429, McNeil Bdg,
Fax: 215 5732057, or 215 573-4217
Econ 702, Spring
Last modified: Fri Apr 14 11:21:51 Eastern Standard Time 2006
This page contains relevant for the course. It grows
with the semester. Students should check it often.
Department of Economics
University of Pennsylvania
3718 Locust Walk
Classes are T. and Th. 1:30-2:50 in 410
Special Classes (rescheduled) may be M
3:30-5:00 or Fr 10:30-12:00 in the Econ Conf
Off Hours: Wed 2:30 to 3:30 and by
and Se Kyu
Off Hrs: Thanasis Th 12:00-1:30 and
Se Kyu M 3-4:30 both in MCNeil 469.
Contingent times and places for teaching are Mon
10:30 to 12 in McNeil 285 and/or Fr 10:30 to 12 in
STIT B26 (Stiteler Hall).
- What are we doing? Brief description of
previous classes and next one.
- Course Description
- Requirements and Grades
- Preliminary List of Material
- 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 Se Kyu. Also last years by
Kagan and Thanasis and the previous years (Ahu and
Vivian, and Makoto).
- Exams. There will be
one or two midterms. The final coincides with the 2006
May Macro Qualifying Examination.
What we are doing each day.
- We will look at a recursive
formulation of the two sided lack of commitment
problem. We will also discuss extensions of the basic
models to accommodate such issues as demographics and
- We briefly reviewed some properties
of the one sided lack of commitment and discussed how it
could be implemented as a contract offered by firms. We
looked at the two sided loke of commitment problem and
discussed the nature of the planning problem and of the
- We discussed the problem of one
sided lack of commitment. We characterized the solution.
- We finished studying the problem
faced by the charitable planner when she cannot observe
the effort placed by the unemployed agent. We saw how an
additional incentive compatibility constraint shows up and
how the optimal solution displays decreasing levels of
promised utility and, consequently, consumption. We
discuss a bit how actual policied get determined.
- We posed and solved the problem of
the unemployed agent and discussed how is it that a
planner would consider helping him.
- We finished the R&D Romer model. We
also discussed why is it that the main questions in
economics about poverty are more related to development and
a theory of TFP than to growth per se. To this end I asked a
few numerical questions.
These notes by Per Krusell on growth might help for the
growth part. We started the next part of the curse where
information and enforcement problems appear and where the
allocations try to get around those problems.
- We continued the growth part of
the course. We looked at the two Romer models: We
completed the study of the economy with an
externality and we started the R&D model.
- We went over growth. In particular,
we saw how to transform a growing economy (either because
of exogenous population or productivity growth) into a non
growing one so that we can solve it. We also covered
endogenous growth models. First AK economies and discussed
how is it that there are no transitional dynamics. We then
went to cover the Lucas human capital model and how the
specifics of human capital accumulation matters for the
possibility of long run growth.
- We finished this part of the course
talking a little about transition and welfare
comparisons. We saw how a wefare comparison requires the
transition and it is assessed wrt to the distribution in
the initial condition (although this was not clear to
everybody. We started talking about growth with an
ececonomy with exogenous population growth.
- We looked at the solution of the
problem of the farmer. We discussed its properties and the
nature of the meaning of a stationary distribution. We
discussed its porperties in the context of an unemployment
problem. We also define equilibrium for the case when this
problem is embodied in a growth model.
- We discussed that the growth model
does not have a good theory of wealth inequality. We then
moved on to the savings problem with incomplete markets
and storage technology and characterized the solution. We
then described an economy with many such farmers and used
measures and its transitions to characterize outcomes. We
stated the theorem that there exists a unique stationary
distribution provided the transition has certain nice
properties. We then moved on to the economy with loans and
discussed the solvency constraint.
- We discussed the calculation of
statistics using measures. We looked at the problem of
individual savers. We discussed the problem of
- We looked at industry equilibria
with adjusment (hiring) costs to employment.
- We continued studying
economies with measures of agents defining
industry equilibria with endogenous entry and exit of
firms. In order to do this we defined the updating
operators that take a meausre and a transition and yield
another measure that we interpreted as the distribution
of firms a period later.
- I started economies with measures
of agents. We looked at the key concepts in measure
theory that we will use and we defined industry equilibria.
- The midterm happened
- We finished talking about Lucas
trees and we priced all types of assets (options shares
and the like under complete markets).
- We continued talking about
stochastic environments. In particular, we discussed how
to implement complete markets in both a sequence of
markets and a recursive structure. We started
describing the Lucas tree model.
- We posed 4 homeworks that define
the big questions in macro so we can get an idea of
their relative importance. The homeworks were about
measuring the welfare costs of various things. The questions where
- Differences in growth rates.
- Business cycles.
- Differences in levels of output (with the
additional problem of how to compare a country that
lags in levels but will catch up eventually).
- Differences in within country income.
- We finished the discussion of
recursive equilibrium with two countries and perfect
capital mobility. We looked at the growh model when
firms own land and choose the stock of capital and
households own firms which they buy and sell. Finally,
we looked at an economy with a consumption tax, debt and
a government that spends some exogenous amounts of the
- We reviewed again RCE by
posing a couple of simple economies: leisure, a
government, debt, multiple agents and multiple
countries. This latter one proved to be tricky as
we had to keep track of how much capital there is in
each country and how much wealth is held by citizens of
- We defined Recursive Competitive
Equilibrium (RCE) by adding to the problem of the
household the condition that it has to be
representative. We also added a rational
expectitations/perfect foresight condition that links
the perceived law of motion of the economy and the
actual law of motion of the economy. We discuss some
issues of existence, uniqueness and computability (the
Debreu, Mantel, Mas-Colell and Sonneschein 1974 theorem
and the 1986 Boldrin and Montruccio result).
- We posed the problem of a consumer
in the SME in a recursive manner, trying to mimic the
logic that uses Bellman equations to solve social
planner problems. In doing so we argued that the set of
state variables should include both individual assets
and aggregate capital.
- We defined sequence of markets
equilibria (SME) by having markets for current goods and
for loans open every period and by adding budget
constraints for each period. We showed how to prove that
a ADE allocation can be supported as a SME and
viceversa. Then we defined another notion of sequence
of markets equilibrium a lot simpler that has the same
features and that saves a lot in notation.
- We talked about how to construct
the price that sustains the PO allocation as an ADE. For
this we got around the problem of transfers (because
there is only one consumer), the problem of
quasiequilibrium (due to the existence of a cheaper
point) and the dot product representation (because a
truncated sequence is almost as valuable as a non
truncated one). We then used the properties of the
maximization problem of the social planner as well as of
the consumer and produders to establish a complete
characterization of the price system in terms of
marginal conditions in preferences and technologies.
- We talked about how to establish
existence and uniqueness of a unique Pareto optimum
(that solves a social planner's problem). We also talked
about 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 growth model and showing how it maps into
the tools of General Equilibrium.
- 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 defined the commodity
space, and the consumption and production possibility
sets. We then defined Arrow Debreu Equilibrium.
complements 704 in its objectives. The order of the
numbers is irrelevant. Essentially, 702 and 704 run
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
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 within specific due dates. While
they are required and have to be submitted to the TA's
they will not be all individually graded. Some random
subset will do but they will not be returned. Answer
keys will be posted after they are due and this is the
mechanism through which you can assess your
progress. The homeworks may count for up to 15% of the
grade. 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
the grades will be based on one or two midterms and a
final (that will take place simulataneously with the
2006 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 responsible for giving you feedback regarding the
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
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
We will use
some bits and pieces of various textbooks. They include
1987], [Stokey and Lucas,
1989], [Cooley, 1995],
[Ljungqvist and Sargent,
2004]. 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
List of Material to Cover.
Equilibrium. What is its meaning.
equilibrium in the growth model. Taking advantage of
the welfare theorems.
[ Stokey and Lucas, 1989],
Chapters 15 and 16; [Harris,
1987], Chapters 3 and 4; [Cooley and Prescott,
- Arrow Debreu.
- Sequence of Markets.
- Recursive Competitive
- A stochastic version of the
growth model. What are complete markets? What are one period ahead
equilibrium in stochastic growth model
endogenous labor choice.
Economies. Sequence of Markets and Recursive Equilibrium.
with public expenditures, income taxes and a period by period balanced
economy with public expenditures, income taxes and a present value
balanced budget constraint.
Finance and asset pricing. What is Lucas tree model and how to
price an arbitary asset. 
Multiple Agents Complete Markets Economies.
economy with two types of agents differing in skills and/or wealth.
- A two
- 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.
- 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 Krusell-Smith solution.
The Moody Government
solution. [Diaz-Gimenez et al., 1992].
Transition and Policy
[Huggett, 1993]; [\.Imrohoroglu, 1989]; [Diaz-Gimenez
et al., 1992]; Diaz-90; [Ríos-Rull, 1995].
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
Economy with Two-side Lack
Economy with Lack of
and Sargent, 2004] [Attanasio and Ríos-Rull, 2000]
The Abreu-Pierce and
and the Marcet-Marimon approach. [Attanasio and Ríos-Rull, 2000]
[Kehoe and Perri,
Optimal Contracting.  and
Limited information. [Atkeson and
Endogenous default. [ Chatterjee et al., 2004].
Epstein-Zin recursive utility. .
and Sargent, 2004]
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
et al., 2004]
- 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
- [Ljungqvist and Sargent, 2004]
- Ljungqvist, L. and Sargent, T. (2004). Recursive
Macroeconomic Theory, 2nd Edition. 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.
from T E X
H, version 3.54.
On 11 Jan 2006, 13:28.