# 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.

Affiliation: Federal Reserve Bank of Atlanta

Dr. David E. Altig is senior vice president and director of research at the Federal Reserve Bank of Atlanta. In addition to advising the Bank president on Monetary policy and related matters, Dr. Altig oversees the Bank's research and public affairs departments. He also serves as a member of the Bank's management and discount committees.

Dr. Altig also serves as an adjunct professor of economics in the graduate school of business at the University of Chicago and the Chinese Executive MBA program sponsored by the University of Minnesota and Lingnan College of Sun Yat-Sen University.

Prior to joining the Atlanta Fed, Dr. Altig served as vice president and associate director of research at the Federal Reserve Bank of Cleveland. He joined the Cleveland Fed in 1991 as an economist before being promoted in 1997. Before joining the Cleveland Fed, Dr. Altig was a faculty member in the department of business economics and public policy at Indiana University. He also has lectured at Ohio State University, Brown University, Case Western Reserve University, Cleveland State University, Duke University, John Carroll University, Kent State University, and the University of Iowa.

Dr. Altig's research is widely published and primarily focused on monetary and fiscal policy issues. His articles have appeared in a variety of journals including the Journal of Money, Credit, and Banking, the American Economic Review, the Journal of Economic Dynamics and Control, and the Journal of Monetary Economics. He has also served as editor for several conference volumes on a wide range of macroeconomic and monetary-economic topics.

Dr. Altig was born in Springfield, Ill., on Aug. 10, 1956. He graduated from the University of Iowa with a bachelor's degree in business administration. He earned his master's and doctoral degrees in economics from Brown University.

He and his wife Pam have four children and three grandchildren.

Visit: David Altig's Page

#### 1 Comment on The (Maybe Not So) Simple Arithmetic of Unemployment and Labor Force Participation

1. Robert Clark

No one yet has provided an explanation of this discrepancy I discuss below:

http://www.marketwatch.com/story/fact-check-most-new-jobs-are-full-time-ones-2012-10-05

Contrary to what most reports have been saying, this report says
almost all of the 873,000 new jobs were full time! Many experts
explained the discrepancy between the BLS household survey and its
employer survey as due to the part-time numbers. But if in fact the
household survey is also measuring full-times, then is nearly 1
million new FULL-TIME jobs in one month really believable? Why is the
household survey new jobs count 8 times higher than the employer
survey if they both are measuring full-time jobs? For statistical
studies, when they most come under question is when they are
INTERNALLY inconsistent.
At the rate the BLS is claiming our economy is now “booming” we can
match the Romney claim of 12 million new jobs over 4 years in just one
year!
I think you’ll agree this number is not believable but that is indeed
what the BLS data seems to be saying near the bottom of this table:

http://www.bls.gov/news.release/empsit.t09.htm

Bob Clark

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