Discussion on Causality

AalborgUniversityFirst, let me congratulate both authors on two ﬁne papers which illuminate important aspectsof causal inference. I have only a little to say about Professor Arjas’ paper which speciﬁcallyilluminates the aspect oftime and causality in an excellent way. I will therefore concentrate onthe concepts described by Professor Rubin which seem to be more controversial, thus lendingthemselves directly to discussion.1. Causal languagesIn the modern revival ofinterest in causal inference in statistics, a number ofcompetingformalisms prevail such as structural equations (Pearl, 2000), graphical models (Spirtes etal.,1993; Pearl, 1995a; Lauritzen, 2001; Dawid, 2002), counterfactual random variables (Robins,1986), or potential responses (Rubin, 1974, 1978; Holland, 1986). Much energy has been usedto promote the virtues ofone formalism versus the other, seemingly without coming nearer toa consensus; see the somewhat relentless discussion ofDawid (2000). Professor Rubin’s paper advocates the use of potential responses in contrast to graphicalmodels, illustrated with a discussion of direct and indirect effects in connection with the use ofsurrogate endpoints in clinical trials.Although discussions ofthis nature can be used to sharpen the minds and pinpointimportant issues, I ﬁnd them generally futile. Personally I see the different formalisms asdifferent ‘languages’. The French language may be best for making love whereas the Italianmay be more suitable for singing, but both are indeed possible, and I have no difﬁcultyaccepting that potential responses, structural equations, and graphical models coexist aslanguages expressing causal concepts each with their virtues and vices.It is hardly possible to imagine a language that completely prevents users from expressingstupid things. Personally I am much more comfortable with the language of graphical modelsthan that ofpotential responses, which I, as also Dawid (2000), ﬁnd just as seductive andpotentially dangerous as Professor Rubin ﬁnds graphical models. I certainly disagree withProfessor Rubin’s statement that graphical models tend to bury essential scientiﬁc and designissues. It is always true that concepts that strongly support intuition in many cases, can seduceone to incorrect conclusions in other cases. Each ofus speaks and understands our ownlanguage most comfortably but, to communicate in a fruitful way, it is indeed an advantage tolearn other languages as well.Professor Rubin invites rebuttal of his statement that causal problems are typically ﬁrstunderstood by the method ofpotential responses and subsequently translated into the lan-guage of graphical models. Honestly, I think this statement is unfair. A new formalism, suchas that ofgraphical models, must ﬁrst earn its keep by showing that it performs in situationsthat are simple and well understood (using e.g. potential responses), hence it may initiallyappear as ifits value primarily lies in reformulating known things. Subsequently it mustdemonstrate successful treatment of more difﬁcult problems, where there is no establishedstandard with which to compare it. Personally I believe that graphical models will prove veryhelpful for the future of causal inference, but I admit that their full power and ﬂexibility forexpressing and manipulating causal concepts has not yet been fully exploited.