A friend asked me about last week’s WSJ op-ed by Christopher Cox and Bill Archer claiming that the government’s true liabilities exceed $86 trillion—not the $16 trillion national debt that people usually talk about. There’s something to it, but there’s also a huge scary story in there that’s purely meant to frighten people.

$16 trillion is the amount of Treasury debt outstanding at the moment. The more relevant figure is the amount of debt the federal government owes to people and institutions other than itself. If, for some reason, I lent money to my wife and she promised to pay it back to me, we wouldn’t count that as part of the debt owed by our household. The debt owed to the public is about $10 trillion these days.

So where do Cox and Archer get $86 trillion? They are counting the present value of future unfunded liabilities. To take one example, if you add up all the money that Medicare Part A is expected to pay out over the next 75 years and figure out how much it would be worth today, you get a total of $21.2 trillion. If you add up all the money that Medicare Part A will bring in from payroll taxes and do the same, you get $15.6 trillion. So to make Medicare Part A balance over seventy-five years, the government would have to have $5.6 trillion that it doesn’t have today. Do the same for all of Medicare and you get a total of $38.6 trillion. This is all from Table V.F2 on page 238 of the latest trustees’ report on the Medicare trust funds. (Cox and Archer, who claim to be citing the same source, have $42.8 trillion in their op-ed; maybe they’re using an infinite time horizon instead of a 75-year timeframe.)

Now, this is a meaningful exercise. It provides information that isn’t captured in the annual deficit figures and the current national debt, neither of which says anything about how spending and tax revenues are likely to evolve in the future. When we make decisions about taxes and spending, we should consider what we know about the future. In this case, we know that Medicare spending, under current law, is likely to increase faster than tax revenues because of demographic changes and health care inflation.

But what does $86 trillion mean? Is it a lot or a little? And this is where Cox and Archer start telling silly stories meant to scare people. They claim that “to collect enough tax revenue just to avoid going deeper into debt would require over $8 trillion in tax collections annually.” This is wrong on two levels.

First, if you did your calculations properly, you don’t “go deeper into debt” each year. You already estimated the amount that you will have to pay out and the amount that you will collect. The present value of your future unfunded liabilities shouldn’t be changing significantly from year to year unless those estimates change. For example, your discount rate might change, or your estimate of health care inflation might go up, or something like that. But these estimates can change in either direction.*

Second, the source they cite already tells us how much we would have to raise taxes (p. 239):

“From the 75-year budget perspective, the present value of the additional resources that would be necessary to meet projected expenditures, at current-law levels for the three programs combined, is $38.6 trillion. To put this very large figure in perspective, it would represent 4.3 percent of the present value of projected GDP over the same period ($907 trillion).”

The appropriate number to compare $86 trillion to is the present value of all future GDP. The Medicare trustees give us the present value of GDP over the next seventy-five years, which is $907 trillion. So $86 trillion is a big number (and I’m still not sure where Cox and Archer got it), but $907 trillion is a much bigger number.

Looking just at Medicare, we would need to increase taxes by 4.3 percent of GDP over the levels set by current law. Today, it would be about $600 billion. That is a lot, but it is certainly doable—and it’s a lot less than $8 trillion.

Why do Cox and Archer mangle their estimates so much?

“Some public officials and pundits claim we can dig our way out through tax increases on upper-income earners, or even all taxpayers. In reality, that would amount to bailing out the Pacific Ocean with a teaspoon. Only by addressing these unsustainable spending commitments can the nation’s debt and deficit problems be solved.”

This is a standard, “we can’t afford it” attack on social insurance programs. But they only arrive at this conclusion by being an order of magnitude wrong about the actual size of the funding gap.

Being bad at math is one thing. But Cox and Archer didn’t even have to do the math; they just had to keep reading until they got to the point where the Medicare trustees did the math for them.

* There’s one exception: Since the most recent year has slipped from the future into the past, it’s no longer part of the calculation. If that was a surplus year, then the present value of your future unfunded liabilities will go up by a bit. But the surplus should have improved your balance sheet by an offsetting amount, so you’re no worse off.