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Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments

Author

Listed:
  • Ryo Kato

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • Takahiro Hoshino

    (Department of Economics, Keio University, Japan and RIKEN Center for Advanced Intelligence Project, Japan)

Abstract
We develop a new semiparametric Bayes instrumental variables estimation method. We employ the form of the regression function of the reduced-form equation and the disturbances are modelled nonparametrically to achieve better preditive power of the endogenous variables, whereas we use parametric formulation in the structural equation, which is of interest in inference. Our simulation studies show that under small sample size the proposed method obtains more e￠ cient estimates and very precise credible intervals compared with existing IV methods. The existing methods fail to reject the null hypothesis with higher probability, due to larger variance of the estimators. Moreover, the mean squared error in the proposed method may be less than 1/30 of that in the existing procedures even in the presence of weak instruments. We applied our proposed method to a Mendelian randomization dataset where a large number of instruments are available and semiparametric specification is appropriate. This is a weak instrument case; hence, the non-Bayesian IV approach yields inefficient estimates. We obtained statistically significant results that cannot be obtained by the existing methods, including standard Bayesian IV.

Suggested Citation

  • Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments," Discussion Paper Series DP2018-14, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2018-14
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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2018-14.pdf
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    References listed on IDEAS

    as
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    Keywords

    Instrumental variable; Mendelian Randomization; Semiparametric Bayes model; Probit stick-breaking process mixture;
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