Consider a model given by Yt = 0 - orb Tt = Tt-1 + K(Yt ...

 

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Consider a model given by Yt = 0₁ - orb Tt = Tt-1 + K(Yt — Y?) - rt = F+Y(πt π) The interest rate rt is determined as a spread over the policy rate r, and given by rt — rt = a-ß - vyt. Assume that σ, v € (0, 1), ß > 0 and a sufficiently large so that r — rt > 0. (a) Solve the model in terms of (yt, πt) as a function of the state variable Tt-1 and parameters. (b) How does the economy initially react to a one-time shock to markups du* = € > 0? [Hint: Transform this shock into a shock dyn]. = (c) How does the economy initially react to a one-time shock to lending margin dß : € > 0. Set now = 7 = 1₁ w = v= 0 = 0.5. (d) Adjust the Python program from class to plot the dynamics over time to these transitory shocks. (e) Compare the dynamics to a persistent shock where p = 0.8 for each shock. Consider a model given by Yt = 0₁ - orb Tt = Tt-1 + K(Yt — Y?) - rt = F+Y(πt π) The interest rate rt is determined as a spread over the policy rate r, and given by rt — rt = a-ß - vyt. Assume that σ, v € (0, 1), ß > 0 and a sufficiently large so that r — rt > 0. (a) Solve the model in terms of (yt, πt) as a function of the state variable Tt-1 and parameters. (b) How does the economy initially react to a one-time shock to markups du* = € > 0? [Hint: Transform this shock into a shock dyn]. = (c) How does the economy initially react to a one-time shock to lending margin dß : € > 0. Set now = 7 = 1₁ w = v= 0 = 0.5. (d) Adjust the Python program from class to plot the dynamics over time to these transitory shocks. (e) Compare the dynamics to a persistent shock where p = 0.8 for each shock.

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a Solving the model stepbystep 1 Take the equation for yt yt Et t t1 2 Take the equation for t t Yt ... View the full answer