Hi. I am trying to examine whether having a household member who is currently migrating has any impact on the education of children in the household. Since the decision to migrate is endogenous, I am using an instrumental variable, which is the share of migrants at the village-level. The idea is that having a network of migrants at the village-level can facilitate the process of migration. Since the same household can have more than one child, I am clustering the standard errors at the household-level as you can see from this command:

Code:
#delimit ; 
ivregress 2sls school (migrant = mig_share nb_children nb_ymale nb_yfemale nb_elderly avg_school) age age2 eldest extended fth_absent i.fteducst i.mteducst i.region 
[pweight=expan_indiv], vce (cluster hhid) first;
#delimit cr
However, one of the papers that have used the same IV as mine have clustered the standard errors at the village-level as the instrumental variable is at the village-level.
I am wondering if it is possible to cluster the standard errors in the first stage at the village-level and then cluster the standard errors in the second stage at the household-level. Is there a way to do so in Stata? and will this make sense or the standard errors need to be clustered at the same level in both equations?
Thanks in advance