Various textbooks suggest that it is essential to test the variables used for stationarity before a VAR anaylse. If the tests give an indication of I(1) variables, these variables should be transformed. This can be achieved by logarithms and differentiation. This can be checked again with stationarity tests.
But now I have seen several well published papers by an author who only uses the logarithm of the variables. As far as I can understand, it should NOT be enough for the variables to become I(0). It is not tested for cointegration. In the paper there is only a reference to Sims, 1990. The author replies by mail, that "If you estimate a VAR in (log) levels, you always have consistent estimates."
- The estimation would only be significantly influenced if first differences were estimated, but the data were co-integrated.
- A VECM is estimated whose long-term involvement is not properly captured. Furthermore, the strength of the tests would be controversial.
"It is therefore better to estimate VARs in (log) levels, unless you are really sure about stationarity and/or long-run relationships in the data."
I would agree about the test power, but everything else doesn't seem to be very consistent with my previous knowledge. Am I missing something here? Is there a special case when it is possible to estimate a VAR with I(1) variables?