t-Tests in a Structural Equation with Many Instruments
This paper studies the properties of t-ratios associated with the limited information maximum likelihood (LIML) estimators in a structural form estimation when the number of instrumental variables is large. Asymptotic expansions are made of the distributions of a large K t-ratio statistic under large-Kn asymptotics. A modified t-ratio statistic is proposed from the asymptotic expansion. The power of the large K t-ratio test dominates the AR test, the K-test by Kleibergen (2002), and the conditional LR test by Moreira (2003); and the difference can be substantial when the instruments are weak.
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- Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
- 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.
- 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.
- Morimune, Kimio, 1989. "Test in a Structural Equation," Econometrica, Econometric Society, vol. 57(6), pages 1341-1360, November.
- Naoto Kunitomo & Yukitoshi Matsushita, 2003. "Asymptotic Expansions of the Distributions of Semi-Parametric Estimators in a Linear Simultaneous Equations System," CIRJE F-Series CIRJE-F-237, CIRJE, Faculty of Economics, University of Tokyo.
- Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, 07.
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