Hi,
Sorry, I used the two variables Debt_ratio and Capital_share, with a restriced contant model. The lag length, according to a majority of information criteria, is 2.
OK, I tried your first subsample (BTW, I found it quite nice how gretl directly imported the series from the xlsx file without a hiccup...), and I also get a p-value below 5%. Remember, however, that this just means that the test finds one stationary component ( = "direction") in the system. By eyeballing that series I would bet that the capital share is an I(0) variable, at least in the perspective of this subsample. So yes, I'd say that the result is reliable, but it may not mean what you were expecting.
cheers
sven