Following is a response from Senior DHS staff member, Tom Pullum:
I will illustrate with v201; you need to revise with your employment variable.
egen v201_total=total(v201), by(v001)
egen v201_n=count(v201),by(v001)
gen v201_mean=v201_total/v201_n
* v201_mean can also be obtained from "egen v201_mean=mean(v201), by(v001)"
* Now construct a mean for the cluster, for each respondent, that omits each respondent
gen v201_mean_adj=(v201_total-v201)/(v201_n-1)
correlate v201 v201_mean
correlate v201 v201_mean_adj
* The respondent's value of v201 is correlated with both of these means, although
* less so with the mean for which she is removed