I have a set of covariance stationary variables which are slightly correlated to each other (<20%). I want to model the dependencies among the variables. I found out, that there are three types of VAR models:

  1. Reduced Form
  2. Recursive
  3. Structural

Which one should I use? When I use the 'wrong' one, how can I detect it?

I'm currently using the reduced form VAR and the CoVar of the residuals shows minor correlation(<5%) among the residuals.


The three forms of the VAR model essentially are equivalent representations of the same underlying model. Therefore, there is no "right" or "wrong", as long as you do not care about subject-matter interpretation.

For estimation you always use the reduced-form model. If you want to answer some subject-matter questions related to the structural form, then you may convert the estimated reduced-form model into the equivalent structural form.

  • $\begingroup$ Thank you very much for your answer! I'm not sure what you exactly mean by subject-matter interpretation. I'm not testing any formal theoretical model. However, I will interpret the interdependencies among the variables resulting from the model. Especially, I will interpret the forecasting ability. Are there any caveats I should consider? $\endgroup$ – nan Jan 5 '17 at 13:53
  • $\begingroup$ For forecasting, reduced-form model should be fine. When estimating the model you could probably wish to place some restrictions due to economic theory, but this need not be necessary. $\endgroup$ – Richard Hardy Jan 6 '17 at 2:57

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