Health Insurance Theory: The Case of the Missing Welfare Gain

June 2, 2007June 2, 2007 Orlando--John A. NymanOrlando--John A. Nyman 11

Health Insurance Theory:Health Insurance Theory:The Case of theThe Case of the

Missing Welfare Gain Missing Welfare Gain

John A. NymanJohn A. NymanUniversity of MinnesotaUniversity of Minnesota

AcademyHealthAcademyHealth


OverviewOverview

New theory based on simple idea:New theory based on simple idea:– What What healthyhealthy person would purchase a coronary bypass person would purchase a coronary bypass

procedure (or leg amputation or liver transplant) simply procedure (or leg amputation or liver transplant) simply because he was insured and the price dropped to zero?because he was insured and the price dropped to zero?

This implies that for many procedures, the price This implies that for many procedures, the price reduction in insurance is effective only for the ill reduction in insurance is effective only for the ill and as such, is the vehicle for transferring income and as such, is the vehicle for transferring income from the healthy to the illfrom the healthy to the ill

Challenges the conventional welfare implications Challenges the conventional welfare implications of health insuranceof health insurance

Organization of talkOrganization of talk– Elizabeth exampleElizabeth example– Indifference curve theoryIndifference curve theory– Translation to demand curvesTranslation to demand curves


Elizabeth ExampleElizabeth Example

Elizabeth becomes one of 12% of women Elizabeth becomes one of 12% of women who is diagnosed with breast cancerwho 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 a $20,000 mastectomy to rid her body of the

cancercancer She would consider purchasing an She would consider purchasing an

additional procedure for $20,000 to additional procedure for $20,000 to reconstruct her breast but without reconstruct her breast but without insurance, she is not willing to pay insurance, she is not willing to pay $20,000 for the reconstruction$20,000 for the reconstruction



Fortunately, Elizabeth had purchased a Fortunately, Elizabeth had purchased a standard insurance policy for $4,000 that standard insurance policy for $4,000 that pays for all her carepays for all her care– Call it Call it “price payoff”“price payoff” insurance insurance

With this insurance, she purchases: With this insurance, she purchases: – $20,000 mastectomy and $20,000 mastectomy and – $20,000 breast reconstruction (moral hazard)$20,000 breast reconstruction (moral hazard)

So, $40,000 is transferred from the insurance So, $40,000 is transferred from the insurance pool to pay for the cost of her care.pool to pay for the cost of her care.

Conventional theory of the welfare Conventional theory of the welfare implications: Pauly, implications: Pauly, AERAER, 1968; Feldstein, , 1968; Feldstein, JPEJPE 19731973


Conventional TheoryConventional Theory

M

$/M

P = Marginal Cost

Mu Mi

A

D

P = 0

BP = MC


Conventional TheoryConventional Theory

M

$/M

P = Marginal Cost

Mu Mi

A

D

P = 0

BP = MC

Moral hazard welfare loss



Now, assume Elizabeth instead purchased Now, assume Elizabeth instead purchased insurance that pays off with lump-sum payment insurance that pays off with lump-sum payment upon diagnosisupon diagnosis– Call it Call it “contingent claims”“contingent claims” insurance. insurance.

Elizabeth purchased a policy for $4,000 and is Elizabeth purchased a policy for $4,000 and is paid a cashier’s check for $40,000 paid a cashier’s check for $40,000

With this income transfer of ($40,000 - $4,000 =) With this income transfer of ($40,000 - $4,000 =) $36,000, plus her original income, she purchases:$36,000, plus her original income, she purchases:– $20,000 mastectomy and$20,000 mastectomy and– $20,000 breast reconstruction (moral hazard), $20,000 breast reconstruction (moral hazard),

What are the welfare implications of the moral What are the welfare implications of the moral hazard?hazard?


Translation to TheoryTranslation to Theory

M

$/M

P = Marginal Cost

Mu Mi

A

B

C

F

E

D

Dwith

contingent claims insurance

P=0



M

$/M

P = Marginal Cost

Mu Mi

A

B

C

F

E

DDwith


P=0

Moral hazard welfare gain



M

$/M

P = Marginal Cost

Mu Mi

A

B

C

F

E

DDwith


P=0

Increase in consumer surplusdue to the income transfers


The problem:The problem: A vanishing welfare gain? A vanishing welfare gain?

Elizabeth’s behavior under the 2 insurance Elizabeth’s behavior under the 2 insurance policies is the same:policies is the same:– Pays same premium, gets same payoff and Pays same premium, gets same payoff and

income transfer, purchases same additional income transfer, purchases same additional consumption (that is, same consumption (that is, same moral hazardmoral hazard))

Most importantly, Elizabeth achieves same Most importantly, Elizabeth achieves same utility level under both of them, bututility level under both of them, but– with contingent claims insurance: with contingent claims insurance: a welfare gaina welfare gain– with price payoff insurance: with price payoff insurance: a welfare lossa welfare loss

Suggests that conventional theory is flawed.Suggests that conventional theory is flawed.


New Theory SummarizedNew Theory Summarized

Consumers purchase insurance in Consumers purchase insurance in order to obtain additional income order to obtain additional income when illwhen ill

Specifically, health insurance is a Specifically, health insurance is a expected expected quid pro quoquid pro quo transaction, transaction, where a (fair) premium is paid if where a (fair) premium is paid if healthy, for an income transfer if illhealthy, for an income transfer if ill

This income transfer generates the This income transfer generates the purchase of additional health care and purchase of additional health care and other commodities other commodities


New Theory SummarizedNew Theory Summarized

The income transfer is accomplished The income transfer is accomplished when insurance pays for care of the ill when insurance pays for care of the ill personperson

That is, the income transfer is contained That is, the income transfer is contained within the insurance price reductionwithin the insurance price reduction

The price reduction is the vehicle for The price reduction is the vehicle for transferring income because transferring income because for most for most medical care expenditures, it is only the medical care expenditures, it is only the ill who would be responsive to the price ill who would be responsive to the price reductionreduction


Steps in the Theoretical Steps in the Theoretical ArgumentArgument

Show demand for medical care Show demand for medical care without insurancewithout insurance

Show demand for medical care with Show demand for medical care with insurance that reduces price from 1 insurance that reduces price from 1 to cto c

Show demand for medical care with Show demand for medical care with insurance that pays off with the insurance that pays off with the same expenditures as above, only in same expenditures as above, only in the form of a lump sum income the form of a lump sum income transfer upon diagnosistransfer upon diagnosis


Compare No Insurance with Compare No Insurance with “Price-Payoff” Insurance“Price-Payoff” Insurance

Ill consumer with Ill consumer with no insuranceno insurance– Max UMax Uss(M,Y), s.t. Y(M,Y), s.t. Yoo = M + Y = M + Y

Solution: (MSolution: (Muu, Y, Yuu) consistent with) consistent with F.O.C.: UF.O.C.: UMM/U/UYY = 1 and = 1 and YYoo = M + Y = M + Y

Ill consumer with Ill consumer with price payoffprice payoff insuranceinsurance– Max UMax Uss(M,Y), s.t. Y(M,Y), s.t. Yoo– R = cM + Y– R = cM + Y

Solution: (MSolution: (Mppippi, Y, Yppippi) consistent with) consistent with F.O.C.: UF.O.C.: UMM/U/UYY = c and = c and YYoo– R = cM + Y– R = cM + Y


DiagrammaticallyDiagrammatically

Y

M

Yo

Mu

Slope = -1

Yu



Y

M

Yo

Mu

Yo - R

Mppi

Slope = -c

Slope = -1

MoralHazard

Yi

Yu


Actuarially Fair Premium and Actuarially Fair Premium and Income TransfersIncome Transfers

Income constraint with insurance:Income constraint with insurance: YYoo - R = cM + Y - R = cM + Y R is taken as givenR is taken as given

Insurer conducts actuarial study to Insurer conducts actuarial study to find AFP:find AFP:

R = R = π(1-c)Mπ(1-c)Mppi, ppi, then substituting for Rthen substituting for R YYoo - - π(1-c)Mπ(1-c)Mppippi = cM= cMppippi + Y + Yppippi



Y

M

Yo

Mu Mppi

Slope = -c

Slope = -1

MoralHazard

Yppi

Yu

Yo –π(1-c)Mppi


Actuarially Fair Premium and Actuarially Fair Premium and Income TransfersIncome Transfers

YYoo - - π(1-c)Mπ(1-c)Mppippi = cM= cMppippi + Y + Yppippi

– Adding (1-c)MAdding (1-c)Mppippi to both sides: to both sides:

YYoo + (1- + (1-π)(1-c)Mπ)(1-c)Mppippi = M= Mppippi + Y + Yppi , ppi , with with insuranceinsurance

YYoo = M = Muu + Y + Yuu , without insurance, so , without insurance, so spending is larger with insurance by spending is larger with insurance by

(1-(1-π)(1-c)Mπ)(1-c)Mppippi,, the income transfer the income transfer


Example of the Example of the Income TransferIncome Transfer

Nigel has income of $40,000.Nigel has income of $40,000. Without insurance, he becomes ill and Without insurance, he becomes ill and

purchases $10,000 of medical care.purchases $10,000 of medical care. With price payoff insurance, where With price payoff insurance, where c = 0c = 0, he , he

would purchase $20,000 worth of medical would purchase $20,000 worth of medical care.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 Actuarially fair premium of $2,000 for a policy

where where c = 0.c = 0. – Assuming everyone has same preferences and Assuming everyone has same preferences and

same probability same probability π = 0.1π = 0.1 of becoming ill each year,of becoming ill each year,– The insurer calculates premium of 0.1($20,000) = The insurer calculates premium of 0.1($20,000) =

$2,000.$2,000.


Example of theExample of theIncome TransferIncome Transfer

The insurer takes $20,000 from the insurance The insurer takes $20,000 from the insurance pool to pay for Nigel’s medical care:pool to pay for Nigel’s medical care:– Nigel has paid $2,000 of that amount as his Nigel has paid $2,000 of that amount as his

premiumpremium..– The rest, $18,000, is transferred from the The rest, $18,000, is transferred from the

insurance pool.insurance pool. So, So, payoff is $20,000payoff is $20,000 of medical care, of medical care,

actuarially fair premium is $2,000actuarially fair premium is $2,000, and , and $18,000 is the income transferred$18,000 is the income transferred to Nigel to Nigel from those 9 out of 10 who purchase from those 9 out of 10 who purchase insurance and remain healthyinsurance and remain healthy


Contingent Claims Contingent Claims Insurance with Same Insurance with Same Premium and PayoffPremium and Payoff Ill consumer with Ill consumer with contingent claimscontingent claims

insuranceinsurance– Max UMax Uss(M,Y), s.t. Y(M,Y), s.t. Yoo– R + I = M + Y– R + I = M + Y

Solution: (MSolution: (Mccicci,Y,Yccicci) consistent with) consistent with F.O.C.: UF.O.C.: UMM/U/UY Y = 1 and = 1 and YYoo – R – Rccicci + I + Iccicci = M + Y = M + Y

Set RSet Rccicci = = π(1-c)Mπ(1-c)Mppippi and and IIccicci = = (1-c)M(1-c)Mppippi

– YYoo – – π(1-c)Mπ(1-c)Mppippi + + (1-c)M(1-c)Mppippi = M = Mccicci + Y + Yccicci

– YYoo + (1- + (1-π)(1-c)Mπ)(1-c)Mppippi = M = Mccicci + Y + Yccicci

So, same income transfersSo, same income transfers


DiagrammaticallyDiagrammaticallyY

M

Yo

Mu Mppi

Slope = -c

Slope = -1

MoralHazard

Yppi

Yu

Yo - π(1-c)Mppi

Yo +(1-π)(1-c)Mppi



M

Yo

Mu Mppi

Slope = -c

Slope = -1

Yppi

Yu

Yo - π(1-c)Mppi

Yo +(1-π)(1-c)Mppi

M*

Assume ill consumer maximizes utility here.



M

Yo

Mu Mppi

Slope = -c

Slope = -1

Yppi

Yu

Yo - π(1-c)Mppi

Yo +(1-π)(1-c)Mppi

M*


Portion of MH generatedby IT

IT



M

Yo

Mu Mppi

Slope = -c

Slope = -1

Yppi

Yu

Yo - π(1-c)Mppi

Yo +(1-π)(1-c)Mppi

M*


IT Portion of MH generatedby price

P


Decomposition of Moral Decomposition of Moral HazardHazard

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


Decomposition of Moral Decomposition of Moral HazardHazard

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


Modified Elizabeth ExampleModified Elizabeth Example

Again assume Elizabeth is diagnosed Again assume Elizabeth is diagnosed with breast cancerwith breast cancer

Without insurance, she purchases Without insurance, she purchases mastectomy for $20,000mastectomy for $20,000

With insurance that pays for all her With insurance that pays for all her care, she “purchases”care, she “purchases”– mastectomy for $20,000mastectomy for $20,000– breast reconstruction for $20,000breast reconstruction for $20,000– 2 extra days in the hospital for $4,0002 extra days in the hospital for $4,000


Elizabeth ExampleElizabeth Example Spending without insurance:Spending without insurance:

– $20,000$20,000 Spending with insurance:Spending with insurance:

– $20,000 + $20,000 + $4,000 = $44,000$20,000 + $20,000 + $4,000 = $44,000 Moral hazard spending:Moral hazard spending:

– $44,000 – $20,000 = $24,000 $44,000 – $20,000 = $24,000 If she had been paid off with an lump sum If she had been paid off with an lump sum

payment equal to the amount the insurer payment equal to the amount the insurer paid for her care ($44,000), assume she paid for her care ($44,000), assume she would have purchased the mastectomy and would have purchased the mastectomy and the breast reconstruction, but not the extra the breast reconstruction, but not the extra hospital dayshospital days



Spending without insurance (MSpending without insurance (Muu) : ) : – $20,000 for mastectomy$20,000 for mastectomy

Spending with “price payoff” Spending with “price payoff” insurance (Minsurance (Mii):):– $44,000 for mastectomy, breast $44,000 for mastectomy, breast

reconstruction, and 2 extra hospital daysreconstruction, and 2 extra hospital days Spending with “contingent claims” Spending with “contingent claims”

insurance (M*):insurance (M*):– $40,000 for mastectomy and breast $40,000 for mastectomy and breast

reconstructionreconstruction



Conclude that, of the total moral Conclude that, of the total moral hazard of $24,000hazard of $24,000– The $20,000 for the breast The $20,000 for the breast

reconstruction is efficient because reconstruction is efficient because Elizabeth would have purchased that Elizabeth would have purchased that with the income transferwith the income transfer

– The $4,000 for 2 extra days in the The $4,000 for 2 extra days in the hospital are inefficient because she only hospital are inefficient because she only purchases them because the insurer had purchases them because the insurer had distorted the pricedistorted the price


PaperPaper

Considers 4 different types of indifference curvesConsiders 4 different types of indifference curves– ““limited” substitutability as depicted here, no limited” substitutability as depicted here, no

substitutability, “total” substitutability and no income substitutability, “total” substitutability and no income transferstransfers

– Shows that Pauly’s analysis is only a special case of Shows that Pauly’s analysis is only a special case of “total” substitutability“total” substitutability

Considers ex ante decision to purchase insuranceConsiders ex ante decision to purchase insurance Considers policy implicationsConsiders policy implications Addresses argument that income transfers to the Addresses argument that income transfers to the

ill equal income transfers from the healthy, so ill equal income transfers from the healthy, so there should be an equal reduction of demand for there should be an equal reduction of demand for medical care from the healthymedical care from the healthy– Only if income elasticities of healthy and ill are the same Only if income elasticities of healthy and ill are the same – Does not change welfare implications for illDoes not change welfare implications for ill

Remaining time, translation to demand spaceRemaining time, translation to demand space


Translate This IntoTranslate This IntoP,Q-SpaceP,Q-Space

Y

M

Yo

Mu Mppi

Slope = -c

Slope = -1

Yppi

Yu

Yo - π(1-c)Mppi

Yo +(1-π)(1-c)Mppi

M*

Increased WTP forMu when evaluatedwith income transfer

IT P


Income transfer shifts out Income transfer shifts out Marshallian demand above Marshallian demand above

P=1P=1$/M

M

P=1

MuMp=0

MC

P=0

D

M*

Greater WTP for Mu


Relationship between buying a Relationship between buying a lower c and demand lower c and demand

A lower c generates a greater amount of A lower c generates a greater amount of income transfers, holding income transfers, holding ππ constant constant

At prices above P, increasingly greater At prices above P, increasingly greater income transfers shifts out demand income transfers shifts out demand moremore

Also, when the consumer purchases a Also, when the consumer purchases a contract with a lower c, it will cost more contract with a lower c, it will cost more in premiumsin premiums

If there is an income effect, higher If there is an income effect, higher premiums reduce M compared to premiums reduce M compared to Marshallian demandMarshallian demand


Compare Purchase of Price Compare Purchase of Price Decrease to Exogenous OneDecrease to Exogenous One

Y

M

Yo

Mu

Yo - π(1-c)Mi

Mi

Slope = -c

Slope = -1

Yi

Yu

Yo +(1-π)(1-c)Mi

If market price fell to cexogenously, ill consumer maximizes utility here

IT P

M* Me

EReduction in demandcaused by paying forprice decrease


DDii shows 2 income effects: shows 2 income effects: premium and income transferspremium and income transfers

$/M

M

1

Mu Mi

MC

0

D

M*

c

Me

Difference in quantitydemanded because ofassumed income effectfrom paying the premiumnecessary to purchasea coinsurance rate of c

Di


Insurance demand captures Insurance demand captures two income effectstwo income effects

$/M

M

1

MuMi

MC

0

D

M*

c

Me

Steeper than Marshalliandemand because to reduceprice requires paymentof ever larger premium


Marshallian demand shows Marshallian demand shows response to exogenous price response to exogenous price

fallfall$/M

M

1

Mu Mi

MC

0

D

M*

c

Me

Steeper than Marshalliandemand because to reduceprice requires paymentof ever larger premium


Marshallian (as Opposed to Marshallian (as Opposed to Hicksian) Consumer SurplusHicksian) Consumer Surplus

This diagram shows that a net This diagram shows that a net consumer surplus is derived from the consumer surplus is derived from the income transfers and the use of a price income transfers and the use of a price distortion to pay off the contractdistortion to pay off the contract

The net consumer surplus is positive The net consumer surplus is positive indicating a moral hazard welfare gainindicating a moral hazard welfare gain

Pauly, Feldstein held that there was Pauly, Feldstein held that there was only a welfare loss associated with only a welfare loss associated with moral hazard, determined by moral hazard, determined by Marshallian demand Marshallian demand


Marshallian consumer surplus Marshallian consumer surplus welfare gain from IT given cwelfare gain from IT given c

$/M

M

1

MuMi

MC

0

D

M*

c

Me

DIT Welfare gain from income transfers


Net welfare gain from using Net welfare gain from using price reduction to c to pay off price reduction to c to pay off

contract contract $/M

M

1

Mu Mi

MC

0

D

M*

c

Me

Welfare loss from usinga price reduction to transfer income Di but the net welfare

effect is positive


Net welfare gain compared Net welfare gain compared with conventional welfare losswith conventional welfare loss

$/M

M

1

MuMi

MC

0

D

M*

c

Me

Net welfare effect is positive

Di

Conventionalwelfare loss


Further ReadingFurther Reading

The Theory of The Theory of Demand for Demand for Health InsuranceHealth Insurance

John A. NymanJohn A. Nyman– Stanford University Stanford University

Press, 2003Press, 2003


Questions?Questions?

Documents

Health Insurance Theory: The Case of the Missing Welfare Gain