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.

In Which I Do Some Bad Econometrics

I decided I would do a linear regression on the growth rate of real GDP per capita (RGDPPC) with respect to the change in the Civilian Employment to Population ratio (EPOP). I used the period between 1950 Q1 and 2015 Q3 and came up with this result:

Vertical Axis: RGDPPC growth, Horizontal Axis: Change in EPOP

So, a linear regression suggests that the relationship between RGDPPC and EPOP is

$$(1)\:100\Delta\ln{y_t} = 2.458 \Delta e_t + 1.9333$$
where $y_t$ is real GDP per capita and $e_t$ is the Employment to Population ratio.

With this relationship, we can make some interesting predictions. It has recently been popular to argue that the employment to population ratio can and should be raised to its April 2000 high (coincidentally, I was born in April 2000). If this were to occur, it would mean that the Employment to Population ratio would go up by 5.1%, which corresponds to an increase in real GDP per capita of about 14.5%. Or, if the change were to take place over ten years, then real GDP per capita would grow at about 3.2% per year.

Given ~1% annual population growth, this could make the extravagant economic promises by the likes of Bernie Sanders and Jeb Bush seem in reach. After all, all we need do is employ as many people as we were in 2000. Unfortunately, it is not that simple. First of all, there are reasons to believe that some, if not most, of the decline in EPOP over the last 16 years is secular. Namely, the working age population (i.e., population between 15 and 65 years of age) has increased a lot less than total population in the last few years. In fact, the Employment to Working Age Population ratio has recovered pretty well since the Great Recession:

Now, there's definitely still a gap; employment still has room to grow, but now at least, it should be clear that there was a lot of over-employment by the end of the Clinton administration. It appears as if the equilibrium Employment to Working Age Population ratio is closer to 74% than 77%, which means that there are a lot less employment gains to be had than a simple look at the EPOP would suggest.

The other issue with both Senator Sanders' and Governor Bush's plans is that it's unclear how they would actually raise the employment to population ratio. In the case of Sanders, programs like expanded Social Security and free college tuition would probably lower the Employment to Population ratio (since we'll be paying people more to retire and getting an education will be so cheap that students won't need to work, or can leave a job to get a degree). With Governor Bush, there is at least a case to be made that significantly lower taxes might incentivize millions of Americans who were otherwise not going to work to now go out and get a job, but I don't really see it.

Yes, a government can increase employment by reducing the labor tax in a simple neoclassical model, but how much does that really map to determining whether or not someone is even in the labor force. Honestly, the tax rate that someone has to pay may lead to changes in hours worked, but says little as to whether or not they work in the first place; to argue that because the tax rate goes down, all of a sudden people who refused to work at the previous after tax wage will now start searching for jobs seems nonsensical. I can see people increasing their hours if they are all of a sudden paid more for work, but not leaving the labor force altogether because taxes are too high or joining it because they are now low.

On top of that, key to the success of any supply side reform is whether or not the lack of employment is voluntary; if people who are unemployed actually want to be employed, then a tax cut won't change anything relating to their job search, whereas, if the people who are not employed are in that state by choice, then a tax cut might make them reassess (personally, I think the case for this is really weak, but I'm open to it). The key question is, then, was the non-secular part of the decline in the EPOP in 2008 caused voluntary or involuntary. There are those that disagree, but personally I think that the obvious answer is that the decline was involuntary. If this is the case, the degree to which supply side reforms would be beneficial is probably low.

So, by now I've spent most of this post complaining about Governor Bush's promise of 4% growth even though I find the crimes of the Sanders campaign more egregious. For this apparent injustice, I offer the following explanation: the reason Bernie Sanders' proposals would fail to create an employment boom is extremely easy to understand, whereas Bush's plan requires a much more in depth criticism to be understood. Regardless, both 4% growth and 5.3% growth are almost equally absurd and no one wishing to be on the side of sane economic analysis should support either claim.