The reasoning is that a company would react to a decline in after-tax profit by reducing payouts to shareholders in the form of stock buybacks and dividends. The company’s share price could also be lower than it otherwise would be, hurting shareholders.

“In the short run, it’s just shareholders, shareholders, shareholders,” said Steve Rosenthal of the Tax Policy Center, a joint venture between the Urban Institute and the Brookings Institution. He described Republicans’ 2017 corporate tax cuts as an enormous giveaway to foreign investors. “The corporate tax is like the best way to collect revenue from foreigners and rich guys,” Mr. Rosenthal said.

A completely different perspective animated that law. Republicans, who controlled Congress and the White House, said workers would gain as corporate taxes declined. The idea was that those cuts would spur investment and make employees more productive and able to claim higher wages. In that view, Mr. Biden’s infrastructure spending to help workers would be funded by workers themselves.

The Biden administration’s infrastructure plan, which seeks to repair roads as part of a broad range of investments, would be funded by $2 trillion in higher corporate taxes over 15 years.

Republicans point to wage increases and low unemployment through 2019 as evidence that Trump administration policies were working before the pandemic stopped any momentum. But it is unlikely that corporate investment flowed into wages so quickly, said Alan Viard, an economist at the conservative-leaning American Enterprise Institute.

Instead, Mr. Viard said, wages could have risen because the same law’s tax cuts for households across all income groups gave workers more money to spend and helped lift the broader economy in the short run.

“It’s kind of surprising and certainly disappointing to see the apparent results of the Tax Cuts and Jobs Act, of the corporate rate cut,” he said of the 2017 law. “Maybe these effects are not as strong as we thought.”

The Biden administration contends that the wave of stock buybacks and dividends after the 2017 tax law bolsters the case that the corporate tax falls largely on shareholders and companies making particularly high profit margins. The Democratic White House plays down the potential long-run effects on wages and growth in calling to increase the corporate tax rate to 28% from 21%—after Republicans lowered it from 35%—and to raise taxes on U.S. companies’ foreign earnings.

Economists have long puzzled over the question of who pays the corporate tax.

“This is one of the great mysteries in public finance, and so empirical estimates are people feeling around to try to figure it out,” said Mihir Desai, a finance professor at Harvard Business School.

One obvious thought is that companies raise prices after tax increases, putting the burden on consumers. Most economists say there is little effect. They say companies compete for customers against entities with different tax rules, such as unincorporated businesses, limiting price changes in response to corporate taxes.

Most analysts divide the corporate tax burden between capital and labor, with shareholders paying short-run costs through fewer buybacks, smaller dividends and lower share prices. Workers would get a long-run hit as companies invest less in equipment, limiting productivity gains and workers’ ability to demand wage increases.

Official estimates from the nonpartisan congressional Joint Committee on Taxation lean toward the Democratic view, assigning 75% of the long-run burden to owners of capital and 25% to workers.

“There’s nothing in the debate that suggests there’s a big investment response” to the 2017 corporate tax cuts, said Dhammika Dharmapala, an economist who teaches at the University of Chicago’s law school. “There may have been wage gains over that period, but connecting it to the corporate tax cut isn’t very straightforward, to say the least.”

The Tax Policy Center, a group run by Mark Mazur until he rejoined the Treasury Department this year as a deputy assistant secretary, assigns 80% of the burden to capital. That means 35% of corporate taxes fall on the top 1% of households, which earn about 16% of total pretax income.

The Tax Foundation, which favors lower rates and fewer tax breaks, says the split is 50-50. Harvard’s Mr. Desai said he thinks the split is about even. Career Treasury Department economists estimated in 2012 that capital bore about 82% of the burden, with labor shouldering the rest.

The Treasury under the Trump administration removed that analysis from its website, and Secretary Steven Mnuchin said much of the burden fell on workers. The Biden administration reposted the analysis.

If most of the burden falls on capital, it is important to understand who owns corporations and whether they can be taxed directly in ways that have a smaller economic impact.

Some shareholders are taxable American investors, particularly high-income ones. Beyond corporate taxes, they face sharply higher taxes from Mr. Biden’s proposal to raise top tax rates on capital gains and dividends to 43.4% from 23.8%. Some owners are tax-preferred investments such as 401(k) plans, which are more evenly distributed among income groups than stock ownership as a whole.

For others—namely foreigners and tax-exempt funds such as university endowments and foundations—the corporate tax is the U.S. government’s only meaningful way of extracting significant revenue from these wealthy institutions while preserving their nonprofit status that would be politically hard to alter. In effect, the U.S. can tax Harvard University or another country’s sovereign-wealth fund by taxing companies they own.

Foreigners own about 42% of U.S. equities, according to the Tax Policy Center, with 23% held by U.S. taxable investors and much of the rest in retirement accounts.

Mr. Desai said lawmakers concerned about income distribution should focus more on assisting poorer households and less on raising corporate taxes that could slow investment.

“The puzzle to me about the entire debate is just how quickly the corporate tax got mired in this issue of fairness when we know the [effect] is so unclear,” he said.

Even models that show most of the corporate tax burden falling on capital affect middle-income households with retirement funds. They also show a modest longer-term effect on workers.

The bottom 80% of households pay more than one-quarter of corporate taxes, according to the Tax Policy Center. The Biden administration, which says it won’t raise taxes on households making under $400,000, doesn’t consider those effects as breaking its pledge.