The graphs Scott Sumner didn't show, and one he did

Reading old posts on my Death of FRED blog I came across Unsaid at FRED, which references the FRED Blog's How much money is the Fed printing? I bring it up because the FRED Blog post shows a graph of the currency component of M1, and a second graph: the currency component of M1 relative to NGDP:

Graphs #1 and #2, from the FRED Blog's How much money is the Fed printing?

That second graph shows the same ratio Scott Sumner used in his Yes, interest rates really do impact the demand for money -- which I have looked at several times of late. Sumner says when interest rates go down, people choose to hold more cash. When interest rates go up, he says, people choose to hold less cash.

It's an interesting idea, I keep saying. But the evidence Sumner shows in support of that idea is no evidence at all. Evidence would be a graph showing the currency component of M1 relative to money in interest-bearing forms. Sumner shows the currency component relative to NGDP. But NGDP is not a form of interest-bearing money. NGDP is not a form of money at all. Scott Sumner's graph is not the evidence he pretends it to be. He needs to be held to account for this.

Look at that currency-to-NGDP graph. It's got the nice "bowl" shape to it. That bowl is the shape you would need in a currency-to-money graph, to show the evidence Sumner wants to show.

Graph #3: Currency Comparison

But not one of the four currency-to-money-measure graphs show a comparable bowl shape. Not M1 money ... not M2 money ... not M3 money ... and not MZM.

I guess you could argue that M2 and M3 show a misshapen bowl of sorts: A sorry excuse for a bowl. To that extent only is there evidence people hold more cash when interest rates are low and all that, that Sumner says.

And that would make sense. M2 and M3 are mostly measures of savings. It is only saved money that people can choose to hold as interest-bearing or as currency. The money that comes as income today and goes as expenditure today, there is no time to hold that money in any form.

Couple comments at Sumner's post are relevant here. Njnnja asks

Who has the hundreds of billions of dollars in currency?

Njnnja runs thru the numbers, and then concludes:

So the response function of currency to interest rates isn’t what the average Joe does to their currency holdings when rates change, but rather, what this unique subset of high-currency holders does.

It's people who hold a lot of money in savings, able to move money into or out of cash, who are chiefly responsible for the relation Sumner describes between interest rates and currency holdings. To the extent the relation exists at all.

The second comment, from Sumner himself, concurs:

I did my PhD dissertation on currency hoarding, and I can assure you that the vast majority of currency is held for saving purposes, not transactions.

It's savers, if anyone, who make currency holdings vary in response to interest rates. Savers and, in our world, the high level of inequality. It's inequality, I think, that makes it so difficult for the rest of us to intuitively see why a change in interest rates would cause changes in currency holdings. Lots of us don't have money to move like that.

Once again, the economy Sumner examines is the high-inequality economy, and the trends he see are those driven by the wealth-holders of that economy.

So, yes: There could be something to it, the relation Sumner sees between interest rates and currency held. But you're damn sure not going to see it by looking at the currency-to-NGDP ratio. NGDP is not money we can choose to hold as currency. NGDP is not money at all. And Scott Sumner's currency-to-NGDP graph is not evidence that changes in interest rates influence currency holdings.


The FRED Blog post looked at the currency component of M1 on a log graph. They said currency is increasing, but not accelerating. They said "if the slope is the same for two years, the growth rate is the same" -- implying you can see it on their graph. As I said at the time: The line goes up, yes, but after the early 1960s it doesn't curve up. It shows a fairly constant rate of increase: increase, but not acceleration.

Then FRED looked at currency-to-NGDP, the same as Sumner uses. They point out the "neat U-shaped long-term trend." Here (somewhat revised) is what I said about FRED's two graphs:

On Graph #2 we have downtrend to about 1985, and then uptrend: The currency component of M1 grew more slowly than NGDP in the early years, and more quickly than NGDP in the late years. I want to say the change occurred around 1985.

From 1960 to 1985 the trend on Graph #2 is down. After 1985 the trend is up. And yet, as the FRED Blog says, Graph #1 shows no acceleration. Graph #1 shows no change.

Graph #1 shows that currency growth did not change. Graph #2 shows that either currency growth or NGDP growth did change. Together, the graphs show that NGDP growth is the one that changed.

I took a closer look:

During the 25 years from 1960 to 1985, currency in circulation increased by a factor of 5.6. During the 25 years from 1985 to 2010, currency in circulation increased by a factor of 5.5. Almost exactly the same. So, a straight line increase. As FRED said.

During the first 25 years NGDP increased by a factor of 8.0. That's faster than currency growth, so the line on Graph #2 goes down between 1960 and 1985.

During the second 25 years NGDP increased by a factor of 3.4. That's slower than currency growth, so the line on Graph #2 goes up between 1985 and 2010.

 
The "bowl shape" of currency-to-NGDP arises from changes in NGDP growth. Not from changes in currency growth. That's a fact. It doesn't sit well with Scott Sumner's claim that changes in interest rates cause changes in currency holdings. If anything, we would have to say changes in interest rates cause changes in NGDP growth. But I for one wouldn't make a claim like that on such sparse evidence.

The claim Sumner makes would be based on sparse evidence, if his graph was evidence. It is not evidence.

Call him on it.