Cointegration test - necessary to use first-differenced variables?

[Elena Diaz]

Hi!

I am working on a project with a short panel data structure and have discovered non-stationarity in two out of four independent variables. However, as the dependent variable is measured with a lag, it appears to be stationary. I am therefore considering testing for cointegration but I am not sure if I need to include a first-difference in all of my variables (or only in the non-stationarity variables?) prior to testing for cointegration or if this only should be done if the variables appear to be non-cointegrated.

If the variables are cointegrated, should a first-differenced model be used or can I use the original, level, version?

Thank you in advance!

[Andrew Musau]

short panel data structure

Describing your panel as above is not very informative. I have heard of short-T panels \(\left(\text{where}\; N>>T\right)\), but not short-N panels. Assuming that you have \(T>N\), see https://www.statalist.org/forums/for...tegration-test

[Dario Maimone Ansaldo Patti]

Elena, if one variable is stationary and another one is not, it is pointless to check for cointegration. One pre-requisite to check for cointegration is that the variables share the same order of integration, i.e. they are both I(1). If not, my suggestion is to take the first difference of the variables that are not stationary and to use them in your model.