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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 both cross sectional and longitudinal data smooth coefficient models (with and without endogeneity problems). 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 - estimation, testing and smoothing parameter selection can be carried out analytically in the cross-sectional smooth coefficient model, and estimation in the hierarchical models only involves simulation from standard distributions. We apply our methods by fitting several hierarchical models using data from the National Longitudinal Survey of Youth (NLSY). We explore the relationship between ability and log wages and flexibly model how returns to schooling vary with measured cognitive ability. In a generalization of this model, we also permit endogeneity of schooling and describe simulation-based methods for inference in the presence of the endogeneity problem. We find returns to schooling are approximately constant throughout the ability support and that simpler (and often used) parametric specifications provide an adequate description of these relationships.

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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
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  3. Koop, Gary M & Tobias, Justin, 2004. "Learning About Heterogeneity in Returns to Schooling," Staff General Research Papers 12008, Iowa State University, Department of Economics.
  4. Gary Koop & Herman K. van Dijk & Henk Hoek, 1997. "Testing for Integration using Evolving Trend and Seasonals Models: A Bayesian Approach," Tinbergen Institute Discussion Papers 97-078/4, Tinbergen Institute.
  5. 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.
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  17. John Cawley & Karen Conneely & James Heckman & Edward Vytlacil, 1996. "Cognitive Ability, Wages, and Meritocracy," NBER Working Papers 5645, National Bureau of Economic Research, Inc.
  18. 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.
  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.
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