### Econ 205A Advanced Macroeconomic Theory I - C. Aspen Gorry

 Modern macroeconomic theory: determination of national income; employment, inflation, and exchange rates; theories of growth and business cycle fluctuations; international transmission of inflation and other disturbances; recent developments in the analysis of macroeconomic policy; modern theoretical and empirical analysis of aggregate relationships. Courses must be taken in sequence.
Christopher Aspen Gorry

Engineer 2 499
Mon & Wed 2:00PM - 3:45PM

starts Sept 24, till Dec 4th 2009

Class Organization
21 Lectures  View Notes
9 Problem Sets View Sets
4 Pop Quizzes Quiz Center
One Mid-Term View
Final Exam

Quizzes

Quiz One - Lecture Two, Sept 30th - Given basic set-up - What is an efficient allocation. If allocation isn't efficient, what can we conclude? What is CE for the economy

Quiz Two - Lecture Five, Oct 11th - Given basic set-up - What is AD CE? What is SoM CE?

Quiz Three - Lecture Fourteenth, Nov 9th - Given preferences with disutility to working, write down social planner's problem and find the two conditions that characterize the optimal solution

Quiz Four - Nov 23rd - Define a recursive competitive equilibrium of the neo-classical growth model (covered Nov 18th)

Mid-Term  - Wed Oct 28th
paraphrased from the professor
In the mid-term you'll be asked to 'solve problems'. Your questions will be similar to the neoclassical growth model, probably adding some twists. The challenge will be getting notation correct, setting up the maximization problem properly, going through the analysis...

A likely set-up; you're given a model or description of an economy. Write down the maximization problem that correctly describes an allocation in that economy -- then solve it. Could be asked to do many things, continuous time, perhaps speed of convergence stuff. You can expect instructions to be as detailed as those found in problem sets -- with far less algebra intensive, luck & experience type questions. [Gorry, 10/19]

The mid-term is going to cover, probably, sequence problems with the neoclassical growth model and twists, such as you saw in the first few homework assignments. Maybe changing preferences around, adding another durable consumption, different types of investment. Simply, the neoclassical growth model with twists in continuous and discrete time. [Gorry 10/19]

Remember the "incantations"
A Competitive Equilibrium is a list of sequences/functions .....
And a Steady State is a level of capital such if k_0 = k*, then.....

In all honesty, it didn't turn out all that helpful

## Lectures & Problem Sets

Lecture One Sept 28th
Course Outline. Resource Allocation Problems. Competitive Equilibrium (CE) introduced. Inserting trade-offs makes model more interesting. NeoClassical Growth Model: consumption, technology, endowments.

Lecture Two Sept 30th
Quiz One. Neoclassical Growth Model. Does a solution exist? is it unique? Is there a steady state? Solving the Planner's Problem; First Order Conditions, find the Steady State. Lastly, the Definition of Competitive Equilibrium.

Basics of the Neoclassical Growth model and solving the Social Planner problem in discrete time. Extensions & complications.

Lecture Three Oct 7th
Competitive Equilibrium, in the Arrow-Debreu Neoclassical Growth Model. Setting up the CE problem, then the steps toward the solution. Finding prices, k* and c*

Problem Set 2   Due Oct 9th Fri
Competitive Equilibrium (CE) in discrete time. Arrow Debreu (AD) compared to Sequence of Markets (SoM)

Lecture Four Oct 9th
Steady State of Arrow-Debreu model. SS in CE. Growth
Model dynamics. Finding the steady state. Continuous
Time introduced. State (stock) & Control (flow) variables.
Step-by-step recipe the find Necessary & Sufficient
Conditions.

Lecture Five Oct 11th
Problem Set Two review. Previous lecture continued. "Necessary & sufficient conditions", in continuous time, setting up the Hamiltonian. An example using the neoclassical growth model approached via the social planner's problem. Solving optimality conditions, for the steady state. Investigating dynamics with phase diagrams.

Problem Set 3   Due Oct 14th Wed

Lecture Six Oct 14th
Continuous time phase diagrams continued. Given initial capital, what does the maximization problem look like on our phase diagram? answer: trying to land on the saddle path. Speed of convergence. Seeking the solution in the time domain & example. Seeking the solution in the state variable domain. Local stability and speed of convergence in state domain - law of motion & half-life.

Lecture Seven Oct 19th
Continuing the Previous Lecture. Looking more deeply into the Steady State. Stable vs Unstable solutions. Convincing ourselves that the infinite time, continuous time maximization problems we have are well posed and the solutions we find are in fact the solutions we're looking for. A comprehensive math review of this problem.

Lecture Eight Oct 21st
Comparative Statics with a simple model. Looking at the trade-off of consumption today vs consumption tomorrow, and the trade-off between Consumption & Leisure. Also, Competitive Equilibrium in Continuous Time

Problem Set 4   due Oct 23 Fri

Lecture Nine Oct 23rd
Problem Set Review. Problem Set Three, Question Three: Arrow Debreu Competitive Equilibrium vs Sequence of Markets. Problem Set Four, Question Two: CE vs Social Planner with pollution.

Lecture Ten Oct 26th
(Review) Cover answers to Problems Set Four No. One, discusses and set-up Problem Set Three No. Three.
(Lecture) Introduce Government and Taxes to the Neoclassical Growth Model. First introducing capital taxation and transfer payments, hinting at other forms of taxation & government expenditure.

Mid-Term Exam  Oct 28th Wed
We Take Our Mid-Term. Not quite as hard as we expected. But still rough, & long. (that's what she said)
Solutions - #1 is part one in problem set five.  #2 gone over in class Oct 30.   80/100 = A.   60/100 = passing.

Lecture Eleven Oct 30th Fri
(Review) Mid-Term Question Two (Question One appears on our next problem Set).
(Lecture) Measuring Welfare Consequence of Public Policy. We also discuss the Prescott Paper Why do Americans Work So Much More than Europeans?"

Lecture Twelve Nov 2nd Mon
Picking up on the Prescott paper and taxation. Frisch Labor Supply Elasticity. Introducing Growth into the Neo Classical Growth Model.

Lecture Thirteen Nov 4th
(Lecture note are sub-standard) Lucas Paper. Economic Growth. Dynamic Programming Introduced.

Lecture Fourteen Nov 9th Mon
Quiz Three. They Dynamic Programming Problem and Bellman Equation Intro. Setting up finite horizon Bellman equation. Recipe for Solving Infinite Horizon Dynamic Programming Problems. Two examples of setting up Bellmans - social planner growth model & the growth model with habit formation

No Class! Nov 11th Wed
Veteran's Day. Thanks Chris Limnios.

### (Review) Problem Six Continued. (Lecture) Mathematical conditions needed for dynamic programming to work.

Lecture Seventeen Nov 18th Wed
(A Mighty Lecture Today) Dynamic Programming Continued.
• Contraction Mapping Theorem.
• Finding the Euler’s Equation. A fancy trick that gets the Envelope Condition to lead to the Bellman Equation Solution.
• The Neo Classical Growth Model with in Bellman Equation Form.
• Finding the Steady State and examining Transition Dynamics.
• Competitive Equilibrium & Dynamic Programming, first looking at Neo Classical Model first, then turning to full Recursive Competitive Equilibrium (this turned out to be a small part of the final exam)

Problem Set 7   due Nov 20 Fri

No Lecture Review Nov 20 Fri
thank you NSF grant writing seminar

Lecture Eighteen Nov 23rd Mon
Quiz Four. Introducing Stochastic Models. An Arrow Debreu Competitive Equilibrium in Static Stochastic Setting. The Neo Classical Growth Model, Competitive Equilibrium in a Stochastic Setting

Problem Set 8   due Nov 25 Wed

Lecture Nineteen Nov 25th Wed
Stochastic Models Continued. Dynamic Programming with Stochastic Models. Markov Processes as State of Nature Variable. Discrete and Continuous Time. Setting up a Stochastic Bellman Equation.

Lecture Twenty Nov 30th Mon
Continuing Notes on Dynamic Programming in Stochastic Setting. The Stochastic Growth Model - A Recursive Competitive Equilibrium for the Stochastic Growth Model. Labour Search – introducing a simple labor search model.

Lecture Twenty-One Dec 2nd Wed
(Lecture) Labor Search Continued (this turned out to comprise half our Final Exam)
(Review) Problem Set Eight.

Problem Set 9   due Dec 4 Fri
Questions (2 Qs, 2 pgs)

Final Exam  Dec 7th Mon
It's going to be very difficult. If you study, you'll likely pass -- but it will be much more difficult to do 'well' compared to the mid-term, (assuming a similar set-up to 2009)

If you're looking for a specific, nuanced topic, try the Search this site bar above. I did my best to ensure that all notes and problem sets are indexed.

PDF File Opening Errors
I've been using Google Docs' PDF viewer to link to the resources we have here. Unfortunately, it's not always the most stable. I've seen it fail to load the preview numerous times. If you have this error, try viewing the link in a different browser or downloading the file to your computer.

Errors & Suggestions? - Just Let Me Know

Textbooks

ECONOMIC GROWTH
BARRO

RECURSIVE MACROECONOMIC THEORY [.PDF]
by Thomas Sargent and Lars Ljungqvist,
2nd edition (1106 pages)
Note, we are working out of the 2nd ed. Red Cover

RECURSIVE METHODS IN ECONOMICS DYNAMICS
STOKEY & LUCAS
[pdf book 19.4MB] - [pdf solutions manual]

Some files are too large to link to. Email me if you want a pdf. economicurtis@gmail.com

What Do Economists Do? [.PDF]
Robert Lucas, 1988, 6 pages
A farewell to UofC graduating economists

The Theory of Money [Online]
by Grard Debreu, 1959 (100 pages)

Back From The Brink [.PDF]
by Christina Romer, Sept 2009 (16 page)

Dynamic Optimization in Continuous-Time Economic Models (a guide for the perplexed) [.PDF]
by Maurice Obstfeld - April 1992 (21 pages)

Why Do Americans Work So Much More Than Europeans?
by Edward Prescott - July 2004 (13 pages) [PDF]

On The Mechanics of Economic Development
by Robert Lucas, Feb 1988 [PDF]

Credits

Problem Sets - Three Groups contributed. Their solutions are given here with permission from at least one group member.
~The League of Nations (LoN): Linh Bun, David Florian-Hoyle, Jacopo Magnani, Yuhan Xue, Yabin Wang
~My Group (My): Maggie apRoberts-Warren, Carmen Flernandez-Lara, Kat Lopiccalo, Jesse Bigley, Curtis Kephart, A. Christopher Limnios
~Other Group (the others): Olya Rud, Jongchan Lee, Glen Wolf, Kevin McLaughlin & Benjamin Linus