Granger Causality

Lesson 4: Temporal Precedence and Lags

Quantitative Methods for Causal Inference

Lag Analysis

The Direction of Influence

In historical datasets, two variables often move together perfectly. But which one is the driver?

"Does increased literacy drive democracy, or does a democratic state invest more in literacy?"

Variable A Literacy

Variable B Democracy

Correlation alone cannot solve this.

Predictive Precedence

The Granger Test

Variable \(X\) "Granger-causes" Variable \(Y\) if past values of \(X\) help predict future values of \(Y\) better than just using past values of \(Y\) alone.

\(Y_t = \sum \alpha_i Y_{t-i} + \sum \beta_i X_{t-i} + \epsilon_t\)

Requirement 1

Temporal order (Cause must precede effect).

Requirement 2

Unique predictive power (Not explained by the trend itself).

Historical Lags

History doesn't happen instantly. Causes have "lag periods" before they register in archival records.

The Policy Lag

A law passed in 1840 might not change trade behavior until 1842.

The Biological Lag

Nutritional shocks in childhood manifest as height data 20 years later.

The Recording Lag

Crisis happens now; it is recorded in tax audits 5 years from now.

Finding the "Sweet Spot"

"If your lag is too short, you miss the effect. If it's too long, the causality is lost in other historical noise."

Temporal Logic Workshop

"You find that grain prices rise in Year T and peasant revolts spike in Year T+1. Does Year T 'predict' Year T+1? How would you test if it's the price causing the revolt, or a hidden third variable (like bad weather) causing both?"

1. Test Lags

2. Check Forecasts

3. Rule out Shocks

Granger Causality Slides

Granger Causality Slides