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A note on the double k-class estimator in simultaneous equations

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  • Gao, Chuanming
  • Lahiri, Kajal

Abstract

Dwivedi and Srivastava (1984, DS) studied the exact finite sample properties of Nagar’s (1962) double k-class estimator as continuous functions of its two characterizing scalars k1 and k2, and provided guidelines for their choice in empirical work. In this note we show that the empirical guidelines provided by DS are not entirely valid since they did not explore the complete range of the relevant parameter space in their numerical evaluations. We find that the optimal values of k2 leading to unbiased and mean squared error (MSE) minimizing double k-class estimators are not symmetric with respect to the sign of the product ρω12, where ρ is the correlation coefficient between the structural and reduced form errors, and w12 is the covariance between the unrestricted reduced form errors. Specifically, when ρω12 is positive,the optimal value of k2 is generally positive and greater than k1, which partly explains the superior performance of Zellner’s (1998) Bayesian Method of Moments (BMOM) and Extended MELO estimators reported in Tsurumi (1990).
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  • Gao, Chuanming & Lahiri, Kajal, 2002. "A note on the double k-class estimator in simultaneous equations," Journal of Econometrics, Elsevier, vol. 108(1), pages 101-111, May.
    • Handle: RePEc:eee:econom:v:108:y:2002:i:1:p:101-111
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    1. Mariano, Roberto S, 1982. "Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous-Equations Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 503-533, October.
    2. Zellner, Arnold & Tobias, Justin, 2001. "Further Results on Bayesian Method of Moments Analysis of the Multiple Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(1), pages 121-140, February.
    3. Srivastava, V K, et al, 1980. "A Numerical Comparison of Exact, Large-Sample and Small Disturbance Approximations of Properties of k-Class Estimators," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 249-252, February.
    4. Zellner, Arnold, 1998. "The finite sample properties of simultaneous equations' estimates and estimators Bayesian and non-Bayesian approaches," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 185-212.
    5. Dwivedi, T. D. & Srivastava, V. K., 1984. "Exact finite sample properties of double k-class estimators in simultaneous equations," Journal of Econometrics, Elsevier, vol. 25(3), pages 263-283, July.
    6. Sawa, Takamitsu, 1972. "Finite-Sample Properties of the k-Class Estimators," Econometrica, Econometric Society, vol. 40(4), pages 653-680, July.
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    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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