Health Insurance Theory: The Case of the Missing Welfare Gain

1. Health Insurance Theory:The Case of the Missing Welfare Gain John A. Nyman University of Minnesota AcademyHealth Orlando--John A. Nyman

2. Overview • New theory based on simple idea: • What healthy person would purchase a coronary bypass procedure (or leg amputation or liver transplant) simply because he was insured and the price dropped to zero? • This implies that for many procedures, the price reduction in insurance is effective only for the ill and as such, is the vehicle for transferring income from the healthy to the ill • Challenges the conventional welfare implications of health insurance • Organization of talk • Elizabeth example • Indifference curve theory • Translation to demand curves Orlando--John A. Nyman

3. Elizabeth Example • Elizabeth becomes one of 12% of women who is diagnosed with breast cancer • Without insurance, she would purchase: • a $20,000 mastectomy to rid her body of the cancer • She would consider purchasing an additional procedure for $20,000 to reconstruct her breast but without insurance, she is not willing to pay $20,000 for the reconstruction Orlando--John A. Nyman

4. Elizabeth Example • Fortunately, Elizabeth had purchased a standard insurance policy for $4,000 that pays for all her care • Call it “price payoff” insurance • With this insurance, she purchases: • $20,000 mastectomy and • $20,000 breast reconstruction (moral hazard) • So, $40,000 is transferred from the insurance pool to pay for the cost of her care. • Conventional theory of the welfare implications: Pauly, AER, 1968; Feldstein, JPE 1973 Orlando--John A. Nyman

5. Conventional Theory $/M D A B P = Marginal Cost P = MC P = 0 Mu Mi M Orlando--John A. Nyman

6. Conventional Theory $/M Moral hazard welfare loss D A B P = Marginal Cost P = MC P = 0 Mu Mi M Orlando--John A. Nyman

7. Elizabeth Example • Now, assume Elizabeth instead purchased insurance that pays off with lump-sum payment upon diagnosis • Call it “contingent claims” insurance. • Elizabeth purchased a policy for $4,000 and is paid a cashier’s check for $40,000 • With this income transfer of ($40,000 - $4,000 =) $36,000, plus her original income, she purchases: • $20,000 mastectomy and • $20,000 breast reconstruction (moral hazard), • What are the welfare implications of the moral hazard? Orlando--John A. Nyman

8. Translation to Theory $/M E B F C P = Marginal Cost A Dwith contingent claims insurance D P=0 Mu Mi M Orlando--John A. Nyman

9. Translation to Theory E $/M B Moral hazard welfare gain F C P = Marginal Cost A Dwith contingent claims insurance D P=0 Mu Mi M Orlando--John A. Nyman

10. Translation to Theory $/M E Increase in consumer surplus due to the income transfers B F C P = Marginal Cost A Dwith contingent claims insurance D P=0 Mu Mi M Orlando--John A. Nyman

11. The problem: A vanishing welfare gain? • Elizabeth’s behavior under the 2 insurance policies is the same: • Pays same premium, gets same payoff and income transfer, purchases same additional consumption (that is, same moral hazard) • Most importantly, Elizabeth achieves same utility level under both of them, but • with contingent claims insurance: a welfare gain • with price payoff insurance: a welfare loss • Suggests that conventional theory is flawed. Orlando--John A. Nyman

12. New Theory Summarized • Consumers purchase insurance in order to obtain additional income when ill • Specifically, health insurance is a expected quid pro quo transaction, where a (fair) premium is paid if healthy, for an income transfer if ill • This income transfer generates the purchase of additional health care and other commodities Orlando--John A. Nyman

13. New Theory Summarized • The income transfer is accomplished when insurance pays for care of the ill person • That is, the income transfer is contained within the insurance price reduction • The price reduction is the vehicle for transferring income because for most medical care expenditures, it is only the ill who would be responsive to the price reduction Orlando--John A. Nyman

14. Steps in the Theoretical Argument • Show demand for medical care without insurance • Show demand for medical care with insurance that reduces price from 1 to c • Show demand for medical care with insurance that pays off with the same expenditures as above, only in the form of a lump sum income transfer upon diagnosis Orlando--John A. Nyman

15. Compare No Insurance with “Price-Payoff” Insurance • Ill consumer with no insurance • Max Us(M,Y), s.t. Yo = M + Y • Solution: (Mu, Yu) consistent with • F.O.C.: UM/UY = 1 and Yo = M + Y • Ill consumer with price payoffinsurance • Max Us(M,Y), s.t. Yo– R = cM + Y • Solution: (Mppi, Yppi) consistent with • F.O.C.: UM/UY = c and Yo– R = cM + Y Orlando--John A. Nyman

16. Diagrammatically Y Slope = -1 Yo Yu Mu M Orlando--John A. Nyman

17. Diagrammatically Y Slope = -1 Yo Yo -R Slope = -c Yi Yu Mppi Mu M Moral Hazard Orlando--John A. Nyman

18. Actuarially Fair Premium and Income Transfers • Income constraint with insurance: • Yo - R = cM + Y • R is taken as given • Insurer conducts actuarial study to find AFP: • R = π(1-c)Mppi, then substituting for R • Yo - π(1-c)Mppi= cMppi + Yppi Orlando--John A. Nyman

19. Diagrammatically Y Slope = -1 Yo Yo – π(1-c)Mppi Slope = -c Yppi Yu Mppi Mu M Moral Hazard Orlando--John A. Nyman

20. Actuarially Fair Premium and Income Transfers • Yo - π(1-c)Mppi= cMppi + Yppi • Adding (1-c)Mppi to both sides: • Yo + (1-π)(1-c)Mppi= Mppi + Yppi , with insurance • Yo = Mu + Yu , without insurance, so • spending is larger with insurance by (1-π)(1-c)Mppi, the income transfer Orlando--John A. Nyman

21. Example of the Income Transfer • Nigel has income of $40,000. • Without insurance, he becomes ill and purchases $10,000 of medical care. • With price payoff insurance, where c = 0, he would purchase $20,000 worth of medical care. • So, $10,000 of this spending is moral hazard. • Actuarially fair premium of $2,000 for a policy where c = 0. • Assuming everyone has same preferences and same probability π = 0.1of becoming ill each year, • The insurer calculates premium of 0.1($20,000) = $2,000. Orlando--John A. Nyman

22. Example of theIncome Transfer • The insurer takes $20,000 from the insurance pool to pay for Nigel’s medical care: • Nigel has paid $2,000 of that amount as his premium. • The rest, $18,000, is transferred from the insurance pool. • So, payoff is $20,000 of medical care, actuarially fair premium is $2,000, and $18,000 is the income transferred to Nigel from those 9 out of 10 who purchase insurance and remain healthy Orlando--John A. Nyman

23. Contingent Claims Insurance with Same Premium and Payoff • Ill consumer with contingent claims insurance • Max Us(M,Y), s.t. Yo– R + I = M + Y • Solution: (Mcci,Ycci) consistent with • F.O.C.: UM/UY = 1 and Yo – Rcci + Icci = M + Y • Set Rcci = π(1-c)Mppi and Icci= (1-c)Mppi • Yo– π(1-c)Mppi+ (1-c)Mppi = Mcci + Ycci • Yo + (1-π)(1-c)Mppi = Mcci + Ycci • So, same income transfers Orlando--John A. Nyman

24. Y Diagrammatically Yo + (1-π)(1-c)Mppi Slope = -1 Yo Yo -π(1-c)Mppi Slope = -c Yppi Yu Mppi Mu M Moral Hazard Orlando--John A. Nyman

25. Y Diagrammatically Yo + (1-π)(1-c)Mppi Slope = -1 Assume ill consumer maximizes utility here. Yo Yo -π(1-c)Mppi Slope = -c Yppi Yu M* Mppi Mu M Orlando--John A. Nyman

26. Y Diagrammatically Yo + (1-π)(1-c)Mppi Slope = -1 Assume ill consumer maximizes utility here. Yo Yo -π(1-c)Mppi Slope = -c Yppi Yu IT Portion of MH generated by IT M* Mppi Mu M Orlando--John A. Nyman

27. Y Diagrammatically Yo + (1-π)(1-c)Mppi Slope = -1 Assume ill consumer maximizes utility here. Yo Yo -π(1-c)Mppi Slope = -c Yppi Yu IT P Portion of MH generated by price M* Mppi Mu M Orlando--John A. Nyman

28. Decomposition of Moral Hazard • Moral hazard can be decomposed into a portion that is due to the income that is being transferred from healthy to ill • This is efficient because if the insurer had actually transferred this income to the ill person and she could have spent it on anything of her choosing… • She would have purchased this much (M* - Mu) more in medical care Orlando--John A. Nyman

29. Decomposition of Moral Hazard • The portion from M* to Mppi is inefficient because more medical care is purchased, but the consumer is moving to a lower indifference curve • The welfare change for the ill person depends on the net welfare change • Whether the efficient or the inefficient portion dominates depends mostly on the consumer’s preferences Orlando--John A. Nyman

30. Modified Elizabeth Example • Again assume Elizabeth is diagnosed with breast cancer • Without insurance, she purchases mastectomy for $20,000 • With insurance that pays for all her care, she “purchases” • mastectomy for $20,000 • breast reconstruction for $20,000 • 2 extra days in the hospital for $4,000 Orlando--John A. Nyman

31. Elizabeth Example • Spending without insurance: • $20,000 • Spending with insurance: • $20,000 + $20,000 + $4,000 = $44,000 • Moral hazard spending: • $44,000 – $20,000 = $24,000 • If she had been paid off with an lump sum payment equal to the amount the insurer paid for her care ($44,000), assume she would have purchased the mastectomy and the breast reconstruction, but not the extra hospital days Orlando--John A. Nyman

32. Elizabeth Example • Spending without insurance (Mu) : • $20,000 for mastectomy • Spending with “price payoff” insurance (Mi): • $44,000 for mastectomy, breast reconstruction, and 2 extra hospital days • Spending with “contingent claims” insurance (M*): • $40,000 for mastectomy and breast reconstruction Orlando--John A. Nyman

33. Elizabeth Example • Conclude that, of the total moral hazard of $24,000 • The $20,000 for the breast reconstruction is efficient because Elizabeth would have purchased that with the income transfer • The $4,000 for 2 extra days in the hospital are inefficient because she only purchases them because the insurer had distorted the price Orlando--John A. Nyman

34. Paper • Considers 4 different types of indifference curves • “limited” substitutability as depicted here, no substitutability, “total” substitutability and no income transfers • Shows that Pauly’s analysis is only a special case of “total” substitutability • Considers ex ante decision to purchase insurance • Considers policy implications • Addresses argument that income transfers to the ill equal income transfers from the healthy, so there should be an equal reduction of demand for medical care from the healthy • Only if income elasticities of healthy and ill are the same • Does not change welfare implications for ill • Remaining time, translation to demand space Orlando--John A. Nyman

35. Y Translate This IntoP,Q-Space Yo + (1-π)(1-c)Mppi Slope = -1 Increased WTP for Mu when evaluated with income transfer Yo Yo -π(1-c)Mppi Slope = -c Yppi Yu IT P M* Mppi Mu M Orlando--John A. Nyman

36. Income transfer shifts out Marshallian demand above P=1 $/M Greater WTP for Mu D MC P=1 P=0 Mp=0 Mu M* M Orlando--John A. Nyman

37. Relationship between buying a lower c and demand • A lower c generates a greater amount of income transfers, holding π constant • At prices above P, increasingly greater income transfers shifts out demand more • Also, when the consumer purchases a contract with a lower c, it will cost more in premiums • If there is an income effect, higher premiums reduce M compared to Marshallian demand Orlando--John A. Nyman

38. Y Compare Purchase of Price Decrease to Exogenous One Yo + (1-π)(1-c)Mi Slope = -1 If market price fell to c exogenously, ill consumer maximizes utility here Yo Yo -π(1-c)Mi Slope = -c Yi Yu Reduction in demand caused by paying for price decrease IT P E M* Mi Mu Me M Orlando--John A. Nyman

39. Di shows 2 income effects: premium and income transfers Difference in quantity demanded because of assumed income effect from paying the premium necessary to purchase a coinsurance rate of c $/M Di D MC 1 c 0 Mu M* Mi Me M Orlando--John A. Nyman

40. Insurance demand captures two income effects Steeper than Marshallian demand because to reduce price requires payment of ever larger premium $/M D MC 1 c 0 Mi M* Me Mu M Orlando--John A. Nyman

41. Marshallian demand shows response to exogenous price fall Steeper than Marshallian demand because to reduce price requires payment of ever larger premium $/M D MC 1 c 0 Mu Mi M* Me M Orlando--John A. Nyman

42. Marshallian (as Opposed to Hicksian) Consumer Surplus • This diagram shows that a net consumer surplus is derived from the income transfers and the use of a price distortion to pay off the contract • The net consumer surplus is positive indicating a moral hazard welfare gain • Pauly, Feldstein held that there was only a welfare loss associated with moral hazard, determined by Marshallian demand Orlando--John A. Nyman

43. Marshallian consumer surplus welfare gain from IT given c $/M DIT Welfare gain from income transfers D MC 1 c 0 Mi M* Me Mu M Orlando--John A. Nyman

44. Net welfare gain from using price reduction to c to pay off contract Welfare loss from using a price reduction to transfer income $/M but the net welfare effect is positive Di D MC 1 c 0 Mu Mi M* Me M Orlando--John A. Nyman

45. Net welfare gain compared with conventional welfare loss $/M Di Net welfare effect is positive D MC 1 Conventional welfare loss c 0 Mi M* Me Mu M Orlando--John A. Nyman

46. Further Reading • The Theory of Demand for Health Insurance • John A. Nyman • Stanford University Press, 2003 Orlando--John A. Nyman

47. Questions? Orlando--John A. Nyman