IDEAS home Printed from
   My bibliography  Save this paper

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


  • 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)


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.

Suggested Citation

  • Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2012. "Bayesian Nonparametric Instrumental Variable Regression based on Penalized Splines and Dirichlet Process Mixtures," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 127, Courant Research Centre PEG.
  • Handle: RePEc:got:gotcrc:127

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
    2. Florens, Jean-Pierre & Simoni, Anna, 2012. "Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior," Journal of Econometrics, Elsevier, vol. 170(2), pages 458-475.
    3. Kleibergen, Frank & Zivot, Eric, 2003. "Bayesian and classical approaches to instrumental variable regression," Journal of Econometrics, Elsevier, vol. 114(1), pages 29-72, May.
    4. Su, Liangjun & Ullah, Aman, 2008. "Local polynomial estimation of nonparametric simultaneous equations models," Journal of Econometrics, Elsevier, vol. 144(1), pages 193-218, May.
    5. Manuel Wiesenfarth & Tatyana Krivobokova & Stephan Klasen & Stefan Sperlich, 2012. "Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1286-1296, December.
    6. Krivobokova, Tatyana & Kneib, Thomas & Claeskens, Gerda, 2010. "Simultaneous Confidence Bands for Penalized Spline Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 852-863.
    7. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    8. 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, vol. 144(1), pages 276-305, May.
    9. 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, vol. 71(2), pages 487-503, April.
    10. Manuel Wiesenfarth & Thomas Kneib, 2010. "Bayesian geoadditive sample selection models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 381-404, May.
    11. Dale J. Poirier & Gary Koop & Justin Tobias, 2005. "Semiparametric Bayesian inference in multiple equation models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(6), pages 723-747.
    12. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    13. 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.
    14. Hall, Peter & Titterington, D. M., 1988. "On confidence bands in nonparametric density estimation and regression," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 228-254, October.
    15. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
    16. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    17. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    18. William A. Link & Richard J. Barker, 2005. "Modeling Association among Demographic Parameters in Analysis of Open Population Capture–Recapture Data," Biometrics, The International Biometric Society, vol. 61(1), pages 46-54, March.
    19. 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, vol. 71(2), pages 505-523, April.
    20. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 533-575.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Mendieta-Muñoz, Ivan, 2017. "On The Interaction Between Economic Growth And Business Cycles," Macroeconomic Dynamics, Cambridge University Press, vol. 21(4), pages 982-1022, June.
    2. Klein, Nadja & Herwartz, Helmut & Kneib, Thomas, 2020. "Modelling regional patterns of inefficiency: A Bayesian approach to geoadditive panel stochastic frontier analysis with an application to cereal production in England and Wales," Journal of Econometrics, Elsevier, vol. 214(2), pages 513-539.
    3. Ruochen Wu & Melvyn Weeks, 2020. "A Semi-Parametric Bayesian Generalized Least Squares Estimator," Papers 2011.10252,, revised Jan 2023.
    4. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    5. Dyevre, Arthur & Lampach, Nicolas, 2018. "The origins of regional integration: Untangling the effect of trade on judicial cooperation," International Review of Law and Economics, Elsevier, vol. 56(C), pages 122-133.
    6. Masahiro Tanaka, 2015. "Measuring Political Budget Cycles: A Bayesian Semiparametric Assessment," Working Papers 1415, Waseda University, Faculty of Political Science and Economics.
    7. Anupriya, & Graham, Daniel J. & Bansal, Prateek & Hörcher, Daniel & Anderson, Richard, 2023. "Optimal congestion control strategies for near-capacity urban metros: Informing intervention via fundamental diagrams," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    8. Antonio R. Linero, 2023. "Prior and posterior checking of implicit causal assumptions," Biometrics, The International Biometric Society, vol. 79(4), pages 3153-3164, December.
    9. Anupriya, & Bansal, Prateek & Graham, Daniel J., 2023. "Congestion in cities: Can road capacity expansions provide a solution?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 174(C).
    10. Anupriya & Daniel J. Graham & Daniel Horcher & Prateek Bansal, 2021. "Revisiting the empirical fundamental relationship of traffic flow for highways using a causal econometric approach," Papers 2104.02399,
    11. Pedro Saramago & Karl Claxton & Nicky J. Welton & Marta Soares, 2020. "Bayesian econometric modelling of observational data for cost‐effectiveness analysis: establishing the value of negative pressure wound therapy in the healing of open surgical wounds," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1575-1593, October.
    12. Didier Nibbering, 2019. "A High-dimensional Multinomial Choice Model," Monash Econometrics and Business Statistics Working Papers 19/19, Monash University, Department of Econometrics and Business Statistics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments," Discussion Paper Series DP2018-14, Research Institute for Economics & Business Administration, Kobe University.
    2. Xiaohong Chen & Timothy M. Christensen, 2015. "Optimal sup-norm rates, adaptivity and inference in nonparametric instrumental variables estimation," CeMMAP working papers 32/15, Institute for Fiscal Studies.
    3. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Sup-norm Rates, Adaptivity and Inference in Nonparametric Instrumental Variables Estimation," Cowles Foundation Discussion Papers 1923R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2015.
    4. Peter Pütz & Thomas Kneib, 2018. "A penalized spline estimator for fixed effects panel data models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 145-166, April.
    5. Joel L. Horowitz, 2013. "Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter," CeMMAP working papers 30/13, Institute for Fiscal Studies.
    6. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    7. Horowitz, Joel L., 2014. "Adaptive nonparametric instrumental variables estimation: Empirical choice of the regularization parameter," Journal of Econometrics, Elsevier, vol. 180(2), pages 158-173.
    8. Joel L. Horowitz, 2013. "Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter," CeMMAP working papers CWP30/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Kim Kyoo il & Petrin Amil, 2022. "A Generalized Non-Parametric Instrumental Variable-Control Function Approach to Estimation in Nonlinear Settings," Journal of Econometric Methods, De Gruyter, vol. 11(1), pages 91-125, January.
    10. Babii, Andrii, 2020. "Honest Confidence Sets In Nonparametric Iv Regression And Other Ill-Posed Models," Econometric Theory, Cambridge University Press, vol. 36(4), pages 658-706, August.
    11. Irene Botosaru & Chris Muris & Senay Sokullu, 2022. "Time-Varying Linear Transformation Models with Fixed Effects and Endogeneity for Short Panels," Department of Economics Working Papers 2022-01, McMaster University.
    12. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    13. Kim, Namhyun & W. Saart, Patrick, 2021. "Estimation in partially linear semiparametric models with parametric and/or nonparametric endogeneity," Cardiff Economics Working Papers E2021/9, Cardiff University, Cardiff Business School, Economics Section.
    14. Florens, Jean-Pierre & Simoni, Anna, 2016. "Regularizing Priors For Linear Inverse Problems," Econometric Theory, Cambridge University Press, vol. 32(1), pages 71-121, February.
    15. K. De Brabanter & Y. Liu & C. Hua, 2016. "Convergence rates for uniform confidence intervals based on local polynomial regression estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 31-48, March.
    16. Siddhartha Chib & Minchul Shin & Anna Simoni, 2022. "Bayesian estimation and comparison of conditional moment models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 740-764, July.
    17. Centorrino Samuele & Feve Frederique & Florens Jean-Pierre, 2017. "Additive Nonparametric Instrumental Regressions: A Guide to Implementation," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-25, January.
    18. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    19. Henderson, Daniel J. & Papageorgiou, Chris & Parmeter, Christopher F., 2013. "Who benefits from financial development? New methods, new evidence," European Economic Review, Elsevier, vol. 63(C), pages 47-67.
    20. Meghir, Costas & Rivkin, Steven, 2011. "Econometric Methods for Research in Education," Handbook of the Economics of Education, in: Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), Handbook of the Economics of Education, edition 1, volume 3, chapter 1, pages 1-87, Elsevier.

    More about this item


    Endogeneity; Markov Chain Monte Carlo methods; Simultaneous credible bands;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:got:gotcrc:127. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Dominik Noe (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.