<p>This site <a href="https://www.statisticshowto.com/granger-causality/" rel="nofollow noreferrer">https://www.statisticshowto.com/granger-causality/</a>  shows about conducting the F-test for granger-causality.     It also talks about  alternative Tests.</p>

<p>"If you have a large number of variables and lags, your F-test can lose power. </p>

<p>An alternative would be to run a chi-square test, constructed with likelihood ratio or Wald tests. Although both versions give practically the same result, the F-test is much easier to run."</p>

CC BY-SA 4.0
2020-10-19T14:07:40.553Z
Links are great, but bringing a summary of the the contents into the answer would make it even better. That way the answer can stand on its own, and in the event that the website disappears your answer can remain a valuable resource.
BKay
CC BY-SA 4.0
2020-05-16T10:19:29.900Z
2020-05-16T10:19:29.900Z
Mike J
<p>I am trying to test if <span class="math-container">$a_t$</span> granger causes <span class="math-container">$b_t$</span>:</p>

<p><span class="math-container">$$a_t=\rho_1+\phi_{11}a_{t-1}+\alpha_{11}b_{t-1}+\beta_{11}c_{t-1}+u_{1t}$$</span></p>

<p><span class="math-container">$$b_t=\rho_2+\phi_{21}a_{t-1}+\alpha_{21}b_{t-1}+\beta_{21}c_{t-1}+u_{2t}$$</span></p>

<p><span class="math-container">$$c_t=\rho_3+\phi_{31}a_{t-1}+\alpha_{31}b_{t-1}+\phi_{31}c_{t-1}+u_{3t}$$</span></p>

<p>I am trying to use an F test.</p>

<p>However, should be null be: <span class="math-container">$\phi_{21}$</span> = 0.</p>

<p>Or do I also need to set: <span class="math-container">$\beta_{21}$</span> = 0 because a impacts b through c.</p>

<econometrics>
How to test for Granger causality?
Sophie L
# How to test for Granger causality?

(Asked by: username_0 on 2020-05-16)

I am trying to test if $a\_t$ granger causes $b\_t$:

$$a\_t=\rho\_1+\phi\_{11}a\_{t-1}+\alpha\_{11}b\_{t-1}+\beta\_{11}c\_{t-1}+u\_{1t}$$

$$b\_t=\rho\_2+\phi\_{21}a\_{t-1}+\alpha\_{21}b\_{t-1}+\beta\_{21}c\_{t-1}+u\_{2t}$$

$$c\_t=\rho\_3+\phi\_{31}a\_{t-1}+\alpha\_{31}b\_{t-1}+\phi\_{31}c\_{t-1}+u\_{3t}$$

I am trying to use an F test.

However, should be null be: $\phi\_{21}$ = 0.

Or do I also need to set: $\beta\_{21}$ = 0 because a impacts b through c.

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2020-05-16. Score: 3

This site <https://www.statisticshowto.com/granger-causality/> shows about conducting the F-test for granger-causality. It also talks about alternative Tests.

"If you have a large number of variables and lags, your F-test can lose power.

An alternative would be to run a chi-square test, constructed with likelihood ratio or Wald tests. Although both versions give practically the same result, the F-test is much easier to run."

> **Comments:**
> **username_2**: Links are great, but bringing a summary of the the contents into the answer would make it even better. That way the answer can stand on its own, and in the event that the website disappears your answer can remain a valuable resource.  

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