## The difference between statistical and causal assumptions

24 Jun, 2019 at 19:57 | Posted in Statistics & Econometrics | Comments Off on The difference between statistical and causal assumptionsThere are three fundamental differences between statistical and causal assumptions. First, statistical assumptions, even untested, are testable in principle, given sufficiently large sample and sufficiently fine measurements. Causal assumptions, in contrast, cannot be verified even in principle, unless one resorts to experimental control. This difference is especially accentuated in Bayesian analysis. Though the priors that Bayesians commonly assign to statistical parameters are untested quantities, the sensitivity to these priors tends to diminish with increasing sample size. In contrast, sensitivity to priors of causal parameters … remains non-zero regardless of (nonexperimental) sample size.

Second, statistical assumptions can be expressed in the familiar language of probability calculus, and thus assume an aura of scholarship and scientific re- spectability. Causal assumptions, as we have seen before, are deprived of that honor, and thus become immediate suspect of informal, anecdotal or metaphysical thinking. Again, this difference becomes illuminated among Bayesians, who are accustomed to accepting untested, judgmental assumptions, and should therefore invite causal assumptions with open arms—they don’t. A Bayesian is prepared to accept an expert’s judgment, however esoteric and untestable, so long as the judgment is wrapped in the safety blanket of a probability expression. Bayesians turn extremely suspicious when that same judgment is cast in plain English, as in “mud does not cause rain” …

The third resistance to causal (vis-a-vis statistical) assumptions stems from their intimidating clarity. Assumptions about abstract properties of density functions or about conditional independencies among variables are, cognitively speaking, rather opaque, hence they tend to be forgiven, rather than debated. In contrast, assumptions about how variables cause one another are shockingly transparent, and tend therefore to invite counter-arguments and counter-hypotheses.

Pearl’s seminal contributions to this research field is well-known and indisputable. But on the ‘taming’ and ‘resolve’ of the issues, yurs truly however has to admit that (under the influence of especially David Freedman and Nancy Cartwright) I still have some doubts on the reach, especially in terms of realism and relevance, of his ‘do-calculus solutions’ for social sciences in general and economics in specific (see here, here, here and here). The distinction between the causal — ‘interventionist’ — E[Y|do(X)] and the more traditional statistical — ‘conditional expectationist’ — E[Y|X] is crucial, but Pearl and his associates, although they have fully explained why the first is so important, have to convince us that it (in a relevant way) can be exported from ‘engineer’ contexts where it arguably easily and universally apply, to socio-economic contexts where ‘manipulativity’ and ‘modularity’ are not perhaps so universally at hand.

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