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

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  • Kajal Lahiri
  • Chuanming Gao

Abstract

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 Chao and Phillips (1998, CP), Geweke (1996), Kleibergen and van Dijk (1998, KVD), and Zellner (1998). Amongst the sampling theory methods, OLS, 2SLS, LIML, Fuller's modified LIML, and the jackknife instrumental variable estimator (JIVE) due to Angrist, Imbens 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 availability 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 rw > 0, where r is the correlation coefficient between the structural and reduced form errors, and w is the co-variance between the unrestricted reduced form errors, BMOM outperforms all other estimators by a wide margin. When the endogeneity is not weak and br

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Bibliographic Info

Paper provided by University at Albany, SUNY, Department of Economics in its series Discussion Papers with number 01-15.

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Date of creation: 2001
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Handle: RePEc:nya:albaec:01-15

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Postal: Department of Economics, BA 110 University at Albany State University of New York Albany, NY 12222 U.S.A.
Phone: (518) 442-4735
Fax: (518) 442-4736

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Postal: Department of Economics, BA 110 University at Albany State University of New York Albany, NY 12222 U.S.A.
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Web: http://www.albany.edu/economics/research/workingp/index.shtml

Related research

Keywords: Limited Information Estimation; Metropolis-Hastings Algorithm; Gibbs Sampler; Monte Carlo Method;

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References

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  1. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August.
  2. Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
  3. 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.
  4. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  5. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  6. 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.
  7. ZELLNER, A. & BAUWENS, Luc & VAN DIJK, H., 1987. "Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods," CORE Discussion Papers 1987056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. 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.
  9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  10. 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.
  11. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
  12. 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..
  13. Dreze, Jacques H, 1976. "Bayesian Limited Information Analysis of the Simultaneous Equations Model," Econometrica, Econometric Society, vol. 44(5), pages 1045-75, September.
  14. Gao, Chuanming & Lahiri, Kajal, 2000. "MCMC algorithms for two recent Bayesian limited information estimators," Economics Letters, Elsevier, vol. 66(2), pages 121-126, February.
  15. 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.
  16. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-53, May.
  17. Kleibergen, F.R., 1998. "Conditional densities in econometrics," Econometric Institute Research Papers EI 9853, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  18. Maddala, G S, 1976. "Weak Priors and Sharp Posteriors in Simultaneous Equation Models," Econometrica, Econometric Society, vol. 44(2), pages 345-51, March.
  19. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  20. Zellner, A., 1992. "Bayesian and Non-Bayesian Estimation using Balanced Loss Functions," Papers 92-20, California Irvine - School of Social Sciences.
  21. John F. Geweke, 1995. "Bayesian reduced rank regression in econometrics," Working Papers 540, Federal Reserve Bank of Minneapolis.
  22. 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.
  23. Pagan, Adrian, 1979. "Some consequences of viewing LIML as an iterated Aitken estimator," Economics Letters, Elsevier, vol. 3(4), pages 369-372.
  24. 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.
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Citations

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Cited by:
  1. Radchenko, Stanislav & Tsurumi, Hiroki, 2006. "Limited information Bayesian analysis of a simultaneous equation with an autocorrelated error term and its application to the U.S. gasoline market," Journal of Econometrics, Elsevier, vol. 133(1), pages 31-49, July.
  2. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(01), pages 42-86, February.
  3. Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variables Regression," Econometrics 9812002, EconWPA.
  4. John Chao & Norman Swanson, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments," Departmental Working Papers 200420, Rutgers University, Department of Economics.
  5. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.

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