Class Notes for Quantitative Macroeconomics-Theory
Omer Acikgoz
January 28, 2015
1
Introduction and Notation
For the entire class, we will use discrete time. Im going to use subscript t to denote time and capital letters
to denote aggregate variables. For

Chapter 2
Continuous State Methods
Most of the methods we examined so far assumed that there were only a nite number of states that approximate the typically continuous state-space of the original problem. While this methods are reliable and
the accuracy

22
CHAPTER 2. CONTINUOUS STATE METHODS
To clarify the imporance of this result: This theorem extends beyond interpolation using Chebyshev
polynomials. It applies to any type of polynomial interpolation. However, we will limit the discussion here
to its us

2.2. DETOUR #2: FUNCTIONAL APPROXIMATION METHODS
19
very close to f (k) though. Similarly, a = 0 might not work, since this means entering the next period with
zero capital, making consumption zero next period, so V 0 (0) = 1, you might want to choose som

u0 (f (k, A)
7
g(k, A) = fk (g(k, A), A0 )u0 f (g(k, A), A0 )
g(g(k, A), A0 )
Modeling Uncertainty
The two main types of modelling techniques that macroeconomists make use of are:
Markov chains
Linear stochastic difference equations
7.1
Markov chains
De

Chapter 1
Finite State Methods
The simplest dynamic programming problems have a nite number of states. Many problems in macroeconomics, however, do not have this property. For example, in the simple deterministic growth model, the state
variable capital i

k1 = g(k0 )
k2 = g(k1 )
k3 = g(k2 )
.
.
.
kt+1 = g(kt )
.
.
.
It is clear that there is a tight connection between the recursive and sequential representation.
Example: Let us apply the functional Euler equation approach to the simple but unrealistic eco

Using the same steps, we derive the Euler equation that looks identical
u0 (f (kt )
kt+2 )f 0 (kt+1 ) for all t = 0, 1, . . . , 1
kt+1 ) = u0 (f (kt+1
Since this is a second-order difference equation, we need two conditions to pin down the full dynamic
p

Assignment 2
Question 1 - Growth Model with Habit Formation
Consider the following version of the neoclassical growth model we discussed in class: Suppose that
the representative agent (or planner) gets utility from the level of consumption relative to th

MQE Quantitative Macroeconomics
Midterm Exam
Spring 2015
This exam is worth 30 points. Answer the questions in the spaces provided on the
question sheets. If you run out of room for an answer, continue on the back of the
page. You can use a calculator. Yo

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Assignment 6
Solving neoclassical model using functional approximation
Consider a neoclassical growth model with endogenous labor supply. Use the following functional as1+1/
sumptions: Per-period utility is represented by u(C) un (L) = log c L
1+1/ and pr

Assignment 5
Solving an RBC model using Discrete State-Space
Consider a neoclassical growth model with aggregate shocks. Use the following functional assumptions:
Per-period utility is represented by u(c) = (c1 1)/(1 ) and production function is zF (k, 1)

LEON M. METZGER is an adjunct professor and lecturer at Columbia, NYU,
and Yale, where he teaches alternative investment management courses. An
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associated with Paloma Partner

Assignment 1
Question 1
Consider the version of the Solow growth model we discussed in class. We make the following assumptions on the production function F (K, L).
1. F (0, L) = 0.
2. FK (0, L) > .
s
3. limK sFK (K, L) + (1 ) < 1.
4. FK (K, L) > 0, FKK (

Assignment 3
Question 1 - Linearizing the Stochastic Growth Model
Consider the stochastic growth model we discussed in class. Agents have the per-period CRRA utility
function u(c) =
c1 1
1
and the production function is zf (k) = zk . Assume that TFP follo

Assignment 2
Question 1 - Growth Model with Habit Formation
Consider the following version of the neoclassical growth model we discussed in class: Suppose that
the representative agent (or planner) gets utility from the level of consumption relative to th

Assignment 3
Question 1 - Linearizing the Stochastic Growth Model
Consider the stochastic growth model we discussed in class. Agents have the per-period CRRA utility
function u(c) =
c1 1
1
and the production function is zf (k) = zk . Assume that TFP follo

Assignment 4
Discrete-space solution to Neoclassical Growth Model
Consider a neoclassical growth model with the following functional assumptions: Per-period utility is
represented by u(c) = (c1 1)/(1 ) and production function is F (k, 1) = k . The represe