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Semiparametric Bayesian inference in smooth coefficient models

  • Koop, Gary
  • Tobias, Justin L.

We describe procedures for Bayesian estimation and testing in cross sectional, panel data and nonlinear smooth coefficient models. The smooth coefficient model is a generalization of the partially linear or additive model wherein coefficients on linear explanatory variables are treated as unknown functions of an observable covariate. In the approach we describe, points on the regression lines are regarded as unknown parameters and priors are placed on differences between adjacent points to introduce the potential for smoothing the curves. The algorithms we describe are quite simple to implement - for example, estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model. We apply our methods using data from the National Longitudinal Survey of Youth (NLSY). Using the NLSY data we first explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. We also examine model of female labor supply and use this example to illustrate how the described techniques can been applied in nonlinear settings.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 134 (2006)
Issue (Month): 1 (September)
Pages: 283-315

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Handle: RePEc:eee:econom:v:134:y:2006:i:1:p:283-315
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  1. Koop, G. & van Dijk, H.K., 1999. "Testing for integration using evolving trend and seasonal models: A Bayesian approach," Econometric Institute Research Papers EI 9934/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. KOOP , Gary & OSIEWALSKI , Jacek & STEEL , Mark, 1995. "Bayesian Efficiency Analysis through Individual Effects : Hospital Cost Frontiers," CORE Discussion Papers 1995036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Thomas C. Buchmueller & Robert G. Valletta, 1996. "The effect of health insurance on married female labor supply," Working Papers in Applied Economic Theory 96-09, Federal Reserve Bank of San Francisco.
  4. Tobias, J.L., 2000. "Are Return to Schooling Concentrated Among the Most Able? A Semiparametric Analysis of the Ability-Earnings Relationship," Papers 00-01-12, California Irvine - School of Social Sciences.
  5. DiNardo, John & Tobias, Justin, 2001. "Nonparametric Density and Regression Estimation," Staff General Research Papers Archive 12020, Iowa State University, Department of Economics.
  6. McKinley L. Blackburn & David Neumark, 1991. "Omitted-Ability Bias and the Increase in the Return to Schooling," NBER Working Papers 3693, National Bureau of Economic Research, Inc.
  7. 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.
  8. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
  9. 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.
  10. John Cawley & Karen Conneely & James Heckman & Edward Vytlacil, 1996. "Cognitive Ability, Wages, and Meritocracy," NBER Working Papers 5645, National Bureau of Economic Research, Inc.
  11. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
  12. Shively, Thomas S. & Kohn, Robert, 1997. "A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 39-52.
  13. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
  14. John F. Geweke & Michael P. Keane & David E. Runkle, 1994. "Statistical inference in the multinomial multiperiod probit model," Staff Report 177, Federal Reserve Bank of Minneapolis.
  15. 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.
  16. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
  17. 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.
  18. Chou, Y. J. & Staiger, Douglas, 2001. "Health insurance and female labor supply in Taiwan," Journal of Health Economics, Elsevier, vol. 20(2), pages 187-211, March.
  19. 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.
  20. Dale J. Poirier, 1995. "Intermediate Statistics and Econometrics: A Comparative Approach," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262161494, December.
  21. Koop, Gary M & Tobias, Justin, 2004. "Learning About Heterogeneity in Returns to Schooling," Staff General Research Papers Archive 12008, Iowa State University, Department of Economics.
  22. Christopher R. Taber, 2001. "The Rising College Premium in the Eighties: Return to College or Return to Unobserved Ability?," Review of Economic Studies, Oxford University Press, vol. 68(3), pages 665-691.
  23. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-22, July.
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