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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?

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