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Rate Optimal Specification Test When the Number of Instruments is Large

Author

Listed:
  • Kohtaro Hitomi

    (Kyoto Institute of Technology)

  • Masamune Iwasawa

    (Graduate School of Economics, The University of Tokyo)

  • Yoshihiko Nishiyama

    (Institute of Economic Research, Kyoto University)

Abstract

We propose a rate optimal specification test for instrumental variable regression models based on the nearest neighbor observation with respect to instruments. The proposed test has uniform power against a set of non-smooth alternatives. The optimal minimax rate is n-1/4 for any dimension of instruments, where n is sample size. This rate coincides with the fastest possible rate achievable by any tests under the local alternative setting when the alternative is constructed by a non-smooth function and/or the dimension of the instrument is large. Since such local alternative belongs to the set of alternatives considered in this study, our test is preferable in a large dimension setting. In the simulation and empirical applications with a large dimension of instruments, we observe that the test works well and the power approaches one reasonably fast as the sample size increase.

Suggested Citation

  • Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2018. "Rate Optimal Specification Test When the Number of Instruments is Large," KIER Working Papers 986, Kyoto University, Institute of Economic Research.
    • Handle: RePEc:kyo:wpaper:986
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    File URL: http://www.kier.kyoto-u.ac.jp/DP/DP986.pdf
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    More about this item

    Keywords

    instrumental variable model; specification test; minimax approach; k- nearest neighbor method;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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