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

About This Presentation

Transcript and Presenter's Notes

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

1
Health Insurance TheoryThe Case of the Missing
Welfare Gain

John A. Nyman
University of Minnesota
AcademyHealth

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

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

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

5
Conventional Theory
/M
D
A
B
P Marginal Cost
P MC
P 0
Mu
Mi
M
6
Conventional Theory
/M
Moral hazard welfare loss
D
A
B
P Marginal Cost
P MC
P 0
Mu
Mi
M
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 cashiers 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?

8
Translation to Theory
/M
E
B
F
C
P Marginal Cost
A
Dwith contingent claims insurance
D
P0
Mu
Mi
M
9
Translation to Theory
E
/M
B
Moral hazard welfare gain
F
C
P Marginal Cost
A
Dwith contingent claims insurance
D
P0
Mu
Mi
M
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
P0
Mu
Mi
M
11
The problem A vanishing welfare gain?

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
with contingent claims insurance a welfare gain
with price payoff insurance a welfare loss
Suggests that conventional theory is flawed.

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

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

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

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 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

16
Diagrammatically
Y
Slope -1
Yo
Yu
Mu
M
17
Diagrammatically
Y
Slope -1
Yo
Yo - R
Slope -c
Yi
Yu
Mu
Mppi
M
Moral Hazard
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 p(1-c)Mppi, then substituting for R
Yo - p(1-c)Mppi cMppi Yppi

19
Diagrammatically
Y
Slope -1
Yo
Yo p(1-c)Mppi
Slope -c
Yppi
Yu
Mu
Mppi
M
Moral Hazard
20
Actuarially Fair Premium and Income Transfers

Yo - p(1-c)Mppi cMppi Yppi
Adding (1-c)Mppi to both sides
Yo (1-p)(1-c)Mppi Mppi Yppi , with
insurance
Yo Mu Yu , without insurance, so
spending is larger with insurance by
(1-p)(1-c)Mppi, the income transfer

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 p 0.1 of becoming ill each year,
The insurer calculates premium of 0.1(20,000)
2,000.

22
Example of theIncome Transfer

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

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 p(1-c)Mppi and Icci (1-c)Mppi
Yo p(1-c)Mppi (1-c)Mppi Mcci Ycci
Yo (1-p)(1-c)Mppi Mcci Ycci
So, same income transfers

24
Diagrammatically
Y
Yo (1-p)(1-c)Mppi
Slope -1
Yo
Yo - p(1-c)Mppi
Slope -c
Yppi
Yu
Mu
Mppi
M
Moral Hazard
25
Diagrammatically
Y
Yo (1-p)(1-c)Mppi
Slope -1
Assume ill consumer maximizes utility here.
Yo
Yo - p(1-c)Mppi
Slope -c
Yppi
Yu
Mu
Mppi
M
M
26
Diagrammatically
Y
Yo (1-p)(1-c)Mppi
Slope -1
Assume ill consumer maximizes utility here.
Yo
Yo - p(1-c)Mppi
Slope -c
Yppi
Yu
IT
Portion of MH generated by IT
Mu
Mppi
M
M
27
Diagrammatically
Y
Yo (1-p)(1-c)Mppi
Slope -1
Assume ill consumer maximizes utility here.
Yo
Yo - p(1-c)Mppi
Slope -c
Yppi
Yu
IT
P
Portion of MH generated by price
Mu
Mppi
M
M
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

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 consumers
preferences

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

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

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

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

34
Paper

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 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

35
Translate This IntoP,Q-Space
Y
Yo (1-p)(1-c)Mppi
Slope -1
Increased WTP for Mu when evaluated with income
transfer
Yo
Yo - p(1-c)Mppi
Slope -c
Yppi
Yu
IT
P
Mu
Mppi
M
M
36
Income transfer shifts out Marshallian demand
above P1
/M
Greater WTP for Mu
D
MC
P1
P0
Mp0
Mu
M
M
37
Relationship between buying a lower c and demand

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

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

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
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
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
46
Further Reading