# Presentation: 040124

## Health Insurance Theory:The Case of the Missing Welfare Gain

- John A. Nyman
- University of Minnesota
- CHPR/CRIISP/Department of Economics Seminar
- University of Iowa

- John A. Nyman, October 21, 2005

## Overview

- New theory is based on simple idea:
- What healthy person would purchase, say, a coronary bypass procedure simply because the price dropped to zero?
- This means that insurance price reduction is effective only for the ill, and thus it is a vehicle for transferring income to them
- Produces dramatic changes welfare implications
- Organization of talk
- Example
- Theory
- Policy

- John A. Nyman, October 21, 2005

## Elizabeth Example

- This year, 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 an additional breast reconstruction procedure to correct the disfigurement for $20,000
- But without insurance, she is not willing to pay the $20,000 to purchase it

- John A. Nyman, October 21, 2005

## 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 both the $20,000 mastectomy and $20,000 breast reconstruction (the moral hazard), and as a result, $40,000 is transferred out of the insurance pool to pay for her care.
- What are the welfare implications of the moral hazard?
- Conventional theory: Pauly, 1968

- John A. Nyman, October 21, 2005

## Translation to Theory

- M

- $/M

- P = Marginal Cost

- Mu

- Mi

- A

- Dw/o insurance

- P = $0

- B

- John A. Nyman, October 21, 2005

## Elizabeth Example

- Now, what if insurance was available that pays off with lump-sum payment upon diagnosis—call it “contingent claims” insurance?
- So, Elizabeth instead purchases an insurance policy for $4,000 that pays her a cashier’s check for $40,000 upon diagnosis of breast cancer.
- With this income transfer of $36,000 and her original income, she purchases the $20,000 mastectomy that she would have purchased without insurance, plus the $20,000 breast reconstruction (the moral hazard)
- Welfare implications of the moral hazard?

- John A. Nyman, October 21, 2005

## Translation to Theory

- M

- $/M

- P = Marginal Cost

- Mu

- Mi

- A

- B

- C

- F

- E

- Dw/o price payoff
-  insurance

- Dwith contingent claims insurance

- P=0

- John A. Nyman, October 21, 2005

## The problem: A vanishing welfare gain?

- Elizabeth’s behavior is same under the 2 insurance policies:
- Pays same premium, gets same payoff and income transfer, purchases same additional consumption (that is, same *moral hazard*)
- Most importantly, Elizabeth is equally happy under both of them, still
- Under price payoff insurance: a welfare loss
- Under contingent claims insurance: a welfare gain
- Suggests that conventional theory is flawed.

- John A. Nyman, October 21, 2005

## New Theory

- Show that within price payoff health insurance there is an income transfer
- Compare *no insurance* with *price payoff* insurance
- Show the income transfer within price payoff insurance
- Give example
- Income transfer in price payoff insurance has same welfare effect as the payoff in a contingent claims policy
- Compare *price payoff* with *contingent claims* insurance
- Show welfare conclusions are the same, but depend on preferences

- John A. Nyman, October 21, 2005

## Price-Payoff Insurance Has Income Transfer

- Ill consumer’s problem 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’s problem with *price payoff* insurance
- 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

- John A. Nyman, October 21, 2005

## Price-Payoff Insurance Has Income Transfer

- Income constraint with insurance:
- Yo - R = cM + Y
- Insurer conducts actuarial study to find actuarially fair premium:
- R =  π(1-c)Mppi
- 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
- (1-π)(1-c)Mppi  is the income transfer

- John A. Nyman, October 21, 2005

## 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.
- Because everyone has same preferences and same π = 0.1 probability of becoming ill each year, the insurer calculates an actuarially fair premium of $2,000 for a policy where c = 0.

- John A. Nyman, October 21, 2005

## Example of theIncome Transfer

- The insurer pays $20,000 out of the insurance pool 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, $18,000 of income is transferred to Nigel from those who purchase insurance and remain healthy

- John A. Nyman, October 21, 2005

## Income Transfer ProducesSame Welfare Gain

- Ill consumer’s problem with *price payoff* insurance (again)
- 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
- Ill consumer’s problem 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 – R + I = M + Y

- John A. Nyman, October 21, 2005

## Income Transfer Produces Same Welfare Gain

- Income constraint for contingent claims insurance:
- Yo – R + I = M + Y
- From price-payoff insurance, _set_ Icci = (1-c)Mppi and Rcci =  π(1-c)Mppi
- Yo – π(1-c)Mppi + (1-c)Mppi = Mcci + Ycci
- Yo + (1-π)(1-c)Mppi = Mcci + Ycci
- So, same income transfer
- Whether Mcci = Mppi or not depends on preferences alone.

- John A. Nyman, October 21, 2005

## Welfare Conclusions 

- Want to show indifference curve diagrams for 3 different cases of preferences
- Want to also show the corresponding demand curve diagrams
- From diagrams, show that the welfare implications depend on preferences
- Show that Pauly’s analysis just special case of a larger model

- John A. Nyman, October 21, 2005

## Welfare Conclusions Case 1:Limited Substitutability

- For example, increase in income leads to purchase of another procedure, but substitutability in preferences also generates the purchase of an extra hospital day.
- The consumer only purchases the extra hospital day because the price is 0.
- Income-transfer-generated MH is efficient
- Substitutability-generated MH is inefficient

- John A. Nyman, October 21, 2005

## Slide 18

- John A. Nyman, October 21, 2005

## Slide 19

- John A. Nyman, October 21, 2005

## Welfare Conclusions Case 2:Total Substitutability

- No income transfer *effect* at all, even though income transfer exists
- MH entirely caused by substitutability in preferences and is, therefore, inefficient
- This is the Pauly (1968) case
- It is possible that no income transfer effects exist at some prices, but they exist at others
- So, demand response to HI price reduction might still not be the same as Marshallian demand

- John A. Nyman, October 21, 2005

## Slide 21

- John A. Nyman, October 21, 2005

## Slide 22

- John A. Nyman, October 21, 2005

## Welfare Conclusions Case 3:No Income Transfers

- For routine care that occurs annually—check-ups, flu shots, annual screening tests, etc.—insurance produces only welfare loss
- If π approaches 1, any demand response to using price reductions as the payoff mechanism must be paid for by an increase in premiums
- Insight: even though price falls, there are no income transfers, so consumer is only worse off
- This is true “moral hazard welfare loss”

- John A. Nyman, October 21, 2005

## Slide 24

- John A. Nyman, October 21, 2005

## Slide 25

- John A. Nyman, October 21, 2005

## Theory: Ex Ante Decision

- The consumer’s decision to purchase price-payoff insurance with a given coinsurance rate and an AFP is:
- EUu = (1-π)UH(0, Yo) + πUS(Mu, Yo - Mu)
- EUs = (1-π)UH[0, Yo - π(1-c)Ms]   +                                               πUS[Ms, Yo - Ms + (1-π)(1-c)Ms]
- This price payoff insurance policy is purchased if EUs – EUu > 0.

- John A. Nyman, October 21, 2005

## Theory: Ex Ante Decision

- EUs - EUu =                                                	(1-π){UH[0, Yo - π(1-c)Ms] - UH(0, Yo)} +        	π{US[(Ms, Yo + (1-π)(1-c)Ms  - Ms)] - 			US(Mu, Yo - Mu)} > 0
- Insurance is purchased when expected utility gain from the income transfer if ill exceeds expected utility loss from paying the premium if healthy
- It’s fair since π(1-π)(1-c)Ms   = -(1-π) π(1-c)Ms

- John A. Nyman, October 21, 2005

## New Theory Summarized

- Most of the insurance price reduction is only effective for those who are ill
- What healthy person would purchase a course of chemotherapy just because the price is $0?
- For most medical care, the price reduction is the vehicle for transferring income to the ill
- This is the “income transfer effect”
- The other “income effect” of health insurance is having to pay a larger premium to obtain a lower coinsurance rate

- John A. Nyman, October 21, 2005

## New Theory Summarized

- Both these income effects derive from the mechanics of the insurance contract
- Premium payment is higher for smaller coinsurance rates
- Smaller coinsurance rates generate larger income transfers
- THEY ARE NOT THE HICKSIAN INCOME EFFECT
- Hicksian income effect occurs when some change in S or D in the medical care market results in an exogenous change in market price
- With health insurance, market price remains constant

- John A. Nyman, October 21, 2005

## New Theory Summarized

- Moral hazard has both a efficient income transfer related portion and an inefficient substitution related portion
- The welfare gain from the efficient portion of moral hazard has not been recognized as a gain from insurance and changes the value of insurance dramatically
- Inefficient portion of moral hazard is smaller than previously thought
- Inefficient MH is just a transaction cost of using price reductions to transfer income to the ill

- John A. Nyman, October 21, 2005

## New Theory Summarized

- Contingent claims insurance with the same premium, payoff, and income transfer would have larger transactions costs
- Hiring physicians to monitor for fraud
- Hiring lawyers to write very complex HI contracts to specify payoffs for primary diagnoses, complications, sequellae, etc.
- Price payoff insurance is a cheaper way to transfer that income
- Policy implication next

- John A. Nyman, October 21, 2005

## 1.  Voluntary Purchase of Health Insurance Increases Welfare

- Studies estimating welfare effects of HI under conventional theory have found that unsubsidized HI *decreases welfare*
- Manning and Marquis, *JHE*, 1996
- If c=0, no stop loss: household loses $1,424 (1995$)
- If c=25%, $4000 stop loss: household loses $131
- Optimal insurance: c~50%, no stop loss
- Martin Feldstein, *JPE*, 1973
- Optimal insurance: c at least 67%, no stop loss
- Many self-employed purchased unsubsidized HI with large loading fees.  Were they irrational?

- John A. Nyman, October 21, 2005

## 1.  Voluntary Purchase of Health Insurance Increases Welfare 

- These studies assume all MH is welfare decreasing
- When portion of MH that was deemed welfare decreasing is *recategorized as welfare increasing*, purchase of insurance becomes welfare increasing
- In Nyman (2003), I estimate that insurance generates about $2,100 per person in net gain from the additional health care.
- Miller, Vigdor, Manning (2004), reach similar conclusion.

- John A. Nyman, October 21, 2005

## 2.  Cost Containment Policies Are Different

- HC costs as % of GDP rising over last 4 decades
- HI theory provided welfare implications
- Cost increases were primarily due to health insurance generating moral hazard, all of which deemed to be welfare-decreasing
- Policies directed at reducing quantity:
- Cost sharing: coinsurance, copayments, deductibles
- Managed care: bundled payments, selection of  low cost providers, risk-sharing contracts with providers
- High medical care prices were ok, *possibly beneficial*

- John A. Nyman, October 21, 2005

## 2.  Cost Containment Policies Are Different

- High medical care prices can be beneficial:
- “...conventional health insurance often causes consumers to demand services worth less than their cost—the so-called moral hazard phenomenon—so that higher medical prices that discourage this inefficient consumption may actually increase net benefit.” Pauly. *Health Affairs*, 1995, p. 72.
- Also, Crew, *AER*, 1969.

- John A. Nyman, October 21, 2005

## 2.  Cost Containment Policies Are Different

- Conventional theory: all moral hazard is bad, so impose cost-sharing on all expenditures
- New theory: cost-sharing and managed care must distinguish between efficient and inefficient moral hazard, and reduce only inefficient moral hazard, a more difficult task.
- New theory: costs can also be reduced by reducing medical care prices, which are too high primarily because of the market power of health plans and providers.

- John A. Nyman, October 21, 2005

## 3.  Theoretical Justification for Government Intervention

- Standard economic theory argues that government should only intervene when the market fails
- Under conventional health insurance theory, *no market failure in present insurance market*:
- Gain from HI is due to achieving consumer’s _preference for certainty of financial losses_: no market failure here
- Existing _subsidy of employee HI premiums_ causes the purchase of _too much HI_

- John A. Nyman, October 21, 2005

## 3.  Theoretical Justification for Government Intervention

- So, economists have called for the repeal of the employee premium subsidy
- Galen Institute’s petition to eliminate tax subsidy of employee HI premiums because it “artificially supports the increased demand for medical services...” November 30, 1994  (370 health economists signed)
- Besides, the purchase of unsubsidized HI makes the consumer worse off

- John A. Nyman, October 21, 2005

## 3.  Theoretical Justification for Government Intervention

- New theory: the voluntary purchase of unsubsidized HI makes consumer better off.
- Main market failure under new theory is the altruistic externality from providing access to health care to those who are ill
- External willingness to pay for health insurance exceeds private willingness to pay because of altruism

- John A. Nyman, October 21, 2005

## 3.  Theoretical Justification for Government Intervention

- This externality justifies government intervention under new theory
- Government intervention could take a number of forms:
- Extending existing coverage, for example, adding the drug benefit to Medicare
- Insuring the uninsured, through premium subsidies or extensions of Medicaid eligibility
- Adoption of a national health insurance scheme with details consistent with new theory

- John A. Nyman, October 21, 2005

## Further Reading

***The Theory of Demand for Health Insurance***
- by John A. Nyman
- Stanford University Press, 2003

- John A. Nyman, October 21, 2005

## Further reading

- _[The Moral-Hazard Myth](http://www.newyorker.com/fact/content/articles/050829fa_fact)__** **_
- The bad idea behind our failed health-care system.
- by Malcolm Gladwell
*New Yorker * (Aug. 29, 2005)

- John A. Nyman, October 21, 2005