Department of Economics University of Minnesota
Phone-(612) 625-0941 4-101 Hanson Hall (off 4-179) Fed
Phone (612) 204-5528 1925 Fourth Street South Fax: (612)
624-0209 Minneapolis, MN 55455
Department of Economics, University of Minnesota,
Tue and Thursday 14:30-15:45 Hanson Hall 4-170. Off Hours:
Before and after class and by appointment.
Fax: (612) 624-0209
Fed Phone (612) 204-5528
TA, Zhifeng Cai,
firstname.lastname@example.org, Office: 3-131 Hanson Hall Office
hour: Friday 0900-1100 or by walk in Link to which notes
will be posted: Recitations: Tuesdays 1600-1715 at HMH
I described the course. I discussed
some context of what are the main facts over which macro has
to be organized around. I discussed what is the meaning of
an equilibrium (a mapping from environment to
allocations). We 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 construct an
Arrow Debreu Equilibrium for the workhorse of macro, the
growth model, using the welfare theorems. We then see how to
build a sequence of markets equilibrium out of an
Arrow-Debreu equilibrium (and viceversa). We 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 recursively. We then defined Recursive
Competitive Equilibrium. We started with that of arbitrary
expectations and moved on to a rational expectations
March 26 Recitation time.
I posed a stochastic
version of the recursive competitive equilibrium using state
contingent capital to be delivered BEFORE production next
period which, using the no-arbitrage condition that puts
constraints on the sum of the state contingent prices. I
asked how to construct a Seq of Mark equilibrium from an
Arrow Debreu and viceversa, and how to transform the prices
from one space to another. We did various examples of
recursive equilibrium (leisure). I then described how to construct a
sequence of markets from a RCE and talked about the problems
for the reverse. I started describing equilibrium of
economies where the welfare theorems are of no use. First, a
government financing a public good with capital income
taxes. We started discussing the problem of debt.
We continued with RCE and in particular
with the problem of the government with debt and how to deal
with the no Ponzi scheme condition in recursive
environments. In doing this we talked about what
constraints do current debt and wealth pose on policy. We
look at other environments where the welfare theorems do not
work. We looked at a "keeping up with the Jones" environment
and at a "catching up with the Jones" environment. We
started discussing how to pose the equilibrium of an economy
where firms own the land and the capital and households own
We finished the problem of the firm with
land. We started with agents differing in wealth in a model
wihout leisure, and move to having them differ in wealth and
efficient units of labor. We then looked at an economy with
two countries and what does this mean.
April 2 Recitation time
We looked at the Lucas
tree economy where the only important thing is to find
prices. We went into many details of how to characterize
the RCE and what are its FOCs. We obtained formulas for the
price of the tree that satisfy a certain functional equation.
We started with the Lucas tree with demand contributing to
We continued with the problem with the
Lucas tree and demand contributing to productivity. We
obtained the Euler equation of the household (with some
mistakes that we will fix the following class).
We discussed the endogenous productivity
with product search in a version of the Lucas tree model
with competitive search. We arrived at the equilibrium of
this economy. We saw the optimality of this equilibrium.
I discussed random search in the
endogenous productivity Lucas tree model. We started
discussing measure theory.
We finished discussing measure theory
and we started Industry equilibria.
We finished Industry equilibria and
started the Aiyagari economy.
We had the midterm.
We talked about the incomplete markets
economies. First, without markets, then the Huggett economy
and then the Aiyagari economy. We described existence of a
unique stationary equilibria and existence of a steady state
that required the finding of a zero of a market clearing
equation. We talked about assessing policy changes in the
We talked about assessing changes and
computing transitions in the economies with measures of
agents. First, those without markets, and then those with
markets. We started growth theory. We went over the AK
model, the model with externalities in capital, and the
humand capital, two sector, growth model. We discussed what
it takes to grow. We started posing the Romer endogeneous
growth model with R&D.
We solved the Romer endogeneous
growth model with R&D. We finish the class discussing a
bit of search theory, whether a worker should take a job or
not. We also talked about some other issues in unemployment
and job search. This finished the course.
We will have the final.
This course complements 8105-8107. 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. Zhifeng 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 Zhifeng 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. 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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