1. Notes on Engel West
G6904

2. Central Banks Follow Taylor Rule
Subtracting we get
UIP in Real Terns

3. Key Result is PV Equation for Real Exchange Rate and Macro Fundamentals
Note that Discount Factor comes from lean against the wind by home central bank. Even if b = 1 , PV can be well defined since rhs variables are zero mean stationary. For example, if q mean zero , u is white, and π and y are AR(1), then q will be linear in π , y, and u even with b = 1.
Empirical approach is to estimate a 3 variable VAR in {π ,y, u} and to use forecast from that VAR to proxy the present value

4. Actual and Fitted Real Exchange Rate

5. But Still Lots of Noise