Hello,
I'm using VAR models in R in order to obtain impulse responses of stock
market shock on US economy.
I have series of quarterly changes in real gdp, S&P 500 and quarterly level
of unemployment for 1985 - 2012 period.
My series are stationary. So I did all the steps below. However I don't
understand what do irf function results mean. These are the cumulative
orthogonal responses to sp variable shock but what is the value of this
shock? If for example I have to assess the response on 10% increase of sp
variable what should I do with these results?
Thanks a lot,
Marion
> #make a data frame
> vardat3<-data.frame(gdp,unemp,sp)
> #select the number of lags: const
> infocrit<-VARselect(vardat3,lag.max=20,type="const")
> infocrit
$selection
AIC(n) HQ(n) SC(n) FPE(n)
20 2 1 2
$criteria
1 2 3 4
AIC(n) -1.862833e+01 -1.880996e+01 -1.868877e+01 -1.863180e+01
HQ(n) -1.849392e+01 -1.857475e+01 -1.835275e+01 -1.819497e+01
SC(n) -1.829502e+01 -1.822667e+01 -1.785550e+01 -1.754855e+01
FPE(n) 8.126326e-09 6.781829e-09 7.669554e-09 8.146337e-09
5 6 7 8
AIC(n) -1.853795e+01 -1.846199e+01 -1.842426e+01 -1.830997e+01
HQ(n) -1.800031e+01 -1.782355e+01 -1.768500e+01 -1.746991e+01
SC(n) -1.720471e+01 -1.687878e+01 -1.659106e+01 -1.622679e+01
FPE(n) 8.995957e-09 9.782674e-09 1.027092e-08 1.168454e-08
9 10 11 12
AIC(n) -1.839671e+01 -1.835691e+01 -1.841065e+01 -1.844365e+01
HQ(n) -1.745585e+01 -1.731524e+01 -1.726817e+01 -1.720037e+01
SC(n) -1.606356e+01 -1.577377e+01 -1.557753e+01 -1.536055e+01
FPE(n) 1.091936e-08 1.164000e-08 1.136733e-08 1.141161e-08
13 14 15 16
AIC(n) -1.844870e+01 -1.841054e+01 -1.842814e+01 -1.845378e+01
HQ(n) -1.710461e+01 -1.696564e+01 -1.688243e+01 -1.680727e+01
SC(n) -1.511562e+01 -1.482748e+01 -1.459510e+01 -1.437076e+01
FPE(n) 1.187493e-08 1.302227e-08 1.365157e-08 1.437544e-08
17 18 19 20
AIC(n) -1.850238e+01 -1.857360e+01 -1.890488e+01 -1.906878e+01
HQ(n) -1.675506e+01 -1.672547e+01 -1.695594e+01 -1.701904e+01
SC(n) -1.416937e+01 -1.399062e+01 -1.407191e+01 -1.398583e+01
FPE(n) 1.501343e-08 1.559817e-08 1.275793e-08 1.265147e-08
> #Estimate VAR
> varestim3<-VAR(vardat3,p=1,type="const",season=NULL,exogen=NULL)
> summary(varestim3)
VAR Estimation Results:
=========================
Endogenous variables: gdp, unemp, sp
Deterministic variables: const
Sample size: 109
Log Likelihood: 564.356
Roots of the characteristic polynomial:
0.9574 0.5034 0.1505
Call:
VAR(y = vardat3, p = 1, type = "const", exogen = NULL)
Estimation results for equation gdp:
====================================
gdp = gdp.l1 + unemp.l1 + sp.l1 + const
Estimate Std. Error t value Pr(>|t|)
gdp.l1 4.006e-01 9.177e-02 4.365 2.98e-05 ***
unemp.l1 5.559e-05 3.629e-04 0.153 0.8785
sp.l1 1.131e-02 6.656e-03 1.699 0.0923 .
const 3.254e-03 2.413e-03 1.349 0.1803
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 0.005577 on 105 degrees of freedom
Multiple R-Squared: 0.2199, Adjusted R-squared: 0.1976
F-statistic: 9.865 on 3 and 105 DF, p-value: 8.683e-06
Estimation results for equation unemp:
======================================
unemp = gdp.l1 + unemp.l1 + sp.l1 + const
Estimate Std. Error t value Pr(>|t|)
gdp.l1 -29.44722 3.55186 -8.291 4.02e-13 ***
unemp.l1 0.96915 0.01405 69.003 < 2e-16 ***
sp.l1 -0.40886 0.25761 -1.587 0.115
const 0.39656 0.09339 4.246 4.71e-05 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 0.2159 on 105 degrees of freedom
Multiple R-Squared: 0.9801, Adjusted R-squared: 0.9796
F-statistic: 1728 on 3 and 105 DF, p-value: < 2.2e-16
Estimation results for equation sp:
===================================
sp = gdp.l1 + unemp.l1 + sp.l1 + const
Estimate Std. Error t value Pr(>|t|)
gdp.l1 4.376417 1.352306 3.236 0.00162 **
unemp.l1 0.007670 0.005347 1.434 0.15444
sp.l1 -0.059427 0.098079 -0.606 0.54588
const -0.050007 0.035556 -1.406 0.16256
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 0.08219 on 105 degrees of freedom
Multiple R-Squared: 0.09843, Adjusted R-squared: 0.07267
F-statistic: 3.821 on 3 and 105 DF, p-value: 0.01211
Covariance matrix of residuals:
gdp unemp sp
gdp 3.111e-05 -0.0005809 9.583e-05
unemp -5.809e-04 0.0466008 -2.886e-03
sp 9.583e-05 -0.0028862 6.755e-03
Correlation matrix of residuals:
gdp unemp sp
gdp 1.0000 -0.4825 0.2091
unemp -0.4825 1.0000 -0.1627
sp 0.2091 -0.1627 1.0000
> #roots inferior to 1
> roots<-roots(varestim3)
> roots
[1] 0.9574116 0.5033992 0.1504822
> irf_unemp3<-irf(varestim3, impulse="sp", response="unemp",
ortho="TRUE",n.ahead=12, cumulative="TRUE",boot=FALSE)
> irf_unemp3
Impulse response coefficients
$sp
unemp
[1,] 0.00000000
[2,] -0.03277601
[3,] -0.08928549
[4,] -0.15473977
[5,] -0.22331618
[6,] -0.29191758
[7,] -0.35908457
[8,] -0.42413901
[9,] -0.48679952
[10,] -0.54698101
[11,] -0.60469490
[12,] -0.65999890
[13,] -0.71297176
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