Lahiri, Kajal and Gao, Chuanming (2002): A note on the double kclass estimator in simultaneous equations. Published in: Journal of Econometrics No. 108 (2002): pp. 101111.

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Abstract
Dwivedi and Srivastava (1984, DS) studied the exact finite sample properties of Nagar’s (1962) double kclass 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 kclass 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).
Item Type:  MPRA Paper 

Original Title:  A note on the double kclass estimator in simultaneous equations 
Language:  English 
Keywords:  Limited Information; Simultaneous Equations; Finite Sample; Mean Squared Error. 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C30  General 
Item ID:  22323 
Depositing User:  Kajal Lahiri 
Date Deposited:  25. Apr 2010 23:20 
Last Modified:  31. Dec 2015 13:22 
References:  Dwivedi, T.D, and V.K. Srivastava (1984). Exact finite sample properties of double kclass estimators in simultaneous equations. Journal of Econometrics 25, 263283. Mariano, R.S. (1982). Analytical smallsample distribution theory in econometrics: the simultaneousequation case. International Economic Review 23, 503533. Nagar, A.L. (1962). Double kclass estimators of parameters in simultaneous equations and their small sample properties. International Economic Review 3, 168188. Sawa, T. (1972). Finitesample properties of the kclass estimators. Econometrica 40, 653680. Srivastava, V.K. (1990). Developments in double kclass estimators of parameters in structural equations. In: Carter, R.A.L., Dutta, J. and Ullah, A., eds., Contributions to Econometric Theory and Application,Essays in honour of A.L. Nagar (SpringerVerlag). Srivastava, V.K., B.S. Agnihotri and T.D. Dwivedi (1980). Dominance of double kclass estimators in simultaneous equations. Annals of Institute of Statistical Mathematics 32, 387392. Srivastava, V.K., T.D. Dwivedi, M. Belinsky and R. Tiwari (1980). A numerical comparison of exact, largesample and smalldisturbance approximations of properties of kclass estimators. International Economic Review 21, 249252. Tsurumi, H. (1990). Comparing Bayesian and nonBayesian limited information estimators. In: Geisser, S., Hodges, J.S., Press, S.J., Zellner, A., eds., Bayesian and Likelihood Methods in Statistics and Econometrics (NorthHolland, Amsterdam). Zellner, A. (1986). Further results on Bayesian minimum expected loss (MELO) estimates and posterior distributions for structural coefficients. In: Slottje, D., eds., Advances in Econometrics, Vol. 5, pp. 171182. Zellner, A. (1998). The finite sample properties of simultaneous equations’ estimates and estimators: Bayesian and nonBayesian approaches. Journal of Econometrics 83, 185212. Zellner, A. and J. Tobias (2001). Further results on Bayesian Method of Moments analysis of the multiple regression model. International Economic Review 42, 121140. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/22323 