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Optimal Inference With Many Instruments

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  • Hahn, Jinyong

Abstract

In this paper, I derive the efficiency bound of the structural parameter in a linear simultaneous equations model with many instruments. The bound is derived by applying a convolution theorem to Bekker's (1994, Econometrica 62, 657–681) asymptotic approximation, where the number of instruments grows to infinity at the same rate as the sample size. Usual instrumental variables estimators with a small number of instruments are heuristically argued to be efficient estimators in the sense that their asymptotic distribution is minimal. Bayesian estimators based on parameter orthogonalization are heuristically argued to be inefficient.

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  • Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(1), pages 140-168, February.
    • Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:140-168_18
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    Cited by:

    1. Markus Frölich & Michael Lechner, 2004. "Regional treatment intensity as an instrument for the evaluation of labour market policies," University of St. Gallen Department of Economics working paper series 2004 2004-08, Department of Economics, University of St. Gallen.
    2. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
    3. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2010. "On the asymptotic optimality of the LIML estimator with possibly many instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 191-204, August.
    4. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    5. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.
    6. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    7. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    8. Carriero, Andrea & Kapetanios, George & Marcellino, Massilimiano, 2015. "A Shrinkage Instrumental Variable Estimator For Large Datasets," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 67-87, Mars-Juin.
    9. Kuanhao Jiang & Rajarshi Mukherjee & Subhabrata Sen & Pragya Sur, 2022. "A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond," Papers 2205.10198, arXiv.org, revised Oct 2022.
    10. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    11. Shane M. Sherlund, 2004. "Quasi Empirical Likelihood Estimation of Moment Condition Models," Econometric Society 2004 North American Summer Meetings 507, Econometric Society.
    12. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    13. Carriero, Andrea & Kapetanios, George & Marcellino, Massilimiano, 2015. "A Shrinkage Instrumental Variable Estimator For Large Datasets," L'Actualité Economique, Société Canadienne de Science Economique, vol. 91(1-2), pages 67-87, Mars-Juin.
    14. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    15. Carlos Velasco & Xuexin Wang, 2021. "Instrumental variable estimation via a continuum of instruments with an application to estimating the elasticity of intertemporal substitution in consumption," Working Papers 2024-09-06, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    16. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    17. Kapetanios, George & Marcellino, Massimiliano, 2010. "Cross-sectional averaging and instrumental variable estimation with many weak instruments," Economics Letters, Elsevier, vol. 108(1), pages 36-39, July.
    18. Tae-Hyoung Tommy Gim, 2016. "Testing the Reciprocal Relationship between Attitudes and Land Use in Relation to Trip Frequencies," International Regional Science Review, , vol. 39(2), pages 203-227, April.
    19. Sølvsten, Mikkel, 2020. "Robust estimation with many instruments," Journal of Econometrics, Elsevier, vol. 214(2), pages 495-512.
    20. Bekker, Paul A. & Crudu, Federico, 2012. "Symmetric Jackknife Instrumental Variable Estimation," MPRA Paper 37853, University Library of Munich, Germany.
    21. John Chao & Norman Swanson, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments," Departmental Working Papers 200420, Rutgers University, Department of Economics.
    22. Haruo Iwakura, 2014. "Deriving the Information Bounds for Nonlinear Panel Data Models with Fixed Effects," KIER Working Papers 886, Kyoto University, Institute of Economic Research.
    23. Kazuhiko Hayakawa, 2006. "Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present," Hi-Stat Discussion Paper Series d05-130, Institute of Economic Research, Hitotsubashi University.
    24. Kapetanios, George & Marcellino, Massimiliano, 2010. "Cross-sectional averaging and instrumental variable estimation with many weak instruments," Economics Letters, Elsevier, vol. 108(1), pages 36-39, July.
    25. Wayne Yuan Gao & Rui Wang, 2023. "IV Regressions without Exclusion Restrictions," Papers 2304.00626, arXiv.org, revised Jul 2023.

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