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A semi-parametric Bayesian approach to the instrumental variable problem

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  • Conley, Timothy G.
  • Hansen, Christian B.
  • McCulloch, Robert E.
  • Rossi, Peter E.

Abstract

We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components. We demonstrate that this procedure is both feasible and sensible using actual and simulated data. Sampling experiments compare inferences from the non-parametric Bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics. When errors are non-normal, our procedure is more efficient than standard Bayesian or classical methods.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:276-305
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    References listed on IDEAS

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    5. Cogley, Timothy & Startz, Richard, 2012. "Bayesian IV: the normal case with multiple endogenous variables," University of California at Santa Barbara, Economics Working Paper Series qt40v0x246, Department of Economics, UC Santa Barbara.
    6. Pelenis, Justinas, 2012. "Bayesian Semiparametric Regression," Economics Series 285, Institute for Advanced Studies.
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    8. Jensen, Mark J & Maheu, John M, 2013. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," MPRA Paper 52132, University Library of Munich, Germany.
    9. Halla, Martin & Zweimüller, Martina, 2014. "Parental Response to Early Human Capital Shocks: Evidence from the Chernobyl Accident," IZA Discussion Papers 7968, Institute for the Study of Labor (IZA).
    10. Manuel Wiesenfarth & Carlos Matías Hisgen & Thomas Kneib & Carmen Cadarso-Suarez, 2014. "Bayesian Nonparametric Instrumental Variables Regression Based on Penalized Splines and Dirichlet Process Mixtures," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 468-482, July.
    11. Sylvia Frühwirth-Schnatter & Martin Halla & Alexandra Posekany & Gerald J. Pruckner & Thomas Schober, 2014. "The Quantity and Quality of Children: A Semi-Parametric Bayesian IV Approach," Economics working papers 2014-03, Department of Economics, Johannes Kepler University Linz, Austria.
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    15. Sjoerd van den Hauwe & Richard Paap & Dick J.C. van Dijk, 2011. "An Alternative Bayesian Approach to Structural Breaks in Time Series Models," Tinbergen Institute Discussion Papers 11-023/4, Tinbergen Institute.
    16. Nomen Nescio, 2013. "Nomen Nescio," Tinbergen Institute Discussion Papers 12-095 not issued, Tinbergen Institute.
    17. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    18. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    19. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    20. Njuki, Eric & Bravo-Ureta, Boris, 2014. "A Bayesian Approach to Analyzing the Economic Costs of Environmental Regulation in U.S. Dairy Farming," Working Papers 33, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    21. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2013. "Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 13-191/III, Tinbergen Institute.
    22. Cem Çakmakli, 2012. "Bayesian Semiparametric Dynamic Nelson-Siegel Model," Working Paper series 59_12, Rimini Centre for Economic Analysis, revised Sep 2012.
    23. Andros Kourtellos & Alex Lenkoski & Kyriakos Petrou, 2017. "Measuring the Strength of the Theories of Government Size," University of Cyprus Working Papers in Economics 11-2017, University of Cyprus Department of Economics.
    24. Han, Yufeng, 2012. "State uncertainty in stock markets: How big is the impact on the cost of equity?," Journal of Banking & Finance, Elsevier, vol. 36(9), pages 2575-2592.
    25. van Hasselt, Martijn, 2011. "Bayesian inference in a sample selection model," Journal of Econometrics, Elsevier, vol. 165(2), pages 221-232.

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