I have two datasets A and B. Both datasets are household surveys for a country where first administrative tier is province and second is district. The respondent households are different in both datasets. The data collection methodology was based on sampling such that in case of dataset A sample is representative at district level and dataset B sample is representative at province level (cannot be disaggregated at district level).
My question is if I can use some statistical technique to infer district level variables from B and use them with other variables provided in A. To explain, let both A and B have variables on household size, income, etc. but only B has variables on household expenditure. So can somehow this information on expenditure variables be utilized with other dataset A that is representative at district level. Also if this is possible please also explain how to use weights in this scheme.