Health Insurance

Health Insurance in Health Economics and Health Systems

Health insurance turns an uncertain and sometimes ruinous bill for treatment into a predictable payment made in advance, whether that payment is a private premium, a payroll contribution or a tax. Health economists value it chiefly as protection against financial risk, which a risk-averse household is willing to pay for in excess of its expected medical costs. The same cover changes what patients demand and what providers supply, and voluntary markets attract the people who expect to need care most, so insurance design is always a compromise between protection and incentives. Within a health system, insurance is one of several ways of organising prepayment and risk pooling, and the label alone says little about how far a population is protected.

Why risk-averse households pay more than their expected costs

Arrow's 1963 paper on the welfare economics of medical care treated illness as largely unpredictable and singled out the missing market for bearing that risk as the gap that most concerned him. Cutler and Zeckhauser, in their chapter for the Handbook of Health Economics, root the value of health insurance in the unpredictability and skewness of medical spending, and note that saving in advance is impractical because the costs of severe illness fall on a few people. Pooling the risk with others cuts each member's annual consumption only by the premium, the average cost of care.

The most a household will pay for full cover is the premium that leaves it as well off, in expected utility terms, as staying uninsured.

$$u(y - \pi^{\max}) = (1-p)\,u(y) + p\,u(y-m)$$

where $u$ is the household's utility of income, $y$ is income before any medical spending, $m$ is the cost of treatment if illness occurs, $p$ is the probability of illness in the year and $\pi^{\max}$ is the maximum premium the household would pay for cover of the whole cost. The actuarially fair premium is $pm$, and the excess of $\pi^{\max}$ over $pm$ is the risk premium, the money value of removing the risk.

Cutler and Zeckhauser approximate that value with a Taylor expansion.

$$\pi^{\max} - pm \approx \frac{1}{2}\, r \, p(1-p)\, m^{2}$$

where $r = -u''/u'$ is the coefficient of absolute risk aversion, evaluated at income net of the fair premium, and $p(1-p)m^{2}$ is the variance of uninsured medical spending. Their conclusion is that fair insurance is preferred to none by a risk-averse person, and that the value of risk spreading rises with risk aversion and with the variability of spending. The approximation suits small risks, and the worked example below shows how far it can fall short when the loss is a large share of income.

Worked example of one household's cover, premium loading and deductible

All figures are illustrative. A household has disposable income of GBP 30,000 and faces a 5% chance in the year of an illness whose treatment costs GBP 20,000. Its utility of income is logarithmic, $u(x) = \ln x$, so it is risk averse.

1. Expected cost and its variability. Expected spending is 0.05 × 20,000 = GBP 1,000. The variance is 0.05 × 0.95 × 20,000² = 19,000,000, a standard deviation of about GBP 4,359.

2. Expected utility without insurance. The natural logarithms of 30,000 and 10,000 are 10.30895 and 9.21034. Weighted by the chances of staying healthy and falling ill, they give 0.95 × 10.30895 = 9.79350 and 0.05 × 9.21034 = 0.46052, so expected utility is 9.79350 + 0.46052 = 10.25402. The certainty equivalent is $e^{10.25402}$, about GBP 28,397.

3. Maximum premium and risk premium. The household would pay up to 30,000 minus 28,397 = GBP 1,603 for full cover. Of this, GBP 1,000 is the expected cost and GBP 603 is the risk premium. The quadratic approximation gives 0.5 × 19,000,000 / 29,000 = GBP 328, little more than half the exact value, because the loss here is two thirds of income.

4. A loaded premium. An insurer that adds 15% to expected claims for administration and other costs charges 1.15 × 1,000 = GBP 1,150. The household buys, since a certain GBP 28,850 beats the uninsured certainty equivalent of GBP 28,397 by GBP 453.

5. A deductible under the loaded premium. With a deductible $D$ the insurer pays $m - D$ and the premium becomes $P = (1+\lambda)\,p\,(m-D)$, where $\lambda$ is the proportional loading. Arrow's first proposition shows that when the premium depends only on the policy's actuarial value, a risk-averse buyer's preferred policy is full cover above a deductible.

For the GBP 4,000 deductible the premium is 1.15 × 0.05 × 16,000 = GBP 920, leaving income of GBP 29,080 if healthy and GBP 25,080 if ill. Their natural logarithms are 10.27781 and 10.12983, so expected utility is 0.95 × 10.27781 + 0.05 × 10.12983 = 10.27041, a certainty equivalent of about GBP 28,866. That is GBP 16 better than full cover. A numerical search over all deductibles puts the best one for this household at about GBP 3,993, while the GBP 8,000 deductible leaves the household worse off than full cover.

6. Interpretation. Insurance is worth far more to this household than its expected cost. Once premiums carry a loading, retaining small losses and insuring large ones raises welfare, and the gain from full cover is mostly protection against the catastrophic outcome. The example holds use of care fixed, so it leaves out the second reason for deductibles, the effect of price on demand.

The trade-off between risk protection and incentives

Cutler and Zeckhauser describe a fundamental trade-off in health insurance between spreading risk and keeping appropriate incentives. More generous cover spreads risk more widely but raises spending, because insured people choose more care, the effect known as moral hazard in health insurance, and providers paid per item supply more care, which is supplier-induced demand. Their review concludes that both effects are quantitatively important, and that optimal patient payments are set where the marginal loss of risk protection when patients pay more is just balanced by the marginal gain from less wasteful care.

Demand-side tools act on the patient through cost sharing, including a deductible, a copayment or coinsurance. Cutler and Zeckhauser call coinsurance based on expenditure a crude control, since it places no direct incentive on physicians, who make most spending decisions. Supply-side tools such as utilisation review and capitation act on providers instead, and managed care in the United States joined insurance and provision in one organisation for that reason.

Selection, premium risk and the regulation of insurance markets

Choice between competing plans can match people to suitable plans and press plans to provide care efficiently. Cutler and Zeckhauser call it a mixed blessing because of adverse selection, the tendency of sick people to choose more generous cover. Plans with a disproportionate share of poor risks must charge more, which discourages healthier people from joining them and gives plans a reason to deter sick applicants, the behaviour also called cream skimming.

A second loss arises when premiums vary with observable health. Because cover is usually bought one year at a time, people cannot insure against being found to be high risk, and Cutler and Zeckhauser describe the right to buy cover at average rates in future, if illness strikes now, as a missing form of intertemporal insurance. Regulators respond with rules such as community rating, which limits how far premiums follow individual risk, and risk adjustment, which adjusts payments to plans according to the expected costs of their members.

Kutzin's 2013 paper takes the system view. Excluding poor people and people with known high risks helps a voluntary scheme stay viable, so its members can gain at the expense of everyone outside it. He cites South Africa, where about 40% of total health spending benefits the 16% of the population covered by employment-linked voluntary medical schemes, while the public facilities that everyone is entitled to use are overcrowded and poorly resourced.

Social, national and voluntary insurance within a health system

The World Health Report 2010 argues that contributions need to be compulsory if a whole population is to be covered, otherwise the rich and healthy opt out and the pool cannot meet the needs of the poor and sick. It states that universal coverage through insurance schemes is impossible when enrolment is voluntary, and that small pools are vulnerable because one high-cost illness can exhaust their reserves. Compulsory earnings-related schemes have their own page on social health insurance, as do small voluntary community-based insurance pools.

Insurance is an instrument, and the share of a population enrolled is a poor guide to protection. Kutzin notes that Germany and Japan use insurance schemes to secure financial access and protection for everyone, whereas Sweden and the United Kingdom achieve the same for all without anything called an insurance scheme. When the Republic of Korea reached universal population coverage under social health insurance in 1989, most citizens still faced potentially catastrophic out-of-pocket payments because cost sharing, particularly in hospital, was large and open-ended. Universal enrolment and universal health coverage are therefore different things.

In European systems with universal or near-universal public cover, voluntary health insurance is classified by its relationship to that cover. Sagan and Thomson's 2016 European Observatory study of 34 countries distinguishes three roles, with complementary cover split between excluded services and user charges, and notes that the OECD's 2004 taxonomy calls the supplementary role duplicate cover.

The study finds that most European markets play a supplementary role, that France and Slovenia have the only really substantial markets covering user charges, and that the most important substitutive market is in Germany.

Health insurance in economic evaluation and coverage decisions

In an insurance-based system the insurer or fund is usually the payer whose budget a cost-effectiveness analysis or budget impact analysis addresses, and its benefit package is the coverage decision that an evaluation informs. The analytical perspective decides which costs count. The NICE manual (PMG36, section 4.2.9) sets the reference-case perspective on costs as that of the NHS and personal social services (PSS), because the aim of its evaluations is guidance that represents an efficient use of NHS and PSS resources.

Cost sharing shifts part of the cost of a technology onto the patient, so a payer-perspective analysis can show savings that are partly transfers to households. Where cover is fragmented, the costs and savings of one intervention can fall on several insurers, and an analysis for one of them misses the rest. Cutler and Zeckhauser found the evidence on which insurance arrangements improve health most cost-efficiently inconclusive.

Common misreadings

Most errors come from treating enrolment or a scheme's name as a description of the whole arrangement. Others read a single price effect as the whole case for or against cover.

1. Enrolment is the same as protection. Korea's universal enrolment in 1989 left most people at risk of potentially catastrophic out-of-pocket payments.
2. Higher use after insurance is all waste. Cutler and Zeckhauser note that insurance also makes people richer when sick, so only part of the extra spending is moral hazard.
3. A deductible exists only to cut use. Arrow's result shows that a loaded premium alone makes a deductible worth choosing, before any effect on demand.
4. The value of cover equals the expected claims. For a risk-averse household the risk premium can be large, GBP 603 on an expected cost of GBP 1,000 in the illustrative example.
5. Voluntary cover always adds protection. Supplementary cover adds little, and selective voluntary schemes can protect members at the expense of everyone else.

Sources

• Arrow KJ. Uncertainty and the welfare economics of medical care. American Economic Review. 1963;53(5):941-973. https://www.jstor.org/stable/1812044
• Cutler DM, Zeckhauser RJ. The anatomy of health insurance. In: Culyer AJ, Newhouse JP, eds. Handbook of Health Economics. Vol 1A. Elsevier; 2000:563-643. https://doi.org/10.1016/S1574-0064(00)80170-5. Working paper version read: NBER Working Paper 7176, 1999. https://www.nber.org/papers/w7176
• Kutzin J. Health financing for universal coverage and health system performance: concepts and implications for policy. Bulletin of the World Health Organization. 2013;91(8):602-611. https://doi.org/10.2471/BLT.12.113985
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Section 4.2.9. https://www.nice.org.uk/process/pmg36
• Sagan A, Thomson S, eds. Voluntary health insurance in Europe: role and regulation. Observatory Studies Series 43. Copenhagen: WHO Regional Office for Europe on behalf of the European Observatory on Health Systems and Policies; 2016. https://eurohealthobservatory.who.int/publications/i/voluntary-health-insurance-in-europe-role-and-regulation-study
• World Health Organization. The world health report: health systems financing: the path to universal coverage. Geneva: WHO; 2010. https://iris.who.int/handle/10665/44371