# 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.

• How are you defining "active?" What is your DV? Why would you not want to condition the estimates by structural factors such as time, sector and company? – Mike Hunter Nov 3 '15 at 15:47
• The most 'active' is defined as the ones with highest trading activity. My DV is levels of corporate disclosure. And the independent variables consist of ownership structure variables as well as other firm characteristics. I am not interested in how different time periods impacted my DV or how companies in different sectors behave differently with regards to disclosure. All I am interested in is how different ownership structures impact the DV. Since the most active companies differ each year, I just pooled them all together as one sample. How strongly can I support this? – user89313 Nov 3 '15 at 20:46
• Trading as in stock market trading volume? "Disclosure" sounds like a judgmentally driven classification, is it? I understand that you only care about ownership but do you also understand the trade-off that entails? In other words, there may be factors moderating the bivariate relationship you care about that, if controlled for, would change aspects of this relationship. At a minimum, it should adjust the model parameters for any bias present if these factors are not used to condition the model estimates. – Mike Hunter Nov 3 '15 at 20:53

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.