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ASYMPTOTICS OF DIAGONAL ELEMENTS OF PROJECTION MATRICES UNDER MANY INSTRUMENTS/REGRESSORS

  • Stanislav Anatolyev (a1) and Pavel Yaskov (a2)
Abstract

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.

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Copyright
COPYRIGHT: © Cambridge University Press 2016 
Corresponding author
*Address correspondence to Stanislav Anatolyev, CERGE-EI, Politických vězňů 7, 11121 Prague 1, Czech Republic; e-mail: stanislav.anatolyev@cerge-ei.cz.
Footnotes
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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.

Footnotes
References
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