The Atlanta Fed's macroblog provides commentary and analysis on economic topics including monetary policy, macroeconomic developments, inflation, labor economics, and financial issues.

Authors for macroblog are Dave Altig, John Robertson, and other Atlanta Fed economists and researchers.

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October 12, 2012

The (Maybe Not So) Simple Arithmetic of Unemployment and Labor Force Participation

I have precisely zero interest in jumping into any fray from the before and after of Wednesday's Wall Street Journal opinion piece by Jack Welch, wherein he defends his previous comments on the reliability of reported unemployment statistics. But there is one particular statement in that editorial that offers up what is sometimes called a teachable moment, to wit,

By definition, fewer people in the workforce leads to better unemployment numbers.

By definition, that's not really correct. Consider a really simple example. Suppose:

Population = 200

Number of Employed People = 92

Number of Unemployed People = 8

Labor Force (Employed + Unemployed) = 100

In this example the labor force participation rate is 0.50 (the labor force divided by the population) and the unemployment rate 0.08, or 8 percent (the number of unemployed divided by the labor force).

Now suppose that five people drop out of the labor force (which would mean that labor force participation would decline from 0.5 to 0.475). What happens to the unemployment rate? Well, it depends what those 5 people were doing before they left the labor force. If they were unemployed, then unemployment falls to 3, the labor force falls to 95, and the unemployment rate is about 3.2 percent (or 0.0316 times 100). But if the 5 people who dropped out the labor force had been previously employed, the unemployment rate would actually rise to about 8.4 percent (because the number of unemployed would still be 8, but it would now be divided by 95 instead of 100).

Hope that clears it up.

Note: You can take a look some actual data on flows into and out of employment, unemployment, and not in the labor force here.

David Altig By Dave Altig, executive vice president and research director at the Atlanta Fed

October 12, 2012 | Permalink


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Dave - thank you for this example. It is simple and to the point and does a great job explaining the numbers "behind" the numbers in this situation. I recommended it to a teacher and her students and they found it to be very helpful in the classroom.

Posted by: Todd Zartman | October 12, 2012 at 01:19 PM

There is no chance that the BLS changed the results of the September CPS in favor of one party. On the other hand, the sample of 70000 households with approximately 200,000 people might not be enough to gaurantee the uncertainty desired during the election race. The fall in the rate of unemployment by 0.3% corresponds to the change in employment status to 300 people. The BLS (TP 66) states that the inherent uncertainty of unemploymemt rate (i.e. the uncertainty associated with measuring and non measuring errors)is 0.2%. Therefore, the outcome of 7.8% might be internally biased, although not intentionally as some experts suggest.

I also think that many experts undertand Welch's statement as suggesting a proportional fall as an extension of ceteris paribus principle. Your take might be counterproductive as it looks like a lawer trick before the court.

Posted by: kio | October 13, 2012 at 03:20 AM

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