A0574
Title: Many instruments under data clustering
Authors: Stanislav Anatolyev - CERGE-EI and New Economic School (Czech Republic) [presenting]
Maksim Smirnov - CERGE-EI (Czech Republic)
Abstract: The literature on many weak instruments in a heteroskedastic environment under data independence is largely developed. When data dependence, in particular clustering, is present, it poses difficulties in making correct and convenient inferences. It is shown that clustering either deems the jackknife instrumental variables estimation inconsistent or makes its inferences hugely distorted. It is suggested, instead of following the "save the Jackknife" approach, an alternative approach, which is computationally attractive and allows general structures of intra-cluster correlations. The natural extension of jackknifing is used, the leave-cluster-out methodology, applied to the instrument projection matrix, which allows one to dispose of the cross-cluster dependencies in the influence function of the structural parameters estimator. A formal asymptotic framework is set out to analyze the proposed cluster-jackknife instrumental variables (CJIV) estimator, with an increasing number of clusters, possibly increasing average cluster size and the possible presence of many weak instruments. A central limit theorem is proven for the influence function embedded in the CJIV estimator and consistency of the associated CJIV variance estimator is shown. The importance of instrument design on the properties of CJIV is studied, and a simulation study reveals its finite sample properties and its computational intensity.
