Solving the dynamic-inconsistency problem through punishment. (Barro and Gordon, 1983.) Consider a policymaker whose objective function is t=0 t (yt at 2/2),

Solving the dynamic-inconsistency problem through punishment.



(Barro and Gordon, 1983.) Consider a policymaker whose objective function is ∞

t=0 βt

(yt − aπt 2/2), where a > 0 and 0 <β< 1. yt is determined by the Lucas supply curve, (12.53), each period. Expected inflation is determined as follows.

If π has equaled ˆπ (where ˆπ is a parameter) in all previous periods, then πe = πˆ.

If π ever differs from ˆπ, then πe = b/a in all later periods.

(a) What is the equilibrium of the model in all subsequent periods if π ever differs from ˆπ ?

(b) Suppose π has always been equal to ˆπ, so πe = πˆ. If the monetary authority chooses to depart from π = πˆ, what value of π does it choose? What level of its lifetime objective function does it attain under this strategy? If the monetary authority continues to choose π = πˆ every period, what level of its lifetime objective function does it attain?

(c) For what values of ˆπ does the monetary authority choose π = πˆ? Are there values of

a, b, and β such that if ˆπ = 0, the monetary authority chooses π = 0?