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Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo

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Author Info

  • Arnold Zellner (posthumously)

    (University of Chicago, USA)

  • Tomohiro Ando

    (Keio University, Japan)

  • Nalan Basturk

    (Erasmus University Rotterdam)

  • Lennart Hoogerheide

    ()
    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    ()
    (VU University Amsterdam, and Erasmus University Rotterdam)

Abstract

We discuss Bayesian inferential procedures within the family of instrumental variables regression models and focus on two issues: existence conditions for posterior moments of the parameters of interest under a flat prior and the potential of Direct Monte Carlo (DMC) approaches for efficient evaluation of such possibly highly onelliptical posteriors. We show that, for the general case of m endogenous variables under a flat prior, posterior moments of order r exist for the coefficients reflecting the endogenous regressors’ effect on the dependent variable, if the number of instruments is greater than m +r , even though there is an issue of local non-identification that causes non-elliptical shapes of the posterior. This stresses the need for efficient Monte Carlo integration methods. We introduce an extension of DMC that incorporates an acceptance-rejection sampling step within DMC. This Acceptance-Rejection within Direct Monte Carlo (ARDMC) method has the attractive property that the generated random drawings are independent, which greatly helps the fast convergence of simulation results, and which facilitates the evaluation of the numerical accuracy. The speed of ARDMC can be easily further improved by making use of parallelized computation using multiple core machines or computer clusters. We note that ARDMC is an analogue to the well-known 'Metropolis-Hastings within Gibbs' sampling in the sense that one 'more difficult' step is used within an 'easier' simulation method. We compare the ARDMC approach with the Gibbs sampler using simulated data and two empirical data sets, involving the settler mortality instrument of Acemoglu et al. (2001) and father's education's instrument used by Hoogerheide et al. (2012a). Even without making use of parallelized computation, an efficiency gain is observed both under strong and weak instruments, where the gain can be enormous in the latter case.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-098/III.

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Date of creation: 24 Sep 2012
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Handle: RePEc:dgr:uvatin:20120098

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Web page: http://www.tinbergen.nl

Related research

Keywords: Instrumental variables; Bayesian inference; Direct Monte Carlo; Acceptance-Rejection; numerical standard errors;

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References

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  1. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Daron Acemoglu & Simon Johnson & James A. Robinson, 2000. "The Colonial Origins of Comparative Development: An Empirical Investigation," NBER Working Papers 7771, National Bureau of Economic Research, Inc.
  3. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 111(2), pages 223-249, December.
  4. HOOGERHEIDE, Lennart F. & KAASHOEK, Johan F. & van DIJK, Herman K., . "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: an application of flexible sampling methods using neural networks," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1922, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. de Pooter, M.D. & Ravazzolo, F. & Segers, R. & van Dijk, H.K., 2008. "Bayesian near-boundary analysis in basic macroeconomic time series models," Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  6. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP): Scope, Evolution and Enhancements," SOEPpapers on Multidisciplinary Panel Data Research 1, DIW Berlin, The German Socio-Economic Panel (SOEP).
  7. Hoogerheide, Lennart & Block, Joern H. & Thurik, Roy, 2012. "Family background variables as instruments for education in income regressions: A Bayesian analysis," Economics of Education Review, Elsevier, Elsevier, vol. 31(5), pages 515-523.
  8. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, Elsevier, vol. 144(1), pages 276-305, May.
  9. Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2012. "A class of adaptive importance sampling weighted EM algorithms for efficient and robust posterior and predictive simulation," Journal of Econometrics, Elsevier, Elsevier, vol. 171(2), pages 101-120.
  10. Zellner, Arnold & Ando, Tomohiro, 2010. "Bayesian and non-Bayesian analysis of the seemingly unrelated regression model with Student-t errors, and its application for forecasting," International Journal of Forecasting, Elsevier, Elsevier, vol. 26(2), pages 413-434, April.
  11. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, Elsevier, vol. 159(1), pages 33-45, November.
  12. Dreze, Jacques H., 1977. "Bayesian regression analysis using poly-t densities," Journal of Econometrics, Elsevier, Elsevier, vol. 6(3), pages 329-354, November.
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Cited by:
  1. Nalan Basturk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers, Tinbergen Institute 14-085/III, Tinbergen Institute.
  2. Frühwirth-Schnatter, Sylvia & Halla, Martin & Posekany, Alexandra & Pruckner, Gerald J. & Schober, Thomas, 2014. "The Quantity and Quality of Children: A Semi-Parametric Bayesian IV Approach," IZA Discussion Papers 8024, Institute for the Study of Labor (IZA).
  3. Nalan Basturk & Cem Cakmakli & Pinar Ceyhan & Herman K. van Dijk, 2013. "Posterior-Predictive Evidence on US Inflation using Phillips Curve Models with Non-Filtered Time Series," Tinbergen Institute Discussion Papers, Tinbergen Institute 13-011/III, Tinbergen Institute.
  4. Nalan Basturk & Cem Cakmakli & Pinar Ceyhan & Herman K. van Dijk, 2013. "Posterior-Predictive Evidence on US Inflation using Extended Phillips Curve Models with non-filtered Data," Koç University-TUSIAD Economic Research Forum Working Papers, Koc University-TUSIAD Economic Research Forum 1321, Koc University-TUSIAD Economic Research Forum.

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