19 February 2016

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.


  1. Hi John. Another interesting piece. Nicely complementing Jason's Bernie posts.

    "per capita would growth at about 3.2% per year."

    Should be "grow" I think.

  2. O/T: John, are you familiar with Mark Blyth or his views? Any opinion?

    1. I hadn't heard of Blyth until you told me about him. I looked him up and watched one of his lectures. He seems interesting, but his focus on Keynesianism vs. other schools of thought seemed a little strange to me.

      I used to think that academia was split along the lines of "Keynesians" and "Austrians," but I've since then realized that the only people worth taking seriously are under the neoclassical umbrella -- this includes everyone from Paul Krugman to Stephen Williamson.

      Otherwise, I thought it was interesting that he classifies the Great Recession and its aftermath in Europe as a political problem instead of an economic one. I'm not sure I agree with his reasoning, but I'm inclined to agree with him, if only because I agree with Wren Lewis who presents austerity as political opportunism as well.