IFin Seminar, Antonio Cosma, University of Luxemburg "Missing endogenous variables in conditional moment restriction models"
Institute of Finance
Date: 13.10.2021 / 12:25 - 13:40
Speaker: Antonio Cosma, University of Luxemburg
Title: "Missing endogenous variables in conditional moment restriction models"
Date: October 13, 2021
Time: 12:25 - 13:40
Room: A12 Red Building
We derive the semiparametric efficiency bound for estimating finite dimensional parameters identified via a system of conditional moment equalities when at least one of the endogenous variables (which can either be endogenous outcomes, or endogenous explanatory variables, or both) is missing for some individuals in the sample. An interesting result we obtain is that if there are no endogenous variables that are not missing, i.e., all of the endogenous variables in the model are missing, then estimation using only the validation subsample (the subsample of observations for which the endogenous variables are nonmissing) is asymptotically efficient. We also propose an estimator, based on the full sample, that achieves the semiparametric efficiency bound. A simulation study reveals that our estimator can work well in medium sized samples, and that the resulting efficiency gains (measured as the ratio of the variance of an efficient estimator based on the validation sample and the variance of our estimator) are comparable with the maximum gain the simulation design can deliver.