Agent-Based Modelling and
Economic Policy:
Some Examples
Thomas Lux
Chair of Monetary Economics and International Finance
CAU Kiel &
Research Area “Financial Markets and Macroeconomic Activity”
Kiel Institute for the World Economy
Email: lux@bwl.uni-kiel.de, http://www.bwl.uni-kiel.de/vwlinstitute/gwrp/team/lux.html
If we restrict ourselves to models which can be
solved analytically,
we will be modeling for our mutual entertainment,
not to maximize explanatory or predictive power.“
HARRY M. MARKOWITZ, Nobel Laureate in
Economics
“.. Macro activity is essentially the result of the interactions between
agents..”
(Economist James Ramsey, 1996)
Evidence for Success of Agent-Based Modelling?
Areas outside Economics

ABMs are the dominating new paradigm for modelling
traffic flows

ABMs are standard tool in epidemics research (with
good coincidence of results between agent-based micro
models and phenomenological macro models)

Apparently, great interest in the U.S. Military and
Homeland Security department...
(modelling of combat, dispersed terrorist activity, impact of attacks on
population etc.)
Evidence for Success of Agent-Based Modelling?
Appetizers from Our Research*

Artificial Financial Markets: Explanation of the Stylized
Facts of financial markets from interaction of
heterogeneous investors

Macro: Formation of animal spirits: Modelling of a
process of social opinion formation, estimation of the
model and use for forecasting

Human behavior in economic decision problems:
Replication and explanation of subjects‘ behavior in lab
experiments via artificial agents

(Work in progress: Interbank market)
* partially from EU-STREP “Complex Markets”
* Partly funded by EU-STREP Complex Markets
Illustration I: The remarkable statistics of financial markets
The important universal facts
 Returns are always bell-shaped, quite symmetric, but
non-Normal
 Universal non-Gaussian behavior of large returns with
scaling coefficient ~ -3 (risk management!
 No correlations in raw data, but long-lasting
correlations in higher moments (fluctuations):
hyperbolic decay of ACFs with universal parameter
 …
 Until recently: no trace of behavioral explanation
Agent-Based Explanation
 different types of traders: "noise traders" and
"fundamentalists"
 noise traders rely on: charts (price trend) and flows (behavior
of others)
- > mimetic contagion, herding
 traders compare profits gained by noise traders and
fundamentalists
and switch to the more successful group.
 External input: changes of fundamental factor
Stylized Facts as Emergent Phenomena
of Multi-Agent Systems
Interacting Agent Hypothesis: dynamics of asset returns
arise endogenously from the trading process,
market interactions magnify and transform exogenous
news into fat tailed returns with clustered volatility
It suffices to take what we see in the market (e.g.,
chartist/fundamentalist behavior)
-> mix of centripedal and centrifugal that can generate
outcome undistinguishable from market statistics
Artificial market
German DAX
Exchange rate DEM-$
returns =
ln(pt) – ln(pt-1)
Threshold
for stability
(in firstorder
approx.)
Example of the Dynamics: returns and simultaneous development of the fraction
of chartists, z. The broken line indicates the critical value at which a loss of stability
occurs.
 simple microscopic models generate surprisingly realistic
market statistics (which are hard to explain by traditional models)
 qualitative features are robust with respect to the details of the
artificial markets (e.g., simple straegies vs. artificially intelligent
traders)
towards policy: Use as test bed for market regulations
(transaction tax, short selling constraints...)
Simulated returns from market with artificially intelligent agents
Example II: Empirical Animal Spirits
Background and Motivation
 Survey data are mostly used to forecast key economic quantities
(GDP, IP, stock prices), but are seldomly treated as endogenous
variables
 What drives expectations expressed in surveys? Rational
expectations vs. animal spirits
 RE tests typically negative, recent revival of interest in animal
spirits (Akerlof and Shiller)
 Research question: Can we identify animal spirits at work? Can
we identify the influence of social interaction on opinion
formation?
____________________________________________________________________________________________________________________________________________________________
Thomas Lux
Department of Economics
University of Kiel
Application II: Macro Sentiment
ZEW Index of Economic Sentiment, 1991 – 2006,
Monthly data, index = #positive - # negative, ca. 350 respondents
____________________________________________________________________________________________________________________________________________________________
Thomas Lux
Department of Economics
University of Kiel
A Canonical Interaction Model à la Weidlich



Two opinions, strategies etc: +
and –
A fixed number of agents: 2N
Agents switch between groups
according to some transition
probabilities w↓ and w↑
v: frequency of switches,
U: function that governs
switches
α 0, α1: parameters
w   v * exp(U )
w   v * exp( U )
U  0  1x
n  n
x
2N
Sentiment index
____________________________________________________________________________________________________________________________________________________________
Thomas Lux
Department of Economics
University of Kiel
Model and Conclusions
 opinion dynamics with social interaction + possible
influence of external information
 estimation possible: econometric model motivated
by agent-based model
 evidence for social interaction effects in ZEW index,
no significant bias, slow development (v small)
 limited evidence of interaction with macro data
 interaction effects are dominant part of the model
 we can identify the formation of animal
spirits and track their development
95% confidence interval from period-by-period predictions
of model of opinion dynamics
____________________________________________________________________________________________________________________________________________________________
Thomas Lux
Department of Economics
University of Kiel
Observation Xs,
approximated by sharp
Normal distr.
Time interval [s, s+1]
Predictive density at t+1
____________________________________________________________________________________________________________________________________________________________
Thomas Lux
Department of Economics
University of Kiel
Example III: Economic Behavior in Laboratory
Experiments
 Subjects have to forecast the price in a market with many
producers
 Subjects manage to arrive at the equilibrium price with some
experience, but fluctuations remain surprisingly high
 Neither learning by representative agent nor heterogeneous
beliefs with two groups explains all features of the
experiments
 Research question: Can we replicate the experiments with y
popolation of artificially intelligent agents?
 Yes, we can (in all respects)
____________________________________________________________________________________________________________________________________________________________
Thomas Lux
Department of Economics
University of Kiel
RE prices,
RE variance: 0.25
The setting: a = 13.8, b = 1.5, Var[εt] = Var[ηt/b] = 0.25,
K = 6 subjects, varying slope parameter λ
Illustration of experimental
setting
Experiments
GA simulations
Indication for appropriate
models of human
behavior
Degree of heterogeneity of subjects, both in experiments (grey) and computer
simulations (blue), averaged over 1,000 runs,
Broken line: “rationality” prediction of economic theory
Conclusions: Benefits of ABMs in
Economics
 Bottom-up approach taking into account
observed behavioral micro characteristics of
agents
 Reality check/validation of ABMs via macro
output
 Easy to combine with insights form other fields > socio-economic models, econo-environmental
models
 Modularity: different levels can be chosen for
different purposes: industry, single market, realfinancial sector, economy-wide ABM