Just over 10 years ago, researchers at the University of Michigan added three questions to their Health and Retirement Study, a biennial survey of Americans over 50:
■ If $100 earns 2 percent per year, in five years will you have more than $102, less than $102 or $102?
■ If the interest rate on your savings is 1 percent per year and annual inflation 2 percent, could you buy more, less or the same with your money in a year's time?
■ Is it true or false that buying a single company stock usually provides a safer return than the stock of a mutual fund?
Researchers aimed to gain some sense of the financial literacy of older Americans, a matter of vital importance as the defined-benefit pensions that had been managed for decades by employers for their workers were giving way to defined-contribution plans like I.R.A.s and 401(k)'s, for which workers had to make their own savings and investment decisions.
The results were not encouraging: Only one-third of respondents answered all three questions right.
These were adults who had been making financial decisions most of their lives. They had experienced high inflation, not once, but twice. And yet only about half correctly answered both the question about inflation and the one on compound interest.
Financial illiteracy is not limited to the 50-plus set. And it has not improved much over the last decade. It underscores just how much the political debate over how to prepare for the aging of the population has misunderstood what is at stake.
Consumed in political argument over the demographic pressure on Social Security, we have bypassed a much more consequential threat: For the first time in generations, a large number of older Americans can expect to suffer a sharp drop in living standards in retirement.
In this light, the standard conservative prescription to address the stress on Social Security — taking it off the government's books and handing control to individual workers — would only compound the problem for most retirees.
Preventing a demographic catastrophe may require, instead, taking more of the decisions out of workers' hands. That might require enhancing Social Security rather than limiting it. Or it might require employers to take back more of the responsibility for employee's retirement savings.
Consider the following calculation by James Poterba, a professor of economics at M.I.T.
If inflation-adjusted investment returns averaged 2 percent a year — not an unreasonable assumption given low interest rates and a stock market likely to deliver subpar returns over the next decade or so — a worker would have to save almost 15 percent of each paycheck for 40 years to get an annuity stream equal to half of final earnings at retirement, assuming a 2 percent risk-free rate of return. A late starter who saved for only 20 years would need to set aside a full third of earnings.
Matters would be easier if investments yielded 4 percent: With a 4 percent risk-free rate, affording an annuity equal to half the last paycheck upon retirement would require saving less than 10 percent for 40 years, or just over 25 percent for 20.
How does that compare with what workers actually save? From 1990 to 2010, the typical contribution to 401(k) accounts ranged from 4.7 to 5.2 percent of earnings.
The typical savings rate of the thriftiest cohort — aged 65 to 69 — topped out at 7.5 percent in 2005. Even adding an employer top-up worth half of workers' contributions wouldn't get them anywhere near where they must be.
Low savings rates aren't the only problem. Another is early withdrawals from retirement savings accounts — which often happen when workers change jobs and must roll their old retirement plan into something else. Another are the large feeseating away at savers' returns.
The most urgent question seems to be, How can workers and their employers be convinced, cajoled or compelled to consistently save more?
John N. Friedman, an economist at Brown University, has two suggestions: First, assign every worker a single lifetime retirement savings account, into which each successive employer will deposit retirement savings. Second, instead of just offering tax breaks to encourage workers to save more, why not offer incentives to their employers too?
In a study for the Brookings Institution's Hamilton Project, scheduled to be presented next week, Professor Friedman proposes that the government cap the tax deductibility on workers' retirement savings — which are relatively inefficient at mobilizing additional saving — and use the money saved to provide tax credits for employers that increase their workers' pension contributions.
Employers are more financially sophisticated. Giving them money to ensure that their workers build up an adequate nest egg is not an unreasonable choice. "Tax credits would directly link worker savings to the company bottom line," he writes, "increasing firms' interest in getting their employees to save."
Under not unreasonable assumptions, Mr. Friedman estimates his proposal could increase the share of private sector workers with retirement savings to at least 65 percent, from 41 percent, mostly among the middle class. By retirement day, a typical working household would have $400,000 in savings, compared to $100,000 today.
That might be enough to buy an annuity of $35,000 a year, which, combined with $25,000 from Social Security, could come close to covering the median household income for a couple. The additional cost to the government, in Mr. Friedman's analysis, would be slight. And government subsidies, today tilted sharply toward affluent workers, would shift toward lower-income workers.
"People who are now coming in with nothing would come in with enough to make a difference in retirement readiness," Professor Freidman said.
Could this be enough?
Prodding workers to save more when real wages have not increased in a quarter-century is not a particularly promising avenue. Conscripting companies to raise workers' savings may help, but it could well fall short.
Maybe the government should do the job.
At a conference hosted by the International Monetary Fund, Brad Delong, an economist at the University of California, Berkeley, argued that private markets were ill suited to handle the sort of long-term assessments needed to ensure a decent retirement.
"The 21st century will see longer life expectancy, and thus a greater role for pensions," he wrote. "Yet here in the United States the privatization of pensions via 401(k)'s has been an equally great disaster."
Rather than shrink Social Security, some experts and liberal politicians like Elizabeth Warren of Massachusetts and the Democratic presidential candidate Bernie Sanders propose expanding it.
Today, more than half of working households do not have enough assets to avoid a drop in consumption in retirement, according to analyses by Alicia H. Munnell from Boston College and her colleagues. The proportion of households in that group has increased by 10 percentage points in just the last 10 years.
Addressing this challenge would require somewhat higher taxes, tilted toward those most able to afford them, not lower taxes on the wealthy in a fruitless bid to encourage them to invest more. That may seem an uphill battle in today's political climate. But the alternative could prove calamitous. Ignoring the problem will condemn a generation of elderly Americans to the kind of poverty we believed we had eradicated long ago.