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Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors

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  • Moreira, Humberto Ataíde
  • Moreira, Marcelo J.

Abstract

This paper considers two-sided tests for the parameter of an endogenous variable in an instrumental variable (IV) model with heteroskedastic and autocorrelated errors. We develop the nite-sample theory of weighted-average power (WAP) tests with normal errors and a known long-run variance. We introduce two weights which are invariant to orthogonal transformations of the instruments; e.g., changing the order in which the instruments appear. While tests using the MM1 weight can be severely biased, optimal tests based on the MM2 weight are naturally two-sided when errors are homoskedastic. We propose two boundary conditions that yield two-sided tests whether errors are homoskedastic or not. The locally unbiased (LU) condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness. The strongly unbiased (SU) condition is more restrictive than LU, but the associated WAP tests are easier to implement. Several tests are SU in nite samples or asymptotically, including tests robust to weak IV (such as the Anderson-Rubin, score, conditional quasi-likelihood ratio, and I. Andrews' (2015) PI-CLC tests) and two-sided tests which are optimal when the sample size is large and instruments are strong. We refer to the WAP-SU tests based on our weights as MM1-SU and MM2-SU tests. Dropping the restrictive assumptions of normality and known variance, the theory is shown to remain valid at the cost of asymptotic approximations. The MM2-SU test is optimal under the strong IV asymptotics, and outperforms other existing tests under the weak IV asymptotics.

Suggested Citation

  • Moreira, Humberto Ataíde & Moreira, Marcelo J., 2015. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 764, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
  • Handle: RePEc:fgv:epgewp:764
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    References listed on IDEAS

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    Cited by:

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    2. Marcelo Moreira & Geert Ridder, 2019. "Efficiency loss of asymptotically efficient tests in an instrumental variables regression," CeMMAP working papers CWP03/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Dennis Lim & Wenjie Wang & Yichong Zhang, 2022. "A Conditional Linear Combination Test with Many Weak Instruments," Papers 2207.11137, arXiv.org, revised Apr 2023.
    4. David S. Lee & Justin McCrary & Marcelo J. Moreira & Jack Porter, 2022. "Valid t-Ratio Inference for IV," American Economic Review, American Economic Association, vol. 112(10), pages 3260-3290, October.
    5. Michael Keane & Timothy Neal, 2021. "Robust Inference for the Frisch Labor Supply Elasticity," Discussion Papers 2021-07b, School of Economics, The University of New South Wales.
    6. Bertille Antoine & Pascal Lavergne, 2020. "Identification-Robust Nonparametric Interference in a Linear IV Model," Discussion Papers dp20-03, Department of Economics, Simon Fraser University.
    7. Sheng Wang & Hyunseung Kang, 2022. "Weak‐instrument robust tests in two‐sample summary‐data Mendelian randomization," Biometrics, The International Biometric Society, vol. 78(4), pages 1699-1713, December.
    8. Sreevidya Ayyar & Yukitoshi Matsushita & Taisuke Otsu, 2022. "Conditional Likelihood Ratio Test with Many Weak Instruments," Papers 2210.07680, arXiv.org.
    9. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    10. Van de Sijpe, Nicolas & Windmeijer, Frank, 2023. "On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference," Journal of Econometrics, Elsevier, vol. 235(1), pages 82-104.
    11. Andrew E Clark & Rong Zhu, 2023. "Taking Back Control? Quasi-Experimental Evidence on the Impact of Retirement on Locus of Control," Working Papers halshs-04335808, HAL.
    12. Yukun Ma, 2023. "Identification-robust inference for the LATE with high-dimensional covariates," Papers 2302.09756, arXiv.org, revised Nov 2023.
    13. Crawford, Gregory S. & Deer, Lachlan & Smith, Jeremy & Sturgeon, Paul, 2017. "The Regulation of Public Service Broadcasters : Should there be more advertising on television?," Economic Research Papers 269092, University of Warwick - Department of Economics.
    14. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jun 2023.
    15. Wang, Wenjie, 2021. "Wild Bootstrap for Instrumental Variables Regression with Weak Instruments and Few Clusters," MPRA Paper 106227, University Library of Munich, Germany.
    16. Matsushita, Yukitoshi & Otsu, Taisuke, 2022. "A jackknife Lagrange multiplier test with many weak instruments," LSE Research Online Documents on Economics 116392, London School of Economics and Political Science, LSE Library.
    17. Wenjie Wang & Yichong Zhang, 2021. "Wild Bootstrap for Instrumental Variables Regressions with Weak and Few Clusters," Papers 2108.13707, arXiv.org, revised Jan 2024.
    18. Keane, Michael & Neal, Timothy, 2023. "Instrument strength in IV estimation and inference: A guide to theory and practice," Journal of Econometrics, Elsevier, vol. 235(2), pages 1625-1653.
    19. Silva, Felipe Bastos Gurgel, 2021. "Fiscal Deficits, Bank Credit Risk, and Loan-Loss Provisions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 56(5), pages 1537-1589, August.
    20. Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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