## Monday, October 26, 2009

### 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.

The last two paragraphs of SE's post come under the heading "The Quantity Theory" and refer to a graph showing the similarity between prices and "M2 divided by output." I've had trouble with such graphs for a long time. My trouble is the same trouble SE has with the Taylor rule: Those graphs always give a good match.

Because our objections to the graphs are comparable, I thought SE would readily understand my objection. I posted a brief comment, using math terms like calculated and factoring and denominator:

In Money Mischief Friedman shows 100 years of comparability between M2 money and real output. But "real" output is calculated by factoring inflation out of actual prices.

Using it as a denominator under M2, Friedman factored inflation into his results.

In private correspondence I pointed this out to Friedman and he replied that the CPI and the output deflator are calculated independently.

I'd say that adds just enough "difference" to the money/output trendline to make it believably similar to the CPI trendline. Sort of like what you show with the Taylor rule.

Well, I'm not an economist. And the Secret Economist is. So I guess we approach things differently. SE responded to my comment:

Authurian: I am not sure I completely understand your comment. It has always seemed to me that we want to factor prices out of output before using it to normalized the money supply. If (and this is a big if) all prices are factored out, we are left with units of output. Money divided by units of output should give us prices (or at least something that trends with prices). I think of the quantity theory equation as reflecting money chasing goods.

I don't know if you can "feel" it. But this response is very much an economist's response. It explains -- clearly, I think -- the economics behind the graph. But it fails to consider the arithmetic. So I gave it another shot:

I do not dispute the link between inflation and money. But I do dispute the validity of graphs such as the one under "The Quantity Theory" in your post above. I present three examples to make my argument.

My first graph compares two time series. I modeled mine after yours, so each series is expressed as a five-year percent change. The blue line represents the CPI trendline. The red line I will identify below. But you can see there is similarity between the two lines.

My second graph contains the same data as the first. But the similarity and closeness of the two trendlines is much greater here, almost as good as in your graph. I achieved this effect by indexing each series on its average value. That is the same technique used by Milton Friedman for his graphs.

Your graph, and Friedman's, compare the CPI to what Friedman called "money supply relative to output," where M2 is the money supply, and real values are used for output. As you say, "we want to factor prices out of output" so that "we are left with units of output." (I assume you use "real output," as Friedman did.)

My graphs compare the CPI to "real population," which is calculated just as real output is calculated: We take the actual number and divide it by the GDP Deflator.

This is just a stupid gimmick that makes my trendline similar to the price trendline. But Milton Friedman used exactly the same gimmick to make "money supply relative to output" similar to prices. And, yes, Friedman's choice of data is much more reasonable than mine. But that does not validate his graphs. It just makes it more difficult to see the stupid gimmick.

In my third graph I remove the population number and in its place use the constant value 1. I divide this value by the GDP Deflator to produce a "real constant" (which, of course, varies). Then I divide M2 by my "real constant" and compare it to prices -- again, indexing each series on its average value as Friedman did. Again, the result is a replica of the price trendline.

You said you didn't understand my previous comment. (It's no secret... I'm no economist.) Just for a moment take the economics out of your money-and-inflation graph, and consider the simple arithmetic. When you factor prices out of the denominator, you factor them into the result. This is the reason our graphs -- yours, mine, and Friedman's -- are all so similar to the price trend.

The similarities here are comparable to the similarity you show in your first graph of the above post, where the Taylor estimate so closely corresponds to the Federal Funds Rate. Fraudulent arithmetic all.

Call me crazy,
Art

That did the trick. SE responded:

Okay, Arthurian. I am going to have to do some homework. Your graphs are quite convincing. Too, I get the rationale behind the graphs. I am going to have to think about this and see how much of what I have done is just reflecting the price movements themselves ...

SE

The Google Docs spreadsheet used to create the graphs is on line here and there.