, 16 tweets, 6 min read Read on Twitter
1/ Alright, today in #EconBookClub I'd like to discuss chapter 4.2 of Guido Imbens' new working paper on the differences between the potential outcomes framework and directed acyclic graphs (link: arxiv.org/pdf/1907.07271…). #BookofWhy #Causality #Econometrics
2/ This chapter is about instrumental variable estimation, a topic to which Guido has contributed tremendously. Imbens and Angrist (1994) was definitely a big milestone in econometrics. I agree less with Guido's opinions on DAGs in this context though—as you might expect by now.
3/ Working with a graphical representation of a structural causal model (SCM) – i.e. the DAG – means that we explicitly refrain from making any distributional or functional form assumptions. That's a feature, not a bug!
4/ In many fields of the social sciences, unlike in physics, we just don't have good theory about the exact functional relationships governing the DGP. Some functional forms might be justified by economic theory, as, e.g., the work by Rosa Matzkin demonstrates.
5/ But in other contexts, explicit shape restrictions feel rather ad-hoc and are more invoked out of habit. In many fields, theory is actually restricted almost exclusively to the qualitative causal relationships between variables.
6/ The causal AI literature focusses on this important special case, because the goal is to equip machines with a flexible representation of causality that doesn't depend on a specific context and that is as general and robust as possible.
7/ But underlying every DAG we still have the functional representation of the structural causal model. For the IV graph the SCM would look like this:

Z = f1(e1)
X = f2(Z, U, e2)
Y = f3(X, U, e3)
8/ In an SCM it's very easy to incorporate a monotonicity assumption on f2, such that f2(Z=1) > f2(Z=0). So the results in Imbens and Angrist (1994) can be captured as a special case in the DAG / SCM framework without further problems.
9/ What is still missing, which was the motivation behind my tweet that Guido cites, are systematic results of the form "if I assume monotonicity for this edge, and linearity here, is the effect identified?" At the moment, we don't yet have a general procedure,
10/ similar to the do-calculus, that would allow us to decide those kinds of question. Developing such a procedure, proving its completeness, and automating it for different distributional and functional-form assumptions, would be a major breakthorugh in the literature.
11/ But, of course, such systematic results are similarly missing from PO, because PO practitioners restrict attention only to a handful of identification templates. So no specific advantage for PO in this regard!
12/ One thing that Guido overlooks in his paper, is that even though we might not have systematic results for "monotone DAGs" yet (although we can easily capture the special case of Imbens and Angrist, 1994), LATEs also aren't the only game in town either.
13/ @eliasbareinboim and @yudapearl (2014) demonstrate that the idea of using surrogate experiments for solving the confounding problem is actually much more general than the canonical IV case. arxiv.org/abs/1210.4842
14/ They show that in many setting, it's possible to identify the average treatment effect instead of only a LATE, and monotonicity isn't even required. With the help of do-calculus, the causal effect P(y|do(x) can be transformed into an expression that
15/ solely contains do(z) operators (the variables that we can intervene on / randomize), which will then be estimaable from the available data. This procedure is called "z-identification". And the best thing is that it is complete and can be fully automated.
16/ Z-identification allows to go beyond the piecemeal identification results of PO and to use surrogate experiments in a fully general manner. And, should it fail (like in the canonical IV case) we always have the approach by Imbens and Angrist (1994) in the backhand still.
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