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Bayesian Model Averaging in the Instrumental Variable Regression Model

  • Gary Koop

    (University of Strathclyde)

  • Roberto Leon-Gonzalez


    (National Graduate Institute for Policy Studies)

  • Rodney Strachan

    (The Australian National University)

This paper considers the instrumental variable regression model when there is uncertainty about the set of instruments, exogeneity restrictions, the validity of identifying restrictions and the set of exogenous regressors. This uncertainty can result in a huge number of models. To avoid statistical problems associated with standard model selection procedures, we develop a reversible jump Markov chain Monte Carlo algorithm that allows us to do Bayesian model averaging. The algorithm is very flexible and can be easily adapted to analyze any of the different priors that have been proposed in the Bayesian instrumental variables literature. We show how to calculate the probability of any relevant restriction (e.g. the posterior probability that over-identifying restrictions hold) and discuss diagnostic checking using the posterior distribution of discrepancy vectors. We illustrate our methods in a returns-to-schooling application.

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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 09_11.

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Date of creation: Jan 2011
Date of revision: Aug 2012
Publication status: Forthcoming in the Journal of Econometrics
Handle: RePEc:rim:rimwps:09_11
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  1. Carmen Fernandez & Eduardo Ley & Mark F J Steel, 1998. "Benchmark priors for Bayesian model averaging," ESE Discussion Papers 26, Edinburgh School of Economics, University of Edinburgh.
  2. ZELLNER, Arnold & BAUWENS, Luc & VAN DIJK, Herman K., . "Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods," CORE Discussion Papers RP 796, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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.
  4. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(02), pages 222-240, April.
  5. Li, Mingliang & Tobias, Justin, 2004. "Returns to Schooling and Bayesian Model Averaging: A Union of Two Literatures," Staff General Research Papers 12011, Iowa State University, Department of Economics.
  6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  7. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
  8. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
  9. Gary Koop & Roberto León-González & Rodney W. Strachan, 2005. "Efficient Posterior Simulation for Cointegrated Models with Priors On the Cointegration Space," Discussion Papers in Economics 05/13, Department of Economics, University of Leicester, revised Apr 2006.
  10. 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.
  11. Dreze, Jacques H, 1976. "Bayesian Limited Information Analysis of the Simultaneous Equations Model," Econometrica, Econometric Society, vol. 44(5), pages 1045-75, September.
  12. Blackburn, McKinley L & Neumark, David, 1995. "Are OLS Estimates of the Return to Schooling Biased Downward? Another Look," The Review of Economics and Statistics, MIT Press, vol. 77(2), pages 217-30, May.
  13. Ethan Cohen-Cole & Steven Durlauf & Jeffrey Fagan & Daniel Nagin, 2007. "Model uncertainty and the deterrent effect of capital punishment," Risk and Policy Analysis Unit Working Paper QAU07-3, Federal Reserve Bank of Boston.
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