Common mistake 1 with Granger causality

Writing "X causes Y" in your conclusion. It is predictive precedence, nothing more.

Common mistake 2 with Granger causality

Running the test on non-stationary levels.

Common mistake 3 with Granger causality

Ignoring that expectations reverse the timing: stock prices move BEFORE earnings, which does not mean prices cause earnings.

Common mistake 4 with Granger causality

Testing on seasonally adjusted data without saying so. Adjustment filters are two-sided, so they move information backwards in time and can manufacture precedence that the raw series does not show.

EconStatsCraft › Granger causality

Granger causality

Pairwise tests of whether the past of one series helps predict another. Both series must be stationary.

What it needs

Variables - Two or more.

The intuition

Granger's definition is deliberately modest: X causes Y if knowing X's past improves the forecast of Y beyond Y's own past. It is a statement about information and timing, not mechanism. Stock prices Granger-cause earnings, because markets anticipate - which shows exactly how far this is from structural causation.

When to use it

Exploring lead–lag structure between stationary series: do money supply changes precede inflation? Do orders precede output?

Where the estimator comes from

Estimate the unrestricted regression y_t=\alpha+\sum_i \beta_i y_{t-i}+\sum_j \gamma_j x_{t-j}+\varepsilon_t and the restricted one without the x lags, then F-test H_0:\gamma_1=\dots=\gamma_p=0. Within a VAR it is the same restriction applied to one block of the coefficient matrix.

The model

y_t=\alpha+\sum_{i=1}^{p}\beta_i\,y_{t-i}+\sum_{j=1}^{p}\gamma_j\,x_{t-j}+\varepsilon_t,\qquad H_0:\ \gamma_1=\dots=\gamma_p=0

What it assumes

Both series are stationary. On non-stationary data the test is invalid.
The lag length is adequate - results are notoriously sensitive to it.
No important omitted variable driving both.
The two series are sampled finely enough to see the lead. If the effect operates within a month and the data are annual, the timing that the test relies on has been averaged away entirely.

Statistical properties

Requires stationarity. On I(1) levels the test over-rejects badly.
Bivariate results can be entirely spurious if a third variable drives both - always condition on what you can.
Sensitive to lag length; report a range.
Toda–Yamamoto provides a version valid with integrated series, by adding extra lags and testing only the first p.
Causality can be bidirectional, one-directional, or absent.

How to read the output

Rejecting means the past of X improves the forecast of Y.
Causality can run both ways, neither way, or one way only.
Report several lag lengths - if the conclusion flips, say so.
The conclusion is about the pair CONDITIONAL on the other variables in the system. Adding a third variable that predicts both can remove an apparent causal direction entirely, which is a feature rather than an instability.

A worked reading

Both series are stationary in levels, so the test is valid without differencing. Growth → inflation is decisive at every lag length tried: F = 46.10 at one lag, 22.63 at two, 14.57 at three, all with p < 0.0001. The reverse direction is weak and unstable - inflation → growth gives F = 0.51 (p = 0.48) at one lag and 0.83 (p = 0.44) at two, then 3.33 (p = 0.021) at three and 2.91 (p = 0.023) at four. Read the pattern rather than any single row: one direction holds at every lag, the other appears only once the lag length is long enough to fit noise, which is what a fragile result looks like. The conclusion is predictive precedence from growth to inflation, consistent with a Phillips-curve story and nowhere near proof of one.

Symptom → diagnosis → what to do

If you see this	It means	Do this
Series are non-stationary	Over-rejection	Difference first, or use Toda–Yamamoto
Conclusion flips with lag length	Fragile	Report several lags and say so
Both directions significant	Feedback	Legitimate - describe it as feedback, not causation
Neither direction significant	No predictive content	Report it; a null is a finding

Common mistakes

Writing "X causes Y" in your conclusion. It is predictive precedence, nothing more.
Running the test on non-stationary levels.
Ignoring that expectations reverse the timing: stock prices move BEFORE earnings, which does not mean prices cause earnings.
Testing on seasonally adjusted data without saying so. Adjustment filters are two-sided, so they move information backwards in time and can manufacture precedence that the raw series does not show.

Where to read this properly

Granger (1969)
Toda & Yamamoto (1995)
Lütkepohl (2005), chapter 2

Related Time series - several series

Yield curve (Nelson–Siegel / Svensson) · Dynamic factor model · Dynamic regression (ARIMAX) · Structural VAR · VAR · Cointegration · VECM · ARDL & bounds test

All analyses

Data & variables

Each example is simulated from a known model, so you can check whether the estimator recovers the truth - and nothing here is anyone's private data.

Filter variables

Drag a variable into a slot on the right - or just click it.

Choose an example dataset above to begin.

Choose a transformation - it opens in the data editor, with a live preview.

Apply to

Multiply by

Columns ctrl-click for several

Group by ctrl-click for several

Within groups

Statistic

Bands

How many

Cut points

Keep rows where

Value

and

Fill with

Value

Also mark which rows were filled

Rules

Base period = 100

Which part

Percent at each tail

Threshold

Survey weight optional

Direction

Names column

Values column

Largest first

Delete them, not just count them

Read this column as

Tidy the text

New name optional

EconStatsCraft rigorous, plain-spoken econometrics

Econometrics that explains itself.

Regression, panel data, time series and the whole battery of tests. Every result is followed by a verdict you can defend.

Load a dataset to see it here.

Granger causality

What it needs

The intuition

When to use it

Where the estimator comes from

The model

What it assumes

Statistical properties

How to read the output

A worked reading

Symptom → diagnosis → what to do

Common mistakes

Where to read this properly

See also

Related Time series - several series

All analyses

Charts

Maps

Explore

Regression

Time series - one series

Time series - several series

Panel data

Multivariate statistics

Marketing research

Causal

Finance & risk

Actuarial

Tests & breaks

Machine learning

Econometrics that explains itself.