June 2, 2007 Orlando--John A. Nyman 1 Health Insurance Theory: The Case of the Missing Welfare Gain John A. Nyman University of Minnesota AcademyHealth

June 2, 2007Orlando--John A. Nyman2 Overview New theory based on simple idea: 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 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 Challenges the conventional welfare implications of health insurance Organization of talk Organization of talk –Elizabeth example –Indifference curve theory –Translation to demand curves

June 2, 2007Orlando--John A. Nyman3 Elizabeth Example Elizabeth becomes one of 12% of women who is diagnosed with breast cancer Elizabeth becomes one of 12% of women who is diagnosed with breast cancer Without insurance, she would purchase: 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 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

June 2, 2007Orlando--John A. Nyman4 Elizabeth Example Fortunately, Elizabeth had purchased a standard insurance policy for $4,000 that pays for all her care 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: 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. 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 Conventional theory of the welfare implications: Pauly, AER, 1968; Feldstein, JPE 1973

June 2, 2007Orlando--John A. Nyman5 Conventional Theory M $/M P = Marginal Cost MuMu MiMi A D P = 0 B P = MC

June 2, 2007Orlando--John A. Nyman6 Conventional Theory M $/M P = Marginal Cost MuMu MiMi A D P = 0 B P = MC Moral hazard welfare loss

June 2, 2007Orlando--John A. Nyman7 Elizabeth Example Now, assume Elizabeth instead purchased insurance that pays off with lump-sum payment upon diagnosis 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 cashiers check for $40,000 Elizabeth purchased a policy for $4,000 and is paid a cashiers check for $40,000 With this income transfer of ($40,000 - $4,000 =) $36,000, plus her original income, she purchases: 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? What are the welfare implications of the moral hazard?

June 2, 2007Orlando--John A. Nyman8 Translation to Theory M $/M P = Marginal Cost MuMu MiMi A B C F E D D with contingent claims insurance P=0

June 2, 2007Orlando--John A. Nyman9 Translation to Theory M $/M P = Marginal Cost MuMu MiMi A B C F E D D with contingent claims insurance P=0 Moral hazard welfare gain

June 2, 2007Orlando--John A. Nyman10 Translation to Theory M $/M P = Marginal Cost MuMu MiMi A B C F E D D with contingent claims insurance P=0 Increase in consumer surplus due to the income transfers

June 2, 2007Orlando--John A. Nyman11 The problem: A vanishing welfare gain? Elizabeths behavior under the 2 insurance policies is the same: Elizabeths 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 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. Suggests that conventional theory is flawed.

June 2, 2007Orlando--John A. Nyman12 New Theory Summarized Consumers purchase insurance in order to obtain additional income when ill 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 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 This income transfer generates the purchase of additional health care and other commodities

June 2, 2007Orlando--John A. Nyman13 New Theory Summarized The income transfer is accomplished when insurance pays for care of the ill person 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 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 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

June 2, 2007Orlando--John A. Nyman14 Steps in the Theoretical Argument Show demand for medical care without insurance 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 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 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

June 2, 2007Orlando--John A. Nyman15 Compare No Insurance with Price- Payoff Insurance Ill consumer with no insurance Ill consumer with no insurance –Max U s (M,Y), s.t. Y o = M + Y Solution: (M u, Y u ) consistent with Solution: (M u, Y u ) consistent with F.O.C.: U M /U Y = 1 and Y o = M + Y F.O.C.: U M /U Y = 1 and Y o = M + Y Ill consumer with price payoff insurance Ill consumer with price payoff insurance –Max U s (M,Y), s.t. Y o – R = cM + Y Solution: (M ppi, Y ppi ) consistent with Solution: (M ppi, Y ppi ) consistent with F.O.C.: U M /U Y = c and Y o – R = cM + Y F.O.C.: U M /U Y = c and Y o – R = cM + Y

June 2, 2007Orlando--John A. Nyman16 Diagrammatically Y M YoYo MuMu Slope = -1 YuYu

June 2, 2007Orlando--John A. Nyman17 Diagrammatically Y M YoYo MuMu Y o - R M ppi Slope = -c Slope = -1 Moral Hazard YiYi YuYu

June 2, 2007Orlando--John A. Nyman18 Actuarially Fair Premium and Income Transfers Income constraint with insurance: Income constraint with insurance: Y o - R = cM + Y Y o - R = cM + Y R is taken as given R is taken as given Insurer conducts actuarial study to find AFP: Insurer conducts actuarial study to find AFP: R = π(1-c)M ppi, then substituting for R R = π(1-c)M ppi, then substituting for R Y o - π(1-c)M ppi = cM ppi + Y ppi Y o - π(1-c)M ppi = cM ppi + Y ppi

June 2, 2007Orlando--John A. Nyman19 Diagrammatically Y M YoYo MuMu M ppi Slope = -c Slope = -1 Moral Hazard Y ppi YuYu Y o – π(1-c)M ppi

June 2, 2007Orlando--John A. Nyman20 Actuarially Fair Premium and Income Transfers Y o - π(1-c)M ppi = cM ppi + Y ppi Y o - π(1-c)M ppi = cM ppi + Y ppi –Adding (1-c)M ppi to both sides: Y o + (1-π)(1-c)M ppi = M ppi + Y ppi, with insurance Y o + (1-π)(1-c)M ppi = M ppi + Y ppi, with insurance Y o = M u + Y u, without insurance, so Y o = M u + Y u, without insurance, so spending is larger with insurance by (1-π)(1-c)M ppi, the income transfer spending is larger with insurance by (1-π)(1-c)M ppi, the income transfer

June 2, 2007Orlando--John A. Nyman21 Example of the Income Transfer Nigel has income of $40,000. Nigel has income of $40,000. Without insurance, he becomes ill and purchases $10,000 of medical care. 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. 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. So, $10,000 of this spending is moral hazard. Actuarially fair premium of $2,000 for a policy where c = 0. Actuarially fair premium of $2,000 for a policy where c = 0. –Assuming everyone has same preferences and same probability π = 0.1 of becoming ill each year, –The insurer calculates premium of 0.1($20,000) = $2,000.

June 2, 2007Orlando--John A. Nyman22 Example of the Income Transfer The insurer takes $20,000 from the insurance pool to pay for Nigels medical care: The insurer takes $20,000 from the insurance pool to pay for Nigels 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 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

June 2, 2007Orlando--John A. Nyman23 Contingent Claims Insurance with Same Premium and Payoff Ill consumer with contingent claims insurance Ill consumer with contingent claims insurance –Max U s (M,Y), s.t. Y o – R + I = M + Y Solution: (M cci,Y cci ) consistent with Solution: (M cci,Y cci ) consistent with F.O.C.: U M /U Y = 1 and Y o – R cci + I cci = M + Y F.O.C.: U M /U Y = 1 and Y o – R cci + I cci = M + Y Set R cci = π(1-c)M ppi and I cci = (1-c)M ppi Set R cci = π(1-c)M ppi and I cci = (1-c)M ppi –Y o – π(1-c)M ppi + (1-c)M ppi = M cci + Y cci –Y o + (1-π)(1-c)M ppi = M cci + Y cci So, same income transfers So, same income transfers

June 2, 2007Orlando--John A. Nyman24 Diagrammatically Y M YoYo MuMu M ppi Slope = -c Slope = -1 Moral Hazard Y ppi YuYu Y o - π(1-c)M ppi Y o + (1-π)(1-c)M ppi

June 2, 2007Orlando--John A. Nyman25 Diagrammatically Y M YoYo MuMu M ppi Slope = -c Slope = -1 Y ppi YuYu Y o - π(1-c)M ppi Y o + (1-π)(1-c)M ppi M* Assume ill consumer maximizes utility here.

June 2, 2007Orlando--John A. Nyman26 Diagrammatically Y M YoYo MuMu M ppi Slope = -c Slope = -1 Y ppi YuYu Y o - π(1-c)M ppi Y o + (1-π)(1-c)M ppi M* Assume ill consumer maximizes utility here. Portion of MH generated by IT IT

June 2, 2007Orlando--John A. Nyman27 Diagrammatically Y M YoYo MuMu M ppi Slope = -c Slope = -1 Y ppi YuYu Y o - π(1-c)M ppi Y o + (1-π)(1-c)M ppi M* Assume ill consumer maximizes utility here. IT Portion of MH generated by price P

June 2, 2007Orlando--John A. Nyman28 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* - M u ) more in medical care

June 2, 2007Orlando--John A. Nyman29 Decomposition of Moral Hazard The portion from M* to M ppi 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 consumers preferences

June 2, 2007Orlando--John A. Nyman30 Modified Elizabeth Example Again assume Elizabeth is diagnosed with breast cancer Again assume Elizabeth is diagnosed with breast cancer Without insurance, she purchases mastectomy for $20,000 Without insurance, she purchases mastectomy for $20,000 With insurance that pays for all her care, she purchases 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

June 2, 2007Orlando--John A. Nyman31 Elizabeth Example Spending without insurance: Spending without insurance: –$20,000 Spending with insurance: Spending with insurance: –$20,000 + $20,000 + $4,000 = $44,000 Moral hazard spending: 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 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

June 2, 2007Orlando--John A. Nyman32 Elizabeth Example Spending without insurance (M u ) : Spending without insurance (M u ) : –$20,000 for mastectomy Spending with price payoff insurance (M i ): Spending with price payoff insurance (M i ): –$44,000 for mastectomy, breast reconstruction, and 2 extra hospital days Spending with contingent claims insurance (M*): Spending with contingent claims insurance (M*): –$40,000 for mastectomy and breast reconstruction

June 2, 2007Orlando--John A. Nyman33 Elizabeth Example Conclude that, of the total moral hazard of $24,000 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

June 2, 2007Orlando--John A. Nyman34 Paper Considers 4 different types of indifference curves Considers 4 different types of indifference curves –limited substitutability as depicted here, no substitutability, total substitutability and no income transfers –Shows that Paulys analysis is only a special case of total substitutability Considers ex ante decision to purchase insurance Considers ex ante decision to purchase insurance Considers policy implications 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 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 Remaining time, translation to demand space

June 2, 2007Orlando--John A. Nyman35 Translate This Into P,Q-Space Y M YoYo MuMu M ppi Slope = -c Slope = -1 Y ppi YuYu Y o - π(1-c)M ppi Y o + (1-π)(1-c)M ppi M* Increased WTP for M u when evaluated with income transfer ITP

June 2, 2007Orlando--John A. Nyman36 Income transfer shifts out Marshallian demand above P=1 $/M M P=1 MuMu M p=0 MC P=0 D M* Greater WTP for M u

June 2, 2007Orlando--John A. Nyman37 Relationship between buying a lower c and demand A lower c generates a greater amount of income transfers, holding π constant 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 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 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 If there is an income effect, higher premiums reduce M compared to Marshallian demand

June 2, 2007Orlando--John A. Nyman38 Compare Purchase of Price Decrease to Exogenous One Y M YoYo MuMu Y o - π(1-c)M i MiMi Slope = -c Slope = -1 YiYi YuYu Y o + (1-π)(1-c)M i If market price fell to c exogenously, ill consumer maximizes utility here ITP M* MeMe E Reduction in demand caused by paying for price decrease

June 2, 2007Orlando--John A. Nyman39 D i shows 2 income effects: premium and income transfers $/M M 1 MuMu MiMi MC 0 D M* c MeMe Difference in quantity demanded because of assumed income effect from paying the premium necessary to purchase a coinsurance rate of c DiDi

June 2, 2007Orlando--John A. Nyman40 Insurance demand captures two income effects $/M M 1 MuMu MiMi MC 0 D M*M* c MeMe Steeper than Marshallian demand because to reduce price requires payment of ever larger premium

June 2, 2007Orlando--John A. Nyman41 Marshallian demand shows response to exogenous price fall $/M M 1 MuMu MiMi MC 0 D M* c MeMe Steeper than Marshallian demand because to reduce price requires payment of ever larger premium

June 2, 2007Orlando--John A. Nyman42 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 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 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 Pauly, Feldstein held that there was only a welfare loss associated with moral hazard, determined by Marshallian demand

June 2, 2007Orlando--John A. Nyman43 Marshallian consumer surplus welfare gain from IT given c $/M M 1 MuMu MiMi MC 0 D M* c MeMe D IT Welfare gain from income transfers

June 2, 2007Orlando--John A. Nyman44 Net welfare gain from using price reduction to c to pay off contract $/M M 1 MuMu MiMi MC 0 D M* c MeMe Welfare loss from using a price reduction to transfer income DiDi but the net welfare effect is positive

June 2, 2007Orlando--John A. Nyman45 Net welfare gain compared with conventional welfare loss Net welfare gain compared with conventional welfare loss $/M M 1 MuMu MiMi MC 0 D M*M* c MeMe Net welfare effect is positive DiDi Conventional welfare loss

June 2, 2007Orlando--John A. Nyman46 Further Reading The Theory of Demand for Health Insurance The Theory of Demand for Health Insurance John A. Nyman John A. Nyman –Stanford University Press, 2003

June 2, 2007Orlando--John A. Nyman47 Questions?