Matt O’Brien has been doing some great coverage of monetary policy recently. He and I agree that the Fed ought to be pursuing a more expansionary monetary policy. However, I think his specific argument for monetary easing isn’t quite right:

Why is steadily rising NGDP so important? It’s about debt. Most contracts assume that NGDP will rise about five-percent a year. If NGDP (and incomes) doesn’t go up that quickly, it becomes harder and harder for people to pay back their debts. That’s what made the Great Recession so great. NGDP growth actually went negative for the first time in half a century.

“NGDP” here is nominal GDP. If you add up the value of all goods and services sold, in non-inflation-adjusted (“nominal”) dollars, that’s NGDP. A growing number of economists and pundits have been arguing that the Federal Reserve should make the growth of NGDP, rather than the inflation rate, its benchmark for whether monetary policy is too tight or too loose. And right now, this rule tells us that monetary policy has been way too tight since 2008 and should be eased. So far, O’Brien and I are on the same page. But his argument above—that the point of monetary easing is to increase the inflation rate—gets things almost exactly backwards.

Unfortunately, it’s hard to explain why without a bit of math. Economists use the “equation of exchange,” MV=PQ, to help them think about monetary policy. The left-hand side of the equation, MV is another way to describe NGDP, the total value of goods and services in the economy. M is the money supply, the number of dollars in circulation. V is the “velocity” of money, the number of times each dollar is spent in a year. By definition, if you multiply the number of dollars by the number of times each dollar is spent you get the value of all goods purchased in a year.

PQ is another way of expressing the same quantity. Q is the quantity of “stuff” produced in a year, and P is the average price of that stuff. If you multiply the quantity of stuff times the average price of that stuff, you get the total value of all output in the economy. MV, PQ, and NGDP are three different ways of describing the same quantity.

OK, so what does this have to do with monetary policy? In late 2008, the Federal Reserve screwed up and allowed the left-hand side of the equation, MV, to decline sharply. (Milton Friedman argues this was also the cause of the Great Depression.) Logically, this meant that the right-hand side of the equation, PQ, also needed to decline. And there are only two ways this can happen. One is for P to fall—deflation. The other is for Q to decline—a recession.

In the 2008-09 contraction, prices only fell by a couple of percentage points, while NGDP fell by much more than that. Math tells us the rest of the decline had to be absorbed Q declining. In other words, because prices didn’t fall fast enough, we got layoffs instead.

So the argument for monetary easing is straightforward: by expanding the money supply (M), the Fed can increase MV, which will necessarily increase PQ. Once again, there are only two ways PQ can change: either P will increase—that is, we’ll get inflation—or Q will increase—we’ll get a larger economy.

In practice, we’d get a mixture of the two, just as we got both deflation and unemployment in 2008–9. But which one you get more of depends on the state of the economy. If the economy is already humming along nicely, there’s not much room for Q to increase; the economy is already producing about as much stuff as it’s capable of producing. So monetary stimulus will mostly lead to an increase in P: inflation. But if the economy is in a recession, with lots of idle workers and factories sitting around, then monetary stimulus will cause an increase in Q, the size of the economy. Firms will see their revenues increase, and that will cause them to hire more workers and increase production.

Now, even if the economy is severely depressed, at least some of the monetary stimulus will occur as an increase in P rather than Q. But that’s a side effect of the stimulus, not its purpose. So it’s important for central bankers to make clear they’re willing to accept some inflation as the cost of economic expansion. But inflation is neither the goal nor a means to the goal.

I think this is a particularly important point because many people have a viscerally negative view of inflation. I think the harms of inflation in the low single digits is often over-stated, but convincing inflation hawks that inflation is a good thing is going to be a really hard sell. Fortunately, supporters of monetary easing don’t need to convince the world that inflation is good! We just need to convince them that a bit of extra inflation is a price worth paying for getting people back to work. But we can’t do that if we describe inflation as the point of monetary easing rather than as a (possibly unwelcome) side effect.