Chapter 12
Social Insurance: The New Function of Government


12.1 What Is Insurance and
Why Do Individuals Value It?

12.2 Why Have Social Insurance?
Asymmetric Information and Adverse
Selection

12.3 Other Reasons for Government
Intervention in Insurance Markets


12.4 Social Insurance Versus
Self-Insurance: How Much

Consumption Smoothing?
12.5 The
Problem with Insurance: Moral
Hazard

12.6 Putting It All Together:

Optimal Social Insurance

12.7 Conclusion
In
the preamble to the United States
Constitution, the framers wrote that they
were uniting the states in order to “provide
for the common defense, promote the
general welfare, and secure the blessings
of liberty to ourselves and our posterity.”
For
most of the country’s history
“common defense,” was the federal
government’s clear spending priority.
Since
then, the government’s spending
priorities shifted dramatically, away from
“common defense” and toward promoting
“the general welfare.”
Important Social Insurance
Programs
Social Security
 Unemployment insurance
 Disability Insurance
 Workers Compensation
 Medicare

CHAPTER 12 ■ SOCIAL INSURANCE: THE NEW FUNCTION OF GOVERNMENT
Public Finance and Public Policy Jonathan Gruber Third Edition Copyright © 2010 Worth Publishers
3 of 29
Common features of Social
Insurance programs
Contributions are mandatory
 A measurable, enabling event
 Benefits are not related to one’s
income or assets (not means tested)

Understanding the economics
of insurance markets
Why individuals value insurance
 Why insurance markets may fail

Adverse selection
 Moral hazard


What tradeoffs in designing social
insurance
Key terms

Adverse selection—the insured
individual knows more about their
own risk level than does the insurer

Moral hazard---when you insure
against adverse events, you can
encourage adverse behavior.
Why insurance
Insurance premium---paid to insurer
 In return, insurer promises payment
to individual if adverse event happens
 Examples: Health, car, property,
farm crops,

Why do individuals value
insurance?
Individuals value because of
Diminishing marginal utility
 Ie. They choose 2 years of smooth
income over 1 year of high consumption
and 1 year of starving



--because excessive consumption does not
raise utility as much as starvation lowers it.
They prefer to smooth out consumption
Why individuals value
insurance?


When outcomes are uncertain, individuals
wish to smooth their consumption over
possible states of the world
Examples:



State1: get hit by a car
State2: not getting hit
Goal is to make choice today that determines
consumption in future for each of these states
Insurance, contd.



Consumers smooth by using some of
today’s income to insure against adverse
outcome tomorrow.
Basic insurance theory suggests that
individuals will demand full insurance to
smooth their consumption across states
of the world.
Same consumption possible whether
accident occurs or not
12.1
What Is Insurance and Why Do Individuals Value It?
Formalizing This Intuition: Expected Utility Model
expected utility model The weighted sum
of utilities across states of the world, where
the weights are the probabilities of each
state occurring.
Expected utility is written as:
actuarially fair premium Insurance
premium that is set equal to the insurer’s
expected payout.
Expected Utility Model
 EU
= (1-p) U(C ) + pU(C )
0
1
 Where
•p stands for the probability of an
adverse event
•C and C stand for consumption in
the good and bad states of the
world
0
1
Analyzing an individual’s
demand for insurance



Assume, a 1% chance for and accident with
$30,000 of damages
Sam can insure some, none, or all of these
medical expenses
Policy cost: m cents per $1 of coverage



A policy pays $b for an accident
His premium is $mb
Full insurance: m x $30,000


State 0: $mb poorer
State 1: $b-$mb richer than if he doesn’t buy
insurance
Expected utility model
Sam’s desire to buy depends on price of
insurance
 An actuarially fair premium sets the price
charged equal to the expected payout


$30,000 x .01 = $300 (act. fair prem.)
Expected (Utility)


Decision to buy insurance also affected by
risk preference
Assume a utility function U= √C. (risk averse)





C0= 30,000
Without insurance:
.99√30,000+.01 √0 =171.5
With actuarially fair insurance:
.99√29,700 + .01√29,700 = 172.3
Utility is higher with insurance
Partial insurance is lower utility
Table 1
The expected utility model
If Sam …
Doesn’t buy
insurance
Buys full
insurance
(for $300)
Buys partial
insurance
(for $150)
And Sam is …
Consu
mption
Utility
√C
Not hit by a car (D=99%)
$30,000
173.2
Hit by a car (D=1%)
0
0
Not hit by a car (D=99%)
$29,700
172.3
Hit by a car (D=1%)
$29,700
Not hit by a car (D=99%)
$29,850
Hit by a car (D=1%)
$14,850
172.3
Expected utility
0.99x173.2 + 0.01x0 = 171.5
0.99x172.3 + 0.01x172.3 = 172.3
172.8
121.8
0.99x172.8 + 0.01x121.8 = 172.2
Result implications
Even if insurance is expensive, if
premium is actuarially fair,
individuals will want to insure
against adverse events.
 Implication:


The efficient market outcome is full
insurance and thus full consumption
smoothing
Role of risk aversion

Risk aversion: extent to which an
individual is willing to bear risk
Risk averse individuals have a rapidly
diminishing marginal utility of
consumption
 Individuals with any degree of risk
aversion will buy insurance priced
fairly.
 If not priced fairly, they will not buy

Why have social insurance?

Asymmetric information
Insurance markets have information
asymmetry between individuals and insurers
 Individual knows more about their likelihood
of an accident than insurer


Example:
Health: the individual knows more about
their health history
 Insurer is reluctant to sell an actuarially fair
policy to a person with “high risk”

Asymmetric Information Ex.

2 groups of 100 people—prob. of $30k accident
1st has 5% chance of injury
 2nd has .5% chance

Table 2---results
 People have the option of buying
insurance and will do so for fair deal
 Only high risks take policy loses
money

12 . 2
Why
Have Social Insurance? Asymmetric
Information and Adverse Selection
Example
with Full Information
Example with Asymmetric Information
150 $150
Adverse Selection Problem

Insurance market fails because of
adverse selection:





Individuals know more about their risks than
insurance company
Only those with high chance of adverse
outcome, or if premium is a fair deal, buy
insurance
Adverse selection causes insurance companies
to lose money
?should we mandate buying insurance?
Example (HIV, pre-existing condition,
Will asymmetric information
lead to Market Failure?


Not if:
Most individuals are fairly risk averse (ie
they will buy an actuarially unfair policy)



Policy has a risk premium above the actuarially
fair price
This leads to a pooling equilibrium where people
buy insurance even though it is not fairly priced
to all individuals
Insurance companies can offer separate
products at different prices


Consumers reveal info on their riskiness
Separating equilibrium- for different individuals
Asymmetric information

Separating equilibrium leads to a
market failure
Insurers force low risks to choose
between expensive (unfair) full
insurance or partial low cost insurance
 Low risk group do not get full
insurance—suboptimal


University health policy options
How does government address
adverse selection problem?

It could:
Impose a mandate that everyone buy
private insurance ($825 per policy)
 Offer insurance directly


Both options have low risks subsidizing
high risks
Other reasons for
government intervention

Externalities


Administrative costs


Economies of scale in administration
Redistribution



Negative health externalities
With full information (genetic testing),
insurers can identify high risks
Fairness of this discrimination?
Paternalism


Individuals won’t insure unless govt. forces
Government failure is refraining from helping
Other ways to smooth
consumption

Self-insurance (Unemployment ex.)





Own savings
Labor supply of family
Borrowing from friends
charity
Government Unemployment Insurance
crowds out private provision


No gain from government action
Efficiency costs from raising government rev.
Example: Unemployment Insurance
The UI replacement rate is the ratio of
unemployment insurance benefits to preunemployment earnings.
 Figure 2a shows some examples of the
possible relationship between the UI
replacement rate and the drop in consumption
when a person becomes unemployed.
 A larger fall in consumption means less
consumption smoothing.

Example: Unemployment Insurance

Panel A shows the scenario in which a person has no
self-insurance (e.g., no savings, credit cards, or friends
who can loan money to her).




With no UI, consumption falls by 100%.
Each percent of wages replaced by UI benefits reduces the
fall in consumption by 1%, shown by the slope equal to 1 in
panel A.
In this case, UI plays a full consumption smoothing
role: there is no crowd-out of self-insurance (because
there is no self-insurance).
Each $1 of UI goes directly to reducing the decline in
consumption from unemployment.
Example: Unemployment Insurance

Consider the other extreme, in panel C. A person has
full insurance (perhaps private UI or rich parents).




With no UI, consumption falls by 0%.
Each percent of wages replaced by UI benefits does not
reduce the fall in consumption at all, as shown by the slope
equal to 0 in panel C.
In this case, UI plays no full consumption smoothing
role, and plays only a crowd-out role.
Each $1 of UI simply means that there is one less
dollar of self-insurance.
Example: Unemployment Insurance
In a middle-ground case (Panel B), UI plays a
partial consumption-smoothing role.
 It is both smoothing consumption and
crowding out the use of self-insurance.
 Figure 2b summarizes these lessons. The UI
consumption smoothing and crowding-out
effects depend on the availability of selfinsurance.

Lessons for Consumption-Smoothing Role
of Social Insurance

In summary, the importance of social insurance
programs for consumption smoothing depends
on:
The predictability of the event.
 The cost of the event.
 The availability of other forms of consumption
smoothing.

THE PROBLEM WITH INSURANCE:
MORAL HAZARD

When governments intervene in insurance
markets, the analysis is complicated by moral
hazard, the adverse behavior that is
encouraged by insuring against an adverse
event.
THE PROBLEM WITH INSURANCE:
MORAL HAZARD

Consider the Worker’s Compensation program,
for example.
Clearly, getting injured on the job is the kind of
event we want to insure against.
 It is difficult, however, to determine whether the
injury was really on-the-job or not.
 The insurance payouts include both medical costs
of treating the injury, and cash compensation for
lost wages.
 Under these circumstances, being “injured” on the
“job” starts to look attractive.

THE PROBLEM WITH INSURANCE:
MORAL HAZARD
By trying to insure against a legitimate event,
the program may actually encourage individuals
to fake injury.
 Nonetheless, moral hazard is an inevitable cost
of insurance, either private or social. Because
of optimizing behavior, we increase the
incidence of bad events simply by insuring
against them.

What Determines Moral Hazard?

The factors that determine moral hazard
include how easy it is to detect whether the
adverse event happened and how easy is it to
change one’s behavior to establish the adverse
event.

APPLICATION
Flood Insurance and the Samaritan’s Dilemma
When
a disaster hits, the government will transfer resources to help those
affected. Since individuals know that the government will bail them out if things go
badly, they will not take precautions against things going badly.
To
reduce taxpayer-funded federal expenditures on flood control, the federal
government established the National Flood Insurance Program (NFIP) in 1968.
• Areas with a 1% chance of flooding in any given year are given the option of
buying flood insurance through the program.
• Following Hurricane Katrina, it was revealed that nearly half of the
victims did not have flood insurance. The claims from those who did
have flood insurance bankrupted the program.
• Failures of the NFIP have many sources. Among these is that many
individuals opt out of paying for insurance.
This
is a classic example of the Samaritan’s Dilemma: If the government is going
to continue to help individuals in disasters, and people are not required by law to
buy flood insurance, then why buy it?
A solution
to this problem would be to mandate the purchase of flood insurance at
actuarially fair prices in areas at risk of flooding.
Moral Hazard Is Multidimensional

Moral hazard can arise along many dimensions.
In examining the effects of social insurance,
four types of moral hazard play a particularly
important role:
Reduced precaution against entering the adverse
state.
 Increased odds of entering the adverse state.
 Increased expenditure when in the adverse state.
 Supplier responses to insurance against the adverse
state.

PUTTING IT ALL TOGETHER:
OPTIMAL SOCIAL INSURANCE

There are four basic lessons:
First, individuals value insurance and would ideally
like to smooth consumption.
 Second, insurance markets may fail to emerge,
primarily because of adverse selection.
 Third, private consumption smoothing mechanisms
may be available; to the extent they are, one must
examine new consumption smoothing versus
crowding out of existing self-insurance.
 Fourth, expanding insurance encourages moral
hazard.

PUTTING IT ALL TOGETHER:
OPTIMAL SOCIAL INSURANCE
These lessons have policy implications.
 First, social insurance should be partial.


Full insurance will almost always encourage adverse
behavior.
Second, social insurance should be more generous
for unpredictable, long-term events where there is
less room for private consumption smoothing.
 Third, more moral hazard should lead to less
insurance.

Recap of Social Insurance:
The New Function of Government
What is Insurance and Why Do Individuals
Value it?
 Why Have Social Insurance?
 Social Insurance versus Self Insurance: How
Much Consumption Smoothing
 The Problem with Insurance: Moral Hazard
 Putting it All Together: Optimal Social
Insurance
