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On Likelihood Ratio Tests of Structural Coefficients: Anderson-Rubin (1949) revisited

Author

Listed:
  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo)

  • T. W. Anderson

    (Department of Statistics and Department of Economics, Stanford University)

Abstract

We develop the likelihood ratio criterion (LRC) for testing the coefficients of a structural equation in a system of simultaneous equations in econometrics. We relate the likelihood ratio criterion to the AR statistic proposed by Anderson and Rubin (1949, 1950), which has been widely known and used in econometrics over the past several decades. The method originally developed by Anderson and Rubin (1949, 1950) can be modified to the situation when there are many (or weak in some sense) instruments which may have some relevance in recent econometrics. The method of LRC can be extended to the linear functional relationships (or the errors-in-variables) model, the reduced rank regression and the cointegration models.

Suggested Citation

  • Naoto Kunitomo & T. W. Anderson, 2007. "On Likelihood Ratio Tests of Structural Coefficients: Anderson-Rubin (1949) revisited," CIRJE F-Series CIRJE-F-499, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2007cf499
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2007/2007cf499.pdf
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    References listed on IDEAS

    as
    1. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    2. Theodore W. Anderson & Naoto Kunijtomo & Yukitoshi Matsushita, 2005. "A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations and Microeconometric Models," CIRJE F-Series CIRJE-F-321, CIRJE, Faculty of Economics, University of Tokyo.
    3. Anderson, T. W. & Kunitomo, Naoto, 1992. "Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 221-243, February.
    4. Yukitoshi Matsushita, 2007. "Approximate Distributions of the Likelihood Ratio Statistic in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-466, CIRJE, Faculty of Economics, University of Tokyo.
    5. Anderson, T. W. & Kunitomo, Naoto, 1994. "Asymptotic robustness of tests of overidentification and predeterminedness," Journal of Econometrics, Elsevier, vol. 62(2), pages 383-414, June.
    6. Anderson, T. W. & Amemiya, Yasuo, 1991. "Testing dimensionality in the multivariate analysis of variance," Statistics & Probability Letters, Elsevier, vol. 12(6), pages 445-463, December.
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    Cited by:

    1. Anderson, T.W. & Kunitomo, Naoto & Matsushita, Yukitoshi, 2011. "On finite sample properties of alternative estimators of coefficients in a structural equation with many instruments," Journal of Econometrics, Elsevier, vol. 165(1), pages 58-69.
    2. Naoto Kunitomo & Yukitoshi Matsushita, 2008. "Improving the Rank-Adjusted Anderson-Rubin Test with Many Instruments and Persistent Heteroscedasticity," CIRJE F-Series CIRJE-F-588, CIRJE, Faculty of Economics, University of Tokyo.
    3. Ribeiro, André L.P. & Hotta, Luiz K., 2013. "An analysis of contagion among Asian countries using the canonical model of contagion," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 62-69.
    4. 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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