Combining First Differences and Levels in PCSE Regression with Unbalanced Panel Data

[Matthew Hammerle]

Hello Statalist Members,

I am working with unbalanced panel data involving 𝑁=5 and 𝑇=20. I have utilized Pesaran's CADF test to check for unit roots in my dataset. The results indicate that some of my variables exhibit unit roots, whereas others do not.

I am considering running a Panel-Corrected Standard Errors (PCSE) regression. My question pertains to the appropriate handling of variables in such a regression model:

• Is it methodologically sound to include a mix of variables in their first differences (to address unit roots) alongside others in their natural logarithms (that do not have unit roots)?

I would appreciate any advice on whether this approach is statistically valid, and if there are any considerations or adjustments I should be aware of when implementing this in a PCSE framework.

Thank you for your guidance.