Hello everybody!

I am running the following models:

1. xtreg DepVar IndepVar1 IndepVar2 IndepVar3, fe. - Fixed effects model
2. xtreg DepVar IndepVar1 IndepVar2 IndepVar3, re. - Random effects model

In both models, the three independent variables result significant (p-value < 0.05 and <0.01). Then I run Hausman test as follows: hausman fixed random, sigmamore. Hausman test rejects Ho, and this suggests me to use Fixed Effects Model.

However, I tried also the following models, using vce(robust):

3. xtreg DepVar IndepVar1 IndepVar2 IndepVar3, fe vce(robust).
4. xtreg DepVar IndepVar1 IndepVar2 IndepVar3, re vce(robust).

In this case, in model 3 IndepVar1 resulted not significant and the other variables resulted significant. In model 4 all variables resulted significant.

I would like to understand why in model 3 IndepVar1 could have resulted not significant and in model 4 they all resulted significant. In models 1 and 2, Hausman test suggested me to trust fixed effects model. In the case of models 3 and 4, how could I know which model to trust? What does the command vce(robust) do exactly? What is the estimator used by this type of regression?

Thank you for reading me!

Best regards!