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
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
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.
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,
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
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
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
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
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
(Sullivan, Timmerman, and White, (1998), "Data-Snooping,
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
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
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
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
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
Since we will be on new ground here, this should be an exciting part of
VII. Cellular Automata, Ising Models, Spin Glass Models
(Mezard, M., Parisi, G., Virasoro, (1987), SPIN GLASS THEORY AND BEYOND,
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,"
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:
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.
Chaos and Complex Systems Seminar Page