To Weight or not to Weight? The Eternal Question of Econometricians facing Survey Data

A recurrent problem in economic studies based on survey data is to determine whether survey weights should be used or not. We show that weighted estimators are more robust than unweighted ones, but less accurate when unweighted estimators are consistent. In some circumstances, a compatibility test between the assumptions underlying the selection mechanism (i.e., the survey design and nonresponse) and the econometric model at hand can be implemented, by comparing these two estimators. Finally, we present some methods to compute the accuracy of weighted estimators.