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I was reading the data as the percentage of people who are unemployed who say they are retired, not percentage of people who say they are retired. So it would be 0.57% of unemployed people are between ages 16 and 40 AND say they are retired.
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The percentage actually is the percentage of the overall population, not of labor force non-participants.
I've attached a screenshot of the non-pivoted data for 2014, and a spreadsheet containing the original dataset I downloaded from the FRB (in case you want to look at it yourself). As you can see, each row adds up to 100% and includes the labor force participants as a whole and the non-participants broken down by reason for non-participation.
Note that the spreadsheet does some of the work for you, because it gives the percentage of the overall population in each age range.
A note on terminology, too:
Even though "Unemployed" and "labor force non-participants" sound very similar, they are two different populations as used in most of the published statistics.
"Unemployed" are people who are not working, but are looking for work.
"Labor force non-participants" are people who are not working and are also not looking for work. This is a little tricky, because non-participants include people who might want to work, but have given up trying to find work for some reason.
By this definition there should be no retired unemployed people.
One reason for the potentially high-sounding number is that these are people who *say* they are retired, not necessarily people who fall into some strict definition of the term. For example, I probably would have said I was retired in a survey back when I took a year off from working in 2007, even though I intended to start working again.
(Thanks, btw, for the positive feedback in this thread - I'll try to keep up the good work :)).