level two weights for multi-level analysis

Since state isn't a stage of selection in ACS (all of the first stage stratification and PSU selection happens at the level wa-a-ay finer than states), you don't have to bother with the scaling issues discussed by Pfeffermann et. al. 1998, say. You can just give the states unit weights.

If you really want to fiddle with the weights to see what alternative specifications could be, then, following Pfeffermann's suggestion, you could produce weights scaled to the effective sample size ( egen sum_wgt = total( perwt ), by(state); egen sum_wgt2 = total( perwt*perwt ), by(state); gen effn_wt = perwt*sum_wgt / sum_wgt2 ). Then you can also entertain allocating the lost weight to the states (gen fake_state_weight = sum_wgt2 / sum_wgt ) so that the total mass in fake_state_weight*effn_wt stays constant.

So in the end, you can run and compare four models, at least:
1. ignore weights whatsoever;
2. level-1 weight = ACS perwt, level-2 weight = 1
3. level-1 weight = effective sample size weight, level-2 weight = 1
4. level-1 weight = effective sample size weight, level-2 weight = fake_state_weight

You can wave hands and come up with relations between weights and outcomes and explanatory variables that would justify any of the four models. In reality, we don't know which one is right.

Since state isn't a stage of selection in ACS (all of the first stage stratification and PSU selection happens at the level wa-a-ay finer than states), you don't have to bother with the scaling issues discussed by Pfeffermann et. al. 1998, say. You can just give the states unit weights.

If you really want to fiddle with the weights to see what alternative specifications could be, then, following Pfeffermann's suggestion, you could produce weights scaled to the effective sample size ( egen sum_wgt = total( perwt ), by(state); egen sum_wgt2 = total( perwt*perwt ), by(state); gen effn_wt = perwt*sum_wgt / sum_wgt2 ). Then you can also entertain allocating the lost weight to the states (gen fake_state_weight = sum_wgt2 / sum_wgt ) so that the total mass in fake_state_weight*effn_wt stays constant.

So in the end, you can run and compare four models, at least:
1. ignore weights whatsoever;
2. level-1 weight = ACS perwt, level-2 weight = 1
3. level-1 weight = effective sample size weight, level-2 weight = 1
4. level-1 weight = effective sample size weight, level-2 weight = fake_state_weight

You can wave hands and come up with relations between weights and outcomes and explanatory variables that would justify any of the four models. In reality, we don't know which one is right.