Why Fixed Effects?
Fixed Effects Regression
What if we can't measure all the variables we need to control for?
We can control for confounders (other variables that correlates with both the independent and dependent variable) by including them in our regression. But that only works when we know what they are and can measure them.
What if we can't?
Fixed effects is a method of controlling for all variables — observed or not — as long as they stay constant within some larger category.
How? We simply control for the category itself. In doing so, we control for everything that doesn't change within it.
Let's say we want to know: does hiring a high-profile manager increase a club's revenue growth?
Think about what might cause a club's revenue to grow. Obviously a new manager might help — but plenty of other things matter too.
There are many factors that can influence it: the club's history, their stadium capacity, the size of their fanbase, the city they're in. A club like Manchester United will always attract more revenue than a newly promoted side, regardless of who manages them.
These are confounders. And some of them — like "club prestige" — are nearly impossible to measure directly.
Here's the causal picture. Many things cause both who gets hired and how revenue grows.
But notice: most of these confounders are fixed within club. They don't change over time.
A club's stadium capacity, its history, the city it's in, the size of its fanbase (which probably don't change much in a short period) — these are essentially constant from one season to the next. They're part of a club's identity.
So what if we observe the same club across multiple seasons? If we control for club identity, we've automatically controlled for everything that doesn't change within that club.
This is the key insight behind fixed effects: collapse all the time-invariant confounders into one variable — the club itself — and control for that.
With fixed effects for club, the diagram simplifies dramatically.
But we haven't collapsed everything into club. Anything that changes over time isn't addressed by fixed effects.
A club's current form, their recent transfer activity, player injuries — these vary from season to season. Fixed effects won't control for them.
So if we want to identify the true effect of hiring a new manager, we'd still need to control for Current Form and other time-varying confounders in addition to club fixed effects.
The core idea, in one sentence:
Fixed effects takes a long list of unobservable, time-invariant confounders and collapses them into a single control: the identity of the unit itself.
In our football example, "club" absorbs stadium capacity, prestige, geography, fanbase — everything that makes Arsenal different from Brighton but doesn't change from season to season.
In other contexts, "the unit" could be a person, a school, a country — any entity you observe repeatedly over time.