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A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments

  • Chuanming Gao

    (SUNY at Albany)

  • Kajal Lahiri

    (SUNY at Albany)

We compare the finite sample performance of a number of Bayesian and Classical procedures for limited information simultaneous equations models with weak instruments by a Monte Carlo study. We consider recent Bayesian approaches developed by Ch ao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the Sample theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imben s and Krueger (1999) and Blomquist and Dahlberg (1999) are also considered. Since the posterior densities and their conditionals in CP and KVD are non-standard, we propose a ''Gibbs within Metropolis-Hastings'' algorithm, which only requires the availabi lity of the conditional densities from the candidate generating density. Our results show that in cases with very weak instruments, there is no single estimator that is superior to others in all cases. When endogeneity is weak, Zellner's MELO does the best. When the endogeneity is not weak and $\rho$$w_{12}>0$, where $\rho$ is the correlation coefficient between the structural and reduced form errors, and $w_{12}$ is the covariance between the unrestricted reduced form errors, BMOM outp erforms all other estimators by a wide margin. When the endogeneity is not weak and $\beta \rho

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Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0230.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0230
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  1. Pagan, Adrian, 1979. "Some consequences of viewing LIML as an iterated Aitken estimator," Economics Letters, Elsevier, vol. 3(4), pages 369-372.
  2. 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.
  3. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
  4. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
  5. Kleibergen, F.R., 1998. "Conditional densities in econometrics," Econometric Institute Research Papers EI 9853, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. Gao, Chuanming & Lahiri, Kajal, 2000. "Further consequences of viewing LIML as an iterated Aitken estimator," Journal of Econometrics, Elsevier, vol. 98(2), pages 187-202, October.
  7. Zellner, Arnold & Bauwens, Luc & Van Dijk, Herman K., 1988. "Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 39-72.
  8. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
  9. Zellner, Arnold, 1978. "Estimation of functions of population means and regression coefficients including structural coefficients : A minimum expected loss (MELO) approach," Journal of Econometrics, Elsevier, vol. 8(2), pages 127-158, October.
  10. Maddala, G S, 1976. "Weak Priors and Sharp Posteriors in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(2), pages 345-51, March.
  11. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-83, January.
  12. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  13. Dreze, Jacques H. & Richard, Jean-Francois, 1983. "Bayesian analysis of simultaneous equation systems," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 9, pages 517-598 Elsevier.
  14. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(06), pages 701-743, December.
  15. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  16. Dreze, Jacques H, 1976. "Bayesian Limited Information Analysis of the Simultaneous Equations Model," Econometrica, Econometric Society, vol. 44(5), pages 1045-75, September.
  17. Zellner, A., 1992. "Bayesian and Non-Bayesian Estimation using Balanced Loss Functions," Papers 92-20, California Irvine - School of Social Sciences.
  18. Frank Kleibergen & Eric Zivot, 2003. "Bayesian and Classical Approaches to Instrumental Variable Regression," Working Papers UWEC-2002-21-P, University of Washington, Department of Economics.
  19. Gao, Chuanming & Lahiri, Kajal, 2000. "MCMC algorithms for two recent Bayesian limited information estimators," Economics Letters, Elsevier, vol. 66(2), pages 121-126, February.
  20. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  21. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  22. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  23. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  24. 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.
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