Non-stationary data

[Andrey]

Hello,

I am trying to run a simple OLS panel data regression, but I encounter several problems.

First, I did a unit root test to check for stationarity. I used a panel unit root test - I looked at ADF – Fisher Chi-square. I thought it is better than the Levin, Lin & Chu test since the latter one is for common unit root, rather than individual, and therefore it would be easier to get a false significant result for some variables. The test showed that the variables are not stationary. I also did univariate unit root tests for the different countries, which also showed that the data is non-stationary.

Therefore I take the differences of the variables to account for stationarity. But when I do this, the regression results make no sense. Almost none of the variables in the model are significant and the signs are totally the opposite from what they should be. If I don't account for stationarity, the results are better, but I have a problem with autocorrelation. Furthermore I think that because of the non-stationarity, this would be a spurious regression and I cannot trust my results.

I also checked for structural breaks in the data. Some of the variables that have such breaks are stationary. I take care of the structural breaks by using log form (which also helps for the autocorrelation), but this makes the variable non-stationary. Then when I take the first difference, the results from the regression are again insignificant.

I am aware that Baltagi (2005) says that for a small number of time periods (T) the stationarity problem can be disregarded. I have 11 years in my data. This is not really small, but perhaps I can still use this statement and not be afraid of a spurious regression?

Second, when doing the regression the results show that there is autocorrelation (Durbin-Watson is less than 1). I use logarithms to correct that, but for some reason it does not solve the problem with autocorrelation, I am unaware of another way to counter that, except perhaps different selection of explanatory variables.

Third, I have a problem with multicollinearity, but when I try to solve it by dropping one or more variables, the results get worse again (not significant; autocorrelation; low R-squared). Maybe it comes again to better selection of the independent variables.

So to sum up, I have 3 main questions:
Do you know how to deal with the non-stationarity and get decent results?
Do you have any idea how to remove the autocorrelation except with log?
Do you know of any technique to remove multicollinearity between the explanatory variables?