"The GOP is looking for ways to pay for tax cuts. Your 401(k) may bear the cost," headlines the Washington Post. Many others have made the same claim, that proposed changes to tax preferences of 401(k)s in the GOP tax plan would hurt retirement savings to benefit the rich. In response, today President Trump declared via Twitter that "there will be NO change to your 401(k). This has always been a great and popular middle class tax break that works, and it stays!"

But what is really going on?

Today, there are two main types of 401(k)s. Each receives a different tax preference. Ordinary 401(k)s, the ones that most Americans have at work, provide an income tax deduction for contributions, but then impose taxes on account balances when they're withdrawn. So-called "Roth 401(k)s," which are less numerous, impose taxes on contributions but then allow for tax-free withdrawals in retirement. Neither is necessarily a bigger tax break over the long term. The main difference is that ordinary 401(k)s provide the tax break up front, while Roths delay the tax break until retirement.

Which is where the Republican tax plan comes in. The Congressional Budget Office scores such a plan over a 10-year period, and the plan needs budget offsets to corporate and individual tax rate cuts. Relative to current law, shifting all 401(k)s to Roth-style tax treatment would front-load tax revenues and help the budget numbers add up, even if the total budget cost of 401(k)s didn't really change. A later iteration of the tax plan would allow up to $2,400 in contributions under ordinary 401(k) rules, but anything above that amount would get Roth-style tax treatment.

If that's the case, why all the hub-bub about the GOP gutting your 401(k)? Part of that panic is because many people, even in the media, don't really understand how the 401(k) tax preference works. Others don't really care and are just looking for a stick to beat Trump and the Republicans with. It's politics, and I'd be hypocritical to condemn a practice that occurs every second of every day in Washington, D.C.

But partly there's a concern that, without the visible, upfront tax preference available to ordinary 401(k)s, many Americans wouldn't bother to save.

But research to date concludes that's not a big concern. In fact, "Rothification" might increase retirement saving. A study published this year by a well-known group of economics examined 11 companies that shifted their 401(k) plans from ordinary tax treatment to Roth treatment. The researchers were interested in how the companies' employees reacted to the change. Would they withdraw from the plan? Would they reduce their annual contributions to make up for the extra taxes they would have to pay that year?

As it turns out, employees kept saving at more or less the same rates as before. But this is a case where "no change" translates into higher retirement saving. The reason is that any given dollar of Roth contributions produces more retirement income, because Roth withdrawals are tax-free while ordinary 401(k) withdrawals are taxed.

The specifics depend upon the precise tax rates paid by workers both before and after retirement. To use an example, if a worker today paid a marginal tax rate of 20 percent, shifting to Roth treatment could increase the net value of his 401(k) withdrawals in retirement by the same amount. Thus, the authors of the study conclude that "governments may be able to increase after-tax private savings while holding the present value of taxes collected roughly constant by making savings non-deductible up front but tax exempt in retirement, rather than vice versa."

But here's the problem. The Republican sponsors of the tax bill didn't make that argument and present that evidence. They didn't make any argument at all, because their focus was on "paying for" a tax cut rather than helping Americans save for retirement. So even if the policy might actually raise savings and improve retirement security, it was perceived as gutting 401(k)s to benefit the rich. And so President Trump was forced to walk away from the idea.

Andrew G. Biggs (@biggsag) is a contributor to the Washington Examiner's Beltway Confidential blog. He is a resident scholar at the American Enterprise Institute. In 2014, Institutional Investor Magazine named him one of the 40 most influential people in the retirement world.

If you would like to write an op-ed for the Washington Examiner, please read our guidelines on submissions here.