 ## April 23, 2021

### Problem 1  代考宏观经济final

a)According to old Keynesian crossmodel

Yt Ct It (1)

Ct C¯ + cYt et (2)

It = I¯(3)

Please log-linearize the model. Can you give an example of shock et? How does consumption change in response to shock et? Suppose that the shock is persistent

et ρet1 + ηt, (4)

where ηt is a white noise  N (0, σ2). How does persistence ρ change the effect of shock ηt in period t? Do you think that the model describes the effect of persistence realistically?

b)Let’s have a simple New Keynesianmodel:

where it corresponds to the interest rate, output gap is described by xt and inflation is given by πt, ut is a niid variable.

1. Makea guess and solve for the model? How many state and jump variables do you have? Is interest rate a state or jump variable, or it should it be just substituted out?
2. Assumethat the model has a unique  What does zt correspond to? Can you give an example of the shock ut?
3. Why does ztlead to a decline in xt?
4. If the shock utis persistent? How does it affect xt, πt? Give me just the intuition. Can you give a realistic example of persistent and temporary shocks?
5. What is the difference between the Old Keynesian model and the New Keynesian for the role of persistence in periodt?