Questions and Problems
1. The government of Westlovakia has just reformed its social security system. This reform changed two aspects of the system: (1) It abolished its actuarial reduction for early retirement, and (2) it reduced the payroll tax by half for workers who continued to work beyond the early retirement age. Would the average retirement age for Weslovakian workers increase or decrease in response to these two changes, or can you tell? Explain your answer.
The first policy change, abolishing the actuarial reduction, would tend to lower the average retirement age. The actuarial reduction is intended to make workers approximately indifferent between retiring early and waiting until standard retirement age. With the reduction, early retirees have a smaller benefit over more years. Abolishing that reduction would make early retirement more attractive: the benefits would be just as high as if workers had waited, and they would be paid over more years. The second policy change would increase the return to working later in life and thus would tend to raise the average retirement age. The overall effect would depend on a number of factors. If people discount the future by enough (that is, have a high enough internal discount rate), they will tend to retire early: the benefit is immediate. People who have a lower discount rate will choose to work longer at the lower tax rate. A second factor that would influence the decision is the potential retiree’s health status or personal (as opposed to statistical) life expectancy. Someone who believes he has a fairly high probability of living long and well late in life will be more likely to opt for later retirement. A third factor that will tend to increase the retirement age is that the early retirement effect is truncated at the age designated for eligibility: even people who choose to retire early will only be able to retire a few years earlier than before in order to benefit. People who choose to retire later may retire many years after the standard retirement age. 2. When you called her last night, your grandmother confided that she is afraid to sell her home because doing so will affect her Social Security benefits. You told her that you’d call her back as soon as you read Chapter 13. Now that you’ve read it, what will you say to her about how her benefits will change when she sells her house?
Social Security benefits do not change with changes in the value of assets held by the beneficiary. The formula used to calculate benefits under Social Security is based on earned income only. Your grandma’s Social Security benefits will not be affected by the sale of her house.
3. Congressman Snicker has proposed a bill that would increase the number of years of earnings counted when computing the Social Security Average Indexed Monthly Earnings amount from 35 to 40. What would be the effects of this policy change on the retirement behavior of workers? Would the Social Security trust fund balance increase or decrease? Why?
Workers may work longer if their best 40 years counted rather than their best 35. Generally, you would expect earned income to increase over a worker’s lifetime; thus, the last several years are likely to yield higher income than the first several years. Being able to count 5 more high-earning years would induce some workers to remain in the workforce to increase their calculated benefits; if they did not work longer, that 40 years might include some very low or zero-earning years (when the worker was in his or her twenties, possibly still in school).
Increasing the number of years of earnings counted would certainly increase the trust fund balance if it caused people to delay their retirement: people would be paying in longer and withdrawing for fewer years. Offsetting that increase would be the increased benefits payable by including 5 higher-earning years in calculating benefits. This offset may not be huge, though. The highest-earning workers would not increase their benefits by very much due to the redistributive nature of the calculations. Low-wage earners who have zero or very-low-wage years among the 40 would have a lower average on which to base the benefit calculation. In addition, by including 5 more years, people who did not delay retirement would have an even lower calculated benefit: their lifetime average would include those low-wage summer or entry-level jobs.
4. Suppose the Social Security payroll tax was increased today to 16.4% in order to solve the 75-year fiscal imbalance in the program. Explain the effect of this change on the value of the Social Security program for persons of different ages, earning levels, and sexes.
An increase in the payroll tax would reduce the value of Social Security for younger workers relative to older workers. Older workers would benefit from having a more secure plan, and they wouldn’t have to pay in at the higher rate for very long. Younger workers would have to pay the higher rate over many more years, and their benefit calculation would not increase (because the increase in taxes is meant to keep the current system solvent, not to increase benefits). The very-highest-earning workers would not be harmed as much as lower-earning workers because the payroll tax is not imposed on earnings above $87,900 (currently); however, their payroll tax burden would increase. Women generally benefit more from Social Security because they live longer than men. They are also more likely than men to have interrupted their careers to raise their families, so they tend to pay in less. They are also more likely to receive benefits as a surviving spouse. All of these factors would continue to exist with a higher tax rate. The higher tax rate would be borne by the employed, not by those who receive benefits because of their survivor spouse status. 5. Senator Deal proposes to offer a choice to future retirees: Retire before age 70 and the benefits are calculated on the last 35 years of income; if you retire at age 73, however, you receive benefits calculated on only the last 15 years of income. Which option are high-income workers likely to choose? Low-income workers? Why?
A high-income worker may not benefit by much if he delays retirement until age 73, and he would lose three years of benefits. He is likely to choose the earlier retirement age. Assuming no major work interruptions, which is perhaps a more reasonable assumption for a high-wage earner than a low-wage earner, his benefits will be calculated based on his wage since he was in his mid-thirties. These are likely to be fairly-high-earning years, as they begin a decade after a person would have completed his education. Because of the regressive nature of benefit calculations, the higher wages of the last 15 years would yield a low marginal benefit. High-wage earners are also better able to save for retirement in other ways, so they may be able to afford retiring three years earlier. Low-wage earners will be more likely to delay retirement until age 73. They would lose three years of benefits, but their benefits, once they do retire, will be higher if their income is higher in the last 15 years of work. This option will be particularly attractive if these workers had some low- or zero-earning years over the course of their working lives. In addition, calculated benefits are a higher percent of average monthly wage for these workers, so they stand to lose less by working more years.
6. A recent study found that people nearing retirement age were more likely to retire early if they experience large windfall gains (that is, sudden large increases) in the value of their homes. The author of that study concluded that this is evidence that Social Security and private savings are substitutes. What are the strengths and weaknesses of this argument and of the empirical evidence?
It seems intuitive that all sources of private wealth combined substitute for, or augment, Social Security, particularly among higher-earning workers, because their Social Security benefits will not replace as high a percentage of their pre-retirement wage. If Social Security benefits are expected to be a relatively small component of post-retirement income, as may be the case for higher-earning workers, then the official Social Security retirement age might be less influential in retirement timing. A sudden increase in the market value of an asset (like housing) might be more influential in the timing decision. One concern this scenario poses, though, is the direction of causality. The implication is that the windfall gain caused early retirement by giving the retiree more money on which to retire. However, retirement may have led to realization of the windfall gain. Increases in the value of a person’s home are realized upon the sale of that home. Perhaps people sold their homes and realized the gain because they were retiring and relocating. Even under this interpretation, though, the windfall gain would contribute to the retiree’s income, augmenting Social Security benefits.
A second concern is that increases in home value are a relatively illiquid form of private savings. Extending this particular correlation (housing value and retirement) to a general statement about private savings requires a bit of a leap of faith. Data on other savings and investment value might help clarify this interpretation. Perhaps these retirees had anticipated inflation in the housing market and included it in their retirement plan portfolio—a portfolio that included assets and Social Security benefits.
Finally, other correlates must be considered. A windfall gain in the housing market may be correlated with geographic location, as housing booms can be local in nature. A gain may also correlate to membership in a demographic group that tends to buy the kind of real estate that is most likely to appreciate and that tends to retire early. Suburban businessmen, for example, may tend to fall into both groups.
7. Senator Dare suggests lowering Social Security benefits by reducing the rates at which Average Indexed Monthly Earnings are converted to the Primary Insurance Amount. Senator Snow instead proposes reducing the rate at which benefits are indexed to inflation so that when the Consumer Price Index rises by one percentage point, Social Security benefits rise by less than one percent. Which proposal will benefit the elderly more?
Senator Dare’s suggestion immediately and certainly reduces the benefits paid to retirees. Senator Snow’s proposal would reduce the benefits gradually, and in unpredictable ways. In times of extremely low inflation, Senator Snow’s proposal would very gradually erode the spending power of retirees’ benefits checks. However, suppose the plan were to increase benefits by, for example, 90% of the Consumer Price Index (CPI) each year. The following year,f the Cinflation-adjuste
10. Dominitz, Manski, and Heinz (2003) present survey evidence suggesting that young Americans are extremely uncertain about the likelihood that they will receive any Social Security benefits at all. How might demographic
trends in the United States contribute to this concern?
The most obvious trend in this regard is the aging of the baby boom generation. Young Americans are aware that, in a few years, the baby boom generation will become an extremely large body of retired people. Exacerbating that retiree population bulge is the fact that people live longer now than they have in the past. Those baby boomers will be around for a long time, collecting their Social Security checks. In addition, family sizes are smaller. Baby boomers may have grown up with several siblings, but they had fewer children as adults. Therefore, there will be fewer workers contributing for each baby boomer collecting.
11. The Social Security Administration Web site has a link to a publication entitled Social Security Programs Throughout the World. The European version is online at http://www.ssa.gov/policy/docs/progdesc/ssptw/2002-2003/europe/index.html. Pick any two countries in Europe and compare the key attributes of their social security programs. Which of these two countries do you think will have the greater rate of early retirement? Why?
Responses to this question will obviously depend on the countries chosen. There are fairly wide variations in the ages at which retirees become eligible for benefits in different countries. Retirement age is lowest in Slovenia, at 58 for men and 54 for women. Other Eastern European countries, such as the Ukraine, Belarus, Russia, and Serbia, also have low ages of eligibility. These countries should see relatively low rates of retirement prior to the local age of eligibility, because eligibility occurs at relatively young ages. In contrast, the Scandinavian countries of Denmark, Iceland, and Norway have the highest age of eligibility, 67. Holding health status equal across countries, countries in which eligibility occurs at older ages should experience higher rates of retirement prior to eligibility. It is difficult to generalize given the different currencies and complex structures of individual countries’ rules. However, most countries generally provide an amount equal to a percent of average working wage. Some calculate it based on a fairly short window of working years; in Serbia, for example, the base is calculated using the best ten consecutive years.
12. Suppose the Social Security system becomes fully privatized, so that all individuals save for their own retirements. Consider two of the various alternative methods of paying off the legacy debt of the program. (One such example is double taxation of existing generations of workers.) Compare and contrast the benefits and drawbacks of each potential “solution.”
An inescapable problem with the Social Security system is that it pays current retirees from current workers’ taxes. If current workers were to “own” their own Social Security accounts, there would be no flow of funds available to pay current retirees, as their deposits have already been paid to the preceding generation. By double taxing a single generation, the system could switch over, but members of that one generation would have to pay their parents’ benefits as well as fund their own retirement accounts. That is a serious burden to impose on them. However, it would only have to be done once. Subsequent generations would simply fund their own retirement accounts.
Another possible solution would be to increase payroll taxes over a longer time period to retire the legacy debt over several generations, while allowing current and future generations to invest privately. The high taxes necessary to accomplish this solution, however, would offset much if not all of the gains from investing in higher-yielding stock funds. An alternative to increasing taxes is reducing benefits. Several options exist to accomplish this reduction. One way would be to increase the full benefits age of retirement and adjust early retirement benefits to be actuarially neutral. An advantage of doing this is that it adjusts Social Security rules to reflect longer and healthier lives among people in their sixties and seventies. Not everyone in those age groups can continue to work, however, and this change would impose a hardship on them.
In addition, there is something essentially unfair about changing the rules of the program after people have been paying into it for their entire working lives. A similar objection would be raised if the system were changed to reduce the benefits paid to the wealthy elderly. This approach seems reasonable; after all, those retirees who are wealthy do not need Social Security to stay out of poverty. But they paid into the program and perceive it to be more of a pension than an anti-poverty program. Making the program more ambitiously means-tested (as opposed to just redistributive) changes the nature and perceived legitimacy of Social Security. 13. Does Social Security provide much benefit in terms of consumption smoothing over the retirement decision? Contrast Social Security with a different social insurance program, unemployment insurance, which provides income support for half a year to individuals who have lost their jobs. Do you think that unemployment insurance is likely to provide more or less consumption smoothing than Social Security?
Unemployment insurance smooths consumption over discrete, fairly brief, unanticipated interruptions in work; Social Security allows retirees to remain out of poverty after stopping work. Retirement is not a surprise. In the absence of Social Security (and even in its presence), people with foresight plan and save for retirement. Social Security payments alone are not enough to allow retirees to maintain their pre-retirement consumption level, but they do substantially reduce the number of retirees in poverty. The purpose of Social Security was not to allow retirees to maintain pre-retirement income (that is, to smooth consumption) but to help them avoid poverty. Unemployment insurance is much more explicitly aimed at consumption smoothing between employment spells. It allows people to maintain their standard of living over intermittent dips in income. Thus, Social Security provides less consumption smoothing than does unemployment insurance. 14. Edwards and Edwards (2002) describe evidence that following a social security reform in Chile that reduced the implicit tax on working in the formal sector, informal sector wages rose. What do you think is the mechanism at work here?
In equilibrium, prices and wages tend to equalize. In the case of Chile, if formal sector wages are particularly low, people will choose to work in the informal sector. One reason formal sector wages are low is that those wages are taxed. When tax rates are high, more people seek work in the untaxed, informal sector. However, when tax rates fall, as they did in Chile, the effective wages in the formal sector increase and people exit the untaxed sector to accept jobs in the formal sector. Wages in the informal sector must then increase to retain those employees who are tempted by higher after-tax wages elsewhere.
15. Suppose that you had information about the amount of private savings during the years before and after the introduction of the Social Security program. How might you carry out a difference-in-difference analysis of the introduction of the Social Security program on private savings?
This data would be helpful in determining the extent to which Social Security crowds out private savings, but there may be reasons for savings rates to change that are unrelated to the introduction of Social Security. You could use difference-in-difference analysis to distinguish between differences in private savings that are related to general trends in saving behavior and those that are associated with the introduction of Social Security. Depending on how many years of data you have, you could determine the difference in savings rates between pairs of years preceding the change. You could also determine the difference in saving rates between pairs of years after the introduction of Social Security. Then you would want to investigate differences in savings rates in the years immediately before and after the institution of Social Security. This test is meant to determine whether that difference is statistically significantly different from the patterns of differences measured for pairs of years in which there was no change. Specifically, if savings rates fell between the year immediately preceding Social Security and the year of the change by more than it fell for other pairs of years, you would have evidence consistent with crowding out.
16. Suppose you find evidence that high school dropout workers are more likely to retire at age 62 than are college-educated workers. You conclude that these workers do so because they are more liquidity-constrained than are other workers. Can you think of alternative explanations for this finding?
One possible explanation is that less-well-educated workers are more likely to have jobs that are relatively more physically demanding and particularly difficult to continue after age 62. Similarly, the physical wear and tear of demanding jobs may leave these workers unable to comfortably work later in life. Another possible explanation is that these workers have already had their 35 best years: they began working at a younger age than college-educated workers and their upward mobility is constrained, so they will be unlikely to have high salaries later in life. Finally, higher education is correlated with better health; less-welleducated workers may retire fairly early if they anticipate having a reduced life expectancy. 17. Consider an economy that is composed of identical individuals who live for two periods. These individuals have preferences over consumption in periods 1 and 2 given by: U = log(C1) + log(C2). They receive an income of 100 in period 1 and an income of 50 in period 2. They can save as much of their income as they like in bank accounts, earning an interest rate of 10% per period. They do not care about their children, so they spend all their money before the end of period 2.
Each individual’s lifetime budget constraint is given by C1 + C2/(1 + r) = Y1 + Y2/(1 + r). Individuals choose consumption in each period by maximizing lifetime utility subject to this lifetime budget constraint.
a. What is the individual’s optimal consumption in each period? How much saving does he or she do in the first period?
Optimizing the utility function subject to the budget constraint yields max U = ln(C1) + ln(C2) subject to C1 + C2/(1 + r) = 100 – C1 + 50/(1 + 0.1), or max U = ln(C1) + ln(C2) + λ(145.45 – C1 – 0.91C2).
This yields first-order conditions of
1/C1 = λ; 1/C2 = 0.91λ; and 145.45 = C1 + 0.91C2.
Solving for C1 yields 0.91C2, and substituting into the budget constraint yields C2 = 79.92, C1 = 72.73, and savings in the first period are 100 – 72.73 = 27.27.
b. Now the government decides to set up a social security system. This system will take $10 from each individual in the first period, put it in the bank, and transfer it to him or her with interest in the second period. Write out the new lifetime budget constraint. How does the system affect the amount of private savings? How does the system affect national savings (total savings in society)? What is the name for this type of social security system?
The new budget constraint reduces first-period income by $10 to $90 but increases second-period income to $50 + $10(1 + r):
C1 + C2/(1 + r) = 90 + 50/(1 + r) + 10(1 + r).
Solving, C1 + C2/(1 + r) = 90 + 45.45 + 11 = 146.45.
Following the same procedure as in a, you would find savings by solving the constrained optimization problem: max U = ln(C1) + ln(C2) + λ(146.45 – C1 – 0.91C2),
C2 = 80.47, C1 = 73.22, and total savings are 10 + (90 – 73.22) = 26.78. This social security system is a funded plan because the money that is paid in during the first period is used to pay the benefits in the second period. c. Now suppose that the existence of the new social security system causes an individual to retire in period 2, so he or she receives no labor income in period 2. Solve for this individual’s new optimal consumption in each period in this case. What is the new level of private and national savings? Does this differ from the level of savings in part b, and if so, why? (Explain intuitively.)
The new budget constraint is C1 + C2/(1 + r) = 100.
The new optimization problem, then, is max U = ln(C1) + ln(C2) + λ(100 – C1 – 0.91C2).
Solving, C2 = 54.95, C1 = 50 and, savings are 100 – 50 = 50. Total savings is greater with earlier retirement, as this consumer must save enough during the first period to completely finance consumption in the second period. 18. For each of the reforms listed below, briefly discuss the pros and cons of the reform, paying attention in particular to efficiency implications (through potential behavioral responses to the change) and equity implications (who wins and who loses). [Note that all reforms are intended to save the system money, so you do not need to list this as a benefit.]
a. Increase the number of years used to calculate benefits from 35 to 40.
Increasing the number of years used to calculate benefits could lower benefits, because more low- or zero-earning years would be included in a retiree’s average wage. To avoid this reduction in benefits, workers might choose to delay retirement so that they had 40 high-earning years included in the calculation. Workers who spent many years in college and graduate school might be most vulnerable, as they will have had fewer fulltime working years by the time they reach retirement age. Similarly, workers who have had some interruptions in their employment, to raise a family or to retrain for a new career, for example, will also have to delay retirement in order to avoid inclusion of zeroor low-wage years. b. Reduce benefits for beneficiaries with high asset levels (wealth).
Means-testing, by considering asset levels, would increase the redistributive nature of Social Security but would induce some perverse behavior. People might be able to increase their benefits by hiding assets, by setting up trusts or other entities, for example. They might also change the timing of selling some of their assets in order to retain Social Security benefits, which distorts resource mobility, an efficiency concern. While this plan may appear to benefit the less wealthy at the expense of the wealthy elderly, it seems vulnerable to loopholes and evasive behavior. c. Add new state and local government workers to the pool of covered workers (i.e., they pay payroll taxes now and receive benefits when they are old).
Broadening the tax base to include these workers would yield a net increase to the system. Current Social Security participants will, over their lifetimes, pay in more than they withdraw. Therefore, increasing the number of workers covered provides a net increase to the cash flow in the system. The new workers stand to lose from this system relative to a plan in which they had their own retirement accounts (because with Social Security they will pay in more than they receive), but the Social Security system benefits. This new rule may induce some to exit these jobs, but since most workers are covered by the system, they will have little choice as to where else to work to avoid this tax. d. Gradually increase the normal retirement age (NRA) from 65 to 70 (under current laws, the NRA will gradually rise to 67 by 2022; the proposal is to speed up this process so the NRA will be 70 by 2022).
Gradually increasing the normal retirement age will save the fund money by reducing the number of years during which retirees can collect. People who need to retire earlier for health or physical limitation reasons will be adversely affected. If they are able to, they may attempt to find less physically demanding work or they may increase private savings in order to be able to afford to retire earlier.
icon indicates a question that requires students to apply the empirical economics principles discussed in Chapter 3 and the Empirical Evidence boxes.