Joe Biden's campaign promise not to raise taxes on households earning less than $400,000 a year may seem straightforward. But in the byzantine world of tax policy, it's anything but.

So far, Biden has not proposed raising any taxes that would directly hit Americans under that income level. However, he has proposed a hike in the corporate income tax, and that change could conceivably affect some Americans earning less than $400,000 annually.

Specifically, Biden has said that his American Jobs Plan — a proposal to spend some $2.65 trillion on both traditional and non-traditional forms of infrastructure — would be paid for by raising the corporate income tax from 21% to 28%. (Sen. Joe Manchin, D-W.Va., whose vote would be necessary to pass the plan into law, has said he wouldn't vote for an increase higher than 25%.)

"Generally speaking, a corporate tax increase is highly progressive — it falls most heavily on wealthy individuals," said Thornton Matheson, a senior fellow at the Urban Institute-Brookings Institution Tax Policy Center. 

That said, it's possible some lower earners would feel the effects of a corporate tax increase. For instance, a higher corporate tax could depress the values for shares that middle- and lower-income taxpayers own, or companies could decide against making investments that increase productivity, which over the long term could reduce workers' wages.

But the effect would likely be small, and when analyzing Biden's promise, there's a relevant distinction between a direct tax and an indirect effect of a tax. 

Meanwhile, several tax analysts told PolitiFact that while Biden's promise may have been politically shrewd, it may not be such wise policy.

"Trying to avoid every instance of a tax increase on those making less than $400,000 will make the tax code more complex than it needs to be," said Kyle Pomerleau, a resident fellow at the American Enterprise Institute. "It will also take certain policies off the table entirely. For example, a gas tax or carbon tax would be reasonable ways to raise revenue for infrastructure."

The fact that he has so far refrained from proposing direct tax hikes on Americans earning $400,000 a year or less is enough to rate the promise In the Works.