In my experiment I want to examine existence of non-linearity in the regression of ownership concentration on firm performance.
My sample is a panel data set (N>T)
Apart from measuring the square of the variable what are the other stuffs I need to take care of ?
Good that you have N>T in your panel dataset. Using square of a variable to capture non-linear relationship is just a starting point of examining non-linear relationship. Why don't you test for threshold effect. This will give you the turning point of the model if it exists. Besides, a look at your regression shows that it might be a good candidate for dynamic regression. Please read around GMM method for robust method that addresses endogeneity and causation that might be inherent in the relationship.
Should you wish to address the two issues together, then adopt dynamic threshold regression method. It is simple!
I wish you success!
Please read my article in this regard:
Article Too Small to Succeed versus Too Big to Fail: How Much Does S...
And go for Threshold analysis as well.
Agree with Segun Thompson Bolarinwa
All the best.
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