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1/ Let's continue with chapter 4.3 of Guido Imbens' new working paper on PO versus DAGs (link: arxiv.org/pdf/1907.07271…), this time with a discussion about simultaneity and cyclic models. #EconBookClub #BookofWhy #Econometrics #Causality #MachineLearning
2/ The chapter raises an important point. Many canonical models in economics are cyclic equilibrium models (in our language, we would call them "nonrecursive"). And DAGs are by definition acyclic, so they cannot really capture such models. But...
3/ The chapter follows a line of argument that is very similar to the last section, and which I don't agree with. It focusses on a special case (here a simple supply-and-demand equilibrium model) that lies outside the realm of DAGs, and which was solved by PO practitioners.
4/ Based on this, however, the paper somehow creates the impression that PO would be able to deal with nonrecursive equilibirum models in full generality (in the last chapter, a similar line was followed for shape restrictions). This is not the case!
5/ The nonparametric functional relationships that determine counterfactuals / potential outcomes here, are equally present in the structural causal model underlying DAGs. And the SCM can be specified in such a way that it represents cyclic relationships too.
6/ So the special case that Angrist, Graddy and Imbens (2000) discuss can likewise be captured by a cyclic SCM. And all of their results are usable without further restrictions.
7/ When we move over to cyclic models, (simple) d-separation and do-calculus don't work anymore. So most of the systematic (and complete) identification results for DAGs will disappear. There are recent advances in the causal AI literature also for cyclic graphs
8/ (Guido cites some of them), that start to work on such systematic results. But what I've seen so far is hella complicated. And I wonder how applicable these approaches will be in practice. Maybe one day, if someone writes a non-technical use manual. :)
9/ But here we come back to the PO framework. PO also doesn't offer such systematic results. In most PO applications, nonrecursive equilibrium models play no role whatsoever. I presume that's also the reason for the follwing statement by Heckmand and Vytlacil (2007):
10/ We have a couple of PO papers that discuss special cases. That's great. But as I said earlier, we can easily incorporate these results into SCMs too. So there's full complementarity.
11/ Because the solutions we have so far for cyclic models are so complex (see for example: arxiv.org/abs/1901.00433), I actually wonder sometimes whether we haven't lead ourselves into a dead end with our focus on nonrecursive equilibrium models in econ.
12/ Of course, equilibrium concepts were tremedously succesful in economic theory and some might say they build the methodological cornerstone in economics. But they're also notoriously hard to deal with when we want to bring them to data,
13/ beyond special cases and heavily parametrized models. See for example the work by Rosa Matzkin on nonparametric, nonrecursive equilibrium models, which is theoretically intruiging, but which hasn't caught on much in applied work yet, as far as I can see.
14/ And then there's of course still the philosophical debate about whether cyclic models can be interpreted as causal relationships, which I would not like to discuss further here though.
15/ In any case, simultaneity is a perfect field, in my view, where econ and CS could join forces to work on new developments together. I'm convinced that we economists have unique skills to bring to the table here
16/ and equilibrium models are so central to our methodology that progress in this area would be tremendously useful to us. And who knows, maybe Guido's new paper will provide the necessary push we needed for more collaborations in the future!
17/ Btw, I didn't understand what Guido means in this last paragraph. In an SCM, nodes are determined by functional relationships q_d(p, x_d). And these nodes can remain latent too, so I don't see the problem here. But maybe this will become clearer in a future version.
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