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I have a student who is interested in post-retirement employment patterns and determinants. She is very interested in looking at trends in the experience and correlates of post-retirement employment. We are thinking about using the CPS and taking advantage of the "month in sample" variables to construct some short longitudinal files so that we can estimate the prevalence and determinants of returning to work after retirement.
So here are my questions:
I actually have a pre-answered question that answers most of your questions:
The part not covered in your question was whether the CPS would ask employment questions about someone who was retired in an interview. Yes, they will get the employment questions again because the CPS is treating these as multiple cross sections.
It is a data collection design choice that they go back to the same housing unit for 4 months; skip 8 months; and then go back to the housing unit for 4 more months.
That's what makes using the CPS for a longitudinal study difficult. Just because you have the same housing unit, you do not know, without some effort, whether it is the same people in the housing unit.
The contact at NBER (who has the best resources for this is Jean Roth).