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I am a bit puzzled on how to interpret the test results cajorls() from the urca-package. This function returns the OLS regressions of a restricted VECM, i.e. it returns a list object with elements of class ‘lm’ containing the restricted VECM and a matrix object with the normalised cointegrating relationships. The output is as follows:

$rlm

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

Coefficients:
                rstar.ger2.d  rstar.nl2.d  rstar.fr2.d  rstar.sp2.d  rstar.it2.d
ect1            -0.0017846     0.0153640    0.0040054   -0.0069455   -0.0001016 
ect2             0.0107730    -0.1374979    0.1362569    0.0798872    0.0291866 
rstar.ger2.dl1   0.0177601    -0.0071459    0.1840403    0.1453076    0.0388310 
rstar.nl2.dl1    0.3616836     0.0006218   -0.2059346   -0.0004955    0.0281643 
rstar.fr2.dl1    0.1159788     0.0083223   -0.0885601    0.0916455    0.0959205 
rstar.sp2.dl1    0.0494191    -0.0308582   -0.0448139   -0.1467505    0.0539171 
rstar.it2.dl1    0.1004643     0.0284516    0.2993759    0.2938969   -0.0073476 
rstar.ger2.dl2  -0.0048584    -0.0060393    0.1232667   -0.0615904    0.0292541 
rstar.nl2.dl2    0.3012379    -0.1223988   -0.1139923   -0.2024982   -0.1418449 
rstar.fr2.dl2    0.0033811     0.0109410   -0.2276895   -0.0343024   -0.1120294 
rstar.sp2.dl2   -0.0187626     0.0241342   -0.0209384    0.2175508    0.0923392 
rstar.it2.dl2    0.0096038    -0.1689995   -0.0548127    0.3646600    0.0143355 


$beta
                   ect1          ect2
rstar.ger2.l3  1.000000  6.938894e-18
rstar.nl2.l3   0.000000  1.000000e+00
rstar.fr2.l3  -7.743012 -9.253440e-01
rstar.sp2.l3   9.681516  6.076362e-01
rstar.it2.l3  -6.690274 -8.328822e-01
constant      -3.566494 -1.377382e+00

Where the Johansen maximum eigenvalue test indicated that there is one cointegrating relationship at the 1% level, and two cointegrating relationships at the 5% level.

How can I translate these results to a coherent story for my thesis? What does this output tell me?

Your help is invaluable!

PS. VECM specification:

VECMcoeff = VECM(combined, lag = 2, r = 2, include = "const", 
            beta = NULL, estim = "ML", LRinclude = "const", exogen = NUL
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I am afraid that it is too late for your thesis. You can get more detailed information (t-statistics, p-values, etc.) if you use the function summary. To be more clear, If you put summary(vecm$rlm), you will get a lot more information. Here vecm is the name you gave to your estimated cajorls function. I hope this is what you are looking for.

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