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Semiparametric Bayesian Inference in Multiple Equation Models

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  • Koop, Gary M
  • Poirier, Dale J
  • Tobias, Justin

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 labor and returns to schooling literatures.

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Bibliographic Info

Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers with number 12009.

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Date of creation: 01 Jan 2005
Date of revision:
Publication status: Published in Journal of Applied Econometrics 2005, vol. 20, pp. 723-747
Handle: RePEc:isu:genres:12009

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Postal: Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070
Phone: +1 515.294.6741
Fax: +1 515.294.0221
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Web page: http://www.econ.iastate.edu
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References

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  1. Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers 2000-17, Centre de Recherche en Economie et Statistique.
  2. Frank Kleibergen & Eric Zivot, 1998. "Bayesian and Classical Approaches to Instrumental Variable Regression," Working Papers 0063, University of Washington, Department of Economics.
  3. Chao, John C. & Phillips, Peter C. B., 2002. "Jeffreys prior analysis of the simultaneous equations model in the case with n+1 endogenous variables," Journal of Econometrics, Elsevier, vol. 111(2), pages 251-283, December.
  4. McKinley L. Blackburn & David Neumark, 1993. "Are OLS Estimates of the Return to Schooling Biased Downward? Another Look," NBER Working Papers 4259, National Bureau of Economic Research, Inc.
  5. James Heckman & Edward Vytlacil, 2001. "Identifying The Role Of Cognitive Ability In Explaining The Level Of And Change In The Return To Schooling," The Review of Economics and Statistics, MIT Press, vol. 83(1), pages 1-12, February.
  6. John DiNardo & Justin L. Tobias, 2001. "Nonparametric Density and Regression Estimation," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 11-28, Fall.
  7. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
  8. Koop, G. & Poirier, D., 2000. "Bayesian Variants of Some Classical Semiparametric Regression Techniques," Papers 00-01-22, California Irvine - School of Social Sciences.
  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. Smith, Michael & Kohn, Robert, 2000. "Nonparametric seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 98(2), pages 257-281, October.
  11. 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.
  12. 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.
  13. Joseph G. Altonji & Robert A. Shakotko, 1985. "Do Wages Rise With Job Seniority?," NBER Working Papers 1616, National Bureau of Economic Research, Inc.
  14. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
  15. DREZE, Jacques H. & RICHARD, Jean-François, . "Bayesian analysis of siultaneous equation systems," CORE Discussion Papers RP -556, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  16. John Cawley & James Heckman & Edward Vytlacil, 1999. "On Policies To Reward The Value Added By Educators," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 720-727, November.
  17. Fernandez, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 1997. "On the use of panel data in stochastic frontier models with improper priors," Journal of Econometrics, Elsevier, vol. 79(1), pages 169-193, July.
  18. Topel, Robert H, 1991. "Specific Capital, Mobility, and Wages: Wages Rise with Job Seniority," Journal of Political Economy, University of Chicago Press, vol. 99(1), pages 145-76, February.
  19. Light, Audrey, 1998. "Estimating Returns to Schooling: When Does the Career Begin?," Economics of Education Review, Elsevier, vol. 17(1), pages 31-45, February.
  20. Whitney Newey & James Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  21. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  22. Richard Blundell & Alan Duncan, 1998. "Kernel Regression in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 62-87.
  23. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
  24. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
  25. 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.
  26. Card, David, 1999. "The causal effect of education on earnings," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 30, pages 1801-1863 Elsevier.
  27. Bernt Bratsberg & Dek Terrell, 1998. "Experience, Tenure, and Wage Growth of Young Black and White Men," Journal of Human Resources, University of Wisconsin Press, vol. 33(3), pages 658-682.
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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. 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.
  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. 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.
  5. 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.

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