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Semiparametric Bayesian inference in multiple equation models

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Author Info

  • Dale J. Poirier

    (Department of Economics, University of California at Irvine, Irvine, CA, USA)

  • Gary Koop

    (Department of Economics, University of Leicester, Leicester, UK)

  • Justin Tobias

Abstract

This paper outlines an approach to Bayesian semiparametric regression in multiple equation models which can be used to carry out inference in seemingly unrelated regressions or simultaneous equations models with nonparametric components. The approach treats the points on each nonparametric regression line as unknown parameters and uses a prior on the degree of smoothness of each line to ensure valid posterior inference despite the fact that the number of parameters is greater than the number of observations. We develop an empirical Bayesian approach that allows us to estimate the prior smoothing hyperparameters from the data. An advantage of our semiparametric model is that it is written as a seemingly unrelated regressions model with independent normal-Wishart prior. Since this model is a common one, textbook results for posterior inference, model comparison, prediction and posterior computation are immediately available. We use this model in an application involving a two-equation structural model drawn from the labour and returns to schooling literatures. Copyright © 2005 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.810
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File URL: http://qed.econ.queensu.ca:80/jae/2005-v20.6/
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Bibliographic Info

Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 20 (2005)
Issue (Month): 6 ()
Pages: 723-747

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Handle: RePEc:jae:japmet:v:20:y:2005:i:6:p:723-747

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  1. 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.
  2. Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers 2000-17, Centre de Recherche en Economie et Statistique.
  3. Altonji, Joseph G & Shakotko, Robert A, 1987. "Do Wages Rise with Job Seniority?," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 437-59, July.
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  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.
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  9. James Heckman & Edward Vytlacil, 2000. "Identifying the Role of Cognitive Ability in Explaining the Level of and Change in the Return to Schooling," NBER Working Papers 7820, National Bureau of Economic Research, Inc.
  10. John C. Chao & Peter C.B. Phillips, 1998. "Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n+1 Endogenous Variables," Cowles Foundation Discussion Papers 1198, Cowles Foundation for Research in Economics, Yale University.
  11. Koop, Gary & Poirier, Dale J., 2004. "Bayesian variants of some classical semiparametric regression techniques," Journal of Econometrics, Elsevier, vol. 123(2), pages 259-282, December.
  12. Audrey Light & Kathleen McGarry, 1998. "Job Change Patterns And The Wages Of Young Men," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 276-286, May.
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  17. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
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  21. Justin L. Tobias, 2003. "Are Returns to Schooling Concentrated Among The Most Able? A Semiparametric Analysis of The Ability--earnings Relationships," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(1), pages 1-29, February.
  22. Blackburn, McKinley L & Neumark, David, 1995. "Are OLS Estimates of the Return to Schooling Biased Downward? Another Look," The Review of Economics and Statistics, MIT Press, vol. 77(2), pages 217-30, May.
  23. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
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Citations

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Cited by:
  1. Nicholas Apergis & Christina Christou & Stephen Miller, 2012. "Convergence patterns in financial development: evidence from club convergence," Empirical Economics, Springer, vol. 43(3), pages 1011-1040, December.
  2. Bin Zhou & Qinfeng Xu & Jinhong You, 2011. "Efficient estimation for error component seemingly unrelated nonparametric regression models," Metrika, Springer, vol. 73(1), pages 121-138, January.
  3. Joshua C.C. Chan & Angelia L. Grant, 2014. "Fast Computation of the Deviance Information Criterion for Latent Variable Models," CAMA Working Papers 2014-09, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  4. Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2012. "Bayesian Nonparametric Instrumental Variable Regression based on Penalized Splines and Dirichlet Process Mixtures," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 127, Courant Research Centre PEG.
  5. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian identification, selection and estimation of semiparametric functions in high-dimensional additive models," Journal of Econometrics, Elsevier, vol. 143(2), pages 291-316, April.

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