IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20110137.html
   My bibliography  Save this paper

Instrumental Variables, Errors in Variables, and Simultaneous Equations Models: Applicability and Limitations of Direct Monte Carlo

Author

Listed:
  • Arnold Zellner

    ((posthumous) Booth School of Business, University of Chicago, USA)

  • Tomohiro Ando

    (Graduate School of Business Administration, Keio University, Japan)

  • Nalan Basturk

    (Econometric Institute, Erasmus University Rotterdam, The Netherlands; The Rimini Centre for Economic Analysis, Rimini, Italy)

  • Lennart Hoogerheide

    (VU University Amsterdam, The Netherlands)

  • Herman K. van Dijk

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

Abstract

See also the publication in 'Econometric Reviews' , 2014, 33(1-2), 3-35. A Direct Monte Carlo (DMC) approach is introduced for posterior simulation in theInstrumental Variables (IV) model with one possibly endogenous regressor, multipleinstruments and Gaussian errors under a flat prior. This DMC method can also beapplied in an IV model (with one or multiple instruments) under an informativeprior for the endogenous regressor's effect. This DMC approach can not be appliedto more complex IV models or Simultaneous Equations Models with multiple endogenous regressors. An Approximate DMC (ADMC) approach is introduced thatmakes use of the proposed Hybrid Mixture Sampling (HMS) method, which facilitates Metropolis-Hastings (MH) or Importance Sampling from a proper marginalposterior density with highly non-elliptical shapes that tend to infinity for a pointof singularity. After one has simulated from the irregularly shaped marginal distri-bution using the HMS method, one easily samples the other parameters from theirconditional Student-t and Inverse-Wishart posteriors. An example illustrates theclose approximation and high MH acceptance rate. While using a simple candidatedistribution such as the Student-t may lead to an infinite variance of ImportanceSampling weights. The choice between the IV model and a simple linear model un-der the restriction of exogeneity may be based on predictive likelihoods, for whichthe efficient simulation of all model parameters may be quite useful. In future workthe ADMC approach may be extended to more extensive IV models such as IV withnon-Gaussian errors, panel IV, or probit/logit IV.

Suggested Citation

  • Arnold Zellner & Tomohiro Ando & Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2011. "Instrumental Variables, Errors in Variables, and Simultaneous Equations Models: Applicability and Limitations of Direct Monte Carlo," Tinbergen Institute Discussion Papers 11-137/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20110137
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/11137.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    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. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    3. Milton Friedman, 1957. "Introduction to "A Theory of the Consumption Function"," NBER Chapters,in: A Theory of the Consumption Function, pages 1-6 National Bureau of Economic Research, Inc.
    4. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
    5. Jana Eklund & Sune Karlsson, 2007. "Forecast Combination and Model Averaging Using Predictive Measures," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 329-363.
    6. Zellner, Arnold & Bauwens, Luc & Van Dijk, Herman K., 1988. "Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods," Journal of Econometrics, Elsevier, vol. 38(1-2), pages 39-72.
    7. Ardia, David & Baştürk, Nalan & Hoogerheide, Lennart & van Dijk, Herman K., 2012. "A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3398-3414.
    8. Various, 1957. "Additional Comments," NBER Chapters,in: The Measurement and Behavior of Unemployment, pages 585-600 National Bureau of Economic Research, Inc.
    9. Kathryn Graddy, 1995. "Testing for Imperfect Competition at the Fulton Fish Market," RAND Journal of Economics, The RAND Corporation, vol. 26(1), pages 75-92, Spring.
    10. 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.
    11. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2008. "Marginal likelihoods for non-Gaussian models using auxiliary mixture sampling," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4608-4624, June.
    12. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
    13. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
    14. 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.
    15. Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
    16. Aliprantis, Charalambos D. & Barnett, William A. & Cornet, Bernard & Durlauf, Steven, 2007. "Special issue editors' introduction: The interface between econometrics and economic theory," Journal of Econometrics, Elsevier, vol. 136(2), pages 325-329, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cogley, Timothy & Startz, Richard, 2012. "Bayesian IV: the normal case with multiple endogenous variables," University of California at Santa Barbara, Economics Working Paper Series qt40v0x246, Department of Economics, UC Santa Barbara.

    More about this item

    Keywords

    Instrumental Variables; Errors in Variables; Simultaneous Equations Model; Bayesian estimation; Direct Monte Carlo; Hybrid Mixture Sampling;

    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
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tin:wpaper:20110137. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tinbergen Office +31 (0)10-4088900). General contact details of provider: http://edirc.repec.org/data/tinbenl.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.