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

Author

Listed:
  • 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

This discussion paper resulted in a publication in Econometric Reviews , 2014, 33(1-4), 3-35. 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.

Suggested Citation

  • Arnold Zellner (posthumously) & Tomohiro Ando & Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2012. "Bayesian Analysis of Instrumental Variable Models: Acceptance-Rejection within Direct Monte Carlo," Tinbergen Institute Discussion Papers 12-098/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20120098
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    References listed on IDEAS

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    1. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "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," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
    2. 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, vol. 31(5), pages 515-523.
    3. 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, vol. 144(1), pages 276-305, May.
    4. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    5. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(6), pages 701-743, December.
    6. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December.
    7. 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, vol. 26(2), pages 413-434, April.
    8. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
    9. 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 EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Zellner, Arnold & Ando, Tomohiro, 2010. "A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model," Journal of Econometrics, Elsevier, vol. 159(1), pages 33-45, November.
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    Cited by:

    1. Halla, Martin & Zweimüller, Martina, 2014. "Parental Response to Early Human Capital Shocks: Evidence from the Chernobyl Accident," IZA Discussion Papers 7968, Institute of Labor Economics (IZA).
    2. Baştürk, Nalan & Grassi, Stefano & Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2017. "The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i01).
    3. Nalan Baştürk & Cem Çakmakli & S. Pinar Ceyhan & Herman K. Van Dijk, 2014. "Posterior‐Predictive Evidence On Us Inflation Using Extended New Keynesian Phillips Curve Models With Non‐Filtered Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1164-1182, November.
    4. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    5. 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 of Labor Economics (IZA).
    6. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2013. "Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 13-191/III, Tinbergen Institute.
    7. Pedro Saramago & Karl Claxton & Nicky J. Welton & Marta Soares, 2020. "Bayesian econometric modelling of observational data for cost‐effectiveness analysis: establishing the value of negative pressure wound therapy in the healing of open surgical wounds," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1575-1593, October.
    8. Chuanming Gao & Kajal Lahiri, 2019. "A Comparison of Some Bayesian and Classical Procedures for Simultaneous Equation Models with Weak Instruments," Econometrics, MDPI, vol. 7(3), pages 1-28, July.
    9. 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 1321, Koc University-TUSIAD Economic Research Forum.
    10. Nalan Baştürk & Stefano Grassi & Lennart Hoogerheide & Herman K. Van Dijk, 2016. "Parallelization Experience with Four Canonical Econometric Models Using ParMitISEM," Econometrics, MDPI, vol. 4(1), pages 1-20, March.
    11. 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 13-011/III, Tinbergen Institute.
    12. Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2017. "Bayesian analysis of boundary and near-boundary evidence in econometric models with reduced rank," Working Paper 2017/11, Norges Bank.
    13. Geweke, John & Durham, Garland, 2019. "Sequentially adaptive Bayesian learning algorithms for inference and optimization," Journal of Econometrics, Elsevier, vol. 210(1), pages 4-25.

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    More about this item

    Keywords

    Instrumental variables; Bayesian inference; Direct Monte Carlo; Acceptance-Rejection; numerical standard errors;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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