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

Published online by Cambridge University Press:  28 July 2016

Stanislav Anatolyev*
Affiliation:
CERGE-EI, Czech Republic and New Economic School, Russia
Pavel Yaskov
Affiliation:
Steklov Mathematical Institute of RAS and NUST ‘MISIS’
*
*Address correspondence to Stanislav Anatolyev, CERGE-EI, Politických vězňů 7, 11121 Prague 1, Czech Republic; e-mail: stanislav.anatolyev@cerge-ei.cz.
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Abstract

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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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ARTICLES
Copyright
Copyright © Cambridge University Press 2016 

Footnotes

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.

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