Lecture 9: Social Insurance: General Concepts
Stefanie Stantcheva
Fall 2019
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DEFINITION
Social insurance programs: Government interventions in the provision of
insurance against adverse events:
Examples: (a) health insurance (Medicaid, Medicare), (b) retirement and
disability insurance (Social Security), (c) unemployment insurance
Growth in government over the 20th century is mostly due to the growth of
social insurance (health and retirement benefits)
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What Is Insurance?
Insurance premiums: Money that is paid to an insurer so that an
individual will be insured against adverse events.
A sampling of private insurance products that exist in the United States
includes:
Health insurance
Auto insurance
Life insurance
Casualty and property insurance
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EXPECTED UTILITY MODEL
Utility function U(c) increasing in consumption c and concave in
consumption c: U
0
(c) > 0 and U
00
(c) < 0
Expected utility model: Individuals want to maximize expected utility
defined as the weighted sum of utilities across states of the world, where
the weights are the probabilities of each state occurring.
If q is probability of adverse event, expected utility is written as:
EU=(1-q)*U(consumption with no adverse evert)+q*U(consumption with
adverse evert)
Actuarially fair premium: Insurance premium that is set equal to the
insurer’s expected payout.
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EXPECTED UTILITY MODEL
Person has income W (regardless of health)
Person is sick with probability q
If sick, person incurs medical cost d to get better
Insurance contract: pay premium p always, and receive payout b only if sick
Expected utility:
EU = (1 − q)U(W − p) + qU( W − p − d + b)
Expected profits of insurers: EP = p − qb
Competition among insurers EP = 0 ⇒ b = p/q
This is called actuarially fair insurance
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EXPECTED UTILITY MODEL
Individual chooses the level of premiums p to maximize:
EU = (1 − q)U (W − p) + qU(W − d − p + p/q)
First order condition:
0 = dEU /dp = −(1 − q)U
0
(W − p) + q[−1 + 1/q]U
0
(W − d − p + p/q)
⇒ U
0
(W − p) = U
0
(W − d − p + p/q)
⇒ W − p = W − d − p + p/q (because U is concave and hence U
0
is strictly
decreasing and hence invertible)
⇒ 0 = −d + p/q ⇒ p = d · q
This implies that the person is perfectly insured: consumption is the same in both
states and equal to W − d · q
Intuition: with concave utility, marginal utility decreases and it is always
desirable to reduce consumption in high income states to increase consumption in
low income states
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Introducing heterogeneity in risk across individuals
Suppose now that there are two types of individuals: sickly and healthy
Sickly have q = q
S
and Healthy have q = q
H
with q
S
> q
H
First scenario: Symmetric Information: Insurance companies and
individuals can observe q
H
vs. q
S
types (for example, could be age status)
Then insurance companies will charge 2 policies, each actuarially fair:
p
S
, b
S
= p
S
/q
S
for the sickly
p
H
, b
H
= p
H
/q
H
for the healthy
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Introducing heterogeneity in risk across individuals (cont.)
Each type will still choose to buy perfect insurance b
S
= b
H
= d and
p
S
= q
S
d, p
H
= q
H
d
Sickly always consume W − q
S
d
Healthy always consume W − q
H
d
Private insurance does not equalize incomes across types only within types
Pre-existing conditions will lead to inequality in insurance premia and
welfare but no failure in the insurance market
What if W − q
S
d < 0? Sickly person cannot afford insurance and dies (or
starves) if sick
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Introducing heterogeneity in risk across individuals
Second scenario: Asymmetric Information: Insurance companies cannot
observe (or cannot price on) q
H
vs. q
S
types but individuals do
If insurance companies charge the same two policies as before
p
S
= q
S
d, b
S
= d for the sickly
p
H
= q
H
d, b
H
= d for the healthy
Then everybody wants to buy the healthy insurance which is cheaper ⇒
Insurance company will make losses ⇒ cannot be an equilibrium [this is
called Adverse Selection]
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Introducing heterogeneity in risk across individuals (cont.)
Two equilibrium possibilities:
1) Pooling equilibrium: Insurance companies offer a contract based on
average risk [good deal for sickly, mediocre deal for healthy but better than
no insurance]
2) Separating equilibrium: Insurance companies offer two contracts: one
expensive contract with full insurance for the sickly, one cheap contract
with partial insurance for the healthy: each type self-select into its
contract ⇒ Outcome not efficient as healthy as under-insured
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Adverse Selection
Adverse selection is when individuals know more about their risk level
than the insurer and hence individuals with higher risk are more likely to
purchase insurance.
Example: people with high risk of getting sick more likely to buy health
insurance than people with low risk of getting sick (if insurers cannot
discriminate)
With adverse selection, market for insurance can unravel in a death spiral:
Insurance is offered at average fair price, bad deal for low risk people and hence
only high risk people buy it ⇒ insurers make losses ⇒ insurers raise the price
further ⇒ only very high risk people buy it ⇒ insurers make losses again ⇒ no
insurance contract is offered at all even though everybody wants full actuarially
fair insurance
This inefficiency (market failure) arises because of asymmetric information
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How Does the Government Address Adverse Selection?
The government can address adverse selection and improve market
efficiency but this involves redistribution
Natural solution is to impose a mandate: everybody is required to
purchase insurance ⇒ If price is the same for everybody, low risk people
end up subsidizing high risk people
From a social perspective, being high risk (e.g. having a sickly constitution)
is rarely consequence of individual choices ⇒ Society might want to
compensate individuals for this
⇒ Explains why all OECD countries (except US until Obamacare) have
adopted universal health insurance
Obamacare three-legged-stool (a) forbids insurers from charging based on
pre-existing conditions, (b) mandates that everybody needs to get
insurance, (c) subsidizes health insurance for low income families
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WHY SOCIAL INSURANCE: OTHER REASONS
Redistribution: Private insurers cannot provide insurance against
pre-existing conditions so those with high risk have to pay more: society
may want to compensate high risk people (as being high risk is often not
the fault of the person)
⇒ Universal health insurance funded by taxation effectively redistributes
from high-risk people to low-risk people
Externalities
Your lack of insurance can be a cause of illness for me, thereby exerting a
negative physical externality.
Example: flu shots protect the individual who gets it from the flu but
indirectly protects others (as the flu is very contagious)
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WHY SOCIAL INSURANCE: OTHER REASONS
Individual Failures
Individuals may not appropriately insure themselves against risks if the
government does not force them to do so (myopia, lack of information,
self-control problems)
If individuals understand their own failures, they will support social insurance (e.g.,
Medicare Health Insurance for elderly is very popular)
If individuals really want to be myopic, they will oppose govt social insurance
(paternalism)
Administrative Costs
The administrative costs for Medicare are less than 2% of claims paid.
Administrative costs for private insurance average about 12% of claims paid.
High administrative costs arise because private insurers try to screen away sickly
customers and steal healthy customers from competitors. Individuals may also not
understand well products and hence be sensitive to flashy advertisements.
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CONSEQUENCE OF INSURANCE: MORAL HAZARD
Moral hazard: Adverse actions taken by insured individuals in response to
insurance against adverse outcomes.
Example: If you receive unemployment benefits replacing lost wages, you
may not search as much for a new job ⇒ Insurance reduces incentives to
remedy adverse events
Moral Hazard exists with both private and social insurance as long as
insurer cannot perfectly monitor the person insured ⇒ Insurers do not offer
perfect insurance
The existence of moral hazard problems creates the central trade-off of
social insurance: insurance is desirable for consumption smoothing but
insurance can create moral hazard
[similar to the problem of optimal income taxation equity-efficiency
trade-off]
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MORAL HAZARD
What Determines Moral Hazard?
-How hard it is to observe whether the adverse event has happened
-How easy it is to change behavior in get into or stay in the adverse event
Moral Hazard Is Multidimensional: In examining the effects of insurance,
three types of moral hazard play a particularly important role:
1) Reduced precaution against entering the adverse state (example: auto
insurance)
2) Increased odds of staying in the adverse state (example: unemployment
insurance)
3) Increased expenditures when in the adverse state (example: health
insurance)
⇒ Moral hazard increases the cost of providing insurance
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PUTTING IT ALL TOGETHER:
OPTIMAL SOCIAL INSURANCE
Optimal social insurance trades-off two considerations:
1) The benefit of social insurance is the amount of consumption smoothing
provided by social insurance programs
2) The cost of social insurance is the moral hazard caused by insuring
against adverse events
⇒ Optimal social insurance systems should partially, but not completely,
insure individuals against adverse events.
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CONCLUSION
Asymmetric information in insurance markets has two important
implications:
1) It can cause adverse selection in private insurance provision (as insurers
cannot perfectly observe risk types) hence the need for social insurance
2) It can cause moral hazard (as insurer cannot perfectly monitor behavior),
hence the need to limit generosity of insurance
The ironic feature of asymmetric information is, therefore, that it
simultaneously motivates and undercuts the rationale for government
intervention through social insurance.
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REFERENCES
Jonathan Gruber, Public Finance and Public Policy, Fourth Edition, 2016 Worth
Publishers, Chapter 12
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