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Semiparametric Bayesian Inference in Multiple Equation Models

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

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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Paper provided by Iowa State University, Department of Economics in its series Staff General Research Papers Archive 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
Contact details of provider: Postal:
Iowa State University, Dept. of Economics, 260 Heady Hall, Ames, IA 50011-1070

Phone: +1 515.294.6741
Fax: +1 515.294.0221
Web page: http://www.econ.iastate.edu
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  1. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. 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.
  3. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
  4. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
  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. Joseph G. Altonji & Robert A. Shakotko, 1987. "Do Wages Rise with Job Seniority?," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 437-459.
  7. Gary Koop & Dale J Poirer, 2001. "Bayesian Variants of Some classical Semiparametric Regression Techniques," ESE Discussion Papers 73, Edinburgh School of Economics, University of Edinburgh.
  8. 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.
  9. Frank Kleibergen & Eric Zivot, 2003. "Bayesian and Classical Approaches to Instrumental Variable Regression," Working Papers UWEC-2002-21-P, University of Washington, Department of Economics.
  10. Smith, Michael & Kohn, Robert, 2000. "Nonparametric seemingly unrelated regression," Journal of Econometrics, Elsevier, vol. 98(2), pages 257-281, October.
  11. DiNardo, John & Tobias, Justin, 2001. "Nonparametric Density and Regression Estimation," Staff General Research Papers 12020, Iowa State University, Department of Economics.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  17. Light, Audrey, 1998. "Estimating Returns to Schooling: When Does the Career Begin?," Economics of Education Review, Elsevier, vol. 17(1), pages 31-45, February.
  18. 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.
  19. Richard Blundell & Alan Duncan, 1998. "Kernel Regression in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 62-87.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
  26. 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.
  27. Siddhartha Chib & Edward Greenberg, 1994. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometrics 9408001, EconWPA, revised 24 Oct 1994.
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