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Causality, Conditional Independence, and Graphical Separation in Settable Systems

Author

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  • Karim Chalak

    (Boston College)

  • Halbert White

    (University of California-San Diego)

Abstract

We study the interrelations between (conditional) independence and causal relations in settable systems. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide necessary and sufficient causal and stochastic conditions for (conditional) dependence among random vectors of interest in settable systems. Immediate corollaries ensure the validity of Reichenbach's principle of common cause and its informative extension, the conditional Reichenbach principle of common cause. We relate our results to notions of d-separation and D-separation in the artificial intelligence literature.

Suggested Citation

  • Karim Chalak & Halbert White, 2008. "Causality, Conditional Independence, and Graphical Separation in Settable Systems," Boston College Working Papers in Economics 689, Boston College Department of Economics, revised 04 Jul 2010.
    • Handle: RePEc:boc:bocoec:689
    Note: Previously circulated as "Independence and Conditional Independence in Causal Systems"
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    File URL: http://fmwww.bc.edu/EC-P/wp689.pdf
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    References listed on IDEAS

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    1. Donald B. Rubin, 2004. "Direct and Indirect Causal Effects via Potential Outcomes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(2), pages 161-170, June.
    2. Steffen L. Lauritzen & Thomas S. Richardson, 2002. "Chain graph models and their causal interpretations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 321-348, August.
    3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    4. Sims, Christopher A, 1972. "Money, Income, and Causality," American Economic Review, American Economic Association, vol. 62(4), pages 540-552, September.
    5. Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
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    Citations

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    Cited by:

    1. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    2. Taoufik Bouezmarni & Jeroen V.K. Rombouts & Abderrahim Taamouti, 2011. "Nonparametric Copula-Based Test for Conditional Independence with Applications to Granger Causality," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 275-287, October.
    3. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
    4. Diebold, Francis X. & Yilmaz, Kamil, 2015. "Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring," OUP Catalogue, Oxford University Press, number 9780199338306, Decembrie.
    5. Karim Chalak & Halbert White, 2011. "Viewpoint: An extended class of instrumental variables for the estimation of causal effects," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 44(1), pages 1-51, February.
    6. Heckman, James & Pinto, Rodrigo, 2015. "Causal Analysis After Haavelmo," Econometric Theory, Cambridge University Press, vol. 31(1), pages 115-151, February.
    7. Lu, Xun & White, Halbert, 2014. "Robustness checks and robustness tests in applied economics," Journal of Econometrics, Elsevier, vol. 178(P1), pages 194-206.
    8. Dionissi Aliprantis, 2017. "Human capital in the inner city," Empirical Economics, Springer, vol. 53(3), pages 1125-1169, November.
    9. Dionissi Aliprantis, 2013. "Covariates and causal effects: the problem of context," Working Papers (Old Series) 1310, Federal Reserve Bank of Cleveland.
    10. White, Halbert & Xu, Haiqing & Chalak, Karim, 2014. "Causal discourse in a game of incomplete information," Journal of Econometrics, Elsevier, vol. 182(1), pages 45-58.
    11. Halbert White & Karim Chalak, 2008. "Identifying Structural Effects in Nonseparable Systems Using Covariates," Boston College Working Papers in Economics 734, Boston College Department of Economics.
    12. Karim Chalak & Halbert White, 2007. "An Extended Class of Instrumental Variables for the Estimation of Causal Effects," Boston College Working Papers in Economics 692, Boston College Department of Economics, revised 30 Nov 2009.
    13. Xun Lu, 2015. "A Covariate Selection Criterion for Estimation of Treatment Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 506-522, October.

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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