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.
Homepage
http://www.econ.umn.edu/~vr0j/index.html
Wed 3:45-6:15 Hanson Hall 4-170. This is a mini course
that will last all semester so some classes will be
shorter, others will be cancelled. The whole teaching time
will be no less than a regular mini course. Off Hours:
Before and after class and by appointment.
email:
vr0j@umn.edu.
Please plan to come and talk to me individually to
tell me which homework are you the proudest of. Any time
that I am around is good.
The Aiyagari calibration homework is ready.
A preliminary version of the
Syllabus. It is very likely that it
will change. I will update it.
Other relevant links.
Here you may find an occasional
paper, homepage or subroutine of interest.
What are we doing?
A class by class diary.
Sept 5.
We talked about the class, and what it
is about, going over all the details. We started with a
discussion of what is the meaning of an approximation to
a function and the criterias (family of approximating
functions, criteria of distance, and method to find it)
that are used to describe a particular approximation
approach. We then went in detail over the first set of
homeworks and its purpose. We finished with a discussion
of the Solow residual. This included the components of
GDP on the income side (and I forgot the difference
between GDP and GNP, this is the payments to foreign
factors net of payments to national factors from abroad
that is also ambiguous). You should read the
Cooley-Prescott chapter on the Cooley book or the -
appendices
here
or here
for details of the construction of the Solow residual
needed to compute it.
Sept 19
We discussed how to use a model to
answer quantitative questions about the economy. In
particular, we talked about how calibration and
estimation operate, and what are their differences and
similarities. We put special emphasis in saying that
what matters is not the statistical techniques as much
as the sources of identification. I refer to the first 5
sections
of
this paper, but in particular, Section 3. Gero and
Arun presented some of the homeworkds (Thanks to
both). Arun will continue with the discussion of the
ordering assumptions in the VAR next class. We then
discussed the next batch of homeworks (and I want
volunteers to present some of them in the next class,
October 3). Such discussion involved a minimal
description of log linearization using dynare as well as
comments on the use of software to take derivatives and
on how to implement the notions of calibration discussed
at the beginning of hte class. While doing this, we
talked about how to calibrate a model economy so that
its steady state looks like the U.S. in the dimensions
that we want. We may start the discussion of global
approximation methods using piecewise linear functions
with exact solution in the grid points.
Oct 3
Arun finished discussing
why some assumptions are made when estimating VARs
(Thanks Arun). Zhifeng presentd the gist of homework 8
and some of the subtle issues that arise (Thanks
Zhifeng). I discussed how to do global approximations
and what do they mean. In particular, I went over
the endogenous grid method. This
paper is a great reference to a particularly
efficient way to obtain a global approximation.
Oct 10
George presented the
endogenous grid method. I then discussed how to adapt
the problem to the Aiyagari economy given its specificities.
Oct 17
Gero and Zhifeng presented
the problem of solving for the Aiyagari decision rules
using endogenous grid methods. Thanks to both. I then
discussed how to store the distribution of types in the
Aiyagari economy using both a large sample of agents and
approximating the cumulative distribution function. I
then talked a bit about Markov perfect equilibria in a
growth model with a public good.
He discussed the mechanics of the CPS.
The organization of the survey with rotating groups and
why "outgoing rotation groups" are special The
supplements, e.g. Displaced Workers and March How hours
are tricky between "actual" and "usual" How employment
status definitions are nuanced and changes by
year
He talked about using the cross-sectional data to
create synthetic panels. He also talked about Autor,
Katz and Kearney (2006) and Juhn, Murphy and Pierce
(1993). He went over about chaining the CPS to get
month-over-month data such as employment status
transitions.
CPS data can be found in three locations
Went to the NBER website and looked at their
chaining programs.
Went to IPUMS for their integrated data, mostly
e March Files.
Went to CEPR data where they have a collection of
the "outgoing rotations groups".
Then he talked about the CEX and SCF.
The SCF website was used to look at some figures
from the 2009 SCF follow-up of the 2007
wave.
He talked about using of panel data. He described
cohort,time and age effects and how fixed effects are
good.
He discussed the mechanics of the PSID: The
individual and family files "line number"
identifiers Occupational codes are relatively
error-free.
He went to the PSID website and talked about
the short-comings of the search feature
He introduced the NLSY79 and NLSY97. He talked
about the ASVAB scores and other unique features.
The NLSY79 website was used to download
some data.
I talked about the SIPP, that it's monthly but
only for 4 years and described where to get it,
Oct 31
Gero and Zhifeng presented
the computation of the stationary distribution of the
Aiyagari economy using the two methods (approximation to
the cdf and a large sample). Thanks to both. I then
discussed how to solve for the steady state of the
Aiyagari economy which involves finding the equilibrium
capital output ratio. From there we discussed some
policies and how to compute a steady state that also
involves a period by period balanced budget
constraint. In this context I showed how steady state
comparisons, while informative about the long run
properties of the economies, do not tell us anything
about welfare. For this we need a transition. I then
asked you to pose a strategy to solve for such a
transition starting with the economy that has no taxes
to another that poses every period a 20\% labor income
tax that is redistributed lump sum, and then to talk
about welfare. I then discussed the
Krusell-Smith method to solve for equilibria
of economies with distributions as state variables when
predetermined variables are sufficient statistics for
current prices. I finished by developing the Generalized
Euler Equation of the Markov perfect equilibrium of an
economy with hyperbolic discounting and how it poses
difficulties to calculate the steady state.
Nov 7
Joao talked about the Fella
paper on solving problems with continuous and discrete
variables. We discussed the intricacies of this problem
which are many. I then discussed solving the hard Krusell
Smith problem, when predetermined variables are not
sufficient statistics of prices (we will also see an
intermediate case with two predetermined state variables).
Nov 21
Joao, Richard, and Radek
did various nice presentations about the homeworks and the
Fella paper. Thanks to all. We are still struggling with
the details of the very difficult, but fascinating, Fella
paper. Another thing that we still have to clarify is how
to approximate aggregate capital in the decision rule of
agents when using the JPE Krusell Smith approximating
method. I started talking briefly about parallel
computing, especially MPI. This was enough about it
Nov 28
Radek finished the
Krusell-Smith I approximation. Zhifeng discussed the
Krusell Smith II approximation when predetermined
aggregates are not sufficient statistics to prices. Thanks
to both. I discussed how to solve n equations with m<
n+1 unknowns. By minimizing (or finding a zero of) a
function of various variables. I discussed various forms
of doing so speaking badly of Newton-Rapson and Nelder and
Mead.
Dec 5
Kai will deal with how to
solve hyperbolic discounting type problems where the
derivatives of equilibrium functions are in the Euler
equations. Rocio will talk to us about how to use both
values and derivatives to construct approximations to the
value function
using this
paper for the three country example . I may talk
about how to solve for problems when the value functions
are not even continuous (marriage). This finishes the
class.
Course Description
The target of this course is for you to be able to go to a
macro seminar and to realize after the layout of the model
that you are able to solve it, and relate it to data, probably
much better than the presenter.
This course can be thought of as an addendum to the Macro
sequence, it follows naturally after 8105-8108. Its purpose is
to learn the map from models to data, i.e. to answer
quantitative questions that we are interested in (in the
process of doing so, some interesting theoretical questions
arise). We will develop tools by stating general questions,
and then discussing how to approach its answer. The tools
that we will be developing beyond those already covered in the
first year can be grouped into:
Theoretical tools. While most of
the necessary theoretical tools have been acquired in the
first year, we may on occasion develop some additional
theory to look at a particular issue. We will use
representative agent models, models with a continuum of
agents represented with measures, overlapping generations
models, as well as models where agents form households. We
will look at models where equilibria are optima and where
they are not. We will look at stationary and
non--stationary equilibria. We will look at models without
perfect commitment and without perfect
information.
Empirical tools. A necessary
condition to be able to do applied theory is to be able to
characterize some properties of the world. This involves
the capability of accessing data sets and of understanding
the way they are organized as well as the principles that
guide the construction of the main data sources. This
requires some knowledge of NIPA and of some software to
read data (eviews, stata, gretl, R).
Computational Tools. Students should
be able to construct and characterize the properties of the
equlibrium allocations of artificial model economies. This
is the main element of the course and where you will spend
most of the time.
Calibration. We will spend a good
deal of time thinking of how a model is related to the
data. This is, I think, the more important part of the
learning process.
This is a Ph.D. course not a Masters course. As such students
are not expected to learn what other people have discovered, but
the tools that are needed in order to discover things by
themselves. Because of this reason the active work of the
students is crucial to achieve the objective of mastering the
tools that are described above. This is a course to learn to do
things, and, therefore, it requires to do some things.
Every class except the first one we will devote the first
twenty minutes or so to students presentations of
homeworks. I expect professional competence in this regard.
Course Requirements
There are various types of requirements that are a necessary
part of the course, all of which are pertinent in order to
achieve fulfillment of the course goals. This course believes
drastically in Learning by Doing but, on the other hand, you
are adults.
Regular Homeworks.The ones posted
here. Full credit only if on time. Partial credit otherwise.
Students will place the solution to the homeworks and to
other requirements in electronic form. You have to send an
email ASAP to help@cla.umn.edu stating your name and
university email and username and that you are in my course
to have access to a directory named /pkg/econ8185 and a
subdirectory your user name.
Class Presentations Every student
will make at least two class presentations with at least
one being of a subset of a homework. The first
presentation should take no more than 15 minutes and it
will be absolutely professional. Every second wasted,
every statement not planned, every bad thing will be
highlighted. The second presentation (that will depend on
class size and interests) maybe on a paper or on another
homework.
Referee Report. I will assign a
paper to each of you as we go along to write a referee
report and perhaps also to present the paper in no more
than 20 minutes. The refere report should be no longer
than five pages and should contain a clear and concise
exposition of the main points of the article as well as a
critical evaluation of the article's contributions. In
addition, you should write a letter to the editor with
your personal recommendations. If very good, I will use
them, anonymously.
Wikipedia Article. Optional, but
excellent training. This is something that should be done
by the end of the course. The moment you post it email me
and place a copy in your directory. Think of a topic of
the course no matter how silly.
Class schedules.
This class occurs mostly on Wed 10:00 to 1 in Hanson Hall
4-170 for the whole first semester. This is a mini length course
yet, the need for long homeworks on your regard makes advisable to
extend its duration. In addition, due to travels and other things
we will teach on other times whenever I am out of town on
Wednesdays. For the sake of paralellism, the main candidate as a
substitute is Monday. See this homepage for details.
What about knowledge of Computers?
This is not a course in computer languages so students are
responsible to learn to write computer programs. Students are
also responsible for learning their way around McNeil
computational facilities. I do not expect anybody to have a
computer at home or anything like that. It is better to work
in McNeill's computer room because you can talk to each other.
There are various general classes of computer languages.
Fortran 90. This is the best and more powerfull computer
language. Among economists very few prefer C. It is a little
bit hard at the beginning (you have to declare variables and
the like) but students have told me it is well worth to learn
as soon as possible. A very good introduction to fortran can
be
found
here.
MPI and open MP. This is the mother of all serious
calculations. It is a form of using f90 to parallelize code
and take advantage of various hardwares.
Matlab, Gauss, Scilab, Octave and R. These are very
popular packages in economics. They are relatively easy to
learn and code writing is easy. They generate a lot slower
code than F90 (about 100 times) but they are probably a good
choice to solve some problems. They may have an interface
with f90 but I have never seen it working. Matlab is by now
used in 90% of the cases. R and Octave are free. Dynare works
with Matlab and Octave and it is dumb simple.
Stata, Eviews, R, Gretl, and Maple, SAS. These are
packages best suited for reading data. State is the most
popular and expensive. (I have used fortran for this which is
insane, others have used Gauss). Still it is worth to learn
stata.
Mathematica and Maple. These are packages capable of
doing symbolic manipulation of equations. Occasionally they
can also be used to do numeric calculations. It does not hurt
to know them. They may work together with matlab and sciword.
Excel, open office Calc. A dirty thing to do fast data
manipulation. Perfect for grades. And to get output of
models. Calc is free and slow.
A program to write plots. Sciword does it as matlab and
excel and gauss. Some dinosaurs like me use gnuplot.
Students should be able to write code in F90 in addition to matlab
or gauss and to stata. Most students tell me in later years that I
should have enforced harder the learning of F90, but I am willing
to consider exceptions. If somebody has a serious reason not to
use F90, please come and talk to me. At least one homework should
be answered in f90.
Grading Rules
To satisfactorily complete the course, students have to do the
requirements well.
For those that do not register but take the course, I recommend
that they do the homeworks. We learn to solve problems by facing
them. Learning jointly with others greatly speeds the process.
Cooley and Prescott,
[1995]. It is now dated but it contains some important
lines of attack on business cycles. The computational
techniques are a little bit obsolete, but the questions less
so.
Judd, [1998].
is a general computational textbook with special attention
to economists. While it is short on some details that we
care about (complicated equilibrium considerations,
multidimensional value functions, multidimensional
interpolation) it is a very useful book for many topics.
Marimon and Scott,
[1998]. It has a bunch of chapters that deal with
specific problems. I find the continuous time chapter nice
as well as some scattered other chapters.
Miranda and Fackler,
[2002]. It is quite a nice book. Like others it is too
irrelevant in some places and too easy in others. It is
designed for matlab which is a pity, but it has a nice
implementation (via a <a
href="http://www4.ncsu.edu/unity/users/p/pfackler/www/compecon/toolbox.html"
> downloadable toolbox</a>) of function global
approximations.
Heer and Maussner,
[2004].
This is a nice book with a lot more economics than the others. Its
consideration of the theory is closest to what we do. It has also many
examples. The codes can be found
here.