1 A note for Svar function in Matlab
Marco Aiolfi
maiolfi@iol.it
Bocconi University and Banca Intesa, Milan
SVAR verifies the identification conditions for a given structural form to
be imposed on an e stimated VAR model. The require inputs are the set of
constraints to be placed on the elements of the A and B matrices so that
V ec(A) = s
A
· γ
A
+ d
A
(1)
V ec(B) = s
B
· γ
B
+ d
B
.
Here is an example.
Consider a 2 variables VAR and suppose you want Choleski identification:
A =
1 0
a
21
1
, B =
b
11
0
0 b
22
. (2)
Using 1 the constraints can be rewritten as follows:
1
a
21
0
1
=
0
1
0
0
· [a
21
] +
1
0
0
1
(3)
b
11
0
0
b
22
=
1 0
0 0
0 0
0 1
·
b
11
b
22
+
0
0
0
0
. (4)
After creating s
A
, d
A
, s
B
, d
B
the SVAR procedure is run with
[a,b,a_se,b_se]=svar1(results,sa,sb,da,db,afree,bfree)
where results is a VARE structure, sa,sb,da,db, are the constraints and afree
and bfree are the number of free parameters in A and B matrices.
The demo file svar d.m gives an example of SVAR procedure for a 5 variables
VAR.
The interested reader can find details about identification and estimation of
a structural VAR models in Amisano and Giannini (1997). A good reference
for alternative identification schemes and their application to monetary policy
analys is Favero (2000).
2 References
Amisano, G., and Giannini, C., (1997). Topics in structural var econo-
metrics. Second edition, Springer Verlag, New York.
Favero, C. A., (2000). Applied Macroeconometrics. Oxford University
Press, Oxford.
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