Granger Causality
I learned today that the idea of “Granger Causality” is not to learn whether variable A causes variable B, but to learn whether if variable A increases in period t we should forecast that B will increase in period (t+1). For example, we might run regressions on Health and Wealth across states:
Ht = alpha + beta*Wealth(1-t) + theta*H(t-1)
and
Wt = gamma + delta*Health (t-1) + mu*W(t-1).
If beta is significant, we’d conclude that Wealth Granger-causes Health. In fact, it may be that it is IQ that causes both Wealth and Health and as an omitted variable is responsible for beta being significant. That’s OK for Granger causality. If we see a state’s wealth increase, we should expect its health to increase. It’s OK to have a biased regression because of omitted variables.
We have to be careful not to think of this as real causality, though. If we kept all other variables the same, including IQ, but we increased the Wealth in a State, the Health would not rise. The reason that usually if we see an increase in Wealth we can predict an increase in Health is that an increase in Wealth is a sign of an increase in IQ, and it is the IQ that will increase Health.
Thus, Granger causality is useful only for positive prediction, not for normative policymaking.
March 28th, 2007 at 4:53 am
Hi,
I’ve looked at Granger-causality recently, me too. And here is my conclusion:
Causality ==> Granger-causality
but the inverse is not true. This means that Granger-causality is a necessary condition for causality, but not a sufficient condition.
After reading a chapter in the time series book of Hamilton, I concluded that, in order to have sufficient condition for causality, we need Granger-causality AND strict exogeneity:
Granger-Causality + strict exogeneity causality
Now strict exogeneity is very difficult to test. We need to condition on every possible information that could affect both variables.
J.L.
March 28th, 2007 at 4:55 am
Somehow, my last logical statement did not come out good. I meant:
Granger-causality + strict exogeity (if and only if) causality
In other words, Granger-causality + exogeity is equivalent to causality.
J.L.
April 2nd, 2007 at 4:36 pm
This is intersting and JL’s explanation is correct. Granger himself said that his tests are not cause & effect tests. If they are, we don’t need economic theory!
I forgot the paper (perhaps in more than 1 or 2) in which he made this clarification and shall be grateful if anyone knows the details.