316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 4a
Chris Edmond [email protected]
In this course, we will consider two ways to model uncertainty. We will adopt the following notational
conventions: random variables will be denoted by capital letter
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 3a
Chris Edmond [email protected]
Dynamic programming and the growth model
Dynamic programming and closely related recursive methods provide an important methodology for
solving a wide variety of econ
316-406 Advanced Macroeconomic Techniques
Problem Set #5
Due 12 November, 2004
Question 1. (Equity Premium Puzzle). Consider the Mehra-Prescott model as described
in the notes. The (gross) growth rate of dividends x0 ≡ y 0 /y follows a symmetric 2-state
M
316-406 Advanced Macroeconomic Techniques Problem Set #4
Selected answers
Question 1. (Deterministic Dynamic Programming). Since answering the first question just involved changing some settings in the "dp_demo.m" program, these answers are brief. With th
316-406 Advanced Macroeconomic Techniques
Problem Set #4
Due 18 October, 2004
Question 1. (Deterministic Dynamic Programming). Consider the social planning problem
of maximizing utility
∞
X
β t U(ct )
t=0
subject to a resource constraint
ct + kt+1 = f (kt
316-406 Advanced Macroeconomic Techniques Problem Set #3
Selected answers
Question 1. (Real Business Cycles). By substituting the constraints into the objective function, the problem can be reduced to one of choosing plans for labor and capital accumulati
316-406 Advanced Macroeconomic Techniques
Problem Set #3
Due 4 October, 2004
For this problem set you should use Harald Uhlig’s Matlab "toolkit" for solving log-linear
models. Save Uhlig’s ﬁles "solve.m" and "options.m" to your local directory, then follo
316-406 Advanced Macroeconomic Techniques Problem Set #2
Selected answers
Question 1. The relevant plots are attached (see Figure 1) and can be produced with the Matlab code "ps2_solutions.m". When a = 0.5, the process quickly begins to fluctuate in an ob
316-406 Advanced Macroeconomic Techniques
Problem Set #2
Due 1 September, 2004
For this problem set you’ll probably have to use a more sophisticated programming language,
and not just Excel. Go on, give Matlab (or Gauss) a whirl!
Question 1. (Stochastic d
316-406 Advanced Macroeconomic Techniques Problem Set #1 Question 1. If the resource constraint and Euler equation are ct + kt+1 = f (kt ) + (1 - )kt U 0 (ct ) = U 0 (ct+1 )[1 + f 0 (kt+1 ) - ] then the steady state (, k) satisfies c c + k = f (k) + (1 -
316-406 Advanced Macroeconomic Techniques
Problem Set #1
Due 18 August, 2004
Please don’t go "over the top" in answering the following questions. In most cases, a couple
of numbers, or a few words or a picture is all that is required. You are encouraged t
Problem Set Zero
This is a model problem set, you do not have to turn it in and it does not count for anything.
Instead, you should read over the questions, and in particular study the associated Matlab
code, to make sure that you understand everything. I
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 7b
Chris Edmond [email protected]
Aiyagari’s model
Arguably the most popular example of a simple incomplete markets model is due to Rao Aiyagari
(1994, QJE). As in Huggett’s paper, market incompletene
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 7a
Chris Edmond [email protected]
Introduction to incomplete markets
We will now turn our attention to models without a representative agent. In particular, we will study
a class of models – sometimes
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 6b
Chris Edmond [email protected]
Mehra and Prescott’s equity premium puzzle
Consider an economy with risky trees ("equity"), denoted s, and sure claims ("bonds"), denoted
B. We could price contingent
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 6a
Chris Edmond [email protected]
Introduction to consumption-based asset pricing
We will begin our brief look at asset pricing with a review of the essentials of Robert Lucas’s
(1978) representative
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 5c
Chris Edmond [email protected]
Introduction to numerical dynamic programming
We’ll now turn to simple numerical methods for solving dynamic programming problems. The main
method we will be interest
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 5a
Chris Edmond [email protected]
Introduction to the stochastic growth model
Now that we have some tools for modeling uncertainty, we can turn back to economic models. To
begin with, let’s consider t
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 4c
Chris Edmond [email protected]
Notes on computing and simulating Markov chains
Consider a two-state Markov chain (x, P, π 0 ) with transition matrix
1−p
P =
q
p
1−q
for 1 > p, q > 0. Then this Mar
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 4b
Chris Edmond [email protected]
Again, we will adopt the following notational conventions: random variables will be denoted by
capital letters, like Xt and Zt , realizations of random variables will
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 2b
Chris Edmond [email protected]
Systems of linear diﬀerence equations
We will frequently want to solve a two-dimensional system of diﬀerence equations
xt+1 − Axt = b,
t≥0
given a 2-by-2 matrix A, a
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 2a
Chris Edmond [email protected]
Optimal growth model
The key diﬀerence between the Solow growth model and the optimal or Ramsey-Cass-Koopmans
growth model is that savings behavior is endogenized. We
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 1c
Chris Edmond [email protected]
Linearizing a diﬀerence equation
We will frequently want to linearize a diﬀerence equation of the form
xt+1 = ψ(xt )
given an initial condition x0 .
We can take a ﬁrs
316-406 ADVANCED MACROECONOMIC TECHNIQUES
NOTE 1b
Chris Edmond [email protected]
Linear diﬀerential equations with constant coeﬃcients
We will frequently want to solve a diﬀerential equation of the form
xt − axt = b,
˙
t≥0
given scalars a, b and a
316-406 ADVANCED MACROECONOMIC TECHNIQUES
Chris Edmond [email protected]
Midterm
This exam lasts 90 minutes and has three questions, each of equal marks. Within each question there are a number of parts and the weight given to each part is also in
316-406/671 ADVANCED MACRO TECHNIQUES
Chris Edmond [email protected]
Final Solutions
This exam lasts 180 minutes and has two questions. The first question is worth 120 marks, while the second question is worth only 60 marks. Allocate your time acc
316-406 ADVANCED MACROECONOMIC TECHNIQUES
Chris Edmond [email protected]
Sample answers
The final will last 180 minutes and has two questions. The first question is worth 120 marks, while the second question is worth only 60 marks. Within each que
316-406/671 ADVANCED MACRO TECHNIQUES
This exam lasts 180 minutes and has two questions. The ﬁrst question is worth 120 marks, while
the second question is worth only 60 marks. Allocate your time accordingly. Within each question
there are a number of par