## 21 February 2016

### Potential GDP is Not Linear

Recently I've seen a few people defending the Friedman analysis of Sanders' economic plan on the grounds that 5.3% growth over a decade would be consistent with closing the output gap. They typically estimate the 'output gap' by comparing GDP to the linear trend implied by the post-WWII time series (excluding data after 2008).

This is ridiculous. I'm tempted to just stop writing here because of how obvious I think this should be, but evidently a lot of people think that potential GDP is linear. The primary problem with this  approach is that it completely ignores demographic factors. If, for instance, you decided that real potential GDP (not per capita) followed a linear trend, then you'd be suggesting that TFP automatically grows faster whenever population growth is low. Naturally, this doesn't make any sense whatsoever, so most people who want to estimate linear trends for RGDP usually go for real GDP per capita.

This has its own problems, however. If real potential GDP per capita grows at a constant linear rate, then TFP growth increases when the working age population shrinks relative to the total population (when the dependency ratio goes up) and vice versa. This also makes no sense whatsoever; to suggest that TFP grows more quickly when people have lots of children or when a bunch of people are reaching retirement age is ridiculous. It's obvious that real GDP per capita should be a negative function of the dependency ratio.

This leaves one option for a demographic-adjusted estimate of potential output: real GDP per working age person.
The output gap that can be extrapolated from this is a lot more sane than the predictions of some of Sanders' defenders -- it's about 9%, but I still have a problem with inferring linear trends from demographically adjusted potential output.
See, my approach so far basically assumes constant TFP growth (which is a whole lot less stupid than TFP growth that changes with population growth), but I don't even think this is really that fair of an assumption. To argue that technological progress always occurs at the same rate and with the same fervor doesn't make any sense.

That being said, I think the best (only) way to measure the output gap is to use some labor market indicator. For some reason, a lot of people seem to hate the unemployment rate for this, so I'll use the employment to working age population ratio:
This suggests that we are pretty close to full employment, but not quite there yet. That's a completely different story from what Sanders supporters (and most people in the GOP) are saying. Granted, I think this approach has its own flaws -- I think it drastically overestimates the output gap in 2000, but it seems to give a pretty good estimate of where the output gap is right now; i.e., somewhat understated in absolute value terms by the unemployment rate, but overstated by the employment to population ratio.

Needless to say, no one should listen to anyone who thinks real potential GDP per capita follows a linear trend.

Update:

Nick Rowe suggested in the comments that I come up with a projection for potential GDP given estimates for the working age population over the next few years. I used the US Census Bureau's estimates for population between 14 and 64 years old and assumed the 14-year-old population will be constant over the next few decades (it's a shortcut, I know, but I can't be bothered to find a better estimate of the future working age population) to get my projections for the working age population. I then took the real GDP to working age population ratio, got the trend growth rate between 1989 and 2007, and extrapolated that to 2026 to get my potential GDP per working age person value.

Then I multiplied the whole thing by the time series for the working age population (including the projected values until 2026) to get potential GDP. Here is my estimate of potential GDP to 2026 compared with the CBO estimate and actual GDP (going up until 2015):
Update #2:

I thought I'd add this comparison between my estimate of potential GDP and what potential GDP would be if it followed the 1990-2007 trend here:
Also I realized I made a couple mistakes when removing the 14-year-olds from the Census Bureau projection. All the graphs on the blog are updated, but not the ones on Twitter, so don't take them from there if you want to use them.