The basic model is u = Fv, where v are the structural shocks, restricted to be orthonormal, that is, Evv'=I. FF' is thus equal to
sigma for a just identified model.
shortandlong.src- Procedure file
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@ShortAndLong(options) sigma
Parameters
sigma (input) the covariance matrix of the VAR residuals
Options (Inputs)
SR=NxN matrix with 0's in the slots in F restricted to be zero.
LR=NxN matrix with 0's in the slots in C(1)F restricted to be zero.
MASUMS=NxN matrix of the sum of the MAR coefficients of the VAR (C(1))
Options (Outputs)
FACTOR=factor matrix (F)
RPERP=mapping from free parameters to vec(F)
Note that the MASUMS options needs to change if the coefficients change. For a VAR that's been just estimated, you can use INV(%VARLAGSUMS), but if you draw a new set of coefficients (by Monte Carlo integration or bootstrapping), you need to recompute those using INV(%MODELLAGSUMS(the model with the new coefficients)).
Example:
This is an example with a just identified model which restricts shocks 2 and 3 to have no long-run effect on variable 1. 2 and 3 are identified (from each other) by the short-run restriction on shock 3 (no impact response for variable 2).
- Code: Select all
compute masums=inv(%varlagsums)
input lr
. 0 0
. . .
. . .
input sr
. . .
. . 0
. . .
@ShortAndLong(lr=lr,sr=sr,masum=masums) %sigma f
disp ###.### "Impact Responses" f
disp ###.### "Long run Responses" masums*f
*
@varirf(factor=f,steps=30,model=myvar,shocklabels=||"Permanent","Trans 1","Trans 2"||)
More complicated examples are: http://www.estima.com/forum/viewtopic.php?f=8&t=309 which uses the RPERP option to estimate an SVAR which has short and long-run restrictions, and includes both "A" and "B" form restrictions on the covariance matrix and http://www.estima.com/forum/viewtopic.php?f=8&t=1118 which is a just-identified model on a five variable system, and includes Monte Carlo integration.
Control options. Calculation of the factor matrix is an iterative process.
[ESTIMATE]/NOESTIMATE
ITERATIONS=maximum number of iterations [100]
CVCRIT=convergence criterion [.000001]. This is checked against the difference between the outer product of the factor and the input covariance matrix.
INITIAL=initial guess for the factor matrix F. By default, this takes a Choleski factor of sigma and picks the closest fit to that.