Endogenous Growth: AK model,
externality model, human capital model. An endogenously
growing economy with monopolistic competition and R&D.
April 24 .
An economy with a distribution of
wealth and wages. The problem of transition and of aggregate
April 19 .
The farmer's problem. The Huggett and
the Aiyagari Economies.
April 17 .
Statistics with Measures and Industry
Equilibria with Endogenous individual State Variables.
April 12 .
Equilibrium with shopping. Finished
Measure Theory and Most of Industry Equilibria.
April 10 .
The first order conditions of the
shopping and the beginning of measure theory.
April 5 .
We look at the Lucas tree with
endogenous productivity. The first order conditions are left.
April 3 .
We had the midterm.
March 29 .
We finish the two country economy. We
go over the Lucas tree economy and we price trees, state
contingent goods and options.
March 27 .
We finish the economy with debt. We look
at externalities and more than one type of agent. We looked
at a two country economy.
March 22 .
We continue 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.
March 20 .
We add uncertainty and talk about what
complete markets mean and how to deal with them in Rec Comp
Eq. We discuss the role of Arrow securities. We pose a
government that spends.
March 15 .
We construct sequence of markets eq
from an Arrow-Debreu Eq. We then define Recursive
Competitive Equilibrium. We look both at rational
expectations equilibria and at recursive equilibria with
I describe 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
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 Omer 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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