Economic Multi Agent Systems E-Book

Gottfried Haber

• Herausgeber: Books on Demand
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 340

Veröffentlichungsjahr: 2014

Beschreibung

The relatively new scientific field of economic agent-based systems is a promising, but yet not completely developed area of economics, at the frontier to business administration, computer sciences, and the social sciences. This book follows a rather interdisciplinary approach while maintaining a focus on the economic dimension of agent-based models. In contrast to other literature in this field, this book aims at developing a framework for modelling an economic system in the sense of a total model of the economy. The design and implementation of the agent-based framework AS1 are described in detail. Some sample applications, such as an analysis of the effects of the presence of different research institutes providing alternative inconsistent forecasts for the private agents, provide an overview of the strengths of an agent-based economic model. This 2nd edition is a reprint of the original Edition (from 2006).

Leseprobe

Preface

This book is designed to describe the theoretical foundations, design considerations, the implementation, and some possible applications of agentbased economic models. It is the summary of several years of research and presents and documents an agent-based application framework, “Agent Simulator 1” (AS1), developed by the author. Some exemplary applications of AS1 are presented, but the nature of agent-based models enables the developer to have the opportunities to include a nearly unlimited set of additional features into the model. So it is not easy to consider such a model ever as being finished. In the light of these considerations, this book is a first step in further developing and establishing agent-based economic models within the scientific community.

The relatively new scientific field of economic agent-based systems is a promising, but yet not completely developed area of economics, at the frontier to business administration, computer sciences, and the social sciences. Thus, this book follows a rather interdisciplinary approach while maintaining a focus on the economic and technological dimensions of agent-based models. Traditional approaches to agent-based modeling have put a focus on the social dimension of agent interaction, e.g. the evolution of cooperation. In contrast to this branch of literature, this book aims at developing a framework for modeling an economic system on the macro level, while maintaining the rich features of agent-based models on the micro level.

There are some methodological innovations introduced in this book with respect to agent-based modeling. First of all, the notion of constructing a total model of the economy on the macro level has not been implemented in a functioning model so far. Second, the expectation formation process in the model is designed very carefully, with the availability of one or even more alternative research institutes applying dynamic models of the economy, which are re-estimated in each period, just as real research institutes would do. In the last chapter, an experiment is presented, in which the agents dynamically build their own individual forecast models of the economy. Moreover, the simplified market processes usually found in agent-based models (simple auctions or double auctions) have been replaced by the more realistic implementation of agents with limited information and (physical) range, which have realistically low market-power as individuals, but determine the market results on the aggregate level. Finally, preferences of the households and the parameters of the production functions are completely dynamic, granting the feature of innovation on the goods level: new goods can be invented, and the utility and production functions of the individual agents are updated automatically. Dynamic changes of these parameters (due to social interaction and evolution) are also included by the means of genetic algorithms.

While the “mechanics” of the agents and the most important components of AS1 will be treated in detail and in non-(IT)-technical terms (as far as possible), the major part of the research – the actual implementation details of computer model – will be documented in this book on a rather abstract level, in the form of a reference of the class libraries in the appendix. This should enable further research using AS1 for everyone who might be interested in applying this economic agent-based framework. Printing the full source code would have produced hundreds of pages with program code, which is of no value-added for most readers. Nevertheless, this class library documentation should enable the reader (with some IT and programming knowledge) to implement his or her own extensions, improvements, refinements, and simulations based upon AS1.

When the first step of developing such a model is finished, an estimation of the effort put into this research can be interesting (especially because my wife always told me not to work as much as I did on this “endless model”). As I argued against the hypothesis to put too much work and spare time into this model, I tried to gather some empirical evidence in favor of my position. There are some methods and models to estimate the “substitution cost” of software, i.e. to find out the cost incurred by commercial software development companies to produce a functionally equivalent piece of software. When calculating the effort needed for development and the substitution value of the AS1 framework including the user interface (but without the setup program), such a software development task with more nearly 25.000 lines of source code (which is equivalent to approximately 350 pages of A4 size paper without any empty lines and without margins) can be estimated to require about 1001 person-months of labor in a software company (for conceptual design, implementation, debugging, etc…), leading to total development cost of approximately EUR 300,000 to EUR 400,000.2 To see the dimension of this project: the complete source code of the software used on board a NASA space shuttle comprises approximately 250.000 lines of code (NASA, 1996), thus AS1 could be seen as about 10% of the software running on a space shuttle, but with the difference, that the space shuttle software does not apply smart agent-based technologies! The bad news is: These calculations had not the desired effect for proving that I had not spent too much time in developing the model…

The compiled class libraries (compatible with Microsoft .NET framework 2.0 and therefore usable from all .NET compatible programming languages, such as C#, C++, VB and J#) and the detailed documentation of the framework are available from the author upon request (http://www.haber.at).

Thanks are due to the people at the Economics Department of Klagenfurt University, who have given me great support during all my research activities. I would like to specifically mention Professor Reinhard Neck, who has always been providing a great environment for my research activities and the best support I could imagine, not only limited to scientific issues. Christina Kopetzky and Anita Wachter did a great job in taking away all “disturbing” other tasks from me and helping me to concentrate on the huge task of developing such a model from scratch. Professor Hans Joachim Bodenhöfer and Professor Reinhard Neck have always proven that high quality research and practical relevance of research by the application of scientific methods are no opposites, but fit together perfectly – and this synthesis is one of the main tasks of my work presented here.

Thanks are also due to my parents who educated me to be critical about everything and to have great interest in always doing something challenging and new. This book is dedicated to my wife, Barbara, and my son, Paul. They gave me all the back-up and support I needed, when preparing this book. I love you and I promise to reduce the daily time spent on this model, now that it works, even if it is very tempting to experiment on various possible extensions. From now on, at least the weekends will be free of AS1 …

Gottfried Haber

1 Given the fact that the author has done research on agent-based techniques for about 15 years and started programming the first simple models ten years ago, these estimates are quite reasonable. Note that commercial software companies would also have some overhead in coordinating teams, doing administration etc.

2 This calculation has been performed using the COCOMO II cost model (COCOMO was originally developed by Boehm, 1981), based upon the number of source lines of code (SLOC) and (very moderate) average cost assumptions for a software developer of EUR 3,500 per month (including taxes and social insurance), with all the other parameters on their default values. If the software is considered to be highly critical in terms of execution time and memory constraints (which is certainly true), even up to 70 percent higher figures might arise.

Contents

1. Introduction

2. Economic Modeling with Agent-based Models

2.1. Traditional Macroeconomic Modeling Approaches

2.1.1. General Considerations

2.1.2. The Cowles Commission Approach

2.1.3. Time-series Models

2.1.4. VAR and VEC Models

2.1.5. General Equilibrium Models

2.1.6. Stylized Mathematical Models

2.2. Agent-Based Models

2.3. Key Concepts in Agent-Based Modeling

2.3.1. What is an Agent?

2.3.2. Genetic Algorithms (GA)

2.3.3. Artificial Neural Networks (ANN)

2.4. Stylized Agent-Based Model Structure

3. Implementation Issues

3.1. Key Concepts in Agent-based Programming

3.1.1. Encapsulation

3.1.2. Active actions

3.2. Platform considerations

3.3. Choice of the programming language

3.3.1. Low-Level languages

3.3.2. High-Level languages

3.3.3. Specialized Languages and Agent-Based Toolkits

3.4. Choosing C# for Agent-Based Modeling

3.4.1. The C# Object Model

3.4.2. Type Safety

3.4.3. Inheritance – a Key Concept for Agent-Based Models

3.4.4. Reflection

3.4.5. Collections and Generics

3.5. Implementation Issues Summary

4. Designing an Agent-Based Economic Model

4.1. Model Overview and Structure

4.2. How to Communicate with Agents: Interfaces

4.2.1. General Interfaces and Related Agent Functionality

4.2.1.1. Age of an Agent: IH

AS

A

GE

4.2.1.2. Identity of an Agent: IH

AS

I

D

4.2.1.3. Position of an Agent: IH

AS

C

OORDS

4.2.1.4. Inspection of the Agent State: IH

AS

S

TATE

I

NFO

4.2.2. Utility and Production Functions

4.2.2.1. Utility Function Interface: IU

TILITY

F

UNCTION

4.2.2.2. Production Function Interface: IP

RODUCTION

F

UNCTION

4.2.3. Control Flow: How and When Things Happen

4.2.3.1. How Agents Become Periodically Alive: IA

CTION

C

LIENT

4.2.3.2. Central Controller of Agent Actions: IA

CTION

D

ISPATCHER

4.2.4. Dynamic Behavior: Genetic Algorithms

4.2.4.1. Changing Agents by Applying a GA: IGAC

LIENT

4.2.5. Different Agent Roles in the Market Process

4.2.5.1. Agents Handling with Money: IF

INANCIAL

A

GENT

4.2.5.2. Buyers and Sellers: IR

ESOURCE

B

UYER

and IR

ESOURCE

S

ELLER

...

4.2.5.3. Labor Demand and Supply: IE

MPLOYER

and IE

MPLOYEE

4.3. Elements of the Model: Classes in AS1

4.3.1. Base Class: B

ASE

S

IMULATOR

O

BJECT

4.3.2. Classes Composing the Model Framework

4.3.2.1. W

ORLD

: An Artificial Universe

4.3.2.2. Countries: the C

OUNTRY

Class

4.3.2.3. S

IM

E

NVIRONMENT

: Central Control of the Models

4.3.2.4. Infrastructure and Spatial Properties: T

RANSPORT

L

AYER

4.3.3. Abstract Agents: Templates for Major Agent Categories

4.3.3.1. Abstract B

ASE

A

GENT

4.3.3.2. Abstract P

RIVATE

A

GENT

4.3.3.3. Abstract P

UBLIC

A

GENT

4.3.3.4. Abstract H

OUSEHOLD

F

IRM

A

GENT

4.3.4. Private Agents

4.3.4.1. Private Households: H

OUSEHOLD

Class

4.3.4.2. Commercial Companies: F

IRM

Class

4.3.4.3. Financial Institutions: B

ANK

Class

4.3.5. Utility and Production Functions

4.3.5.1. Utility Function: U

TILITY

F

UNCTION

Class

4.3.5.2. Elements of the Utility Function: U

TILITY

S

CHEME

I

TEM

4.3.5.3. Production Function: the P

RODUCTION

F

UNCTION

Class

4.3.6. Public Agents

4.3.6.1. The Public Sector: G

OVERNMENT

Class

4.3.6.2. Monetary Control by the Central Bank: C

ENTRAL

B

ANK

4.3.6.3. B

ASE

R

ESEARCH

I

NSTITUTE

: A Source for Expectations

4.3.6.4. Statistical Office: S

TATISTICS

P

ROVIDER

class

4.3.7. Resources

4.3.7.1. Resource Types: B

ASE

R

ESOURCE

, I

NPUT

R

ESOURCE

, G

OOD

R

ESOURC

4.3.7.2. Containers for Resources

4.3.8. Financial Relations

4.3.8.1. Account

4.3.8.2. Account Inventories (A

CCOUNT

I

NVENTORY

class)

4.3.8.3. Quoting Financial Transactions (F

INANCIAL

Q

UOTE

I

TEM

Class)

4.3.8.4. Requesting Central Bank Money (T

ENDER

R

EQUEST

I

TEM

Class)

4.3.8.5. Central Bank Tender Inventory (T

ENDER

I

NVENTORY

class)

4.3.9. Genetic Algorithm Classes

4.3.9.1. Driving Evolution: the GA class

4.3.9.2. Genetic Information: DNA Class

4.3.10. Data Management in an Agent-Based Model

4.3.10.1. Internal Data: T

IME

S

ERIES

and T

IME

S

ERIES

P

OOL

4.4. How to implement models inside models

4.4.1.1. OLS Regressions: OLSM

ODEL

class

4.4.1.2. VAR Model Estimation and Forecasts: V

AR

M

ODEL

class

4.5. Control Flow

4.6. Graphical User Interface (GUI)

4.7. Remarks on Model Estimation and Validation

5. Application of the Model

5.1. A Standard Baseline of the Model

5.2. Expectation Formation Example

6. Summary and Concluding Remarks

7. Appendix

7.1. System Requirements

7.2. Installation Instructions

7.3. AS1 Class Reference

8. Literature

Figures and Tables

Figure 2-1: Simplified GA algorithms (general; social and individual)

Figure 2-2: Basic structure of an ANN

Figure 2-3: Simplified structure of a macroeconomic agent-based model

Figure 2-4: Stylized control flow for invoking the agents

Figure 4-1: Hierarchy of the interfaces in the AS1 framework

Figure 4-2: Control flow in the action cycle

Figure 4-3: Hierarchy of the private agents in the model

Figure 4-4: Schematic bank calculation

Figure 4-5: Hierarchy of the public agents in the model

Figure 4-6: Monetary instruments of the ECB (Source: Scheller, 2004)

Figure 4-7: Hierarchy of the resource classes in AS1

Figure 4-8: Resource inventories and the “availability” inventory

Figure 4-9: Structure of the “ResultTracking” database in AS1

Figure 4-10: Class hierarchy of the logger component

Figure 4-11: Class details of the MATRIXCOMPUTATIONS namespace

Figure 4-12: Console view of the AS1 GUI

Figure 4-13: Object browser

Figure 4-14: Landscape Browser

Figure 4-15: Result Browser

Figure 5-1: Baseline results (firm)

Figure 5-2: Baseline results (firm and household)

Figure 5-3: Baseline results (household)

Figure 5-4: Baseline results (household and statistical office)

Figure 5-5: Baseline results (statistical office)

Figure 5-6: Baseline results (central bank)

Figure 5-7: Baseline results (central bank and bank)

Figure 5-8: Baseline results (bank)

Figure 5-9: Baseline results (bank and government)

Figure 5-10: Growth rate differentials

Figure 5-11: Average growth rate differentials for the scenarios

Table 4-1: Estimation results of a simple VAR model (Haber, 2002)

Table 5-1: Significance of the differences (t-test)

1. Introduction

Economic multi-agent systems have gained more and more attention for the last decade. The basic idea of this innovative approach to model certain aspects of the economy is comparable to some well-known computer games3: By modeling individual economic agents on the micro level and subsequently aggregating their behavior on the macro level, artificial economies can be constructed. The main difference of this paradigm compared to the traditional modeling strategies is the absence of behavioral equations on the aggregate level and the ability to take into account different strategies regarding information processing and action patterns of the agents. Advantages of economic agent-based models are primarily (but not limited to):

the possibility to model dynamic or evolutionary processes,

the room for heterogeneity of the agents,

the application of dynamically evolving expectation models embedded within the agents,

the scaleable degree of detail in certain areas of the model, and

the support of highly non-linear and/or probabilistic models.

Traditionally, agent-based economic research activities have been focused on isolated sociological or economic issues, following a partial modeling approach. On the other hand, toolkits for general purpose agent-based simulations have been developed using different IT platforms and computer languages.

The aim of this book is different from previous work in the field in the sense that the objective is arriving at a complete (total) macro model of the economy, which can be applied to different economic policy issues. The sections in this book are structured as follows:

In the first part, some theoretical considerations concerning economic modeling and especially agent-based modeling are presented. This chapter briefly describes the various alternative approaches to economic modeling with their advantages and limitations and then provides more detailed information on the multi-agent methodology. Agent-based models can overcome several of these traditional restrictions of the more traditional modeling methodologies, but on the other hand some specific characteristics have to be recognized. The key concepts of agent-based models, most prominent genetic algorithms (GA) and artificial neural networks (ANN) are described. Another focus of this chapter is the basic structure of agent-based models.

After having discussed the theoretical pros and cons of the methodological approach and the theoretical structure of an agent-based model, the following chapter throws some light on the technical dimension of implementing an agent-based model. First of all, the key concepts of agent-based programming are described. Naturally, this leads to a discussion of choosing the development and execution platform of such a model in a more technical manner. The next step is to choose an appropriate programming language, which is not an easy task, as there are several dimensions to keep in mind: code efficiency and speed, memory management and constraints, extensibility, usability, stability, etc. Finally the key advantages of choosing C# are described. This section also gives an overview of the most important C# 2.0 language features relevant to the agent-based programmer. Note that this part of the book is not intended as a C# primer, but rather as a discussion of C# programming concepts closely related to agent-based models.

The next section presents the design of the agent-based economic model AS1 developed by the author, which consists of an extensible and re-usable class library and a graphical user interface (GUI). The main focus of the discussion is on the structure and functioning of the core elements of AS1. Classes represent types of agents and are the basic elements of the artificial economic system. After showing the model structure, interfaces, classes, and the control flow in the model are presented. Due to the large number of classes and other elements, only the most important features of the most interesting classes are described in detail. A complete (but very short) class reference is given in the appendix. Additional information on all the classes can be found in the online documentation of AS1, available upon request from the author.

The last chapter in this book presents some hints on the possible applications of the previously developed model AS1. The exercises comprise the development of a model baseline that can be used for further analyses and an application on the information formation mechanisms of the agents. These applications should be some illustrative examples for the large number of possible research questions that could be treated with an agent-based model, but should be seen as only the beginning of a bunch of simulation experiments with AS1.

In the summary, the benefits of agent-based modeling as well as the special issues associated with this methodology are summed up. Extensions already in progress and further future enhancements of the agent-based model AS1 are presented.

The appendix contains a class reference of the AS1 core classes for economists and IT specialists who would like to use AS1 for their own experiments. AS1 is available as a compiled class library and a fully-featured application from the author upon request. Although the present version of AS1 is completely functional as a class library (including the GUI) no special efforts have been made testing the framework (and especially the installer) in different environments apart from the Microsoft Windows XP platform. Everybody planning to use AS1 is therefore encouraged to contact the author and/or visit the author’s website (http://www.haber.at/) for the most recent version.

3 For example, “SimCity” was one of the first computer games to implement a micro model of a large number of agents.

2. Economic Modeling with Agent-based Models

2.1. Traditional Macroeconomic Modeling Approaches

2.1.1. General Considerations

The first choice when developing an economic model is to decide upon the general type of model. As this a rather complex decision with several dimensions, various aspects ranging from data availability to the application context have to be taken into account. To identify the specific strength and weaknesses of agent-based model, pros and cons of the other wide-spread modeling methodologies have to be investigated (see e.g. Haber, 2002).

Macroeconomic models are expected to resemble reality as close as possible while maintaining a high level of abstraction. Abstraction is necessary in order to focus on the most relevant features of the economic system, at the same time neglecting aspects which do not substantially influence overall economic output and other key variables in the model. The basic structure of an economic model is the first decision that has to be taken. When evaluating this decision regarding the modeling approach, several different paradigms can be chosen. Alternative modeling strategies differ with respect to premises, objectives and typical difficulties associated with each of the approaches. Several models used for empirical purposes follow very different methodologies and paradigms (for a hint on the range of different approaches see e.g. Bradley et al, 1995; Bundesbank, 1996; Fair, 1984 and 1994; McKibbin and Sachs, 1991; Url, 1998).

The most important traditional approaches for macroeconomic modeling are the Cowles Commission approach (Fair, 1992), several types of time-series models, vector auto-regressive models, and (computable) general equilibrium models.

There is another line of modeling methodology as well that focuses more on the derivation of stylized interdependencies than on empirically valid projections and forecasts: mathematical models with a limited number of equations and variables on the one hand, and Markov process type models on the other hand. Models involving game theoretic algorithms usually belong to the first kind, while statistical models of economic policy regimes often can be found in the latter category.

Agent-based models can be seen as an intermediate approach combining the philosophy of both lines of thought: While sticking to rather detailed microeconomic mechanisms and containing a large amount of stylized behavior with respect to the agents, these models generally aim at reproducing and revealing empirically valid economic mechanisms – enriched by partly rational expectations, selective perception, smart learning and strategic interaction.

2.1.2. The Cowles Commission Approach

In the 1970ies, the approach suggested by the Cowles Commission was very popular. This methodology still stands for medium to large structural macro-econometric models of the economy (see e.g. Fair, 1992). The general objective of this approach is to capture observable relations among the main economic variables in structural equation systems by applying econometric methods, thus identifying behavioral equations. Each endogenous variable in the model is explained by an equation in the model. Variables that cannot be observed, such as the deep parameters of utility functions or similar “hidden” variables are omitted in this approach by purpose. Modeling usually comprises these three steps:

specification of the model equations

estimation of the system

evaluation of the model

When specifying the model, economic theory is used to derive the equations of the linear or non-linear system. The elements of the model are endogenous variables, pre-determined variables (exogenous and lagged endogenous variables), the unknown parameters and stochastic disturbances.

Estimation of the model is done by applying econometric methods and techniques. Originally, these methods were limited to traditional singleequation methods (such as ordinary least squares – OLS), but later on with the availability of sophisticated simultaneous methods, system estimation techniques have become more popular.

The last stage of modeling is evaluating the model. On the one hand, the consistency, significance, and compatibility of the estimated parameters with economic theory are checked. On the other hand, the empirical power (ex-post forecasting, ex-ante forecasting) of the model is evaluated.

All of the three stages might make it necessary to return to an earlier stage in the modeling process and to alter the structure of the model. But in principle, theory comes first and then econometric methods are applied. This is in contrast to “data mining”, which is the main feature in vector autoregressive models (VARs), which will be discussed below.

In spite of the fact that most models used for forecasting by various research institutes can still be seen as following this methodology, the Cowles Commission approach has become rather unpopular in economic modeling due to several issues that have been raised in the literature:

Application of single-equation methods. OLS and other singleequation techniques do not account for restrictions and interdependencies of the parameters (Sims, 1980).

Parameters are supposed to be constant (in the sense of “timeinvariant”) and invariant to changes in policy regimes, learning, etc. This is the classical “Lucas critique” raised by Lucas (1976).

Identification issues, especially when including lagged endogenous variables and expectation variables as regressors (also raised by Sims, 1980).

The first issue can be regarded as more or less obsolete due to the development of powerful methods for simultaneous system estimation, such as seemingly unrelated regression estimators (SURE) two-stage least squares (2SLS), three-stage least squares (3SLS), limited information maximum likelihood (LIML), full information maximum likelihood estimators (FIML), and other even more sophisticated non-linear estimators. This is also true to some extent for the last issue, because there are some small-sample and largesample inference results together with system estimation techniques, cointegration and error correction approaches, that alleviate the identification problems to some extent. Especially the question, if lagged endogenous variables should be used for identification can be regarded as solved in the light of the development of error correction models (ECM). These considerations have been treated in detail e.g. in Engle and Granger (1987) or Taylor and Dixon (1997). Short-run dynamics (the error correction component) might be estimated separately from long-run co-integrating relations.

The traditional Lucas critique on the other hand is more important for structural models than the previous two concerns. The core argument can be formulated as follows: The parameters of the model are no longer constant, if backward-looking expectations are present and economic policy is changed. If this issue is taken very seriously and also applied to all parameters in the model, even to the deep parameters of the utility functions, the Lucas critique is purely destructive for structural models and leads to the conclusion that no econometric modeling is possible at all. Alternatively, the Lucas critique has been taken as a point in favor of structural models as opposed to reduced form approaches and has been also put forward as an argument against VAR models and in favor of the Cowles Commission approach (e.g. Sims, 1980 and 1996; Taylor, 1993).

Regardless of the interpretation of the Lucas critique, there still remains the problem of constant parameters, which might be less of a problem, when there is not much change within the economic environment. Reasons for a relative constancy of the environment might be the time-horizon or an economic situation close to a steady state or at least close to some stable adjustment path towards the steady state. Structural models with a clear inheritance from the Cowles Commission paradigm still exhibit some properties which make them first-choice for short-run or medium-run forecasts of the economy. This is the reason, why this model type is still very popular with research institutes all over the world. The drawbacks of this approach with respect to the forecasting power of the models are also well-known:

In dynamically changing environments (e.g. catching-up processes in the transformation economies since the 1990ies), the assumption of constant parameters cannot be justified.

Structural breaks inherently call for changes in the structural parameters of structural models. More over, the introduction of the common currency in Europe in 1999 has produced severe problems for structural model designers due to a small number of observations available since 1999, making it nearly impossible to estimate the most recent sub-period or to capture the structural break in the parameters.

For transformation countries, there are limited an unreliable timeseries which render most of the large-sample results of the econometric techniques (such as super-consistency) useless and leave us with the most basic problems of multi-collinearity and auto-correlation.

Structural models are very “sluggish” in forecasting changes in trends, such as the beginning of a boom phase or a recession. Best forecasts are obtained if there will be “business as usual”.

Dynamic learning can be implemented in such models only to a very limited extent.

Forward-looking expectations can be applied to structural models of the Cowles Commission type, but estimation and solution of these models is very complex and subject to a large number of restrictions, due to the arising two-point boundary issues. Moreover, there is no possibility to gain fine control over individual expectation formation and bounded rationality.

A more modern approach to large structural models can be seen in economic policy research and the application of dynamic stochastic optimization algorithms to represent the objective functions of the policy makers. When extending this analysis to dynamic games and coalitions, the Lucas critique becomes less important – on the other hand, the quality of forecasts depends more heavily on the assumptions for the objective functions (specification and parameter values).

2.1.3. Time-series Models

Small time-series models have become very popular in the 1990ies with the development of the theory around different time-series processes, such as the auto-regressive (AR) process, the integrated (I) process, and the moving average (MA) process. Co-integration theory and empirical methods, as well as the development of error correction models (ECM) have further promoted the success of time-series modeling.

Traditional modeling has always had a problem in providing the projections for the exogenous variables. Thus, originally, time-series models were a good means for providing forecasts for those variables as an input for structural models. But as the focus changed from the simple ARIMA models to other, even more complex, statistical processes, such as the Markov process, time-series modeling got an entirely new dimension.

Although there are several interesting issues related to time-series modeling, both on the theoretical and on the econometric levels, with respect to agent-based models, there are only a few key issues of relevance:

Time-series models often suffer from degrees of freedom problems. This is also true when trying to calibrate agent-based models, that also tend to have a huge number of parameters (as they might be different for all individual agents in the model – thus the number of parameters for an agent class is the number of parameters in that class multiplied by the number of instances of this particular agent class!).

The fit of a model can be improved by including a higher number of lags (e.g. auto-regressive terms), but at the same time, predictive power in dynamic simulations decreases. Agent-based models also suffer from this problem, which inherently decreases the ability of agent-based models to produce valid forecasts (in levels).

Time-series models can be used inside agent-based models for getting forecasts of some expectations variables. Note: The preferred approach taken in this book is different, as time-series models have serious lack of (economic) theory. In the agent-based paradigm developed here, agents do not do anything based upon purely “mechanic” forecasts – in contrast, agents always have some “imagination” and “perception” on why to do what.

2.1.4. VAR and VEC Models

From the Sims (1980) criticism concerning the problems of structural models as favored by the Cowles Commission approach, an alternative to these models is readily available: If theory and estimation of structural models cannot be free of errors, errors originating from theory could be avoided by avoiding theory itself.

Vector auto-regressive models (VARs) follow this idea and regard all variables in the model as endogenous. All model variables are explained by all other variables and lags of the other variables (and, of course, the respective variable itself). In the famous example by Sims (1980), who can be seen as the “inventor” of VAR models, there are six variables with four lags – leading to 144 parameters to be estimated. This requires of course a huge number of degrees of freedom, which cannot easily be provided given the time-series for only six variables. Moreover, the estimators for VARs are often inefficient, aggravating the problem even further (Hall, 1995). This may cause two annoying properties of such models:

Poor quality of out-of-sample forecasts. Due to the big confidence intervals of the parameters caused by identification problems and inefficient estimators, the forecasts might suffer from high variance. Moreover, dynamic forecasts might sometimes exhibit explosive or oscillating behavior.

Unfeasible solutions. A large number of included variables may lead to an exploding number of regressions to be run. With each regression, some of the parameters become insignificant, and the model has to be re-estimated. Even if some high-frequency data is available and there is no degrees of freedom problem, the question of model selection becomes increasingly important.

From the methodological point of view, the latter problem was one of the issues driving the development of one of the most important agent technologies – genetic algorithms (GAs). A GA is (or should be) capable of finding appropriate models for a given problem, in situations that do not permit to evaluate all of the possible solutions to a problem.

But even if the model selection problem can be solved by applying a GA, there still remains the problem of parameters that are inconsistent with economic theory or inconsistent with other model parameters. A solution to this problem would certainly be the inclusion of some theory-guided parameter restrictions on the VAR system, but strictly speaking, this is of course a violation of the objective to omit theory from the modeling process.

Critics of the VAR approach have denoted this approach as pure “data mining”, but an increasing number of applications of VARs in economic research prove that this type of model has found its place in modern economics. Especially the development of vector error correction models (VECs) has boosted the use of the VAR philosophy, as VECs combine the advantages of VARs and implement the more recent development of error correction models, thoroughly differentiating between long-run relations given by co-integrating equations and the short-run dynamics of the model. Nowadays, the predictive power of VARs and VECs has to be regarded as having improved due to methodological advances – but still this type of model is rather used for partial models and for identifying “hidden” relations than for more complete models with a focus on economic forecasting.

The evolution of VARs and VECs has provided many important inputs for the development of agent-based models: genetic algorithms, the idea to put less emphasis on stylized behavioral equations on the macro level, and the approach, that forecasting power may not necessarily be the one and only objective in modeling economic systems.

2.1.5. General Equilibrium Models

Computable general equilibrium (CGE) models rely on assumptions taken from the neoclassical theory and originate from the analysis of input-output tables.4 The different sectors of the economy are modeled usually in a disaggregated manner. Newer forms of CGE models also include the theory of real business cycles and disequilibria in the Keynesian sense.

CGE models are rarely econometrically estimated, but in most cases calibrated to fit the empirical observations. Calibration means, that the parameters of the model are adjusted so that the model reaches equilibrium at a given point in time. More advanced techniques refrain from assuming permanent equilibrium and only assume that the model is on a stable adjustment path towards general equilibrium in the reference period.

CGE models are most appropriate, whenever realistic forecasts of the levels of certain variables are less important, but when the focus is on analyzing differences among alternative scenarios. They are also well-suited for numerically examining theoretical mechanisms. On the other hand, even if enriched with some Keynesian features, CGE models are usually not capable of explaining persistent disequilibria. Moreover, the effects of the economic policy instruments on real variables is generally limited to short-run effects, because the model always strongly tends to return to the equilibrium (adjustment) path. Advantages of CGE models can be seen in the well-defined long-run properties, which are usually in line with (the neoclassical) theory.

Agent-based models show some similarities with CGE models regarding their application – but are completely different in the modeling approach. While agent-based models also strongly rely on disaggregated behavior, this foundation is on the (individual agent) micro level for agent-based models and on the intermediate sectoral level for CGE models. The concept of equilibrium is of no importance when designing the agent-based model, but might only be an issue in the calibration and validation stages in order to exclude explosive model setups.

From the application perspective, agent-based models work very similar. Emphasis is also put on the dynamic comparative analysis of alternative institutional or policy scenarios. Generally, a baseline solution is calculated, and subsequently deviations from this baseline are evaluated for the different scenarios. Agent-based models are also very well suited for analyzing economic mechanisms with an empirical model.

2.1.6. Stylized Mathematical Models

Small stylized mathematical models have become increasingly popular, especially for analyzing stylized facts in economic policy evaluation and the effects of different policy rules. This type of models usually consists of a relatively small number of variables and equations, because higher-order problems cannot easily be solved analytically. In most cases, objective functions are included which can then be optimized in order to find some necessary or sufficient conditions for the optimum.

The system can be specified in discrete time or in continuous time. Often, general conclusions are found by deriving the first-order conditions for some equilibrium or optimal values of an objective function, or by examining restrictions on the parameters for some feasible solution space of the system. Optimization and game theoretic methods can easily be applied to these models and might give even more detailed insights in the economic mechanisms (see Shubik, 1991).

The main drawback of this approach is the fact, that this paradigm necessarily follows a partial modeling strategy, neglecting a large number of potentially relevant variables. While small mathematical models can be an important source for theoretical considerations, empirical relevance (in terms of forecasting power) is usually very low – but this is of course not an objective when implementing such models.

Agent-based models share some properties with this model type as well, even if this is not so obvious due to completely different model structures: The idea of very narrow partial models is also inherent to agent-based systems in some sense, as each agent can be seen as a partial model of itself. The main difference is the fact, that agent-based models link these low-level partial models by interaction patterns and some active behavior of the agents and that the models might dynamically change.

2.2. Agent-Based Models

Agent-based models have become a promising field of research in the social sciences. Generally, the application of agent technologies to model social and economic systems can be referred to as an alternative to traditional modeling.

Robert Axelrod, one of the pioneers in agent-based modeling, gave a perfect description of the methodological approach: “Agent-based modeling is a third way of doing science. Like deduction it starts with a set of explicit assumptions. But unlike deduction, it does not prove theorems. Instead an agent-based model generates simulated data that can be analyzed inductively.” (Axelrod, 1997a)

The agent-based modeling approach cannot be seen as a theoretically consistent methodological paradigm, because there are several different interdisciplinary approaches to this field of research. A natural foundation of agent-based models can be derived from experimental economics (e.g. Kagel and Roth,1995; Roth and Erev, 1995; Prescott, 1996; Roth, 2002), while other roots can be seen as originating from research rather related to the social and behavioral aspects of agent-based systems (e.g. Young, 1998; Durlauf and Young, 2001; Akerlof, 2002). Other approaches to agent-based modeling have been taken by separate trails of literature focusing on evolutionary economics (e.g. Nelson and Winter, 1982; Anderson et al., 1988; Day and Chen, 1993; Witt, 1993; Nelson, 1995), interaction (e.g. Kirman, 1997), game theory and evolutionary game theory (e.g. Marks, 1992; Samuelson, 1997; Erev and Roth, 1998; Gintis, 2000; Camerer, 2003), or computational numerical approaches in general (e.g. Judd, 1998). It is in the nature of agent-based models, that historically, the modeling of trade and trade networks is one of the key domains of this approach (e.g. Rubinstein and Wolinski, 1990; Tesfatsion, 1997b; McFadzean and Tesfatsion, 1999), and big emphasis has been put on theory and implementation of trade setups and auctions (e.g. Albin and Foley, 1992; Cliff and Bruten, 1997; Klemperer, 2002; Koesrindartoto, 2002; Cliff, 2003). Other papers have investigated market organization issues (e.g. Vriend, 1995); some of them specialized to financial markets (Arthur et al., 1997). A genuine idea behind agent-based models also relates to chaos, complexity, and the evolvement of order (Holland, 1995; Brock et al., 1991; Flake, 1998).

An excellent overview of agent-based modeling can be obtained from several special issues and handbooks on agent-based modeling (Tesfatsion, 2001a, 2001b, and 2001c; Tesfatsion and Judd, 2006) and from some survey journal articles (e.g. Tesfatsion, 1997a and 2002). Especially Tesfatsion and Judd (2006) provide a very recent and complete overview, so there will be no further extensive survey presented here.

Traditional agent-based models can be designed following two main philosophies:

“stylized models” very similar to mathematical models

“artificial worlds”, which allow for complex interactions of the agents