12 firms and a total of 204 observations, can I use pooled OLS with firm-dummies or should I use fixed factor? I am studying the effect of government ownership on firm performance, more specifically I am studying the effect of the government reducing their share in companies which are already partly privatized. 
I have collected relevant data for 12 firms where the state have reduced (or increased in some firms) their share since 1990. For a limited number of firms I have data from 1990, but for most of the firms the data starts in the 90`s (all firms have observations until 2013). So the data is unbalanced with a total of 204 observations.

I want to estimate the effect of "STATE SHARE" on "ROS" where "INDEX" and "YEAR" will be control variables.
My initial thoughts were to create dummies for every firm so that differences in the firm-averages would not influence my results. After trying to google the issue I have started to wonder if I should do a fixed-effects analyses, but I am struggling to understand the difference between just adding firm-dummies and doing a fixed effects regression where the firms are the fixed factors. 
How can I best study the effect of reduced government ownership with the dataset I have collected? All help will be highly appreciated.
 A: What you called "pooled OLS with firm dummies" is essentially fixed effects. Subtracting firm means from your variables for each firm (the so-called within transformation) that is done by computing the fixed effects estimator is the same as including dummies for your firms. A similar question has been asked here before so this answer will provide the technical details and the reference you need.
If you want to know whether you should run pooled OLS (without firm dummies) or a fixed (or random) effects regression you can use the Hausman test to make a decision. In most economic applications of panel data it is very likely that some of your observed control variables are correlated with the firm fixed effect. For instance, the number of exports/sales is likely to be correlated with the location of the firm (which usually doesn't change over time).
Another issue is: why did the government reduce their share in those firms? They might have just gotten rid of the bad firms that were already declining. In that case it will look as if reduced government ownership will make firms worse off. Fixed effects will not deal with such selection problems unless the reasons for the selection are fixed over time - and typically they are not. The econometric solution for this would be instrumental variables but generally it is not easy to find a good instrument.
