b Suppose that policy is set according to a feedback rule of the form δ 1last

# B suppose that policy is set according to a feedback

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b. Suppose that policy is set according to a feedback rule of the form: 𝑚 𝑡 = δ𝑣 𝑡−1 (last period’s demand shock, 𝑣 𝑡−1 is known to all agents in period 𝑡 , including the central bank, so this is feasible). Using the AS and AD equations, together with this feedback rule, derive an equation describing the price level solely in terms of expected prices and the demand shock. c. Looking at the equation you (should) have obtained, you might conjecture that the price level has a solution of the general form: 𝑝 𝑡 = φ𝑣 𝑡 + ψ𝑣 𝑡−1 , where φ and ψ are constants that depend on α, β, γ and δ. Assume that this is indeed the case. What are 𝐸 𝑡−1 [𝑝 𝑡 ] and 𝐸 𝑡−1 [𝑝 𝑡+1 ] ? Now substitute your conjectured solution into your equation for the price level to get an expression written solely in terms of the demand shock. Using the fact that this equation must hold for all possible values of the demand shock, find φ and ψ . (This technique for solving rational expectations models is known as the “method of undetermined coefficients”.) d. Using your results from part (c.), derive an expression for output in terms of the demand shock. Does your expression depend on δ ? What do you conclude about the effectiveness of systematic monetary policy in stabilising output?

• Fall '19
• Kevin Sheedy

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