Can I compare and analyse the coefficients of two random effect models? Can I compare and analyse the coefficients of two random effect models? The details of my model are below: 


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*Model 1: 2 main+ 4 controls + Time + industry dummy

*Model 2: 2 main+ 4 controls + Time
The only difference between the two models is that the second model has no industry dummy. The rest of the variables are the same. Do I have to conduct some statistical test to prove comparability?
I am using Eviews8. 
 A: Comparing these two models amounts to a test of the industry dummy variable.  Standard output (I don't know Eviews) will typically compute a t or z statistic (depending on the nature of the model).  The fact that there are random effects doesn't change the fundamental issues here.  If your output does not give you a p-value (R's lmer() doesn't, e.g.), you can refit the models without using REML and perform a nested model test using the likelihood ratio test.  
If you are asking whether you should drop the industry dummy variable if it is not significant, you generally shouldn't.  It is better to make that kind of decision based on theory, and if it is a-priori.  Dropping variables that are not significant is a form of data dredging ultimately analogous to stepwise regression methods.  To understand better why this is a bad idea, it may help to read my answer here Algorithms for automatic model selection.  
If you are asking whether the other variables (i.e., the main, controls, and time variables) will change if the industry dummy is included vs. excluded, that depends on whether the dummy is correlated with both those variables and the response.  If so, the coefficients will change, with the amount depending on the strength of those correlations; if they are perfectly uncorrelated, the other coefficients will not change.  The issue is called endogeneity.  For an example to help understand how this could happen, it may help to read my answer here: Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?
A: You could compute ANOVA to test for differences between each model fit.  This will indicate whether your variable of interest has an effect on your outcome. 
Anova(m1,m2)
