1 κ where u t is an unpredictable cost shock with mean zero and variance s 2 a

# 1 κ where u t is an unpredictable cost shock with

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𝑡 = 𝐸 𝑡 [? 𝑡+1 ] + κ𝑥 𝑡 + 𝑢 𝑡 where u t is an unpredictable cost shock with mean zero and variance s 2 . a. Suppose first that the policymaker observes the current cost shock and sets policy under discretion (i.e. treating 𝐸 𝑡 [? 𝑡+1 ] as given) in order to minimise the social loss, 𝐿 𝑆 . Find the equilibrium level of ? 𝑡 and 𝑥 𝑡 and draw a diagram, analogous to that of the lectures, illustrating the equilibrium. Now assume that the government can delegate the setting of policy to an independent central bank. This delegation must take place before the realisation of the cost shock, but policy itself is set after the cost shock is known. The central banker ’s preferences are represented by the loss function (there are lots of possible central bankers, each with a different μ ): 𝐿 ?? = 1 2 ? 𝑡 2 − μ𝑥 𝑡 b. Find the equilibrium level of ? 𝑡 and 𝑥 𝑡 for a central banker with a given μ . How does the central banker’s type (his/her 𝜇) affect the average inflation rate and the response to a cost shock, 𝑢 𝑡 ? c. Now calculate the expected value of society’s loss , 𝐸[𝐿 𝑆 ] , given that a central banker with parameter μ has been appointed. d. What μ minimises the expected social loss and how does it relate to λ ? Explain.

• Fall '19
• Kevin Sheedy

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