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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...

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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 $y_t=a+bx_t$.

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    $\begingroup$ 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 economics.stackexchange.com/a/3056/61 $\endgroup$ – Alecos Papadopoulos Mar 22 '19 at 18:41
  • $\begingroup$ 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. $\endgroup$ – dlnB Mar 22 '19 at 18:42
  • $\begingroup$ Yes, that was an excellent remark by John Cochrane. $\endgroup$ – Alecos Papadopoulos Mar 22 '19 at 19:20

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