Santiago Acerenza, 3rd year grad student, had his paper, "AsymptoticTheory for M-Estimators Under Clustering and with Missing Data," accepted to the 2019 Midwest Econometrics Group Meeting in Columbus, Ohio, from October 11-12, 2019.
Abstact: This paper combines clustering, M-estimation and missing data. First, we extend an identification result from Wooldridge (2002) to this setting. Secondly, we formalize conditions for an M-estimator with missing data to be consistent when the number of clusters increases and the size of the clusters remains fixed. We then characterize the the asymptotic properties of the estimator that involves correcting the missing data with inverse probability weighting. We also provide a simple proof for efficiency gains. Our main result is providing the form of the inconsistency induced in the parameters of interest by not taking into account the dependence in the inverse probability weighting of individuals inside a cluster. We then propose and present a correction mechanism. We provide evidence of the small sample properties of the correction mechanism using simulations. Finally, we develop a test for non nested model selection under in this setup.