## Tuesday, November 30, 2010

### A critique of Granger causality

Continuing the journey that I began with "causation" and continued in "Granger causality and cointegration," today I’m pitting the recipient of a MacArthur “genius” grant against a Nobel Prize winner. Nancy Cartwright, a philosopher of science (no, not the voice of Bart Simpson), claims that the argument structure of Granger causality is “exceedingly simple.” But, she continues, “the premises are concomitantly exceedingly strong.” That is, “every possible source of variation of every kind must be controlled if a valid conclusion is to be drawn.” (Hunting Causes and Using Them [Cambridge University Press, 2007], p. 29)

Her critique is straightforward though stylistically dense. First, we must “suppose that for populations picked out by the right descriptions Ki, if X and Y are probabilistically dependent and X precedes Y then X causes Y. If any population P contains such a Ki as a subpopulation, then X causes Y in P in the sense that for some individuals in P, X will cause Y (in the ‘long run’). …

“The argument is deductive because of the way the Ki are supposed to be characterized. Begin from the assumption that if X and Y are probabilistically dependent in a population that must be because of the causal principles operating in that population. (Without this kind of assumption it will never be possible to establish any connection between probabilities and causality.) The trick then is to characterize the Ki in just the right way to eliminate all possible accounts of dependency between X and Y other than that X causes Y (there is no correlation in Ki between X and any ‘other’ causes of Y, there is no ‘selection bias’, etc.). Given that Ki is specified in this way, if X and Y are probabilistically dependent in population Ki, there is no possibility left other than the hypothesis that X causes Y.” That is, everything that has occurred up to the time of the putative cause must be held fixed.

“Of course the epistemic problems are enormous. How are we to know what to include in Ki? … Knowledge of just the right kind is thought to be rare in the social sciences…. Granger causality solves the problem of our ignorance about just what to put in the descriptions Ki by putting in everything that happens previous to X. That of course is literally impossible so in the end very specific decisions about the nature of the K’s must be made for any application.” (p. 30)

If we say that X Granger-causes Y, we have to know that “all other sources of probabilistic dependence have been randomized over or controlled for” and that “we are studying systems where all dependencies are due to causal connections.” (pp. 33-34) This is most likely impossible.

Which takes us back to Logic 101. If the premises of a deductive argument are true the conclusion must be true. If we aren’t sure whether the premises of the argument are true but are willing to assign a 90% probability of their being true, it is “reasonable to assign a probability of 90 percent to the conclusion.” But, Cartwright continues, that “is very different from the case where we are fairly certain, may even take ourselves to know, nine out of ten of the premises, but have strong reason to deny the tenth. In that case the method can make us no more certain of the conclusion than we are of that doubtful premise. Deductions can take us from truths to truths but once there is one false premise, they cannot do anything at all.” (p. 34)

Cartwright’s critique ultimately hinges on her characterization of Granger causality as a deductive scheme that clinches causal inferences rather than merely inductively vouches for them. Kevin Hoover grants her claim that “many arguments take the form of clinchers, conditional on background assumptions.” But, he counters, “she is wrong to imply that advocates of these forms of argument are insensitive to the tentativeness and the fallibility of those strong background assumptions. Such sensitivity means that arguments that take the form of clinchers are, in reality, always practically vouchers.” (review of Cartwright’s book) In another piece (“RCTs and the Gold Standard”) Hoover repeats his contention, arguing that all methods—clinchers and vouchers—“require good judgment to draw relevant conclusions—and a great deal of it. Since judgment cannot be eliminated, we had best get on with managing it. This however requires judgment!”

To my mind Cartwright’s criticism stands unscathed. There is a philosophical chasm between “X Granger-causes Y” and “In my judgment X Granger-causes Y.” The former is intended to be viewed probabilistically; the latter introduces elements of subjectivity and uncertainty.

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Now that you’ve eaten your brussel sprouts, tomorrow you’ll get dessert—a very short non-financial YouTube video that you’ve probably already seen but then again maybe you haven’t.