1. Demand for Private Health Insurance
Chapter 4
Demand for Private Health Insurance

2. Context
Private health insurance offered in some countries, in some as supplement to public health insurance
Even when there is only public health insurance, theory underlying demand for private health insurance explains why people may be better off when covered by health insurance.
Insight of economics that it is possible to be over-insured as well as to be under-insured. Occurs when welfare loss from moral hazard exceeds the welfare gain from expenditure risk protection that health insurance provides.
Chapter will explain why

3. Key Premises Underlying Demand for Health Insurance
Future expenditures on personal health care services during a policy year are uncertain.
Health per se is uninsurable, but health care services are potentially insurable. Why is this so?
Other choices that people make that involve uncertainty

4. Insurance Concepts and Terminology
First-party and third-party insurance: examples of each
Pecuniary and non-pecuniary loss. Why non- pecuniary loss is real.
Expected loss
Price of insurance
--what the price is
--why insurers incur costs in excess of expected loss on sale of insurance policy and what types of costs they incur

5. Theory of Demand for Insurance Explains
Why do people purchase insurance at all?
Why do they not self insure?
Why would a person ever pay for a load on an insurance policy? (what a load is?)

6. Diminishing Marginal Utility of Wealth and the Demand for Insurance
What is utility as the term is used in economics?
Why does a person’s utility depend on his or her wealth or income?
What is the difference between wealth and income?
What is meant by marginal utility of wealth (income)?
3 possibilities: (1) marginal utility of wealth does not depend on wealth; (2) marginal utility of wealth increases with increases in wealth; (3) marginal utility of wealth decreases with increases in wealth.
Which of the 3 possibilities do you think is most likely?

7. Fig. 4. 1. Possible Relationships between Wealth and
Fig Possible Relationships between Wealth and the Utility of Wealth

8. Concepts of Expected Loss, Expected Utility
Expected utility is distinct from expected loss
At a given point in time, e.g., a year, an individual can either have
wealth Wh if s/he is healthy or wealth Ws if s/he is sick
Wh > Ws, and expected loss (E(L)) = (1-Θ)0 – ΘL =- Θ(Wh –Ws)
Individuals derive a level of utility from having Wh available for consumption,
U(Wh), and a level of utility to having Ws, U(Ws), where U(Wh) > U(Ws)
We do not know how much higher U(Wh) is than U(Ws), only that utility is higher. In this simple model, health only affects utility through its effect on personal wealth. We do not allow utility to be a direct function of health here.

9. Expected Loss, and Wealth if Healthy or Sick
If the person remains well, L=0, wealth = Wh
However, if s/he becomes ill, the loss is L and the person is left with
Ws = Wh – L
Ex ante, it is expected loss (EL) not loss per se (L) that is relevant to the individual in deciding whether or not to purchase an insurance policy
E(L) < L. Wh – E(L) = Ww.
Ww thus reflects the weighted average E(L)
At end of year, the individual will never have Ww. Rather if sick, will have Ws.and if healthy during year will have Wh.

10. Risk Neutral, Risk Averting, and Risk Loving Individuals
Risk neutral individuals have constant marginal utility of
wealth.
Risk averting individuals have decreasing marginal utility
of wealth= motive purchase insurance
Risk loving individuals have increasing marginal utility
of wealth= motive to gamble

11. Fig.4.2. Utility of a Person Who Is Both a Risk Loving and a Risk-Averse Individual

12. The expected utility of wealth is given by
E(U(W)) = (1- Θ)U(Wh) ＋ Θ U(Ws) (4.1)

13. Deriving Maximum Willingness to Pay for
Insurance Policy
Recall that E(U)= (1- Θ)U(Wh) + Θ U(Ws)
Now suppose that the probability of becoming sick rose from Θ to Θs.
Then E(U) becomes
E(U’) = (1- Θs)U(Wh) + ΘsU(Ws) EU’ < EU. If (Θs/ Θ) = 0.9, EU’ = 0.9EU
Expected loss and expected utility vary as Θ varies.
Now consider how much utility the person derives from Ww, which is Wh minus the expected loss from health expenditures incurred by the individual.

14. Fig Expected Utility and Maximum Willingness-to-Pay to Avoid Expected Loss (EL): Risk Averse Individual

15. Deriving Maximum Willingness to Pay for Insurance Policy
If insurer set premium of insurance policy at actuarial value, Ww , level of wealth person would have left after paying this premium, Ww corresponds to utility levels at C and D. Utility at D is higher than at C.
Point D is utility this risk-averse individual would obtain if wealth level Ww were certain.
However, without full insurance, Ww is an expected value, not a certain value.
Thus, the risk averse individual prefers certainty to the chance that s/he will end up with Ws.
Difference in utility between certain & uncertain wealth of Ww is the vertical distance between D & C.

16. Compare with Risk Lover Case
Now let the person’s initial wealth be WA (Fig. 4.4). The probability of winning is Θ w. Then the expected gain is EG where
EG = Θ wG where G (= Wc-Wa) is the amount the gambler wins if s/he wins.
A risk lover is willing to pay more than EG for the opportunity to gamble.
The person in Fig. 4.4 has higher utility when WA is uncertain (see point A’) than when wealth is certain (point A)
So the person has a maximum willingness to pay for a gamble which is W”A - WA
This loading factor is a substantial share of the price of the gamble, which is WA – WB

17. Fig. 4. 4. Expected Utility and Maximum Willingness-to-Pay to
Fig Expected Utility and Maximum Willingness-to-Pay to Engage in a Gamble: Risk Lover

18. The Premium of a Health Insurance Policy
Let R be the health insurance premium of a health insurance policy. Then
R=(1+Ld)(1-c)ΘMM (4.2)
where R is the premium, Ld, loading, c, coinsurance rate specified in insurance policy, and Θ M, price of medical care, and M, number of units of medical care. ΘMM= L.
E.g., if loading is 0.4 and c is 0.2, the premium is 1.4 times 0.8 times ΘMM.

19. Empirical Issues

20. Why Do the Probability and Magnitude of Loss Vary?
Health status
Medical care prices
Household income: availability of public health insurance; tax subsidy of employer-provided health insurance coverage in U.S.

21. Health Insurance and Welfare: The Deadweight Loss of Excess Insurance Revisited
Welfare loss from moral hazard: show this loss geometrically versus
Welfare gain from expenditure risk protection, implying that relative magnitudes of moral hazard and degree of risk aversion matter

22. Role of Tax Subsidies in Demand for Health Insurance (U.S.)
Why tax subsidy greater for persons with higher income
Why the load on a health insurance policy may be less than the tax subsidy for high income persons
Policy solutions for dealing with the tax subsidy issue

23. Concept of Adverse Selection
What is adverse selection?
Why does it arise?
Give some examples outside of the insurance field in which adverse selection is likely to arise.
Adverse selection is source of market failure in insurance market. Why is this so?

24. Adverse Selection by Consumers versus Preferred Risk Selection and Risk Rating by Insurers
Experience rated versus community rated insurance premiums
Insurer underwriting practices
Public policies against experience rated premiums and insurer underwriting: pros and cons
Policies enacted as part of U.S. health legislation in 2010
Pros and cons of these policies?

25. Adverse Selection and Unraveling in Insurance Markets
Assume initially: all people identical. Use $800/year if become ill
Person survives illness.
No moral hazard
2 policies in market, 1 offering maximum payment of $600 per period and the other $800
Premium difference $60/year reflecting both difference in E(L) and extra cost of administering more costly plan
Choice of 2 policies made entirely on basis of degree of person’s risk aversion
Load on insurance policy efficient—sufficient to cover cost of administering insurance plan

26. Fig. 4.5. Adverse Selection: Only One Health Type- of PersonΘ

27. Now Assume That There Are 2 Persons
One has a high probability of becoming ill ΘH and the other a low probability of become ill ΘL
Insurer cannot tell which is the H-type and which is the L-type consumer.
If there are equal numbers of H- and L-type consumers in the market, Θ =(ΘL + ΘH)/2. The insurer charges both consumers the same difference of $60 in premium, not knowing which are H- and which are L-type consumers.
The H-type select the $800 plan and the L-type select the $600 plan.
The insurer makes money on the $600 plan but loses money on the $800 plan. So insurer sets the premium differential at $80.

28. Fig Adverse Selection: Two Health Types of Persons, One Having a Higher Probability of Becoming Ill ΘL ΘH

29. Beginning of Unraveling of Insurance Market
Assume that there is further heterogeneity in H category consisting of HH and and HL-type persons.
Then HHs go for the high option ($800) and HLs go for the low option ($600).
Now insurer loses money on the the high option even with a larger premium differential
Raises premium differential again and get more splitting of market

30. Fig. 4.7. Adverse Selection: Individual Choices When Premium Difference is $60
Expecting lower than average loss, the individual with a lower probability of becoming ill (ΘL) picks policy with the $600 limit. ΘH
Expecting higher than average loss, the high risk individual with ΘH of becoming ill picks the policy with the $800 limit.
Insurer charges both individuals $60 difference in premium for two policies. Choice made on basis of risk aversion and expected loss.

31. Fig. 4.8. Adverse Selection: Individual Choices When Premium Difference is $80
Insurer observes $80 difference in cost of issuing the two policies because EL for the higher risk person almost (less load) $80 higher than for insuring low risk person.
Thus, the insurer raises the difference in the premium for the two plans paid by the policyholder to $80 per year.
Chooses low coverage ΘL
ΘHL
Chooses high coverage
ΘHH

32. Upshot
There are fewer and fewer persons selecting the high option plan to the point that this plan disappears. The high option is no longer available.
Why is society worse off after this process unfolds?
Cutler and Reber (1998) discuss how this process occurred at Harvard University—a useful illustration of the unraveling process under adverse selection.

33. Empirical Evidence On Adverse Selection in Private Health Insurance Markets
Adverse selection in such markets is widespread (Cutler and Zeckhauser 2000).
Also evidence on existence of adverse selection in such markets from Netherlands (Van de Ven and Van Vliert 1995).
Adverse selection in Australia (Savage and Wright 2003), in Chile (Sapelli and Vial 2003) and in China (Wang et al. 2006).
And in Medigap in the U.S. Explain what Medigap is.

34. Risk Adjustment and Adverse and Preferred Risk Selection
Difference between adverse selection and preferred risk selection
Risk adjust to mitigate problem of preferred risk selection
How risk adjustment done in practice. It is hard to risk adjust accurately.