A new book-length study on the tax burden of the ultrarich begins with a startling finding: In 2018, for the first time in history, America's richest billionaires paid a lower effective tax rate than the working class.

"The Triumph of Injustice," by economists Emmanuel Saez and Gabriel Zucman of the University of California at Berkeley, presents a first-of-its kind analysis of Americans' effective tax rates since the 1960s. It finds that in 2018 the average effective tax rate paid by the richest 400 families in the country was 23 percent, a full percentage point lower than the 24.2 percent rate paid by the bottom half of American households.

In 1980, by contrast, the 400 richest had an effective tax rate of 47 percent. In 1960, their tax rate was as high as 56 percent. The effective tax rate paid by the bottom 50 percent, by contrast, has changed little over time.

The analysis differs from many other published estimates of tax burdens by encompassing the totality of taxes Americans pay: not just federal income taxes but also corporate taxes, as well as taxes paid at the state and local levels. It also includes the burden of about $396 billion of what Saez and Zucman call "indirect taxes," such as licenses for motor vehicles and businesses.

The analysis, which was the subject of a column in The New York Times on Monday, is also notable for the detailed breakdown of the tax burden of not just the top 1 percent but also the top 0.1 percent, the top 0.01 percent and the 400 richest households.

The focus on the ultrarich is necessary, Saez and Zucman write, because those households control a disproportionate share of national wealth: The top 400 families have more wealth than the bottom 60 percent of households, while the top 0.1 percent own as much as the bottom 80 percent. The top 400 families are a "natural reference point," Zucman says, because the IRS publishes information on the top 400 taxpayers as a group, and other sources, such as Forbes, track the fortunes of the 400 wealthiest Americans.

The relatively small tax burden of the super-rich is the product of decades of choices made by American lawmakers, some deliberate, others the result of indecisiveness or inertia, Saez and Zucman say. Congress has repeatedly slashed top income tax rates, for instance, and cut taxes on capital gains and estates. Lawmakers have also failed to provide adequate funding for IRS enforcement efforts and allowed multinational companies to shelter their profits in low-tax countries.

But the tipping point came in 2017, with the passage of the Tax Cuts and Jobs Act. That bill, championed by President Donald Trump and then-House Speaker Paul Ryan, was a windfall for the wealthy: It lowered the top income tax bracket and slashed the corporate tax rate.

By 2018, according to Saez and Zucman, the rich were already enjoying the fruits of that legislation: The average effective tax rate paid by the top 0.1 percent of households dropped by 2.5 percentage points. The benefits the bill's supporters promised - higher rates of growth and business investment and a shrinking deficit - have largely failed to materialise.

Not all economists accept Saez and Zucman's analysis. It is based in part on their previous work, along with French economist Thomas Piketty, on the distribution of wealth and income in American society. Other economists have generated estimates of that distribution that show smaller disparities between the country's haves and have-nots. Saez, Zucman and Piketty have defended their research and maintain that their methods are the most accurate.

On the question of tax burdens, Jason Furman, an economics professor at Harvard who chaired the White House Council of Economic Advisers under President Barack Obama, noted that Saez and Zucman did not include refundable tax credits, such as the earned-income tax credit (EITC), in their analysis.

The credit, which is intended to encourage low-income families to work, "is part of the tax code," Furman said. A person who paid $1,584 in federal income taxes and then received a $2,377 credit would have a total federal tax burden of -$500, but Furman said that under Saez and Zucman's analysis, that person would instead show a burden of $0. That result would make total tax burdens at the lower end of the income spectrum appear higher than they actually are.

"The best estimates indicate that the tax system is progressive - with the rich paying a higher tax rate than everyone else," Furman said.

Zucman countered that his and Saez's analysis considers the EITC and other credits like it as transfers of income, akin to food stamps or jobless benefits, rather than tax provisions.

"If you start counting some transfers as negative taxes, it is not clear where to stop," he said via email. "Do you treat the EITC as a negative tax? Veterans' benefits? Medicaid? defense spending? . . . There's no clear line, and the results become arbitrary."

There is general agreement among economists, however, that the tax burden of the rich has fallen considerably in recent decades.

"The rich definitely pay less in taxes than they did in the past and less than they should," Furman said.

The bulk of Saez and Zucman's new book explores how that happened, and how the trend might be reversed.