## Tuesday, December 17, 2013

### Worst-Case Unemployment and the Output Gap

Part six in a series that starts here.

A while back I looked at The Myth of 'Jobless Recoveries', Okun's law, and Hodrick-Prescott calculations.

The Hodrick-Prescott calc can be used to smooth out a data series like GDP or the unemployment rate. It smooths out the ups and downs of the business cycle so you can see the underlying trend.

Okun's law says there is a consistent relation between unemployment and output. It says when output drops one percent below trend, unemployment rises half a point above trend. When output rises one percent above trend, unemployment falls half a point below.

These "trends" that are part of the Okun's law calculation -- you can use the Hodrick-Prescott calculation to get them.

Now... Here is what I did, a while back, in a follow-up post, after first vehemently denying that such calculations are reasonable:

I took the unemployment numbers from FRED and figured the HP trend for unemployment. Then I set the original unemployment numbers aside.

I took the Real GDP numbers from FRED and figured the HP trend for Real GDP. Then I subtracted the trend from the original numbers. This gave me a measure of how far Real GDP was off its trend.

Then I took those off-trend numbers and divided them in half. In half, because Okun's law says what happens to unemployment is half as big as what happens to output. So I just scaled the off-trend output values down to fit the unemployment rate.

Then I took those scaled-down output values and added them to the underlying trend for unemployment, the Hodrick-Prescott trend. Subtracted maybe, I forget.

Then I took these unemployment-trend-plus-off-trend-output numbers and put them on a graph along with the original unemployment numbers. The idea -- which I got from the Myth of Jobless Recoveries post, was that if the two lines turned out similar, it was evidence that there is a strong, reliable relation between unemployment and real GDP.

The two lines turned out similar. Despite my initial objections, I was forced to admit the arithmetic was good, and I learned of the strong, reliable relation between unemployment and real GDP.

Here's what I'm thinking: If there is a strong, reliable relation between unemployment and real GDP, then we should be able to compare gaps. We should be able to look at the gap between official unemployment and "worst-case" unemployment, and look at the gap between real and potential GDP, and maybe see something interesting in the two gaps. I'm thinking we can use the output gap and the unemployment gap to establish whether those calculations are valid.

At the start, I was thinking I could use those gaps to establish that at least one of the data series is not valid. Maybe to show that the revised-down version of Potential GDP is wrong. That would be interesting. But I'm no longer sure I could pull that from the numbers.

I need some time with this. I want to set this topic aside for a while and come back to it later. I've been sitting down to write the next posts in series, but end up writing other things. It's just not there, yet.

Meanwhile, if anyone else is looking into this, do let me know.