Difference between VAR and Structural VAR and Cholesky Estimation in R

Question

I am studying the Autoregressive Vectors (VAR) method. The pet part I am understanding, but there is a question that intrigues me. Is there a differentiation between VAR and structural Var? Isn’t it the same thing? Because there is this division?

Once estimated the coefficients I "recover" the true Betas of the "true" VAR that would be the Structural? That’s it?

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2L, 3L, 356L, 357L, 358L), .Names = c("1", "2", "3", "356", "357", 
"358"), class = "omit"))

Now I spin the VAR:

p1ct.y<- VAR(data, p = 1, type = "both") 
plot(irf(p1ct.y, impulse = "x", ci = 0.95, n.ahead = 30, response = c("y"), boot = FALSE))

My second doubt is whether this result of the impulse response function already considers the decomposition of Cholesky? Otherwise, how do I have an impulse response function that takes into account cholesky decomposition?

Answer 1

The SVAR differs from the VAR in that it imposes relations to the left of the non-existent equality sign in the VAR. These relations supposedly come from a view of the functioning of the economy and therefore there is a structure and so it is said that the SVAR is a view of the data from a theory. What’s the big deal? With some algebraism you realize that the SVAR is similar to the VAR (It is called reduced form) but there is no way to estimate all matrices separately from this new VAR model (SVAR in reduced form). How do you solve it? They artificially impose restrictions on the matrices. For example, if you hit the SVAR (know well how your economy works) most likely the noise matrix (or innovations as it is said) will be diagonal (it is said that innovations will not be crossed) and therefore may be heterocedastic but the noise will be diagonal at the end, After all, the structure of the economy is correct. Other restrictions may be imposed, for example on directionality between variables.