A DVANCED M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #3
D UE O CT 27, 2014
S ANG Y OON (T IM ) L EE
1. (Two-planners, thanks to Rody Manuelli). Consider a simple two planner economy. The rst
planner picks taxes (denoted by the at tax rate ) and makes tra
A DVANCED M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #5
D UE N OV 17, 2014
S ANG Y OON (T IM ) L EE
1. (Habit persistence and growth). Consider the problem of choosing a consumption sequence to
maximize
t cfw_log(ct ) + log(ct1 )
t =0
subject to
ct + k
A DVANCED M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #6
D UE N OV 24, 2014
S ANG Y OON (T IM ) L EE
1. (Stocks and bonds). Let us modify the standard savings problem just a little bit. Now, instead
of assuming that individuals just randomly receive stoch
A DVANCED M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #4
D UE N OV 10, 2014
S ANG Y OON (T IM ) L EE
1. (Missing market). In class we only studied the OLG model in general equilibrium (with a
representative rm). Let us now consider a simpler case, in whic
A DVANCE M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #7 S OLUTION T
1.
D UE D EC 3, 2014
S ANG Y OON (T IM ) L EE
(a) Let ei (st ) denote the endowment of agent i in period t when the history is st . An Arrowt
Debreu equilibrium is a sequence of state-con
A DVANCE M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #7
D UE D EC 3, 2014
S ANG Y OON (T IM ) L EE
1. (Perfect risk-sharing). There are two agents i cfw_1, 2 who live forever and get stochastic
endowments (e1 , e2 ) every period. Denote the state of the w
A DVANCED M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #2
D UE O CT 20, 2014
S ANG Y OON (T IM ) L EE
1. (Representative rm). A rm has a production function F ( x ), where x Rn , i.e. x is a non+
negative, (nite) n-dimensional vector. Assume F is strictly
A DVANCED M ACROECONOMICS I @ M ANNHEIM
P ROBLEM S ET #1
D UE O CT 13, 2014
S ANG Y OON (T IM ) L EE
1. (Taxing capital?) Recall the standard Solow model. Suppose that there is a government that
needs to spend G (t) = gAL at every point in time, and uses
A DVANCED M ACROECONOMICS I
Sang Yoon (Tim) Lee
Universitt Mannheim
Lehrplan fr Herbstsemester 2014
1. Course Description
Macroeconomic research requires theoretical, empirical, and quantitative skills. In the rst year,
we focus mainly on the rst. That do
A DVANCED M ACROECONOMICS I @ M ANNHEIM
S EPTEMBER 30, 2014
O PTIMAL C ONTROL AND R AMSEY-C ASS -K OOPMANS G ROWTH M ODEL S ANG Y OON (T IM ) L EE
The subscripts on continuous time variables mean that they are functions of time. Derivatives without
argume
T OPICS IN Q UANTITATIVE M ACROECONOMICS I @ M ANNHEIM
A RROW-D EBREU AND A RROW S ECURITIES
O CTOBER 21, 2013
S ANG Y OON (T IM ) L EE
Many of you may alread know this, so I wont spend too much time here. However, remember
the implications for asset pric
S TEADY S TATES AND D YNAMICS IN I NCOMPLETE M ARKETS M ODELS
PART I: S TATIONARY D ISTRIBUTIONS
F EBRUARY 28, 2013
S ANG Y OON (T IM ) L EE
Solve the Aiyagari (1994) model for
1. Stationary distributions: Huggett (1993); Aiyagari (1994); Castaeda, Daz-Gi
A DVANCED M ACROECONOMICS I @ M ANNHEIM
S OLOW G ROWTH M ODEL IN C ONTINUOUS T IME
S EPTEMBER 30, 2014
S ANG Y OON (T IM ) L EE
1. Whats a Model?
Models are just an approximation constructed to explain a specic (set of) fact(s). A model will
always be wro
A DVANCED M ACROECONOMICS I @ M ANNHEIM
N EOCLASSICAL G ROWTH M ODEL IN D ISCRETE T IME
S EPTEMBER 25, 2014
S ANG Y OON (T IM ) L EE
1. Discrete Time Growth Model
Now that were done with the continuous time model, the discrete time model should be easy.
F
T OPICS IN Q UANTITATIVE M ACROECONOMICS I @ M ANNHEIM
I NCOME F LUCTUATION P ROBLEM AND I NCOMPLETE M ARKETS
O CTOBER 21, 2013
S ANG Y OON (T IM ) L EE
1. Warmup: Permanent Income Hypothesis
Solve the deterministic individual problem
t u(ct )
max
cfw_ct
N OTES ON M ARKOV C HAINS
F EBRUARY 19, 2013
S ANG Y OON (T IM ) L EE
The setup I use in these notes will be the followingmostly taken from Resnick (1992); Ljungqvist
and Sargent (2004).
- state space S = cfw_s1 , s2 ,
- stochastic process cfw_ xt , t =