Saturday, September 22, 2012

The Uses of Fake GDP (1): Evidence of Inflation

All the graphs in this post are FRED graphs, because FRED graphs are trustworthy.

Graph #1 is my attempt to duplicate Figure 1 from Milton Friedman's book Money Mischief. The graph compares "money per unit of output" to a measure of prices that Friedman described as "the deflator implicit in computing real national income"1 for the United States. My measure of prices, the blue line on Graphs #1, 2, and 3, is the "Implicit Price Deflator" from FRED.

For "money" Friedman used "the total designated M2 in the United States". I have used M2NS (M2 money, not seasonally adjusted) from FRED. Finally, for "output" Milton Friedman used "real national income". I didn't find measures of National Income at FRED, so I am using "Real Gross Domestic Product", the FRED series GDPC1.

National Income is slightly less than Gross Domestic Product. GDP is slightly more than NI. Assuming the same deflator is used to remove price changes from National Income and GDP, "real GDP" is slightly more than "real national income". Dividing M2 money by real GDP gives a result that is slightly less than Friedman's result. My result is the red line on Graph #1.

On the graph you can see the red line is a bit lower than the blue line representing prices. A slightly higher result would have been a better match. You can applaud Friedman for selecting the number set that best shows that printing money causes inflation; or you can say he did a little fine-tuning by picking the version of output that gave him the best results.

Graph #1: Duplicating Milton Friedman's 'Money relative to Output' Graph

Graph #2: As above, with "real output" exploded into components

Graph #2 is identical to Graph #1. The only difference is in the second line of the blue border above the plot. I have replaced FRED's "real GDP" number series GDPC1 with the calculation that produces that series.

Where Graph #1's formula shows GDPC1, Graph #2 has (GDP/GDPDEF).

(Also I no longer multiply by 100 in the second formula on the top border of Graph #2, because I no longer need to compensate for the way GDPC1 was calculated.)

The red line on Graph #2 is identical to the red line on Graph #1. The (GDP/GDPDEF) calculation produces numbers identical to the series GDPC1. "Real GDP", its name notwithstanding, is calculated by taking GDP at actual prices and dividing it by the price numbers of GDPDEF.

Thus, when Friedman uses "real output" for his graph, he brings the price numbers into his results. Milton Friedman's graph uses the price series as a factor in the calculation that he compares to the price series. GDPDEF is in both lines in the blue border above the plot -- and in both lines plotted on the graph as well.

Does it matter? Yes, it matters very much. Milton Friedman faked it. If you take Graph #2 and change the second formula in that upper border by removing the price numbers, the red line changes significantly. All similarity to the blue line disappears. All similarity between "money relative to output" and the price level disappears:

Graph #3
Milton Friedman shows similarity between "money relative to output" and the price level. That similarity is artificial. It is a result of using a price series to create numbers, and then comparing those numbers to that price series.

He faked it.

Now let's do something different. Let's throw away the implicit price deflator. Let's make up a number series and pretend it is our price index. Let's see if we can create a "money relative to output" graph that shows similarity to the price index we made up.

There is a number series I like a lot. It is a measure of consumer debt, relative to Gross Domestic Product. I like it because it is easily recognizable. It has a face in it:

Graph #4: FPI, the Face Price Index

I will use this in place of GDPDEF.

I want to compare this blue line, the Fake Price Index, to the quantity of money relative to output. But this time, "fake" output. I intend to show that I can force "money relative to output" to look similar to my fake price numbers, by using my fake price numbers in the calculation of the "money relative to output" numbers.

Where before we saw GDPDEF in the formula, now we will see (CMDEBT/GDP).

As Milton Friedman did, I divide the quantity of money by fake output and compare the result to the price index used to calculate that output, looking for similarity:

Graph #5: Faking the Friedman Graph
Not bad! The red line does go high at the end, when debt was going up like crazy. But other than that, the red line fits the blue very well. As Milton Friedman might have said, it shows a lot of similarity.

The trick to making one number series similar to another is to make the one series part of the calculation of the other. To do that is cheating, of course, if you then claim that the similarity is evidence of something. To avoid being called a cheater, it is essential to hide the cheating.

One can for example bury the offending number series by dividing it into another series and giving that ratio a name. This would give the impression that the ratio is not, in fact, a ratio but is itself an independent series.

Then, to solidify the impression you create by this deception, you must choose a name for that ratio carefully. Choosing a name like "fake" might make people question your work. It is wiser, perhaps, choose a name like "real".


1. From a footnote in Chapter 8: The Cause and Cure of Inflation in Money Mischief by Milton Friedman. This is the footnote:

That word "extrapolated" bothers me. It means he made up the numbers after 1975.


Jazzbumpa said...

The Friedman part is what we discussed in email quite some time ago. I think you have it precisely correct.

Friedman cooked the numbers to make an invalid point look valid. Now, Rethugs do it every day.

Good piece of work!


The Arthurian said...

Thanks, Jazz!!