In the “Economic Report of the President” released on Feb. 19, the White House’s Council of Economic Advisers defines “middle class economics” primarily by the average income of the bottom 90%. “Average income for the bottom 90 percent of households,” according to the ERP, “functions as a decent proxy for the median household’s income growth.”

This is absurd: The average income for the bottom 90% is not a decent proxy for the median nor even a decent measure of household income. It is instead a roughly fabricated estimate of pretax “market income” reported on tax returns that falls below some threshold for the top 10% ($114,290 in 2013). But this dodgy number does serve as the basis for CEA Chairman Jason Furman ’s assertion a day later on the Vox blog that the U.S. has suffered a “40-year stagnation in incomes for the middle class and those working to get into the middle class.”

The measure has become popular on the left. Sen. Elizabeth Warren (D., Mass.) recently asked an AFL-CIO conference, “Since 1980, guess how much of the growth in income the [bottom] 90% got? Nothing. None. Zero.” NPR displayed the same bottom 90% data and stretched it even further, claiming that “after 1980, only the top 1% saw their incomes rise.”

The source cited in the ERP for the claims about stagnating average incomes is the World Top Incomes Database. The U.S. data come from economists Thomas Piketty and Emmanuel Saez, the same source cited by Sen. Warren and NPR.

Amazingly, these same statistics also show there has been no increase for the “bottom” 90% since 1968. Measured in 2013 dollars, average income of the bottom 90% was supposedly $32,730 in 1968, $32,887 in 1980, $35,326 in 2007 and $32,341 in 2013.

This is totally inconsistent with the data the Bureau of Economic Analysis uses to calculate GDP. For example, real personal consumption per person has tripled since 1968 and doubled since 1980, according to the BEA. Are all those shopping malls, big box stores, car dealers and restaurants catering to only the top 10%? The question answers itself.

Instead of the White House concoction, consider the Congressional Budget Office estimates of actual median household income. Measured in 2013 dollars, after-tax median income rose briskly from $46,998 in 1983 to $70,393 in 2008 but remained below that 2008 peak in 2011. The sizable increase before 2008 is partly because the average of all federal taxes paid by the middle fifth has almost been cut in half since 1981—from 19.2% that year to 17.7% in 1989, 16.5% in 2000, 13.6% in 2003 and 11.2% in 2011.

Census Bureau estimates of median “money income,” on the other hand, do not account for taxes, so they miss a major source of improved living standards. They also exclude realized capital gains, public and private health insurance, food stamps and other in-kind benefits. Even so, the Census Bureau’s flawed estimate of median income rose 13.7% from 1984 to 2007 before falling 8% from 2007 to 2013.

Both CBO and Census estimates show only six years of middle-class stagnation, not 40.

The Piketty and Saez data are crucially flawed. The total income reported on individual tax returns, which is the basis of their estimates, is substantially less than any official measure of total income, and the difference keeps getting wider. In their original 2003 study, Messrs. Piketty and Saez mentioned one rapidly expanding source of missing income—disappearing dividends in tax-return data. These were “due mostly to the growth of funded pension plans and retirement savings accounts through which individuals receive dividends that are never reported as dividends on income tax returns.”

The same is true of interest and capital gains accumulating inside such tax-free savings accounts. These have grown to nearly $20 trillion, according to a 2014 report by Tax Foundation economist Alan Cole.

Messrs. Piketty and Saez shrink the total income numbers further by subtracting all transfer payments, such as Social Security and unemployment benefits, and excluding all health and retirement benefits provided by private employers or government agencies. The result, as Brookings Institution’s Gary Burtless noted, is that, “The Piketty-Saez measure [of total income] excluded 24% of NIPA [National Income and Product Accounts] ‘personal income’ in 1970, but it excluded 37% of ‘personal income’ in 2008.” It excluded 40% of personal income by 2011.

Because of their increasingly understated estimates of total income, Messrs. Piketty and Saez estimate that in 2013 the “other 90 percent”—meaning all incomes smaller than $114,290—had an average income of only $32,341. That number is not remotely credible.

According to the CBO, that $32,341 would have been below the $34,000 needed to escape from the poorest fifth of two-person households in 2011, when half of all households earned more than $75,200 before taxes. Even using the Census Bureau’s narrow definition of money income, average income for the middle fifth was $72,641 in 2013, and half of us earned more than $51,939.

In short, the Piketty-Saez average of all incomes below the top 10% is far lower than any official estimate of incomes among the middle fifth of the income distribution. This means their comparisons of cyclical shares of income growth among the top 10% and bottom 90% during booms and busts are invalid. And so too are their estimates of the shares of mismeasured “total income” supposedly received by the top 1%-10%.

People often form strong opinions on the basis of weak statistics, but this “bottom 90%” fable may be the worst example yet. The Economic Report of the President’s description of “middle-class economics” rests on a far-fetched claim that middle incomes have stagnated for four decades rather than from 2008–13—most of these years during the Obama presidency.