Cross-sectional averaging and instrumental variable estimation with many weak instruments

Instrumental variable estimation is central to econometric analysis and has justifiably been receiving considerable and consistent attention in the literature in the past. Recent developments have focused on cases where instruments are either weak, in terms of correlations with the endogenous variables, or many or both. The present paper suggests a new way to deal with many, possibly weak, instruments. Our suggestion is to cross-sectionally average the instruments and use these averages as instruments. Intuition and interesting recent work by Hahn (2002) suggest that parsimonious devices used in the construction of the final instruments, may provide effective estimation strategies. Our use of cross-sectional averaging promotes parsimony and therefore falls within the context of such arguments. We provide a theoretical analysis of this approach in terms of its consistency properties and also show, via a Monte Carlo study, that the approach can provide improved estimation compared to standard instrumental variables estimation.