Mathematics
Fixed Effects
Quick fact
Fixed effects models are often implemented by simply including a dummy variable for each entity (e.g., each person, each company), but mathematically, they are equivalent to subtracting each entity's average over time before analyzing the data.
Why this is interesting
You've likely heard that correlation doesn't imply causation. What if you could remove all the 'background noise' that stays constant over time, getting closer to a cause? That's exactly what fixed effects do.