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Bayesian Nonparametric Instrumental Variable Regression based on Penalized Splines and Dirichlet Process Mixtures

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Author Info

  • Manuel Wiesenfarth

    (University of Mannheim)

  • Carlos Matías Hisgen

    (Universidad Nacional del Nordeste, Argentina)

  • Thomas Kneib

    (Georg-August-University Göttingen)

  • Carmen Cadarso-Suarez

    (University of Santiago de Compostela)

Abstract

We propose a Bayesian nonparametric instrumental variable approach that allows us to correct for endogeneity bias in regression models where the covariate eff ects enter with unknown functional form. Bias correction relies on a simultaneous equations speci cation with flexible modeling of the joint error distribution implemented via a Dirichlet process mixture prior. Both the structural and instrumental variable equation are specified in terms of additive predictors comprising penalized splines for nonlinear eff ects of continuous covariates. Inference is fully Bayesian, employing efficient Markov Chain Monte Carlo simulation techniques. The resulting posterior samples do not only provide us with point estimates, but allow us to construct simultaneous credible bands for the nonparametric e ffects, including data-driven smoothing parameter selection. In addition, improved robustness properties are achieved due to the flexible error distribution speci fication. Both these features are extremely challenging in the classical framework, making the Bayesian one advantageous. In simulations, we investigate small sample properties and an investigation of the eff ect of class size on student performance in Israel provides an illustration of the proposed approach which is implemented in an R package bayesIV.

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File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_127.pdf
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Bibliographic Info

Paper provided by Courant Research Centre PEG in its series Courant Research Centre: Poverty, Equity and Growth - Discussion Papers with number 127.

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Date of creation: 15 Oct 2012
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Handle: RePEc:got:gotcrc:127

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Related research

Keywords: Endogeneity; Markov Chain Monte Carlo methods; Simultaneous credible bands;

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References

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  1. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, Elsevier, vol. 144(1), pages 193-218, May.
  2. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, Econometric Society, vol. 79(2), pages 347-394, 03.
  3. Manuel Wiesenfarth & Thomas Kneib, 2010. "Bayesian geoadditive sample selection models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, Royal Statistical Society, vol. 59(3), pages 381-404.
  4. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, Elsevier, vol. 139(1), pages 154-180, July.
  5. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, Elsevier, vol. 144(1), pages 276-305, May.
  6. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers, Massachusetts Institute of Technology (MIT), Department of Economics 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Philip T. Reiss & R. Todd Ogden, 2009. "Smoothing parameter selection for a class of semiparametric linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 71(2), pages 505-523.
  8. DAROLLES, Serge & FLORENS, Jean-Pierre & RENAULT, Éric, 2002. "Nonparametric Instrumental Regression," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2002-05, Universite de Montreal, Departement de sciences economiques.
  9. Frank Kleibergen & Eric Zivot, 2003. "Bayesian and Classical Approaches to Instrumental Variable Regression," Working Papers, University of Washington, Department of Economics UWEC-2002-21-P, University of Washington, Department of Economics.
  10. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  11. Koop, Gary M & Poirier, Dale J & Tobias, Justin, 2005. "Semiparametric Bayesian Inference in Multiple Equation Models," Staff General Research Papers, Iowa State University, Department of Economics 12009, Iowa State University, Department of Economics.
  12. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 71(2), pages 487-503.
  13. Alejandro Jara & Timothy Hanson & Fernando A. Quintana & Peter Müller & Gary L. Rosner, . "DPpackage: Bayesian Semi- and Nonparametric Modeling in R," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 40(i05).
  14. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  15. 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, Elsevier, vol. 87(1), pages 49-86, August.
  16. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, Elsevier, vol. 156(2), pages 322-336, June.
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