Ex post, ex ante, the Taylor rule is cyclic

John Taylor, in his reassessment of the 2008 financial crisis after 10 years, concluded:

There was a significant deviation in 2003–2005 from the more rules-based monetary policy strategy [the Taylor rule] that had worked well in the two prior decades. The resulting extra low policy interest rates were a factor leading to a search for yield, excessive risk taking, a boom and bust in the housing market, and eventually the financial crisis and recession. . . . These actions spread internationally as central banks tended to follow each other in setting their policy interest rate” [Taylor 2018

 Measurement of a price index is a lagged variable relative to borrows circumstances and will cycle. 

Economists, if it means anything, closes the loop in reality which means that the Taylor rule eventually ends up with    ]p(k+11)-p(k)]  at the bottom of a ratio, and a neutral price change causes rates to become unstable.  It is a spectral issue, borrowers judge their current prices which are not reflected in the central bankers lagged inflation measure.  Economists has the same problem Einstein had, divide by  zero is impossible, something has to find another line of symmetry.