Pooled data in regression analysis I am performing my research on the most active 50 companies for a period of 5 years.  The most active 50 companies change every year.  I want to determine how my dependent variable is impacted by the explanatory variables without regarding the time and the companies.  So can I just pool all the data as one group and run my regression.  
 A: Pooled OLS regressions in the case of Panel Data are usually frowned upon.First, if the conditional exogeneity condition holds, that is:
$$
E[(\alpha_{i}+u_{it}|X_{it})]=0
$$
 holds, then you might as well use a random effects estimator (In
the above expression, $\alpha_{i}$is the time invariant, individual
specific nuisance paramter and $u_{it}$ is the general error term)
Random Effects estimator is a GLS type estimator and is more efficient
that the pooled OLS estimator. In many cases, however , this condition
does not hold. As such, people invoke a Fixed Effects estimator that
effectively removes the nuisance paramter and uses within subject-over
time variation. You can actually 'test' the condition by conducting
a Hausmann test, which tests the weighted "squared'' difference
between the fixed effect and random effects estimators. If you reject
the null, you are better off using a fixed effects estimator. In any
case, it is weakly better to use a Randome effects estimator than
a pooled OLS one. 
