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

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Author Info
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.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-499.

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Length: 32 pages
Date of creation: Jun 2007
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Handle: RePEc:tky:fseres:2007cf499

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  1. 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. [Downloadable!]
  2. 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. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
  4. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  6. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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