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Consider, for simplicity, a bivariate SVAR(p) model. Structure is imposed through Choleski, whereby $Y_{1,t}$ is ordered first, before $Y_{2,t}$.

Now, when estimating the SVAR(p) model, let's say for ease, $p=1$ due to some criterion such as AIC or BIC.

The estimated equation becomes, essentially,

$Y_{1, t} = A_{1} + B_{11} Y_{1, t-1} + B_{12} Y_{2, t-1} + u_{1, t}$

and

$Y_{2, t} = A_{2} + B_{21} Y_{1, t-1} + B_{22} Y_{2, t-1} + u_{2, t}$

However, let's say you're dealing with data whereby $Y_{2,t}$ is largely explained by $Y_{1,t}$, and not $Y_{1,t-1}$. Is it possible to have $Y_{1,t}$ leading in the SVAR? Obviously you can do this in your software for example.

But my question is- what does this mean for the impulse response function analysis? If you have $Y_{1,t}$ as a leading variable in your SVAR setup, and then shock $u_{1,t}$ for a response of $Y_{2,t}$, what is the implication of this?

Or, is entering $Y_{1,t}$ as a leading variable in the SVAR not necessary because Cholesky allows for the first-ordered variable to contemporaneously affect the subsequent variables?

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  • $\begingroup$ I´m not sure if Cholesky decomposition is appropriate for your model. Don't your actions violate the assumptions of cholesky decomposition? Your $u_(1,t)$ influence Y_(1,t) and is therefore contemporaneous? $\endgroup$ – Martin Oct 23 '19 at 7:45

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