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@steventberry Was planning to ask you to weigh-in. Agree with all of the above--seems like structural models in econ illustrate both the limits of DAGs as a "universal theory of identification" but also are perhaps the setting where they can potentially be of most use. On the limits side,
@steventberry weak restrictions on utility such as monotonicity assumptions may be a more defensible source of identification than the kinds of exclusion restrictions seen in DAGs. But by the same token, it seems like DAGs can be immensely helpful in probing the source of identification,
@steventberry and helping to clarify what is identified by models which are non-parametric in the @yudapearl sense and what is identified by the additional restrictions that are sometimes called non-parametric in econ. Additionally, while I've said that a 20 variable DAG is a bad way of
@steventberry @yudapearl arriving at an identification strategy, it seems like it could be an excellent way of understanding the complex structural model you have already written down. If you have insurers choosing goods, downstream and upstream firms each with market power bargaining over prices,
@steventberry @yudapearl you already have a 20 variable DAG. And it's incredibly easy to lose track of the assumptions one is making about, e.g. how the error terms in these different equations relate to each other. Writing the DAG can help summarize these assumptions in a transparent way. In a good
@steventberry @yudapearl model identification of key parameters still follows from ready-made DAGs (or to use @yudapearl 's terminology, t-DAGs)--in other words, there is clean identification that could be used to generate reduced-form regressions and graphs separately from the model. But it's very easy
@steventberry @yudapearl to convince oneself that identification is coming from the well-understood t-DAG when in fact it's coming from other assumptions buried in your model, and a full DAG can help list that full set of assumptions in a transparent way.
@steventberry @yudapearl But to be honest, I haven't thought through carefully the relationship between DAGs and equilibrium / simultaneous equation models (beyond the vague notion that DAGs don't capture restrictions coming from utility-maximization).
@steventberry @yudapearl Can we clarify the notion that simultaneous equation models are more general than DAGs. i.e. what causal questions / counterfactuals can we address in simultaneous eqn models that cannot be asked in DAGs?
@steventberry @yudapearl I can of course write a DAG for cost -> price -> quantity and price of substitute -> demand -> price, but what do I do when I want to clarify how these relate to each other? Are we stuck because combining them makes things "cyclic"?
