# Lags of dependent variable in regression with non-stationary variables

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, when estimating in levels, yields very fine results (good R² and great results from autocorrelation tests). Can I trust these results or are they spurious? That is, are they unbiased and consistent? Should I fear the Nickel-bias?

Are there ways to deal with nonstationarity other than first differencing in the absence of cointegration?

I am using OLS in EViews and include cross-sectional fixed effects.

They are spurious because you have integrated variables on both sides of the regression equation. In such cases $R^2$ behaves in a nonstandard way and a high $R^2$ value arises by construction. Also, coefficient estimators do not have their standard distributions so you cannot rely on $t$ and $F$ tests of statistical significance, for example. So essentially it is difficult to use such a model and it is better to first-difference the variables before using them in the regression.