Taylor rule formulas

Just read the Taylor rule and the formula in the note stated as:

  1. r(target)=r(netural)+0.5(GDP expected - GDP trend)+0.5(expected inflation rate - target inflation rate)

Then, I opened my CFA level 2 note and found a Taylor formula to forecast exchange rate below:

  1. R= r(neutral)+ Pi + Alpha*(Pi-Pi*)+ Beta *(y-y*)

Are these formulas the same? If so,

  1. Why would the first formula’s alpha and beta set to 0.5 by default?

  2. Why would the second formula has an additional Pi (inflation) added to the neutral rate?

Thank you!

They are basically the same.

  1. α and β are simply weights, and Taylor suggested as a rule of thumb to use 50/50.

  2. The first formula is in real terms and the second one is nominal terms. Pi is the inflation rate. You can take Pi to the left hand side and you would have R-Pi, which reduces it to real terms, in this case r(target).