## Friday, March 27, 2015

### Potential RGDP and forecast RGDP

Brad DeLong had a post up a month ago on a study (well, blog post) of the various forecasts of potential RGDP and their changes over time. He quotes the study's (well, blog post's) authors Cecchetti and Schoenholtz:
We should all be wary of anyone who claims to be able to forecast trend growth accurately and reliably. Even after the fact, it takes some time to discern the underlying trend.
I (sort of) reproduce the authors' chart 2 (shown at DeLong's link), and add the information transfer model (ITM) trend in gray derived from the partition function approach:

Note that potential RGDP isn't some sort of speed limit, although there are some interpretations that are more like one. Like the Fed's estimate of potential RGDP, the ITM trend isn't a speed limit -- it's more of an equilibrium level above which there is a greater tendency to fall.

With the exception of 2000-2015 [1], the ITM lines up relatively well with the Fed's estimate. Of course, both of these measures are looking at trends in the roughly the same data so this overlap is not surprising. It's the differences that are interesting.

One way to interpret these two measures over the past 30 or so years in the graph is that both the ITM and the Fed say the 1990s dot-com boom was sustainable (it was recovery from low performance after the financial crises of the late 1980s and early 90s), but they differ on the housing boom of the 2000s. The ITM effectively says that boom was unsustainable [2], while the Fed's estimate shows potential RGDP decaying away -- as if something could have been done in the aftermath of the 2008 financial crisis.

One useful feature of the Fed's estimate is that the differences between potential and measured RGDP match up with the unemployment rate (modified by the "natural rate"):

This is not true in the ITM. However this is not much more than Okun's law (already a part of the ITM) -- changes of RGDP relative to any smooth baseline will result in a pattern that looks like the unemployment rate because changes in RGDP and changes in employment are correlated (i.e. Okun's law). The Fed's version does this without a derivative -- the absolute difference between potential RGDP and actual RGDP is proportional to the unemployment rate. Mathematically we have the Fed's

$$u \sim RGDP - RGDP_{p}$$

versus the ITM's

$$\frac{d}{dt} \log u \sim \frac{d}{dt} \log (RGDP - RGDP_{p}) \sim \frac{d}{dt} \log RGDP + c$$

where we've used the smoothness of potential RGDP to reduce it to a constant $c$.

Footnotes:

[1] And in the longer view, there's a discrepancy between the Fed's estimate and the ITM for 1960-1980. Here is the longer view:

[2] Actually, the ITM hints that the boom (and its inevitable bust) was caused by Fed policy.

Update 4/8/15: For the comments below, the Fed effectively begins raising interest rates in 2004 or 2005 (both long term and short term interest rates) relative to where they would have been if monetary policy had followed a linear trend. The relevant posts are here and here and here are the two relevant graphs:

1. Very interesting. One implication of the ITM analysis might be that the housing boom (bust) really was Greenspan's fault. Also, the idea that "unsustainable" growth can be identified real time might be an important one.

1. Hi Todd,

Sorry for the delay in getting back to you ...

One of the weird things is that it was a relative rise in interest rates coincident with the bubble.

I've mentioned this before, but it appears that the traditional view of monetary policy where interest rate rises stifle investment is not actually accurate. Interest rate rises are like piling more snow on a hillside until it causes an avalanche (or stalling an aircraft to lose altitude).

In that sense the easy money of the 90s held the path of NGDP below trend and the tighter money of the Bernanke era was worse.

It's something of a counterintuitive view, and may not be correct. It does put the 80s and the 2008 crisis in the same framework, though.

2. Another way to see it: NGDP above trend means interest rates are also above trend.

3. Hmm not sure I see the relationship with regard to interest rates in your graphs for this post, but I will take your word for it.

4. You are correct. It's not actually in that graph ... it is here though:

http://informationtransfereconomics.blogspot.com/2014/08/are-interest-rates-good-indicator-of.html

5. The Fed started raising short-term interest rates in 2004 but long-term rates (on 10 year Treasury bonds or 30 year fixed mortgages, foe example) pretty much stayed the same for the next few years.

6. It's actually a relative rise in rates compared to a linear trend (I added some graphs and an update to the post above). Effectively the monetary base rose more slowly than it had leading to higher rates (both long and short term) than they would have been had the monetary base continued along the linear path from before 2004.

In the information transfer model, that is. At the time there was little difference between the monetary base and its currency component (reserves were small), so as the base grew more slowly, both long and short rates effectively rose.

The noisy fluctuations in the data obscure the rise but its there, at least for the 10 year, 3 year and 3 month rates ...

http://research.stlouisfed.org/fred2/graph/?g=170X

2. Very interesting. One implication of the ITM analysis might be that the housing boom (bust) really was Greenspan's fault. Also, the idea that "unsustainable" growth can be identified real time might be an important one.