j )denotethemeasureofagej agentswithx j D.Thefraction µ j Λ(x j ) then denotes the measure of age-j agents with x j D with respect to the entire population of agents in the economy Workers Agents are endowed with one unit of time that they supply inelastically to the labor market. Agents therefore receive income in the form of wages, interest income, accidental bequests, and social insurance. The latter guarantees a minimum consumption level of c. After health shocks arerealized,agentssimultaneouslydecidetheirconsumptionc j,stocksofcapitalforthenext period a j+, and health service expenditures m j. They also pick the insurance state for the nextperiodin j+ ={,2},whichrequiresthemtopayapremiump j forin j =ornothingfor in j =2.Thehouseholdproblemforworkersj={,..., }canbeformulatedrecursively as V (x j ) = max {u(c j,s j )+βπ j E ε [V (x j+ ) ε j ]} {c j,m j, a j+,in j+ } s.t. (8) 4 AccordingtotheMedicalExpendiurePanelSurvey(MEPS)200,only5%oftotalhealthexpendituresof individuals older than 65 are covered by supplementary insurances. Cutler and Wise (2003) report that 97% of people above age 65 are enrolled in Medicare which covers 56% of their total health expenditures. Medicare PlanBrequiresthepaymentofamonthlypremium andayearlydeductible. SeeMedicare and You(2007)for a brief summary of Medicare. 9

10 ( +τ C ) c j +(+g)a j+ +o W (m j )+I {inj+=2}p j = w j +R ( a j +T Beq) Tax j +T SI j +v j, 0 a j, v j p j, where ( w j = 0.5τ Soc 0.5τ Med) we(j,h j ), (9) Tax j = τ ( ỹj W ) ( +0.5 τ Soc +τ Med) w j, ỹ W j = w j +ra j +RT Beq, T SI j = max [ 0,c+Tax j w j R ( a j +T Beq j )]. Variable c j is consumption, a j+ is next period s capital stock 5, g is the exogenous growth rate, o W (m j ) is out-of-pocket health expenditure, m j is total health expenditure, p j is the insurance premium for the low deductible health insurance, p j is the insurance premium for the high deductible health insurance, w j is wage income net of the employer contribution to SocialSecurityandMedicare,Risthegrossinterestratepaidonassetsa j fromtheprevious period and accidental bequests T Beq j, Tax j is total taxes paid 6 and Tj SI is Social Insurance (e.g. Medicaidandfoodstampprograms). ( ) Thefactthatweuse w j inthetaxbaseforincome tax τ ỹj W leadstoadoubletaxationofaportionofwageincomeduetotheflatpayrolltax 0.5 ( τ Soc +τ Med) w j thatisadded. Thismimicstheinstitutionalfeatureofincomeandpayroll taxes. 7 ( ) Theeffectivewageincomeiswe(j,h j ), τ ỹj W capturesprogressiveincometax,0.5 ( τ Soc +τ Med) w j isthepayrolltaxthatthehouseholdpaysforsocialsecurityandmedicare,andỹj W isthetax base for the income tax composed of wage income and interest income on assets and accidental bequests. The Social Insurance program Tj SI guarantees a minimum consumption level c. If Social Insuranceispaidoutthenautomaticallya j+ =0andin j =(thenoinsurancestate)sothat SocialInsurancecannotbeusedtofinancesavingsandprivatehealthinsurance. 8 5 Agentsareborrowingconstrained,in thesensethatthata j+ 0.Withoutaborrowingconstrainthouseholds would make the maximum allowable contribution to their HSAs if interest rates were fully tax deductible (this was possible until 986). Borrowing constraints can either be modeled as a wedge between the interest rates on borrowing and lending, or a threshold on the minimum asset position. See also Imrohoroglu, Imrohoroglu and oines(998) for a further discussion. 6 Ifhealthinsurancewasprovidedbytheemployer,sothatpremiumswouldbepartlypaidforbytheemployer, then the tax function would change to ( ) Tax j = τ ỹj W +0.5 ( τ Soc +τ Med)( w j {inj =} ( ψ)pj {in j =2} ( ψ)p j whereψisthefractionofthepremiumpaidforbytheemployer. eskeandkitao(2005)useasimilarformulation to model private vs. employer provided health insurance. They pick ψ = 0.85 based on MEPS data in 997. We simplify this aspect of the model and assume that all health insurance policies are offered via the employer andthattheemployeepaystheentirepremium,sothatψ=0.thepremiumisthereforetaxdeductibleinthe employee(or household) budget constraint. 7 CompareSocialSecurityTaxReform(Art#3). 8 ThestipulationsforMedicaideligibilityencompassmaximumincomelevelsbutalsomaximumwealthlevels. Some individuals who fail to be classified as categorically needy because they have to much savings could still be eligibile as medically needy (e.g. caretaker relatives, aged persons older than 65, blind individuals, etc.) We will therefore make the simplifying assumption that before the Social Insurance program kicks in the ), 0

11 Agentscanonlybuyinsuranceiftheyhavesufficientfundstodoso,thatiswhenever ( ) p j < w j +R a j +T Beq j +R m a m j o W (m j ) Tax j. The social insurance program will not pay for their health insurance. In their last working period, workers will not buy insurance anymore, because they become eligible for Medicare when retired Retirees Retired agents are insured under Medicare and by definition do not buy any more private health insurance. Thehouseholdproblemforaretiredagentj +canbeformulatedrecursively as where V (x j ) = max {c j,m j, a j } {u(c j,s j )+βπ j E ε [V (x j+ ) ε j ]} s.t. ( +τ C ) ) c j +(+g)a j+ +o R (m j ) = R(a j +T Beq j Tax j +Tj Soc +Tj SI +v j, (0) 0 a j, Tax j = τ ( ỹj R ), ỹj R = ra j +RT Beq T SI j = max j v j p j, [ 0,c+o W (m j )+Tax j R ( a j +T Beq j ) ] Tj Soc. Note that since retired agents cannot buy private health insurance anymore the state of private healthinsurancein j isunitybydefinition. 3.8 Equilibrium Definition Given the exogenous, transition probabilities P, realizations of health shocks ε={ε,..,ε k },thesurvivalprobabilities{π j } j= andtheexogenousgovernmentpolicies { τ(ỹ(xj )),τ K,τ C,v(x j ) }, a competitive equilibriumisacollectionof sequencesof distributions { µ j,λ j (x j ) } j= j= ofindividualhouseholddecisions {c j (x j ),a j+ (x j ),m j (x j ),in j+ (x j )} j=,aggregatestocksofphysicalcapitalandhumancapital{k,l},factorprices{w,q,r},andinsurancepremiums{p j (x j )} j= suchthat (a) {c j (x j ),a j+ (x j ),m j (x j ),in j+ (x j )} j= solvestheconsumerproblem(8), individual has to use up all her wealth. eske and Kitao(2005) follows a similar approach. See for details on Medicaid eligibility.

12 (b) the firm first order conditions hold w = F L (K,L), q = F K (K,L) R = q+ δ, (c) markets clear K = S= µ j= j (a(x j ))dλ(x j ), T Beq = µ j=j j a j (x j )dλ(x j ), L = e(j,x j )dλ(x j ), j= µ j (d) the aggregate resource constraint holds G+(+g)S+ (c(x j )+p m (x j )m(x j ))dλ(x j )=Y +( δ)k+t Beq, j= µ j (e) thegovernmentprogramsclearsothat(5), (6), (7),and(??)hold, (f) the budget constraints of insurance companies(3) and(4) hold (g) the distribution is stationary Λ(x j+ )= j= µ j { a =a(xj), m =m(xj)} P ( ε,ε ) dλ(x j ), where is an indicator function. We use a standard numeric algorithm(gauss Seidl algorithm) to solve the model. 4 Parameterization and estimation THIS CALIBRATION IS VERY PRELIMINARY AND NOT YET COMPLETE. Steady state equilibrium results for the benchmark economy are presented in the first column of table (4) and in figure (??). We next discuss how we chose the parameters that resultintheseoutcomes. Wesummarizeallparameterchoicesintables()and(2).Wealso present a table that matches model outcomes to data(table(3)). 4. Demographics Oneperiodisdefinedas5years. Wemodel=4periods,thatishouseholdsfromage20to 90. The annual conditional survival probabilities are taken from the U.S. Life-Tables in 2003 andadjustedfortheperiodlength. 9 ThepopulationgrowthratefortheU.S.was.2%in2006 accordingtotheu.s.census. Inthemodelwepickn=3%inordertomatchthepopulation percentageoftheelderly. Inthemodelthetotalpopulationovertheageof65is.49%,which 9 ftp://ftp.cdc.gov/pub/health_statistics/nchs/publications/nvsr/54_4/table0.xls 2

13 isbetweenthenumbersintheu.s.census(2.4%)andthe20%usedineskeandkitao(2005) who only look at heads of households. 4.2 Preferences We choose a Cobb-Douglas type utility function of the form u(c,s)= ( c η s η) σ, σ where η is the intensity parameter of consumption, and σ is the inverse of the intertemporal rate of substitution(or relative risk aversion parameter). Wesetσ=.85andtheannualdiscountfactortoβ=.02.Bothparametersarepickedto matchthecapitaloutputratioandtheinterestrate. Itisclearthatinageneralequilibrium model every parameter affects all equilibrium variables. Here we associate parameters with those equilibrium variables that are the most directly(quantitatively) affected. Theweightofconsumptionintheutilityfunctionisη=0.96.Inconjunctionwiththemagnitudes of the health shocks this weight ensures that the model matches total health spending and the take-up ratio of health insurance of the different age groups. 4.3 Technology and firms We impose a standard Cobb-Douglas production technology, F(K,L)=AK α L α, andchooseacapitalsharetobeα=0.33whichisastandardvalue. NadiriandPrucha(996) report estimates for depreciation rates of physical capital of 5.9% and depreciation of R&D capitalis2%. Inourmodelwepickacapitaldepreciationrateofδ=0%whichisastandard value in the calibration literature (e.g. Kydland and Prescott(982)). The depreciation per periodisthen ( δ) (years/) = /8 = Production of health and the human capital profile The new health investment is produced according to i(m j )=φm ξ j. The productivity parameter φ of the health production function is normalized to unity. This is similar to the production parameter in Suen (2006) for a very similar production function of health. In addition, Grossman (972a) and Stratmann (999) estimate positive effects of medical services on measures of health outcomes. We start the analysis with a linear production function and set ξ =. We do not have data on these parameters and conduct( sensitivity ) analysis. The relative price of health and consumption can be expressed as p m φξ m ξ, where the term in brackets is the marginal contribution to health of an additional unit of healthcare. 0 We assume that health depreciation depends on age. Health depreciates at rates between δ j= =0.00andδ j= =0.8. This choiceensures thathealthdepreciates fasterastheagent 0 CompareSuen(2006)forasimilarformulation. 3

14 ages. Wepickthesenumberstomatchtotalhealthexpendituresintheeconomyandthetake up ratios for insurance over the life-cycle Transition probabilities We chose the Markov transition matrix for health shocks as P(ε j,ε j )=Pr(ε j ε j )= , to match aggregate health service expenditure as well as average insurance pickup rates over the agents life cycle. [We plan to estimate the health shocks using data from seven waves of the RAND-HRS (Health and Retirement Survey) between 992 and 2004.] Magnitude of health shocks We chose the magnitude of the health shocks to match the insurance coverage take-up rate(percentage of workers buying health insurance per age group) and the share of medical spending in GDP: ε={0,0.05,0.95}. [We plan to estimate the magnitude of shocks to health ε = {ε,ε 2,ε 3 } using a Methods of Moments estimation procedure. This procedure will estimate the health shocks as part of the equilibrium formation.] Human capital profile Effectivehumancapitale(j,h j )evolvesaccordingto e(j,h j )= ( e β 0 +β j+β 2 j2) χ ( h θ j ) χ for j={,..., }, () where β 0,β 2 < 0, β > 0, χ [0,], and θ 0. This formulation mimics the usual humpshaped income process over the life-cycle and makes the wage income of agents dependent on their health state. An otherwise identical individual will be more productive and have higher income if she has relatively better health(e.g. fewer sick days, better career advancement of healthy individuals, etc.). Tuning parameter θ allows us to gradually diminish the influence of health on the production process holding the exogenous age dependent component fixed. This parameter determines to whatdegreehealthisaninvestmentgood. Ifθ=0thenhealthisaconsumptiongoodonly. } We use the following estimates for {ˆβ0,ˆβ,ˆβ 2 ={8.2, 0.4, 0.005}, the parameters determining the efficiency profiles of the workers. These estimates are obtained by fitting a second order polynomial to summarized income data from the CPS(see Income, Poverty, and Health Insurance Coverage in the United States: 2005(2006)), according to log(income)=β 0 +β age+β 2 age 2 +ε. This represents the exogenous part of expression (). After taking the endogenous health capital into account, the model reproduces the hump shaped average efficiency units of the human capital profile. We normalized the profile and compare it to the normalized income 4

15 profile from the data. Fernandez-Villaverde and Krueger(2004) show similar income patterns using data from the Consumer Expenditures Survey over the period Forparameterχwepick,.sothathumancapitalisindependentofhealthinthebenchmark economy and health is a consumption good only. Using this parameterization will give us a lowerboundoftheeffectsofhealthcarereform, sinceweturnofftheinvestmentfunctionof health. We are not aware of any estimates for parameter χ and will therefore conduct sensitivity analysis. We later plan to analyze the effects of health on production. Using 0<χ<we cannowuseparameterθtodeterminethedegreeoftheinvestmentgoodfunctionofhealth. A parameterθ=0indicatesthathealthisapureconsumptiongoodandassuchunproductive andθ=indicatesthathealthisalsoaninvestmentgoodwithstrongeffectsontheformation of human capital. 4.5 Health insurance markets 4.5. Insurance premiums, deductibles and coinsurance rates Insurance premiums are age dependent. We use a base premium p 0 and an exogenous age dependentpremiumgrowthrateg j tocalculatethepremiumforeachagegroup. Weexpress thepremiumofj yearoldagentsas p j =p 0 g j,forallj {,..., }. (2) We estimate a common growth factor for insurance premiums g j for each age group using summary data on individual health insurance premiums from The Cost and Benefit of Individual Health Insurance Plans (2005). We then fit a simple second order polynomial to the growth rate of age dependent premiums which results in an estimate of the following equation g j =x 0 +x age+x 2 age 2 +ǫforallj {,..., }. (3) Theestimatesfortheregressorsare{ˆx 0,ˆx,ˆx 2 }={0.778, , }.Expressions(2) and (3) together with endogenous base premiums p 0 will determine all insurance premiums (low-andhighdeductibles)forallagegroups. Followingwepickcoinsurancerateρ=24%(Suen(2006)usesacoinsurancerateof25%). Deductibles are endogenous in the model and are expressed as fractions of average health expenditure. We impose that the deductible for private health insurance is γ = 23% of average health expenditure. We also relate the private insurance premiums to premiums from Medicare Plan B according to Claxton, Gabel, Gil, Pickreign, Whitmore, Finder, Diulio and Hawkins (2006). These parameters result in insurance premiums that are close to the average insurance premiumasafractionofincomeinthedata. Allratios,dataandmodelgenerated,arereported intable?? Price of medical services Inordertopindowntherelativepriceofconsumptiongoodsvs. medicalservices,weusethe averageratiooftheconsumerpriceindex(cpi)andthemedicalcpibetween992and2006. Wecalculatetherelativepricetobep m = The price of medical services for uninsured agents is higher than for insured agents. Various studies have pointed to the fact that uninsured individuals pay up to 50%(and more) higher Basepremiumsp 0 willadjusttocleartheinsurancecompaniesbudgetconstraint(??). 2 Compare: 5

16 prices for prescription drugs as well as hospital services(see Playing Fair, State Action to Lower Prescription Drug Prices (2000)). The national average is a markup of around 60% for the uninsured population(brown(2006)). Wethereforepickamarkupfactorof.6sothatp m,nins =.6 p m,ins.accordingtothe U.S.Census2004,thefractionofthepopulationwithoutinsuranceisroughly5.7%. 3 Using all this information we solve the following system of equations for the relative prices that the insured and uninsured pay for medical services {.52=0.843 pm,ins p m,nins, p m,nins =.6 p m,ins, which results in p m,nins = and p m,ins =.389. This assumes that the overall price difference between consumption and health services is a weighted average of the prices that the insured and uninsured pay for health services. 4.6 Government Socialsecuritytaxesareτ Soc =2 6.2%onearningsupto$97,500.Thiscontributionismade by both employee and employer. The Old-Age and Survivors Insurance Security tax rate is a littlelowerat0.6%andhasbeenusedbyeskeandkitao(2005)inasimilarcalibration. We thereforematchτ Soc at0.6%pickingtheappropriatepensionreplacementratioψtobe30%. 4 Thesizeofthesocialsecurityprogramisthen6%ofGDP.Thisisclosethenumberreported in The 2002 Annual Report of the Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds(2002) which is 5% for Medicaretaxesareτ Med =2.45%onallearningsagainsplitinemployerandemployee contributions(see Social Security Update 2007(2007)). In order to get an appropriate premium formedicarep Med,sothattheMedicarepremiumislowerthantheprivatehealthinsurance premiums, we have to pick the payroll tax(which helps to finance Medicare) sufficiently high. We useτ Med =8% which leads to a slightly larger Medicare program (4.44% of GDP) than whatweobserveinthedata(2.5%ofgdpaccordingto2002annual Report of the Boardof Trustees of the Federal Hospital Insurance and Federal Supplementary Medical Insurance Trust Funds(2002)). UsingtheincometaxratesoftheU.S.incometaxof2005wefollowGuner,Kaygusuzand Ventura(2007) and estimate the following equation marginaltaxrate(income)=β 0 +β log(income)+ε, (4) where marginalt axrate(income) is the marginal tax rate that applies when taxable income equals income. Variable income is household income normalized with an assumed maximum income level of $400,000. We then fit equation (4) to the normalized income data. The estimatedcoefficientsforthetaxfunctionarethen ˆβ 0 =0.34and ˆβ =0.0659sothatthe income tax function becomes T(income)= marginalt axrate(income) { }} { [ log(income)] taxable income, (5) SocialsecuritytransfersaredefinedasTj Soc (x)=ψwe j(h j )andtheyarethesameforallagents. Transfers areafunctionoftheactivewageofaworkerin herlastperiodofwork,sothatj=. Inadditionweassume thath j isaconstantandthesameforallagents. Wepickittobeequal h 0, +h ggridh, 2,whichisthe middle health state of the health grid vector. Biggs, Brown and Springstead(2005) report a 45% replacement rate for the average worker in the U.S. and Whitehouse(2003) finds similar rates for OECD countries. 6

17 wheret(income)istotalincometaxpaid. Inaddition,weimposealowerboundof0%andan upperboundof35%onthemarginalincometaxrate. Pickingthemaximumincomelevelat $400,000willaffecttheestimatesforthemarginaltaxfunctionin(4)sinceitwilldetermine the tax bins that individuals fall into. In our model, we similarly normalize taxable income of everyagentwiththemaximumincomeoftherichestagentintheeconomytogetthenormalized variable income. We use this normalized income directly in(5) to get the marginal tax rate andthesumtotalofpayableincometaxforeachindividual. 5 Since income tax revenue is collected to pay for the social insurance program T SI (e.g. foodstamps, etc.) and the residual becomes government consumption G, we want to make sure that the size of government consumption also conforms to the data(g/y = 20.3% compared to 20.2% reported in Castaneda, Diaz-Gimenez and Rios-Rull(2003)). FollowingSuen(2006)wepickcoinsurancerateforMedicareρ Med =5%. 6 Deductibles are endogenous in the model and are expressed as fractions of average health expenditure. WeimposethatthedeductiblefortheMedicaredeductibleisγ Med =2%ofaveragemedical expenditure. 5 Results After calibrating the model to its initial steady state(see first column in table(4)) we introduce universal health insurance vouchers and calculate the new steady state equilibrium(see second columnintable(4)andfigure()). The introduction of health insurance vouchers together with the elimination of Medicare results in large general equilibrium effects on savings, output, and aggregate medical expenditures. We find two effects that drive the observed increase in the savings rate of more than 5% First, health insurance vouchers are financed by a consumption tax. When the government decides to abolish Medicare which is financed by a payroll tax in order to replace it with vouchers that are financed by a consumption tax, the effective price of final goods increases as the consumption tax increases from 3.3% in the initial steady state to almost 2.7% in the new steady state. Agents will start consuming less of the final good and start directing their spending towards medical services and savings. Second, the increase in the savings rate is linked to the abolishment of Medicare. Since Medicare is more generous than private health insuranceplans (lowerdeductibles, lowercoinsurancerates) 7 agents will startcompensating forthisincomelossathigheragesbysavingmore. In a similar way we can explain the decrease in aggregate health expenditures as fraction of GDP. First, the increase in health spending by previously uninsured young agents is more than compensated for by the decrease of health spending of older agents who previously had the generous Medicare insurance. Faced with the less generous private insurance, old agents will spend less on their health. Second, the growth in output outgrows any potential spending increase from universal insurance coverage due to the large general equilibrium savings effects. Summarizing our results we find that universal health insurance vouchers transform an 5 AnothermethodistousethetaxfunctionestimatedinMiguelandStrauss(994). 6 According to Medicare News from November 2005 the coinsurance rates for hospital services under the Outpatient Prospective Payment System(OPPS) will be reduced to 20% of the hospital s total payment. Overall, average beneficiary copayments for all outpatient services are expected to fall from 33% of total payments in 2005to29%in2006. Visit: 7 Thismakessenseasprivateinsurancecompanieshaveaprofitmotiveandthereforeastrongerincentiveto curb moral hazard. 7

18 economy with high aggregate consumption rates, high health expenditure rates by old agents, and low aggregate savings rates into an economy with lower aggregate consumption rates, lower health expenditure rates by the old, higher health expenditure by the young, and higher aggregate savings rates. 5. Transitions We solve the model for transition dynamics from the status quo equilibrium without vouchers to an equilibrium with universal health insurance vouchers. We present first results in figure(2). The transitions are fairly smooth and clearly indicate the increases in capital and consumption and the decrease in medical expenditures. Welfareresultsarepresentedinfigure(3).Weusetwowelfaremeasures,thefirstiscompensating consumption as percentage of lifetime income for each generation and the second measure is compensating consumption per GDP in each time period. The first measure identifies the winner or loser generation from the reforms whereas the second measure puts a price tag on thereform as it expresses lost (orgained)consumption in terms of GDP. We present details of the welfare measures in the appendix. The first panel in figure (3) indicates that the generations born before the health care vouchers are introduced stand to lose from the reform. They need to be compensated with up to 5% of their lifetime consumption in order to become indifferent between the voucher regimeand the status quoeconomy. Agentsborn afterthereform aretheclearwinners and theycanfullybenefitfromthehighercapitalstockintheeconomy. Theygainroughly5%of their lifetime consumption. The second panel indicates how much it would cost in terms of GDP to make all agents indifferent between the reform and the status quo. The graph indicates that only the initial period would require extra funds to finance compensating consumption streams to generations born before the reform. Starting from 2 periods after the reform the number of winning agents exceeds the number of losing agents so that the reform results in welfare gains. 6 Conclusion Health insurance vouchers are proposed as solutions to increase insurance coverage to up to 00% of the U.S. population while at the same time controlling the steady increase in health care expenditures. Proponents of vouchers have argued that the government is better able to control the rise in health care spending as vouchers will replace government run Medicare (which will be insolvent soon) with private health insurances who can better control health care providers. Our analysis however suggests, that the primary reason why health vouchers decrease the fraction of GDP spent on health care is caused by a general equilibrium savings effect. This effect is caused by increased sales taxes that are needed to finance the health insurance vouchers. In our model, universal health insurance vouchers transform an economy with high aggregate consumption rates, high health expenditure rates by old agents, and low aggregate savings rates into an economy with lower aggregate consumption rates, lower health expenditure rates by the old, higher health expenditure by the young, and higher aggregate savings rates. Health vouchers therefore seem to be able to generate sustainable health expenditures by providing full health insurance coverage. 8

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