I have three variables (monthly for 25 years) including wages (e.g. skilled and unskilled) and food price (P). I am interested to see if there any relationship exist between them, either short or long term and which one has the greater influence on other.
All the variables are non-stationary at levels but stationary at first differences. But when I check the cointegration rank in 'Stata' ('vec rank', for your information, I run this command with the variables in their levels ) then it suggests no cointegration. In that case, 1. What should I do? Will I go for a VAR model of the first-differenced series? 2. Why there is no cointegration among the variables?( while I found through unit root rest that all the series are stationary after first difference) 3. When I check the cointegration of the first-differenced series then I find the cointegration rank equal to 1. But is it feasible to run a VECM model to first- differenced series?