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Test in a Structural Equation

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  • Morimune, Kimio

Abstract

Properties of t ratios associated with the limited information maximum likelihood, two-stage least squares, and ordinary least squares estimators in a structural form estimation are studied. The existence of moments of these t ratios, including the limited information maximum likelihood form, is proved first. Second, Monte Carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test. Third, asymptotic expansions of the distributions of t ratios are derived to find out deviations of real sizes from nominal sizes. The t ratios associated with the limited information maximum likelihood and two-stage least squares estimators are proved asymptotically as powerful as the likelihood ratio test. Copyright 1989 by The Econometric Society.

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  • Morimune, Kimio, 1989. "Test in a Structural Equation," Econometrica, Econometric Society, vol. 57(6), pages 1341-1360, November.
    • Handle: RePEc:ecm:emetrp:v:57:y:1989:i:6:p:1341-60
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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. Oya, Kosuke, 1995. "Size corrections for the Wald statistic in structural equation models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 317-322.
    3. Maurice J. G. Bun & Frank Windmeijer, 2010. "The weak instrument problem of the system GMM estimator in dynamic panel data models," Econometrics Journal, Royal Economic Society, vol. 13(1), pages 95-126, February.
    4. Randolph G. K. Tan, 2000. "Finite-Sample Optimality of Tests in a Structural Equation," Econometric Society World Congress 2000 Contributed Papers 1853, Econometric Society.
    5. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," Journal of Econometrics, Elsevier, vol. 232(2), pages 346-366.
    6. Yukitoshi Matsushita & Taisuke Otsu, 2020. "Second-order refinements for t-ratios with many instruments," STICERD - Econometrics Paper Series 612, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. 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.
    8. Matsushita, Yukitoshi & Otsu, Taisuke, 2023. "Second-order refinements for t-ratios with many instruments," LSE Research Online Documents on Economics 111065, London School of Economics and Political Science, LSE Library.
    9. Yukitoshi Matsushita, 2007. "t-Tests in a Structural Equation with Many Instruments," CIRJE F-Series CIRJE-F-467, CIRJE, Faculty of Economics, University of Tokyo.

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