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Bayesian Model Averaging in the Instrumental Variable Regression Model

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Author Info

  • Gary Koop

    (University of Strathclyde)

  • Roberto Leon-Gonzalez

    ()
    (National Graduate Institute for Policy Studies)

  • Rodney Strachan

    (The Australian National University)

Abstract

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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Bibliographic Info

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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Keywords: Bayesian; endogeneity; simultaneous equations; reversible jump Markov chain Monte Carlo;

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References

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  1. McKinley L. Blackburn & David Neumark, 1993. "Are OLS Estimates of the Return to Schooling Biased Downward? Another Look," NBER Working Papers 4259, National Bureau of Economic Research, Inc.
  2. 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.
  3. 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.
  4. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
  5. Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2011. "A Class of Adaptive EM-based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation," Tinbergen Institute Discussion Papers 11-004/4, Tinbergen Institute.
  6. 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.
  7. Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
  8. Zellner, A. & Bauwnes, L. & Van Dijk, H.K., 1988. "Bayesian Specification Analysis And Estimation Of Simultaneous Equation Models Using Monte Carlo Methods," Papers m8804, Southern California - Department of Economics.
  9. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  10. repec:dgr:uvatin:2098025 is not listed on IDEAS
  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. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
  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.
  14. 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.
  15. 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.
  16. Lennart Hoogerheide & Anne Opschoor & Herman K. van Dijk, 2011. "A Class of Adaptive EM-based Importance Sampling Algorithms for Efficient and Robust Posterior and Predictive Simulation," Tinbergen Institute Discussion Papers 11-004/4, Tinbergen Institute.
  17. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
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Citations

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Cited by:
  1. Ampaabeng, Samuel K. & Tan, Chih Ming, 2013. "The long-term cognitive consequences of early childhood malnutrition: The case of famine in Ghana," Journal of Health Economics, Elsevier, vol. 32(6), pages 1013-1027.
  2. Roberto Leon-Gonzalez & Thanabalasingam Vinayagathasan, 2013. "Robust Determinants of Growth in Asian Developing Economies: A Bayesian Panel Data Model Averaging Approach," GRIPS Discussion Papers 13-12, National Graduate Institute for Policy Studies.
  3. Roman Horváth, 2012. "Does Trust Promote Growth?," Working Papers 319, Institut für Ost- und Südosteuropaforschung (Institute for East and South-East European Studies).
  4. Martins, Luis F. & Gabriel, Vasco J., 2014. "Linear instrumental variables model averaging estimation," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 709-724.
  5. Samuel K. Ampaabeng & Chih Ming Tang, 2012. "The Long-Term Cognitive Consequences of Early Childhood Malnutrition: The Case of Famine in Ghana," Working Paper Series 64_12, The Rimini Centre for Economic Analysis.

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