Suppose running a VAR system featuring the central bank interest rate, inflation and GDP.

Start by estimating each equation by OLS. How should you interpret the OLS residuals to these equations?

My take:

Suppose inflation equation is estimated, then it means the OLS residuals mean that these are the shocks that only effect inflation and no other variable

Similarly for the other two equations.

Would appreciate if anyone could share their two cents?

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  • $\begingroup$ I think you need to take a step back and think about why you use VAR in the first place rather than OLS for individual equations. If each individual equation only has shocks that effect itself and not the others then there is no benefit to modelling them jointly i.e. they are all weakly exogenous. However, if this assumption is invalid and there is feedback between the variables through their unobserved terms, then it is invalid to model them independently and trying to interpret the residuals as fundamental shocks is misleading. $\endgroup$ – Andrew M May 14 '19 at 19:19
  • $\begingroup$ very nice comment. $\endgroup$ – mark leeds May 14 '19 at 19:58

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