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Semiparametric Bayesian inference in smooth coefficient models

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  • Gary Koop

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  • Justin Tobias

Abstract

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.

Suggested Citation

  • Gary Koop & Justin Tobias, 2003. "Semiparametric Bayesian inference in smooth coefficient models," Discussion Papers in Economics 04/18, Department of Economics, University of Leicester.
  • Handle: RePEc:lec:leecon:04/18
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    References listed on IDEAS

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    1. Scott E. Atkinson & Jeffrey H. Dorfman, 2009. "Feasible estimation of firm-specific allocative inefficiency through Bayesian numerical methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 675-697.
    2. Dorfman, Jeffrey H. & Karali, Berna, 2010. "Do Farmers Hedge Optimally or by Habit? A Bayesian Partial-Adjustment Model of Farmer Hedging," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 42(04), pages 791-803, November.
    3. Huang, Ho-Chuan (River) & Lin, Shu-Chin, 2008. "Smooth-time-varying Okun's coefficients," Economic Modelling, Elsevier, vol. 25(2), pages 363-375, March.
    4. Karali, Berna & Dorfman, Jeffrey H. & Thurman, Walter N., 2008. "Do Inventory and Time-to-Delivery Effects Vary Across Futures Contracts? Insights from a Smoothed Bayesian Estimator," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6084, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Dorfman, Jeffrey H. & Patridge, Mark D. & Galloway, Hamilton, 2008. "Are High-Tech Employment and Natural Amenities Linked?: Answers from a Smoothed Bayesian Spatial Model," 2008 Annual Meeting, July 27-29, 2008, Orlando, Florida 6459, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. Suzanna-Maria Paleologou, 2016. "The long-run tendency of government expenditure: a semi-parametric modelling approach," Empirical Economics, Springer, vol. 50(3), pages 753-776, May.
    7. Bacolod, Marigee P. & Tobias, Justin L., 2006. "Schools, school quality and achievement growth: Evidence from the Philippines," Economics of Education Review, Elsevier, vol. 25(6), pages 619-632, December.
    8. Amin Mugera & Michael Langemeier & Allen Featherstone, 2012. "Labor productivity convergence in the Kansas farm sector: a three-stage procedure using data envelopment analysis and semiparametric regression analysis," Journal of Productivity Analysis, Springer, vol. 38(1), pages 63-79, August.
    9. Zheng, Xiaoyong, 2008. "Semiparametric Bayesian estimation of mixed count regression models," Economics Letters, Elsevier, vol. 100(3), pages 435-438, September.
    10. Agee, Mark D. & Atkinson, Scott E. & Crocker, Thomas D. & Williams, Jonathan W., 2014. "Non-separable pollution control: Implications for a CO2 emissions cap and trade system," Resource and Energy Economics, Elsevier, vol. 36(1), pages 64-82.
    11. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.

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