Lags of dependent variable: correct use and interpretation

[Wecon]

Dear fellow eviews users,

I am currently doing some econometrics with, probably, nonstationary variables in a panel setting. I was hoping for cointegration, but, ADF-test on stationarity of residuals of a cointegrating regression performs rather bad. A regression using first differences performs even worse.
Nevertheless, I found out that including two lags of my dependent variable yields very fine results (good R² and great results from autocorrelation tests). Can I trust these results? That is, are they unbiased and consistent? If so, can these lags be reasonably interpreted?

Many thanks!