On your CPS replicate weights page, https://cps.ipums.org/cps/repwt.shtml…, you first describe a method of calculating estimate variance by recalculating the estimate 160 times, once for each replicate weight, and then taking the variance of the weights so calculated. You then go on to state how you calculate variance estimates with Stata (and older Stata). The Stata method appears specific to successive difference replication, though your documentation above says that half the weights are calculated using balanced replication and Hadamard matrices. (And the older Stata directions say to use jackknife replication).
Is the simple repeat-and-take-the-variance method you first describe equivalent to the second? I’m trying to do this in R, and the first method id easy to implement. I’m not familiar enough with replicate weight methodology to easily duplicate the second method.