Preference between 2 models in Panel data, using different forms of the same non-linear variable.

[Maha Natsheh]

Hello everybody,
Hope this finds you well !

Could you provide me an advice of what regression is better, by knowing that I have 76 cooperatives and 3 years, please note that random effect have been chosen in both by Hausman test:

1) regression containing assets in both forms: (LogAssets)^2 + LogAssets, in addition to interaction between dummy variables of region with Log Assets:

xtreg Netsurplusachievedafterrese SqlogAss logAss EqCap_Ass SumNoManaging CoopsAgeconstant cash_ass ID_RGN_MID ID_Rgn_SWTH MidRgn_lgAss SthRgn_lgAss, re

please note that vif test reveal on the value of 118.

2) other one with Assets it self and Log Assets, the interaction variables between regional dummy variables with total assets; as the usage here of interaction with log Assets -that used in the first case- lower R^2 to 0.41:

xtreg Netsurplusachievedafterrese TotalAssets logAss EqCap_Ass SumNoManaging CoopsAgeconstant cash_ass ID_RGN_MID ID_Rgn_SWTH MidRgn_Ass SthRgn_Ass, re

Here, vif test shows the value of 11.19,
but the problem is that sigma_u = 0, which -as I know- equalize this regression with pooled OLS, which actually provide approximately the same coefficients with same significance,
By experiment to add i.year, both years didn't show significant effects.

from your experience, which regression better to choose?

The same problem shown by using (Total Assets^2 + Assets), but also more than one important coefficients didn't show significant effects, so that why I ignored it.

Thanks in Advance for your help!

Maha H. Natsheh

[Carlo Lazzaro]

Maha:
1) I would go with the first one, as the second one shows no panel-wise effect (I assume here that you gave a true and fair view of the data generating process you're intreseted in);
2) I would switch from default to cluster-robust standard standard error and check via the community-contributed module -xtoverid- if -re- is actually the way to go with your dataset.

[Maha Natsheh]

Thanks Carlo,
Here is the xtoverid result for the first regression:


Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re
Sargan-Hansen statistic 10.197 Chi-sq(8) P-value = 0.2515

While the second one refused to execute, and showed this message:
Error - saved RE estimates are degenerate (sigma_u=0) and equivalent to pooled OLS.

[Carlo Lazzaro]

Maha:
I would go -re- with your first regression code (the -xtoverid- null is that -re- is the way to go and the null has not been rejected in your case).