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Agent-Based Economic Model and Econometrics International Workshop on Nonlinear Economic Dynamics and Financial Mar

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Agent-Based Economic Model and Econometrics

International Workshop on Nonlinear Economic Dynamics and Financial Market Modelling

Oct 9 -- 10, 2008

Peking University, Beijing

Shu-Heng Chen, Chia-Ling Chan and Yen-Jung Du

chchen@nccu.edu.tw

http://www.aiecon.org/

AI-ECON Research Center

Department of Economics

National Chengchi University

Taipei, Taiwan

Outline

- In this paper, we present the development of agent-based computational economics in light of its relation to econometrics.
- We propose a three-stage development and illustrate the development using the literature of agent-based financial modeling.
- The three-stage development is
- Presenting ACE with Econometrics
- Building ACE with Econometrics
- Emerging Econometrics with ACE
- Concluding Remarks

ACF Models (50)

Autonomous-Agent

Designs (12)

N-Type Designs (38)

2-Type Designs (18)

3-Type Designs (9)

Many-Type Designs (11)

Collection of ACF Models

- In this paper, we survey a large number of agent-based financial market models, to be exact, 50.
- This size of survey allows us to examine models crossing many different classes.
- While in the literature there are already some taxonomies of agent-based financial models, our perspective here concerns more with the simplicity and complexity of the models, in particular, the number of possible behavioral rules used in the model.
- This concern draws our attention to the software-agent designs and divide the literature into the following two groups:
- N-Type Designs (N can be few, such as 2 or 3, or many)
- Autonomous-Agent Designs

The Two Groups

- The first group corresponds to the survey given by Hommes (2006), whereas the second group corresponds to the survey given by LeBaron (2006).
- The two groups can also been put into an interesting contrast.
- If we considers heterogeneity, adaptation, and interactions as three essential ingredients of ACF, then the first group tends to be simpler in each of these three elements, while the later are more complex in each of the three.
- This contrast, from simple to complex, therefore, enables us to reflect upon the heating discussion on the simplicity principle in modeling complex adaptive systems. The specific question, for example, is what the ``marginal gains’’ by making more complex models are.
- Alternatively put, what are the minimum number of clusters of financial agents required to replicate financial stylized facts?

N-Type Models and the SFI models

- Models with the N-type designs mainly cover the three major classed of ACF, namely,
- Kiram’s Ant Models (Kirman, 1991, 1993)
- Lux’s IAH Models (Lux, 1995, 1997, 1998; Lux and Marchesi (1999, 2000)
- Brock and Hommes’ ABS Models (Brock and Hommes, 1998)
- They also include some others which may be distinguished from the three above, such as the Ising models, minority games ($ games) models, prospect-theory-based models, and threshold models.
- Models with the autonomous-agent designs are mainly either SFI (Santa Fe Institute) models or their variants.

Distribution of the 50

- This sample is by no means exhaustive, but we hope that it well represent the population underlying it.
- Sample Size: 50
- N-Type Designs: 38
- 2-Type Designs: 18
- 3-Type Designs: 9
- Many-Type Designs: 11
- Autonomous-Agents Designs: 12

Demographic Structure

- These four tables are by no means exhaustive, but just a sample of a large pile of existing studies.
- Nonetheless, we believe that they well represent some basic characteristics of the underlying large pile of literature.
- The largest class of ACF models is the few-type design (50%).

Two Remarks

- We do not verify the model, and hence do not stand in a position to give a second check on whether the reported results are correct. On this regard, we assume that the verification of each model has been confirmed during the referring process.
- We, however, do make a minimal effort to see whether proper statistics have been provided to support the claimed replication. The study which does not satisfy this criterion will not be taken seriously.

There are four stylized facts which obviously receive more intensive attention than the rest of others.

- These four are
- fat tails (41 counts),
- volatility clustering (37),
- absence of autocorrelations (27), and
- long memory of returns (20).
- Second, we also notice that all stylized facts explained are exclusively pertaining to asset prices; in particular, all these efforts are made to tackle with the low-frequency financial time series.

The Role of Heterogeneity and Learning

- Do many-type models gain additional explanation power than the few-type models?
- Many-type models do not perform significantly better than the few-type models.
- Would more complex learning behavior help?
- Little marginal gain over the baseline models (2 or 3-type models).
- Furthermore, baselines models facilitate the estimation or calibration work, which characterizes the second-stage development.

Building ACE with Econometrics

- In the second stage, an ACE model is treated as a parametric model, and its parameters are estimated using real financial data.
- What concerns us are no longer just the stylized facts, but also the behavior of financial agents and their embeddings.
- Up to the present, only the three major N-type models (ANT, IAH and ABS) have been seriously estimated.
- Given the differences among the three models, what are estimated are obviously different, but, generally, they include two things, namely, the behavioral of financial agents and their embeddings.

What to Estimate and What to Know

- Despite their technical details and differences, the three estimation works share a common interest, namely, the evolving fraction of financial agents.
- Two features are involved.
- first, large swing between fundamentalist and chartists;
- second, dominance of one cluster of financial behavior for a long period of time.
- Putting them together, we may call it market fraction hypothesis.

Applications of the ABS Models

- Here, an illustration is provided, based on the application of the 2- and 3-type ABS models to 10 stock indexes and 21 foreign exchange rates.
- They are all daily data from 2005.1.1-2006.12.31..

Data: Stocks, daily data from 2005/1/1 to 2006/12/31

- (1) CAC 40
- (2) German DAX
- (3) Dow Jones Industrial Average
- (4) British FTSE 100
- (5) Hang Seng Index
- (6) Nikkei 225
- (7) S&P 500 Index
- (8) Seoul Composite
- (9) Straits Times
- (10) Taiwan Weighted Index

(1) Australia

(2) Brazil

(3) Canada

(4) China

(5) Denmark

(6) EURO

(7) Hong Kong

(8) India

(9) Japan

(10) Malaysia

(11) Mexico

(12) New Zealand

(13) Norway

(14) Singapore

(15) South Africa

(16) South Korea

(17) Sri Lanka

(18) Switzerland

(19) Taiwan

(20) Thailand

(21) United Kingdom

Data: FXs, daily data from 2005/1/1 to 2006/12/31Market Fractions in 10 Stock Markets and 21 FX Markets: 2- and 3-type ABS Model

What to Estimate

- In addition to the evolving market fractions, more details of financial agents’ behavior, such as
- Beliefs: reverting coefficients, extrapolating coefficients,
- Memory: memory in fitness and memory in belief formation,
- Intensity of Choices,
- Risk perceptions,
- The length of the moving-average window (fundamentalists),
- Fitness measure (realized profits or risk-adjusted profits),

but they received relative less attention.

- Amilon (2008) addressed the behavioral aspects found in his empirical study of a 2-type and 3-type ABS models.

Challenges

- However, a detailed look of the each parameter across each market also reveals another problem, i.e., some wide distributions of the estimated parameters over all markets.
- How can we make sense of this divergence given the globalization of the financial market?

Parameter: Fitness Criterion, Realized Profits vs. Risk-adjust Profits

Parameter: Window Size for Moving Averaging (Fundamentalists)

Parameter Dispersion over Different Markets

- We examine the possible heterogeneity of market participants over different markets.
- It also allows to see which aspect of investing behavior is commonly shared by all investors in various financial markets.

Measure Dispersion

- Dispersion based on the minimization of the range with the indicated coverage.

We can see that generally the dispersion statistics are below the benchmark value 0.65.

- Traders' behavior in stock markets is less heterogeneous than that in the foreign exchange market.

Aggregation Problems: Aggregation over Evolving Interacting Heterogeneous Agents

- Aggregation problems are among the most difficult problems faced in either the theoretical or empirical study of economics. …There is no quick, easy, or obvious fix to dealing with aggregation problems in general (Blundell and Stoker, 2005, JEL)

Example: Agent-Based CCAPM

- Chen and Huang (2008, JEBO) and Chen, Huang and Wang (2009) .
- We assume that all financial agents have unitary risk aversion coefficient, and starting from there we can generate a series of artificial data from the artificial market.

We then considered this dataset as a counterpart of the real world data, and then applied standard econometrics to estimate the risk aversion coefficient and see how far we are away from the truth.

- Here is the answer.

So, basically, regardless of using data at individual level or at macro level, we are far away from the true value (which is one) but the one with aggregated data are further away.

- If we ignore the error, and take the econometric findings without hesitation, then we can ever come up with some spurious relations, for example, the relation between risk aversion and wealth.

Information Sciences (2007)

- ``If agents are heterogeneous, some standard procedures (e.g. cointegration, Granger-causality, impulse-response functions of structural VARs) loose their significance. Moreover, neglecting heterogeneity in aggregate equations generates spurious evidence of dynamic structure.’’

Concluding Remarks

- The agent-based financial market has made itself as a promising example for agent-based social sciences.
- It, to an extent, successfully replicated some familiar stylized facts, and points to the possible causes of them, so it enriches theory of financial economics.
- However, based on the progress achieved so far, 2-type or 3-type models seems to be good enough. In this manner, finance is more like the complex science in the 1980s.
- Econometric estimations of the agent-based financial models enables us to learn further from the data, in particular, the behavioral aspects of financial agents.
- When applied to different markets, it may also shed light on the heterogeneity of financial agents in different markets.

Concluding Remarks

- Nevertheless, there are also few questions observed.
- First, is the observed sustaining heterogeneity of financial agents across different markets is an empirical fact or is just an spurious outcome from this simple agent-based model.
- Second, introducing the addition type of financial agents to the market can, in some cases, result in significant change of the estimated parameters. This also requires a careful addressing.
- Complex agent-based financial models are not unemployed. In fact, it is expected, when we move to other less exploited stylized facts, the autonomous-agent designs may become more helpful as a few studies recently have already indicated.
- Nevertheless, it remains to be an issue whether one should seriously estimate this complex agent-based models. Why and how?
- The SFI-like agent-based models should not be evaluated purely based on with their econometric or forecasting performance.

Concluding Remarks

- Instead of searching for an econometric foundation of these models, one may think in a reverse way, that the best role for them to play is to serve as an agent-based foundation of econometrics, as they can contribute to our study of aggregation problem.
- Solving aggregation problem involve the various use of micro-macro models, and these complex agent-based models may enabled us to know more about the complex micro-macro relations than the simple agent-based model.

Parameter Sensitivity to the Third Type

- Since different parameters have different ranges, to make the stability results more comparable among the parameters, we take the following normalization for each parameter.

Parameter Sensitivity to the Third Type

- Most of the parameters experience a degree of variation more than 20%.
- The most sensitive two are (the extrapolating coefficient of the momentum traders) and (the sensitivity of risk aversion to loss).
- The two parameters pertaining to fundamentalists‘ forecasting behavior, and L, are relative stable with a variation less than 20% or so.

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