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.
 A: 
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?

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.

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

Not that I am aware of. If your variables have unit roots and are not cointegrated, then the natural solution is to first-difference the data. If you keep them in levels and use in regressions, you will at least have the trouble of nonstandard distributions of estimators (as noted above), but you may also have cases where the left hand side of an equation diverges from the right hand side as they are driven by different stochastic trends.
