2. Social Insurance: The New Function of Government Chapter 12
12.1 What Is Insurance and
Why Do Individuals Value It?
12.2 Why Have Social Insurance? Asymmetric Information and Adverse Selection
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.”
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

3. Important Social Insurance Programs
Social Security
Unemployment insurance
Disability Insurance
Workers Compensation
Medicare

5. 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)

6. 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

7. 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.

8. Why insurance Insurance premium---paid to insurer
In return, insurer promises payment to individual if adverse event happens
Examples: Health, car, property, farm crops,

9. 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

10. 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

11. 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. Expected Utility Model
EU = (1-p) U(C0) + pU(C1)
Where
p stands for the probability of an adverse event
C0 and C1 stand for consumption in the good and bad states of the world

13. 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

14. 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.)

15. Expected (Utility)
Decision to buy insurance also affected by risk preference
Assume a utility function U= √C.
C0= 30,000
Without insurance:
.99√30, √0 =171.5
With actuarially fair insurance:
.99√29, √29,700 = 172.3
Utility is higher with insurance
Partial insurance is lower utility

16. The expected utility model
Table 1
The expected utility model
If Sam …
And Sam is …
Consumption
Utility √C
Expected utility
Doesn’t buy insurance
Not hit by a car (D=99%)
$30,000
173.2
0.99x x0 = 171.5
Hit by a car (D=1%)
Buys full insurance
(for $300)
$29,700
172.3
0.99x x172.3 = 172.3
Buys partial insurance
(for $150)
$29,850
172.8
0.99x x121.8 = 172.2
$14,850
121.8

17. 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

18. 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

19. 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”

20. Asymmetric Information Ex.
2 groups of 100 people
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

21. Example with Full Information
12 . 2
Why Have Social Insurance? Asymmetric Information and Adverse Selection
Example with Full Information
Example with Asymmetric Information

22. 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,

23. 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

24. 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

25. 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

26. Other reasons for government intervention
Externalities
Negative health externalities
Administrative costs
Economies of scale in administration
Redistribution
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

27. 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.

29. Example: Unemployment Insurance
The UI replacement rate is the ratio of unemployment insurance benefits to pre-unemployment 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.

31. 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.

32. 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.

33. 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 self-insurance.

34. 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.

35. 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.

36. 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.

37. 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.

38. 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.

39. Flood Insurance and the Samaritan’s Dilemma
A P P L I C A T I O N
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.

40. 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.

41. 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.

42. 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.

43. 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