Across the political spectrum, people warn of a coming time bomb in our retirement system. Many analysts believe the growing population of retirees will overwhelm the Social Security program, and that something must be done to shore up its finances.

However, there’s another slow-moving time bomb out there, and that’s the gradual retirement of workers in an era where 401(k)-style defined-contribution plans have become dominant, replacing defined-benefit pensions. A new study of the state of U.S. retirement shows that this change leaves Americans woefully unprepared for their non-working years, with resources too meager to uphold their standard of living.

Economist Monique Morrissey of the Economic Policy Institute makes this case with 32 charts that present a sobering picture for our nation’s retirees. She first analyzed data from the Federal Reserve Survey of Consumer Finances for all families with heads of household between the ages of 32 and 61, covering the thirty years before Social Security’s early retirement kicks in at age 62. And she found major disparities caused by the shift from pensions to 401(k) plans.

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Retirement savings have mostly stagnated since the turn of the century for large cohorts of Americans. On average, families had $95,776 saved in 401(k) or IRA plans in 2013 (the last year studied), compared to $91,243 in 2001. This is not nearly enough to make up for the disappearance of defined-benefit pensions. More important, the averages, which include people who have saved millions, don’t show the whole picture.

Nearly half of all working-age families have no money in retirement accounts at all. The median family has $5,000 saved. Even for people between the ages of 56 and 61, the median retirement account savings is a paltry $17,000. While the top 10 percent have at least $274,000 saved, the bottom 50 percent have next to nothing. “We are moving toward a retirement system that magnifies inequality instead of just reflecting it,” Morrissey said on a conference call Thursday.

This was not always the case. Pensions used to be far more egalitarian, held by people of modest incomes as much as the wealthy. Pensions were even held relatively equally by white and black populations. (Hispanics, Morrissey points out, always lagged behind.)

The 401(k) revolution changed this. Low-income Americans are more likely to have jobs that don’t offer 401(k) plans. And as financial risks are shifted to individual employees, the poor are increasingly unable to afford to put portions of their paychecks into their own retirement funds. Relatively complex 401(k) plans are also more difficult to understand when compared to having a pension benefit manager handle the details.

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As a result, higher-income families are ten times as likely to hold a retirement account as lower-income families. Most African-Americans and Hispanics have no retirement savings, and the ones that do have smaller balances. Families without college education mostly don’t have retirement accounts, and 82 percent of those lacking a high school diploma don’t. Single Americans are also less likely to have retirement accounts.

Looking at retirees through U.S. Census data, Morrissey found that pension plans remain a far more important source of income than retirement accounts, twenty-five years after 401(k) plans became more popular. Interestingly, African-American and female retirees especially benefit from pensions, likely because they hold a disproportionate share of public-sector jobs, among the few that still offer defined benefits.

This switch to 401(k) plans began at the same time that Social Security benefit cuts kicked in with 1983 legislation raising the retirement age. Also in this period, wages started to lag behind productivity, with the labor share of income falling.

“The timing couldn’t have been worse for switching to a 401(k) system,” Morrissey said. But they are so lucrative to Wall Street fund managers, with much higher fees than pensions, that reverting back to pensions wholesale is an unlikely scenario.

In effect, we have kicked two of the legs out of the three-legged retirement stool. Individual savings have stagnated along with wages, as more and more of workers’ paychecks cover little more than everyday needs. The pension has been substituted with a stock plan that was never intended to serve as an adequate replacement. The new 401(k)’s “were initially viewed as a supplement to traditional pensions,” Morrissey said. “It’s not surprising that they haven’t worked out, because they weren’t intended to serve that purpose.”

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