## Sunday, September 26, 2010

### Measures of unemployment closely track U3

This is pretty cool.

Everybody knows that the "official" unemployment rate isn't really an accurate measure of unemployment. Why? Well, it only counts people who have been looking for jobs in the last 15 weeks and haven't found them. That's such a restrictive measure of unemployment that one can't help but wonder whether the BLS is using "Lie with Statistics 101," which tells us (inter alia) to never cite a statistic that measures what you claim it's measuring.

The problem here is that "unemployment" is not a simple concept. Are people who aren't looking for jobs "unemployed"? What about people who look for jobs sometimes, but not always? People who are taking whatever they can get, instead of picking the best job for them? People who are between jobs? And so forth.

The BLS number represents essentially an arbitrary measure. It captures some, but not all, of what we mean when we say "unemployed" --- it's the best we can do with a single number. But in addition to the "unemployment rate", the BLS also tracks five other numbers of varying restrictiveness: U1, U2, U4, U5, and U6. The unemployment rate you hear in the news is called U3.

The BLS has been following U1 and U3 since 1948, U2 since 1967, and U4-6 since 1994. U6 is the most expansive measure of unemployment --- it measures not only who are unemployed individuals, but those who have taken part-time jobs for lack of anything better and those who aren't looking for jobs at all, but would start if the economy improved (the so-called 'marginally unattached').

Is it possible to figure out U4-6 for past recessions, so we can get a better picture of how past labor markets compare to today's labor markets?

Turns out, yes. Very definitely. I ran some regressions this afternoon on the BLS employment numbers and the five unemployment measures U1, U2, U4, U5, and U6 are very, very tightly correlated in the short-run with U3:

$U_1 = (0.76 \pm 0.01)U_3 − (2.31 \pm 0.07)$
$U_2 = (0.78 \pm 0.01)U_3 − (1.47 \pm 0.05)$
$U_4 = (1.066 \pm 0.003)U_3 − (0.09 \pm 0.01)$
$U_5 = (1.099 \pm 0.005)U_3 − (0.43 \pm 0.03)$
$U_6 = (1.70 \pm 0.07)U_3 − (0.3 \pm 0.1)$

Isn't that beautiful? This is from the 1994-2010 panel data. Look at how tight those spreads are! Apparently, over short (one-two decade) periods, U3 is able to predict upwards of 95% of the variation of U1-6.

This breaks down over the longer run, as you might expect. The linear correlation actually migrates slowly over time. I believe this reflects changing population demographics, such as the aging of the baby boomers, and technological change. So you can't take these numbers and extrapolate backwards with them too carelessly. However, it does mean that you can get a good idea of how past labor markets compare to this labor market just by comparing U3, and bearing in mind that the relationship between U3 and U1-6 across many decades isn't as tight as you might want it to be.