The Schwartz

The name Anna Schwartz should ring a bell. She wrote a very great book (which I never read) with Milton Friedman, who was a very great man. Schwartz has some thoughts on the money supply, here. I have just a few remarks.

Previously on the New Arthurian Blog...

Last time, we looked at a typical "money supply relative to output" graph. Then I drew the graph again with the deflator inverted. Inverting the deflator flipped the blue line. The line moved with the deflator. I said this shows that the deflator -- the "correction" to output -- is the reason the typical graph mimics the CPI so closely.

People say it is the relation between money and output that mimics the CPI. But when I inverted the deflator, the blue line inverted. In other words, the line shows what the deflator is doing. Not what "money relative to output" is doing. Money and output play an insignificant role in the graph, despite what people say.

What would happen if we left the deflator alone, and flipped money and output?

What If...

Messin' with the numbers.

Okay, let's do a typical "money supply relative to output" graph. We take the GDP as it comes, purchased at actual prices, and total it up. (That's nominal output.) Then we divide the GDP number by the price level (to "deflate" the GDP down to what it would have been if there was no inflation). This calculation gives us "real output", which is often just called "output."

Next, we take the quantity of money (M2) and divide it by the "real output" number. This gives us the famous "money supply relative to output."

Then we "index" this number: Figure the average value for the whole series, and divide each number in the series by the average. The new values we get are the ones we will display on a graph.

We also grab the CPI, which shows the level of prices. And we index this series of numbers just as we indexed our "money supply relative to output."

We index both sets of numbers, as Milton Friedman said, "To make the two series comparable."

Important Stuff

(Important to me, anyhow.)

The Secret Economist recently posted an evaluation of the Taylor rule.

What's the Taylor rule? According to the Wik, the Taylor rule "stipulates how much the central bank ... should change the nominal interest rate" when inflation and economic growth wander from their targets.

Long story short, the Secret Economist became "suspicious" of the good match between the Taylor numbers and the "Federal Funds" interest rate, and decided to investigate. The bold conclusion: "The Taylor rule fits because it is an identity."

Now, Wikipedia says, "An identity is an equality that remains true regardless of the values of any variables that appear within it." So SE's conclusion is that the Taylor calculation will always give a good match to the interest rate. Suspicions justified.

But -- as Arlo Guthrie said -- that's not what I came to tell you about.

Fractions

"To divide by a fraction, invert and multiply."

Suppose we have a calculation like . But we know that is a fraction, and that . In order to understand our calculation, we can replace the in the calculation with the thing it equals, thus: . It is evident now that in our calculation, we are dividing by a fraction.

To divide by a fraction, use the rule they teach in elementary school: invert and multiply. Inverting the fraction gives us . Now, multiply by the inverted fraction: .

In this form our calculation is simpler because there is only one division. It is okay to remove the parentheses: , and to rearrange terms: . We can add parentheses to show we do the division first: . All of this is valid arithmetic.

Our new formula will produce the same result as , our original calculation.


is the quantity of money.
is real output.
is output in actual prices.
is the price level (the "deflator").

In its final version, our calculation divides the quantity of money by output in actual prices, and multiplies the result by the price level.

The calculation we started with was used by Milton Friedman in Money Mischief to produce all those graphs that show how "money relative to output" follows the same trend-line as prices.

His numbers follow the price trend because he multiplies by the price level.

You can mimic the price trend in many ways. You don't have to use the quantity of money and output. You can use any number you want, pretty much. Just multiply by the price level, and your answer takes on the shape of the price trend.

The Three Little Graphs

Wow! This was easy to do!

Below is a Google Docs spreadsheet. It contains three pages. Each page has calculations and a graph. The graphs are off to the right, near the top, but you won't see them unless you go looking.

This post is mostly in the nature of a test. Probably not much here of interest. This is the spreadsheet used to develop graphs for my comments at The Secret Economist.

No, That's Not True

Mankiw, again.

From Chapter 2 of Macroeconomics:

"The goal of GDP is to summarize in a single number the dollar value of economic activity in a given period of time."

Endogenous Drivel

(and other big words)

Looking thru N. Gregory Mankiw's Macroeconomics (fourth edition, 2000). He writes:

"Models have two kinds of variables: endogenous variables and exogenous variables."

Ooh, I need this. I don't know these big words. I'm interested in the economics, but the big words are a problem for someone of little memory. (The big words are so troubling that I don't even notice Mankiw uses the word variables three times in that sentence.)

"Endogenous variables are those variables that a model tries to explain. Exogenous variables are those variables that a model takes as given. The purpose of a model is to show how the exogenous variables affect the endogenous variables."

Okay this is good. I'm looking at it like computer programming. Send some values to a function, and get a return value. The values I send are exogenous. The return value (calculated by the function, based on the values I send) is endogenous. I get it.

Mankiw continues:

"In other words, as Figure 1-4 illustrates, exogenous variables come from outside the model and serve as the model's input, whereas endogenous variables are determined inside the model and are the model's output."

Just like a function in C. Arguments come from outside the function and serve as the function's input, while return values are determined inside the function and are the function's output. Okay.... (Arguments, or parameters maybe. I'm not always clear on the big words.)

Anyway I wanna see his Figure 1-4...

The Wrong War

Back in the early 1990s I was all gung-ho for Milton Friedman: Prices go up because the quantity of money goes up, always and everywhere. Amen.

And then I got a new job with a small steel warehouse. The counter man -- Wesley, his name was -- once said something I never forgot. He said, "We have to raise our prices, because our costs are going up."

This wasn't Milton Friedman's explanation. It was something else. As I look back now, it is clear to me that "always and everywhere" is not the same as "only." Friedman said prices go up when the quantity of money goes up, always and everywhere. He didn't say that was the only reason prices go up.

When you raise your prices because your customers have "too much money," your good profit gets better. When you raise your prices because you have to, it's because your profit is being squeezed. These two worlds are totally unlike one another.

Milton Friedman explained demand-pull inflation. Wesley introduced me to cost-push. Everybody today is familiar with Wesley's problem. Our costs are going up. Health care costs. Gasoline and heating oil. Candy bars and coffee. Costs are going up and it's tough to make ends meet. We have met the enemy and it is cost-push inflation.

All In Fun

It's all fun and games until somebody gets hurt.

From Krugman of 15 October 09:

...one thing that’s hard to convey is how boring business seemed in the 1960s and 1970s. (”I’ve got just one word for you: plastics.”)

But even a decade later, it was the guys who went off to investment banks who were buying the third homes.... And it wasn’t just the money: business stopped being so boring, and was even getting to be fun for some people.

I thought that was an interesting observation. What else was happening at that time?

And While We're On the Subject

Pandering to Bad Arithmetic

The problems of our economy are often attributed to excessive government spending.

I have all kinds of problems with that. But suppose it is true. If excessive government spending is the cause of our economic problems, then a lessening of the excess should reduce our economic troubles. Right?

Balancing Act

Was It Worth It?

Bush the Elder went into Iraq with 500,000 troops. Bush the Younger couldn't muster 200,000. In the intervening years Bill Clinton balanced the budget. He did it by cutting the military.

Krugman, Again

I'm not picking on him. Honest.

From PK's post of 7 October 09:

Everyone agrees that this is a stopgap, and we want to get the Fed out of the business of private lending over time.

But here’s my question: why does it have to be a return to shadow banking? The banks don’t need to sell securitized debt to make loans — they could start lending out of all those excess reserves they currently hold. Or to put it differently, by the numbers there’s no obvious reason we shouldn’t be seeking a return to traditional banking, with banks making and holding loans, as the way to restart credit markets. Yet the assumption at the Fed seems to be that this isn’t an option — that the only way to go is back to the securitized debt market of the years just before the crisis.

Why? Are we still convinced that securitization is a far superior system to conventional banking, and if so why?

Inquiring minds want to know.

Negative Feedback

It's not what you think.

If I said I was getting "positive feedback" you'd probably figure I heard from people who like my posts. If I said "negative feedback" you'd figure they didn't like 'em. Fair enough. That's probably what I'd mean. But y'know, if that was all there was to it, I wouldn't be writing this post.

Tack the word "loop" on to those feedback phrases, and the meanings are totally different. A positive feedback loop is a self-reinforcing loop. A negative feedback loop is self-negating. These are not at all the meanings we ordinarily use. We might think of a bad situation making itself worse as a negative thing. But it's a positive feedback loop.