# Is it possible to enter a variable into an SVAR with a lead?

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?

• 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? – Martin Oct 23 '19 at 7:45