# VECM - interpreting output from cajorls()

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?

VECMcoeff = VECM(combined, lag = 2, r = 2, include = "const",