Wednesday, March 15, 2017

Principal component analysis of jobs data

Narayana Kocherlakota tweeted about employment making a random claim about the "steady state" employment growth that seems to come from nowhere which inspired me to do something I've been meaning to do for awhile: a principal component analysis of the Job Openings and Labor Turnover time series data ('JOLTS'):

I used a pretty basic Karhunen–Lo√®ve decomposition (Mathematica function here) on several seasonally adjusted hires time series from FRED (e.g. here). For those interested (apparently no one, but alas I'll do it anyway) the source code can be found in the Dynamic Equilibrium GitHub repository I set up. Here's the result (after normalizing the data):

The major components are the blue and yellow one (the rest are mostly noise, constant over time). I called these two components the "cyclical" (blue) and the "growth/decline" (yellow) for fairly obvious reasons (the growth/decline is strongest after 2011). It's growth or decline because the component can be added with a positive (growth) or negative (decline) coefficient. Here are how those two components match up with the original basis:

The story these components tell is consistent with the common narrative and some conventional wisdom:

  • Health care and education are not very cyclical
  • Health care and education are growing 
  • Manufacturing and construction are declining  

Here's health care on its own (which looks pretty much like the growth/decline component):

And here's manufacturing (durable goods):

To get back to Kocherlakota's claim, the "steady state" of jobs growth then might seem to depend on the exact mix of industries (because some are growing and some are declining) and where you are in the business cycle. However, as I showed back in January, total hires can be described by constant relative growth compared to the unemployment level and the number of vacancies ‒ except during a recession. This is all to say: it's complicated [1]. 

PS Here are all of the components (here's a link to my Google Drive which shows a higher quality picture):


Update 16 March 2017

I added government hiring, normalized data to the mean, and standardized the output of the algorithm. The results don't change, but it looks a bit better:

Here are the two main vectors (standardizing flipped the sign of the growth/decline vector):

And here's the original data, updated with the new data points released today (I subtracted the census peak by interpolating between the two adjacent entries):



[1] Although I'm still not sure where the 1.2 million jobs per year comes from; here's the employment change year over year:
The bottom line is Kocherlakota's 1.2 million figure. The second from the bottom is the 1.48 million rate that comes from averaging the growth rate including recessions (it's almost 1.6 million for just post 1960 data). The upper line is my "guesstimate" for the average excluding recessions (2.5 million). Maybe it was a typo and he meant 2.2 million.


  1. Kocherlakota may have been referring to the working age population (15-64), which increased by about 1.2 million annually between January 2008 and March 2015 ( or Unfortunately either FRED doesn't have the more recent data from the OECD, so I don't know about the last 2 years, but it seems relatively plausible.

    1. That is possible, but then wouldn't that imply a constant unemployment rate if jobs were increasing at exactly the same rate as the labor force increase?

      The data is broadly inconsistent with a constant unemployment rate (except for recessions, it is pretty much almost always decreasing).

    2. The unemployment rate cannot keep decreasing forever, so it is perfectly reasonable to expect that employment will grow at the same rate as the labor force in the long run.

      Regarding constant unemployment, the rate of decline in the unemployment rate has declined significantly since it reached 5% (, so while it decreased by almost 1 percentage point in 2015, it only fell by 0.4 percentage points in 2016 and has only fallen by 0.3% since it reached 5% in September 2015.

      Also, before the 1970s, the data is more consistent with the unemployment rate falling quickly after a recession and then remaining roughly constant at a lower level until either starting to fall again or rising because of a recession. This is also somewhat visible later, as the unemployment rate was pretty much constant from 1980-81, 1984-86, 88-90, 94-96, 2002-2003, 2006-2007, and now late 2015-2017.

      Again, the unemployment rate cannot continue to decline forever, so if you take "steady state" to be "consistent with full employment" or "consistent with growth in the population able and willing to work", Kocherlakota's estimate doesn't seem too far off...

    3. It can keep decreasing at a constant fractional rate forever, however (which is the form that is consistent with the data).

      Falling more quickly from a higher unemployment rate is then expected using that model.

      What there really is no evidence for is unemployment falling to some constant rate and then staying there (in fact, the model linked above describes the "bottoming out" of unemployment after a recovery ends much better than the peaks and in that model the fractional decline only stops because another recession hits).

      I am not saying the model is necessarily the only correct one or even a correct one, just that no constant unemployment rate (even one approached at infinity) is supported by the data (except zero).


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