Imputed welfare estimates in regression analysis

We discuss the use of imputed data in regression analysis, in particular the use of highly disaggregated welfare indicators (from so-called 'poverty maps'). We show that such indicators can be used both as explanatory variables on the right-hand side and as the phenomenon to explain on the left-hand side. We try out practical ways of adjusting standard errors of the regression coefficients to reflect the error introduced by using imputed, rather than actual, welfare indicators. These are illustrated by regression experiments based on data from Ecuador. For regressions with imputed variables on the left-hand side, we argue that essentially the same aggregate relationships would be found with either actual or imputed variables. We address the methodological question of how to interpret aggregate relationships found in such regressions.