Thanks for your post. The CPS is often treated as a repeated cross-section without any special adjustments for the panel component of the survey, though I recommend consulting any papers in your specific field using CPS to see how others have approached this problem. IPUMS does not have any specific recommendations on how to address repeated observations in pooled analyses of the CPS. A former colleague of mine shares a few ideas on this topic in a separate post; I will recap them here as well.
- You could keep only a single rotation group per sample to avoid repeat observations (as you note), but this reduces your sample size considerably
- Davern et al. (2006, 2007) have suggestions on estimating standard errors with the public use data in the absence of sample design variables, including using the household SERIAL number as the cluster in standard error estimation. Using CPSID, the household-linking key from IPUMS CPS, instead of SERIAL would treat observations of a given household as having correlated errors.