Part VI · Chapter 19
Granger Causality
x Granger-causes y if lagged x improves the forecast of y beyond what lagged y already provides. It's about PREDICTIVE content, not structural causation.
Learning objectives
Set up restricted vs unrestricted regressions.
Interpret F-tests for Granger causality.
Avoid the trap of equating prediction with causation.
Handle stationarity requirements.
Prediction Causality Lab
Seed:
Test results (pseudo)
x → y F-stat (pseudo): —
y → x F-stat (pseudo): —
Verdict: —
Crude SSR comparison; in Gretl use VAR + Granger test.
📐 Granger test
\[ \text{Restricted: } y_t = \sum_{i=1}^p \alpha_i y_{t-i} + u_t \]
\[ \text{Unrestricted: } y_t = \sum \alpha_i y_{t-i} + \sum \beta_j x_{t-j} + u_t \]
\[ F = \frac{(SSR_R-SSR_U)/q}{SSR_U/(T-k)} \]
H₀ x does NOT Granger-cause y
Reject x has predictive content
Both directions feedback system
🔍 What to look for
- If x leads y in the plot, you'll likely reject "x does not Granger-cause y".
- Bidirectional rejection ⇒ feedback (no single causal direction identified).
- Granger requires stationary variables; use VECM-based test if I(1).
⚠️ Pro Tip: What to Avoid
Student says
"x Granger-causes y, so x is the structural cause of y."
Why this is wrong
Granger causality is a statement about FORECAST IMPROVEMENT. It does NOT identify a structural causal mechanism. Reverse causality, omitted common factors can produce the same evidence.
Correct interpretation
Report "x has predictive content for y, conditional on lagged y." Structural causation requires identification (IV, sign restrictions, RCT).
📝 Mini-quiz
📋 Key Takeaways
| Concept | Note |
|---|---|
| Granger causality | Predictive content, not structural |
| Test | F-test on cross-lag coefficients |
| Bidirectional | Feedback system — common in macro |
| Stationarity | Required — use differencing or VECM |