Should I test for all the OLS assumptions for a pooled OLS from panel data? As the title says, I need to perform a Pooled OLS, a Fixed effects and a Random effects analysis.  In the case of a normal OLS, one should test for normality, collinearity, homoscedasticity, linearity, etc.
I have been following the steps described here, but I am not so sure if I should do that in my case.  My model is like the one described here.

Should I follow the same tests as in a normal OLS regression? If so, should I include the time dummy in the tests?
 A: It's nice to test for normality, homoskedasticity, etc. but there are two more pressing issues with pooled OLS. The first is to test whether pooled OLS is consistent, i.e. your $x_{it}$ are uncorrelated with the fixed effects $c_{i}$. Of course they should also be uncorrelated with $u_{it}$ but that you cannot test so it must hold by assumption. Concerning the fixed effects, you can compare pooled OLS and FE regressions via the Hausman test as we discussed in another question earlier (remember that FE is consistent if $x_{it}$ and $c_{i}$ are correlated but pooled OLS is not). Also when you run the FE model it will display a test at the bottom of the regression table, F test that all u_i=0. If this is rejected you should favor FE over pooled OLS.
The second issue concerns the standard errors. As I understand, you have panel data on several banks. In pooled OLS the errors are likely to be serially correlated but you can (and should, according to Cameron and Trivedi (2009)) control for this by clustering the errors on the bank id variable. In Stata you can do this via
reg y x, cluster(id)

Where x includes your independent variables and the time dummies. If you don't use this correction, your standard errors will be very small and you are more likely to draw wrong inference. Since you have a large time component serial correlation will almost surely be there. But if you need a formal test for this you can use the xtserial command which can be downloaded via net install st0039 in Stata.
The steps described in the website you linked are nice to do but given the set-up of your regression analysis you already know that homoskedasticity and time independence in the errors are unlikely to happen. These ideal conditions rarely hold in applied work anyway but it's okay because we can correct this with the clustered standard errors. The same holds for normality. You should check for highly collinear variables as they might impact on the consistency of the estimator.
As a side-note I think a very good book for you would be Cameron and Trivedi (2010) "Microeconometrics Using Stata". It covers all of the methods you are working with, it discusses potential problems, how to diagnose and to solve them, etc. It's a bit pricy but perhaps you can find a copy in your university library. If you intend to do empirical work in the future it's definitely a good buy though.
