I agree that this is true of structural equation models, taken in a fairly narrow sense. However, econometricians commonly generalize these to simultaneous equation models, which include equations where one simply asserts an algebraic equation involving variables, with no one variable having a privileged status of being “determined”, or an “outcome” of others. This means that do(.) cannot carry over to such models in a straightforward way. And yes, this is standard practice in econometrics when modeling equilibrium, feasibility constraints and the like.
To the extent that constraints are simply constraints and not a result of causal structure, the model representing them is partly non-causal (so do(.) or some other representation of causation is irrelevant for such constraints). To the extent that constraints represent some consequence of graphical causal structure I am not aware of a single example where a potential outcome model is not appropriate. Do you have an example in mind?
In some sense if you have constraints that represent consequence of causality, such as feedback, and there is no story relating them to interventions/generative mechanisms, then I am not sure in what sense the model is causal. I am not saying it is not possible, but the burden of proof is on whoever proposed the model to clearly explain how causality works in it. There is a lot of confusion in economics and sometimes even in stats about causality (Judea is fairly unhappy with incoherence that many economics textbooks display when discussing causation, actually).
I agree that this is true of structural equation models, taken in a fairly narrow sense. However, econometricians commonly generalize these to simultaneous equation models, which include equations where one simply asserts an algebraic equation involving variables, with no one variable having a privileged status of being “determined”, or an “outcome” of others. This means that do(.) cannot carry over to such models in a straightforward way. And yes, this is standard practice in econometrics when modeling equilibrium, feasibility constraints and the like.
This is probably a good read also:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.29.1408
To the extent that constraints are simply constraints and not a result of causal structure, the model representing them is partly non-causal (so do(.) or some other representation of causation is irrelevant for such constraints). To the extent that constraints represent some consequence of graphical causal structure I am not aware of a single example where a potential outcome model is not appropriate. Do you have an example in mind?
In some sense if you have constraints that represent consequence of causality, such as feedback, and there is no story relating them to interventions/generative mechanisms, then I am not sure in what sense the model is causal. I am not saying it is not possible, but the burden of proof is on whoever proposed the model to clearly explain how causality works in it. There is a lot of confusion in economics and sometimes even in stats about causality (Judea is fairly unhappy with incoherence that many economics textbooks display when discussing causation, actually).