A Note on Imperfect Credibility

We explore how outcomes of optimal monetary policy with loose commitment
(Schaumburg and Tambalotti, 2007; Debortoli and Nunes, 2010) can be observationally
equivalent, or interpretable as outcomes of deeper optimal policy under sustainable
plans (Chari and Kehoe, 1990). Both interpretations of “imperfect credibility” in optimal
monetary policy design are attempts to rationalize outcomes that lie in between the
conventional extremes of optimal policy under commitment and under discretion. In a
standard monetary-policy framework, when we match impulse responses of inflation and
the output gap to large enough markup shocks, we find that a small probability (1 – 􀄮 =
0.05) of replanning in the quasi/loose commitment world corresponds to N = 18 in the Nperiod
punishment optimal sustainable monetary policy, in terms of observable
outcomes. For plausible cases of loose-commitment model economies (with a between
0.77 and 1) we can find an observationally equivalent sustainable-plan economy indexed
by some N.