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

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

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Chuanming Gao (SUNY at Albany)
Kajal Lahiri (SUNY at Albany)

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Kajal Lahiri

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 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 $\beta \rho <0$ ($\beta$ being the structural parameter), KVD approach seems to work very well. Surprisingly, the performance of JIVE was disappointing in all our experim ents.

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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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Paper
- Kajal Lahiri & Chuanming Gao, . "A Comparison of Some Recent Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Discussion Papers 01-15, State University of New York at Albany, Department of Economics. [Downloadable!]

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Other versions:
- 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.
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Other versions:
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Other versions:
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Other versions:
- Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
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Other versions:
- Kleibergen, F. & Van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Papers 9714/a, Erasmus University of Rotterdam - Econometric Institute.
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repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
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Frank Kleibergen, 1997. "Equality Restricted Random Variables: Densities and Sampling Algorithms," Tinbergen Institute Discussion Papers 97-005/4, Tinbergen Institute.
Other versions:
- Kleibergen, Frank, 1996. "Equality restricted random variables: densities and sampling algorithms," Econometric Institute Report 36, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
- Kleibergen, F., 1996. "Equality Restricted Random Variables: Densities and Sampling Algorithms," Papers 9662/a, Erasmus University of Rotterdam - Econometric Institute.
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. [Downloadable!] (restricted)

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Cited by:
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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. [Downloadable!]
Other versions:
- Norman R. Swanson & John C. Chao, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions with Many Weak Instruments," Econometric Society 2004 Far Eastern Meetings 668, Econometric Society.

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