# Interpretation of vector error correction model in R

I estimated a VECM using the following code:

mysample<-Canada[,c("e", "prod", "rw", "U")]
myvecm<-ca.jo(mysample,ecdet="const",type="eigen",K=2,spec="longrun")
myvecm.ols<-cajools(myvecm)
myvecm


I got the results below:

###################################################
# Johansen-Procedure Unit Root / Cointegration Test #
#####################################################

The value of the test statistic is: 6.8796 10.512 24.9145 63.5378

> myvecm.ols

Call:
lm(formula = substitute(form1), data = data.mat)

Coefficients:
e.d         prod.d      rw.d        U.d
e.dl1        0.63782    -0.17277    -0.26883    -0.58076
prod.dl1     0.16727     0.15043    -0.08107    -0.07812
rw.dl1      -0.06312     0.05130    -0.10452     0.01866
U.dl1        0.26558    -0.47850     0.01213    -0.38107
e.l2         0.14069     0.21249     0.09902    -0.17095
prod.l2      0.06562    -0.02198    -0.08625    -0.02600
rw.l2       -0.05927    -0.06755    -0.05185     0.06046
U.l2         0.39827     0.53742    -0.11558    -0.45224
constant  -136.99845  -166.77552   -33.18834   149.78056


I have a few questions though.

1. First of all, how do we interpret these results?
2. What do the coefficients on e.dl1 , prod.dl1, rw.dl1, U.dl1, rw.l2, U.l2, e.l2, prod.l2 imply ?
3. How do we relate this to the VECM equation in theory?

$$\Delta y_t=c+ \Pi y_{t-1}+ \Gamma_1 \Delta y_{t-1}+ ... +\Gamma_{p-1} \Delta y_{t-(p-1)}+\varepsilon_t$$

where $\Pi=\sum A_j -I_k$ and $\Gamma_i=A_j$.

• I corrected your formatting - please check if it is correct. What is your question in here? What is unclear in the output? – Tim Dec 22 '15 at 19:42
• Thank you very much. so I dont understand what does the coefficients for e.dl1 , prod.dl1,rw.dl1 stand for ? Are these coefficients in the result the Π or the Γ? What does cajools do ? Why is there 4 values of the test statistics in the Johansen test ? – Ashleyshime Dec 22 '15 at 20:07
• Please edit your question to add those information and describe your question in greater detail. – Tim Dec 22 '15 at 20:17
• Judging on how basic (and also how numerous) your questions are, you may benefit from reading some introductory material such as Pfaff "Analysis of Integrated and Cointegrated Time Series with R" and the "vars" vignette. Then you may come back and ask what is unclear. – Richard Hardy Dec 22 '15 at 21:15