The shift from pensions to 401(k) plans is making retirement inequality much worse — and education is what separates the haves from the have-nots, a new study has found.

College graduates have always been able to get better jobs. What's new in recent decades is that traditional pensions have all but vanished, replaced by 401(k)-style plans.

In 1980, 38 percent of private sector workers had a pension and 19 percent a 401(k). By last year, according to the U.S. Department of Labor, the numbers had more or less reversed —just 15 percent had a pension and 43 percent a 401(k).

That shift is creating "double disadvantages for the less educated," wrote University of Kansas sociology professor ChangHwan Kim and Social Security Administration researcher Christopher Tamborini in a paper presented Tuesday at the American Sociological Association's annual conference.

The authors analyzed surveys linked to W-2 tax data to figure out how much Americans with varying levels of education were saving in their retirement accounts.

Among workers who hold similar jobs with the same pay and who both contribute to 401(k) plans, a college graduate tends to save 26 percent more than a worker with just a high school diploma, the study concluded.

Workers with college degrees aren't only far more likely to hold jobs that offer retirement plans. When offered the plans, they're also far more likely to sign up and to contribute enough to retire comfortably.

The median private sector worker without a college degree is contributing nothing to a retirement plan, while the median college graduate pitches in more than $2,000 a year, the study found.

One reason is that workers who are less educated are likelier to hold lower-paying jobs that don't offer retirement plans. According to the study, 83 percent of workers with a bachelor's degree have access to some kind of retirement plan — compared with 62 percent of high school graduates and 43 percent of high school dropouts.

Even when they are offered 401(k)s, the less educated workers find it much more difficult to take full advantage of them.

One advantage of a traditional pension is that it's automatic: A set amount is contributed for each worker — an amount that's supposed to guarantee a good income in retirement — and investments are managed by professionals.

The typical 401(k) is anything but automatic. Workers must decide whether to participate, how much to contribute, and which investments to choose.

While more than 80 percent of college graduates sign up for the 401(k) offered to them, only 69 percent of high school graduates do the same. Less than 61 percent of those without a high school diploma fill out the 401(k) paperwork.

College graduates are also saving more, pitching in 7.3 percent of their salaries if they're participating in a retirement plan — still less than the 10 percent or 15 percent experts usually recommend, but more than the 5.1 percent that workers with high school degrees contribute.

That's not necessarily surprising: By earning more, the college-educated can afford to save more. Tamborini and Kim found that if workers earn an extra 1 percent in salary, they tend to contribute an extra 1.28 percent to their retirement plans.

But the researchers also wanted to know if factors other than income are influencing how workers save. When they controlled for these factors — income, occupation, industry, company size, and years on the job — they found college graduates were still saving 26 percent more than similar high school graduates.

To explain this gap, the researchers looked at surveys that asked about savings habits and financial knowledge. The less educated workers tended to be less financially sophisticated, with less familiarity with investing and how to save for the future.

"The advantage of college education goes beyond the monetary return during the work-life," Tamborini and Kim write. "College-educated workers are taking steps to better prepare financially for retirement, even when the earnings levels are taken into account."

As workers spend their entire careers in this system, the authors warn, the inequalities will widen between the well-educated and everyone else. The only fallback for many workers will be Social Security, which now covers 40 percent to 45 percent of the average retiree's career earnings (and has its own fiscal challenges).

What might be done to narrow the gap?

Financial education could help, although studies have cast doubt on the effectiveness of financial literacy programs.

Some employers have experimented with making the 401(k) more automatic — signing up all workers and setting default contribution rates and investments, while letting workers adjust them or decline to participate. (Few workers do.)

But the number of new companies introducing these automatic features is no longer rising. Vast swaths of the workforce aren't covered by any retirement plan at all.

In response, lawmakers in a growing number of states are passing legislation to force employers without 401(k)s to sign up workers for state plans, with the goal of ensuring they can save for retirement without filling out confusing paperwork or picking their own investments.

The next state to approve such a plan could be the largest: California lawmakers could vote as early as this week to create what's known as the Secure Choice Retirement Savings Program.