Social Insurance: Social Security Chapter 12 Social Insurance: Social Security

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

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

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.

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)

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.

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.

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)

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

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

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

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

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

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)

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

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…

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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