Causal Inference in Economic Time Series

Understanding causal inference in time series

Causal inference in economic time series aims to answer questions like "Does monetary policy cause changes in inflation?" or "Do commodity prices drive currency movements?" Unlike standard statistical correlations, causal analysis seeks to establish directional relationships while accounting for:

• Temporal precedence (causes must precede effects)
• Confounding variables
• Feedback loops
• Structural breaks
• Non-linear relationships

Key methodological approaches

Granger causality

The most widely used framework for testing causality in time series is Granger causality. A variable X is said to Granger-cause Y if past values of X help predict future values of Y beyond what Y's own history predicts.

Mathematically, for time series $X_t$ and $Y_t$:

$Y_t = \sum_{i=1}^p \alpha_i Y_{t-i} + \sum_{i=1}^p \beta_i X_{t-i} + \epsilon_t$

Where:

• $p$ is the lag order
• $\alpha_i$ and $\beta_i$ are coefficients
• $\epsilon_t$ is the error term

Structural vector autoregressions (SVAR)

SVARs extend basic time series analysis by imposing economic theory-based restrictions to identify causal relationships:

Applications in financial markets

Market microstructure analysis

Causal inference helps understand:

• How order flow affects price formation
• Impact of market liquidity on asset prices
• Transmission of information between related markets

Policy impact evaluation

Researchers use causal inference to study:

• Effects of regulatory changes
• Impact of central bank interventions
• Consequences of market structure modifications

Advanced techniques

Instrumental variables

When dealing with endogeneity, instrumental variables provide a way to identify causal effects. The approach requires finding variables that:

1. Correlate with the causal variable of interest
2. Affect the outcome only through the causal variable
3. Are not influenced by common confounders

State-space models

State-space models combine with causal inference to:

• Handle unobserved variables
• Account for measurement error
• Model complex dynamic relationships

The general form is:

$y_t = Z_t \alpha_t + \epsilon_t$ $\alpha_{t+1} = T_t \alpha_t + \eta_t$

Where $\alpha_t$ represents the unobserved state vector.

Challenges and considerations

Temporal aggregation

The choice of sampling frequency affects causal inference:

• High-frequency data may capture immediate effects
• Lower frequencies might better reveal long-term relationships
• Aggregation can mask or create spurious relationships

Non-stationarity

Many economic time series are non-stationary, requiring:

• Cointegration analysis
• Error correction models
• Careful interpretation of results

Structural breaks

Major economic events can cause structural breaks, necessitating:

• Break point detection
• Regime-switching models
• Robust estimation methods

Best practices for implementation

1. Begin with clear theoretical foundations
2. Test for stationarity and cointegration
3. Consider multiple time horizons
4. Validate results with out-of-sample tests
5. Account for structural breaks
6. Document and justify identification assumptions

Modern developments

Recent advances include:

• Machine learning for causal discovery
• Bayesian approaches to uncertainty quantification
• Nonlinear causal models
• High-dimensional causal networks

These methods help handle the complexity of modern financial markets and big data environments.