# RE: st: AW: cumulative impulse response functions after long-run SVAR

 From "David M. Drukker, StataCorp" <[email protected]> To [email protected] Subject RE: st: AW: cumulative impulse response functions after long-run SVAR Date Mon, 23 Feb 2004 10:24:53 -0600

```Katerina <[email protected]> asked whether it is
possible to compute the structural IRF's after estimating the parameters of
a long-run SVAR.  The answer is yes.  However, following Amisano and
Giannini (1997), the standard errors must be obtained by a bootstrap
procedure instead of an analytic asymptotic approximation.

Here is an example that uses data from the [TS] var svar manual entry.

. webuse m1gdp

. mat lr = (.,0\0,.)

. svar d.(ln_m1 ln_gdp ), lreq(lr)
Estimating long-run parameters

Iteration 0:   log likelihood = -27.958026
Iteration 1:   log likelihood =  895.37393
Iteration 2:   log likelihood =  1116.3226
Iteration 3:   log likelihood =  1150.8327
Iteration 4:   log likelihood =  1151.6135
Iteration 5:   log likelihood =  1151.6143
Iteration 6:   log likelihood =  1151.6143

Structural vector autoregression

Constraints:
( 1)  [c_1_2]_cons = 0
( 2)  [c_2_1]_cons = 0

Sample:  1959q4   2002q2                     Number of obs    =        171
Log likelihood   =  1151.6143
LR test of overidentifying restrictions      LR chi2(  1)     =  .13675517
Prob > chi2      =     0.7115

--------------------------------------------------------------------------
Equation          Obs  Parms        RMSE     R-sq        chi2        P
--------------------------------------------------------------------------
D.ln_m1           171      5     .008509    0.4732   153.5779   0.0000
D.ln_gdp          171      5     .008448    0.1140   22.00553   0.0002
--------------------------------------------------------------------------

VAR Model lag order selection statistics
----------------------------------------
FPE           AIC         HQIC         SBIC         LL        Det(Sigma_ml)
5.444e-09  -13.353014   -13.278467   -13.169291   1151.6827      4.843e-09

------------------------------------------------------------------------------
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
c_1_1        |
_cons |   .0301007   .0016277    18.49   0.000     .0269106    .0332909
-------------+----------------------------------------------------------------
c_2_2        |
_cons |   .0129691   .0007013    18.49   0.000     .0115946    .0143436
------------------------------------------------------------------------------

. varirf table sirf , impulse(D.ln_m1) response(D.ln_gdp)

Results from lr1

+--------------------------------------------+
|        |    (1)         (1)         (1)    |
|  step  |   sirf       Lower       Upper    |
|--------+-----------------------------------|
|0       | -.002513    .           .         |
|1       | -.00037     .           .         |
|2       | .000102     .           .         |
|3       | .000333     .           .         |
|4       | .000418     .           .         |
|5       | .000395     .           .         |
|6       | .000349     .           .         |
|7       | .000289     .           .         |
+--------------------------------------------+
95% lower and upper bounds reported
(1) irfname = lr1, impulse = D.ln_m1, and response = D.ln_gdp

As noted on pages 266-267 of the [TS] manual, -varirf create- follows
Amisano and Giannini (1997) and does not estimate the asymptotic standard
error of the structural IRF's from long-run models.  Of course, estimates of
these standard errors could be obtained via the -bs- option.

--David
[email protected]

References
----------

Amisano, G. and Giannini, C. 1997. Topics in Structural VAR Econometrics. 2d
Ed. Heidelberg: Springer.
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```