Does panel data analysis is enough for controlling the unobserved heterogeneity and invariant heterogeneity? If not, How can we control these kinds of heterogeneity?
These are underlying data and a Factor Analytic approach can easily solve this. The unobserved and invariant heterogeneity show multidimensionality holds for that kind of data,therefore Using PCA will give you the groups (components) available in the data with eigen values of 1+ and % variance explained by each factor. And then the Rotated Factor Matrix will help u show which of these data belong under the same group. By so doing you can identify these data and make amends .
One of the most important features of panel data analysis is that it provides the opportunity to include unobserved heterogeneity in the model. Your question is quite general. There are many different methods and techniques. Heterogeneity is dealt with in different ways depending on the method used.