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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