Structural equations is a useful language for causal analysis in economics. In Causality Pearl (2009 cap 5) we can find the best discussion about this.
My question: is possible to use the concept of structural equation for non causal reasoning?
For example in ARMA framework is used the concept of "true model" or "data generating process" that sound like structural equation. However I don't know if this interpretation is correct. However if so, seems that ARMA parameters do not have only correlational/associational meaning but something more.
For example if we estimate an $AR(1)$ but the underlying "true" process is an $AR(2)$ we achieve a biased ($AR(1)$) parameter.This is an example of underspecified model, his problem is something like omitted variables bias problem that is relevant in causal analysis. We have to noted that also the biased parameter maintain a genuine correlational meaning (correlation is "free" concept).Then the interpretation of "true" $AR(2)$ parameters are something more than merely correlational; is not causation but go beyond correlation. What is the correct meaning?