Matrix A and B in an SVAR Model - leaving the diagonal unrestricted in Matrix A?

[Ben Tippet]

Hi there,

I'm running an SVAR model with the following code:


matrix A1 = (.,.,.,.\0,.,.,0\.,.,.,0\0,0,0,.)
matrix B1 = (1,0,0,0 \ 0,1,0,0 \ 0,0,1,0\ 0,0,0,1)

svar wealth1 Profitsharetax income1 diffequityhouse, lags(1/2) aeq(A1) beq(B1)


I just want to check that the way I have specified Matrix A and B are correct. In the Stata examples online and in the manual, usually the diagonals on the A and B matrix are the opposite way around to how they are above. Above I have left the diagonal of A unrestricted and imposed 1s along the diagonal of B. However, in the Stata manual, the diagonal of B is left unrestricted and the 1s are imposed on the diagonal of A. (See here for an example - https://www.stata.com/manuals13/tsvarsvar.pdf)

I don't see any theoretical reason why the version I am doing above should be wrong. In fact, in Kilian and LÜtkepohl (2015, p.218) they say, "There are three equivalent representations of structural VAR models that differ only in how the model is normalized." Before going on to say that the version I have above (where the diagonal on matrix A is unrestricted and the diagonal on Matrix B are restricted to 1) is one of the three equivalent representations.

But is there any reason why leaving the diagonal of A unrestricted and imposing 1s on the diagonal of B would cause a problem in Stata?


Thanks!



References:

Kilian and LÜtkepohl (2015) Structural Vector Autoregressive Analysis, Cambridge University Press

[Eric de Souza]

No, it would not create any problems. Some prefer normalising the diagonal of A. This way the variable attached to the normalised coefficient can be interpreted as the "dependent" variable for that equation. Just check that your system is identified; it appears at first glance to be so.

On edit: in fact you don't need to normalise the diagonals of A or of B: you just need to make sure that the system is identified.

[Ben Tippet]

Hi Eric,

Thanks for clarifying this.

All the best,
Ben