Estimating confidence intervals of the cumulative structural impulse–response functions

[Jose Luis Saboin]

Hello,

I have estimated csirf following the instructions from this post: https://blog.stata.com/2016/10/27/lo...utoregression/

But I wonder how can I estimate the CIs considering that there are no standard erros for the cumulative structural impulse–response functions I just created.

Thanks,
JL

[Justin Niakamal]

Try removing noci.

clear all
use http://www.stata-press.com/data/r13/lutkepohl2

var dln_inv dln_inc dln_consump if qtr<=tq(1978q4), lags(1/5) dfk

irf create irf_graph, step(10) set(my_irf)
irf graph cirf, impulse(dln_inc) response(dln_consump)

[Jose Luis Saboin]

Thanks very much Justin! This is highly appreacited.

However, as you can see from the post, he creates the cummulative structural irf ("csirf") by adding up the structural irf ("sirf"). What I need to create is the confidence interval for the "csirf" which is something not available in the lrirf.irf file.

For instance, if you take a look at the lrirf.irf file, there's a variable called "stdcirf" which are the standard errors of the cirf which when multiplied by +-2 give the confidence interval analog to the picture you are showing.

But if you investiguate the lrirf.irf file further, you'll see there is another variable called sirf which is the one that he adds to get the csirf. You'll also note there is a stdsirf, but there is no equivalent stdcsirf because csirf is something that is being calculated "manually".

My question is: is there a way to produce the standard errors of the cummulative sirf (i.e. csirf) that he builds?

Regards,
JLS

[Justin Niakamal]

I think you can accomplish this by specifying graph coirf without the noci option specified. Here's an example which you can compare the two (the data are similar to what's used). Hope this helps.

clear
tempfile temp 

local v = "UNRATE" // unemployment rate 
!curl -L https://fred.stlouisfed.org/series/`v'/downloaddata/`v'.csv > "`v'.csv"
insheet using "`v'.csv", comma clear
            
gen quarter = qofd(date(date, "YMD"))    
collapse (mean) value, by(quarter)              

ren value unrate 
save `temp'

local v = "A001RP1Q027SBEA" // GNP
!curl -L https://fred.stlouisfed.org/series/`v'/downloaddata/`v'.csv > "`v'.csv"
insheet using "`v'.csv", comma clear
               
ren value growth   
gen quarter = qofd(date(date, "YMD"))    
merge 1:1 quarter using `temp', keep(match) nogen 
drop date 
format quarter %tq

gen year = yofd(dofq(quarter))

keep if year >= 1952 & year <= 1987
gen t = _n 
tsset quarter, quarterly  

quietly regress unrate t
predict unrate_adj, resid

generate bp1 = (year<1974)
generate bp2 = (year>=1974)

quietly regress growth bp1 bp2, noconstant
predict growth_adj, resid

matrix C = (., 0 \ .,.)
svar growth_adj unrate_adj, lags(1/8) lreq(C)


irf create lr, set(lrirf) step(40) replace
irf graph sirf, yline(0,lcolor(black)) xlabel(0(4)40) byopts(yrescale)

use lrirf.irf, clear

sort irfname impulse response step

gen csirf = sirf

by irfname impulse: replace csirf = sum(sirf) if response=="growth_adj"
order irfname impulse response step sirf csirf

save lrirf2.irf, replace

use lrirf.irf, clear

irf graph coirf, yline(0,lcolor(black))  xlabel(0(4)40) byopts(yrescale)
graph export coirf.png , replace 

irf set lrirf2.irf
irf graph csirf, yline(0,lcolor(black)) noci xlabel(0(4)40) byopts(yrescale)
graph export blogpost.png , replace 

exit

[Jose Luis Saboin]

Thanks Justin! Just tried it on my project and unfortunately, for the case I'm studying, csirf and coirf are not the same/similar. Any other ideas on how to build those confidence intervals for csirf?

[Justin Niakamal]

I'm not sure. To get the standard errors from SVAR you need to use bsp in irf create. I suppose one crude way would be simply just to create a rolling sum of the standard errors. I'm not sure how inappropriate that is honestly. If it were me, I would use a software that can produce GIRFs with confidence intervals (I think Eviews does this but it's been a while).

use http://www.stata-press.com/data/r13/m1gdp, clear 

matrix lr = (.,0\0,.)
svar d.ln_m1 d.ln_gdp, lreq(lr)

irf create lr, set(lrirf)  bsp  step(20) replace
use lrirf.irf, clear

sort irfname impulse response step

gen double csirf = sirf
gen double stdcsirf = stdsirf

bys irfname  response impulse (step): replace csirf    = sum(sirf) 
bys irfname  response impulse (step): replace stdcsirf = sum(stdsirf) 
order irfname impulse response step sirf csirf stdcsirf

save lrirf2.irf, replace

irf set lrirf2.irf
irf graph csirf, yline(0,lcolor(black))  xlabel(0(1)20) byopts(yrescale)

[Jose Luis Saboin]

Thanks Justin! I agree with you that Eviews would do better. In fact, what I'm actually doing is trying to replicate the CSIRFs that were produced in Eviews in Stata. Everything looks the same except the CIs. I actually did the rolling sum, and the CIs were clerarly wider than those reported by Eviews. That's why I came here in the first place. Let me show you some pictures:

Eviews:

Stata (column 1 here is column 2 in Eviews)

[haiyan lin]

I have the same problem. Does anyone know how to build the standard error (and therefore the confidence interval) for the cumulative sirf in STATA? Many thanks!

[haiyan lin]

I'm not sure. To get the standard errors from SVAR you need to use bsp in irf create. I suppose one crude way would be simply just to create a rolling sum of the standard errors. I'm not sure how inappropriate that is honestly. If it were me, I would use a software that can produce GIRFs with confidence intervals (I think Eviews does this but it's been a while).

use http://www.stata-press.com/data/r13/m1gdp, clear

matrix lr = (.,0\0,.)
svar d.ln_m1 d.ln_gdp, lreq(lr)

irf create lr, set(lrirf) bsp step(20) replace
use lrirf.irf, clear

sort irfname impulse response step

gen double csirf = sirf
gen double stdcsirf = stdsirf

bys irfname response impulse (step): replace csirf = sum(sirf)
bys irfname response impulse (step): replace stdcsirf = sum(stdsirf)
order irfname impulse response step sirf csirf stdcsirf

save lrirf2.irf, replace

irf set lrirf2.irf
irf graph csirf, yline(0,lcolor(black)) xlabel(0(1)20) byopts(yrescale)

I tried this way, and found that cumulative standard errors would be smaller if they are generated by sqrt(sum(stdsirf^2)), instead of by sum(stdsirf).