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
notes taken in class and posted by Sasha
What we are doing each day.
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 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 welfare theorems. I referred to
how to build a sequence of markets equilibrium out of an
Arrow-Debreu equilibrium (and viceversa) and argued 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.
March 25 Recitation time.
We then defined Recursive
Competitive Equilibrium. We started with that of arbitrary
expectations and moved on to a rational expectations
equilibria. I went over equilibria with valued leisure
emphasizing always what are the state variables. I talked
about the 3 equations of macro and of how the fail (or not)
to account for business cycles. I then defined a Markovian
stochastic process with finite support.
I defined recursive compet. eq. for a
stochastic economy emphasizing market completenes, and state
contingent markets to deliver capital. I then started to
describe equilibrium of economies where the welfare theorems
are of no use. First, a government financing a public good
with capital lump sum taxes and then with income taxes. We
started talking about the state variables of the economy
when the government issues debt.
I went over the economy with government debt
and how to deal with the no Ponzi scheme condition in
recursive environments. In doing this we talked about what
are the constraints that current debt and wealth pose on
policy. We discussed how to pose the equilibrium of an
economy where firms own the land and the capital and
households own the firms.
We continued looking at environments where
the welfare theorems do not work. We look at a "keeping up
with the Jones" environment and at a "catching up with the
Jones" environment. We will also looked at economies with
agents differing in wealth in a model wihout leisure, and
discussed how to write the model if agents differ in wealth
and efficient units of labor. Then we looked at an
economy with two countries and what does this mean.
We will wrote the two country model this
time with aggregate shocks with households owning their own
capital but trading state continget shares which allows them
to differ in wealth. We started discussing the
Lucas tree model of asset pricing building the Arrow-Debreu
prices and the determination of the price of the tree in a
recursive equilibrium. We obtained formulas for the
price of the tree that satisfy a certain functional equation.
We priced all kinds of assets
(options, futures) in the Lucas tree. We started
with the Lucas tree with demand contributing to
productivity. We discussed the endogenous productivity
with product search in a version of the Lucas tree model.
We discussed the Lucas tree with
demand contributing to productivity with competitive
search. We arrived at the equilibrium of this
economy by constructing the two functional equations that
determine price and market tightness.
We saw the optimality of Competitive
search equilibrium. I talked briefly about other search
protocols such as Nash bargaining. We rapped up Lucas trees
with search frictions and we started measure theory.
We will continue with the basics of measure theory and go on
to start industry equilibria.
We had the midterm.
We finished Industry
Equilibria (stationary equilibria, adjustment costs) and we
started the standard incomplete markets problem.
We continued the study of the standard
incomplete markets problem by looking at general equilibrium
versions of it. We started growth.
We finished growth by looking at the Rohmer
R&D model. And I talked briefly about the Piketty
stuff. This finishes 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. Sasha 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 Sasha 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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