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Stein-like 2SLS estimator

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  • Bruce E. Hansen

Abstract

Maasoumi (1978) proposed a Stein-like estimator for simultaneous equations and showed that his Stein shrinkage estimator has bounded finite sample risk, unlike the three-stage least square estimator. We revisit his proposal by investigating Stein-like shrinkage in the context of two-stage least square (2SLS) estimation of a structural parameter. Our estimator follows Maasoumi (1978) in taking a weighted average of the 2SLS and ordinary least square estimators, with the weight depending inversely on the Hausman (1978) statistic for exogeneity. Using a local-to-exogenous asymptotic theory, we derive the asymptotic distribution of the Stein estimator and calculate its asymptotic risk. We find that if the number of endogenous variables exceeds 2, then the shrinkage estimator has strictly smaller risk than the 2SLS estimator, extending the classic result of James and Stein (1961). In a simple simulation experiment, we show that the shrinkage estimator has substantially reduced finite sample median squared error relative to the standard 2SLS estimator.

Suggested Citation

  • Bruce E. Hansen, 2017. "Stein-like 2SLS estimator," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 840-852, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:840-852
    DOI: 10.1080/07474938.2017.1307579
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    References listed on IDEAS

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    1. Phillips, P C B, 1980. "The Exact Distribution of Instrumental Variable Estimators in an Equation Containing n + 1 Endogenous Variables," Econometrica, Econometric Society, vol. 48(4), pages 861-878, May.
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    3. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    4. Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 14-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Dec 2014.
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    2. Hao Hao & Bai Huang & Tae-Hwy Lee, 2022. "Model Averaging Estimation of Panel Data Models with Many Instruments and Boosting," Working Papers 202212, University of California at Riverside, Department of Economics.
    3. Huang, Bai & Lee, Tae-Hwy & Ullah, Aman, 2020. "Combined estimation of semiparametric panel data models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 30-45.
    4. Shirleen Manzur & Krishna Pendakur, 2023. "Labeling vs Targeting: How did the Canada Child Benefit affect household bargaining and preferences?," Discussion Papers dp23-01, Department of Economics, Simon Fraser University.
    5. Black, Dan A. & Joo, Joonhwi & LaLonde, Robert & Smith, Jeffrey A. & Taylor, Evan J., 2022. "Simple Tests for Selection: Learning More from Instrumental Variables," Labour Economics, Elsevier, vol. 79(C).
    6. Akio Namba, 2021. "Bootstrapping the Stein-Rule Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 219-237, December.
    7. Stéphane Bonhomme & Martin Weidner, 2018. "Minimizing sensitivity to model misspecification," CeMMAP working papers CWP59/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Xin Liu, 2019. "Averaging estimation for instrumental variables quantile regression," Working Papers 1907, Department of Economics, University of Missouri.
    9. Stéphane Bonhomme & Martin Weidner, 2020. "Minimizing Sensitivity to Model Misspecification," CeMMAP working papers CWP37/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. David M. Kaplan, 2019. "Unbiased Estimation as a Public Good," Working Papers 1911, Department of Economics, University of Missouri.
    11. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    12. Doko Tchatoka, Firmin & Wang, Wenjie, 2021. "Uniform Inference after Pretesting for Exogeneity with Heteroskedastic Data," MPRA Paper 106408, University Library of Munich, Germany.
    13. Jann Spiess, 2017. "Bias Reduction in Instrumental Variable Estimation through First-Stage Shrinkage," Papers 1708.06443, arXiv.org, revised Oct 2017.
    14. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    15. Bai Huang & Tae-Hwy Lee & Aman Ullah, 2017. "A combined estimator of regression models with measurement errors," Indian Economic Review, Springer, vol. 52(1), pages 73-91, December.
    16. Li, Haiqi & Chen, Xingyi & Liang, Jufang, 2022. "Shrinkage estimation of panel data models with interactive effects," Economics Letters, Elsevier, vol. 210(C).
    17. Edvard Bakhitov, 2020. "Frequentist Shrinkage under Inequality Constraints," Papers 2001.10586, arXiv.org.
    18. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.

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