I am using panel data and I have to choose between fixed-effects and random-effects models.
I run the Hausman test, the H0 (i.e., the difference in the coefficients from the two models is not systematic) is rejected. Thus, I should use the fixed-effects.
I also run a second test, which is based on the Mundlak model. So, I run the Mundlak regression (i.e., a random-effects model where I also add the individual means of the time-varying characteristics) and I run an F-test on the extra coefficients (the coefficients of the individual means of the time-varying characteristics). I cannot reject the null hypothesis. Thus, I should use the random-effect model (although also the fixed-effect is unbiased, the random effect is more efficient).
I am puzzled. I test the same hypothesis in two different ways, obtaining two opposite results.