Causal Analysis in Theory and Practice

Dear friends in causality research,

In this brief greeting I would like to first call attention to an approaching deadline and then discuss a couple of recent articles.

1.
Causality in Education Award – March 1, 2017

We are informed that the deadline for submitting a nomination for the ASA Causality in Statistics Education Award is March 1, 2017. For purpose, criteria and other information please see http://www.amstat.org/education/causalityprize/ .

2.
The next issue of the Journal of Causal Inference (JCI) is schedule to appear March, 2017. See https://www.degruyter.com/view/j/jci

MY contribution to this issue includes a tutorial paper entitled: “A Linear ‘Microscope’ for Interventions and Counterfactuals”. An advance copy can be viewed here: http://ftp.cs.ucla.edu/pub/stat_ser/r459.pdf
Enjoy!

3.
Overturning Econometrics Education (or, do we need a “causal interpretation”?)

My attention was called to a recent paper by Josh Angrist and Jorn-Steffen Pischke titled: “Undergraduate econometrics instruction” (A NBER working paper) http://www.nber.org/papers/w23144?utm_campaign=ntw&utm_medium=email&utm_source=ntw

This paper advocates a pedagogical paradigm shift that has methodological ramifications beyond econometrics instruction; As I understand it, the shift stands contrary to the traditional teachings of causal inference, as defined by Sewall Wright (1920), Haavelmo (1943), Marschak (1950), Wold (1960), and other founding fathers of econometrics methodology.

In a nut shell, Angrist and Pischke  start with a set of favorite statistical routines such as IV, regression, differences-in-differences among others, and then search for “a set of control variables needed to insure that the regression-estimated effect of the variable of interest has a causal interpretation”. Traditional causal inference (including economics) teaches us that asking whether the output of a statistical routine “has a causal interpretation” is the wrong question to ask, for it misses the direction of the analysis. Instead, one should start with the target causal parameter itself, and asks whether it is ESTIMABLE (and if so how), be it by IV, regression, differences-in-differences, or perhaps by some new routine that is yet to be discovered and ordained by name. Clearly, no “causal interpretation” is needed for parameters that are intrinsically causal; for example, “causal effect”, “path coefficient”, “direct effect”, “effect of treatment on the treated”, or “probability of causation”.

In practical terms, the difference between the two paradigms is that estimability requires a substantive model while interpretability appears to be model-free. A model exposes its assumptions explicitly, while statistical routines give the deceptive impression that they run assumptions-free (hence their popular appeal). The former lends itself to judgmental and statistical tests, the latter escapes such scrutiny.

In conclusion, if an educator needs to choose between the “interpretability” and “estimability” paradigms, I would go for the latter. If traditional econometrics education
is tailored to support the estimability track, I do not believe a paradigm shift is warranted towards an “interpretation seeking” paradigm as the one proposed by Angrist and Pischke,

I would gladly open this blog for additional discussion on this topic.

I tried to post a comment on NBER (National Bureau of Economic Research), but was rejected for not being an approved “NBER family member”. If any of our readers is a “”NBER family member” feel free to post the above. Note: “NBER working papers are circulated for discussion and comment purposes.” (page 1).

What do we know about counterfactuals in linear models?

Here is a neat result concerning the testability of counterfactuals in linear systems.
We know that counterfactual queries of the form P(Y_x=y|e) may or may not be empirically identifiable, even in experimental studies. For example, the probability of causation, P(Y_x=y|x',y') is in general not identifiable from experimental data (Causality, p. 290, Corollary 9.2.12) when X and Y are binary.¹ (Footnote-1: A complete graphical criterion for distinguishing testable from nontestable counterfactuals is given in Shpitser and Pearl (2007, upcoming)).

This note shows that things are much friendlier in linear analysis:

Claim A. Any counterfactual query of the form E(Y_x |e) is empirically identifiable in linear causal models, with e an arbitrary evidence.

Claim B. E(Y_x|e) is given by

E(Y_x|e) = E(Y|e) + T [x – E(X|e)]      (1)

where T is the total effect coefficient of X on Y, i.e.,

T = d E[Y_x]/dx = E(Y|do(x+1)) – E(Y|do(x))      (2)

Thus, whenever the causal effect T is identified, E(Y_x|e) = is identified as well.

(more…)