The code given below estimates a VEC model with 2 cointegrating vectors. It is a reproducible code, so just copy and paste into your R console (or script editor).
> library ("urca")
Created articial data
> nobs = 200 # number of observations
> e = rmvnorm(n=nobs,sigma=diag(c(.5,.5,.5)))
> e1.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,1])
> e2.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,2])
> e3.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,3])
> y1 = cumsum(e[,1]) + e1.ar1
> y2 = cumsum(e[,1]) + e2.ar1
> y3 = cumsum(e[,1]) + e3.ar1
> data = cbind(y1,y2,y3)
Run Johansen cointegration test
> jcointt = ca.jo(data,ecdet="const",type="trace",K=2,spec="transitory")
> summary(jcointt)
Got the following output
######################
# Johansen-Procedure #
######################
Test type: trace statistic , without linear trend and constant in cointegration
Eigenvalues (lambda):
[1] 1.687740e-01 1.236672e-01 1.585399e-02 -1.127570e-17
Values of teststatistic and critical values of test:
test 10pct 5pct 1pct
r <= 2 | 3.16 7.52 9.24 12.97
r <= 1 | 29.30 17.85 19.96 24.60
r = 0 | 65.90 32.00 34.91 41.07
Eigenvectors, normalised to first column:
(These are the cointegration relations)
y1.l1 y2.l1 y3.l1 constant
y1.l1 1.0000000 1.0000000 1.0000000 1.0000000
y2.l1 -1.6101627 0.2364580 -1.2230052 -0.3278262
y3.l1 0.5528387 -1.2114606 0.4912319 -1.2940967
constant 0.0194457 0.3828253 17.8007975 -5.7790394
Weights W:
(This is the loading matrix)
y1.l1 y2.l1 y3.l1 constant
y1.d -0.02527895 -0.20388227 -0.010868003 -3.312924e-16
y2.d 0.14717590 -0.08609772 -0.006322288 -3.215611e-17
y3.d -0.04415827 0.04065915 -0.009347712 -1.830715e-18
It appears there are two cointegrating relations in the data. So estimated the VECM as follows:
> vecm <- cajorls(jcointt,r=2)
> summary(vecm$rlm)
> print(vecm)
Here comes the restricted VECM
$rlm
Call:
lm(formula = substitute(form1), data = data.mat)
Coefficients:
y1.d y2.d y3.d
ect1 -0.229161 0.061078 -0.003499
ect2 -0.007506 -0.257336 0.080716
y1.dl1 -0.151601 -0.170430 0.003316
y2.dl1 0.103196 0.159032 0.041342
y3.dl1 0.079732 0.025258 -0.054296
$beta
ect1 ect2
y1.l1 1.0000000 0.0000000
y2.l1 0.0000000 1.0000000
y3.l1 -0.9855438 -0.9554206
constant 0.3362949 0.1967809
Now, I want to put exclusion restrictions on the above cointegrating vector ($beta$). What function I should use in urca, and how I should construct the restrictions matrix if I want to test that the coefficient on variable y3.l1 is 0 in the first equation. Thanks.
EDITED
I read that the function blrtest can be used to do likelihood ratio test for restrictions on beta. Following the examples from the R vignette I did this:
> rstrictcoint = blrtest(jcointt, H,r=2)
H is the restrictions matrix that has to be constructed by myself, though, this is where I am stuck currently - I could not figure out the dimension and elements of this matrix. How I should construct it to test if the above coefficient is 0. I can do this procedure in Eviews, but want to learn it in R.
