<p>Causality between time-series variables does not require the two to be cointegrated. </p>

<p>First, cointegration requires that each series be <span class="math-container">$I(1)$</span>. It is certainly possible for two <span class="math-container">$I(0)$</span> series to follow a causal relationship (or two <span class="math-container">$I(d)$</span> variables for that matter). </p>

<p>Second, cointegration implies a long-run equilibrium among the series, which is not required for a causal relationship. A long-run equilibrium between two time series variables <span class="math-container">$x$</span> and <span class="math-container">$y$</span> implies that
<span class="math-container">$$y_t-a-bx_t$$</span>
is a stationary process. In other words, if shocks are 'turned off', the values of <span class="math-container">$x$</span> and <span class="math-container">$y$</span> will converge such that <span class="math-container">$y_t=a+bx_t$</span>. </p>

CC BY-SA 4.0
2019-03-22T18:41:19.463Z
I would suggest to rethink the part on Granger Causality. "Granger Causality" has nothing really to do with a causal relationship, it i just about predictive power, see https://economics.stackexchange.com/a/3056/61
Alecos Papadopoulos
CC BY-SA 4.0
2019-03-22T18:42:14.453Z
You are right. I edited the post. Interesting discussion on the thread you posted. The statement 'weathermen Granger-cause the weather' is very illuminating about what Granger-causality really tells us.
dlnB
CC BY-SA 4.0
2019-03-22T19:20:01.080Z
Yes, that was an excellent remark by John Cochrane.
Alecos Papadopoulos
CC BY-SA 4.0
2019-03-22T18:12:00.877Z
2019-03-22T18:41:57.373Z
2019-03-22T18:41:57.373Z
dlnB
<p>For part of a project, I wanted to see if electricity consumption causes GDP in Colorado. I initially intended to follow the approach of Mozumder and Marathe (2007), who use a VECM approach, but that requires cointegration.</p>

<p>I'm not sure what to do now. I tried the Toda-Yamamoto method but my errors seem to be serially correlated...</p>

<econometrics><time-series><co-integration>
If two variables are not cointegrated, can one still cause the other?
leecarvallo
# If two variables are not cointegrated, can one still cause the other?

(Asked by: username_0 on 2019-03-22)

For part of a project, I wanted to see if electricity consumption causes GDP in Colorado. I initially intended to follow the approach of Mozumder and Marathe (2007), who use a VECM approach, but that requires cointegration.

I'm not sure what to do now. I tried the Toda-Yamamoto method but my errors seem to be serially correlated...

**Tags:** econometrics, time-series, co-integration

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## 1 answers

### Answer by username_1 on 2019-03-22. Score: 2

Causality between time-series variables does not require the two to be cointegrated.

First, cointegration requires that each series be $I(1)$. It is certainly possible for two $I(0)$ series to follow a causal relationship (or two $I(d)$ variables for that matter).

Second, cointegration implies a long-run equilibrium among the series, which is not required for a causal relationship. A long-run equilibrium between two time series variables $x$ and $y$ implies that
$$y\_t-a-bx\_t$$
is a stationary process. In other words, if shocks are 'turned off', the values of $x$ and $y$ will converge such that $y\_t=a+bx\_t$.

> **Comments:**
> **username_2**: I would suggest to rethink the part on Granger Causality. "Granger Causality" has nothing really to do with a causal relationship, it i just about predictive power, see https://economics.stackexchange.com/a/3056/61  
> **username_1**: You are right. I edited the post. Interesting discussion on the thread you posted. The statement 'weathermen Granger-cause the weather' is very illuminating about what Granger-causality really tells us.  
> **username_2**: Yes, that was an excellent remark by John Cochrane.  

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