Thank you Dr. Nurul Islam for this amazing and complex question. Since, you did CSD test & slope homogeneity test and found heterogeneity & CSD problem, you can apply CS-ARDL approach for long-run estimation. You can also apply AMG and CCEMG for robustness and making sure your result is valid and acceptable. Thank you.

Thanks, Ridwan Ahmed for your answer. But my confusion is I have found cross-sectional dependence in a few variables not all variables. As far as I know, if all variables have a CSD problem then one should do CCEMG and AMG.

ChatGPT's response

If you have short panel data and some variables have cross-sectional dependency while others do not, you can use a Hausman test to determine whether to use a fixed effects model or a random effects model.

The Hausman test compares the estimated coefficients from a fixed effects model and a random effects model, and tests the null hypothesis that the random effects estimator is more efficient. If the null hypothesis is rejected, then the fixed effects model should be used. If the null hypothesis cannot be rejected, then the random effects model is preferred.

Alternatively, you could also use an Arellano-Bond test, that test for the presence of autocorrelation in the residuals of a panel data model with fixed effects.

It is important to note that both test have assumptions, so it is important to check for the assumptions before using the test.