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Financing Universal Health Care in the United States

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Abstract – We study the efficiency and distributional effects offinancing universal health-insurance coverage, using a computa-tional general equilibrium model of the United States for 1991,with considerable disaggregation among families. Aggregate effi-ciency losses (primarily from labor supply distortions) range from0.2 percent to nearly 1 percent of net output. Losses are consider-ably smaller for a “mandate-with-tax-credit” plan than for full taxfinance. All plans redistribute in favor of the poor. The mandatewith credit is much better for the highest income groups, but worsefor the lower-middle class. The elderly lose in all plans we consider.

INTRODUCTION

In 1996, an estimated 41.7 million Americans were withouthealth insurance (Bennefield, 1997). Among 28 industrial-

ized countries in 1995, health-care coverage was publiclymandated for at least 99 percent of the population in all butfive (Anderson, 1997). The United States is the only countryin the group in which less than half of the population is eli-gible for publicly mandated coverage. Although PresidentClinton’s 1993 Health Security Plan proposal ultimatelyfailed, the goal of universal health-care coverage is still ofconsiderable interest.

The purpose of this paper is to expand our understandingof the effects of a move toward universal health-care cover-age in the United States. We do not emphasize the effects onthe health-care system itself. Instead, we focus on the way inwhich the financing of care affects the efficiency with whichlabor markets operate, and on the distribution of welfareamong families.

Proposals for universal health-insurance coverage fall intotwo broad categories. The first category involves proposalsfor a Canadian-style, single-payer system of coverage. Un-der a system of this type, consumers would be entitled tohealth insurance without direct payment, but taxes wouldneed to be increased to pay for the system. When we simu-late the effects of implementing this type of proposal, we re-fer to these as “full-tax-finance” simulations.

Charles L. Ballard &John H. GoddeerisDepartment ofEconomics, MichiganState University, EastLansing, MI 48824-1038

Financing Universal Health Care in theUnited States: A General Equilibrium

Analysis of Efficiency andDistributional Effects

NATIONAL TAX JOURNAL

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The second category includes propos-als for some form of mandated coverage.Some of these proposals involve an “in-dividual mandate,” under which eachfamily would be responsible for obtain-ing health insurance. Other proposals, in-cluding Clinton’s 1993 plan, involve an“employer mandate,” under which em-ployers are required to provide coveragefor their employees.

We also present simulations of a man-date-type plan. The mandate modeledhere is more like an individual mandatethan an employer mandate.1 However, weargue that the results from our mandatesimulations are relevant for understand-ing either an individual mandate or anemployer mandate. In a well-functioninglabor market, employer-provided cover-age is largely a substitute for wages. Thus,regardless of the way in which the man-date is imposed, a system with mandatedcoverage is likely to resemble a system inwhich each family bears the cost of its owncoverage.

Moreover, our emphasis is on pro-posals for universal coverage. If amandate-type proposal has the goal ofachieving universal coverage, it must in-clude some system of subsidies for thepoor, regardless of whether the responsi-bility for obtaining coverage is focusedprimarily on the individual or on the em-ployer. The subsidies must be financed bytaxes.

The share of health care that is financedby taxes would be larger under either amandate plan or a full-tax-finance planthan under the current health-care system.The increased level of taxation has impli-cations for distribution and efficiency. Thepotential efficiency losses from tax-in-duced distortions certainly should be con-sidered when we design a system ofhealth-care finance.2

In this paper, we incorporate health-care coverage into a computational gen-eral equilibrium (CGE) model of the U.S.economy. The model disaggregates fami-lies by income, size, composition, labortype, and age of head. The production sideof the economy is based on a three-factortranslog structure, in which the factors arelow-skill labor, high-skill labor, and capi-tal. In the “base-case” simulations usingour model, households make an endog-enous choice about whether to obtainhealth insurance. We choose the param-eters of the model in such a way that theseinsurance choices are roughly in line withthose made in the real economy. We thenconduct experiments in which we imposehealth coverage on all families and financeit using versions of the two prototype sys-tems outlined above.3

Our results indicate that significant ef-ficiency costs are created by either ap-proach to financing universal health care.The costs can be 0.2 percent of net nationalproduct (NNP), or perhaps considerably

1 For example, the proposals for employer mandates often involve complicated arrangements for part-timeworkers and small firms, and we do not deal with these issues explicitly.

2 See Ballard and Fullerton (1992) for a survey of the literature on the marginal efficiency costs of tax-financedgovernment expenditure. In this literature, it is common to find estimates of at least 30 cents of efficiency lossper dollar of additional revenue raised. However, the efficiency losses from higher taxes have received sur-prisingly little attention in discussions of health-care reform. An exception is Browning and Johnson (1980),who estimate efficiency losses due to taxation of perhaps 20 cents for every dollar of health care transferredfrom the private to the public sector. More recently, Newhouse (1992) and Danzon (1992) have discussed theimportance of the deadweight costs of taxes to the debate over health financing reforms.

3 When either of the prototype systems is implemented in our model, it is necessary to raise additional taxrevenue. In the simulations reported here, the additional revenues are collected by an income tax that isimposed on both capital and labor. The labor income taxes create labor-market distortions, but taxes oncapital have no first-order distortionary effects in this static, one-sector model. However, many other modelshave shown that capital taxes can lead to very substantial efficiency losses, either by distorting the intersectoralallocation of capital or by interfering with intertemporal consumption choices. Therefore, in this regard, oursimulations may understate the true efficiency costs of the proposed policy changes.


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more, depending on the exact configura-tion considered. The overall efficiencycosts appear to be a good deal lower forthe “mandate-with-tax-credit” approachthan they are for full tax financing. This isprimarily because the amount by whichdistortionary taxes must be increased isso much less in the mandate-with-creditcase.

Not surprisingly, the distributional con-sequences of the two approaches to fi-nance are also rather different. Comparedwith the current system, both plans favorthose at very low incomes at the expenseof those at the top. But mandated cover-age is much more favorable to those withhigh incomes, because they subsidizethose below them to a smaller degree. Onthe other hand, mandated coverage is lessfavorable to those in the lower-middlerange of the income distribution.

Our model also yields results for anothertype of distributional effect. Currently,nearly all U.S. citizens aged 65 and overreceive health-insurance coverage throughthe Medicare system. We model reformsthat do not change health-care coverage forthe elderly, but we subject all groups in thepopulation (including the elderly) to thesame tax changes. Consequently, the eld-erly suffer losses as a result of each of thereform plans simulated here.

THE MODEL AND DATA

Much of the structure of our model issimilar to that of Ballard (1988). We furtherdisaggregate and modify that model in anumber of ways, and we make use of morerecent data. We discuss the data in the nextsection. Then, we discuss our main mod-eling innovations, which include the intro-duction of health care, the disaggregationto two labor skill types, the introductionof a three-factor translog production struc-ture, and the disaggregation by age.4

The Family Database

Our primary data source is the March,1992, Current Population Survey (CPS) ofthe U.S. Bureau of the Census. We adjustthe CPS values of labor income and capi-tal income so that our aggregates match thetotals for the two types of income from theNational Income and Product Accounts.Thus, the sum of pretax labor and capitalincome across all families in our model isequal to NNP for 1991. We also includetransfer income as part of total family in-come for each family.

After adjusting the income data, we cre-ate family groups by taking averages ofthe CPS sample observations falling intoparticular cells.

(1) Single persons are distinguished byincome decile, by gender, bywhether the person is aged 65 andover, by whether the person has anylabor income, and by labor skill type.(The classification by skill is dis-cussed below.)

(2) Single-parent families are alsodivided by income decile, gender ofhousehold head, age of householdhead, labor income, and labor skilltype, as well as into two size classes:two and three persons and morethan three persons.

(3) Married-couple families are also di-vided by all of the characteristicsthat were used to distinguish single-parent families, as well as into threesize classes: two persons (no chil-dren), three or four persons, and morethan four persons. Married-couplefamilies are also divided amonggroups with two earners and groupswith fewer than two earners. Thetwo-earner couples are further sub-divided among four skill combina-tions.

4 Some of the details of model construction are omitted here because they have been discussed in Ballard(1988). More details are available on request.


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Some of the family cells with no earn-ers are also subdivided in order to singleout those who are Medicaid recipientsin the current system. Ultimately, weuse a total of 542 family groups in themodel, each of which is weighted by theshare of the U.S. population that it repre-sents.5

Table 1 gives some summary informa-tion about the population represented inthe model, broken down by income decile.Income is more concentrated at the top endof this distribution than in standard tablesof income distribution. This results fromthe way in which we have constructedfamilies, which leads to a large number ofone-person families, who tend to havelow incomes. (More conventional presen-tations of the income distribution excludeone-person families or group togetherunrelated individuals who share livingquarters.) The bottom of Table 1 includessome information on the families that arecomposed only of elderly persons. The eld-erly account for a large share of transferincome, which includes Social Securitybenefits.

Health Insurance and ConsumerOptimization

Our most important addition toBallard’s earlier model is the introductionof health insurance. We do not attempt tomodel all of the complexities of the health-insurance market. Instead, we seek asimple model of demand for health insur-ance, but one that leads to a split of thepopulation into insured and uninsuredgroups that roughly matches the actualdivision, and one in which the impliedvalue of health insurance to families iscaptured as accurately as possible.

The approach we take may be moti-vated as follows. The current system in-cludes “safety nets,” such as Medicaid,other state and local programs of medicalassistance, and charity care. The unin-sured typically receive care when seri-ously ill, even if they cannot pay for it,although the quality and quantity of careis likely to be lower than that received bythe insured. The amount paid by an un-insured person will depend on his income.For example, an uninsured person must

5 Some of the cells created by these procedures are empty, or nearly empty, in the CPS data set (e.g., singleparents without labor income in the top income decile). We include in the model only those cells that have atleast five CPS observations. Less than one percent of the U.S. population is omitted as a result of this rule.

TABLE 1SUMMARY OF INCOME DISTRIBUTION BY DECILE

Percentages of Population Totals

0–5.0 5.0–9.0 9.0–14.514.5–21.021.0–28.528.5–37.237.2–48.248.2–62.862.8–88.1

>88.1

17.5

0.30.82.24.06.18.4

11.315.020.531.3

0.10.41.43.04.66.78.6

11.615.648.0

4.113.613.612.010.710.49.58.37.5

10.2

0.51.72.94.46.28.2

10.713.918.632.8

7.27.17.88.28.89.8

11.012.513.713.8

Shares of Population Totals

1.5 35.3 47.8 11.4 11.1

LaborIncome

CapitalIncome

TransferIncome

TotalIncome Persons

Income Bounds($1,000s)

All Elderly-Only Families

Median Income($1,000s)


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simulate the welfare effects of providinginsurance coverage to the uninsured, weneed values for V that are specific to thefamily groups.

We assume that insurance is chosen(I = 1) in the base case if:

[3] (ZI=1 – ZI=0) = [V + (GI=1 – GI=0)] > 0.

In equation 3, (GI=1 – GI=0) is the expectedsacrifice of consumption of other goodsassociated with having insurance. Insimple terms, insurance is chosen if itsvalue to the family exceeds its cost (interms of foregone consumption).

We use equation 3 as the basis for esti-mating V. Treating V as a function of fam-ily characteristics, we specify the probitfunction:

[4] I* = γ0 + γ1ADULTS + γ2KIDS

+ γ3NOEARN + γ4(GI=1 – GI=0) + υ

where ADULTS is the number of adultsunder the age of 65 in the family, KIDS isthe number of children, NOEARN takesthe value 1 if the family has no earnersand 0 otherwise, and υ is a standard nor-mal variable. The term I* is unobserved,but I = 1 whenever I* > 0. Otherwise, I = 0.(Equation 4 applies for multiperson fami-lies. We estimate an analogous equationfor one-person families.)

The difference in G between being in-sured and being uninsured (GI=1 – GI=0) isaccounted for by the difference in ex-pected payments for medical care. Theseinclude expected out-of-pocket payments,and they also include insurance premiumspaid by the insured. We construct GI=1 byassuming that, if a family is insured, itsexpected medical expenditure is equal tothe actuarial value of the amount of medi-cal care that is appropriate for a family

6 The links between health insurance, health status, and health care in the model also require some explanation.We do not disaggregate families by health status or by actual health-care expenditures. Thus, the model isbest interpreted as one in which utility is evaluated ex ante before health status is known and health care isconsumed. Utility depends on insurance coverage rather than on health status or health care.

frequently “spend down” to a sufficientlylow level of income before becoming eli-gible for Medicaid. Thus, reliance on thesafety net may be regarded as a form ofinsurance. The quality of the safety net isinferior to the quality of private insurance,and the expected cost of using the safetynet increases with income.

Families with low incomes will tend torely on the safety net, because its cost islow for them, compared to the cost of pri-vate insurance. Those with higher in-comes have more at risk before the safetynet becomes available. Therefore, higher-income families have a stronger motive forbuying private insurance coverage.

We capture these ideas formally by as-suming a family utility function with con-sumption and leisure as arguments, wherethe consumption component includeshealth insurance. We use a constant-elas-ticity-of-substitution (CES) utility func-tion, as in Ballard (1988):

where Z represents consumption, L is lei-sure, and ε and φ are parameters that varyby family group. We define Z to includeboth the value of health insurance andconsumption of other goods:

[2] Z = G + (I · V).

In equation 2, G is consumption of othergoods, I is an indicator variable equal to 1if the family has health insurance and 0otherwise, and V is the extra value of be-ing insured rather than uninsured, mea-sured in terms of goods.6 In our base-casesimulations, I is 1 for some families and 0for others. In our revised-case simulations,I will be 1 for all families (i.e., everyonewill have health insurance). In order to

+ φ(1/ε)L(ε–1)/ε ] (ε–1) ,

[1] U = [(1 – φ)(1/ε) Z(ε–1)/ε

ε


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with its characteristics, adjusted for the taxsubsidy for employer-provided insurance.If the family is uninsured, the expectedcost of medical care is assumed to be afixed fraction of after-tax income, but notmore than the value that would be paid ifthe family were insured.7

We estimate one probit model for multi-person families and another for one-per-son families, using data from the March,1992, CPS. We exclude those families thatare composed exclusively of individualsaged 65 and over. The multiperson fam-ily data set includes 34,336 observations,and the data set for one-person familieshas 27,982 observations. To construct thedependent variable for each of the probitequations, we classify families as insuredor uninsured, on the basis of whethermore than two-thirds of the family mem-bers report having private health insur-ance.

The results of the estimations are shownin Table 2. As expected, the coefficientsfor (GI=1 – GI=0) are positive, and manytimes larger than their standard errors. Ac-cording to the estimates for multipersonfamilies, the value of insurance increaseswith the number of adults and with thenumber of children and is lower in fami-lies with no earners (holding (GI=1 – GI=0)constant).8

Returning to the 542 family groups, weuse equation 3 and our probit results toclassify the nonelderly as insured or un-insured in our base-case simulations. In ourbase-case simulations, 36.9 million peopleare classified as uninsured in 1991. (This isabout 17.1 percent of the population un-

der the age of 65.) Thus, our base-casesimulations come fairly close to matchingthe actual number of uninsured: Based onthe full CPS, the actual number of unin-sured people in 1991 was estimated to be34.7 million (Levit, Olin, and Letsch, 1992).

In the base case, we also classify 8.5million persons as having Medicaid cov-erage, which we interpret as equivalentin quality to private coverage.9 Nearly allindividuals aged 65 and over have at leastsome health-insurance coverage throughthe Medicare program. Because we onlyconsider reforms that leave health-carecoverage for the elderly unchanged, wedo not need to enter the value of insur-ance explicitly into the utility functions ofthe elderly-headed families.

Many economists believe that much ofthe population is “overinsured” due to thedistortion induced by the tax-preferred

TABLE 2RESULTS OF PROBIT ESTIMATION FOR

INSURED STATUS

Constant

Adults

Children

No earnings

(GI=1 – GI=0)

Sample size

–0.838(–21.3)

0.953(47.5)

0.270(30.4)

–0.283(–8.37)

0.00042(69.1)

34,336

1.43(88.5)

—

—

0.016(–0.65)

0.0011(73.6)

27,982

t-statistics are in parentheses.

VariableMultiperson

FamiliesOne-Person

Families

7 In the simulations reported in this paper, we assume that the expected cost of medical care for the uninsuredis 11 percent of after-tax income for multiperson families and six percent for single individuals. The probitlikelihood functions are maximized in the vicinity of these parameter values. The main features of our resultsare not very sensitive to changes in these parameters. Additional simulation results, based on other values ofthese parameters, are available on request.

8 From equations 3 and 4, the value of insurance, V, can be estimated for multiperson families by (γ0 + γ1ADULTS+ γ2KIDS + γ3NOEARN)/γ4, using the estimated probit coefficients. A similar procedure is used to calculate Vfor one-person families. Some illustrative estimates of V are $1,293 for a working single adult, $3,853 for afamily of four with at least one earner, and $3,176 for a family of four with no earners. The V’s are importantin assessing the gains from insuring the uninsured in our revised-case simulations.

9 The details of this classification procedure are available upon request.

ˆ

ˆˆˆ

ˆ


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status of employer-provided insurance(for example, see Feldstein and Friedman(1977)). Although we incorporate the taxsubsidy in modeling the discrete choiceof insurance, as well as in our distribu-tional analyses, the model is not designedto measure welfare losses from ineffi-ciently extensive coverage.

Two Labor Types

In the current health-care system,health-insurance coverage is strongly cor-related with wage rates. Because financ-ing reforms might affect low-wage andhigh-wage workers quite differently, wedisaggregate the labor force. We distin-guish the two types of labor (referred toas low skill and high skill) using CPS in-formation on occupation. We classify pro-fessionals and managers as high skill andother occupations as low skill. Two-earnerfamilies are subdivided into cells for eachof the four possible skill combinations.10

The most common production functionin the CGE literature is the CES produc-tion function. However, the disadvantageof CES is that it constrains all of the elas-ticities of substitution to be the same. Wewant our model to reflect empirical esti-mates suggesting that the elasticities ofsubstitution among capital, low-skill la-bor, and high-skill labor are not identical.The transcendental logarithmic (translog)production function is one of several func-tional forms that allow for such differ-ences in elasticities of substitution. Weemploy a three-factor translog function,because the translog is the flexible func-

tional form that has been used most oftenin empirical estimation.

CALIBRATING THE BASE CASE

To begin the calibration process, eachfamily group is allocated its income fromlabor, capital, and transfers, and tax ratesare set.

The actual tax/transfer system in theUnited States is extremely complicated. Inconstructing the tax-rate schedules usedhere, we concentrate on the features of thetax system that we believe to be most es-sential. These include (1) the payroll tax,(2) the personal exemptions in the federalindividual income tax, (3) the marginal taxrates on taxable income in the federal in-dividual income tax, and (4) the EarnedIncome Tax Credit. In addition, we adopta simple representation of the standarddeduction and the itemized deductions inthe federal individual income tax. Allother taxes combined (including State-and-local income taxes) are approximatedby a flat seven-percent tax on income.

The details of our specification of the1991 U.S. tax system are given in an Ap-pendix, which is available on request.However, we provide a few illustrativeexamples here. In our model, a marriedcouple with one child will face a payrolltax of 15.3 percent on the first dollar ofearnings.11 Because of the personal ex-emptions, this household’s marginal taxrate in the federal individual income tax iszero on the first dollar of earnings, assum-ing that the household has no capital in-come. However, the household is assumed

10 It should be noted that we do not disaggregate on the basis of whether workers are engaged in part-time orfull-time work. Currently, full-time workers are much more likely to have health insurance than are part-timeworkers. It is possible that the current health-insurance system creates a distortion in the labor market be-tween part-time and full-time work. Thus, if our model were to distinguish between part-time and full-timework, our simulations would probably generate smaller efficiency losses from the adoption of universal cov-erage.

11 We assume that the entire payroll tax is distortionary. Consequently, we are abstracting from any perceivedlinkages between payroll taxes and Social Security benefits. For a discussion of such linkages, see Feldsteinand Samwick (1992). If we were to assume that some portion of the payroll tax is nondistortionary, oursimulated efficiency costs would probably be reduced modestly. See Ballard and Goddeeris (1996a) for addi-tional sensitivity analysis with respect to the marginal tax rates.


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to face the seven percent marginal rate forother taxes on the first dollar of earnings.In addition, the household is assumed toface a subsidy rate of 17 percent in theEarned Income Tax Credit. Consequently,the first dollar of earnings for this house-hold is taxed at a combined marginal rateof (15.3 + 0 + 7 – 17) percent = 5.3 percent.12

The highest combined marginal taxrates are faced by households whose in-comes are sufficient to be in the topbracket of the federal individual incometax but still low enough to be subject tothe full payroll tax. These upper-middle-income households are assumed to face amarginal tax rate on earnings of 30 per-cent for the federal individual incometax,13 7 percent for other taxes, 15.3 per-cent for the payroll tax, and zero for theEarned Income Tax Credit. Thus, the com-bined marginal tax rate for these house-holds is 52.3 percent. Similar calculationsare made throughout the income range forevery type of household, producing apiecewise-linear budget constraint.14

For workers who are insured, employerpayments for health insurance are ex-cluded from taxable income and fromearnings subject to the payroll tax. Basedon data from the 1987 National MedicalExpenditure Survey (NMES), we assumethat, for workers who are insured, 71 per-cent of their health-care spending is pro-vided through insurance and, therefore,shielded from income and payroll tax.

Insurance Status and Health-CareSpending

In our model, health-care consumptiondepends on family composition and

insurance status. According to the 1987NMES, health-care consumption per in-sured adult under age 65 was $1,455(Hahn and Lefkowitz, 1992). We updatethis to $2,129 for 1991, using the overallchange in health-care expenditures percapita over the intervening period, basedon Letsch et al. (1992). Insured individu-als under age 19 had health-care expen-ditures about 62 percent as large as thoseof insured adults in the 1987 NMES, andwe use this factor in setting health-care ex-penditure for children.

A number of studies have found thatthe uninsured use less health care than theinsured. We assume that uninsured fami-lies use 64 percent as much care as insuredhouseholds of similar composition (U.S.Congressional Budget Office, 1993).Spending for families with Medicaid is as-sumed to be equivalent to what it wouldbe if the family were insured.

Labor-Supply Behavior

Our approach to modeling labor sup-ply, including the treatment of two-earnerfamilies, follows Ballard (1988). We set theutility-function parameters for each fam-ily, so that the base-case simulationsreplicate the actual labor supply and con-sumption, and so that the model’s re-sponses are consistent with target valuesfor the labor-supply elasticities. In ourcentral case, we assume rather modest la-bor-supply responses to changes in wages(see reviews of the literature in Burtless(1987), Heckman (1993), and Pencavel(1986)). In the central case, uncompen-sated labor-supply elasticities are –0.05 formen, 0.2 for women, and 0.1 for couples.

12 We do not directly incorporate the deductibility of State-and-local income taxes in the federal individualincome tax. Our treatment of itemized deductions is described in an Appendix, which is available on request.

13 By assuming that all high-income taxpayers face a federal marginal income tax rate of 30 percent, we abstractfrom the fact that the actual 1991 tax code had separate rates of 28 percent and 31 percent for different groupsof high-income taxpayers, and we also abstract from the “bubble” associated with the phasing out of the taxbenefit from the personal exemptions.

14 The tax rates discussed in this section are expressed as percentages of earnings exclusive of the employer’sshare of the payroll tax. Because the employer’s share is part of the pretax price of labor, marginal tax rateswould be somewhat lower if they were expressed as a percentage of gross-of-tax earnings.


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The total-income elasticities of labor sup-ply are –0.15 for all groups. We also per-form a number of sensitivity analyses withrespect to the labor-supply elasticities.

Substitution in Production

The cost function for the translog is

[5]

where C is cost, Y is output, the w’s arethe input prices, and αi and βij are param-eters. By assuming constant returns toscale, symmetry, and homogeneity, we cansolve for the α ’s and β’s that are consis-tent with the production data, as well aswith the desired combination of Allenpartial elasticities of substitution.15

A well-behaved production functionhas convex isoquants, but the translogfunction does not satisfy this restrictionglobally (Berndt and Christensen, 1973).Whether we have convexity depends onthe signs of the determinants of a borderedHessian matrix. Convexity is satisfied inall equilibria reported here.

An econometric literature has exploredthree-factor production schemes similar toours (see Hamermesh (1986) for a thoroughreview). In much of that literature, capitaland high-skill labor have been found to bemore substitutable for low-skill labor thanfor each other. For our central-case valuesfor the Allen partial elasticities of substi-tution, we use σhk = 0.4, σlk = 1.2, andσhl = 0.8, where h denotes high-skill labor, lis low-skill labor, and k is capital.

Model Closure: Government BudgetBalance

Output is divided among health care,goods other than health care (G), andexhaustive government expenditure. Toassure that aggregate demand equals out-

put, we calibrate the model so that exhaus-tive government expenditure equals totaltax revenue minus other governmentspending. Other government spending isfor transfer payments, Medicaid, and thehealth-care expenditures of the uninsuredthat are not paid for by the uninsuredthemselves.

SIMULATION EXPERIMENTS

Once the model has been calibrated, weproceed to the simulations. Regardless ofwhether we are simulating a fully-tax-financed plan or a mandate-with-tax-creditplan, we impose universal health-care cov-erage in the same way: The level of healthcoverage is no longer a choice for non-elderly families. We leave health coveragefor the formerly insured (and for those withMedicaid) the same as it was in the basecase, and bring the level of coverage for theformerly uninsured up to that of insuredfamilies of similar size and composition.For the formerly uninsured, the value of Zin equation 2 is increased by their value ofV, to reflect the utility gain they receivefrom improved health coverage.

Under our approach to modeling uni-versal coverage, we assume away possibleeffects (in either direction) on efficiencyin the delivery of care, such as the poten-tial for administrative cost savings, thepotential for greater central control of ag-gregate expenditures, and the possibilityof greater nonprice rationing. These arecertainly important considerations in thechoice among health-care financing sys-tems. We abstract from these other issuesin order to focus on the distributional is-sues and tax-related efficiency effects.

Full Tax Finance

In our experiments with a fully-tax-financed system of health insurance,families do not have to make direct pay-

15 See Ballard and Goddeeris (1996b) for a detailed discussion of the calibration technique.

ln C = Σ α i ln wi + 1 ΣΣβij ln wi ln wjY 2

n

i=1

n

i=1

n

j=1


40

ments for insurance coverage. Instead, weincrease the income tax rates for all fami-lies by an amount that is sufficient to fi-nance all health care through government.Specifically, we add the same number ofpercentage points to all of the income taxrates facing each of the consumer groupsin the model.16 This added tax is treated asa flat-rate tax on all adjusted gross income.Therefore, the added tax leads to equal in-creases in average and marginal tax rates.

Figure 1 shows a stylized version of thebudget constraint associated with the full-tax-finance plan. In the figure, AB is the

original budget constraint. (For the sakeof simplicity, Figure 1 is drawn as if thebase case had no government programs.Thus, the figure abstracts from the manynonlinearities in our model, such as theEarned Income Tax Credit and the gradu-ated marginal tax rates in the individualincome tax.) OB is the consumer’s totalendowment of time. For the full-tax-fi-nance plan, the budget constraint is givenby CDB. DB is the government grant ofhealth insurance. The slope of CD is lessthan the slope of AB because of the taxesthat must be raised in order to finance the

16 Consumption taxes, such as a new value-added tax, have sometimes been suggested as a source of finance fora universal health-care system. Consumption taxation raises dynamic efficiency issues that are not capturedwell in a static model such as ours. However, using a broad-based consumption tax would distort laborsupply in much the same way as would an increase in labor taxes.

Figure 1. The Household’s Budget Constraint Under Full Tax Finance and Under the Mandate-With-Tax-Credit Plan


41

program. This budget constraint is simi-lar to the budget constraint for a simplenegative-income-tax plan. This type ofplan will distort the decisions of all house-holds, regardless of whether they werepurchasing insurance before the policychange.

A Mandate with Income-Related TaxCredits

In our experiments with mandate-with-credit plans, health-insurance coverage ismandatory, and low-income families aregiven assistance to pay for it. This assis-tance comes in the form of refundable taxcredits. If a family’s income, exclusive oftransfers, is below the poverty line for1991, the tax credit is equal to the full costof coverage. If a family’s income is abovethe poverty level, the net amount of thetax credit is reduced. Under our central-case assumptions, the marginal tax ratesare increased in the income range betweenone and two times the poverty level, sothat the tax credits are phased out at in-comes of twice the poverty level. We alsoexplore variation in the income range overwhich the credit is phased out.

Figure 1 also shows a stylized versionof the budget constraint for the mandate-with-credit plan. As before, thehousehold’s budget constraint in the ab-sence of the program is AB, and thegovernment’s grant of health-insurancecoverage is DB. When the mandate-with-credit plan is instituted, the consumer’sbudget constraint is AEDB. The budgetsegment ED is less steep than the segmentCD, because the phaseout of the creditinvolves very substantial increases inmarginal tax rates.

The mandate-with-tax-credit approachusually requires some additional net pub-lic revenues to finance coverage for thoseformerly uninsured families who receiveinsurance in the move to universal cover-age, as well as for any formerly insuredfamilies who stop working when the

policy change is instituted. In order toraise the needed revenue in our model,we increase the marginal and average in-come tax rates on all families by the samenumber of percentage points. However,the amount of extra revenue that must beraised is much smaller under the mandate-with-credit plan than under full tax fi-nance. In most cases, the budget constraintfor the mandate-with-credit plan wouldbe very slightly below AE because of theadditional taxes that are necessary to fi-nance the program. However, we have notshown separately the actual budgetsegment to the left of point E for the man-date-with-credit plan, because it isextremely close to the base-case budgetsegment, AE. For example, in the simula-tion using our central-case parameters, thegeneral increase in tax rates is only 0.12percentage points.

Under the mandate plan, the govern-ment requires that everyone get insurance,but subsidizes it for those at low incomes.Some households maximize utility by lo-cating in the subsidized range, along thebudget segment ED. The decisions ofthese households will clearly be distortedby the mandate-with-credit plan. How-ever, many households will locate alongthe budget segment AE. These householdswill purchase private health insurance (asmost of them already do), but they willnot use the government subsidy. Forhouseholds with incomes that are abovethe end of the phaseout, and which al-ready had private health insurance beforethe mandate, the policy change does notcreate any new tax distortion at the mar-gin, except for the very small increase inthe overall level of taxation, as mentionedin the previous paragraph.

For either method of finance, we elimi-nate the tax-exempt status of employer-provided health insurance, and thisbroadening of the tax base creates anothersource of revenue for financing coverage.

Under either method of finance, familybudget constraints are nonlinear. In the


42

base case, utility functions are calibratedso that all families with earnings are atinterior optima, given their actual laborsupplies and levels of nonlabor incomeand the implied marginal tax rates. In therevised-case simulations, however, utilitymay be maximized at a level of labor sup-ply at which the marginal tax ratechanges. Our simulations incorporatesuch “kink-point” optima.

RESULTS

Efficiency Effects

Table 3 focuses on the efficiency costsof a move to universal coverage. We usethe equivalent variation (EV) to measurethe change in well-being for each family

group. The EV measures the dollar adjust-ment in lump-sum income, measured inbase-case prices, that is necessary to movea family from the base-case level of utilityto the level of utility that is obtained afterthe policy change. If the EV is positive, thefamily group is better off after the change,and conversely. Aggregate measures of ef-ficiency cost are simply the negative of thesum of the EVs across family groups.

We also calculate the “Efficiency Cost ofRedistribution” (ECR). The ECR is analo-gous to the MECR of Ballard (1988) for thenonmarginal changes represented by ourpolicy experiments. The ECR takes the form:

[6] ECR = 100 × ((– Σ EV losers

/ΣEVgainers) – 1)

TABLE 3EFFICIENCY COSTS OF REPLACING THE CURRENT HEALTH-INSURANCE SYSTEM

WITH FULL UNIVERSAL COVERAGE, FOR DIFFERENT LABOR SUPPLY ELASTICITIES

(1) (2) (3) (4)

Full Tax FinanceTax rate increase(Percentage points)

Efficiency cost($ billions)

ECR

7.5

$27.0

6.5

–$14.9

7.7

$34.6

7.8

$39.3

Labor supply effects:

27.5 percent –14.1 percent 35.7 percent 41.3 percent

Insured

Uninsured

97.5

94.0

100.0

100.0

97.0

92.1

96.8

94.1

Mandate with Tax Credit, Phased Out at Twice Poverty Level

Tax rate increase(Percentage points)

Efficiency cost($ billions)

ECR

Labor supply effects:

0.12

$10.6

17.1 percent 24.3 percent 17.9 percent 27.6 percent

–0.61

–$14.9

0.17

$11.3

0.31

$17.4

Insured

Uninsured

99.0

90.5

100.0

99.9

99.0

88.3

98.7

90.1(1) Central case: income elasticity for all groups = –0.15;

uncompensated elasticities: men = –0.05, women = 0.2, and couples = 0.1.(2) Uncompensated wage elasticities = 0.0; income elasticities = –0.001.(3) Central case with income elasticities = –0.2, instead of –0.15.(4) Central case with uncompensated wage elasticities increased by 0.05;

income elasticities remain at –0.15.Labor supply is reported as a percentage of base-case labor supply.


43

where the sums are over the family groupsthat lose and gain in the experiment be-ing analyzed, and multiplication by 100converts the expression to a percentage.The ECR gives a summary measure of thepercent of a dollar that is lost to dead-weight loss per dollar of gain to the ben-eficiaries.

Table 3 presents results for each of thetwo financing mechanisms, for severalsets of assumptions. Column (1) of Table3 involves our standard assumptionsabout labor supply (noted at the bottomof the table). Tax rates rise by 0.12 percent-age points for the mandate with tax creditversus 7.5 percentage points for full taxfinance. Under the mandate, most fami-lies choose to pay for their own health careoutside the tax system, and the only rea-son to increase tax rates is to finance sub-sidies for the poor. On the other hand,under the full-tax-finance approach, allhealth care is financed with taxes.

Under our central-case assumptions,both methods of finance lead to efficiencylosses. In other words, costs are createdby the increase in labor-supply distor-tions, and these costs are greater than theaggregate gains from expanding health-care coverage. In absolute terms, the an-nual efficiency costs are $10.6 billion (in1991 dollars) for the mandate plan, orslightly less than one-quarter of one per-cent of total net output. For full tax fi-nance, the efficiency costs are $27 billion,or about three-fifths of one percent of to-tal net output. Viewed another way, theefficiency costs are in the range of 2.8 to7.0 percent of health-care spending by thenonelderly in the base case. These costscannot be considered small. On the otherhand, the ECR numbers are smaller thanmost of the MECRs reported by Ballard(1988). This is due in part to our use ofsomewhat smaller labor-supply elastici-ties than were used by Ballard.

The efficiency costs are a good dealhigher for full tax finance than for themandate with credit. In fact, it may seem

surprising that the mandate approachdoes not do even better than it does, inview of the modest increases in overallmarginal tax rates that accompany it.However, we must recognize that thisapproach increases the effective marginaltax rates very substantially for those fami-lies who are in the income range in whichthe tax credit phases out. For the central-case version of the mandate, with thephaseout complete at twice poverty in-come, about 15.7 percent of working fami-lies end up in the phaseout range. Thephaseout itself adds between 20 and 38percentage points to their marginal taxrates (with a median of 34 points). Anadditional 2.6 percent of working familieschoose to stop working at the point atwhich the phaseout begins.

Still, the overall efficiency cost of themandate-with-credit plan is substantiallylower than that of full tax finance. Themandate-with-credit plan does imposevery large increases in marginal tax rateson nearly one-sixth of working families.However, for the other five-sixths, full taxfinance requires tax-rate increases that areabout 60 times as large as those that arenecessary for the mandate-with-creditplan.

The labor-supply results in Table 3 arealso of interest. In the full-tax-finance case,the percentage reductions in labor supplyare larger for the previously uninsuredthan for the insured, even though the la-bor-supply elasticities are not assumed tovary by income or by insurance coverage.The reason is that the policy change be-ing evaluated has two types of incomeeffect, which work in opposite directionsand which vary in relative importanceacross the income distribution. The taxincrease has the usual adverse effect onincome, which tends to increase labor sup-ply, and largely offsets the substitutioneffect for those at higher incomes. How-ever, the guarantee of health coverage ef-fectively increases income, and this dis-courages labor supply. The latter effect is


44

relatively important at the lower end ofthe income distribution, where the unin-sured are concentrated.

Comparing the two methods of financein column (1), the mandate with tax creditleads to a smaller labor-supply responseby those who were previously insured anda larger one by those who were previouslyuninsured. This is as expected, given thatmany of the formerly insured (thosebeyond the phaseout of the tax credit)face only a small—and uncompensated—increase in tax rates under the mandate.On the other hand, many of the formerlyuninsured face very large marginal rateincreases, which are largely compensatedby the improvement in their health cover-age.

We have also experimented with phas-ing out the tax credit over a broader rangeof income. If we do so, the add-on to themarginal tax rate is reduced for those withpartial tax credits, but the number of fami-lies subject to the phaseout is increased.Because the aggregate subsidy for healthcare is increased, the required tax rate issomewhat higher as well. With this com-bination of effects moving in different di-rections, it turns out that the aggregateefficiency costs do not vary much, evenwhen the phaseout range is expandedconsiderably. For example, if the phase-out range is doubled, so that tax creditsare fully phased out at three times thepoverty level, the efficiency cost increasesonly from $10.6 to $11.9 billion. In thatcase, about 31 percent of working fami-lies face marginal tax rate increases of be-tween 11 and 24 percentage points due tothe phaseout, and 0.7 percentage pointsare added to all marginal tax rates (seeSheiner (1994) for additional discussion ofefficiency considerations in the choice ofa phaseout range).

The other columns of Table 3 explore therelationship between the efficiency resultsand labor-supply elasticities. Column (2)of Table 3 shows what happens if all elas-ticities are close to zero. Uncompensatedwage elasticities are all set to zero, and in-come elasticities to –0.001.17 In this case,the EC becomes negative, i.e., the modelimplies welfare gains from the move touniversal coverage. This result is explainedas follows: In our model, the provision ofhealth insurance to the uninsured increasestheir welfare by more than the resource costof the extra health care that they receive.18

When labor supply is almost completelyunresponsive, the tax-induced welfarelosses are much smaller than they wouldbe under more plausible labor-supply elas-ticities. Therefore, in this case, the tax-in-duced welfare losses are outweighed bythe welfare gain from moving to universalcoverage. In addition, in the mandate case,a small tax-rate reduction is possible, de-spite the increase in insurance coverage forthe uninsured. This is because of the endof the tax subsidy for insurance and be-cause some formerly uninsured familiesnow pay for more of their own health care.

Columns (3) and (4) of Table 3 show theresults for cases in which the labor-sup-ply elasticities vary modestly from ourcentral case. In column (3), income elas-ticities are all set at –0.2, instead of –0.15as in the central case. This increases thecompensated wage elasticities by 0.05,without changing the uncompensatedelasticities. In column (4), the compen-sated and uncompensated wage elastici-ties are both increased by 0.05, leaving theincome elasticities unchanged. Not sur-prisingly, if labor-supply responsivenessis increased in either of these ways, theefficiency costs of universal coverage arehigher than in the central case. As for the

17 Our utility function has strictly convex indifference curves between consumption and leisure, so that thecompensated wage elasticities cannot be exactly zero.

18 This leads to the question of why these families did not choose to be insured in the base case. The answer isthat the safety net is subsidized to such an extent that the extra cost (to the family) of becoming insured exceedsthe extra value.


45

labor-supply responses, they are larger forthe insured in column (3) and for the un-insured in column (4). As these resultshighlight, the policy changes being evalu-ated are neither purely compensated norpurely uncompensated changes, so thatboth types of elasticity matter. In addition,the income effect of gaining coverage isparticularly important for the low-incomeuninsured, which is why their responseis largest in column (3). For further dis-cussion of these results, see Ballard andGoddeeris (1996a).

Distributional Effects

Tables 4 and 5 provide some illustrativedistributional results using our central-case assumptions. The tables report thewelfare gains or losses as average dollaramounts per family (in 1991 dollars) andas average shares of base-case money in-come. While the precise numerical valuesshould be interpreted with caution, webelieve that the general patterns shownin the tables are meaningful.

Table 4 presents the results for the caseof full tax finance. The leftmost columnsshow that, on average, the reform leadsto substantial gains for the families in thelowest deciles, as a result of improvedhealth-care coverage and reduced out-of-pocket payments. In contrast, those in thetop two deciles have very significant netlosses. The loss is as much as 4.2 percentof base income for the average family inthe top decile.

Because different demographic groupsare affected in different ways, the othercolumns of Table 4 display some illustra-tive effects for different groups. As ex-pected, low-income nonelderly familiesgain and high-income nonelderly familieslose. However, the pattern is rather dif-ferent between one-person families andmultiple-person families. Losses are suf-fered by one-person families as low as thesixth decile (which has a lower income

limit of $28,500), while married-couplefamilies gain through the eighth decileand single-parent families through theseventh. This happens largely because thedollar value of health-care coverage islower for the singles, but they are assumedto pay the same additional taxes that arepaid by other families with similar in-comes. All of the elderly lose, because theypay higher taxes without receiving anyincrease in health coverage.

In Table 5, we consider the mandatewith tax credit, with the phaseout rangeequal to poverty income. As comparedwith Table 4, the results are very similarfor the nonelderly in the bottom decile. Indeciles 2 and 3, however, the nonelderlydo somewhat better under the mandatethan with full tax finance. They receive thesame health care in both cases but payless for it in the mandate case. The man-date with tax credit is also much betterthan full tax finance for those at high in-comes, as well as for all elderly, becauseof the smaller increase in the overall levelof tax rates. To take an extreme example,Table 5 shows that nonelderly single per-sons in the tenth decile lose by only $928in the mandate case, compared with lossesof over $7,300 when full tax finance isused.

However, for those nonelderly personswho are affected by the phaseout of thetax credit, the welfare changes are worsein the mandate case than with full tax fi-nance. This effect is most evident for mar-ried-couple families in the fifth throughseventh deciles. In each of those deciles,the loss per family between Tables 4 and5 is six percent or more of base-case in-come. Nonelderly single individuals inthe fourth and fifth deciles also do con-siderably worse under the mandate, as dosingle-parent families in the fifth throughseventh deciles.

Distributional results for a variety ofother simulation experiments are avail-able on request.

NAT

ION

AL TA

X JO

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NA

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46

Financing U

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47


48

ADDITIONAL SENSITIVITY ANALYSES

Labor Supply of Medicaid Recipients

Until now, we have not incorporatedone effect that deals with the laborsupply of those currently covered by Med-icaid. A nonworking Medicaid recipientmay lose health-insurance coverage if heobtains a job that does not provide cover-age. It is plausible that the potential lossof Medicaid coverage already creates astrong work disincentive and that somecurrent Medicaid recipients would chooseto work under a system of universal cov-erage. Research by Moffitt and Wolfe(1993) suggests that a system of universalcoverage comparable to Medicaid mightlead to as many as 915,000 Aid to Fami-lies with Dependent Children familiesleaving the welfare rolls.

In order to capture an effect of this type,we calibrate the utility functions for someof our Medicaid families, so that theequivalent variation from choosing Med-icaid (rather than working) is ten percentof base-case income. As a result, it is opti-mal for these families to choose Medicaidin the base case if working would causethem to lose coverage. These familieschoose to work in the revised-case simu-lations, because their coverage is thenguaranteed. We adjust the model in thisway for 40 percent of our Medicaid fami-lies with one or two children and for 30percent of those families with more thantwo children. When these assumptions areincorporated into the model, they haveeffects that are roughly consistent with theresults of Moffitt and Wolfe (1993): Oursimulations indicate that about 941,000

Medicaid recipients would join theworkforce.

Compared with the central-case versionof the model, this version results in ahigher level of labor supply for the for-merly uninsured (which here includes theMedicaid families) and a lower efficiencycost. The efficiency cost of universal cov-erage decreases by about $1.3 billion un-der either financing mechanism. In lightof the paucity of evidence on the size ofthis positive labor-supply response, aswell as the somewhat arbitrary assump-tions needed to adapt the Moffitt–Wolferesults to our model, these results shouldonly be viewed as indicating a rough or-der of magnitude. They suggest that thegains from improved work incentives forthose on Medicaid may be appreciable,but that they are not likely to outweighthe distortions created elsewhere by thefinancing of universal coverage.19

Substitution between Capital andHigh-Skill Labor

General-equilibrium price effects in ourmodel are usually rather modest. In thecentral case with full tax finance, the ag-gregate reduction in labor supply leads toa fall in the price of capital (relative to ei-ther labor type) of almost three percent.Under the mandate with tax credit, theaggregate labor supply reduction issmaller, but it is larger for low-skill labor.Consequently, the price of low-skill laborincreases by about two percent, relativeto capital and high-skill labor. We haveexperimented with changing the Allenpartial elasticity of substitution between

19 The distortion of the labor-supply decisions of Medicaid recipients is not the only labor-market distortionthat could have an effect on our results. For example, some have suggested that the current system ineffi-ciently inhibits job switching for those with employer-provided coverage (Madrian, 1994) and that universalcoverage would eliminate this “job-lock” effect. However, the magnitude of this effect and its efficiencyconsequences are unclear (Holtz-Eakin, 1994). Also, the Health Insurance Portability and Accountability Actof 1996 should have lessened the importance of job lock. Another potentially important labor-market effect ison retirement decisions. Gustman and Steinmeier (1994), Gruber and Madrian (1995), and Karoly and Rogowski(1994) all find that the availability of health insurance is associated with early retirement. Induced retirementwould reduce the income tax base and thereby make larger tax increases necessary. Incorporation of theseeffects would be a valuable goal for future research.


49

capital and high-skill labor from 0.4 to–0.2, in order to capture “capital-skillcomplementarity,” which is sometimesfound in the econometric literature. Thechange has relatively little effect on theresults, especially in the mandate case.When full labor tax finance is used, thischange leads to a further reduction in theprice of capital, and the aggregate effi-ciency cost falls by about $1 billion whencompared with the central-case simula-tion.

Valuation of Insurance

In the central case, the valuation of in-surance by the uninsured is taken directlyfrom the probit estimates. We have seenthat, under this formulation, the valueplaced on health insurance is greater thanthe resource cost of providing it. This factplays an important role in explainingsome of the efficiency results, as seenabove. An alternative is to assume that thevalue of insurance for the uninsured isexactly equal to the resource cost of theextra care that they can expect to consume.Not surprisingly, this change causes theaggregate efficiency cost to increase sub-stantially for either financing approach.The aggregate efficiency cost goes from$27.0 to $35.7 billion with full tax financeand from $10.6 to $19.3 billion under themandate with tax credit. This change inthe model has very little effect on thelabor supply of the formerly insured.However, the labor supply of the formerlyuninsured is higher when the value ofinsurance is assumed to be lower, becausethe move to universal coverage does notcreate such a large income effect. Furtherresults are available on request.

CONCLUSIONS

Using a computational general equilib-rium model of the U.S. economy and taxsystem, we have studied the efficiencyand distributional effects of financing uni-

versal health-insurance coverage. Our re-sults suggest that the efficiency costsassociated with the distortion of labormarkets are likely to be substantial, evenif labor supply is only modestly elastic.For our central-case parameter values, ifwe replace the existing health-insurancesystem with a fully tax-financed plan ofuniversal coverage, we require an increasein tax rates of 7.5 percentage points. Theresulting efficiency losses amount to 0.59percent of NNP. If we replace the existingsystem with mandated coverage, com-bined with tax credits for families withincomes less than twice the poverty level,we need an extra increase in tax rates of0.12 percentage points, and we find effi-ciency losses of 0.23 percent of NNP. Be-cause of the size of these efficiency losses,we might expect strong pressures to re-duce other government expenditures, sothat the move to universal health-insur-ance coverage would not ultimately beassociated with such large tax increases.

In any case, the relative efficiency costsof different financing mechanisms are onefactor that should be weighed in choos-ing among them. One of the interestingfeatures of our results is the apparent su-periority (on efficiency grounds) of themandate with tax credit, as comparedwith full tax finance. Our results also sug-gest that a slow phaseout of the tax credit(so that families with income as high asthree times the poverty level receive apartial credit) would have efficiency costsclose to those for a more rapid phaseout.

Our results also show that the financ-ing approach used can have importantimplications for the distribution of thecosts and benefits of health-care reform.Both full tax finance and a mandate-with-tax-credit plan create gains for the poor-est members of society. However, for thehighest income groups, full tax financeleads to losses that are sometimes severaltimes as large as the losses that they suf-fer under the mandate with tax credit. Onthe other hand, the lower-middle-income


50

groups fare much more poorly under themandate with tax credit. Some of thesegroups suffer losses under that approach,while experiencing gains if full tax financeis used.

In our simulations, the elderly are as-sumed not to receive any additional healthinsurance, but they are assumed to bearsome of the costs. Thus, the elderly losein all of our simulations. However, theirlosses are much smaller under the man-date approach than with full tax finance.

Acknowlegments

We are grateful for helpful commentsfrom Len Burman, Roger Feldman, JonGruber, Douglas Holtz-Eakin, JoelSlemrod, and John Whalley, from partici-pants in seminars at Michigan State Uni-versity, Wayne State University, the Uni-versities of Michigan, Virginia, and Wa-terloo, the Midwest Economics Associa-tion 1993 meetings, and the 1994 HealthEconomics Conference, and from fouranonymous referees. John Goddeeriswishes to thank the Tax Analysis Division,Congressional Budget Office, where hewas a visiting scholar during the earlywork on this paper. Any errors are ourresponsibility.

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