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Causal effects and counterfactual conditionals: contrasting Rubin, Lewis and Pearl

Published online by Cambridge University Press:  11 February 2021

Keith A. Markus*
Affiliation:
Department of Psychology, John Jay College of Criminal Justice, CUNY, 524 West 59th Street, New York, NY10019, USA

Abstract

Rubin and Pearl offered approaches to causal effect estimation and Lewis and Pearl offered theories of counterfactual conditionals. Arguments offered by Pearl and his collaborators support a weak form of equivalence such that notation from the rival theory can be re-purposed to express Pearl’s theory in a way that is equivalent to Pearl’s theory expressed in its native notation. Nonetheless, the many fundamental differences between the theories rule out any stronger form of equivalence. A renewed emphasis on comparative research can help to guide applications, further develop each theory, and better understand their relative strengths and weaknesses.

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Article
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© The Author(s), 2021. Published by Cambridge University Press

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References

Baumgartner, M. and Gebharter, A. 2016. Constitutive relevance, mutual manipulability, and fat-handedness. British Journal of Philosophy of Science 67, 731756.CrossRefGoogle Scholar
Bennett, J. 2003. A Philosophical Guide to Conditionals. Oxford: Oxford University Press.CrossRefGoogle Scholar
Bollen, K.A. and Pearl, J. 2014. Eight myths about causality and structural equation models. In Handbook of Causal Analysis for Social Research, ed. S.L. Morgan, 301328. Dordrecht: Springer.Google Scholar
Briggs, R. 2012. Interventionist counterfactuals. Philosophical Studies 160, 139166.CrossRefGoogle Scholar
Cartwright, N. 2017. Can structural equations explain how mechanisms explain? In Making a Difference: Essays on the Philosophy of Causation, ed. H. Beebee, C. Hitchcock and H. Price, 132152. Oxford: Oxford University Press.Google Scholar
Fisher, T. 2017. Causal counterfactuals are not interventionist counterfactuals. Synthese 194, 49354957.CrossRefGoogle Scholar
Galles, D. and Pearl, J. 1998. An axiomatic characterization of causal counterfactuals. Foundations of Science 3, 151182.CrossRefGoogle Scholar
Hall, N. 2004. Rescued from the rubbish bin: Lewis on causation. Philosophy of Science 71, 11071114.CrossRefGoogle Scholar
Halpern, J.Y. 2000. Axiomatizing causal reasoning. Journal of Artificial Intelligence Research 12, 317337.CrossRefGoogle Scholar
Halpern, J.Y. 2013. From causal models to counterfactual structures. Review of Symbolic Logic 6, 305322.CrossRefGoogle Scholar
Halpern, J.Y. and Hitchcock, C. 2015. Graded causation and defaults. British Journal for the Philosophy of Science 66, 413457.CrossRefGoogle Scholar
Hausman, D.M. 1998. Causal Asymmetries. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hiddleston, E. 2005. Causal powers. British Journal for the Philosophy of Science 56, 2759.CrossRefGoogle Scholar
Holland, P. 1986. Statistics and causal inference. Journal of the American Statistical Association, 81, 945970.CrossRefGoogle Scholar
Hoover, K.D. 2001. Causality in Macroeconomics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Imbens, G.W. 2019. Potential outcome and directed acyclic graph approaches to causality: relevance for empirical practice in economics. National Bureau of Economic Research working paper no. 26104. doi: 10.3386/w2614.CrossRefGoogle Scholar
Imbens, G.W. and Rubin, D.B. 2015. Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. New York, NY: Cambridge University Press.CrossRefGoogle Scholar
Jackson, F. 1977. A causal theory of counterfactuals. Australasian Journal of Philosophy 55, 321.CrossRefGoogle Scholar
Kim, J. 1974. Noncausal connections. Noûs 8, 4152.CrossRefGoogle Scholar
Lewis, D. 1973a. Causation. Journal of Philosophy 70, 556567.CrossRefGoogle Scholar
Lewis, D. 1973b. Counterfactuals. Malden, MA: Blackwell.Google Scholar
Lewis, D. 1973c. Counterfactuals and comparative possibility. Journal of Philosophical Logic 2, 418446.CrossRefGoogle Scholar
Lewis, D. 1986a. On the Plurality of Worlds. Malden, MA: Blackwell.Google Scholar
Lewis, D. 1986b. Philosophical Papers, Vol. 2. Oxford: Oxford University Press.Google Scholar
Lewis, D. 1999. Papers in Metaphysics and Epistemology. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lewis, D. 2004. Causation as influence. In Causation and Counterfactuals, ed. Collins, J., Hall, N. and Paul, L.A., 75106. Cambridge, MA: MIT Press.Google Scholar
Markus, K.A. 2011. Real causes and ideal manipulations: Pearl’s theory of causal inference from the point of view of psychological research methods. In Causality in the Sciences, ed. McKay Illari, P., Russo, F. and Williamson, J., 240269. Oxford: Oxford University Press.CrossRefGoogle Scholar
Markus, K.A. 2013. An incremental approach to causal inference in the behavioral sciences. Synthese 191, 20892113.CrossRefGoogle Scholar
Markus, K.A. 2016. Consistent treatment of variables and causation poses a challenge for behavioral research methods: a commentary on Nesselroade and Molenaar (2016). Multivariate Behavioral Research 51, 413418.CrossRefGoogle Scholar
McGee, V. 1985. A counterexample to modus ponens. Journal of Philosophy 82, 462471.CrossRefGoogle Scholar
Morgan, S.L. and Winship, C. 2007. Counterfactuals and Causal Inference: Methods and Principles for Social Research. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pearl, J. 2009a. Causality: Models, reasoning and inference, 2nd edn. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pearl, J. 2009b. Remarks on the method of propensity score. Statistics in Medicine 29, 14151416.CrossRefGoogle Scholar
Pearl, J. 2009c. Myth, Confusion, and Science in Causal Analysis. Unpublished. http://ftp.cs.ucla.edu/pub/stat_ser/r348-warning.pdf.Google Scholar
Pearl, J. 2012. The causal foundations of structural equation modeling. In Handbook of Structural Equation Modeling, ed. Hoyle, R.H., 6891. New York, NY: Guilford Press.Google Scholar
Pearl, J. 2018. Does obesity shorten life? Or is it the soda? On non-manipulable causes. Journal of Causal Inference 6. doi: 10.1515/jci-2018-2001.CrossRefGoogle Scholar
Pearl, J. 2019. On the interpretation of do(x). Journal of Causal Inference 7. doi: 10.1515/jci-2019-2002.CrossRefGoogle Scholar
Pearl, J. and Bareinboim, E. 2014. External validity: from Do-calculus to transportability across populations. Statistical Science 29, 579595.CrossRefGoogle Scholar
Pearl, J. and Mackenzie, D. 2018. The Book of Why: The New Science of Cause and Effect. New York, NY: Basic Books.Google Scholar
Pearl, J., Glymour, M. and Jewell, N.P. 2016. Causal Inference in Statistics: A Primer. Chichester: Wiley.Google Scholar
Pollock, J.L. 1990. Nomic Probability and the Foundations of Induction. New York, NY: Oxford University Press.CrossRefGoogle Scholar
Rosenbaum, P.R. and Rubin, D.B. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70, 4155.CrossRefGoogle Scholar
Rubin, D.B. 1974. Estimating causal effects of treatments in randomized and non-randomized studies. Journal of Educational Psychology 66, 688701.CrossRefGoogle Scholar
Rubin, D.B. 1978. Bayesian inference for causal effects: the role of randomization. Annals of Statistics 6, 3458.CrossRefGoogle Scholar
Rubin, D.B. 1980. Randomization analysis of experimental data: the Fisher randomization test comment. Journal of the American Statistical Association 75, 591593.Google Scholar
Rubin, D.B. 2007. The design versus the analysis of observational studies for causal effects: parallels with the design of randomized trials. Statistics in Medicine 26, 2036.CrossRefGoogle ScholarPubMed
Rubin, D.B. 2009. Should observational studies be designed to allow lack of balance in covariate distributions across treatment groups? Statistics in Medicine 29, 14201423.CrossRefGoogle Scholar
Schaffer, J. 2016. Grounding in the image of causation. Philosophical Studies 173, 49100.CrossRefGoogle Scholar
Schmaltz, T.M. 2014. Efficient Causation: A History. Oxford: Oxford University Press.CrossRefGoogle Scholar
Shadish, W.R., Cook, T.D. and Leviton, L.C. 1991. Foundations of Program Evaluation: Theories and Practice. Newbury Park, CA: Sage.Google Scholar
Shrier, I. 2008. Letter to the Editor. Statistics in Medicine 27, 27402741.CrossRefGoogle Scholar
Sjolander, A. 2009. Propensity scores and M-structures. Statistics in Medicine 29, 14161420.CrossRefGoogle Scholar
Spirtes, P., Glymour, C. and Scheines, R. 2000. Causation, Prediction and Search, 2nd edn. Cambridge, MA: MIT Press.Google Scholar
Stalnaker, R. 1968. A theory of conditionals. In Studies in Logical Theory, ed. Rescher, N., 98112. Oxford: Blackwell.Google Scholar
Stalnaker, R. 1976. Possible worlds. Noûs 10, 6575.CrossRefGoogle Scholar
Stalnaker, R. 1981. A defense of conditional excluded middle. In Ifs, ed. Harper, W.L., Stalnaker, R. and Pearce, G., 87104. Dordrecht: D. Reidel.Google Scholar
Starr, W. 2019. Counterfactuals. In The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), ed. E.N. Zalta. <https://plato.stanford.edu/archives/fall2019/entries/counterfactuals/>..>Google Scholar
Steyer, R. 2005. Analyzing individual and average causal effects via structural equation models. Methodology 1, 3954.CrossRefGoogle Scholar
Woodward, J. 2003. Making Things Happen: A Theory of Causal Explanation. Oxford: Oxford University Press.Google Scholar
Woodward, J. 2015. Interventionism and causal exclusion. Philosophy and Phenomenological Research 91, 303347.CrossRefGoogle Scholar
Woodward, J. 2016. The problem of variable choice. Synthese 193, 10471072.CrossRefGoogle Scholar
Zhang, J., Lam, W.-L. and De Clercq, R. 2013. A peculiarity in Pearl’s logic of interventionist counterfactuals. Journal of Philosophical Logic 42, 783794.CrossRefGoogle Scholar
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