Agent-Based Modelling and Economic Policy: Some Examples Thomas Lux Chair of Monetary Economics and International Finance CAU Kiel & Research Area Financial.

Agent-Based Modelling and Economic Policy: Some Examples

Thomas Lux

Chair of Monetary Economics and International FinanceCAU Kiel &

Research Area “Financial Markets and Macroeconomic Activity” Kiel Institute for the World Economy

Email: [email protected], 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

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 .. Macro activity is essentially the result of the interactions between agents..”agents..”(Economist James Ramsey, 1996)(Economist James Ramsey, 1996)

Evidence for Success of Agent-Based Modelling?Evidence for Success of Agent-Based Modelling?Areas outside EconomicsAreas outside Economics

ABMs are the dominating new paradigm for ABMs are the dominating new paradigm for modelling traffic flowsmodelling traffic flows

ABMs are standard tool in epidemics research ABMs are standard tool in epidemics research (with good coincidence of results between (with good coincidence of results between agent-based micro models and agent-based micro models and phenomenological macro models)phenomenological macro models)

Apparently, great interest in the U.S. Military Apparently, great interest in the U.S. Military and Homeland Security department...and Homeland Security department... (modelling of combat, dispersed terrorist activity, impact of (modelling of combat, dispersed terrorist activity, impact of attacks on attacks on population etc.)population etc.)

Evidence for Success of Agent-Based Modelling?Evidence for Success of Agent-Based Modelling?Appetizers from Our Research*Appetizers from Our Research*

Artificial Financial Markets: Explanation of the Artificial Financial Markets: Explanation of the Stylized FactsStylized Facts of financial markets from of financial markets from interaction of heterogeneous investorsinteraction of heterogeneous investors

Macro: Formation of animal spirits: Modelling of a Macro: Formation of animal spirits: Modelling of a process of social opinion formation, estimation of process of social opinion formation, estimation of the model and use for forecastingthe model and use for forecasting

Human behavior in economic decision problems: Human behavior in economic decision problems: Replication and explanation of subjects‘ behavior Replication and explanation of subjects‘ behavior in lab experiments via artificial agentsin lab experiments via artificial agents

(Work in progress: Interbank market)(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 marketsIllustration I: The remarkable statistics of financial markets

The important universal The important universal factsfacts

Returns are always bell-shaped, quite symmetric, Returns are always bell-shaped, quite symmetric, but non-Normalbut non-Normal

UniversalUniversal non-Gaussian behavior of large returns non-Gaussian behavior of large returns with scaling coefficient ~ -3 (risk management!with scaling coefficient ~ -3 (risk management!

No correlations in raw data, but long-lasting No correlations in raw data, but long-lasting correlations in higher moments (fluctuations): correlations in higher moments (fluctuations): hyperbolic decay of ACFs with universal parameterhyperbolic decay of ACFs with universal parameter

…… Until recently: no trace of behavioral explanationUntil recently: no trace of behavioral explanation

Agent-Based ExplanationAgent-Based ExplanationAgent-Based ExplanationAgent-Based Explanation

different types of traders: "different types of traders: "noise tradersnoise traders" and " and ""fundamentalistsfundamentalists" "

noise traders rely on: noise traders rely on: charts charts (price trend) and (price trend) and flowsflows (behavior of others)(behavior of others)

- > mimetic contagion, herding - > mimetic contagion, herding

traders compare profits gained by noise traders and traders compare profits gained by noise traders and fundamentalists fundamentalists

and and switch to the more successful groupswitch to the more successful group..

External input: changes of fundamental factorExternal input: changes of fundamental factor

Stylized Facts as Emergent Stylized Facts as Emergent PhenomenaPhenomena

of Multi-Agent Systems 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., take what we see in the market (e.g., chartist/fundamentalist behavior) chartist/fundamentalist behavior)

-> mix of centripedal and centrifugal that can generate -> mix of centripedal and centrifugal that can generate outcome undistinguishable from market statisticsoutcome undistinguishable from market statistics

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., take what we see in the market (e.g., chartist/fundamentalist behavior) chartist/fundamentalist behavior)

-> mix of centripedal and centrifugal that can generate -> mix of centripedal and centrifugal that can generate outcome undistinguishable from market statisticsoutcome undistinguishable from market statistics

returns =

ln(pt) – ln(pt-1)

Artificial market

German DAX

Exchange rate DEM-$

Example of the Dynamics:Example of the Dynamics: returns and simultaneous development of the fraction returns and simultaneous development of the fraction of chartists, z. The broken line indicates the critical value at which a loss of stability of chartists, z. The broken line indicates the critical value at which a loss of stability occurs.occurs.

Threshold for stability (in first-order

approx.)

simple microscopic models generate surprisingly simple microscopic models generate surprisingly realistic market statistics (which are hard to explain by realistic market statistics (which are hard to explain by traditional models)traditional models)

qualitative features are robust with respect to the qualitative features are robust with respect to the details of the artificial markets (e.g., simple straegies vs. details of the artificial markets (e.g., simple straegies vs. artificially intelligent traders)artificially intelligent traders)

towards policy: Use as test bed for market regulations towards policy: Use as test bed for market regulations (transaction tax, short selling constraints...)(transaction tax, short selling constraints...)

Simulated returns from market with artificially intelligent agents

____________________________________________________________________________________________________________________________________________________________Thomas Lux

Department of EconomicsUniversity of Kiel

Example II: Empirical Animal SpiritsExample II: Empirical Animal SpiritsBackground and MotivationBackground and Motivation

Survey data are mostly used to forecast key economic quantities Survey data are mostly used to forecast key economic quantities (GDP, IP, stock prices), but are seldomly treated as endogenous (GDP, IP, stock prices), but are seldomly treated as endogenous variablesvariables

What drives expectations expressed in surveys? Rational What drives expectations expressed in surveys? Rational expectations vs. animal spiritsexpectations 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 Research question: Can we identify animal spirits at work? Can we identify the influence of social interaction on opinion we identify the influence of social interaction on opinion formation?formation?

____________________________________________________________________________________________________________________________________________________________Thomas Lux

Department of EconomicsUniversity 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 EconomicsUniversity of Kiel

A Canonical Interaction Model à la WeidlichA Canonical Interaction Model à la Weidlich

Two opinions, strategies etc: + Two opinions, strategies etc: + and –and –

A fixed number of agents: 2NA fixed number of agents: 2N Agents switch between groups Agents switch between groups

according to some transition according to some transition probabilities wprobabilities w↓↓ and w and w↑↑

v: frequency of switches,v: frequency of switches,

U: function that governs U: function that governs switchesswitches

α α 00, , αα11: parameters: parameters

)Uexp(*vw

)Uexp(*vw

xU 10

N2

nnx

Sentiment index

Model and ConclusionsModel and ConclusionsModel and ConclusionsModel and Conclusions

opinion dynamics with social interaction + possible opinion dynamics with social interaction + possible influence of external informationinfluence of external information

estimation possible: estimation possible: econometric model motivated econometric model motivated by agent-based modelby agent-based model

evidence for social interaction effects in ZEW index, evidence for social interaction effects in ZEW index, no significant bias, slow development (v small)no significant bias, slow development (v small)

limited evidence of interaction with macro datalimited evidence of interaction with macro data

interaction effects are dominant part of the model interaction effects are dominant part of the model

we can identify the formation of animal spirits we can identify the formation of animal spirits and track their developmentand track their development

____________________________________________________________________________________________________________________________________________________________Thomas Lux

Department of EconomicsUniversity of Kiel

95% confidence interval from period-by-period 95% confidence interval from period-by-period predictions of model of opinion dynamicspredictions of model of opinion dynamics

____________________________________________________________________________________________________________________________________________________________Thomas Lux

Department of EconomicsUniversity of Kiel

Observation Xs,approximated by sharp Normal distr.

Time interval [s, s+1]Predictive density at t+1

____________________________________________________________________________________________________________________________________________________________Thomas Lux

Department of EconomicsUniversity of Kiel

Example III: Economic Behavior in Laboratory Example III: Economic Behavior in Laboratory ExperimentsExperiments

Subjects have to forecast the price in a market with many Subjects have to forecast the price in a market with many producersproducers

Subjects manage to arrive at the equilibrium price with some Subjects manage to arrive at the equilibrium price with some experience, but fluctuations remain surprisingly highexperience, 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 Research question: Can we replicate the experiments with y popolation of artificially intelligent agents? popolation of artificially intelligent agents?

Yes, we can (in all respects)Yes, we can (in all respects)

The setting: a = 13.8, b = 1.5, Var[εt] = Var[ηt/b] = 0.25,

K = 6 subjects, varying slope parameter λ

RE prices,

RE variance: 0.25

Illustration of Illustration of experimental setting 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 Conclusions: Benefits of ABMs in EconomicsABMs in Economics

Bottom-up approach taking into account Bottom-up approach taking into account observed behavioral micro characteristics of observed behavioral micro characteristics of agents agents

Reality check/validation of ABMs via macro Reality check/validation of ABMs via macro outputoutput

Easy to combine with insights form other fields Easy to combine with insights form other fields -> -> socio-economic models, econo-socio-economic models, econo-environmental modelsenvironmental models

Modularity: different levels can be chosen for Modularity: different levels can be chosen for different purposes: industry, single market, different purposes: industry, single market, real-financial sector, economy-wide ABMreal-financial sector, economy-wide ABM