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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  and
Pavel Yaskov
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: [email protected].
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 3 , June 2017 , pp. 717 - 738
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.

References

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