## Saturday, March 14, 2015

### Leaving things out

Jim writes

I see the period from the mid 1960's to the early 80's as a period where household debt stayed about proportional to GDP after that it increased faster than GDP.

He provides this graph:

I have taken the liberty of putting start- and stop-points on the graph so we can talk particulars. For the 1960s I went with a high point. For the 1980s I stopped just before the big increases begin. Just by eye.

For the dates shown, household debt increased from 44.6% of GDP in 1964Q4 to 46.0% in 1984Q3. (You have to multiply by 100 to get percent.)

Okay, I'll agree that household debt stayed "about proportional" to GDP during that time. Heck, I'd even go so far as to call it "stable". I'm easy.

But I want to go back to FRED and look at the numbers. I want to look at the numbers for household debt and for GDP separately, for the dates shown. And I want to take GDP and separate the wheat from the chaff. I want to separate the increase in real product from the increase in prices. That's common practice you know. FRED has those numbers already. Jim drew conclusions without looking at them. I don't have that kind of confidence, myself.

I gathered up some data in a FRED graph -- http://research.stlouisfed.org/fred2/graph/?g=14a1# -- picked out what I wanted between episodes of Luther, and here we are.

The first column is labels. The second column is the debt-to-GDP ratio from Jim's graph. It shows the same values as the graph above, except they're rounded: 44.6% in 1964 and 46.0% in 1984.

It also shows the 1984 value is 3.1% more than the 1964 value (the 1984 value is 1.031 times the 1964 value. You see it in the row labeled "Increase".)

The next two columns show the debt and the GDP values separately. For household debt, the 1984 value is a little over 6 times the 1964 value. For GDP, the 1984 value is a little under 6 times the 1964 value. The two "Increase" values are not far apart. That's why the CMDEBT/GDP Increase is very close to one.

But the CMDEBT Increase is a little bigger than the GDP Increase, so the CMDEBT/GDP Increase is a little bigger than one.

Now it gets interesting. The last two columns show RGDP ("Real" or "Inflation Adjusted" GDP) and GDPDEF, which is the inflation they took out of GDP to get RGDP.

The increase in RGDP between 1964 and 1984 is 1.941. That means if you take the 1964 value and multiply it by 1.941 you get the 1984 value, or a number that's only off by a rounding error.

If the 1984 value was exactly twice as big as the 1964 value, the RGDP Increase number would be 2.0. But it is a little less than that, at 1.941. That means the 1984 value is a little less than twice the 1964 value. Almost twice as much, but not quite.

So now we know that CMDEBT (household debt) increased 6-fold or a bit more. And we know that real output almost doubled but not quite. In round numbers, CMDEBT increased by a factor of 6 and RGDP increased by a factor of 2.

And the last column shows that GDP Prices increased by a factor of 3 (or just a hair over). So now you know what happened: In the 20 years between 1964 and 1984 Real GDP doubled, prices went up by a factor of 3, and household debt increased by a factor of 6.

When you look at nominal GDP, like Jim does, you are looking at Real GDP with the price increases stuffed back into it. RGDP increased by a factor of 2. Multiply that by the 3-fold price increase, and it tells you that GDP (nominal GDP) increased 6-fold. That's close to the 5.853 shown in the table.

And yes, the increase in household debt was also a 6-fold increase. Both that debt and the GDP increased about 6-fold. So as Jim says, "household debt stayed about proportional to GDP". However, the 6-fold increase in debt was all debt. The 6-fold increase in GDP was one-third an increase of output and two-thirds an increase in prices.

Jim left that part out.