24 Oct – DEM Research Seminar: Missing endogenous variables in conditional-moment-restriction models

  • Faculty of Law, Economics and Finance (FDEF)
    19 October 2023

Missing endogenous variables in conditional-moment-restriction models

Speaker: Andreï Kostyrka
DEM, Université du Luxembourg

DATE: Tuesday, 24 October 2023

TIME: 13.00 – 14.00


Campus Kirchberg
6, Rue Richard Coudenhove-Kalergi
L-1359 Luxembourg

– Free seminar
– Registration to (please specify full name and institution)

Tel: +352 46 66 44 6283


We consider the estimation of 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. We derive the semi-parametric efficiency bound for estimating the parameters, and use it to demonstrate that if 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 non-missing) is asymptotically efficient. We also propose an estimator, based on the full sample, that achieves the semi-parametric 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. In an empirical application, we revisit the female labour supply model of Angrist & Evans (1998) and show that, had 40% respondents not reported their labour income (the outcome variable), a researcher using the 2SLS estimator would likely conclude that female labour income is not impacted by the third childbirth. In contrast, with standard errors as small as those under no missingness, we find that our semi-parametrically efficient estimator substantially increases the likelihood of finding a significant negative effect of multi-child parenting on female labour income even when 40% of the outcomes are missing.