Bathtubs for Beginners

In economics life there’s a basic conceptual distinction between a flow and a stock. A flow is a something that occurs over some period of time, like water pouring from a faucet into a bathtub. A stock is something that exists at a specific moment of time, like the water in that bathtub. You measure a flow over a period of time (e.g., gallons per minute); you measure a stock at a specific moment in time (e.g., gallons). For a business, the income statement (revenues and costs in a year) measures flows, while the balance sheet (assets and liabilities) measures a stock. That’s why the income statement is dated for a year (or a quarter) and the balance sheet is dated for a specific day. Everyone understands this. If you didn’t, you would get confused between your salary and your bank account.

But not David Brooks.

In today’s self-indulgently contrarian column, Brooks argues that the Occupy Wall Street movement is made up of “small thinkers.” Here’s his evidence:

“They will have no realistic proposal to reduce the debt or sustain the welfare state. Even if you tax away 50 percent of the income of those making between $1 million and $10 million, you only reduce the national debt by 1 percent, according to the Tax Foundation. If you confiscate all the income of those making more than $10 million, you reduce the debt by 2 percent. You would still be nibbling only meekly around the edges.”

This is incoherent to begin with. Tax policy directly affects flows, not stocks, so its impact on the national debt (a stock) is indeterminate unless you specify a length of time for the policy to be in place.

If you look at the Tax Foundation report, it says that those two policies would increase taxes by $306 billion. The Tax Foundation doesn’t even say in what year that would happen, but they link to a series that ends in 2009, so let’s say they’re using 2009 data. In 2009, GDP was $14.1 trillion, so $306 billion is 2.2 percent of GDP.

Now let’s apply that to the CBO baseline. Right now, my updated CBO-style baseline shows national debt at 61 percent of GDP in 2021 and 59 percent in 2035. If you add 2.2 percent of GDP to revenues in every year beginning in 2012, those numbers fall to 44 percent in 2021 and 5 percent in 2035 (a reduction in the debt of 54 percentage points, or 92 percent). In other words, the entire long-term deficit problem goes away.

If you prefer to use the CBO alternative scenario (in which, among other things, the Bush tax cuts are made permanent), my updated alternative scenario shows the debt at 80 percent of GDP in 2021 and 142 percent in 2035. Increase revenues by 2.2 percent of GDP and those number become 63 percent and 91 percent. These are big, big differences—a lot more than “1 percent” and “2 percent” and “nibbling meekly around the edges.”

Saying these tax changes would reduce the deficit by 3 percent (that’s 1 percent + 2 percent, by the way) is a mistake that guts the rest of the column, which is based on the idea that major tax increases on the rich wouldn’t matter. It doesn’t surprise me that David Brooks can’t do basic math, but doesn’t he have a fact checker? Or at least an editor?

The people at the Tax Foundation, I assume, are not innumerate. David S. Logan, the person who wrote the analysis that Brooks cites, must have realized that, when you open the tap further, you can’t estimate how much the water level in the bathtub will increase without specifying how long the tap will be open.* But their job is to come up with analyses that prove what they want to prove and hope that journalists will take the bait. Every so often one does.

Now, I don’t think we should have a 100 percent effective tax rate on people who make more than $10 million. But the idea that increasing taxes on the rich will have a minimal impact on the national debt is pure innumeracy. David Brooks may have something valuable to say about, well, I don’t know, but something else. But why is the Times letting someone who doesn’t understand arithmetic write about budgetary issues and the national debt?

* At least I assume he knows it. His bio says that he is in a Ph.D. program in business economics at Washington University, a school where they know their math. (When I was in the Math Olympiad Program one of the teaching assistants was a student there.)