## Monday, August 13, 2012

### Comparing the six measures of unemployment

Some two years ago, I wrote a post about comparing the six measures of unemployment the Bureau of Labor Statistics measures.  After I read Evan Soltas' post today about unemployment, and since it's been, well, two years, I thought I'd revisit the subject and add some sexy graphs to my original analysis.

### Unemployment

Unemployment can be a sticky topic.  It seems simple enough at first blush: If you have a job, you're employed.  If you don't have a job, you're unemployed.  But when you start to think about it (as you do in your first semester of macro), you realize that you have to be a little bit more careful.  Should a three-year-old count as "unemployed"?  Perhaps in the broadest sense, but probably not for macroeconomic policy-makers.

What about people with college degrees who, say, could only find work at Kroger?  If I have a BS in physics and I'm swiping items at a cash register in a supermarket, I'm obviously not unemployed, but I'm not really employed, either.

What about people who lost their jobs, looked for a new job for two years, and then gave up?  They're not even looking for jobs, but if the economic situation brightened, perhaps they would start again -- do they count as unemployed?

To answer these questions, economists have developed the notion of the "labor force" and various measurements of unemployment.  The labor force is a rough measure of how many people the economy has available for work at any given time.  If you've looked for a job in the last four weeks, or you have a job, you're in the labor force.  Usually, the labor force comprises 60-70% of the country's population.  (Note that even the definition of the labor force can be debated: should someone who has stopped looking for work because of a downturn be counted as a member of the labor force?)

"The" unemployment rate, then, is a measure of what proportion of the labor force has a job.  I put "the" in scare quotes because, as we saw, there are many different, but related, ways of defining the notion of "unemployment."  There are, correspondingly, many ways different, but related, measures of unemployment.

### The six measures of unemployment

The Bureau of Labor Statistics (BLS) maintains six different measurements of unemployment.  They are creatively named:

• U-1: The proportion of the labor force who have been unemployed for 15 weeks or longer.
• U-2: The proportion of the labor force who have lost jobs or done temp work.
• U-3: The official unemployment rate (this is the number you see in the headlines at the start of each month): The proportion of the labor force who have lost jobs.
• U-4: The proportion of workers who are in U-3, or who are not looking for a job because of economic conditions.  (These workers are called "discouraged workers.")
• U-5: The proportion of workers who are in U-4, or who would like to work and can work but are not seeking work.
• U-6: The proportion of workers who are in U-5, or who are employed part-time and would like full-time work, but cannot.
U-1, U-2, and U-3 operate in the labor force as I defined it above.  U-4, U-5, and U-6 all expand the labor force to include people who are "marginally attached" to the labor force: unemployed individuals who would like to participate in the labor force but are not currently looking for work.

Here is a graph of all six unemployment rates since 1994:

Observe that they all move more or less together.  This suggests that perhaps they all tell more or less the same story.  If I know the headline unemployment rate, just how much of the other unemployment rates can I figure out?

The BLS data are accessible from the link above.  In my previous post, I looked at the data (then, through 2010) and found the following:
$U_1 = (0.76 \pm 0.01)U_3 − (2.31 \pm 0.07)$
$U_2 = (0.78 \pm 0.01)U_3 − (1.47 \pm 0.05)$
$U_4 = (1.066 \pm 0.003)U_3 − (0.09 \pm 0.01)$
$U_5 = (1.099 \pm 0.005)U_3 − (0.43 \pm 0.03)$
$U_6 = (1.70 \pm 0.07)U_3 − (0.3 \pm 0.1)$
That is, if at any point between 1994 and 2010, you know the headline unemployment rate U-3 (currently $$8.3$$%), you can compute the other five unemployment rates with reasonably high precision.  For example, U-6 should be near 13.8%.  In fact, it is currently 15.0%.

### Graphs

I went back and grabbed the data again, but this time, instead of running regressions on them, I just made some pretty pictures.

Here is a graph of U-3 against U-1 since 1948 (which is how long the BLS has been measuring both of them):

Interesting patterns, eh?  There's definitely a positive correlation, just like you'd expect, but it does some wandering too.  I chalk that up to structural and demographic change.  What would happen on a shorter time scale?  Well, the BLS has only been measuring U-4, U-5, and U-6 since 1994.  To stay consistent, let's only consider U-1 and U-2 against U-3 from 1994.  Here is a graph measuring all five against U-3, 1994-2012:

Neat, isn't it?  You can see that there is a strong linear relationship between each of the other unemployment rates and the headline rate of unemployment.  To highlight that linear relationship, here's a graph of each of the five alternate timeseries divided by the headline rate:

### Discussion

Let's refer back to the graph of all unemployment rates as well as to the graph of the ratios of the unemployment rates to U-3 and see if we can make some sense of them.

Several interesting things have happened since 2008.  First, U-1 has risen almost exactly to U-2.  Since both use the same definition of "labor force", it suggests that the proportion of the labor force which is long-term unemployed has risen.  We might perhaps think that U-1 and U-2 are measuring the same people, but we cannot conclude that from these data.

Second, U-4 has stayed exactly proportional to U-3.  This indicates that the labor force "breathes": change in the number of discouraged workers moves in direct proportion to the change in the number of unemployed workers.  This is all the more interesting because there has not been any measurable change in this during the 2008 recession.

Meanwhile, third, there has been a visible change in the proportion of U-5 and of U-6 to U-3.  This indicates that while workers become discouraged in proportion to becoming unemployed, during a recession workers become slightly more reluctant to move further from the labor force (or to become underemployed? or workers who move beyond discouraged actually become less than marginally attached?).  The same phenomenon is visible with U-6 during the 2001 recession, when it fell in proportion to U-3 and only slowly moved back up to levels it reached during the 1990s.  It fell again in 2008, and is inching back up as the economy slowly recovers.

Evan Soltas, in the post that inspired this one, pointed out that unemployment rates do not capture changes in the labor force participation rate.  He is probably correct in this - the unemployment rates can only indirectly see labor force participation rates by measuring the spread across different definitions of the labor force, and then only as in a mirror darkly.

Later he posited that perhaps the broader definitions of unemployment, U-4, U-5, and U-6, might better catch changes in labor force participation.  They won't; they move in close to lockstep with U-3 (especially U-4).  The only glimmer of changing labor force participation rates might be in the deviations of U-5/U-3 and U-6/U-3 over the course of the business cycle.

### Conclusion

To answer the original question, since all six measures of unemployment are very tightly correlated, they all convey roughly the same information.  (This is not a vacuous statement! It is an observation about the behavior of the labor force, and working-age population in general, through the business cycle.)

By looking closely, we do see that the rates do convey information that differs in the details.  For instance, U-1 and U-2 do not track U-3 as closely as U-4 does.  Perhaps we can see underlying facts about demographics and labor force participation from these subtle differences.  But on the whole, any structural changes in the economy are only dimply reflected in these unemployment rates.  They do track each other closely!

Addendum: There is some question about whether U-3 should be "the" unemployment rate reported in headlines -- whether U-4, U-5, or U-6 more accurately captures what people mean when they informally discuss "unemployment" -- but that's not what I mean here.  What I mean to say is that if you know the relationships between the other Us and U-3, then when you hear the U-3 rate announced, you can get a good idea of what the spread of the unemployment rates looks like.

I also don't mean to imply that Evan is wrong in his assertion that the unemployment rate is incomplete information.  Declining labor force participation rates are very important pieces of information - in fact, the labor force participation rate (or the employment:population rate) should be announced in conjunction with the headline unemployment rate to indicate whether the cause of change in the rate is worker sentiment, a change in the rate of job creation, or both.