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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.

Suggested Citation

  • 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. 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.
    2. 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.
    3. Moral-Benito, Enrique & Bartolucci, Cristian, 2012. "Income and democracy: Revisiting the evidence," Economics Letters, Elsevier, vol. 117(3), pages 844-847.
    4. 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.
    5. Rodrigo Alfaro, 2008. "Higher Order Properties of the Symmetricallr Normalized Instrumental Variable Estimator," Working Papers Central Bank of Chile 500, Central Bank of Chile.
    6. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.
    7. Hillier, Grant, 2009. "On The Conditional Likelihood Ratio Test For Several Parameters In Iv Regression," Econometric Theory, Cambridge University Press, vol. 25(02), pages 305-335, April.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Randolph G. K. Tan, 2000. "Finite-Sample Optimality of Tests in a Structural Equation," Econometric Society World Congress 2000 Contributed Papers 1853, Econometric Society.
    13. 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.
    14. Manresa, Elena & Pe�aranda, Francisco & Sentana, Enrique, 2017. "Empirical Evaluation of Overspecified Asset Pricing Models," CEPR Discussion Papers 12085, C.E.P.R. Discussion Papers.
    15. 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.
    16. Guido Imbens, 2014. "Instrumental Variables: An Econometrician's Perspective," NBER Working Papers 19983, National Bureau of Economic Research, Inc.
    17. 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.
    18. Enrique Sentana, 2015. "Finite Underidentification," Working Papers wp2015_1508, CEMFI.

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