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

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Author Info

  • 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

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 11-137/4.

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Date of creation: 27 Sep 2011
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Handle: RePEc:dgr:uvatin:20110137

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

Related research

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

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Kleibergen, F.R. & Zivot, E., 1998. "Bayesian and classical approaches to instrumental variable regression," Econometric Institute Research Papers EI 9835, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  5. Attfield, C L F, 1976. "Estimation of the Structural Parameters in a Permanent Income Model," Economica, London School of Economics and Political Science, vol. 43(171), pages 247-54, August.
  6. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging Using Predictive Measures," CEPR Discussion Papers 5268, C.E.P.R. Discussion Papers.
  7. 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.
  8. HOOGERHEIDE, Lennart F. & KAASHOEK, Johan F. & VAN DIJK, Herman K., 2005. "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 2005029, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
  10. Dreze, Jacques H, 1976. "Bayesian Limited Information Analysis of the Simultaneous Equations Model," Econometrica, Econometric Society, vol. 44(5), pages 1045-75, September.
  11. 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.
  12. 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.
  13. Dreze, Jacques H., 1977. "Bayesian regression analysis using poly-t densities," Journal of Econometrics, Elsevier, vol. 6(3), pages 329-354, November.
  14. 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.
  15. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
  16. R. J. Cameron, 1957. "Comment," The Economic Record, The Economic Society of Australia, vol. 33(65), pages 261-264, 08.
  17. 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.
  18. 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.
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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.

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