1. Social Insurance: Social Security
Chapter 12
Social Insurance: Social Security

2. What have we done so far…
We did an overview of the history of social welfare programs in the United States, especially focusing on the Social Security Act of 1935
We then we over a lot of the practical issues in designing these systems
As well as a few of the different tax options

3. What is the purpose of this Chapter?
To focus exclusive on Social Security
What it is, how big it is, how it works, the major worrying problems coming up with it
About actuarially fair and full insurance
Risk premiums, social insurance, moral hazard, adverse selection

4. Introduction
Provision of social insurance is now the most expensive function of federal government in the United States
Revenue to finance Social Security is collected through payroll tax on employers and employees
75-year projections suggest that, at current tax rates, future revenue will not be high enough to finance current benefit levels for future generations
This is an important political issue in the US but as of yet, nothing has really been done to mend this issue.

5. Introduction Continued
Social Security is not means-tested like public assistance (i.e. a majority of payments go to the non-poor)
It is designed to protect people of all income levels from suffering a large decrease in their standard of living due to events that affect earning power
Potential events covered are retirement (Social Security), illness (Medicare) and unemployment (Unemployment Insurance)

6. The Demand for Insurance
Demand for insurance is based on desire to guarantee against bad outcomes which might greatly reduce income and consumption
People are willing to give up some of their income and consumption during the good times to pay a premium that insures against loss of consumption and income during bad times.
This smoothes consumption over time.

7. The Demand for Insurance
Assume individual has diminishing MU(Y)
Means that at current level of income, lost utility from big loss in income is greater than lost utility from small losses in income
Implies that people are risk averse and will pay to insure against bad outcomes.

8. Demand for Insurance Assume identical individuals with either:
Good state (Y1 = $60,000)
Bad state (Y2 = $20,000)
p is the probability of a bad state
(1-p) is the probability of a good state
Expected utility is weighted averages of utilities in the different states
E(U) = (1-p)*U($60,000) + p*U($20,000)

9. Demand for Insurance Suppose p = 0.1
Expected income is E(Y) = 0.9*($60,000) + 0.1*($20,000) = $56,000
Expected utility is E(U)$56,000

10. Actuarially Fair and Full Insurance
Loss associated with bad state is $40,000
Expected loss is p*(Loss) = 0.1*40,000 = $4,000
Suppose insurance firm insures large number of people and probability of bad state occurring to one person is independent of probability of it occurring to another person
If firms can charge each person $4,000 it will break even
Economists refer to this break-even premium as being actuarially fair

11. Actuarially Fair and Full Insurance
An actuarially fair premium is one that is equal to the expected value of a loss ($4,000 in this example)
An insurance policy that pays the full loss suffered when a bad outcome is referred to as full insurance
$40,000 in this example

12. Actuarially Fair and Full Insurance
Risk averse individuals are better off with an actuarially fair, full insurance policy because they remove the uncertainty associated with the bad state
With insurance, person never suffers loss: income is $56,000 either way
U($56,000) > E(U)$56000 so individual is better off with insurance than without

13. Actuarially Fair and Full Insurance: Few Notes
This result does not depend on individuals being risk-averse
If person is risk-averse, full insurance always dominates partial insurance (i.e. payment of less than full amount of loss, say $10,000, instead of $40,000)
Then outcomes are either $59,000 or $29,000 instead of $56,000

14. The Risk Premium
If people are risk-averse, they would be willing to accept an insurance policy that is not actuarially fair
Individuals are indifferent between being uninsured and purchasing full-insurance policy that guarantees income Yc
The amount $60,000 – Yc is referred to as the risk premium (i.e. the amount they would be willing to pay to turn a risky situation into a certain situation)

15. The Risk Premium and Social Insurance
Even though risk-averse individuals are willing to pay a risk premium that allows insurance companies to cover their costs and turn a profit, there are several difficulties that prevent them from functioning efficiently, including:
Adverse selection
Moral hazard
In such situations, the government steps in and provides social insurance

16. Adverse Selection
Different people have different risks for the occurrence of the bad state
If the insurance firm does not know each individual’s true risk then the private insurance market fails
Add a second individual to our above example who has same preferences but p = 0.8 of the bad state occurring…

17. Adverse Selection For the high-risk individual: The expected value is
E(Y) = 0.2($60,000) + 0.8($20,000) = $28,000
The expected loss is
0.8*($40,000) = $32,000
Actuarially-fair full insurance premium for high risk people is $32,000

18. Adverse Selection
If insurance company knows who is low-risk and who is high-risk, they offer actuarially-fair full insurance with premiums of $4,000 to low-risk and $32,000 to high-risk people
BUT suppose they do not know each individual’s risk…
They are forced to change same full insurance premium to every individual, which equals
0.5*($4,000) + 0.5*($32,000) = $18,000

19. Who is willing to buy insurance in this case?
High-risk certainly will as $18,000 is less than their actuarially fair premium of $32,000
Low-risk will not if $18,000 > $60,000 – Yc (risk premium)
If low-risk individuals refuse to insure (select out of market), then only high-risk individuals are left
Private insurance companies now lose money because the expected loss for each high-risk individual ($32,000) exceeds the premium they pay ($18,000)
In such cases, the private insurance market does not function efficiently and the only way to satisfy every person’s demand for insurance is for the government to provide

20. Moral Hazard
Individuals can influence probability that bad state occurs
If fully-insured against bad state, individuals may not have as much incentive to try to prevent it
Bad states might actually become more likely
Presence of insurance might give increased incentive to increase total expenditures
Example: Health Insurance
Reduces to almost 0 the MC of doctor visits
People have incentive to visit doctor too often which increases health care costs

21. Implications for Social Insurance
1. Optimal level of social insurance is not full insurance
2. Social insurance might not always dominate private insurance
The primary benefit of social insurance is that it allows individuals to smooth consumption over time

22. The Optimality of Partial Insurance
Full insurance maximizes consumption-smoothing benefits but also maximizes moral hazard costs
Given the trade-off between these benefits and costs, the optimal level of insurance is most likely less than full insurance
Partial insurance usually takes the form of deductibles or co-payments

23. No Social Insurance
To dominate private insurance, social insurance must satisfy the total benefit-cost test
It may not if social insurance crowds out private insurance or if moral hazard costs are very high
In such cases, people might refuse social insurance

24. Social Security Pensions: Structure
Social Security Act of 1935 established a Social Security Trust Fund overseen by a board of trustees
This program has the following features:
1. Principle source of income to the Trust Fund is the tax on payrolls of covered employees
2. Pension benefits are in the form of an annuity, which is payable each month from retirement to death
3. Spouses and dependents of the beneficiary are entitled to an annuity

25. Social Security Pensions: Modifications
The age at which a beneficiary could claim full retirement was originally set at 65, but it increase to 67 in 2012
They system set up in 1935 was arranged so that all the money paid in by current workers was paid out to support current retirees
In 1983, President Reagan convinced Congress to build up a Trust Fund in anticipation of the coming baby boomer retirement years
Trust Fund has been accumulating surplus since 1983, funded by increase in payroll tax and retirement age

26. At this point the book goes into OLG Models
OLG Models are Overlapping Generation Models
These models are a bit too complicated for this class, so we are going to skip this section
If you are interested in Overlapping Generation Models, feel free to come ask me about them

27. Social Security as a Redistribution Program
Social Security is intended to be more than a straight pension program:
1. It is intended to redistribute wealth across generations by redistributing more to lower-income people than higher- income people
2. The pay-as-you-go feature redistributes a large amount of wealth across generations
Such large redistributions across generations might appeal to societies that place greater value on equity

28. Social Security as Social Insurance
The date of retirement and the length of retirement cannot be known by workers
This introduces adverse selection into the private pension market which makes it function inefficiently
Offering payments as an annuity helps reduce this problem as there is a chance that people may die early, which works in insurers favor
Annuities are underutilized in the U.S. because of the adverse selection problem
For this reason, the government steps in and provides public annuities

29. Problems with Public and Private Annuities
Problems with Public Annuities
They necessarily redistribute wealth from those with low life expectancies to those with high life expectancies
Problem with Private Annuities
People might simply not understand the advantages offered by annuities and might fail to plan adequately for retirement
Private annuities do not adjust for inflation because most are not indexed
Public insurance programs are likely to be much cheaper to administer than private insurance programs

30. Social Security Reform
There have been many proposals to reform the current system to address several potential problems
The most well-known is the retirement of the baby boom generation
Ratio of workers to retirees was 16:1 in 1950, but only 2:1 by 2040
Longer-term problems are that:
People now live longer than they did when they system originated in 1935
Due to increasing income inequality more individuals have incomes above the payroll tax limit

31. Social Security Reform
Because all of these problem lead to a shortfall in the program, proposals to fix the system require altering either the revenues or the benefits streams
The magnitude of changes is not that large
It is estimated that solvency would require increased savings of 2.6% of GDP, which is about equal to the buildup in defense spending during the 1990s