Measuring the value of central bank commitment in the benchmark New Keynesian model

We measure the value of commitment in executing monetary policies in context of the benchmark New Keynesian model and where "value" is represented by the standard quadratic welfare function containing weighted output gap and inflation variances. The value of commitment is calculated as the difference in this welfare across commitment regimes of which there are at least six. Inspired by Bilbie (2014) we show how by means of selecting the optimal level of a single parameter in the setup of several so-called "discretionary" targeting regimes (price-targeting, speed-limit, etc.) one can produce optimal inertia identical to that of the Clarida, Gali, and Gertler (1999) "global commitment." Combining the targeting regimes with the commitment regime, we are left with three levels of commitment. Deriving welfare analytically as a function of all permissible parameters, rather the standard practice of calculating welfare based on a single or handful of parameter sets, we can measure the gain that would occur from jumping to higher commitment levels over all permissible sets. We also compare welfare surfaces with parameter combinations we have sampled. Result: depending on parameter selection the gains from optimal inertia may be high or low. Our sample of parameters actually used in the literature puts many near the high end, a few not. We find no parameter sets where a switch from no- to high-commitment would imply low or negligible gains. A side-effect of the analysis is that the optimal inertia regimes reduce nominal and real interest rate variance even when interest stability is not an objective of the central bank. We include Taylor-type rules that satisfy the requirements of each commitment level. Conceptually, the results indicate that at least in the benchmark NKM long-time questions such as whether price- or inflation-targeting is preferable are off point. The pertinent question is: in what commitment regime does the central bank find itself in?