[R] Testing Restrictions on Beta (long-run coefficients), reproducible example

[mrrox]

The code given below estimates a VEC model with 4 cointegrating vectors. It
is a reproducible code, so just copy and paste into your R console (or
script editor).

nobs = 200
e = rmvnorm(n=nobs,sigma=diag(c(.5,.5,.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])
e4.ar1 = arima.sim(model=list(ar=.75),nobs,innov=e[,4])
y5 = cumsum(e[,5])
y1 = y5 + e1.ar1
y2 = y5 + e2.ar1
y3 = y5 + e3.ar1
y4 = y5 + e4.ar1
data = cbind(y1,y2,y3,y4,y5)

jcointt = ca.jo(data,ecdet="const",type="trace",K=2,spec="transitory")
summary(jcointt)
# estimate VECM with 4 cointegrating vectors
vecm <- cajorls(jcointt,r=4)
summary(vecm$rlm)
print(vecm)


I want to re-estimate the model with the following restrictions put on the
coinegrating vectors:
            
                   ect1   ect2  ect3   ect4
y1.l1               1      0      0     0
y2.l1            b1.1     1      0     0
y3.l1            b2.1     0      1     0
y4.l1            b3.1     0      0     1
y5.l1            b4.1    b4.2   b4.3   b4.4
constant        c1      c2     c3    c4      


here, b1.1 through to b4.1 are the coefficients (β1,β2,β3,β4) of the first
cointegrating vector. Similarly, b4.4 and c4 are coefficients of the fourth
cointegrating equation. Then, in order to test the restrictions on
Coinegrating Vectors, I run the following code:

test <- blrtest(jcointt,H=H1,r=4)


However, I do not know how I should specify the H1 matrix in this instance.
I was wondering if someone could demonstrate how I should go ahead with
testing the restrictions on long run equations and then re-estimate the
model using the above restrictions:

vecm2 <- cajorls(test,r=4)
summary(vecm2$rlm)
print(vecm2)


How should I specify the H1 matrix above in order to re-estimate the
re-parameterised cointegrating equations? I want to use the coefficients of
the first cointegrating equation (ect1) for inference.



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