Procrustean Art of Backtracking: “The Taylor Rule”

 

“For the sake of convenience,” we copy the following from somewhere else:

[The Taylor rule] can be rearranged as r= 1.5π+ 0.5(Y– Y*)/ Y*+ 1 from the original version. Here, (Y– Y*)/Y* represents the percentage gap of the real GDP from its natural level. As a result, its coefficient 0.5, with the time dimension (T-1), cannot work as an exponent. Unfortunately, however, some macroeconomists expediently associate such a coefficient with logarithm and effectively take Y/ Y* for log Y – log Y* (e.g. G. Mankiw, Macroeconomics, Ch. 15): they seem to fall into the logarithm trap in that there is no place for the time dimension in the exponent.

         At any rate, it is not conceptually easy to link a percentage gap [T0, (Y– Y*)/ Y*] to a percentage rate   (T-1, r or π) with a constant coefficient. Even worse, here again in the rule is the natural level. In the first place, there cannot be such a thing as a natural state or equilibrium as far as an organism is concerned. 


No wonder, central bankers around the world seem to doubt the practicality of such a rule.

 

Note. We hereunder quote from Prof. John B. Taylor, “Discretion versus policy rules in practice,” Carnegie-Rochester Conference Series on Public Policy 39 (1993), p.202:

r = p + .5y + .5(p - 2) + 2

                     where   r is the federal funds rate,

                                 p is the rate of inflation over the previous four quarters

                                 y is the percent deviation of real GDP from a target.

                     That is, y = 100(Y - Y*)/Y* where

                                  Y is real GDP, and

                                  Y* is trend real GDP (equals 2.2 percent per year from

                                             1984.1 through 1992.3).

                      … … This policy rule has the same coefficient on the deviation of real GDP                       from trend and the inflation rate.

 

One may be amazed how many things taken for granted in the next single paragraph “for the sake of convenience”; at least six including the target inflation rate being 2% PA. The only regret: The first “coefficient” 0.5 per annum and the second 0.5 free of metric (cf. Figure 2, ibid) don’t add up to 1.00, or the whole weight of 100%, metric-free of course.

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