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One of the most widely dispensed and universally accepted pieces of financial advice is that you should contribute at least enough to your 401(k) to get the full match from your company. If you don’t, so the wisdom goes, you will be giving up free money. Well, it turns out that money isn’t exactly “free.” In a sense, it’s coming right out of your paycheck.

That is among the findings of a study by the Urban Institute’s Eric Toder and Karen Smith, which was published last month by the Center for Retirement Research. Traditional pension plans tended to be an extra perk that employers provided on top of salary. In the past decade or so, though, many companies closed those plans in favor of 401(k) savings plans. As part of that switch, it has been well understood that workers need to put more of their income into retirement accounts. What is less understood is that even the money that employers contribute to those accounts is really coming from workers as well.

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Toder and Smith looked at a Census database on pay and pension plans, and how much employers contribute. They looked at workers who had 401(k) plans in which their employers contributed to retirement savings automatically or by matching employee contributions and compared them with workers who had either a 401(k) with no employer contribution or no 401(k) at all. All else being equal, they found that workers at companies that contributed to their employees’ 401(k) accounts tended to have lower salaries than those at companies that gave no retirement contribution. In fact, for many employees, the salary dip was roughly equal to the size of their employer’s potential contribution.

I should point out that I am not entirely objective when it comes to retirement accounts. I have studied our nation’s 401(k) system and generally come away with the feeling that it doesn’t work all that well. A little over two years ago, I wrote the TIME cover story “Why It’s Time to Retire the 401(k).” Nonetheless, the popularity of 401(k) plans continues. Investors deposited an additional $200 billion in 401(k) plans in 2010 (2011 data isn’t out yet). And Fidelity recently said that 84% of the participants in the plans it manages contributed to their 401(k)s in 2011, the highest level in two years.

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What’s more, the conclusion that Toder and Smith draw from their data is that for low-wage workers, 401(k) plans might actually be better than is thought. That’s because when you factor in the contributions that employers make and the changes in salary, low-wage workers seem to do considerably better than their higher-earning peers. For example, the average salary of a high-earning female (Toder and Smith break the data out by gender) tends to drop 99 cents for every dollar her company contributes to a retirement plan. A low-wage female-worker salary drops by only 11 cents for every dollar of company match. The salary of a low-income male worker drops by 29 cents. Combined 401(k) contributions and compensation of a low-wage worker at a firm that provides a 401(k) match is higher than that of a peer at a firm that doesn’t offer 401(k) contributions.

The problem with Toder and Smith’s analysis is that not everyone participates in their company’s 401(k) plan. And low-wage workers tend to have much lower participation rates than high earners. A recent study from Vanguard found that of workers who make $30,000 or less, just 50% participated in their company’s 401(k) plan. On the other hand, nearly 90% of all workers who make $100,000 or more contributed. Nonetheless, according to Toder and Smith’s findings, everyone who works at a company that offers a 401(k) employer contribution receives a lower salary, whether you participate in the 401(k) plan or not.

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That means for nearly all workers making $100,000 or more, the 401(k) trade-off is a wash. They get the money they aren’t getting in their paycheck deposited in their 401(k) plans. In the long haul, that will probably make them richer. That’s not the case for many low-income workers. For the half who don’t participate, working at a company with a generous 401(k) plan will actually make them poorer. I pointed all this out to Toder, who agreed that even considering the different impacts on wages, the benefits of our nation’s 401(k) system still go overwhelmingly to the rich.

It’s tempting to dismiss all this and say that if low-wage workers don’t take advantage of their company’s matching 401(k) plan, it’s their fault. But that’s living in fantasyland. Many low-wage workers can’t afford to defer a portion of their salary for later. Also, Social Security, assuming it’s still around when they retire, may be all they need. So not participating in a 401(k) might be a rational choice. The bottom line is that 401(k)s for many poor workers are not a better deal than we had thought. They’re worse.

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