I am testing for cointegration between the Real GDP per capita of England and France. I use a Dickey-Fuller test to test for stationarity and concluded that both of my series are non-stationary. So I then ran the regression and did the second Dickey-Fuller test for co-integration on the residual. Here is what I am confused about:
If I ran the regression and had rgdpe of England as a dependent variable I concluded that my regression was spurious. (My residuals were non-stationary).
If I ran the regression and had rgdpe of France as a dependent variable I concluded that the rgdpe are cointegrated (My residuals were stationary).
Can anyone explain the reason for this discrepancy?