The Taylor of the rule is not the same as the Taylor of the series expansion....The Taylor rule has been proposed by John B Taylor when he worked for the Board of Gov of the Fed in the early 90's : studying the optimal monetary policy rules, Taylor showed that an optimal rule can be proxied by very simple (linear) ones, linking the nominal short term interest rate to four variables :-long term real interest rate (normally constant, and equal to the potential growth of the economy)-Central bank inflation target (constant)-anticipated inflation (usually proxied by the bserved current (core ?) inflation rate)-output gap (spread between potential GDP and current GDP)the most famous formula is, if I remember well (please check) : i= r + target + 1.5*(inflation-target) + 0.5*(output gap)Taylor proposed to use a 'portfolio' of simple rules, ans you can find more about this on his web page (
http://www.stanford.edu/~johntayl/)