Consider an economy in which the central bank minimizes the following loss function Lt = (yt...

  

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Consider an economy in which the central bank minimizes the following loss function Lt = (yt - y) + x(Ast - t) where yt is output; Ast denotes the time-variation of the nominal exchange rate defined as Ast = St St-1, X is a positive parameter. is a constant target for output, while t is a stochastic time-varying target for exchange rate stabilization with mean zero, E(t) = 0, and standard deviation o. Output depends on the following relationship - Yt = y + [Ast-Et-1(Ast)] - Zt where y is the potential level of output with y > y and y - y = k> 0 while zt is a stochastic disturbance with mean zero, E(zt) = 0, and standard deviation . Finally, we assume that zt and t are uncorrelated. A) (20 points) Consider the following timing protocol. Private sector forms expectations Et-1(Ast), shocks realize, the central bank chooses Ast. Compute output and exchange rate in the discretionary equilibrium. B) (20 points) Consider now a central bank that can commit to a rule Ast= a + bzt + cst. Find the optimal values for a, b, c which minimize the expected loss function: = E(yt - y) + xE(Ast - t) E(Lt): Compare the commitment solution, for output and exchange rate, with respect to the discretionary equilibrium and comment the results. Consider an economy in which the central bank minimizes the following loss function Lt = (yt - y) + x(Ast - t) where yt is output; Ast denotes the time-variation of the nominal exchange rate defined as Ast = St St-1, X is a positive parameter. is a constant target for output, while t is a stochastic time-varying target for exchange rate stabilization with mean zero, E(t) = 0, and standard deviation o. Output depends on the following relationship - Yt = y + [Ast-Et-1(Ast)] - Zt where y is the potential level of output with y > y and y - y = k> 0 while zt is a stochastic disturbance with mean zero, E(zt) = 0, and standard deviation . Finally, we assume that zt and t are uncorrelated. A) (20 points) Consider the following timing protocol. Private sector forms expectations Et-1(Ast), shocks realize, the central bank chooses Ast. Compute output and exchange rate in the discretionary equilibrium. B) (20 points) Consider now a central bank that can commit to a rule Ast= a + bzt + cst. Find the optimal values for a, b, c which minimize the expected loss function: = E(yt - y) + xE(Ast - t) E(Lt): Compare the commitment solution, for output and exchange rate, with respect to the discretionary equilibrium and comment the results.