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Some Properties of the LIML Estimator in a Dynamic Panel Structural Equation

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  • Kentaro Akashi

    (The Institute of Statistical Mathematics)

  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo)

Abstract

We investigate the finite sample and asymptotic properties of several estimation methods (Within-Group, GMM and LIML) for a panel autoregressive structural equation model with random effects when both T and N are large. When we use the forward-filtering to a structural model as Alvarez and Arellano (2003), both the WG and GMM estimators are significantly biased when both T and N go to infinity while T/N is different from zero. The LIML (limited information maximum likelihood) estimator has consistency and the asymptotic normality when T/N converges to a constant as both T and N go to infinity. Its asymptotic distribution has some bias and covariance which depend on the limiting behavior of T/N.

Suggested Citation

  • Kentaro Akashi & Naoto Kunitomo, 2010. "Some Properties of the LIML Estimator in a Dynamic Panel Structural Equation," CIRJE F-Series CIRJE-F-707, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2010cf707
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    References listed on IDEAS

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    1. Arellano, Manuel, 2016. "Modelling optimal instrumental variables for dynamic panel data models," Research in Economics, Elsevier, vol. 70(2), pages 238-261.
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    8. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments," CIRJE F-Series CIRJE-F-542, CIRJE, Faculty of Economics, University of Tokyo.
    9. Kentaro Akashi & Naoto Kunitomo, 2010. "The Limited Information Maximum Likelihood Approach to Dynamic Panel Structural Equations," CIRJE F-Series CIRJE-F-708, CIRJE, Faculty of Economics, University of Tokyo.
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    11. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2006. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments," CIRJE F-Series CIRJE-F-399, CIRJE, Faculty of Economics, University of Tokyo.
    12. 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.
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    14. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2008. "On Finite Sample Properties of Alternative Estimators of Coefficients in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-577, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

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    2. Hsiao, Cheng & Zhou, Qiankun, 2018. "Jive For Panel Dynamic Simultaneous Equations Models," Econometric Theory, Cambridge University Press, vol. 34(6), pages 1325-1369, December.
    3. Yongfu Huang & M. G. Quibria, 2013. "The Global Partnership for Inclusive Growth," WIDER Working Paper Series wp-2013-059, World Institute for Development Economic Research (UNU-WIDER).
    4. Cheng Hsiao, 2016. "Panel Macroeconometric Modeling," Working Papers 2016-02-21, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. Kentaro Akashi & Naoto Kunitomo, 2015. "The limited information maximum likelihood approach to dynamic panel structural equation models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 39-73, February.
    6. Bain, Robert & Bartram, Jamie & Luyendijk, Rolf, 2013. "Universal Access to Drinking Water: The Role of Aid," WIDER Working Paper Series 088, World Institute for Development Economic Research (UNU-WIDER).
    7. Arturas Juodis, 2015. "Iterative Bias Correction Procedures Revisited: A Small Scale Monte Carlo Study," UvA-Econometrics Working Papers 15-02, Universiteit van Amsterdam, Dept. of Econometrics.
    8. Lee, Nayoung & Moon, Hyungsik Roger & Zhou, Qiankun, 2017. "Many IVs estimation of dynamic panel regression models with measurement error," Journal of Econometrics, Elsevier, vol. 200(2), pages 251-259.
    9. Joura, Essam & Xiao, Qin & Ullah, Subhan, 2021. "The impact of Say-on-Pay votes on firms' strategic policies: Insights from the Anglo-Saxon economy," International Review of Financial Analysis, Elsevier, vol. 73(C).
    10. Oliver Linton & Ji-Liang Shiu, 2018. "Semiparametric nonlinear panel data models with measurement error," CeMMAP working papers CWP09/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Kentaro Akashi & Naoto Kunitomo, 2010. "The Limited Information Maximum Likelihood Approach to Dynamic Panel Structural Equations," CIRJE F-Series CIRJE-F-708, CIRJE, Faculty of Economics, University of Tokyo.
    12. Hsiao, Cheng & Zhou, Qiankun, 2015. "Statistical inference for panel dynamic simultaneous equations models," Journal of Econometrics, Elsevier, vol. 189(2), pages 383-396.
    13. Essam Joura & Qin Xiao & Subhan Ullah, 2023. "The moderating effects of CEO power and personal traits on say‐on‐pay effectiveness: Insights from the Anglo‐Saxon economies," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(4), pages 4055-4078, October.
    14. Naoto Kunitomo & Kentaro Akashi, 2010. "An Aysmptotically Optimal Modification of the Panel LIML Estimation for Individual Heteroscedasticity," CIRJE F-Series CIRJE-F-780, CIRJE, Faculty of Economics, University of Tokyo.
    15. Tom Wansbeek & Dennis Prak, 2017. "LIML in the static linear panel data model," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 385-395, March.
    16. Cobo-Reyes, Ramón & Katz, Gabriel & Meraglia, Simone, 2019. "Endogenous sanctioning institutions and migration patterns: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 158(C), pages 575-606.
    17. Akashi, Kentaro & Kunitomo, Naoto, 2012. "Some properties of the LIML estimator in a dynamic panel structural equation," Journal of Econometrics, Elsevier, vol. 166(2), pages 167-183.
    18. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.
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    20. Robert Bain & Rolf Luyendijk & Jamie Bartram, 2013. "Universal Access to Drinking Water: the Role of Aid," WIDER Working Paper Series wp-2013-088, World Institute for Development Economic Research (UNU-WIDER).

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    More about this item

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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