## Monday, October 26, 2009

### 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."

Sure enough, the two lines on the graph are "comparable."

This graph is a big deal, you know. Well, not this one. But it's famous; all the economists use it. People take it as evidence. They take it as proof of the claim that printing money causes inflation.

It isn't proof. It isn't even evidence.

Sure, printing money causes inflation. Absolutely. If the quantity of money doubles, then we can expect prices roughly to double. It's a scarcity thing: When money becomes less scarce, it becomes less valuable. There is no question about it.

But the famous graph is junk. It is not evidence. It is just bad arithmetic.

Everybody says the graph shows that the quantity of money relative to output follows a path almost identical to the path of prices. Okay. I don't have a problem with the economics. I have a problem with the math.

The first thing we did, after we got our GDP numbers, was to take the inflation out of them. Everybody, or everybody that's aware of it, thinks this is perfectly reasonable. Everybody except me. I say it's this so-called correction that does the magic. It's the correction that makes "money supply relative to output" follow the same path as the CPI.

Here. Here's my proof. I'm gonna do exactly the same calculation as everybody else, except for one thing. Before I make the "correction" I'm gonna invert the deflator. And I'm gonna make the correction using the inverted deflator.

Now, if money and output are the reasons the "money supply relative to output" graph matches the CPI, then inverting the deflator will not be significant. On the other hand, if it is the "correction" that makes the famous graph match the CPI, then inverting the deflator will make our line go the wrong way. And if our line goes the wrong way, we know that the so-called correction was the source of the similarity. And in that case, the graph of money relative to output is junk.

Here's what the graph looks like using my inverted deflator:

The graph of "money relative to output" is junk.

You can access the Google Docs spreadsheet used to create these graphs.