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Approximate Distributions of the Likelihood Ratio Statistic in a Structural Equation with Many Instruments

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Yukitoshi Matsushita (CIRJE, Faculty of Economics, University of Tokyo)
Abstract

This paper studies the properties of Likelihood Ratio (LR) tests associated with the limited information maximum likelihood (LIML) estimators in a structural form estimation when the number of instrumental variables is large. Two types of asymptotic theories are developed to approximate the distribution of the likelihood ratio (LR) statistics under the null hypothesis H0 : ƒÀ = ƒÀ0: the (large sample) asymptotic expansion and the large-Kn asymptotic theory. The size comparison of two modified LR tests based on these two asymptotics is made with Moreira's conditional likelihood ratio (CLR) test and the large K t-test.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-466.

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Length: 24 pages
Date of creation: Feb 2007
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Handle: RePEc:tky:fseres:2007cf466

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  1. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November. [Downloadable!] (restricted)
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  2. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
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  3. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September. [Downloadable!] (restricted)
  4. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05. [Downloadable!] (restricted)
  5. Fujikoshi, Yasunori & Morimune, Kimio & Kunitomo, Naoto & Taniguchi, Masanobu, 1982. "Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system," Journal of Econometrics, Elsevier, vol. 18(2), pages 191-205, February. [Downloadable!] (restricted)
  6. Naoto Kunitomo & Yukitoshi Matsushita, 2003. "On Finite Sample Distributions of the Empirical Likelihood Estimator and the GMM Estimator," CIRJE F-Series CIRJE-F-200, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
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