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I am running a BEER model (Behavioral Equilibrium Exchange Rate Model) and using VAR/VECM and Johansen method to estimate the equation. For context, I am looking at the XR of Czech crown and the euro.

The equation takes the following form: $RER=b_1*TS_1+b_2*TS_2+b_3∗TS_3+b_4∗TS_4$, where RER is the real exchange rate (nominal rate adjusted for price levels) and $TS_i$ are the relevant time series determinants.

The goal is to get Behavioral Equilibrium Exchange Rate - a variable/time series that does not appear in the equation. When I run co-integration analysis and use VAR/VECM model, how do I get the BEER time series? In all relevant literature I have read, this step is essentially skipped and results are shown.

Understanding check: the $b_i$ values are given by the co-integration vector? Correct?

TL;DR: How do I get what I am trying to estimate when it doesn't even appear in the equation?

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