A Solow system

Social Security is a hybrid between a pay-as-you-go and an advance-funded pension system, with most benefits paid out of current taxes but some potentially paid out of trust fund savings. Under ordinary circumstances, the trust fund serves more like a checking than a saving account, though substantial savings may be amassed in advance of bigger-than-usual outlays like the Baby Boomer retirement. This (mostly) pay-as-you-go design allowed Social Security to start paying out benefits shortly after its inception and helps insulate the system from financial market fluctuations.

Nobel Prize-winning economist Robert Solow highlighted the system’s pay-as-you-go properties in a characteristically simple and elegant model presented at a National Academy of Social Insurance gathering last week. Headlining a panel on the Baby Boomers, Solow framed a discussion in terms of basic economic constraints (math-phobes can skip the equations):

1. Labor Productivity x Hours Worked Per Worker x Active Workers = Gross National Product

2. Gross National Product = Labor Income + Capital Income

3. Labor Income = Active Worker Share + Retiree Share


Labor Income = Wage x Hours Worked Per Worker x Active Workers

Active Worker Share = Labor Income – Social Security Taxes

Retiree Share = Social Security Benefit x Retirees

With some rearranging, it follows from Equation 3 that:

4. (Social Security Benefit/Wage) = (Active Workers/Retirees) x (Social Security Taxes/Labor Income)

Solow emphasized that most of the factors in his simple model were determined outside the Social Security system, with the obvious exceptions of the first and last terms in Equation 4.1 This suggests that a decline in the worker-beneficiary ratio requires a reduction in benefits, an increase in the effective tax rate, or both.

Economic models are simplifications, and treating Social Security as a pay-as-you-go system is in one sense a welcome respite from the usual fear-mongering around the exhaustion of the trust fund. But the trust fund actually does matter in a discussion that is specifically about the Baby Boomers, because the fund can be built up and drawn down to deal with such one-time demographic booms and busts. Though the model can be expanded to show this—Solow pointed out that capital income in Equation 2 includes income flowing to retirees from pension funds—the point was lost in the general discussion. The model also ignores the rest of the world, though lending to or borrowing from other countries can also serve to smooth the effects of demographic fluctuations.

In a pure pay-as-you-go system, even a temporary drop in the worker-beneficiary ratio due to delayed child-bearing in wartime, for example, must result in a benefit cut or a payroll tax increase. In other words, someone has to pay because the Baby Boomers are retiring. This isn’t necessarily the case if national saving increased, or borrowing decreased, during the Boomer working years. This is what happened with the build-up of the trust fund, unless you believe there was a dollar-for-dollar reduction in other forms of saving in response.

This isn’t to suggest that demographic challenges aren’t real or that the system doesn’t need tweaking. But as Social Security Chief Actuary Stephen Goss pointed out, the main demographic challenge isn’t the retirement of the Baby Boomers or an increase in life expectancy (another topic that receives too much attention), but rather a permanent decline in the birth rate from three children per woman to two.

With population growth dependent on immigration, the number of workers supporting each beneficiary is projected to drop from roughly three to two. Given the attention paid to this statistic by some of the panelists, audience members could be forgiven for assuming that Social Security would eventually consume 33 cents on the wage dollar, as two active workers would be supporting three people. But because Social Security benefits are modest and wages tend to rise over time, the Social Security actuaries project that an increase in the Social Security tax rate from 12.4 to 15.1 percent (split between employers and employees) would put the system in long-term balance. Or, to put it another way, Social Security costs will rise from around 5 percent to 6 percent of GDP over the next 75 years, leveling off after the peak Boomer retirement years.2

It’s also important to keep in mind that Solow’s model doesn’t necessarily imply intergenerational warfare, since most workers eventually become beneficiaries. Another way to frame the issue is to ask whether workers would be better off paying higher taxes today or receiving smaller benefits tomorrow. The answer depends on the Social Security replacement rate and the other two legs of the proverbial three-legged retirement stool—employer pensions and savings. Social Security replaces only 41 percent of the average worker’s wage if he or she retires at 65, a replacement rate that is scheduled to decline as the full retirement age increases from 66 to 67 (it used to be 65). Meanwhile, fewer and fewer Americans are covered by secure and adequate employer pensions. Therefore, it should come as no surprise that most Americans would prefer to close the projected Social Security shortfall on the revenue side.

Lastly, Solow’s model focuses on two groups—active workers and retirees—ignoring intra-generational distribution of income. This is no reflection of Solow’s politics, since he is a stalwart ally of low-wage workers. However, as panelist Jacob Hacker* pointed out, growing inequality has been a major factor in the emergence of a projected shortfall since 1983. First, slow wage growth has caused a decline in the labor share of national income (Equation 2). Second, Social Security taxes have fallen as a share of payroll because earnings above a taxable maximum are exempt from Social Security tax (Equation 4).3 As Goss noted in response to a question, most of the projected shortfall could be eliminated simply by lifting or eliminating the cap on taxable earnings. In an atmosphere of fiscal austerity, we should also keep in mind that while productivity growth, hours worked, employment, and the labor share of national income may be largely determined outside the Social Security system,4 they aren’t outside the policy sphere.


1. Solow also suggested that the worker-beneficiary ratio wasn’t simply a function of demographics but could be influenced by the age of eligibility for full retirement benefits. The Brookings Institution’s Henry Aaron pushed back on this point, noting that an increase in the full retirement age was simply a benefit cut that appeared to have little influence on when people actually retire.

2. This was apparently not alarming enough for panelist Michael Graetz, who insisted that the worker-beneficiary ratio, rather than the cost as a share of GDP, was the relevant measure. However, Graetz later cited costs as a share of GDP to illustrate how Social Security and Medicare would together eat up two-thirds of the federal budget, because Medicare costs are projected to more than double to 6 percent of GDP and federal revenues have historically averaged 18 percent. While there’s no denying that reining in health care inflation should be a top priority, 18 percent is an artificial limit on the size of government, as Graetz, a tax law professor, is surely aware.

3. Another factor has been the growing share of compensation going to untaxed health benefits.

4. In response to a question from the audience, Solow said Social Security cut could have macroeconomic implications because it would redistribute income from retirees, who tend to spend the money quickly, to active workers who are more likely to save. Cuts in a pay-as-you-go system would also presumably cause an increase in retirement saving, though not enough to fully offset the effect of the cuts on retirement incomes. This would also have negative implications in a demand-constrained economy.

*Hacker is on EPI’s Board of Directors