宏观经济学代考 macroeconomics代写 final代写

Practice Final 2017

April 24, 2017

宏观经济学代考 Explain whether demand υtor supply shocks st get amplified as people become less rational and more behavioral or m goes down.

1 Problem 1   宏观经济学代考

In the New Keynesian model linear system of equations has the following form:

where xˆ_t is the output gap between actual output and flexible prices output, πˆ_t is inflation level, ˆi_t is the interest rate, Zˆt  is a technology growth shock.  Ex- ogenous shocks υ_t and s_t are niid (normal identically independently distributed) variables.

1.Assume that δ > 1 and find the solution for output gap in terms of s_tand υ_t.

2.Explain why New Keynesian model amplifies demand shocks υ_tand sta- bilizes supply shocks s_t.

2 Problem   宏观经济学代考

2: A Behavioral New Keynesian Model (by Gabaix 2016)

Expected interest rate in macroeconomics is equal to the nominal interest rate divided by expected inflation.  More precisely, R_t = E_t   ⁱt       or Rˆt  = ˆi_t − E_tπˆ_t+1.

1.Iterate forward Euler equation toobtain

(6)

Notice that according to this model expected shock after 300 years u_t+300 has the same effect on output gap as expected shock to u_t+1 in one year. Is this realistic?

Of course not! Euler equation thus overestimates the effect of the future on the present.    宏观经济学代考

2.To fix this problem Xavier Gabaix offered the following behavioral ap- proach: agents have kind of blurry look to the future, and whenever the system has expected future variable, the way agents actually behaves is by replacing  this  future  variable  E_txˆ_t+i  with  mⁱE_txˆ_t+i.   This  allows  all agents to think that far in the future system will be at its steady state    on average and their forecasting power declines over Solve the be- havioral system by replacing all E_txˆ_t+i by mⁱE_txˆ_t+i in the following New Keynesian system:

xˆ_t = E_txˆ_t+1 − σ (i_t − E_tπˆ_t+1) + u_t   (7)

πˆ_t = βE_tπˆ_t+1 + κxˆ_t   (8)

ˆi_t = δπˆ_t + υ_t    (9)

u_t = E_tZˆt+1 − Zˆt   (10)

Zˆt  = ρZˆt−1 + s_t   (11)

Focus on the unique equilibrium.

3.Explain whether demand υ_tor supply shocks s_t get amplified as people become less rational and more behavioral or m goes down.

3 Problem  宏观经济学代考

 3: Financial Frictions and Hetero- geneity

There are two types of agents: patient households with discount β and impatient households with discount γ such that γ < β. Both types of agents have linear preferences over consumption.

For patient households optimization problem is the following:

(12)                                                                                                                                                 (13)

where they consume c^‘t  and receive interest rate R on their assets b_t−1.  We can express consumption as a function of other variables in the budget constraint and plug it in the utility to obtain the expression below:

Impatient households maximize their discounted flow of consumption subject to the budget constraint where they produce output y and borrow b_t units of final goods, consume c_t units of final output, and pay back their debts Rb_t−1.   宏观经济学代考

c_t + Rb_t−1 = y + b_t (15)

Transversality conditions says that

1.Let’sassume that impatient household borrows in the first period and then pays back constant amount of money from the next period and  What is the optimal solution?

2.Suppose that impatient household can borrow in the first and second pe- riod and repay his debt thereafter (consume constant amount of final output)

3.What do you think is the optimal solution that will satisfy transversality condition?

 

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