Friday, November 29, 2013

The Output Gap Closes in 2014

Enlarged Portion of Yesterday's Graph
Thursday's post left me with questions. At right, in the enlarged detail of yesterday's graph, note that the most recent values for Potential GDP line up nicely with the "real GDP" values in black, where the black line ends. A remarkable coincidence, isn't it?

It's almost like they planned it -- gradually lowering their estimate of Potential Output, and at the same time having that very nice Comprehensive Revision that pushed RGDP up. Almost like they planned it. Couldna ben. Musta benna coincidence.

Below is an ALFRED graph showing the most recent Potential GDP (red) and the last set of RGDP values from before the Revision, both in 2005 dollars. (RGDP switched from 2005 dollars to 2009 dollars in the Comprehensive Revision of 2013, but Potential GDP was left in 2005 dollars, so at FRED the two series are not directly comparable.)

Graph #1: Current Potential GDP (red) and the last RGDP given in 2005 Dollars
Relative to Potential GDP, the blue RGDP here is still much lower than the black RGDP in the enlarged view from yesterday's graph. Significantly lower.

I went back to FRED and checked: The current version of Potential GDP is the 2013-02-05 version. It's the same version in the ALFRED graph and in the clip from yesterday's graph. So, it's not Potential GDP that's different. It is real GDP that differs in the two pictures.

I'm wondering why, and I have a thought. I think it's because of the other changes to RGDP that were made during the Comprehensive Revision, the changes other than changing the base year. (I have some notes on the revision here.)

I see a note on the FRED GDPPOT page:

The CBO (source of the potential GDP data) does not have the necessary data to complete the rebasing of the gdp projections. The data availability have been even more delayed due to government shutdown.
The next issue of the Budget and Economic Outlook will be published in early 2014.

Wow. I never saw FRED make excuses before.

But that's okay. I can do the "rebasing" right now. Let me take Graph #1 and add the incompatible RGDP to it, in green:

Graph #2: The Latest Data for RGDP, base year 2009 (green) added to Graph #1
The green line shows 2009 dollars, which were worth a little less than 2005 dollars. To buy a given amount of stuff, it takes more 2009 dollars than 2005 dollars. That's why the green line runs higher than the blue line.

But really, the green line shouldn't even be on the same graph with the red and blue lines, because the dollars are not the same. (If you make graphs, you have to watch for things like that.) In what follows, I make the dollars the same.

I was saying, I had a thought. Maybe the difference in RGDP is due to the comprehensive revision of 2013. Or maybe it is due to some error in the way I converted between base years for yesterday's graph.

Here's what I did: Take each RGDP value. It is expressed in 2009 dollars. Divide the 2009 price level out of it, and multiply the 2005 price level into it. Now it is expressed in 2005 dollars. That's how I always do it. Maybe I always do it wrong? That's something I would want to know.

I'll do the conversion again. I need the Deflator numbers for 2005 and 2009. The next graph shows those numbers expressed as annual values. The blue bars show the average of four quarterly values; the red show end-of-period values.

Graph #3: Average (blue) and End-of-Period (red) Deflator Values, 2005-2009
The data in an Excel file from FRED
See how for the 2009 values, the blue bar stops just at the 100 level, and the red bar is a little off? Makes me think that the blue -- the average of quarterly values -- is what the professionals use when they do this kind of figuring.

That's what I'll use, then.

The average for 2005 is 91.985. The average for 2009 is 100.000. To convert 2009 dollars to 2005 dollars, I'll divide by 100.000 and multiply by 91.985. (So, for example, something that cost $100 in 2009, divide by 100, multiply by 91.985, it cost $91.99 in 2005 dollars.)

Now I can take Graph #2, take the green line, divide out the 2009 prices, and multiply in the 2005 prices. That'll put everything in 2005 dollars. Then we can compare the green (comprehensively revised) RGDP and the blue (pre-revision) RGDP, and maybe see something interesting.

(It takes a while to work up to interesting, some days.)

Graph #4: Like Graph #3, but with the Green Line converted to 2005 Dollars
The green (revised RGDP) line is only a little above the blue (unrevised) line when both are expressed in the same dollars.

More interesting -- I did promise you interesting, didn't I -- the most recent years of the revised RGDP now show a smooth transition to the red line representing Potential GDP. Exactly like the black RGDP line in the enlarged view at the top of this post.

So I'm satisfied now that I didn't mess up the base year conversion. I'm satisfied that the remarkable coincidence that puts RGDP and Potential GDP back on the same path is something in their numbers, not in mine. And I'm satisfied this post is now interesting.

Graph #1 shows the last pre-revision real GDP running far below the latest estimate of Potential GDP, leaving a massive output gap. Coincidence or no, Graph #4 shows that because of the "Comprehensive Revision", the output gap has closed.

Enlarged Detail from the "Click-On" version of Graph #4
There was a comprehensive revision of economic data in 2013. In the case of "real GDP" certain things were added, causing the number to rise. Meanwhile, CBO has been gradually lowering their estimates of Potential GDP.

These changes work together to reduce the size of the output gap. But because the base year for RGDP changed from 2005 to 2009, and the base year for Potential GDP did not change, the reduced size of the output gap has been hidden from view.

Because the two series have different base years, one cannot make a simple comparison. And the base-year difference complicates the relation between the numbers, so that an analysis is liable to discover things other than what we have discovered here today.

Finally, instead of "rebasing" the numbers to make the two series comparable, FRED offers excuses for the failure to rebase. They suggest it will get done "in early 2014."

Hey, I'm just a hobbyist, I know, but "rebasing" is not the same as a comprehensive revision. Rebasing is just a matter of changing the base year. You know -- divide by one year's price number, and multiply by another. Kids learn how to do that kind of arithmetic in the third grade.

The simple rebasing performed in this post allows us to compare the comprehensively revised RGDP and the unrevised RGDP, in order to see the changes other than price changes. It allows us to see the "real" changes in real GDP. (Is that too much to ask?)

This simple rebasing also allows us to compare real and potential GDP, and to see that the output gap will close the moment real and potential output are expressed in terms of the same base year.

The output gap closes in 2014 when Potential GDP is rebased, because of the revisions that pushed real GDP up and potential GDP down.

By accident or by design, recent changes to real and potential GDP bring the paths of the two lines together, closing the output gap and making things "normal". Before long, then, we shall again be thinking of things as normal, and the present-day concern with output gaps and under-performing economies will all be well behind us. We shall live again, as happy as Stepford wives.

And those of us who know better will have no leg to stand on.