I want to test the influence of exchange rates on a price index and struggle with the interpretations. My variables are I(1)
First, I ran an OLS on first differenced variables which indicated a negative short term relation between FX and PI. Then, I tested it on co-integration and constructed a VECM.
My VECM suggests that there is a long term equilibrium with a speed of adjustment of 50% per period but no short term effect.
Both of my models are robust.
So, what is the implication of my VECM finding?
Does a long term equilibrium mean that, in the long-run, FX will not be able to influence the price index, since these variables always rebalance back to equilibrium?