Demand for Health Insurance Lecture 10 Assoc. Prof. Sencer Ecer HEALTH ECONOMICS

Health Insurance The market for different types of insurance Health insurance is pervasive: Table 10.1 Coverage rates in the US Medicare > 65 (mandatory) (Federal) Medicaid for poor (state-federal partnership) Turkish yesil kart (green (poverty) card) SCHIP for kids (state-federal partnership) “Save the women and children first” Too high income for Medicaid and no private health insurance

The Demand for Health Insurance We need to think of demand for medical care and insurance together, which we actually did before by thinking of demand conditional of having health insurance Health and illness is random. Health insurance insures the financial risk that medical care will cost that a rational person is expected to seek, the derived risk With no formal medical care, health insurance could be additional help in home production in the form of labor or simply help due to marriage (not the case by providing health insurance but by providing care and help as a substitute) No technology can help insure health directly, we can’t make it up hundred percent Reasons people want insurance: Figure 10.1 Two goods: income in bad state and income in good state p is the probability of bad state, 1-p: no loss p/(1-p) is the odds ratio Price should equal odds ratio in an actuarially fair world

A simple approach γ = (p/1-p)γ*, where γ*>1 is the positive real price of insurance Typo, p.304, line 2, should be γ not γ* Comparative statics: Flatter budget line (cheaper insurance) implies buying more coverage If marginal utility of income changes (decreases) rapidly with income, then that implies buying more coverage

A more detailed approach We assume stable preferences (don’t change with health or income shock etc.) and so income, health level, medical care consumption level all determine a person’s utility Risk aversion derives from decreasing marginal utility of income Figures 10.2 and 10.3 There is decreasing marginal utility to income Utility from expected income is higher than expected utility The expected utility can be obtained by a lower income level than expected income The difference is the risk premium, basis for insurance, assuming that the individual maximizes expected utility

The insurance proposition Offer payment at least as high as the IC and in return obtain the individual’s income IC depends o the variance of the gamble and the curvature of the utility curve r(I) = -U’’ / U’ Absolute risk aversion Welfare gain = u(E(IC)-insurance charge)-u(IC) Note: No trade unless E(IC)-insurance charge > IC

Choice of Insurance Policy Intuition of the maximization problem can be captured with choosing the best coinsurance rate Given coinsurance rate C and distribution of f, Expected Benefits from N different illnesses equal: E(B) = Σfi(1-C)pmmi or =(1-C)pmm* where m*= Σfimi pm could actually be pmi but we are simplifying to one type of medical care, such as hospital days The dependence between m and C is called the moral hazard (Pauly, 1968). It is a predictable response of rational consumers. To the extent that it can be planned for (see RHIS), it is not a big problem

Moral Hazard Initially, private insurance companies may not estimate patients visiting a doctor for every minor illness. This extra quantity demanded doesn’t just hurt profits but may cause the market to shrink, some may be left uninsured. Insurance may become dysfunctional Welfare loss due to value of marginal consumption being exceeded by its marginal cost Optimal choice of C optimizes between this welfare loss and the fundamental welfare gain from insurance

Example Figure 10.4 (think as representative consumer) A and B: welfare loss due to moral hazard E(B)=pm(f1m1+f2m2)(1-C) = $840 Total insurance premium = E(B) + loading fee (%10) = $924 Loading fee = risk bearing + profits + admin costs Consumer welfare gain depends on two things Amount of risk premium = .5 x r(I) x σ2 = .5 x -.0003 x $1,552,500 = $220 Size of A and B: MH=f1A+f2B=.3 x $200+.1 x $200 = $80 Consumer’s WTP=E(B)+risk premium-MH = $840 + $200 - $80 = $980 WTP-charge = $980 - $924 = $56 = welfare from risk reduction Pick optimal C by balancing A and B and risk reduction

Moral Hazard Figure 10.5 MH depends on demand elasticity for the medical care at hand The higher demand elasticity, the higher MH See formula at fn 15 Then, insurance companies will prefer not to insure such services

Empirical Regularities in Insurance Coverage Demand for insurance should be higher the higher the financial risk (measured by variance) and should be lower the more price elastic the demand for that type of medical care Confirmed Table 10.2 Hospital (highest financial risk and lowest elasticity) v dental (smallest financial risk and largest elasticity of demand) Dental insurance emerged relatively recently and probably because of tax treatment

Price of insurance R=(1+L)(1-C)pmm*, L=loading fee R= (1-C)pmm* (actuarially fair) If L increases then consumers choose a higher C, so that insurance portion will be lower

Prevention Normally, preventive care does not have much uncertainty, so insuring them may not seem to make sense as insuring medical risks. However, subsidizing them makes sense because: It can reduce financial risk from illness It can also reduce the expected welfare losses from MH Figure 10.6

Prevention example Without vaccination flu occurs w/prob. 30 %. Mean expenditure = πpm1 Variance = π(1-π)(p x m1)2 Risk premium = ½ x Variance x r, where (Assume that prevention completely eradicates the risk of illness) r= Arrow-Pratt measure of absolute risk aversion The Book omits 1/2 , so assume r=.0004 and use the calculations in the book, which yield $10.50. (P.316) Add $10.50 to $500 (flu treatment cost) x .30 = $160.50 If insured with C=.2 and assume demand increases by 20%, then m2=1.2m1 so mean = π x.2 x p x 1.2 x m1, and financial risk is original risk x .04 x 1.44 = .0576 => .0576 x $10.5 = $.60

Prevention example If insured, individual also captures the reduction in expected medical expense .30 x 120 = $36, so total gain for insured individual is $36.60 in contrast to the uninsured individual whose gain was $160.50 With vaccination, the insurance company saves $600 x (1-.2) x .3 = $144 > $36.60 So insurance company would like to induce the individual to get preventive action It can insurance prevention It can charge premium based on preventative behavior like in smoking status and life insurance (experience rating) –seldom happens due to group insurance Also, there are externalities: flu shot is worth it because it is effective for a given year, but benefits of obesity reduction may go to another insurer (due to directly changing the carrier or indirectly to changing jobs) (Externality). As such, employers have less risk than insurers, so they have more incentive to induce preventive care: wellness plans.

Self Selection =Adverse Selection People who suspect or plan high health expenditures buy more insurance coverage The people with low risks in the insurance pool will end up paying higher Figure 10.7 Budget curve is curved because price of health insurance changes with higher medical care consumption: not only more health care bills, but bigger amounts per bill due to moral hazard

Adverse Selection Figure 10.8 Marginal utility from X is higher for the healthy, so flatter indifference curve This would be the full information case. So, budget for the sickly would be smaller due to higher premium What if insurance companies can’t distinguish? Figure 10.9, limited coverage, experience rating Separating equilibrium, the standard outcome in a competitive market Healthy person made worse off

Community rating Figure 10.10 A budget curve between IS and IH Same price for a community e.g. New York State Pareto superior to separating equilibrium only if healthy people form a majority, they could be made worse off if in minority Sickly people will always be better off

Transaction Costs Group insurance through employers is similar to community rating People need to be healthy at least to some extent Median voter at firm wins in choosing the insurance plan Hence, most companies offer only one type of health insurance Long term insurance is very vulnerable to self-selection Hence it has just been forming

Job Lock Pre-existing conditions may prevent people from changing jobs

Empirical estimates of demand for insurance Micro v macro data Ecer and Koc (2011): micro Effect of income on demand Macro: Entire economy How total insurance premiums and income, loading fees, tax subsidies relate Income elasticity is <1 in micro data But we don’t know the income of median worker, who is probably calling the shots, so prediction is difficult In macro data income elasticity is between 1 and 2

Price effects Aggregate data yields -1.5 to -2 Elastic Micro data yields less than -1 Nothing comparable to RAND HIS exists for the demand for health insurance When Reagan reduced the tax subsidy for health insurance there was a considerable decline in, for example, hospital insurance

Optimal insurance Keeler (1988) estimated the best (maxing expected utility) plan in RAND HIS C=25% + $100-300 deductible