Does this variable identify the same household over time, the way the CPS variables do? For example, suppose the CPSHHID=101, and IPUMS assigns it a number=1001. The next month, CPSHHID identifies **the same HH**. Is this true for the IPUMS household ID? Due to the fact that HRHHID and HRHHID2 aren’t available in March, is Serial a substitute for these?
Does a serial number (SERIAL) correspond to a combination of the two household ID's in the regular census data?
No, SERIAL cannot be used as a substitute for HRHHID and HRHHID2, unfortunately. If you wish to link respondents in the IPUMS March CPS data across months then you will have to add longitudinal identifiers from the corresponding sample available through NBER. IPUMS and NBER files share a common sort order, so you can perform a sequential merge in your stats package to merge the NBER identifiers onto the IPUMS file. You can then use the NBER identifiers as usual.