What Invariance Is and How to Test for It

Abstract

Causal assessment is the problem of establishing whether a relation between (variable) X and (variable) Y is causal. This problem, to be sure, is widespread across the sciences. According to accredited positions in the philosophy of causality and in social science methodology, invariance under intervention provides the most reliable test to decide whether X causes Y. This account of invariance (under intervention) has been criticised, among other reasons, because it makes manipulations on the putative causal factor fundamental for the causal methodology; consequently, the argument goes, the account is ill-suited to those contexts where manipulations are not performed, for instance, the social sciences. The article aims to extend the account of invariance (under intervention), in a way that manipulations on the putative causal factors are not methodologically fundamental, and yet invariance remains key for causal assessment both in experimental and non-experimental contexts.

Acknowledgements

The idea of writing this article emerged some time ago during a fascinating conversation with Brendan Clarke, Donald Gillies, and Phyllis Illari. I am very grateful for their insights on this difficult topic and for their valuable comments and suggestions on early drafts of the article. I am also hugely indebted to Michel Mouchart and Guillaume Wunsch: their input on causal modelling ‘in practice’ is, as usual, invaluable. Many thanks also to Jossi Berkovitz, Grazia Ietto-Gillies, Mike Joffe, Bert Leuridan, Alex Marcellesi, and Jon Williamson for extremely useful discussions and suggestions on later drafts and presentations of this article. Finally, comments from three anonymous referees and from the editor of this journal have been incredibly useful to clarify some thorny points. Any mistakes or inaccuracies remain of course mine.

Notes

[1] It is worth noting that the philosophy of mechanisms developed in the past 20 years or so is also a viable alternative to laws in order to provide explanations in the special sciences (and elsewhere)—for an overview of mechanisms and their relation to causality and explanation, see, for instance, Illari and Russo (2014, chap. 10).

[2] Exogeneity is widely discussed in economics and econometrics. Mouchart and Russo (2011) reassess the locus classicus (Engle, Hendry, and Richard 1983) and other important contributions and interpret exogeneity as a condition of separability of inference between causes and effects in the marginal-conditional decomposition.

[3] I use ‘invariance’ and ‘stability’ interchangeably; Haavelmo also used ‘constancy’ or ‘persistence’, which I take all to be synonymous.

[4] It is worth recalling that invariance tests are not sufficient to establish causal relations. They play an important role in deciding about the validity of the whole model, but they are not the only test. They are the focus of this article, though.

[5] Other commentators, mentioned earlier in the article, raised concerns about aspects of ‘conceptual’ manipulationism, but not specifically on the relations between metaphysics and methodology.

[6] Woodward (2008) does not agree with this objection, and, again, Strevens (2008) is not convinced by Woodward's counterarguments.