## Sunday, September 11, 2011

### The Arithmetic Problem

From the Money Growth and Inflation PDF:

When the money supply grows faster than the money demand associated with rising real incomes and other factors, the price level must rise to equate supply and demand. That is, inflation occurs. This situation is often referred to as too many dollars chasing too few goods. Note that this theory does not predict that any money-supply growth will lead to inflation -- only that part of money-supply growth that exceeds the increase in money demand associated with rising real GDP (holding the other factors constant).

The excess of money-growth over and above real-output-growth gets burned off as inflation. Makes perfect sense to me. But when you try to show it using numbers and maybe a graph, there is a problem.

You cannot convert actual-price output to "real" output without bringing the price-trend into the numbers.

After you do that, anything you do with those numbers will show the price trend. It happened with Milton Friedman's graphs. And it happens with Terry Fitzgerald's graphs. Fitzgerald sees it in his Figure 3 graphs, and thinks the graphs show a relation between money and prices. They do not.

The graphs only show a relation between prices and prices.

#### 11 comments:

Clonal said...

OK Art

I just did a correlation between the annual percent change in the CPI, and the annual percent change in M1 -- guess what!

A correlation coefficient of close to zero (0.07 to be exact Rsq of 0.006) In other words no explanatory power at all.

I am just aligning nominal gdp percent changes. So will have the results soon.

The Arthurian said...

Pretty low numbers, Clonal... Perhaps you should try the Friedman method: Multiply your M1 numbers by the CPI, and THEN figure the correlation. The coefficient should be much higher. :)

But seriously... Friedman used M2, not M1. Fitzgerald in the PDF used M2 and found similar results for M3 but not for M1.

I like M1 because it is a measure of circulating money. I think that for changes in money to cause changes in prices, the money must not only exist, but it must also be circulating. Thus, money in savings is not driving prices up.

M2 is composed of M1 and money in savings.

I think economists use M2 because (after you multiply it by the price level and divide it by nominal output) it gives a result more similar to the price level. I have never seen any other explanation of why M2 or money-in-savings would have any bearing on inflation.

There is of course the matter of lending, which may or not be related to money-in-savings, but which most certainly circulates a costly form of money.

Clonal said...

Art

Here are two graphs
Graph1
Graph 2

Just the axes are interchanged

This is % annual changes in CPI and M1

Also, very little correlation between GDP or Real GDP and M1

There is a positive correlation of 0.55 between annual change in GDP and annual change in CPI

There is a negative correlation of -0.27 between change in CPI and change in Real GDP

The Arthurian said...

Star clusters!!

Hey, I don't want to make extra work for you, but I'm wondering if the dots group up in different groups when you divide the 1960-2011 period into different periods.

Say, using Jazzbumpa's Four Realms...

What I'm picturing is groups like you can see in the second graph here when you hover onto the second graph, and hover off it.

You MUST have groupings like that, I think.

Clonal said...

Actually,

M2 shows a high negative correlation with CPI

This really kills the Monetarists

Separate the years 1960-1970; 1971 to 1983 and 1984-2011. You get three very interesting correlations all negative.

R = -0.38, R = -0.75, R = -0.20

Clonal said...

The M2 Graphs

Vietnam Years
The Oil Crisis
Reagan Plus to Now

Clonal said...

To me it appears that the solution to the oil crisis would have been to have engaged in deficit spending and increased the money supply. That would have taken care of the stagflation. The problem just like today was - Not Enough Stimulus

The Arthurian said...

"...the solution to the oil crisis ..."

Dunno... There was plenty of inflation in those years. Of course we HAVE been talking today about how inflation does not correlate to the quantity of money... Still, there had to be some kind of adjustment or rebalancing after the price of energy increased relative to everything else... Dunno.

Hey, if you have the energy, I have one more for you to check: the correlation between annual percent change in CPI and annual percent change in Total Debt, FRED TCMDO or something.

Jerry said...

Are these year-by-year comparisons? I guess I think that it might be a good idea to do an average over several years (by 5-year-bracket or by decade or something). For instance, if growth in money caused inflation, but it took a year for it to happen, I think this graph wouldn't show that correlation, right? Or maybe, it would show it but it wouldn't be as obvious as one would like (it'd be going around in a circle or something instead of making a x/y correlation). So, I think that might be useful to try out.

Clonal said...

Jerry,

These are month by month comparisons of the %age annual change. So the XY scatter and correlation is a perfectly valid way of looking at the data. There is always a possibility of lagged effects, but that is a much poorer explanation, as there appear to be no lagged effects when looking at M1, the most liquid money.

When using M2, there are artifacts that could be interpreted as cyclicity between 1972 and 1983, but when you look closely at the data, the spike in inflation is explained by the two oil crises, which were actually not price or money related phenomenon, but rather were large disruptions in the oil supplies.

The high negative correlation between changes in inflation and changes in M2 is easily explained by savings expanding M2 as a consequence of inflation. In other words, in periods of high inflation, less money is available for saving, and more is available when inflation is low.

The Arthurian said...

re: lagged effects and five-year-brackets...

The original PDF that Jazz turned up was an analysis of 2-year, 4-year, and 8-year lagged relations, to answer the question, "How long is the long run?"