Confidence Intervals for Impulse Response Functions

[Gianluca Cafiso]

Dear Statalisters,
here I am again for your help.

I have estimated a VAR, actually a Structural VAR but I don't think this makes a difference in relation to my question.

I want to compute Cumulative Orthogonal Impulse Response Functions based on Parametric-Bootrastrap. This is done with this line:

irf create sVAR_US_A6, step(12) replace est(sVAR_US_A6) bsp bsaving( bsp_sVAR_US_A6, replace)

Then I generate the IRF table with this command:

irf table coirf, irf(sVAR_US_A6) impulse(mmXRq) response(D.Lgdp_nc3) std

the output is:
_

Results from sVAR_US_A6
step	coirf	Lower	Upper	S.E.
0	0	0	0	0
1	0.000053	-0.00067	0.000775	0.000369
2	-0.000018	-0.001206	0.00117	0.000606
3	-0.000132	-0.001727	0.001464	0.000814
4	0.000042	-0.001999	0.002083	0.001041
5	-0.000489	-0.002961	0.001982	0.001261
6	-0.00054	-0.003264	0.002183	0.00139
7	-0.000907	-0.003793	0.001979	0.001472
8	-0.001127	-0.004187	0.001934	0.001562
9	-0.0013	-0.004486	0.001886	0.001625
10	-0.001356	-0.004576	0.001865	0.001643
11	-0.001272	-0.004481	0.001937	0.001637
12	-0.001106	-0.004275	0.002064	0.001617

_
200 replications for the bootstrap. The SE is calculated as the standard deviation of all the bootstrap IRFs by Step

I do not understand how the Confidence Intervals are generated given the IRF value and its SE. I have tried the cii command:

cii 200 -0.001106 0.001617

but this is what I get:

Variable | Obs Mean Std. Err. [95% Conf. Interval]
-------------+---------------------------------------------------------------
| 200 -.001106 .0001143 -.0013315 -.0008805


Does anyone can help?

Does it matter they are Cumulative IRFs?

Thanks a lot.

[Gianluca Cafiso]

I found the answer myself a couple of weeks ago. I report it here for the sake of completeness, just in case someone'll have the same problem:

1. Calculate the Standard Deviation (SD) of the Bootstrap Distribution. That approximates the Standard Error of the IRF. In this case, for the 12th step, it is

0.001617

2. The lower bound CI is: EST - (1.96*SD) =>

-0.001106 - (1.96*0.001617)=-0.004275

3. The upper bound CI is: EST + (1.96*SD) =>

-0.001106 + (1.96*0.001617)=0.002064

1.96 is the 2.5/97.5 quantile of the Normal Distribution.

Hence, these are 95% Normal-Approximation Bootsrap-based Confidence Intervals.