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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.

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Should I follow the same tests as in a normal OLS regression? If so, should I include the time dummy in the tests?

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  • $\begingroup$ No by assumption if the individual specific effects exist, OLS estimators appear bias and inconsistent. Therefore, introduce diferential dummies to eliminate these effects or demean the model $\endgroup$ Jun 26, 2018 at 4:27

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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.

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  • $\begingroup$ Andy, I truly don't know how to thank you for this and all your other answers. I was so puzzled by the whole OL thing! Please allow me 2 more questions. When I do FE, clustered, the F(x,x) and F>p values disappear, is this normal? Also, I am not seeing this: F test that all u_i=0. Look, this is what I get: imgur.com/AzV70Ve. Is that last test that "test whether pooled OLS is consistent, i.e. your xit are uncorrelated with the fixed effects ci"? // I'm getting the book now, I have several other, but some are too technical and I get lost, I hope this one is easier to understand :) $\endgroup$ Jul 28, 2013 at 9:41
  • $\begingroup$ Ah yes, I forgot that this F-test for u_i=0 only holds under homoskedasticity (try without the cluster option but either way the proper comparison test should be the Hausman test - with xtoverid you can do this also with cluster robust errors). The Hausman test is to see whether pooled OLS is consistent. The missing F value for the model is okay. In Stata the F(x,x) should be in light blue color - you can click on it and an explanation will appear as to why the F statistic is missing. I'm glad you are finding my answers useful :) $\endgroup$
    – Andy
    Jul 28, 2013 at 9:50
  • $\begingroup$ Thanks again! Isn't the Hausman test to compare FE with RE? The F(x,x) is in blue color, and I read the help, but I didnt understand wheter it was ok that it was missing or not, until now. $\endgroup$ Jul 28, 2013 at 10:18
  • $\begingroup$ Hausman is a very general test, that's why it became so famous. You just have to have a consistent estimator (FE in this case) and you must be able to rank the variances (Var(FE)>Var(OLS)) to compare two models with Hausman. Concerning the missing model F, the help says: "Your estimation results show an F or chi2 model statistic reported to be missing. Stata has done that so as to not be misleading, not because there is something necessarily wrong with your model." $\endgroup$
    – Andy
    Jul 28, 2013 at 10:47
  • $\begingroup$ OK, nice. I didn't know I could use it to compare with OLS too, everywhere I've read it always is mentioned for comparing FE and RE. Regarding the Stata help, I read that, but since I didn't know it was dependent on whether the data was homoscedastic or not, I thought that anyway was there something wrong with my model. Thank you again Andy, I'll compile all your answers now and try again. Hopefully this time I'll be able to get this done! Have a great Sunday! $\endgroup$ Jul 28, 2013 at 10:50

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