Department of Economics University of Pennsylvania. 507
Mon and Wed 10:30-12:00 McNeil 309. Off Hours:
Before and after class and by appointment.
TA, Sumedh Ambokar
firstname.lastname@example.org The recitation is on Mondays,
Room 395 in McNeil Building from 3.30 pm to 5 pm. His
office hours are office hours will be on Tuesdays 1-3 pm
in my office room 452.
We will have a test on the last day of class. A preview of
I described the course and discussed
some context of what are the main facts over which macro has
to be organized around:
output per capita has grown at
a roughly constant rate
the capital-output ratio (where
capital is measured using the perpetual inventory
method based on past consumption foregone) has
remained roughly constant
the capital-labor ratio has
grown at a roughly constant rate equal to the growth
rate of output
the wage rate has grown at a
roughly constant rate equal to the growth rate of
the real interest rate has been
stationary and, during long periods, roughly constant
labor income as a share of
output has remained roughly constant
hours worked per capita have
been roughly constant.
I discussed what restrictions do these facts pose on the models
that we use.
I discussed some of the limitations of this point of view.
I also discussed what is the meaning of an equilibrium (a
mapping from environment to allocations) and then talked
about why the social planner problem may be a problem whose
solution is interesting (it is because it is the unique
equilibrium of the economy once we use the welfare and other
theorems). We talked of how an Arrow Debreu Equilibrium for
the growth model, supports the social planners solution
using the second welfare theorem. I refer to how to build a
sequence of markets equilibrium out of an Arrow-Debreu
equilibrium (and viceversa) and argue that we can then solve
for Social Planner problem sometimes, but that we do so
using recursive methods (dynamic programming). Why not then
always recursive methods? This is to define equilibria
March 14 .
We defined Recursive Competitive
Equilibrium. We looked both at rational expectations
equilibria and at recursive equilibria with arbitrary
I went over the role of the first
welfare theorem (to yield uniqueness). I defined a
Markovian stochastic process with finite support. I defined
sequence of markets equilibria with complete one period
ahead Arrow securities. I defined recursive compet. eq. for
a stochastic economy emphasizing market completenes, and
state contingent markets to deliver capital.
There will be two recitations by
Sumedh. He will go over the details of the construction of
the Arrow Debreu equilibria from the social planner's
solution and also on the equivalence of Arrow Debreu and
sequance of markets equilibria.
I continued to describe equilibrium of
economies where the welfare theorems are of no use. A
government financing a public good with lump sum, labor and
capital income taxes, and then with debt. We clarified some
I described in detail the equilibrium
conditions of RCE with debt, especially those that deal with
the no Ponzi scheme condition in recursive environments. We
view economies with two types of agents in deterministic
environments. These agents differ in wealth or skill levels,
or there are multiple countries. We did this in deterministic
I finished the lstudy of RCE by looking
at a stochastic environment with valued leisure with two
types of agents that differ in labor efficiency. We went
over the Lucas tree economy and we priced trees, state
contingent goods and options.
We viewed stock returns and the risk free
rate. We started looking at search frictions in the goods markets.
We finished the discussion of the
equilibrium conditions in the Lucas tree with search
frictions and competitive search. We started measure
We went over measure theory and talked
about the meaning of stationary distributions both from the
point of view of describing the stochastic properties of a
system and for describing heterogeneous objects. w
We started Industry Equilibria.
We finished Industry Equilibria by
looking at an economy with adjustment costs to labor.
We started an economy with
idyosincratic shocks to household's income and incomplete
markets. We reviewed the case of agents that do not trade
with each other and the case where agents borrow and lend
from each other (The Huggett Economy).
We went over the Aiyagari economy where
the incomplete markets economy is built on top of a growth
model. We then talked about what happens when we are not in
a stationary equilibria by talking about transitions and the
full recursive equilibria. We made very clear the extent
that one can talk about optimality. We also pointed out the
usefulness of environments where agents are not fully
rational but where being more rational does not pay.
We will have a test.
This course complements the rest of 702-704. In my view, the
ultimate goal of this course is to learn to use a variety of
models that can be used to give quantitative answers to
economic questions. The models can generate artificial data of
both allocations and prices that can be meaningfully related
to actual data. In this course most (if not all) of the
material will be studied from the strict point of view of the
theory, so we will not look at data in any serious manner nor
at solving the models with the computer. The emphasis is
on economic rigor, i.e. the target is to learn tools
that will be useful later. The course, then, is not a survey
of topics in macroeconomics. When some specific topic is
addressed the objective is not to give 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.
Homeworks and Grades
In the context of the course, I will assign some
homeworks: usually I will ask you to prove something during a
lecture, sometimes they will be posted in the homepage. These
problems are not required but will give you an idea of what is
expected for the exams, and especially for the prelim. The
grades will be based 30% on a midterm, 60% on a final that
will take place the last day of class and 10% on class
participation. Sumedh will give you feedback regarding the
He may post them on the web as well as post answers to it at a
later day. Or he may not. We will see about it.
Textbooks and papers
No special textbooks. There are notes from
previous years and Keyvan may post class notes of this year's
class. It never hurts to have the usual suspects, but I do not
dwell on them. Besides those used and recommended by my
colleagues, there is a good little book (out of print
actually) that is useful,
. 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. A fantastic
book is being written now by Per Krusell. We will
ocassionally use bits of it.
First year is to learn tools, not to
Preliminary List of Material to Cover
This list is of material that I
want to go over. The first few items you have seen in a very
similar way, so I will go very fast over it, but I find it
very useful to go over them again.
Competitive equilibrium in the
growth model. Taking advantage of the welfare theorems.
Stokey and Lucas,
, Chapters 15 and 16; Harris, , Chapters 3 and
4; Cooley and Prescott,
A stochastic version of the
growth model. What are complete markets? What are one
period ahead Arrow-securities? How to define Competitive
equilibrium in stochastic growth model.
COOLEY, T. F., AND E. C. PRESCOTT (1995): "Economic Growth
and Business Cycles," in Frontiers of Business Cycle Research, ed. by
T. F. Cooley, chap. 1. Princeton University Press, Princeton.
HARRIS, M. (1987): Dynamic Economic Analysis. Oxford
LUCAS, R. E. (1988): "On the Mechanics of Economic Development,"
ROGERSON, R., R. SHIMER, AND R. WRIGHT (2005):
"Search-Theoretic Models of the Labor Market: A Survey," Journal of
Economic Literature, 43, 959-988.
ROMER, P. M. (1986): "Increasing Return and Long-run Growth," 94,
(1990): "Endogenous Technological Change," 98, S71-S102.
STOKEY, N. L., AND E. C. LUCAS, R. E. WITH PRESCOTT
(1989): Recursive Methods in Economic Dynamics. Harvard University
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