ECONOMICS 606, NEW TRENDS IN ECONOMIC THEORY, W.A. BROCK, SPRING, 2001
Remark 2: The topics below seem disparate and unrelated.
I shall show how a
few analytical principles organize the lot. There will
be some similarity
between the material of previous 606 courses but 606 S2001 will
contain much
more work on dynamical systems approaches to
learning and to design of
experiments following recent
work by CeNDEF
in Holland
(http://www.fee.uva.nl/cendef), as well as
recent work on systems with
multiple time scales and multiple "spatial" ("space" is
widely interpreted)
scales, as well as a detailed contrast and comparison of different
methods of
presenting "stylized facts." For example in much of natural
science it is
popular to present facts in the form of "scaling laws" but in
social science
it is popular to present facts in
the form of conditional predictive
distributions.
We shall also discuss complex systems approaches
to the analysis of time
series data and of panel data in an attempt to separate "spurious"
"spatial"
and temporal dependencies from "true" dependencies that have
some notion of
"multiplier." There will also be more attention
paid to the relationship
between dynamical systems phenomena such as bifurcations and jumps
caused by
presence of "multipliers" to assist identification
of such "endogenous
interactions" than recent work on identification of self selection
effects and
treatment effects which was treated in years before. This will
be a blending
of stochastic dynamical systems approaches with the review for the
HANDBOOK OF
ECONOMETRICS by Brock and Durlauf. Researchers
such as N. Bockstael of
University of Maryland, E. Irwin of Ohio
State (see the dramatic maps
generated by simulated urban/suburban interacting systems models compared
with
actual on E. Irwin's website) have recently taken interactive
systems models
towards exciting empirical applications. We shall cover
some of this new
work.
Remark 3: The topics below have become very popular,
not only because of
their intrinsic interest, but also because
of the recent entry of
"establishment" figures. The popularity is projected to
increase even more
due to recent empirical applications to issues of high political salience
such
as the control of urban sprawl. The purpose of this course is
to bring our
students to the research frontier as well as to inform our students
of recent
empirical applications as well as to suggest open research problems.
OVERVIEW
Since much of the material that I have taught
before in this course is
available elsewhere (Examples: Dynamic Programming is taught
in first year
macroeconomics, Stochastic Calculus and Stochastic Optimal Control
Theory is
taught in the Business School and the Math Department, Game Theory
is taught
by other courses here) I keep revamping this course to teach
material that
is not so easily available elsewhere on campus.
I will teach newer
methods that have become popular in recent years. I list
these methods and
topics below. The emphasis in teaching the
methods will be to isolate
potential PhD thesis topics. More will be said about this below.
Some major writers and/or sources are
included in parentheses beneath
each topic. However, these will be very
incomplete because, during the
course, I shall make up lists of current papers and their website locations
in
order to build the good research habit of drawing up a list of
high priority
websites and the havit of continuously monitoring these in order to
keep up in
today's fast moving research environment.
This course will be accessible to students
with preparation at the level
of "mature" first year graduate students in economics and business.
Hence, I
am choosing a mathematical level to widen the accessibility
of the course
compared to the past. I will also attempt to make the course
accessible to
students in other disciplines such as statistics, physics, biology,
ecology,
limnology, etc.
Since much of the material for the course
consists of current working
papers as well as many published papers, I will make much use of websites
and
other internet resources. I shall teach my
own favorite internet search
methods for framing a research topic and projecting potential
value-added of
the proposed topic before investing time on it. While this might
seem banal,
it is surprising how many people fail to do this and end up re-inventing
the
wheel. Students here have too many time committments to have
their research
time wasted on projects that have already been done by someone else.
This course will represent a good hunting
ground for potential thesis
topics because the new methods can be applied to
many different areas of
economics and finance. I shall try to outline potential
topics during the
lectures. For other students, the course will give a tour of
some interesting
scenery on the research frontier of economics. The course is
also designed to
be useful to advanced undergraduate students that are contemplating
academic
research careers.
The unifying concepts and tools of the course
will be: (i) stochastic
dynamical systems theory, (ii) self-organization theories
of the Santa Fe
Institute variety, and some of the tools being used
by papers posted on
websites such as "econophysics," "the New England Complex Systems
Institute,"
and many more, (iii) econometric methods
that stress heterogeneity.
Interesting material may be found by simply doing a netscape
search on the
words "econophysics," "complex systems," "genetic
algorithms," and other
jargon words from "complexity theory."
The Santa Fe Institute website
http://www.santafe.edu
is a good place to start looking at complex systems materials.
For applications of complex adaptive systems
ideas and related ideas to
ecological economics, see Carpenter, S., Brock, W., Hanson,
P., "Ecological
and Social Dynamics in Simple Models of Ecosystem Management," SSRI
W.P. 9905,
for ecology. For some mathematical tools and their applications,
see, Brock,
W., "Some Mathematical Tools for Analyzing Complex-Nonlinear
Systems," SSRI
W.P. 2020. SSRI Working Papers are available on the Sixth Floor
in the SSRI
Office.
AN OVERVIEW OF POTENTIAL TOPICS
I. Recent econometric and theoretical
modelling of Increasing Returns,
Threshold Effects, Interaction Effects.
(Anderson, Arrow, Pines, (1988), THE ECONOMY AS AN EVOLVING
COMPLEX SYSTEM,
Addison Wesley: Redwood City, CA. Brock, W., (1993), "Pathways
to Randomness
in the Economy: Emergent Nonlinearity and Chaos in Economics
and Finance,"
SSRI Reprint 410; Brock, W., (1991), "Understanding Macroeconomic Time
Series
using Complex Systems Theory," SSRI Reprint
392. Manski, C., (1993),
"Identification Problems in the Social Sciences," SSRI Reprint
409. Manski,
C., "Dynamic Choice in Social Settings," SSRI Reprint 408. A
main source of
recent work is Arthur, Durlauf, and Lane, eds., (1997),
THE ECONOMY AS AN
EVOLVING COMPLEX SYSTEM II, Addison Wesley: Redwood City,
CA.). Brock and
Durlauf "Interactions-Based Models," SSRI W.P. 9910.)
This material will be taught and used in
a rather different way this
year, than in past years. See the discussion below.
II. Neural Nets, Connectionist Networks, Bootstrapping,
Surrogate Data and
their relationship to other received methods in econometrics such as
nonlinear
least squares.
(Sullivan, Timmerman, and White, (1998), "Data-Snooping,
Technical Trading
Rule Performance and the Bootstrap," Department of Economics,
UCSD and LSE
Finance), Casdagli, M., Eubank, S., (1990),
NONLINEAR MODELLING AND
FORECASTING, Addison-Welsey: Redwood City, CA. Work of Halbert White
and his
students at UCSD on estimating neural nets using "Robbins-Monro"
procedures
and nonlinear least squares. Similar methods
are used in the adaptive
learning literature below.)
This year's 606 will also
discuss the problem of controlling for
data-snooping in econometric methodology in
general as well as in the
application of bootstrap-based specification tests (cf. Sullivan,
Timmerman,
and White). See also the discussion below on how this material
will be taught
and used this year.
III. Self Organized Criticality Models
(Bak, P., Chen, K., Scheinkman, J., Woodford,
M., (1993), RICHERCHE
ECONOMICHE. Krugman, P., (1995), THE SELF
ORGANIZING ECONOMY. Purpose:
Attempt to explain the evidence for long dependence in economic and
financial
data stressed by Mandelbrot and others. Recent articles
on SOC that are
mentioned in Per Bak's new book, HOW NATURE WORKS, Springer 1996 will
also be
covered. See also the ECONOPHYSICS website for much material
on SOC applied
to economics. See especially the joint
work of Martin Shubik of Yale
Economics with Per Bak of Physics.)
This year's emphasis will be to review high
points of the work posted on
ECONOPHYSICS websites as well as other related websites such as the
Santa Fe
Institute from the point of view of assisting the construction of
econometric
structures as discussed below.
IV. Econometric and Theoretical issues raised by the
possible presence of
chaos and other forms of deep nonlinearity in economic
and financial data.
The Problem of Detecting "Spurious" Nonlinearity in Data.
(NONLINEAR DYNAMICS AND ECONOMETRICS SPECIAL
ISSUE: JOURNAL OF APPLIED
ECONOMETRICS, December, 1992. Barnett,
W., Gallant, A., Hinich, M.,
Jungeilges, J., Kaplan, D., Jensen, M., "A Single-Blind Controlled
Competition
between Tests for Nonlinearity and Chaos," Washington University,
St. Louis
working paper. See William Barnett's website at Washington
University, St.
Louis for many interesting papers and well as useful links. Benhabib
J., ed.,
(1992), CYCLES AND CHAOS IN ECONOMIC EQUILIBRIUM, Princeton University
Press:
Princeton, NJ. Brock, W., Hsieh, D., LeBaron, B., (1991), NONLINEAR
DYNAMICS,
CHAOS, AND INSTABILITY: STATISTICAL THEORY AND
ECONOMIC EVIDENCE, MIT
Press: Cambridge, MA. Granger,
C., Terasvirta, T., (1993), MODELLING
NONLINEAR ECONOMIC RELATIONSHIPS, Oxford University
Press: Oxford. De
Grauwe, P., Dewachter, H., Embrechts,
M., (1993), EXCHANGE RATE THEORY:
CHAOTIC MODELS OF FOREIGN EXCHANGE RATES,
Basil Blackwell: Oxford. A
challenge to this literature is posed by Bickel and Buhlmann, (1996)
"What is
a Linear Process?" PROC.NAT. ACAD. SCI. USA,
Vol. 93, pp. 12128-12131,
December. BB argue that the closure of the set of ARMA
processes "under a
suitable metric" is "unexpectedly large" (Caution:
This is NOT the Wold
representation). Further work on this problem should
be at Peter Bickel
(Berkeley Statistics) and Peter Buhlmann's websites.)
This area has grown rapidly. I shall
pick highlights, teach the basics,
and show what still needs to be done. New work that
has become available
recently will be covered. The emphasis will be to inform
students on what
research problems are still open in this area and how it relates to
the recent
surge of interest in modelling "bounded rationality" and "process
approaches"
to economics rather than "equilibrium" approaches.
V. Complex Systems Modelling and Scaling "Laws"
(Stein, D., (1988), ed., LECTURES
ON THE SCIENCES OF COMPLEXITY,
Addison-Wesley: Redwood City, CA. Brock,
W., "Scaling in Economics: A
Reader's Guide," SSRI Reprint. Blake LeBaron's website at Brandeis
(http://stanley.feldberg.brandeis.edu/~blebaron)
LeBaron, B., 1999, "Volatility Persistence and
Apparent Scaling Laws in
Finance," (available at LeBaron's website).
ECONOPHYSICS website (see
especially the links to "minority games."))
Examples of Scaling "Laws" in economics and
finance: (i) Gibrat's Law of
firm size distribution, (ii) logistic "laws" of growth and
diffusion, (iii)
Pareto's Law of income distribution,
(iv) Mandelbrot's "self similar"
stochastic processes and "1/f" scaling in economics
and finance, (v) the
stylized facts of finance such as autocorrelation
structure of returns,
volatility measures, and volume measures across individual stocks and
indices,
(vi) the stylized autocorrelation and
cross correlation structure of
aggregative and less aggregated macroeconomic time series.
An attempt will be made to show what useful
insights can be learned from
locating scaling laws and how to
correct for improper treatment of
heterogeneity. In particular we will stress how "spurious"
"unconditional"
scaling "laws" can easily be produced from a system of individual
stochastic
processes relaxing to different stochastic steady states
(even though the
relaxation rate is the same for each process). This exercise
will stress the
importance of correctly controlling for heterogeneity.
Scaling laws appear
also in ecology and we will teach some of this material and draw lessons
from
it for econometric practice.
VI. Adaptive Learning
(T. Sargent, (1993), BOUNDED RATIONALITY IN MACROECONOMICS, Oxford
University
Press. Chen, X., White, H., (1994), "Nonparametric
Adaptive Learning with
Feedback," UCSD Working Paper. Holland, J., (1992), ADAPTATION
IN NATURAL AND
ARTIFICIAL SYSTEMS, MIT Press: Cambridge,
MA. CeNDEF experiments on
expectation formation as well as other CeNDEF research on bounded rationality.
Fudenberg/Levine's book, THE THEORY OF LEARNING
IN GAMES (1998), Larry
Samuelson's book on evolutionary games, Peyton Young's book on
evolution of
conventions in games, ECONOPHYSICS website (see
especially the links to
"minority games"), R. Selten's lab on strategy
experiments in oligopoly
theory, CeNDEF work on strategy experiments in other types of games.)
The basic first year courses say
little about dynamics and adaptive
learning towards a notion of "equilibrium." For example, Selten's
lab at Bonn
has recently shown that optimization appears to play
no role at all in
repeated oligopoly games (i.e. finite horizon supergames) with
small numbers
of players. Rather something somewhat like Axelrod's TIT-FOR-TAT
emerges as
players evolve "ideal points" and induce play towards them
by "measure for
measure".
First year courses say even less about any
kind of socially interactive
learning on any kind of network or Selten-like behavior
of players trying
to "train" each other towards a more cooperative outcome.
Since, much of economics is based on equilibrium
concepts which impose
restrictions on data which can
be tested and since introduction of
"disequilibrium" concepts such as adaptive learning introduces
extra "free
parameters," this imposes an even higher priority to discipline
theorizing by
data than usual.
Researchers here, at the Santa Fe Institute,
and other research centers
are trying to carry out this kind of research program consistent with
observed
"scaling laws" and observed estimated conditional distributions
in economics
and finance. We shall cover the basic methods and
highlights of this new
literature. We shall also review experimental results.
For example CeNDEF
has been using strategy experiments (originating
from Selten's work) to
produce a set of stylized regularities about
the expectations formation
process which is separated from other aspects of the game (such
as strategy
involved via sharing a market as in oligopoly games) via a special
design of
the experiment to "control-out" all other expects of the game except
for the
expectation formation process itself.
Research on the "El Farol"
problem (called the "minority game" by
physicists) has documented a "phase transition" and a "scaling law"
(cf. work
on the ECONOPHYSICS website by Robert Savit of the University of Michigan
and
many others). The parameters are "s" the "size of
brain" of each player
(measured by the size of the strategy set available to each player),
the "size
of the universal brain" (measured by the size of the universal set
Omega(m) of
potential strategies that could be played) and memory "m"
(measured by the
number of lagged observations allowed to be in each prediction function
which
describes each forecasting strategy). The focus of the CeNDEF
group is on the
dynamic evolution of adaptive forecasting systems whereas the focus
of Savit
et al. is on uncovering "scaling" relationships
and evidence of "phase
transitions" via computational experiments. There is
also analytical work
reported on the ECONOPHYSICS website.
We shall spend some time
comparing and contrasting these different
approaches to the modelling of adaptive learning as well as learning
what we
can from results reported from laboratory experiments around the
world. The
emphasis of this part of the course will be to develop
model systems that
replicate experimental results, but at the
same time develop analytical
methods for general use in this area.
Development of methods from natural
science in searching for useful
"order parameters" to uncover "phase transitions"
and "scaling laws" and
relating these to "scaling laws" from sampling theory in statistics
(such as
central limit theorems, Edgeworth expansions,
large deviations "scaling"
relations, breakdowns of central limit theorems
due to series of cross
correlations diverging) will be stressed.
We will stress the incentive differences
inherent in "small numbers"
adaptive (or other) "learning" situations of repeated play
in contrast to
"large numbers" situations of repeated play.
Selten's lab stressed the
inherent incentives of repeated "small numbers" play to "train" each
other to
reach a cooperative outcome. Such incentives will get smaller
as the number
of players increases because each player will
be increasingly unable to
capture the benefits of her own "training efforts" onto
the other players.
This relates to work on "evolution of norms and conventions" in Peyton
Young's
book.
As one varies the number
of players, the memory allowed in their
strategies, the size of their individual strategy sets and the
size of the
size of all potential strategies of fixed memory as well as other quantifiable
aspects of the game the "order parameter" approach suggests looking
for key
"order parameters" such that when an order parameter increases,
the system
goes through an abrupt change in dynamical behavior
(a "phase transition"
and/or a "bifurcation"). Analysis of continuous state space dynamical
systems
of increasing size creates a demand for analytic results
on eigenvalues of
dynamical systems of increasing size. Alan Edelman's
website at MIT Math
contains very nice papers on this problem (e.g. "circular
laws") which we
shall discuss.
Since we will be on new ground here, this
should be an exciting part of
the course.
VII. Cellular Automata, Ising Models, Spin Glass Models
(Mezard, M., Parisi, G., Virasoro, (1987), SPIN GLASS THEORY AND BEYOND,
World
Scientific. Durlauf, S. (1993), REVIEW OF
ECONOMIC STUDIES and various
working papers. Mitchell, M., Crutchfield, J., Hraber, P., (1994),
"Evolving
Cellular Automata to Perform Computations:
Mechanisms and Impediments,"
PHYSICA D, 75, 361-391. Doyon, B., Cessac, B., Quoy,
M., Samuelides, M.,
(1993), "Control of the Transition to Chaos in Neural Networks
with Random
Connectivity," INTERNATIONAL JOURNAL OF BIFURCATION
AND CHAOS, 3, #2,
279-291. Material on eigenvalues of large systems from Alan Edelman's
website
at MIT Math. Material from Jim Crutchfield, Melanie
Mitchell, and others
available by linking from the Santa Fe Institute's website.)
This material will give math modules from which
we can build models of
adaptive interaction and parse out the components due to socially
interactive
learning from "plain vanilla" adaptive expectations formation and other
kinds
of "individualistic" adaptation. Much in the style of Peyton
Young's book's
approach to recovering results from "common knowledge
ultra rationalistic"
game theory via adaptation we shall take a related
approach to recovering
results from rational expectations theory. Our
posture will be somewhat
different however. It will be guided by a desire
to formulate econometric
frameworks where tools like the Efficient Method
of Moments (cf. George
Tauchen's website at Duke) and Computational Bayes (cf. John Geweke's
website
and his paper, "Computational Experiments and
Reality" available at his
websites at Minnesota and Iowa along with software available
there) can be
used to measure the "statistical significance" of the "extra free
parameters"
brought by adaptive theory. Emphasis will also be placed upon
econometrically
separating interactive effects from empirically similar looking effects
due to
correlated unobservables and other phenomena.
VIII. Information Contagion, Polya Processes,
Cascades, Self Reinforcing
Mechanisms, Magnification Mechanisms of Income and Wealth.
(Arthur, W., (1988), "Self Reinforcing Mechanisms in Economics,"
in Arrow,
Anderson, Pines, op.cit. Bikhchandani, S.,
Hirshleifer, D., Welch, I.,
(1992), "A Theory of Fads, Fashion,
Custom, and Cultural Change as
Informational Cascades," JOURNAL OF POLITICAL ECONOMY, 100 (5): 992-1026.
De
Vany, A., and Walls, W., (1994), "Information,
Adaptive Contracting, and
Distributional Dynamics: Bose-Einstein Statistics and the Movies,"
University
of California, Irvine, Working Paper, recently appeared in ECONOMIC
JOURNAL.
Rosen, S., "The Economics of Superstars," AMERICAN
ECONOMIC REVIEW, 71:
167-183.)
This material relates naturally to the above
discussions in the sense
that it lays out a variety of channels through which interaction
may operate
in a dynamically evolving social system as an economy.
Emphasis will be
placed on econometric identification of the different "observable
empirical
signatures" produced by each of these very different mechanisms of
interaction
that may look the same to an econometric exercise if
it is not carefully
formulated. Formulation of econometric exercises to differentiate
different
channels of interaction including "social learning," "informational
cascades,"
"positional reward structures" (e.g. "tournament"
payoff structures), and
other related channels of possible interaction will take a very high
priority
in this year's 606.
IX. "Process vs. Equilibrium"
A common theme thoughout the above materials
is moving thinking about the
economy away from "equilibrium" (even that of the stochastic process
RBC type
modelling) towards a view more like Artificial Life and John Holland's
Complex
Adaptive Systems (cf. Leigh Tesfatsion's website, Tom Ray's TIERRA,
The Santa
Fe Artificial Stock Market, "Sugarscape" and other ALife frameworks)
where the
system never settles down. This kind of approach to economics
can be viewed
as a modern form of Austrianism. We shall try
to develop some analytics
(rather like large system limits over a hierarchy of "spatial"
and temporal
scales) to complement the exciting computational work in this area.
X. Bayesian Model Averaging and
other methods of appraising "Model
Uncertainty". Econometrics and Decision Theory: New Approaches.
The paper "Growth Economics and Reality" by
Brock and Durlauf (available
at the SSRI office and website) reviews this area and applies
it to growth
econometrics. We will discuss some
of these methods and potential
applications for them in the course.