Developments in Double k—Class Estimators of Parameters in Structural Equations

  • V. K. Srivastava


For estimating the parameters in a structural equation of a simultaneous equations model, Nagar proposed the family of double k—class estimators characterized by two scalars. This article reviews briefly the results dealing with the properties of estimators. Specifically, the issues in finite sample properties are highlighted and an appraisal is presented.


Variance Covariance Matrix Simultaneous Equation Model International Economic Review Noncentrality Parameter Bias Vector 
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  1. Agnihotri, B.S. [1980], Some Properties of Double k-Class Estimators and Their Generalization in Simultaneous Equation Econometric Models, unpublished Ph.D. Thesis, Lucknow University, India.Google Scholar
  2. Anderson, T.W. and T. Sawa [1973], Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions, Econometrica,Vol. 41, 683–714.CrossRefGoogle Scholar
  3. Anderson, T.W., N. Kunitomo and K. Morimune [1986], Comparing Single Equation Estimators in a Simultaneous Equation, Econometric Theory,Vol. 2, 1–32.CrossRefGoogle Scholar
  4. Basmann, R.L. [1974], Exact Finite Sample Distribution for Some Econometric Estimators and Test Statistics—A Survey and Appraisal, Chapter 4 in Frontiers in Quantitative Economics, Vol. 2 (edited by M.D. Intriligator and D.A. Kendrick), North-Holland Publishing Company.Google Scholar
  5. Brown, G.F., J.B. Kadane and J.G. Ramage [1974], The Asymptotic Bias and Mean Squared Error of Double k-Class Estimators when Disturbances are Small, International Economic Review, Vol. 15, 667–679.CrossRefGoogle Scholar
  6. Dhrymes, P.J. [1969] - An Identity Between Double k-Class and Two Stage Least Squares Estimators, International Economic Review, Vol. 10, 115–116.Google Scholar
  7. Dwivedi, T.D. and V.K. Srivastava [1984] - Exact Finite Sample Properties of Double k-Class Estimators in Simultaneous Equations, Journal of Econometrics, Vol. 23, 263–283.CrossRefGoogle Scholar
  8. Lye, J.N. [1987], Further Exact Finite Sample Properties of Double k-Class Estimators in Simultaneous Equations,“ paper presented at the Econometric Society Australian Meeting, Christchurch, New Zealand.Google Scholar
  9. Mariano, R.S. [1973], Approximations of the Distribution Functions of Theil’s k—Class Estimators,“ Econometrica,Vol. 41, 715–21.CrossRefGoogle Scholar
  10. Mariano, R.S. [1982], Analytical Small—Sample Distribution Theory in Econometrics—The Simultaneous—Equations Case, International Economic Review, Vol. 3, 168–188.Google Scholar
  11. Phillips, P.C.B. [1983], Exact Small Sample Theory in the Simultaneous Equations Model, Chapter 8 in Handbook of Econometrics, Vol. 1, (edited by Z. Griliches and M.D. Intriligator) North—Holland Publishing Company.Google Scholar
  12. Roy, A.R. and V.K. Srivastava [1966], Generalized Double k—Class Estimators,“ Journal of the Indian Statistical Association, Vol. 4, 38–46.Google Scholar
  13. Sawa, T. [1972], Finite—Sample Properties of the k—Class Estimators, Econometrica, Vol. 40, 653–680.CrossRefGoogle Scholar
  14. Scharf, W. [1976], K—Matrix—Class Estimators and the Full Information Maximum—Likelihood Estimator as a Special Case, Journal of Econometrics, Vol. 4, 41–50.CrossRefGoogle Scholar
  15. Srivastava, V.K. and B.S. Agnihotri [1979], A Linear and Consistent Class of Econometric Estimators in Simultaneous Equations,“ Journal of the Korean Statistical Society, Vol. 8, 117–124.Google Scholar
  16. Srivastava, V.K., B.S. Agnihotri and T.D. Dwivedi [1980], Dominance of Double k—Class Estimators in Simultaneous Equations, Annals of the Institute of Statistical Mathematics, Vol. 32, 387–392.Google Scholar
  17. Srivastava, V.K., T.D. Dwivedi, M. Belinksy and R. Tiwari [1980], A Numerical Comparison of Exact, Large—Sample and Small—Disturbance Approximations of Properties of k—Class Estimators, International Economic Review, Vol. 21, 249–252.Google Scholar
  18. Srivastava, V.K. and A.K. Srivastava [1983], A Note on Moments of k—Class Estimators for Negative k, Journal of Econometrics, Vol. 21, 257–260.CrossRefGoogle Scholar
  19. Srivastava, V.K. and R. Tiwari [1977], A Simple Derivation of the Identity Connecting Double k—Class and Two Stage Least Squares Estimators, Sankhya, Series C, Vol. 30, 1–2.Google Scholar
  20. Taylor, W.E. [1983], On the Relevance of Finite Sample Distribution Theory, Econometric Reviews,Vol 2, 1–40.CrossRefGoogle Scholar
  21. Tsurumi, H. [1987], Comparing Bayesian and Non—Bayesian Limited Information Estimators, Working Paper, Rutgers University.Google Scholar
  22. Zellner, A. [1986], Further Results on Bayesian Minimum Expected Loss (MELO) Estimates and Posterior Distributions for Structural Coefficients, Advances in Econometrics, Vol. 5, 171–182.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • V. K. Srivastava
    • 1
  1. 1.Lucknow University and University of Western OntarioCanada

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