# What we ll be discussing

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1 Teaching programme: Course: Main text: Master of Public Health, University of Tromsø, Norway Health economics and policy (HEL3007) JA Olsen (2009): Principles in Health Economics and Policy, Oxford University Press, Oxford Lecture 7 ( ) Uncertainty and the welfare gain from health insurance Teacher: What we ll be discussing The insurance motive for free health care For which risk*loss combinations do we most prefer insurance? Market failures from private health insurance 1

2 The principle of insurance in all its simplicity... Suppose that, out of a village of 1,000 people, one whose identity is now unknown will need to pay \$5,000 for medical care next year. The 1,000 villagers can each put \$5 into a pot, and the resulting \$5,000 will be available to bail out the unlucky person next year. Most people do not like to face the possibility of financial losses, especially large financial losses (they are risk averse), and would view this as a good deal. That is how markets for insurance of all kinds have arisen: auto, homeowners, renters, etc The key issues Each villager has similar probability 1/1000 They are averse to the prospect of loosing \$5000 The villagers form a risk pool by contributing \$5 each The financial risk disappears but not the health risk 2

3 2 alternatives Alternative A (uninsured) Healthy: p = 99% Income 200,000 Sick: p = 1% Income 100,000 Alternative B (insured) Healthy: Income 199,000 Sick: income 199,000 Would you prefer A or B? Same expected loss A: p = 1% of loosing 100,000 C: p = 50% of loosing 2,000 i.e. expected loss is identical: 1,000 Insurance premium 1,000 for each of A & C Which insurance would you buy, A and/or C? 3

4 The welfare gain model Assumption: - Risk aversion, i.e. certain outcomes are preferred to gambles - Diminishing marginal utility, i.e. utility increases with wealth, but at a diminishing rate Without insurance: If healthy, you enjoy wealth, W If ill, you suffer a money equivalent loss, L, thus resulting in wealth W L. Probability of illness, q Probability of not being ill: 1 q. The welfare gain model Expected utility, E(U): (1) E(U) = q U(W L) + (1 q) U(W) Wealth without insurance = Wealth with insurance (when p = ql): (2) q (W L) + (1 q) W = W ql The utility of wealth with insurance is higher than the expected utility without insurance: (3) q U(W L) + (1 q)u(w) < U(W ql) 4

5 B A = (potential) welfare gains C A = p* - ql = (potential) administration costs and profits The higher the administration costs and profits, the less welfare gains 5

6 C = the highest WTP for insurance: same utility level as if uninsured p* = the highest premium that insurance company can charge no welfare gains to the consumer, BUT profits (p* - ql) to the company Health insurance premium Actuarially fair premium = expected health care costs (= ql) Real world premium (p*) = expected health care costs + loading Load factor (p* - ql) / ql 6

7 Loading fee as % of benefits Loading factor by group size ,5 11,5 6, Individual policies Small groups (1-10) Moderate groups (11-100) Source: Phelps, Health Economics, 1992, p Medium groups ( ) Large groups ( ) Very large groups (over 1000) Weighted average all plans The probability and the loss: Aversion to large losses Small probability and high loss vs high probability and small loss q S L H = q H L S q S = 0.01 L H = 5,000 q H = 0.5 L S = 100 For which of the two risks would people tend to prefer insurance? 7

8 The large loss situation: high (potential) welfare gains The small loss situation: small (potential) welfare gains Implications Risk aversion involves welfare gains from insurance Demand for insurance Smaller losses involve smaller welfare gains Less demand for insurance Higher probabilities involve less scope for loading Less supply of insurance 8

9 Moral hazard Moral hazard (MH) refers to any tendency for the presence of insurance to increase the probability of loss or its amount. Ex ante MH the probability increases: The insured becomes less cautious to avoid the incidence Ex post MH its amount (costs) increases: This supplier moral hazard may exist when doctors have discretion over the type of care they provide Moral hazard depends on: Ex ante MH The extent to which there are non-monetary losses involved in the consequence of risky behaviour. If significant non-monetary losses, the insured will be cautious to avoid the incidence. Ex post MH The types of remuneration system and control/regulation. If salaried doctors and/or strong practice guidelines, less scope for cost explosions. 9

10 The welfare loss from insurance P D P = MC MC P = 0 X* X P=0 X Reducing the welfare loss: co-insurance Co-insurance reduces excess consumption from X P=0 to X P>0 and the welfare loss to the dark blue triangle. P D P = MC MC P > 0 P = 0 X* X P>0 X P=0 X 10

11 A contradiction or a dilemma The welfare loss evaporates when p = MC but that implies no insurance and thus no welfare gain is being exhausted Community rating Premium = expected loss p = q L Community rating p C = q C L C But, we all differ, both in terms of probability and of loss There is ex ante cross-subsidisation from net-contributors whose expected loss < p C to net-beneficiaries whose expected loss > p C 11

12 Actuarially fair insurance The expected losses differ across sub-groups q 1 L 1 < q 2 L 2 < < q C L C < < q N-1 L N-1 < q N L N Community rating: net-contributors to the left of q C L C, where the expected loss is less than community premium: q 1 L 1 < q 2 L 2 < p C What happens to the average premium when the left tale opts out? Actuarially fair insurance = individual rating p i = q i L i No ex ante cross-subsidisation Adverse selection Problem with actuarially fair insurance: Asymmetric information about the risks faced by individuals - Buyers of insurance wish to signal a lower than true risk - Sellers need to identify and separate false risks from true risks A solution is to offer two types of contracts: - Reduced coverage (deductibles or co-insurance) - Complete coverage The solution induces self-selection - Low risk buyers go for reduced coverage - High risk buyers go for complete coverage 12

13 Adverse selection cont Problem is: Low-risk buyers might still prefer complete coverage if it were available at actuarially fair rates, but complete coverage contracts are offered at rates that reflect the expected losses of high-risk groups. Low-risk buyers are faced with the choice between - Partial insurance at a low rate, or - Full insurance at an excessively high rate Adverse selection and transaction costs Private insurance is bureaucratic and costly, requiring armies of accountants, actuaries, billers, checkers, fraud detectors, lawyers, managers and secretaries. Culyer (1989) 13

14 Efficiency arguments for public insurance A single tax-financed system involves less administrative costs: 1) No additional costs involved with revenue collection when health taxes (set independent of individual risk) are included in an existing tax system 2) Providers of health care face no costs of collecting reimbursements from the insurance companies 3) No costs involved in designing insurance packages for different risk groups 4) No advertising costs of the kind found in competitive insurance markets. Key characteristics of three different health insurance systems Cost of managing the system (revenue collection, and determining access) Private health insurance Expensive Social health insurance From quite expensive to quite cheap Coverage Limited Formal sector only (or extended to universal) Choice of participation Voluntary Compulsory for all in the formal sector Cross subsidization No Across other members of the formal sector Cheap Universal Compulsory Taxation Source of funding Individual premia Pay roll tax Direct and indirect taxes Contributions based on Access based on Secure funding Incentive on healthy behaviour (i.e. link between own premium and own expected use) Yes Health risks Income Income and consumption Willingness and ability to pay Yes, increased costs increased premia Needs Yes, earmarked to sickness funds Needs Yes No No Depends on political system 14

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