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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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 x $1,552,500 = $220
Size of A and B: MH=f1A+f2B=.3 x $ 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

10. 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

11. 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

12. 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

13. 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

14. 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 $ (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 = => x $10.5 = $.60

15. 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.

16. 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

17. 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

18. 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

19. 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

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

21. 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

22. 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

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