Thursday, January 7, 2016

Still troubled by Sumner's graph

Following-up on yesterday's evaluation of Scott Sumner's graph.

Here's my re-creation of the graph Scott Sumner showed on 3 January 2016, which I looked at on the 6th:

Graph #1: Currency Relative to GDP (blue) and the Interest Rate, à la Sumner
Here's what Sumner says immediately after showing his graph:
Notice that the two variables tend to move inversely. After 2008, the yield on T-bills fell close to zero, and the demand for cash soared from just over 5% of GDP to just over 7%.

Just to be clear about what Sumner is saying, I marked up a copy of the above graph to show the "just over 5%" and the "just over 7%" and exactly which part of the blue line he is talking about.

Graph #2: A Markup of Graph #1
The bright red oval identifies the region Sumner described. The bright red arrows indicate the top and bottom of that region, and also which axis shows the values. The black arrow shows where the pukey-red line (the yield on T-bills, which I am ignoring today) falls close to zero, where it remains.

Sumner's argument is that "the demand for cash is negatively related to the market interest rate". That is what his graph shows. The demand for cash (blue) falls for the whole left half of the graph, while the pukey-red market interest rate is rising. And for the whole right half, the blue line rises while the pukey line falls. As Sumner put it, "the two variables tend to move inversely."

Yes, what we see on Sumner's graph is the same as he has described. I had some complaints yesterday about his graph. Have no fear, I have those same complaints today. But to be fair and balanced here, I wanted to be clear on what Sumner said about his graph.

That's out of the way now.

Scott Sumner is telling us that interest rates influence how we hold our money. When rates are low, he says, we hold more of our money as cash. And when rates are high he says, we hold less of it as cash. As I noted yesterday, it's a reasonable argument and it makes sense.

But I do graphs. It's what I do. I can't tell you why his graph bothers me. But it bothers me, and I do graphs. So I had to look at Sumner's graph and see if it made sense or not.


That was yesterday's post.

Today ... today I was looking at his graph again because it shows money relative to GDP ... and I also show money relative to GDP, but different money ... and Milton Friedman also showed money relative to GDP -- but a different GDP.

(Look, in Money Mischief, Friedman used "national income" for GDP. But that's not the different that I'm talking about. National income is either the same as GDP or a bit less, it seems, depending who you ask on the internet. But they run together, GDP and national income. There's no big difference between them. Friedman, though, didn't just use national income: He used "real national income", which is national income with the numbers changed to take inflation out. It's what national income would have been, if prices never went up at all. And that's a big deal. That's what I mean by a different GDP. But that's off-topic. Shame on me.)

Today I was looking at his graph again, Sumner's graph, and it was bothering me, again, and it wouldn't leave my mind alone. Here: If Scott Sumner wants to show that we hold more of our money as cash when interest rates go down, he has to show us the money we hold as cash, compared to all the money we hold. That's what more of our money as cash means: our cash as a share of our money.

He doesn't. He shows the money we hold as cash, compared to the size of the economy. Should be, compared to all the money we hold. Like this:

Graph #3: Currency as a Percent of M1 Money (two measures).
The red line is the better measure, in my view.
If you look at a graph of the currency component of M1, relative to M1 money, the currency component is going down since the crisis. Not up, as Sumner says. It goes down.

Currency relative to the money measure provides a good picture of our inclination to keep our money as cash. Currency relative to GDP, the measure Sumner uses, does not.

I have to assume that Sumner used currency relative to GDP on his graph because it gives results that by dumb luck appear to support what he's saying. And that's very nice for him, because apparently most people don't question graphs. Most people take graphs as evidence. I know I usually do.

Maybe that's why I'm so troubled by Sumner's graph, this time.


The Arthurian said...

Scott, why does your graph not show currency relative to *money* ?

You say that when interest rates fall, currency holdings rise. To my mind “currency holdings rise” is the same as “we hold more of our money as cash”. To look at “holding more of our money as cash” the graph would have to show currency relative to M1 or some broader money.

jim said...

Hi Art,

The problem with M1 is that a lot of it pays interest and the rate of interest is not much different than other bank deposits. So there is not much that distinguishes it from savings accounts.

If you look at money that is interest free, that money declined relative to GDP all along until 2008 when interest free money shot up.

Of course none of this accounts for the transactions conducted with plastic money. There is a huge amount of interest free money in use by credit card users that pay their monthly bill on time. I think that increase in interest free credit card money accounts for most of the decline in other forms of interest free money before 2008.

The Arthurian said...

Thank you, Jim.
I don't believe I ever looked at that before.
Your explanation helps, too.

What you said about "plastic money" makes sense to me. There is no data on that, is there?

My problem with Sumner's graph is that he uses GDP as a context variable while making the argument that changes in interest rates induce us to change our holdings of cash. I think he should be using some measure of money as the context variable. If I use your (Demand Deposits: Total+Currency Component of M1) as context, and look at the "currency component of M1" relative to it, I get another graph like #3, going up-up-up without regard for interest rates, and then suddenly down since the crisis:

Oilfield Trash said...


You are correct in your thinking, your graphs supports the fact that currency hoarding is an archaic concept in the digital age and(in the US) it is far safer and cost effective to hold deposits in a positive interest rate environment.

The argument that if interest rates move down the demand for currency goes up is highly unconventional in the digital age.

When you get into negative territory maybe you can start the argument, but the link below supports the idea that people will still prefer to hold deposits even at some level of negative interest rates, due to the fact they are a superior, cheaper, and more convenient means of payment.

The Arthurian said...

Sumner replied to my comment:
"I use currency to NGDP, because I’m interested in explaining changes in NGDP, not the broader aggregates."

Bullshit. His graph is not about "explaining changes in NGDP". His graph is about the relation between interest rates and our inclination to hold our money as cash.

My question is simple, really: What is the best way to look at our inclination to hold our money as cash?

My answer is to look at our cash holdings relative to our money holdings.
Sumner's answer is to look at our cash holdings relative to NGDP.

Sumner's answer is completely irrelevant.

Why is it so hard for people to see this?