What do the wealthy pay in federal taxes? On paper, the top marginal income-tax rate is 37% on ordinary income and 23.8% on capital gains. Government estimates put high-income filers’ average rates in the mid-20s.

A new Biden administration analysis, however, pegs the average tax rate for the 400 wealthiest households at 8.2% from 2010 to 2018. If that is right, the administration has a firmer case to raise taxes on the ultrarich.

But it isn’t so simple. To understand why, we’ll get to tax policy, but let’s start with fourth-grade math. Fractions!

Percentages are basically fractions and every fraction, from food’s fat content to presidential approval ratings, has a numerator and a denominator. If you don’t know how both are defined—Saturated fats or all fats? Likely voters or registered voters?—you don’t know what you’re measuring.

Income-tax rates are similar. Taxes are the numerator. Income is the denominator. Figuring your rate—or Elon Musk’s—is easy. Right?

It isn’t, and the complexities are enormously important as Congress debates the Biden agenda.

In writing the White House study, administration economists Greg Leiserson and Danny Yagan chose a numerator and denominator reflecting their approach to analyzing tax policy.

First, the denominator.

They include increases in unrealized capital gains. That is the change in the value of assets, including stocks, that haven’t been sold. Such gains are a significant part of the wealthiest Americans’ net worth; the administration approach effectively assumes those paper gains should be income subject to taxation.

Conventional analyses and the current income-tax law don’t include unrealized gains. Advocates of the conventional approach note that such gains fluctuate with markets and that taxpayers might be forced to sell assets to pay the taxes. However, “it’s another thing if they’re using that to borrow against to buy a yacht,” said Garrett Watson, senior policy analyst at the Tax Foundation. Indeed, wealthy people often borrow against assets at low rates to fund their lifestyles.

How the administration measures the tax rate on the wealthy bolsters its policy preferences. President Biden points to low tax rates to justify his calls for higher taxes. He has proposed taxing unrealized gains at death and setting the top capital-gains rate at 43.4%. Both plans are flailing in Congress.

Currently, unrealized gains escape the individual income tax at death, though they may face estate taxes. Mr. Biden also backs annual taxes on billionaires’ unrealized gains. House Democrats offered a more modest plan to set the top capital-gains rate at 31.8%. Legislative negotiations continue.

The numerator in the White House study, like its denominator, is selective, a point the authors acknowledge. By excluding corporate and estate taxes, it drives the tax rate down and focuses the analysis on individual income taxes and the gaps in that part of the tax system. But corporate taxes can be important for billionaires. Warren Buffett, who supports higher taxes on the rich, often notes his own low income taxes. They would be higher if they included corporate taxes paid by his holding company, Berkshire Hathaway Inc.

Indeed, Democrats often defend higher corporate taxes precisely because they take money from wealthy shareholders. They shouldn’t ignore that effect when calculating tax rates, said University of Chicago law professor Daniel Hemel.

Estate taxes should be included in the numerator too, said Columbia University economist Wojciech Kopczuk. Many wealthy people avoid them through creative estate planning or charitable bequests. But some pay.

So if you want to compare yourself with a billionaire, can you put total taxes from Form 1040 in the numerator and adjusted gross income in the denominator?

Not for an apples-to-apples comparison with the White House’s estimate.

Let’s start again with the denominator. Adjusted gross income is a broad income measure, but it doesn’t include untaxed employer-provided health insurance or retirement contributions. It excludes untaxed gains in retirement accounts or 529 savings plans, which have been increasing along with billionaires’ stocks. It ignores rising home values, the smaller analog to Mr. Musk’s Tesla Inc. stock.

“If you include unrealized capital gains in an analysis of some taxpayers, then you should for all,” said Alex Brill, an American Enterprise Institute economist and former GOP congressional aide.

The numerator is also tricky for middle-income households. Federal payroll taxes aren’t part of individual income taxes, and they’re more important in the middle than at the top. So they can’t be ignored—and that would drive up federal tax rates.

With that muddle in mind, let’s return to the 8.2% estimate.

It’s far below traditional estimates from government number crunchers, who largely exclude unrealized capital gains. Recent estimates of a broader group of rich people from the Congressional Budget Office, Treasury Department and the Joint Committee on Taxation fall between 23% and 26%.

Economists Emmanuel Saez and Gabriel Zucman in their 2019 book “The Triumph of Injustice: How the Rich Dodge Taxes and How to Make Them Pay” found the top 400 households by income paid an average individual income-tax rate of 9.2%. Adding other taxes, including corporate and estate taxes, brought the average to 23%. Their analysis generally didn’t include unrealized gains.

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The White House figure sounds shockingly low for a country that favors progressive taxes where burden rises with income.

“It’s meaningful,” Mr. Hemel said. “Jeff Bezos is getting a lot richer. And Elon Musk is getting a lot richer, and the federal government is getting a very small piece of that.”

Who’s right?

It depends what point you’re trying to make. Every definition of income and taxes has assumptions buried inside. How you choose to measure—and how you apply fourth-grade math—can reflect your approach to policy and wealth.

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Write to Richard Rubin at [email protected] and Rachel Louise Ensign at [email protected]

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This post first appeared on wsj.com

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