429, McNeil Bdg,
Tfn: 2158987767
Fax: 215 5732057, or 215 5734217
http://www.ssc.upenn.edu/~vr0j/cc70207/
vr0j@econ.upenn.edu

Econ 702, Spring
2007
Professor
JoséVíctor RíosRull
Last modified: Mon Apr 23 14:00:27 Eastern Daylight Time 2007
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
Philadelphia, PA
19104 USA

Classes are T. and Th. 1:302:50 in 410
McNeil. Special Classes (rescheduled) may be M
3:305:00 or Fr 10:3012:00 in the Econ Conf
Room. Off Hours: Wed 2:30 to 3:30 and by
appt and after class.

T.As.: Se
Kyu Choi
and
Serdar Ozkan. Off Hrs:
Se Kyu Off Hrs: Se Kyu Mondays, 1012
(Mcneil 438) and Serdar Tue and Th 3:30 to 4:30 in
MCNeil 419.
Contingent time and place for teaching is Mon
5:00 to 6:30 in McNeil 169.


 What are we doing? Brief description of
previous classes and next one.
 Course Description
 Requirements and Grades
 Prerequisites
 Textbooks
 Preliminary List of Material
to Cover
 References
 Problem Sets
problems and solutions with due dates. Do not wait for
the posting to answer them.
 Class Notes taken
in class by Serdar and Se Kyu. Also last years by
Thanasis and Sekyu the previous years (Kagan, Ahu,
Vivian, and Makoto).
 Exams. There will be
one or two midterms. The final coincides with the 2007
May Macro Qualifying Examination.

What we are doing each day.
 We ended the course with a
discussion of how people both choose to have children (as in
the Alvarez model) and how do they choose partners. We
discussed a variety of issues that these models can address:
the fall in the marriage prevalence, the implications of
uneven numbers of each sex and the nature of interracial
marriage. This ended the course.
 We discussed models of mulitperson
households going over topics of what is marriage, how do
preferences change, how are assets split, who makes the
decisions in case of disagreement and so on. We also talked
about having health being a state variable and how to model
the investments (either in terms of goods or effort) in
health. This took us to the issue of the value of life.
 We build the growth model on
top of an OLG structure and discussed its recursive
representation. We started discussing some demographics
beginning with early death and of how to handle the assets
of the dead.
 We discussed the determination of
wages in the life cycle. We posed and characterized the
properties of various theories (hormones, learning by
doing, learning by not doing) and of what are the
implications for the allocation of consumption and of time
over the life cycle with constant interest rates. We
talked about non separability of utility and about
borrowing constraints. We also talked briefly about how to
model the education decision (whether by the agents or its
parents) and talked about possible theories of educational
attainment and what do they imply.
 We looked at the OLG model in its
simplest form. We discussed how different equilibrium
concepts fare and how is it that money can have value. We
then turned to discuss the role of the welfare theoremes
in this environment and of how to characterize the set of
monetary equilibria. We also pointed to the issue of what
is so special about the first old.
 We discussed the problem of one
sided lack of commitment, and how would an insurance
company effectively provide as much insurance as
possible. 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 posed and solved the problem of
an unemployed agent that optimally chooses search effort
to find jobs and discussed how is it that a
planner would consider helping him.
 We finished the Romer model with
product development and the growth part of the
course.
 We looked at the model with
externalities and started the Romer model with product
development.
 We looked at
exogenous productivity growth, its balanced growth path and
how to transform the economy so that it looks like a non
growing economy that is easy to work with. Then we looked
at the AK model, discussed its lack of transitional
dynamics. We finished with a discussion of how models with
human capital may look like the standard growth model (if
there are limits to its accumulation with goods) or like
the AK model (if it can be accummulated without decreasing
returns).
 We finished talking about the
Aiyagari economy and associated transition and welfare
issues. We also discussed how it works with leisure and
whether the calculation of a stead state is a one or two
equation/s (and unknown/s) system. We started talking about
growh. First, with population growth.
 We continued with the Huggett
economy. We defined equilibria, talked abouot existence
and discussed how to compute some statistics about the
economy. We briefly mentioned how difficult is to talk
about non steady states in this economy. We started the
Aiyagari economy.
 We started the problem of the
household with linear saving technology and talked
about why there are bounds on the amount of assets that
it holds as long as beta / q < 1. We also constructed
.
 We finished industry equilibria
looking at economies where there are adjustment costs to
both labor and capital. We then talked about how to model
the problem of a single agent facing stochastic endowment
and a linear storage technology.
 Midterm.
 We continued to look at industry
equilibria, now with endogenous entry and exit. We looked
at other important theoretical concepts such as a
transition function and the
updating operator.
 We started to look at economies with measures
of agents. We looked at the concepts in measure
theory that we use (what is a measure, a sigma algebra a
measurable function) and we defined industry equilibria.
 We finished the Lucas tree and
pose homeworks that define the big questions in macro so
we can get an idea of their relative importance. The
homeworks are about measuring the welfare costs of various
things:
 Amount of risk aversion needed to account for the
equity premium.
 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 talked about
stochastic environments in Recursive Equilibria and how
to post both securities that pay in terms of the
consumption good and those that pay in terms of capital.
We talked about the Lucas tree model and learned to
price assets (options). I asked the homework of
the equity primium and how to obtain it.
 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. We
also looked at an economy with a consumption tax, debt and
a government that spends some exogenous amounts of the
good. This finishes our discussion of Rec Comp Eq in
determinisitic economies.
 We reviewed again RCE by
posing first an economy where agents differ in
wealth. We used it to discuss the need to keep track of
the wealth distribution in the state vector. We then
turned to look at a two country world with perfect
capital markets and discussed how capital differs from
wealth. 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
each country. We also talked about the fact that there are
many ways to write down the recursive problem but that
one needs to be consistent.
 We reviewed the notion of
Recursive Competitive and discussed existence and
uniqueness both when it is optimal and when it is not. We
then extended to environments with leisure and with a
public sector with and without government expenditures
affecting utility and with and without lump sum
taxation. We started discussing the ingredients of a
multiple agent type RCE.
 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 wend on to define recursive
equilibrium with arbitrary expectations and with perfect
foresight or rational expectations.
 We went over valuation equilibrium
and sequence of markets equilibrium in stochastic
environments.
 We talked about
how to get the valuation equilibrium with a dot product
representation. Then we completely characterized the prize
sequence in terms of the properties of the allocation that
solved the social planner problem. We then defined a SME,
by having markets for current goods and for loans open
every period and by adding budget constraints for each
period and talked about how to proof equivalence between
the two equilibrium concepts (which I asked as a
homework). Finally, we started to talk about stochastic
environments.
 We defined a utility function over
the consumption possibility set and we defined the production
possibility. We defined valuation equilibrium. We then
stated the welfare theorems and uniqueness of the Pareto
Optima. We talked about sufficient conditions for a
Quasiequilibrium with Transfers to be a valuation
equilibrium. We then stated the Prescott and Lucas 71
result for having the price functional have an inner
product representation. We then moved on to map the growth
model into the structure of a valuation equilibrium to be
able to use the welfare theorems.
 We went over the homepage
contents. We also talked about the differences between
equilibrium and Pareto Optima and what role does the
latter play in Macro. We argued that an
equilibrium concept is aa the tool to pick outocomes
(allocations). We defined the commodity
space, and the consumption possibility set.
Course Description.
This course
complements 704 in its objectives. The order of the
numbers is irrelevant. Essentially, 702 and 704 run
parallel.
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 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
exams.
In addition,
the grades will be based on one or two midterms and a
final (that will take place simulataneously with the
2007 June QUALIFYING EXAMINATION. The midterms counts
for one third of the nonhomework 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
homeworks.
Prerequisites.
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 CassKoopman'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 historydependence. 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.
Textbooks.
We will use
some bits and pieces of various textbooks. They include
[Harris,
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
useful.
Preliminary
List of Material to Cover.

Equilibrium. What is its meaning.

Competitive
equilibrium in the growth model. Taking advantage of
the welfare theorems.
 Arrow Debreu.
 Sequence of Markets.
 Recursive Competitive
Equilibrium.
[ Stokey and Lucas, 1989],
Chapters 15 and 16; [Harris,
1987], Chapters 3 and 4; [Cooley and Prescott,
1995].
 A stochastic version of the
growth model. What are complete markets? What are one period ahead
Arrowsecurities?

Competitive
equilibrium in stochastic growth model

Models with
endogenous labor choice.

Nonoptimal
Economies. Sequence of Markets and Recursive Equilibrium.

An economy
with public expenditures, income taxes and a period by period balanced
budget constraint.
 An
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.
 An
economy with two types of agents differing in skills and/or wealth.
 A two
country economy.

Industry Equilibria

Exogenous Entry and Exit

Endogenous Entry and Exit

Endogenous Entry and Exit with Endogenous State
Variables

Growth:

Exogenous growth
 Transforming the economy
 The AK model: one and two
sectors.
 Externalities.
 Research and development
(Romer 86).
 Non balanced growth paths.
 Economies without Complete
Markets and with Large Numbers of SelfInsuring 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 nonstate contingent loan.
 A General Lack of Insurance
Model with Production.
 A General Lack of Insurance
Model with Aggregate Uncertainty and aggregate endogenous state
variables.

The mess.

The KrusellSmith solution.

The Moody Government
solution. [DiazGimenez et al., 1992].

Transition and Policy
Analysis.
[Huggett, 1993]; [\.Imrohoroglu, 1989]; [DiazGimenez
et al., 1992]; Diaz90; [RíosRull, 1995].

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 Oneside Lack
of commitment.

Economy with Twoside Lack
of commitment.

Economy with Lack of
Observbility.
[Ljungqvist
and Sargent, 2004] [Attanasio and RíosRull, 2000]

The AbreuPierce and
Stachetti aproach.

Constrained arrangements,
and the MarcetMarimon approach. [Attanasio and RíosRull, 2000]
[Kehoe and Perri,
1997].

Optimal Contracting. [] and
[Quadrini, 2001].

Limited information. [Atkeson and
Lucas, 1992].

Endogenous default. [ Chatterjee et al., 2004].

Recursive Preferences.
EpsteinZin recursive utility. [].
[Ljungqvist
and Sargent, 2004]

Models with demographic
detail.

Overlapping Generations with
many periods.

Overlapping Generations with
variable demographics.

A hybrid. The exponential
population, exponential aging, model.

Fertility in the utility.

Multiplicity of Equilibria.
References
 [Atkeson and
Lucas, 1992]
 Atkeson, A. and Lucas, R. E. (1992). On efficient
distribution with private information. Review of Economic Studies,
59:427453.
 [Attanasio and RíosRull, 2000]
 Attanasio, O. and RíosRull, J.V. (2000). On the optimal
provision of aggregate insurance in the presence of enforceability
problems in the provision of private insurance. Mimeo, University
College, London.
 [Chatterjee
et al., 2004]
 Chatterjee, S., Corbae, D., Nakajima, M., and RíosRull,
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.
 [Cooley
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
Press, Princeton.
 [DíazGiménez,
1990]
 DíazGiménez, J. (1990). Business cycle
fluctuations and the cost of insurance in computable general
equilibrium heterogeneous agent economies. Working Paper, Universidad
Carlos III de Madrid.
 [DiazGimenez
et al., 1992]
 DiazGimenez, J., Prescott, E. C., Fitzgerald, T., and
Alvarez, F. (1992). Banking in computable general equilibrium
economies. Journal of Economic Dynamics and Control,
16:533559.
 [Harris, 1987]
 Harris, M. (1987). Dynamic Economic Analysis. Oxford
University Press.
 [Huggett, 1993]
 Huggett, M. (1993). The risk free rate in heterogeneousagents,
incomplete insurance economies. Journal of Economic Dynamics and
Control, 17(5/6):953970.
 [\.Imrohoroglu, 1989]
 \.Imrohoroglu, A. (1989). The cost of business cycles with
indivisibilities and liquidity constraints. Journal of Political
Economy, 97(6):136483.
 [Kehoe and
Perri, 1997]
 Kehoe, P. and Perri, F. (1997). International business cycles
with endogenous incomplete marjets. Working Paper, Federal Reserve bank
of Minnepolis.
 [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
renegotiationproof contracts with moral hazard.
 [RíosRull,
1995]
 RíosRull, 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.
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