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I would want to make a study about the influence of some regressors in the evaluation of the effects of increment of subsidy in an economic sector. I would use SEM (Structural Equation Model) to investigate the connections between the variables in a model with three equation (equation A, B, C).

Eq. A --> Value Added= f(Labour, investments, subsidies)
Eq. B --> Labour = f(Valued Added, investments, subsidies)
Eq. C --> Investment = f(Valued Added, Labour , subsidies)

In this first stage, I use a cross-section. Can SEM permit to understand the causality ad his direction between the different models and regressors?

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    $\begingroup$ I’ve always thought ‘causality’ is a misnomer in SEM. Unless I’m mistaken, what matters is the number of imposed constraints, not the directionality. If that’s true, it’s kind of hard to say it’s causal. If the model reproduces a correlation/covariance matrix it is plausible but not necessarily causal or even the only unique solution $\endgroup$ – HEITZ Apr 24 '18 at 21:56
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    $\begingroup$ First off, an SEM is by definition a causal model. The equality in each SEM equation is an assignment, i.e., the left-hand side is fixed once all the variables on the right-hand side are assigned. So I guess you mean a model in which the observed variables always fulfill the equations - which is not the same thing. If you have such a model, the causal directions can sometimes be assigned, but it depends on how the variables appear in the equations. If you can construct the underlying graph of your model, the direction-finding step of the SGS algorithm allows you to make the assignment. $\endgroup$ – Dave Kielpinski Apr 24 '18 at 23:50
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    $\begingroup$ Please explain what you mean by "SEM is by definition a causal model". Many models produce identical covariance matrices with the directions pointing either way. $\endgroup$ – Gregg H Apr 27 '18 at 20:21
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As appear from the comments the meaning of SEM (Structural Equation Model) is matter of debate among researchers. Sometimes peoples/books speak about SIM (Simultaneous Equation Model) that, algebraically speaking, seems a synonym but it can convey more general ideas. Some confusions can come from conflation between SEM and SIM. Infact the word “structural” was proposed exactly in order to move beyond purely statistical associations. So It seem me that SEM are, or should be, causal by definition while SIM not necessarily. This discussion can help: Difference Between Simultaneous Equation Model and Structural Equation Model

Then

Can SEM permit to understand the causality ad his direction between the different models and regressors?

Yes. SEM was proposed exactly for this reason. However keep attention about the word "understand". Do not forget that causal assumptions needed, and them are in the responsibility of the modeler.

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