Causation vs. Correlation
From associations to mechanisms
Prof. Dr. Claudius Gräbner-Radkowitsch
2026-05-28
Today’s session
- Where we are: You can specify, estimate, and diagnose regression models
- Today’s question: What do those coefficients actually claim?
- The shift: From estimation to interpretation — from how to what it means
No new estimator today. The methodological move is entirely in interpretation.
A puzzle from hiring data
A consultancy analyses firm-level data and finds:
“Firms that hired more sales staff last year had lower revenue this year.”
Conclusion: Hiring sales staff reduces revenue. Cut the sales team.
Wait. What else might explain this pattern?
The confounder hiding in plain sight
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Product quality drives both hiring decisions and revenue.
- Firms with poor products hire more staff to compensate
- Poor products also depress revenue
The correlation between hiring and revenue is real — but the causal story is backwards.
The identification question
Regression answers:
“How does Y vary with X, holding controls constant?”
That is not the same as:
“What is the effect of X on Y?”
The gap between the two is closed — or not — by an identification argument.
Association vs. causation: A regression coefficient is associational by default. Causal interpretation requires an identification argument that lives outside the regression output.
Three levels of causal questions
Not all causal questions are the same. Judea Pearl’s Ladder of Causation:
- Seeing (Association): “Women earn 20% less on average.” This is what regression gives us by default.
- Doing (Intervention): “If employers couldn’t see a candidate’s gender, what would happen to the gap?” Requires a research design — not just more data.
- Imagining (Counterfactual): “Would she have earned more if she had been a man?” Requires a structural model of the individual.
Regression answers Level 1 only. Moving to Level 2 requires an identification strategy.
Preview — Session 7: A résumé audit study randomly assigns gendered names to otherwise identical applications. That is a Level 2 answer. That is why experimental designs are so valuable.
DAGs: a language for causal structure
DAG (Directed Acyclic Graph): A diagram where nodes are variables and arrows represent direct causal effects. Acyclic means no variable causes itself.
We use DAGs to make our causal assumptions explicit and testable.
Three structural roles a variable can play:
- Confounder
- Mediator
- Collider
Three structural roles
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- Confounder: Common cause of X and Y → must control
- Mediator: On the causal path from X to Y → must not control (if you want the total effect)
- Collider: Caused by both X and Y → must not control — conditioning on it creates a spurious correlation between X and Y that wasn’t there before
Collider trap: Unlike a confounder (where not controlling causes bias), controlling for a collider introduces bias. It is the most counterintuitive of the three.
Application: the gender wage gap
We want to know: does gender affect wages?
Let’s draw the causal structure before running a single regression.
What factors are in play?
- Direct effect: gender → wage (e.g. discrimination in pay setting)
- Occupational sorting: gender → occupation → wage
- Unobserved background: family background, networks → both occupation and wage
The gender wage gap DAG
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Key question: What happens when we add occupation as a control variable?
The bad control
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Reading the figure: The square node marks that Occupation is in the regression — we are actively controlling for it. Circles = not controlled for. Dashed arrows = paths that are now blocked.
Controlling for occupation blocks the path: gender → occupation → wage
Key question: What happened to the coefficient on gender?
The bad control — what it means
- The coefficient on gender shrinks — but not because we found a better estimate
- We are now estimating a different, narrower question: the direct pay gap within occupations
- Whether that is interesting depends on the research question
Bad control: A mediator or collider incorrectly added as a control variable. The result is not more precise — it answers a different question.
Live demo: three models, three questions
Using CPS earnings data (149,316 US workers, 2014):
| 1 |
wage ~ gender |
Raw gap |
| 2 |
wage ~ gender + age + education |
Gap controlling for demographics |
| 3 |
wage ~ gender + age + education + occupation |
Gap within occupations |
The coefficient on gender shrinks from Model 1 → 3.
This does not mean Model 3 is more correct. It means each model answers a different question.
What makes a coefficient causal?
Not the regression itself — the identification argument.
An identification argument claims: “The variation in X I am exploiting is as good as random with respect to Y.”
Two strategies you will learn:
- Session 6 — Panel fixed effects: Control for all stable unobserved differences across units
- Session 7 — Randomised experiments: Randomisation makes treatment assignment independent of everything else
These strategies are not more credible because the math is different. They are more credible because they provide an identification argument.
In-class exercise
Task 1 — Reproduce and interpret: Run the three-model progression on cps-earnings. For each model, write 3–5 sentences: “What causal claim, if any, can this model support — and why?”
Task 2 — Draw the DAG: A firm wants to know whether advertising causes sales. Both are also driven by product quality, and advertising success may itself affect product investment.
- Draw the DAG
- Identify any confounders, mediators, or colliders
- What would you need to control for — and what should you avoid controlling for?
Where we go next
Today: You know what an identification argument is, and why regression alone cannot provide one.
Session 6: Panel fixed effects — exploiting within-unit variation over time to control for all stable unobserved differences.
Session 7: A randomised experiment — where randomisation itself is the identification argument.
Now you know why those sessions matter.
