Victor teaches Mon and Tue (26 and 27), Jinfeng Wed (28)
What we are doing each day.
March 28 .
Jinfeng will discuss additional problems.
March 27 .
We continue with the Lucas Tree.
March 26 .
We look at a two country economy. We
start the Lucas tree.
March 21 .
Cancellation due to snow.
March 20 .
Jinfeng discussed the economy with land
and answered many questions.
March 19 .
We look at externalities and more than
one type of agent.
March 14 .
We finish the economy with debt.
March 13 .
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. 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.
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 discuss 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
talk 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 recursively.
We define Rational Expectations Recursive Competitive Equilibrium
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 be take place during the prelim and 10% on class
participation. Jinfeng 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 Jinfeng 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.
Review: Neoclassical Growth Model
The Neoclassical Growth Model Without Uncertainty
A Comment on the Welfare Theorems
Recursive Competitive Equilibrium
Economy with Government Expenditures
Lump Sum Tax
Labor Income Tax
Capital Income Tax
Taxes and Debt
An Economy with Capital and Land
Adding Heterogeneity (Wealth, Skills, Countries)
Shocks, Markov Processes, Complete and Incomplete Markets
Asset Pricing: Lucas Tree Model
The Lucas Tree with Random Endowments
Endogenous Productivity in a Product Search Model
Business Cycles in this Model
A Simple Dynamic Environment
Introducing Exit Decisions
Incomplete Market Models
A Farmer’s Problem
Endogenous Growth and R&D
The notes are the evolution of class notes by many students
over the years, both from Penn and Minnesota including
Makoto Nakajima (2002), Vivian Zhanwei Yue (2002-3), Ahu
Gemici (2003-4), Kagan (Omer Parmaksiz) (2004-5), Thanasis
Geromichalos (2005-6), Se Kyu Choi (2006-7), Serdar Ozkan
(2007), Ali Shourideh (2008), Manuel Macera (2009), Tayyar
Buyukbasaran (2010), Bernabe Lopez-Martin (2011), Rishabh
Kirpalani (2012), Zhifeng Cai (2013), Alexandra (Sasha)
Solovyeva (2014), Keyvan Eslami (2015), Sumedh Ambokar
(2016), and Omer Faruk Koru (2017).
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 University Press.
LUCAS, R. E. (1988): "On the Mechanics of Economic Development,"
R. SHIMER, AND
R. WRIGHT (2005):
"Search-Theoretic Models of the Labor Market: A
Survey," Journal of Economic Literature, 43,
P. M. (1986): "Increasing Return and Long-run
Growth," 94, 1002-36.
P. M. (1990): "Endogenous Technological
Change," 98, S71-S102.
N. L., AND
E. C. LUCAS,
R. E. WITH
PRESCOTT (1989): Recursive
Methods in Economic Dynamics. Harvard University