1 Lecture 7: Uncertainty and the welfare gain from health insurance Jan Abel Olsen University of Tromsø, Norway www.janabelolsen.org Teaching programmes: Master of Public Health, University of Tromsø, Norway HEL-3007 Health Economics and Policy Master of Public Health, Monash University, Australia ECC-5979 Health Economics Master of Health Administration, Monash University ECC-5970 Introduction to Health Economics Main text: Olsen JA (2009): Principles in Health Economics and Policy, Oxford University Press, Oxford What we’ll be discussing • The insurance motive for free health care • For which risk*loss combinations do we most prefer insurance? • Market failures from private health insurance
Transcript
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Lecture 7:
Uncertainty and the welfare gain from health insurance
Jan Abel OlsenUniversity of Tromsø, Norway
www.janabelolsen.org
Teaching programmes: Master of Public Health, University of Tromsø, NorwayHEL-3007 Health Economics and Policy
Master of Public Health, Monash University, AustraliaECC-5979 Health Economics
Master of Health Administration, Monash UniversityECC-5970 Introduction to Health Economics
Main text: Olsen JA (2009): Principles in Health Economics and Policy, Oxford University Press, Oxford
What we’ll be discussing
• The insurance motive for free health care
• For which risk*loss combinations do we most prefer insurance?
• Market failures from private health insurance
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The principle of insurance in all its simplicity...
“Suppose that, out of a village of 1,000 people, one whose identity is now unknown will need to pay $5,000 for medical care next year. The 1,000 villagers can each put $5 into a pot, and the resulting $5,000 will be available to bail out the unlucky person next year.
Most people do not like to face the possibility of financial losses, especially large financial losses (they are risk averse), and would view this as a good deal. That is how markets for insurance of all kinds have arisen: auto, homeowners’, renters’, etc”
The key issues
• Each villager has similar probability 1/1000
• They are averse to the prospect of loosing $5000
• The villagers form a risk pool by contributing $5 each
• The financial risk disappears
– but not the health risk
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2 alternatives
• Alternative A (uninsured)– Healthy: p = 99% Income 200,000– Sick: p = 1% Income 100,000
• Alternative B (insured)– Healthy: Income 199,000 – Sick: income 199,000
• Would you prefer A or B?
Same expected loss
• A: p = 1% of loosing 100,000
• C: p = 50% of loosing 2,000
– i.e. expected loss is identical: 1,000
• Insurance premium 1,000 for each of A & C
• Which insurance would you buy, A and/or C?
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The welfare gain model
Assumption:- Risk aversion, i.e. certain outcomes are preferred to gambles- Diminishing marginal utility, i.e. utility increases with wealth,
but at a diminishing rate
Without insurance:If healthy, you enjoy wealth, WIf ill, you suffer a ‘money equivalent loss’, L, thus resulting in
wealth W–L.
Probability of illness, qProbability of not being ill: 1–q.
Wealth without insurance = Wealth with insurance (when p = qL):
(2) q (W – L) + (1 – q) W = W – qL
The utility of wealth with insurance is higher than the expected utility without insurance:(3) q U(W – L) + (1 – q)U(W) < U(W – qL)
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B – A = (potential) welfare gains
C – A = p* - qL = (potential) administration costs and profits
The higher the administration costs and profits, the less welfare gains
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C = the highest WTP for insurance: same utility level as if uninsured
p* = the highest premium that insurance company can charge
no welfare gains to the consumer, BUT profits (p* - qL) to the company
Health insurance premium
• Actuarially fair premium = expected health care costs (= qL)
• Real world premium (p*) = expected health care costs + loading
• Load factor (p* - qL) / qL
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Loading factor by group size
70
35
25
17,5
11,5
6,5
20
0
10
20
30
40
50
60
70
80
Indi
vidu
al p
olicie
s
Sm
all g
roup
s (1
-10)
Mod
erat
e gr
oups
(11-
100)
Med
ium
gro
ups
(100
-200
)
Larg
e gr
oups
(201
-100
0)
Ver
y la
rge
grou
ps (o
ver 1
000)
Wei
ghte
d av
erag
e al
l pla
ns
Lo
ad
ing
fe
e a
s %
of
be
ne
fits
Source: Phelps, Health Economics, 1992, p. 297.
The probability and the loss: Aversion to large losses
Small probability and high loss vs high probability and small loss
qSLH = qHLS
qS = 0.01
LH = 5,000
qH = 0.5
LS = 100
For which of the two risks would people tend to prefer insurance?
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The large loss situation: high (potential) welfare gains
The small loss situation: small (potential) welfare gains
Implications
• Risk aversion involves welfare gains from insurance
Demand for insurance
• Smaller losses involve smaller welfare gains
Less demand for insurance
• Higher probabilities involve less scope for loading
Less supply of insurance
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Moral hazard
Moral hazard (MH) refers to any tendency for the presence of insurance to increase the probability of loss or its amount.
Ex ante MH – the probability increases:The insured becomes less cautious to avoid the incidence
Ex post MH – its amount (costs) increases:This supplier moral hazard may exist when doctors have discretion over the type of care they provide
Moral hazard depends on:
Ex ante MHThe extent to which there are non-monetary losses involved in the consequence of risky behaviour.
If significant non-monetary losses, the insured will be cautious to avoid the incidence.
Ex post MHThe types of remuneration system and control/regulation.
If salaried doctors and/or strong practice guidelines, less scope for cost explosions.
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The welfare loss from insurance
XP=0X*
MC
D
P
P = MC
P = 0
X
Reducing the welfare loss: ‘co-insurance’
XP=0X*
MC
D
P
P = MC
P = 0XXP>0
P > 0
Co-insurance reduces ‘excess consumption’ from XP=0 to XP>0
and the ‘welfare loss’ to the dark blue triangle.
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A contradiction – or a dilemma
• The welfare loss evaporates when p = MC
• but that implies no insurance
• and thus no welfare gain is being exhausted
Community rating
Premium = expected loss
p = q L
‘Community rating’
pC = qCLC
But, we all differ, both in terms of probability and of loss
There is ex ante cross-subsidisation
from ‘net-contributors’ whose expected loss < pC
to ‘net-beneficiaries’ whose expected loss > pC
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Actuarially fair insurance
The expected losses differ across sub-groups
q1L1 < q2L2 < … < qCLC < … < qN-1LN-1 < qNLN
Community rating: ‘net-contributors’ to the left of qCLC,
where the expected loss is less than community premium:
q1L1 < q2L2 < pC
What happens to the average premium when the left tale opts out?
Actuarially fair insurance = individual rating
pi = qiLi
No ex ante cross-subsidisation
Adverse selection
Problem with actuarially fair insurance:
Asymmetric information about the risks faced by individuals
- Buyers of insurance wish to signal a lower than true risk
- Sellers need to identify and separate false risks from true risks
A solution is to offer two types of contracts:
- Reduced coverage (deductibles or co-insurance)
- Complete coverage
The solution induces self-selection
- Low risk buyers go for reduced coverage
- High risk buyers go for complete coverage
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Adverse selection cont
Problem is: Low-risk buyers might still prefer complete coverage if it were available at actuarially fair rates,
but complete coverage contracts are offered at rates that reflect the expected losses of high-risk groups.
Low-risk buyers are faced with the choice between
- Partial insurance at a low rate, or
- Full insurance at an excessively high rate
Efficiency arguments for public insurance
A single tax-financed system involves less administrative costs:
1) No additional costs involved with revenue collection when ‘health taxes’ (set independent of individual risk) are included in an existing tax system
2) Providers of health care face no costs of collecting reimbursements from the insurance companies
3) No costs involved in designing insurance packages for different risk groups
4) No advertising costs of the kind found in competitive insurance markets.
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Key characteristics of three different health insurance systems
Private health insurance
Social health insurance
Taxation
Cost of managing the system (revenue collection, and determining access)
Expensive From quite expensive to quite cheap
Cheap
Coverage Limited Formal sector only (or extended to universal)
Universal
Choice of participation Voluntary Compulsory for all in the formal sector
Compulsory
Cross subsidization No Across other members of the formal sector
Yes
Source of funding Individual premia Pay roll tax Direct and indirect taxes
Incentive on healthy behaviour (i.e. link between own premium and own expected use)
Yes No No
The essence on
private health insurance vs tax-financed health care
Private
health insurance
vs Taxation
Cost of managing the system Expensive Cheap
Coverage Limited Universal
Choice of participation Voluntary Compulsory
Cross subsidization No Yes
So, PHI gives you freedom; it is voluntary and doesn’t coerce you to payfor others’ health care use, But, the system comes with a cost; it is costly and not available to all
