Published online by Cambridge University Press: 28 July 2016
This article sheds light on the asymptotic behavior of diagonal elements of projection matrices associated with instruments or regressors under many instrument/regressor asymptotics. When the diagonal elements do not exhibit variation asymptotically, certain results in the many instrument/regressor literature lead to elegant solutions and conclusions. We establish conditions when this happens, provide relevant examples, and analyze instrument designs, for which this property does or does not hold.
We would like to thank the editor Peter Phillips and co-editor Victor Chernozhukov for their quick and professional handling of the manuscript, as well as a diligent referee who provided very useful comments. The second author gratefully acknowledges the financial support of the Russian Science Foundation via grant 14-21-00162.