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On the Normalization of Structural Equations: Properties of Direct Estimators

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  • Hillier, Grant H

Abstract

In a single structural equation, only the direction of the vector of coefficients of the endogenous variables is determined. Estimators for that direction can be defined directly, but are also induced by classical estimators that embody the traditional normalization rule. Exact distribution results show that the properties of estimators that depend on the usual normalization rule--which gives special emphasis to a particular direction--are distorted by that dependence, while those of the direct estimators are not. Thus, the traditional normalization rule may serve to define the parameters of interest, but should not be embodied in the estimation procedure. Copyright 1990 by The Econometric Society.

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  • Hillier, Grant H, 1990. "On the Normalization of Structural Equations: Properties of Direct Estimators," Econometrica, Econometric Society, vol. 58(5), pages 1181-1194, September.
    • Handle: RePEc:ecm:emetrp:v:58:y:1990:i:5:p:1181-94
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    Cited by:

    1. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    2. Moral-Benito, Enrique & Bartolucci, Cristian, 2012. "Income and democracy: Revisiting the evidence," Economics Letters, Elsevier, vol. 117(3), pages 844-847.
    3. Rodrigo Alfaro, 2008. "Higher Order Properties of the Symmetricallr Normalized Instrumental Variable Estimator," Working Papers Central Bank of Chile 500, Central Bank of Chile.
    4. Hillier, Grant, 2009. "On The Conditional Likelihood Ratio Test For Several Parameters In Iv Regression," Econometric Theory, Cambridge University Press, vol. 25(2), pages 305-335, April.
    5. J. David López-Salido & Pilar Velilla, 2002. "La dinámica de los márgenes en España. Una primera aproximación con datos agregados," Investigaciones Economicas, Fundación SEPI, vol. 26(1), pages 59-85, January.
    6. Badi H. Baltagi & Chihwa Kao, 2000. "Nonstationary Panels, Cointegration in Panels and Dynamic Panels: A Survey," Center for Policy Research Working Papers 16, Center for Policy Research, Maxwell School, Syracuse University.
    7. Randolph G. K. Tan, 2000. "Finite-Sample Optimality of Tests in a Structural Equation," Econometric Society World Congress 2000 Contributed Papers 1853, Econometric Society.
    8. Manresa, Elena & Peñaranda, Francisco & Sentana, Enrique, 2023. "Empirical evaluation of overspecified asset pricing models," Journal of Financial Economics, Elsevier, vol. 147(2), pages 338-351.
    9. Marmer, Vadim & Sakata, Shinichi, 2011. "Instrumental Variables Estimation and Weak-Identification-Robust Inference Based on a Conditional Quantile Restriction," Microeconomics.ca working papers vadim_marmer-2011-26, Vancouver School of Economics, revised 28 Sep 2011.
    10. Andreas A. Andrikopoulos & Dimitrios C. Gkountanis, 2011. "Issues and Models in Applied Econometrics: A partial survey," South-Eastern Europe Journal of Economics, Association of Economic Universities of South and Eastern Europe and the Black Sea Region, vol. 9(2), pages 107-165.
    11. Imbens, Guido W., 2014. "Instrumental Variables: An Econometrician's Perspective," IZA Discussion Papers 8048, Institute of Labor Economics (IZA).
    12. Sentana, Enrique, 2024. "Finite underidentification," Journal of Econometrics, Elsevier, vol. 240(1).
    13. Jean‐Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 36(4), pages 767-808, November.
    14. Chao, John C. & Phillips, Peter C. B., 2002. "Jeffreys prior analysis of the simultaneous equations model in the case with n+1 endogenous variables," Journal of Econometrics, Elsevier, vol. 111(2), pages 251-283, December.
    15. T. W. Anderson & Naoto Kunitomo & Yukitoshi Matsushita, 2009. "The Limited Information Maximum Likelihood Estimator as an Angle," CIRJE F-Series CIRJE-F-619, CIRJE, Faculty of Economics, University of Tokyo.
    16. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.
    17. Andrew M. Jones & José M. Labeaga, 2003. "Individual heterogeneity and censoring in panel data estimates of tobacco expenditure," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 157-177.
    18. Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2008. "Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 146(2), pages 241-254, October.
    19. Elena Manresa & Francisco Peñaranda & Enrique Sentana, 2017. "Empirical Evaluation of Overspecified Asset Pricing Models," Working Papers wp2018_1711, CEMFI.
    20. Giovanni Forchini, 2006. "Tests for Over-identifying Restrictions in Partially Identified Linear Structural Equations," Monash Econometrics and Business Statistics Working Papers 20/06, Monash University, Department of Econometrics and Business Statistics.

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