The New York Times eagerly pushed a narrative with massive holes.

The truth gets its boots on pretty quickly in the Internet age. On October 6, the New York Times ran a piece broadcasting the striking claims made by the economists Emmanuel Saez and Gabriel Zucman in the new book The Triumph of Injustice. Just a couple of weeks later, it’s clear that these claims are built atop a foundation of often questionable and sometimes indefensible assumptions.

Per Saez and Zucman, while the rich have been pulling in more and more of the nation’s income — grabbing about a fifth of it now, double what they got a few decades back — they’re paying lower and lower tax rates. Indeed, in 2018, the richest 400 Americans paid the lowest overall tax rate (including state, local, and federal taxes) of any income group. While the very richest Americans in 1950 paid two-thirds of their income in taxes, in 2018 it was down below a quarter; even the full top 0.1 percent barely pay more than the bottom 90 percent these days. It’s not that much of an exaggeration to say we have a flat tax system, not a progressive one.

The debunkings came from everywhere: a Twitter thread by Journal of Public Economics editor Wojtek Kopczuk, an article by the economic historian Phil Magness, an academic response from the economist David Splinter, a report from the Republican side of the Senate’s Joint Economic Committee (JEC), a traditional book review in Le Grand Continent, and more.

Let’s take the two claims, rising inequality and rich people paying low tax rates, in turn. Both of these problems are probably overstated, in the latter case quite dramatically, in Saez and Zucman’s numbers. And I say “probably” only because no one writing about these trends should pretend that even the best estimates are much more than guesswork, and necessarily so, because the data here are spotty and there are legitimate disagreements over what should even count as income and tax payments.

The alleged rise of income inequality was recently the focus of some congressional hearings about the government’s plan to start reporting more data on the topic, as well as an extensive but readable summary of the academic literature from the JEC Republicans. You might think this would be an easy question to answer, whether the rich are pulling away from the rest of us, because the IRS can tell you how much income people report to the government. But — I hope you’re sitting down — not all income is reported to the government. And that’s only the first big obstacle to measuring inequality accurately.

We know from the “national accounts,” the data we use to monitor overall economic activity, approximately how much money goes unreported overall. But to account for the missing money while measuring inequality, we need to know how much unreported income goes specifically to the rich versus the poor, and that is hard to do. Splinter, for example, argues that Saez and Zucman use a method that gives too much of this income to the rich; Splinter’s own approach relies on data from IRS audits and gives more of it to folks down the income scale.

If your eyes are glazing over, I have bad news: As the JEC report details, this is only the first of many technical decisions researchers must make that affect the results. Should we worry about income inequality before or after taxes are taken out? Should we include governmental transfers as income? Should we analyze married couples together or separately, bearing in mind the decline of marriage in recent decades, especially among the poor? How to handle corporate profits that are retained rather than given out to shareholders? How to handle stocks that have grown in value but have not been sold?

The JEC report provides a remarkable buffet of options to anyone wanting to find a study to cite in favor of a preferred narrative, with the general pattern being that Saez and Zucman’s work is on the high end. By all accounts, pre-tax income has become more concentrated at the top, though this trend is more dramatic in some estimates than others. But the share of post-tax income going to the top 1 percent may have risen only from 7.2 to 8.5 percent from 1979 to 2015.

If it’s hard to tell how much money people make, it’s even harder to calculate their total tax rates, which requires you to know not only their income but also their payments to several levels of government. Once again the IRS is very helpful when it comes to what’s reported to the federal government, but then you also have to estimate how much money people across the income spectrum spend on state income taxes, sales and property taxes, etc. It’s no easy task.

And here too, beyond problems with the basic data, there are arguments over what to include. A big one — a way that The Triumph of Injustice departs even from its authors’ own previous work — has to do with the tax on corporate profits, which has fallen significantly in recent decades. Since corporations are just legal entities, they don’t really pay these taxes; people do. And there’s a lot of debate over how much of this tax burden falls on corporate shareholders, as opposed to other folks, including workers and customers, who tend to be less wealthy and might benefit if the government didn’t take this money. Faced with this conundrum, the right-leaning Tax Foundation will point to studies showing “that labor bears between 50 and 100 percent of the burden of the corporate income tax,” while the left-leaning Tax Policy Center assigns 60 percent of the burden to shareholders, 20 percent to capital in general (because the corporate tax has spillover effects for other forms of capital), and 20 percent to labor.

Saez and Zucman’s approach? To assume the entire corporate tax falls on shareholders, and to make this clear only after their number-crunching has been reported as fact in the national media. As the economist Tyler Cowen put it in a scathing post, “no Western fiscal authority I have heard of thinks of tax incidence in these terms.” And as this animation from Kopczuk shows, this new assumption largely explains a big change in the trend for rich people’s taxes even relative to Saez and Zucman’s own approach in a recent paper with Thomas Piketty:

There are other points too at which anyone making a chart like this needs to make decisions about what to include as taxes, and for whom. For instance, what are we to make of “refundable” income-tax credits that are paid even to people with no income-tax liability to offset? Should we treat those as offsetting the other taxes that people pay, which after all is one of their purposes? Or should we just classify them as outright transfers, not part of the tax system at all? Unsurprisingly, Saez and Zucman do not include them, because they would boost income and thereby reduce taxes as a percentage of income for the poor.

As with inequality, we can point to other sources of data on tax progressivity to show that Saez and Zucman are an outlier. Splinter’s response illustrates this, and so does this from Jason Furman, who headed the Obama administration’s Council of Economic Advisers:

At every step of the way, Saez and Zucman made decisions that skewed the income distribution toward the top and the tax burden away from it. You can have a reasonable debate about the best way to analyze these data and what they say about our tax policies. But it does no one any favors to treat these estimates as established fact, the way the New York Times did.