How to decide to choose between OLS regression & regression with Fixed effect model?

[Andy Lee]

Hello everyone!! I'm reseaching on impact of capital structure on profitbility of comercial bank. My DV is ROE and main IV is Total debt/Assets. My control variables are Assets Growth, Assets Size and CPI. Firstly, I decided to choose FEM & REM and after using Hausman test, my model is suitable with FEM. However, in the result regression with FEM, my control variable Assets SIZE is insignficant. But when I try to run OLS regression, Assets SIZE is signficant. Theoretically, Assets SIZE is a factor that affects to ROE, also by some of papers I have read. So did I do anything wrong when solving datas? If not, how can I choose between OLS regression & FEM? Result after running regression of both of them in below. Thanks!!

[Carlo Lazzaro]

Andy:
as reported many times on this list, statististical significance of one or more predictors is not the right approach to select your regression model (see the literature in your research field, instead).
Moreover, your regression models are by no means mutually exchangeable: you're seemigly dealing with a panel dataset (and so -xtreg- is appropriate); however, in your second regression model you go -regress-, implicitly pretending that you are dealing with independent observations rather than with repeated measures of the same variables on the same panel units. By the way, please note that robustified and clustered standard errors under -regress- do not do the same job (as they do under -xtreg-); hence, you should have clustered standard errors on panel_id in OLS.
At the top of that, please note that there's only one instance in which pooled OLS outperforms -xtreg, fe-: it happens when the F-test reported as a footnote of -xtreg,fe- (with default standard errors) outcome table fails to reach statistical significance (that is, there's no evidence that the individual effects are different from zero).

[Rose Simmons]

Please may I ask what would be the difference between running a regression with -xtreg- and -reg, cluster(panelid)- ? Is the latter appropriate to use with panel data too? Thanks