Consider the equilibrium dynamic model for given values for the exogenous and pa

Question

Consider the equilibrium dynamic model for given values for the exogenous and parameters of the model. Use the following values to solve for the impulse response function of output (Y) for period t and t+1 i.e. Y_t and Y_t + 1. Y_t = 100, pi*_t = 2, alpha = 1, rho = 1, theta_pi = 0.5, theta_Y = 0.5. Also assume the demand shock epsilon_t increases by 1 in period t and shock ends at the end of period t i.e. shock is zero at period t+1 whereas, supply shock is zero. Y_t = Y_t - A(pi_t - pi*_t) + B epsilon_t, A = alpha theta_pi/1 + alpha theta_Y > 0, B = 1/1 + alpha theta_Y > 0

Explanation / Answer

A = (1 * 0.5) / 1 + (1*0.5) = 0.5 / 1.5 = 0.33

B = 1 / (1+0.5) = 1 / 1.5 = 0.66

Given Demand shock increases by 1, wheras supply shock is 0 at the end of period/

Hence Yt = 100 - 0.33 * ( 0 - 2 )+ 0.66 * 1

Yt = 100 + 0.66 + 0.66 = 101.32

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