## 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?

### Problem 2    代考宏观经济final

Let’s think about two possible structural bivariate VARs. One model de- scribes the effect of fiscal policy and contains fiscal spendings and GDP. The second model describes the impact of monetary policy on the domestic economy and includes the Fed fund rate and GDP.

1. Do we have to worry about stationarity issues in each of thesemodels?
2. Should you modify the original variables in each model to obtainstation- arity? If you should, then how?  代考宏观经济final
3. What are the most appropriate short-run restrictions for each of these models? How many restrictions do you need in each case? Can you providean economic intuition for each of the restrictions? In which of the two models the policy variable is more likely to react to contemporaneous economic conditions?