Economic Models - Convex Optimization

90 Andrew Hughes Hallet
This is always smaller than the loss incurred when fiscal leadership is combined
with a dependent central bank. However, the optimal degree of conservatism
for an independent central bank, in this case, is obtained by setting
δ = 0 in Eq. (25) to yield:
λ cb∗ = (αγs)2 λ g 1
(αγs) 2 + φ 2 λ g . (27)
2
It is straightforward to show that the value of EL g in Eq. (24) is always
less than Eq. (26) as long as:
λ cb < [λ g 1 λcb∗ ] 1/2 . (28)
It is also evident that λ cb∗ 0. Consequently, fiscal leadership
with any λ cb