| 429, McNeil Bdg,
Fax: 215 5732057, or 215 573-4217
Econ 702, Spring
Last modified: Thu Apr 21 17:42:48 Eastern Standard Time 2005
This page contains relevant for the course. It grows with the semester.
Students should check it often.
3718 Locust Walk
| Classes are T. and Th.
1:30-2:50 in 410 McNeil.
Special Classes (rescheduled) may be M 3:30-5:00 or Fr 10:30-12:00 in
the Econ Conf Room.
Off Hours: Wed 2:30 to 3:30 and by appt.
| T.As.: Kagan (Omer Parmaksiz) and Thanasis, (Geromichalos).
Off Hrs: Kagan Tu 3:30-5:00, Thanasis Fr 1:30-3:00 both in MCNeil 469.
Do not think that I have
forgotten the beer and the wings that I talked about. Since I am on a
trip next week, we will let it for September, unless there is enought
of you after the 22 of May.
- What are we doing? Brief description of previous
classes and next one.
- Course Description
- Requirements and Grades
- Preliminary List of Material to Cover
- Problem Sets problems and
solutions with due dates. Do not wait for the posting to answer them.
- Class Notes taken in class by
Thanasis and Kagan. Also last year's (Ahu and Vivian) and the year
- Exams. There was a midterm.
The final coincides with the 2005 June Macro Qualifying Examination.
What are we doing each day.
- We finished talking
about extensions to the basic model. We briefly described how to
pose Overlapping Generations Models recursively. This finished the
- We posed and solved a problem with one sided lack of
commitment. We talked about why upon hitting the constraint the new
allocation is independent of the previously promised utility. We also
talked about two sided lack of commitment. We started talking about
some extensions of the basic growth model that have proved popular in
- We talked about how to deal with the private information
problem and how to solve a planner's problem that incorporates the
private information friction as a constraint. We characterized
properties of the solution (the decreasing amount of unemployment
- We talked about a model of unemployment with search
intensity. We then described how a benevolent planner guarantees a
certain utility level with minimum cost. We described how private
information on the part of the agent's effort poses a moral hazard
- We finished talking about how to compare models with data.
We started with a model with private information by looking at a model
of unemployment with search intensity. We also started describing how
would a planner guarantee a certain level of utility ao agents.
- We finished the Romer R&D model, although a chunk of it
was left as a homework. We discuss how to do welfare comparisons. We
also talked about how to construct predictions of the model.
- We continued with the Romer R&D model.
- We discussed the behavior of the skilled wage premia since
1960. More importantly, in doing so we discussed the difference between
using the model to make a statement and using the model to measure
- We discussed the Romer model with externalities in capital
and how it leads to a balanced growth path. We also discussed the
differences between the market and the planner's allocation. We started
the Romer model with development of new varieties.
- We talked about endogenous growth. We started with the AK
model. We moved on to the Lucas human capital model with schools as a
way to accumulate, and we compared this with studying.
- We talked about growth. First the growth and development
facts, and then how to transform the economy when there is population
growth and when there is labor augmenting technological change. The
transformed economy's steady state is a balanced growth path of the
original economy. These notes by Per
Krusell on growth might help for Today's and for next week's material.
- We talked about the economy with many agents and
uninsurable shocks. First we gave the interpretation of savings as
storage which allows us to characterize the allocations both in a
steady state and outside the steady state. We then posed the model as a
lending economy and in the context of a growth model which poses some
difficulties when characterizing non steady state behavior. Still we
define both in sequence space and recursively what non steady state
equilbria are for these economies.
- We looked at a distribution of firms in an industry
equilibria where now it is endogenous in the sense that firms are
choosing whether to leave the industry or to continue operating. Then
we discussed how to use this model to put policies that limit the size
of firms or to put policies that protect employment by making it
expensive to fire workers. We used this example to distinguish once
again between the properties of a stationary distribution and those
generated by the policy in the periods subsequent to its implementation.
- We talked about transition probabilities and some of its
properties. We started developing a multiple agents model with
idiosyncratic, uninsurable shocks: the pig farmers' model. We then
talked about a distribution of firms. First we looked at exogenous
entry and exit.
- We continued with the second part of the course. We finished
with the necessary notions of measure theory.
- First midterm.
- We talked about a variety of issues raised throughout the
first part of the course. We started the second part of the course by
looking at the basic notions of measure theory.
- We continued with the Lucas tree economy, obtaining formulae
to compute share prices in addition to state contingent prices. We also
priced some other assets such as options.
- We finished the land economy with dynamic firms establishing
the definition of equilibrium. We started the Lucas tree economy
constructing the equilibrium allocation, and finding the necessary
Arrow Debreu prices that sustain the allocation. We then defined and
priced some assets (stocks, bonds) and went over the recursive
- We finished the debt economy and started an economy with two
social classes where the A agents are poorer, have lower wages and care
about average consumption of those of their own type. We started an
economy where firms own the land.
- We define equilibria for a variety of growth economies with
taxing governments. We started with a government that taxes lump sum
and then throws away the stuff. We then moved to a proportional income
tax. Then we went to a government with a constant expenditure
requirement and we finally moved to a government that can issue debt.
We have not finihed the latter.
- We went again over Recursive Competitive Equilibrium. We saw
an Economy with labor-leisure choice and an economy with an externality
in leisure. We discussed the set of variables that are needed and the
set of functions that describe the equilibrium of the economy. We
talked about steady states.
- We defined Recursive Competitive Equilibria for the growth
model with and without rational expectations. For this we constructed
the problem of the individual agent with state variables a and K.
- We described in detail how to model the
stochastic growth economy. We described the welfare theorems there and
repeated the analysis that we did about arguing existence.
- We proved equivalence of SME and AD equilibrium (we have to
check that the SME prices are a cont linear functional, i.e. bounded).
We started defining a stochastic version of the growth model.
- We reviewed the definitions of the production possibility
set Y and of the consumption possibility set X. We then defined
valuation equilibrium and applied the second welfare theorem. We
discussed the meaning of quasiequilibrium with transfers, and of the
conditions necessary to have the implied price have a linear product
representation. We then used the first order conditions from the
planners problem and from the agents problem to establish properties of
the price vector. We started describing what a sequence of market
- We looked at the neclassical growth model in its simplest
form (the Cass (yes David Cass) and Koopmans model) and described how
to solve for its Pareto optimal allocation. We looked at the necessary
Euler equation that partially characterizes an interior optimum. We the
defined a topological vector space and production and consumption
possibility sets that implement the growth model and that we will use
to be the define Arrow-Debreu (valuation) equilibrium next day.
- We went over the homepage contents. We also talked about the
course and the concept of equilibrium as the tool to pick outocomes
(allocations and prices). We talked about Arrow Debreu Equilibrium and
the theorems that it provides. We stated the existence of a unique
Pareto optimum (that solves a social planner's problem), the 1st
welfare theorem and the second welfare theorem. We provided the logic
under which we will operate, that is, pose a model that macroeconomists
like, look for its Pareto Optimal allocations, and use the Welfare
Theorems to support them as Walrasian equilibria. We finished by
reporting the rudiments of the standard growht model.
This course complements
704 in its objectives. The order of the numbers is
irrelevant. Essentially, 702 and 704 run parallel except the first and
last two weeks which are part of 704 while the last two weeks are part
The ultimate goal of this
course is to learn to use a variety
of models that can be used to give quantitative answers
to a number of economic questions. These models can be used
to produce time series that can be meaningfully related to
data. However in this course all the material will be studied
from the strict point of view of the theory, so we will not
look at data nor at solving the models with the computer.
This is done in second year (mostly in 714). The emphasis
will be on economic rigor, i.e. the target is to learn
tools that will be useful later in a variety of contexts. The
course, then, is not a survey of topics in macroeconomics.
When some specific topic is addressed as, say, optimal fiscal
policy, the objective is less that of giving a review of
known results but rather to give an example of how an issue
is addressed and of how tools are used.
There will be recitations once
a week. These will be used either to
introduce some mathematical apparatus that we need, to solve
homeworks, or to explore issues related to those presented in
class. The material covered in recitations constitutes part of the
required curriculum. The TAs will discuss with you the time and
location of the recitations.
Requirements and Grades.
I will ask some homeworks.
Sometimes I will ask you to prove
something during a lecture, sometimes they will be posted here. These problems ARE required
specific due dates. While they are required and have to be submitted
to the TA's they will not be individually graded and returned. Answer
keys will be posted after they are due. The homeworks may count for
up to 15% of the grade. We may look at them selectively after the
exams. They play the key role of giving feedback to the students and
of assuring that students are going along with the course rather than
waiting till the exams.
In addition, the grades will
be based on one or two midterms and a final (that
will take place simulataneously with the 2005 June QUALIFYING
EXAMINATION. The midterms counts for one third of the non-homework
grade and the final will count for the rest. If there are two midterms
the first one will be weighted considerably less. The TA's are
for giving you feedback regarding the homeworks.
We start the course in the
third week of the semester so that students
learn the fundamentals of dynamic programming and how it can be
applied to a problem like the social planner problem of the
Cass-Koopman's growth model. This will be done in 704. By the time 702
starts, I assume that students know how to solve infinite dimensional
maximization problems, interpret Bellman equations, know the
conditions necessary to iterate on value functions, and know what is
obtained as limits of such iterations.
Some understanding of
stochastic processes will be very
helpful, including the notions of random variable, Markov
processes, and history-dependence. We will use some amount of
measure theory. Overall the math requisites would not be very
hard since we do not have to go very deep into these
concepts. Students are advised to master these concepts, but
not doing so should not prevent going through 702.
We will use some bits and
various textbooks. They include [Harris, 1987], [Stokey
and Lucas, 1989], [Cooley,
1995], [Ljungqvist and Sargent, 2000]. I
recommend every student interested in Macro to have the last three,
and every student to have [Stokey and Lucas, 1989]. [Harris, 1987] is out of
print but it can be found. The papers that I cite (in a very
incomplete form below) are not to be read in general, although some
students may find them useful.
Preliminary List of Material to
- Equilibrium. What is its
- Competitive equilibrium in the
growth model. Taking advantage of the welfare theorems.
and Lucas, 1989], Chapters 15 and 16; [Harris, 1987], Chapters 3 and 4; [Cooley and
- Arrow Debreu.
- Sequence of Markets.
- Recursive Competitive
- A stochastic version of the
growth model. What are complete markets? What are one period ahead
- Competitive equilibrium in
stochastic growth model
- Models with endogenous labor
- Non-optimal Economies.
Sequence of Markets and Recursive Equilibrium.
- An economy with public
expenditures, income taxes and a period by period balanced budget
- An economy with public
expenditures, income taxes and a present value balanced budget
- Finance and asset pricing.
What is Lucas tree model and how to price an arbitary asset. 
- Multiple Agents Complete
- An economy with two types of
agents differing in skills and/or wealth.
- A two country economy.
- Exogenous growth
- Transforming the economy
- The AK model: one and two
- Research and development
- Non balanced growth paths.
- Economies without Complete
Markets and with Large Numbers of Self-Insuring Agents. Introduce
measure theory, transition function and statistics describing economy
inequality and mobility.
[Huggett, 1993]; [\.Imrohoroglu, 1989]; [Diaz-Gimenez
et al., 1992]; Diaz-90; [Ríos-Rull, 1995].
- A simple model without
insurance markets but with individual shocks, and no aggregate
uncertainty. Two examples are farmer economy with storage technolagy
but no trade and economy with non-state contingent loan.
- A General Lack of Insurance
Model with Production.
- A General Lack of Insurance
Model with Aggregate Uncertainty and aggregate endogenous state
- The mess.
- The Krusell-Smith solution.
- The Moody Government solution.
et al., 1992].
- Transition and Policy
- Industry Equilibria.
- Exogenous entry and exit. A
measure of firms.
- Endogenous entry and exit.
- How to use models to look at
data: Generating statistics from models.
- Economies with contractual
problems. Lack of observabiliy and lack of commitment.
- Economy with One-side Lack of
- Economy with Two-side Lack of
- Economy with Lack of
and Sargent, 2000] [Attanasio and Ríos-Rull, 2000]
- The Abreu-Pierce and Stachetti
- Constrained arrangements, and
the Marcet-Marimon approach. [Attanasio and Ríos-Rull, 2000]
[Kehoe and Perri,
- Optimal Contracting.  and [Quadrini, 2001].
- Limited information. [Atkeson and
- Endogenous default. [Chatterjee et al., 2004].
- Recursive Preferences.
Epstein-Zin recursive utility. .
and Sargent, 2000]
- Models with demographic
- Overlapping Generations with
- Overlapping Generations with
- A hybrid. The exponential
population, exponential aging, model.
- Fertility in the utility.
- Multiplicity of Equilibria.
- [Atkeson and
- Atkeson, A. and Lucas, R. E. (1992). On efficient
distribution with private information. Review of Economic Studies,
- [Attanasio and Ríos-Rull, 2000]
- Attanasio, O. and Ríos-Rull, J.-V. (2000). On the optimal
provision of aggregate insurance in the presence of enforceability
problems in the provision of private insurance. Mimeo, University
- [Chatterjee et al.,
- Chatterjee, S., Corbae, D., Nakajima, M., and Ríos-Rull,
J.-V. (2004). A quantitative theory of unsecured consumer credit with
risk of default. Unpublished Manuscript, CAERP.
- [Cooley, 1995]
- Cooley, T. F. (1995). Frontiers of Business Cycle
Research. Princeton, N. J.: Princeton University Press.
and Prescott, 1995]
- Cooley, T. F. and Prescott, E. C. (1995). Economic
growth and business cycles. In Cooley, T. F., editor, Frontiers
of Business Cycle Research, chapter 1. Princeton University
- Díaz-Giménez, J. (1990). Business cycle
fluctuations and the cost of insurance in computable general
equilibrium heterogeneous agent economies. Working Paper, Universidad
Carlos III de Madrid.
et al., 1992]
- Diaz-Gimenez, J., Prescott, E. C., Fitzgerald, T., and
Alvarez, F. (1992). Banking in computable general equilibrium
economies. Journal of Economic Dynamics and Control,
- [Harris, 1987]
- Harris, M. (1987). Dynamic Economic Analysis. Oxford
- [Huggett, 1993]
- Huggett, M. (1993). The risk free rate in heterogeneous-agents,
incomplete insurance economies. Journal of Economic Dynamics and
- [\.Imrohoroglu, 1989]
- \.Imrohoroglu, A. (1989). The cost of business cycles with
indivisibilities and liquidity constraints. Journal of Political
- [Kehoe and
- Kehoe, P. and Perri, F. (1997). International business cycles
with endogenous incomplete marjets. Working Paper, Federal Reserve bank
and Sargent, 2000]
- Ljungqvist, L. and Sargent, T. (2000). Recursive
Macroeconomic Theory. MIT Press.
- [Quadrini, 2001]
- Quadrini, V. (2001). Investment and default in
renegotiation-proof contracts with moral hazard.
- Ríos-Rull, J.-V. (1995). Models with heterogenous agents.
In Cooley, T. F., editor, Frontiers of Business Cycle Research,
chapter 4. Princeton University Press, Princeton.
- [Stokey and Lucas, 1989]
- Stokey, N. L. and Lucas, R. E. with Prescott,
E. C. (1989). Recursive Methods in Economic Dynamics.
Harvard University Press.
File translated from
On 11 Jan 2005, 13:28.