My goal is to estimate nutrition indicators of children less than 5 years old at the subnational level (say provinces) in a given country. I have two datasets: i) survey data that includes this nutritional information and some variables regarding the socioeconomic status of the household in which the children lives; and ii) census data, which includes only the socioeconomic characteristics information, as in the survey data (no nutrition). The methodology (called nutrition mapping) relies on two stages: first, using survey data, model the nutrition status (left-hand variable) using the household characteristics (right-hand variables) and get a vector of 'b_hat'. Second, using b_hat, impute the nutrition values using the more comprehensive information from census data. What I would like to have is some measure of the quality of the prediction/forecast in this second stage. How can I get some kind of robust confidence level or standard error that includes the first stage modelling? Any orientation will be greatly appreciated.