Hausman test is used to compare two estimators which are both consistent under the null hypothesis but one is less efficient than the other.
During my course of Econometrics, I have found that Hausman test can be used in many different settings and I am a bit confused about that.
The first time I find it was used to choose between fixed and random effect models when dealing with panel data and it was called simply Hausman test. There was also a kind of generalization, the so-called Mundlak's test.
Now, I am working with instrumental variables and I've found Durbin-Wu-Hausman test that seems to me another generalization of the classical Hausman test, besides the fact that it is used to check for exogeneity of the regressors.
My question is: is Hausman test a general procedure that can be applied to different frameworks? Which are the differences among those test I mentioned above?