Time, Knowledge and Procedural Rationality with an Application to Environmental Economics
D ISSERTATION
zur Erlangung des akademischen Grades eines Doktors der Wirtschaftswissenschaften (Dr. rer. pol.) durch die Fakultät für Wirtschaftswissenschaft der FernUniversität in Hagen
vorgelegt von
Diplom-Volkswirt Frederik Schaff
∗Hagen, den 27.04.2016
∗frederik.schaff@fernuni-hagen.de
Wissenschaftliche Beratung:
Prof. Dr. Alfred Endres
Lehrstuhl für Volkswirtschaftslehre, insb. Wirtschaftstheorie Universitätsstraße 11, 58097 Hagen
Gutachter:
1. Prof. Dr. Alfred Endres. FernUni Hagen
2. Prof. Dr. Klaus G. Troitzsch, Universität Koblenz-Landau
Tag der Disputation:
24.08.2016
Time
The relative autonomy of individual choice clearly implies the imperfect predictability of the future consequences of choices. When an individual decides to embark upon a particular course of action, the consequences will depend, in part, on what courses of action other individuals are, or will be, choosing.
[. . . ]
Choices made in real time are thus never made with complete knowledge (either deterministic or stochastic) of their consequences. The recognition of this fact by individuals is the source of rule-following behaviour and, on a social level, of the development of institutions.
— Gerald P. O’Driscoll, Mario J. Rizzo, and Roger W. Garrison (1985, p. 2-3)
Knowledge
The assumption of a perfect market then means nothing less than that all the members of the community, even if they are not supposed to be strictly omniscient, are at least supposed to know automatically all that is relevant for their decisions. [. . . ] The assumption of a perfect market in this sense is just another way of saying that equilibrium exists but does not get us any nearer an explanation of when and how such a state will come about. It is clear that if we want to make the assertion that under certain conditions people will approach that state we must explain by what process they will acquire the necessary knowledge.
— Friedrich A. von Hayek (1937, p. 45)
Procedural Rationality
Uncertainty, however, exists not in the outside world, but in the eye and mind of the beholder.
[. . . ] We are concerned with how men behave rationally in a world where they are often unable to predict the relevant future with accuracy. In such a world, their ignorance of the future prevents them from behaving in a substantively rational manner; they can only adopt a rational choice procedure, including a rational procedure for forecasting or otherwise adapting to the future.
— Herbert A. Simon (1976, p. 143)
Abstract
The mainstream of economic research follows the paradigm of neoclassical economics with its strong emphasis on equilibrium. Since this approach depends upon analytical solutions (existence-proof), it cannot represent time as a (historical) process. Unfortunately, it is thus limited to substantive ra- tionality (maximisation principle) and does not allow for an explicit knowledge representation. The computer simulation technique of agent-based modelling allows for these properties and embraces complexity. By the name ofpure agent-based computational economics (pACE), such an approach to economics with a strong emphasis of time, knowledge and procedural rationality is described. The potential ofpACE is highlighted with a first modelling exercise: thebakerymodel. The analysis shows that the neoclassical competitive equilibrium can be an emergent result ofpACE, but as a special case only. Furthermore, in an extended version of the same model, the classical environmental economics’
question of “prices vs quantities” (taxes vs. quotas) is analysed. The duality known from comparat- ive static analysis does not hold when it comes to the analysis of the adjustment process, and in the
“prices” setting it becomes important who bears the tax. The adjustment process under an effluent charge differs from that under an equivalent sales tax, and both differ again from that under a quotas regime. As a side-effect of the research conducted, some new methods for the analysis of ACE models are introduced.
Journal of Economic Literature classification:
B41 Economic Methodology
B50 Current Heterodox Approaches
C10 Econometric and Statistical Methods and Methodo- logy: General
C63 Computational Techniques
D83 Search, Learning, Information and Knowledge, Com- munication, Belief, Unawareness
Q50 Environmental Economics
Contents
Abstract e
Abbreviations vii
List of Figures ix
List of Tables xiii
List of Algorithms xv
List of Symbols xvii
Preface I
Introduction and Purpose 1
Neoclassical Methodology . . . 2
(Pure) Agent-based Computational Economics . . . 3
TheBakeryModel . . . 7
Intertemporal Welfare and Environmental Policy . . . 11
Research Questions and Outline. . . 11
I Neoclassical Methodology and itsPureAgent-based Complement 15 1. Reciprocity of Methodology and Theory in Economics 15 1.1. The Formal Corpus of Neoclassical Economic Methodology (NCM) . . . 15
1.2. Methodology Shapes Theory . . . 18
2. Representation in Neoclassical Methodology 24 2.1. The Individual as Homo Oeconomicus . . . 25
A: Uncertainty . . . 25
B: Rationality . . . 30
C: Utility . . . 33
2.2. Representing Market Interaction: The Concept of Equilibrium . . . 36
D: Perfect Divisibility / Marginal Approach . . . 37
E: No Time & No Trade . . . 38
F: Existence of Representative Agent(s) . . . 41
G: Market Interaction Hypothesis I (Atomistic Behaviour) . . . 42
H: Market Interaction Hypothesis II (Instantaneous Action) . . . 43
2.3. Synopsis . . . 45
3. Representation inPureAgent-based Computational Economics 46 3.1. Elements ofpACE . . . 47
3.2. Knowledge Representation . . . 51
3.2.1. Kind of Knowledge and Knowledge Representation . . . 51
3.2.2. An Epistemic Concept of Knowledge . . . 58
3.3. Procedural Rationality . . . 64
3.4. The Generative Approach . . . 67
3.4.1. Interaction Target Selection . . . 69
3.4.2. Updating Scheme . . . 72
3.4.3. An Explicit Action-time Framework forpACE . . . 75
3.5. Propositions . . . 77
3.6. Synopsis . . . 78
4. Conclusion 79
4.1. Reasons for an Agent-based Approach to Economics . . . 79
4.2. Reasons Against an Agent-based Approach to Economics . . . 81
4.3. Theoretical Alignment:pACE meets NCM . . . 82
II TheBakeryModel: AligningpACE to NCM 85 1. Introduction 85 2. Motivation and Methodological Remarks 87 2.1. Place within the General Context of the Thesis . . . 87
2.2. Modelling Guidelines . . . 90
2.3. Notation . . . 91
3. Model 93 3.1. TheBakery Problem . . . 93
3.1.1. General Problem Statement . . . 93
3.1.2. Equilibrium Expectation: A Neoclassical Benchmark . . . 95
3.1.3. (Further) Assumptions for thepACE Implementation . . . 101
3.2. Main Building Blocks of theBakeryModel . . . 102
3.2.1. Time & Updating Scheme . . . 104
3.2.2. Entry Rule . . . 105
3.2.3. Knowledge Representation . . . 109
3.2.4. ANormalDay in theBakery Model: Nontechnical Introduction . . . 113
3.3. Consumer Model . . . 116
3.3.1. Preface . . . 116
3.3.2. Goals and Expectations. . . 118
3.3.3. Where To Buy . . . 120
3.3.4. When To Buy. . . 122
3.3.5. Evaluation of Companies - Search under Ignorance . . . 124
3.3.6. Zombies, Inactivity and Related Issues . . . 127
3.3.7. Overview of Parameters . . . 129
3.4. Company Model . . . 129
3.4.1. Preface . . . 129
3.4.2. Company Statistics . . . 132
3.4.3. Company Heuristics . . . 143
3.4.4. Overview of Parameters . . . 152
3.5. Implicit and Discrete Parameterisation . . . 153
3.5.1. Selection and Discretisation of Appropriate Demand Functions . . . 153
3.5.2. Parameterisation and (Discrete) Representation of the Cost Function . . . 156
4. Methodology for the Simulation Experiment 158 4.1. Measurements at Each Point in Time . . . 159
4.1.1. Measures of Routine Behaviour . . . 159
4.1.2. Efficiency Measures . . . 160
4.1.3. Miscellaneous Statistics and Normalisation . . . 164
4.2. Response Variables . . . 165
4.2.1. Characteristics of Genuine Distributions. . . 166
4.2.2. Convergence Statistics . . . 167
4.2.3. Overview of the Response Variables Covered . . . 168
4.3. Automated Statistical Analysis of a Single Experiment . . . 171
4.3.1. Stopping Criteria . . . 172
4.3.2. Truncation Heuristic . . . 173
4.3.3. A Test for Reasonable Stationarity . . . 177
4.3.4. Implementation . . . 178
5. Analysis 179 5.1. Hypothesis and Testing . . . 179
5.1.1. Reasonable Equilibrium . . . 180
5.1.2. Reasonable Convergence. . . 181
5.1.3. Reasonable Resemblance . . . 183
5.2. Design of Experiment . . . 185
5.2.1. Experimental Set-ups . . . 185
5.2.2. Design Matrix for the Screening Experiments and the Proof of Concept . . . . 187
5.2.3. Ex-post Conditional Analysis . . . 188
5.3. Screening . . . 189
5.3.1. Screening Experiment I: LINEARCONST . . . 190
5.3.2. Screening Experiment II: LINEARCONST_COURNOT. . . 195
5.3.3. Summary and Parameter Space Refinement . . . 199
5.4. One-at-a-time: Explorative Analysis . . . 203
5.4.1. M axN umberOf Companies . . . 205
5.4.2. M inimumU nitP rof it . . . 208
5.4.3. Rating_Atrophy . . . 210
5.4.4. alpha_talk . . . 212
5.4.5. Rating_AdjSpeed . . . 214
5.4.6. AdaptiveSatLvlAdjW eight . . . 216
5.4.7. AdaptiveP riceExpAdjW eight . . . 218
5.4.8. AspirationLvlHunger . . . 220
5.4.9. AspirationLvlF rugalness . . . 222
5.4.10.AcceptedP riceM arkup . . . 224
5.4.11.AllowInactivity . . . 226
5.4.12.AllowInactiveExploration . . . 228
5.4.13.RSquareSwitch. . . 230
5.4.14.RiskAverseF actor . . . 232
5.4.15.P ropensityT oInertia . . . 234
5.4.16.RatioConsumers_insolvent. . . 236
5.4.17.Consumers_BudgetsDistributionSkewness . . . 238
5.4.18.P roduction_minAT C_quantity . . . 240
5.4.19.P roduction_DiseconomiesOf Scale . . . 243
5.4.20.OptimalN umberOf Companies . . . 245
5.5. Proof of Concept. . . 247
5.5.1. Set-up . . . 247
5.5.2. Analysis . . . 247
5.6. Synopsis . . . 254
6. Conclusion 259
III Intertemporal Welfare and Environmental Policy:
Prices vs Quantities in theBakeryModel 263
1. Introduction 263
1.1. Status Quo . . . 263
1.2. Intertemporal Welfare Analysis . . . 264
1.3. Related Literature . . . 266
1.4. Basic Properties . . . 267
1.5. Layout of Part III . . . 268
2. Extension of theBakeryModel: Quotas vs. Tax 269 2.1. Policy Options . . . 269
2.2. Company Model . . . 270
2.2.1. Quota . . . 271
2.2.2. Tax . . . 272
2.3. Miscellaneous . . . 274
2.3.1. Consumer model . . . 274
2.3.2. Oligopoly Setting . . . 274
2.3.3. Equilibrium Expectation - Neoclassical Benchmarks for the Tax . . . 275
2.4. Discussion . . . 275
2.4.1. Conditional Analysis . . . 275
2.4.2. A Note on Tax Incidence . . . 276
3. Design of Experiment 277 3.1. Intertemporal Welfare . . . 277
3.1.1. Limit Welfare . . . 278
3.1.2. (Time-)Conditional Welfare . . . 279
3.1.3. Smoothness of the Adjustment Process . . . 280
3.1.4. Industry Stability . . . 281
3.1.5. Response Variables: Summary. . . 281
3.2. Analysis . . . 284
3.2.1. Automated Phase Detection and Stopping . . . 284
3.2.2. Set-up . . . 286
4. Results 292 4.1. Pretest . . . 292
4.2. Main Experiment . . . 298
4.2.1. Detailed Graphical Analysis I . . . 298
4.2.2. Example, Explorative Time-series Analysis . . . 307
4.2.3. Detailed Graphical Analysis II . . . 312
4.3. Synopsis . . . 319
5. Conclusion 321
Summary 323
Appendix 329 A Additional Remarks to the Implementation of theBakeryModel 329
A1. Known Issues in the Implementation . . . 329
A2. Derivation of the Implicit Parameterisation of the Demand Function . . . 329
A3. Calculation of the Skewness Parameter . . . 331
A4. Conversion from Continuous to Discrete Demand . . . 331
A5. Derivation of the Implicit Parameterisation of the Cost Function . . . 332
A6. Conversion from Continuous to Discrete Cost . . . 333
A7. Sequential Randomisation Method . . . 334
A8. Ex-post Marginal Parameter Refinement Technique . . . 338
B Configurations, Part II 339 B1. LINEARCONST . . . 339
B1.1. Configuration Matrix . . . 339
B1.2. Input Factor Distribution . . . 341
B1.3. Exp-mPRT results . . . 343
B2. LINEARCONST01_COURNOT . . . 344
B2.1. Configuration Matrix . . . 344
B2.2. Input Factor Distribution . . . 346
B2.3. Exp-mPRT results . . . 348
B3. PROOFOFCONCEPT . . . 349
B3.1. Configuration Matrix . . . 349 C Equilibrium Expectation - Neoclassical Benchmarks for the Tax (continued) 353
Bibliography 357
Abbreviations
ACE agent-based computational economics CAS complex adaptive systems
CGE computational general equilibrium
DSGE dynamic stochastic (computational) general equilibrium DOE design of experiment
EBM equation-based models ESS evolutionary stable strategy EUT expected utility theory
ExP-mPRT ex-post marginal parameter refinement technique
HC Homo Oeconomicus
IQR inter quartile range LHS latin hypercube sampling
loess also calledlowess,locallyweightedscatter-plotsmoother LSD laboratory for simulation development
MAE mean absolute error
MSER marginal standard error rules NCM neoclassical methodology
NLS non-linear least squares regression
OAT one-at-a-time
OLS ordinary least squares regression
pACE pureagent-based computational economics PRNG pseudo-random number generator
RCT rational choice theory RMSE root mean square error UML unified modelling language WOM word-of-mouth communication w.r.t. with respect to
WTP willingness-to-pay
List of Figures
Part I 15
1 Interconnection of time, knowledge and rationality. . . 48
2 Knowledge Representation in NCM andpACE. . . 60
3 Some scheduling options . . . 74
Part II 85 4 ACE articles published and their citation counts . . . 85
5 UML Main Class Diagram - Overview . . . 102
6 UML Main Class Diagrams - Overview of consumer and company . . . 113
7 UML Main Class Diagram - Detailed overview . . . 114
8 Selection of companies / simulacra viatake the best . . . 121
9 High-Info-Scenario selection . . . 147
10 Parametric choice of the inverse demand curve . . . 156
11 Parametric choice of the average total cost curve . . . 157
12 Example Tukey-Boxplot fromgretluser guide . . . 185
13 (Screening): Overview of stopping conditions fired . . . 190
14 LINEARCONST: Distribution of different efficiency measures (full sample) . . . 191
15 LINEARCONST: Distribution of key quantities (full sample) . . . 192
16 LINEARCONST: Distribution of extreme excess . . . 193
17 LINEARCONST: Reduction of the parameter space usingExP-mPRT . . . 194
18 LINEARCONST_COURNOT: Factorised company routine indices (full sample) . . . 196
19 LINEARCONST_COURNOT: Factorised prices and quantities . . . 197
20 LINEARCONST_COURNOT: Efficiency levels (full sample) . . . 198
21 LINEARCONST_COURNOT: Reduction of the parameter space usingExP-mPRT . . . . 199
22 (Screening) Adjusted parameter space . . . 200
23 (Screening) Example distribution of factor levels . . . 201
24 (Screening) Reasonable stationarity in the complete and the conditioned samples . . 202
25 (Screening) Reasonable convergence ofConsumer_Routinewithin 400 days . . . 202
26 (OAT) Oligopoly behaviour by number of companies . . . 206
27 (OAT) Oligopoly behaviour - Time series plots . . . 207
28 (OAT)M inimumU nitP rof it- Stationary distribution . . . 208
29 (OAT)M inimumU nitP rof it- Time series plots . . . 209
30 (OAT)Rating_Atrophy- Stationary distribution . . . 210
31 (OAT)Rating_Atrophy- Time series plots . . . 211
32 (OAT)alpha_talk- Stationary distribution . . . 212
33 (OAT)alpha_talk- Time series plots. . . 213
34 (OAT)Rating_AdjSpeed- Stationary distribution . . . 214
35 (OAT)Rating_AdjSpeed- Time series plots . . . 215
36 (OAT)AdaptiveSatLvlAdjW eight- Stationary distribution . . . 216
37 (OAT)AdaptiveSatLvlAdjW eight- Time series plots . . . 217
38 (OAT)AdaptiveP riceExpAdjW eight- Stationary distribution . . . 218
39 (OAT)AdaptiveP riceExpAdjW eight- Time series plots . . . 219
40 (OAT)AspirationLvlHunger- Stationary distribution . . . 220
41 (OAT)AspirationLvlHunger- Time series plots . . . 221
42 (OAT)AspirationLvlF rugalness- Stationary distribution . . . 222 43 (OAT)AspirationLvlF rugalness- Satisfaction level frugalness /different aspiration . 223
44 (OAT)AspirationLvlF rugalness- Time series plots. . . 223
45 (OAT)AcceptedP riceM arkup- Stationary distribution . . . 224
46 (OAT)AcceptedP riceM arkup- Time series plots . . . 225
47 (OAT)AllowInactivity- Stationary distribution . . . 226
48 (OAT)AllowInactivity- Time series plots . . . 227
49 (OAT)AllowInactiveExploration- Stationary distribution . . . 228
50 (OAT)AllowInactiveExploration- Time series plots . . . 229
51 (OAT)RSquareSwitch- Stationary distribution . . . 230
52 (OAT)RSquareSwitch, Profit margins . . . 231
53 (OAT)RSquareSwitch- Time series plots . . . 231
54 (OAT)RiskAverseF actor- Stationary distribution . . . 232
55 (OAT)RiskAverseF actor, Profit margins . . . 233
56 (OAT)RiskAverseF actor- Time series plots . . . 233
57 (OAT)P ropensityT oInertia- Stationary distribution . . . 234
58 (OAT)P ropensityT oInertia- Time series plots . . . 235
59 (OAT)RatioConsumers_insolvent- Stationary distribution . . . 236
60 (OAT)RatioConsumers_insolvent- Time series plots. . . 237
61 (OAT)Consumers_BudgetsDistributionSkewness- Stationary distribution . . . 238
62 (OAT)Consumers_BudgetsDistributionSkewness- Time series plots . . . 239
63 (OAT)P roduction_minAT C_quantity- Stationary distribution . . . 240
64 (OAT)P roduction_minAT C_quantity- Time series plots. . . 241
65 (OAT)P roduction_minAT C_quantity- Profit margin and scaling . . . 242
66 (OAT)P roduction_DiseconomiesOf Scale- Stationary distribution . . . 243
67 (OAT)P roduction_DiseconomiesOf Scale- Time series plots . . . 244
68 (OAT)OptimalN umberOf Companies- Stationary distribution . . . 245
69 (OAT)OptimalN umberOf Companies- Time series plots. . . 246
70 (PoC) Distribution of efficiency measures . . . 248
71 (PoC) Distribution of aggregate statistics . . . 249
72 (PoC) Distribution of individual statistics . . . 250
73 (PoC) Distribution of (mean) long-run efficiency, restricted & unrestricted sample . . 251
74 (PoC) Effect of nuisance factors (according to NCM) on long-run efficiency . . . 252
75 (POC) Convergence statistics . . . 253
76 (PoC) Reasonable stationarity (share) . . . 253
Part III 263 77 (PvQ) Time-line and different phases . . . 285
78 (PvQ) Pretest: relative abatement vs tax level . . . 292
79 (PvQ) Ols regressions for the empirical tax function . . . 296
80 (PvQ) Sample configuration . . . 298
81 (PvQ) (Relative) conditional standard vs target standard . . . 299
82 (PvQ) Adjustment time (days) vs conditional standard . . . 300
83 (PvQ) Relative deviation of the emissions standard in the transition phase . . . 301
84 (PvQ) Smoothness of the transition phase . . . 303
85 (PvQ) Welfare (mean) for the first 5, 30, 100 and 400 days, part I. . . 304
86 (PvQ) Welfare (mean) for the first 5, 30, 100 and 400 days, part II. . . 305
87 (PvQ) Welfare (cv) . . . 306
88 (PvQ) Example time series, evolution of aggregate statistics . . . 308
89 (PvQ) Example time series, evolution of distribution of individual quantities . . . 310
90 (PvQ) Time-series: Example distribution of quantity mismatch . . . 312
91 (PvQ) Welfare (mean) . . . 314
92 (PvQ) Distributive efficiency (mean) . . . 315
93 (PvQ) Market efficiency (mean) . . . 316
94 (PvQ) Productive efficiency (mean) . . . 317
95 (PvQ) Breakthrough and stay-in rate . . . 318
96 (PvQ) Welfare levels interim and ex-post by policy . . . 319
Appendix 328 97 Distribution of factors for configuration LINEARCONST. . . 342
98 Distribution of factors for configuration LINEARCONST_COURNOT . . . 347
List of Tables
Part I 15
2 Solving theproblemsof NCM by means of simulation . . . 80
Part II 85 3 Miscellaneous settings (onlytechnicalparameters). . . 103
4 Entry_Settings . . . 108
5 Consumer_Settings . . . 130
6 Company: Descriptive statistics . . . 133
7 Company: Untruncating demand . . . 134
8 Company: Reference statistics . . . 135
9 Company: Median statistics . . . 135
10 Company: Statistics based on statistical inferences . . . 137
11 Company: Indicator variables . . . 142
12 Company_Settings . . . 152
13 Individual-level response variables describing thebakerymodel . . . 169
14 Aggregate-level response variables describing thebakerymodel . . . 169
15 Control Factors . . . 186
16 Parameter variations in the OAT Analysis . . . 204
17 Parameter settings for PROOFOFCONCEPT(excerpt) . . . 248
Part III 263 18 Policy_Settings . . . 270
19 Response variables describing the impact of the environmental policy . . . 282
20 Parameter Settings for config POLICYFACTORIAL_FINAL . . . 288
21 Average conditional abatement:[ΔQ(ρ, n;z)]μ . . . 293
22 Regression results forΔQ(ρ, n;z), non-standardised quantities . . . 294
23 Regression results forz(ρ, n;ˆ QIIIμ ) . . . 297
24 Example time series: descriptive statistics . . . 307
Appendix 328 25 Artificial sequential permutation results . . . 337
26 Parameter Settings for configLinearConst . . . 339
27 Results of theEx-post marginal parameter refinement technique (ExP-mPRT) . . . 343
28 Parameter Settings for configLinearConst_Cournot . . . 344
29 Results of theEx-post marginal parameter refinement technique (ExP-mPRT) . . . 348
30 Parameter Settings for configProofOfConcept . . . 349
List of Algorithms
Part II 85
1 calc_BM_joint(n): Joint profit maximisation quantity . . . 98 2 calc_BM_Sales(n): Aggregate attractor in sales maximisation . . . 99 3 calc_BM_Competition(n): Aggregate quantity attractor in Marshall competition . . . 99 4 calc_BM_Cournot(n): Aggregate quantity attractor in Cournot competition . . . 100 5 Updating Scheme . . . 105 6 ConsumerAction() . . . 122 7 estimate_inertiaDemand() . . . 136 8 estimate_DemandF unction() . . . 137 9 Pricing heuristic. . . 150 10 Updating ofCompanyExitLevel . . . 151 11 Robust truncation heuristiccalc_M SER_M inpos_Robust(Y) . . . 176
Appendix 328
12 OptimiseRobustness(matrix m) . . . 338 13 ApproxT ax(n, Q,mode): Approximate tax level . . . 354 14 calc_BM_joint(n, markup) . . . 355 15 calc_BM_Sales(n, markup) . . . 355 16 calc_BM_Competition(n, markup) . . . 356 17 calc_BM_Cournot(n, markup) . . . 356
List of Symbols (bakery model only)
Seepart IIsection2.3. on page 91for the general notation.
The bakery model
Miscellaneous
N The set of natural numbers.
P The set of monetary numbers,P≡ 100Z ={. . . ,−0.01,0.00,0.01, . . .}. R The set of real numbers.
Z The set of integer numbers.
A Arbirary variable used within theList of Symbolsto introduce the notation of indices.
A0 Ifdorrare substituted by 0, this indicates the initial value ofA.
APC Results/expectations underperfect competitionwith free entry & exit, see page95.
Ad Index forCurrentDay.
Ai, i∈ {1, . . . , m} There aremconsumer agents (excludingzombies) indexedi={1, . . . , m}. Aj, i∈ {1, . . . , n} There arencompany agents indexedj={1, . . . , n}.
Ar Index forT urn.
At Arbitrary index denoting time, also: one (time-) step in the simulation run.
AdT,ArT Indicates thecurrentstate of this variable, i.e. the last computation.
Variables / Response Factors
AT CC(q), AT CD(q) Average total cost, continuous / discrete case, see page94.
AT Copt Minimum average total cost, see page94.
BF AId, j Indicates whether the price was too low (+1), too high (-1) or just about right (0), see table11 on page 142.
BF AIRef,d,j Reference version ofBF AI, see table11 on page 142.
BComp,j,0 Initial budget of companyj, see page108.
CC(q), CD(q) The cost function of typeC(q) =a+bq+cqα : a, b, c∈R>0, α∈N>1, the subscriptC stands forcontinuous. ConverslyDdenotes the discrete case.
Consumer_Inactived,i Indicates whether the consumeriis active (0) or inactive (1), see page127.
EntryChanced Chance that a new company will enter at the given day, see page106.
GH,d,i, GF,d,i∈ {0,1}andGL,d,i∈[0,1] Indicator variables for goals Hunger (H), Frugalness (F) and Leisure (L), see page118.
LExit,d,j Exit level, a measure of the propensity to voluntarily quit business. See page151.
LastV isitd,i,j The last time the companyjhas been visited by consumeri, see page121.
M CC(q), M CD(q) Marginal cost, continuous case / discrete case, see page94.
M R(q, P) Hypothetical marginal revenue at given priceP and demand/quantityq, see page148.
M RHyp(q,↑), M RHyp(q,↓) Hypothetical marginal revenue resulting from a marginal change in prices, see page140.
PEntry,min Minimum entry price, see page17.
PInv(Q) The inverse demand function in the equilibrium benchmarks. See page94.
PInit,j Initial Price of companyj, see page107.
PLIS,d,j The price in theLIS, see page149.
PRef,d,j The reference price for companyjat dayd, see table8 on page 135.
PminExp,d,i Minimum price experienced by consumeri, in the recent past, at dayd. See page127.
Pd,j The price charged by companyjat dayd, see table6 on page 133.
PExp,d,i Myopic price expectation of consumeriat dayj, see page120.
PMyopic,d,i Myopic price experience of consumeriat dayj, see page120.
PNice,d,i The price that satifies the goalfrugalness, see page123.
Qopt Aggregate demand in optimum.Qopt ←qopt∙nopt, see page See page96.
Qd Aggregate production quantity.
R2ˆ
D(P),d,j TheR2value of the intermediate-run estimate demand function. See table10 on page 137.
RS,d,i,j, RS,d,i,j ∈(−2,2) Stock (S) and Price (R) rating for of consumerifor companyjat timed, see page120.
SLH,d,i, SLF,d,iandSLL,d,i∈[0,1] Satisfaction levels for goals Hunger (H), Frugalness (F) and Leis- ure (L), see page119.
T W Pd,j Number of consecutive days with the given price for companyj, see table6 on page 133.
W T Pd,i Willingness to pay of consumeriat dayd, see page123.
ΔP,LIS,d,j Adjustment speed for the price in theLIS, see page149.
ΔP,raw(P) Raw adjustment speed for the price in theLIS, see page149.
Φinterim,d,j Time in recent past plus if there wasn’t at least one change of price within, the interval is empty.136.
Φshort,d,j Depicts the time since the last price change, see page136.
Π(.5),d,j (Recent) median profit of companyj, see table9 on page 135.
ΠRef,d,j The reference profit for companyjat dayd, see table8 on page 135.
Πd,j Profit.
D˘(.5),d,j (Recent) median untruncated demand of companyj, see table9 on page 135.
D˘Ref,d,j The reference untruncated demand for companyjat dayd, see table8 on page 135.
D˘Spill,d,j The estimate of spilled demand for companyjat dayd, see table7 on page 134.
D˘Spill (.5),d,j (Recent) median spilled demand of companyj, see table9 on page 135.
D˘d,j The estimated untruncated demand for companyjat dayd, see table7 on page 134.
D, d, jˆ The demand estimate for the current day. See table10 on page 137.
DˆAdjusted,d,j(Pd,j) The estimate of the demand function used in theHIS, see page146.
DˆInertia,d,j Weighted demand estimate for the short run. See table10 on page 137.
Dˆshort,ls,d,j Semi-robust short-run estimate of demand at given price. See table10 on page 137.
Π(Pˆ ) The profit maximising price in theHIS. The denominatorIis for inertia,P ↑for an increase in prices andP ↓for a decrease. See page146.
ΠˆInertia,d,j Weighted profit estimate for the short run. See table10 on page 137.
Πˆshort,ls,d,j Semi-robust estimate of profit at given price. See table10 on page 137.
κExplore,d,j ∈[0,1] The chance that individualjwill look for a company yet unknown at timed, see page121.
κLIS,d,j TheLIS_M ultiplicator, controls the escalation of the price adjustment in theLIS, see page 149.
ILIS,d,j∈ {0,1}, LISindicator, see page140.
IMS,d∈ {0,1} Market satiation index, see page106.
IPA,d,j ∈ {−1,0,1}, Price action indicator, see page140.
IS,d,j ∈ {0,1}, Scenario indicator, see page140.
BCons,j Budget of consumer j (constant), see page122.
σD(Pˆ ),d,j The RMSE of the intermediate-run estimate demand function. See table10 on page 137.
εΠshort,Ref,d,j The mean absolute error (MAE) of the reference profit in the short-run horizon. See table10 on page 137.
εD˘
short,Ref,d,j The mean absolute error (MAE) of the reference untruncated demand in the short-run horizon. See table10 on page 137.
εD˘
short,ls,d,j The mean absolute error (MAE) of the short-run estimate of demand. See table 10 on page 137.
εD˘
short,Ref,d,j The mean absolute error (MAE) of the reference untruncated demand in the short-run horizon. See table10 on page 137.
εD(Pˆ ),d,j The MAE of the intermediate-run estimate demand function. See table 10 on page 137, εDˆ
Inertia,d,j Weighted demand estimate error for the short run See table10 on page 137.
εΠˆ
Inertia,d,j Weighted demand estimate error for the short run. See table10 on page 137.
εΠˆ
short,ls,d,j The mean absolute error (MAE) of the short-run estimate of profit. See table 10 on page 137.
constD(Pˆ ) The const of the intermediate-run estimate demand function. See table10 on page 137.
nd Number of companies at timed.
qopt Minimum average total cost quantity, see page97 qmax,Πˆ(P) Profit maximising quantity in theHIS, see page146.
qMCP(P) Qunatity where marginal cost paid are approximately equal to the price, see page144.
qRF,d,j The demand that ismost certainat daydfor companyj, see page144.
qd,j ∈N Individual production quantity.
qmax,d,j The maximum feasible quantity to be produced at daydby companyj, see page144.
qRopt,d,j Optimal quantity for companyjat daydgiven riskaversity and past demand, etc., see page 145.
qMCP,d,j(P) Quantity where marginal cost paid are approximately equal to the price, see page140.
sft,d,j The number of sales for companyjin the first turn of dayd, see table6 on page 133.
sd,j The number of sales for companyjat dayd, see table6 on page 133.
vft∧wb,d,j The number of visitors with buy option for companyjin the first turn of dayd, see table6 on page 133.
vft,d,j The number of visitors for companyjin the first turn of dayd, see table6 on page 133.
vwb,d,j The number of visitors with buy option for companyjat dayd, see table6 on page 133.
vd,j The number of visitors for companyjat dayd, see table6 on page 133.
slopeD(Pˆ ),d,j The slope of the intermediate-run estimate demand function. See table10 on page 137.
Parameters / Input Factors
AT Copt∈P>0 Minimum average total cost, equilibrium price., see table3 on page 103.
AF ∈[0,1] Aspiration level for goalfrugalness, see table5 on page 130.
AH ∈[0,1] Aspiration level for goalhunger, see table5 on page 130.
AllowInactiveExploration Switch, allow inactive consumers to search for the companies, see table5 on page 130.
AllowInactivity ∈ {0,1} Switch, allow consumers to become inactive(1), see table5 on page 130.
BCons,i∈P≥0 The individual budget of the consumer agenti.
Bj,0 The initial budget in quantities ofC(qopt), see table4 on page 108.
BaseEntryF requency ∈N Determines the average number of days which pass until a new com- pany enters, see table4 on page 108.
DM ∈N>0 Number of past days experiences that are reflected in the behavioural model,
see table5 on page 130.
LBM S ∈N0 Number of days that are attributed equal weights in demand estimation, see table12 on page 152.
LBM ∈N0 Maximal number of days gone to be still considered for estimation., see table 12 on page 152.
LIS_M L∈N>1 Number of times with subsequent price changes in the LIS scneario necessary until the maximal possible price change is allowed., see table12 on page 152.
LP AD∈N>1 Limit price action delay, defines the number of days to abide before a price change is allowed. See table12 on page 152.
Simulacra_M emory ∈N>0 Number of days a company will be remembered after its simulacrum has last been updated, see table5 on page 130.
TExit∈N1 Number of subsequent days with negative profit expectations necessary for a volun- tary exit, see table12 on page 152.
TR2 ∈[0,1] MinimumR2value of demand estimate in order to useHISprice strategy, see table12 on page 152.
Πq,min∈R≥0 Minimum expected profit margin necessary for a new company to enter, see table 4 on page 108.
η∈[0,118) Thediseconomies of scale, see table3 on page 103.
κR Discount factor for risk attitude. See page145.
ωPTI ∈[0,1] Propensity to inertia, see table12 on page 152.
ωB(1) ∈R≥1 Relative budget of the most wealthy consumer agent, see table3 on page 103.
ωB(Qopt) ∈R≥1 Relative budget of the least wealthy solvent consumer, see table3 on page 103.
ωZombie ∈R≥0 Fraction (additional) of consumers with insufficient budgets, see table3 on page 103.
ωRA∈(−∞,∞) Risk aversity factor, see table12 on page 152.
ωAPM∈[0,1] Accepted markup on the price in relation to the budget, see table5 on page 130.
ωRefAS ∈[0,1] Adjustment weight for adaptive expectations / reference statistics, see table 12 on page 152.
ωAP E ∈[0,1] Adjustment speed for the price expectations, see table5 on page 130.
ωAS ∈[0,1] Adjustment speed for the satisfaction levels, see table5 on page 130.
θSkew∈(−1,1) Shape of the implicit demand function, see table3 on page 103.
alpha_talk Chance per turn to triggerT alkT oConsumer()action , see table5 on page 130.
n0 ∈ {<0; (0,1)} The initial number of companies, see InitN umberOf Companies in table 4 on page 108.
nPC∈N1 The equilibrium number of companies under perfect competition with free entry &
exit, see table3 on page 103.
nmax∈ {0,N>1} If positive, defines the maximal number companies allowed to exist. See table 4 on page 108.
qopt ∈N>1 The level of efficient production/ equilibrium level of production, see table3 on page 103.
rmax Turns (alias consumer actions) per day, see table3 on page 103.
wAtr ∈[0..1] Rating atrophy, see table5 on page 130.
wR ∈(0,1) Rating adjustment speed, see table5 on page 130.
wTD ∈(0,1) Discount off information gained via talk, see table5 on page 130.
Statistics / Response Factor Analysis
BCons,d,iactive Same asBCons,d,ibut only active consumers, see page127.
EDist Distributive efficiency, see page161.
EMarket Market efficiency, see page162.
EProd Productive efficiency, see page163.
Elong−run Long-run efficiency, see page164.
HHI Inverse Herfindahl-Hirschman index, see page165.
PExp,d,iactive Same asPExp,d,ibut only active consumers, see page127.
PNice,d,iactive Same asPNice,d,ibut only active consumers, see page127.
RConvIQR Reasonable convergence of the IQR, see page182.
RConvmed Reasonable convergence of the median, see page182.
RCons,act Consumer routine index (active consumers only), see page160.
RCons Consumer routine index, see page160.
RCons,IQR A measure of the IQR of the routine index for consumers, see page172.
RCons,Skew A measure of the Skewness of the routine index for consumers, see page172.
Routine_P rice Company prices routine index, see page160.
Routine_Quantity Company quantities routine index, see page160.
SLactiveH,d,i, SLactiveF,d,i andSLactiveL,d,i ∈[0,1] Same as SLH,d,i, SLF,d,i, SLL,d,i but only active consumers, see page127.
T0,IRQ Test statistic for stationarity of the IRQ (original composition), see page177.
T0,med Test statistic for stationarity of the median (original composition), see page177.
TIRQ Test statistic for stationarity of the IRQ (permutation), see page177.
Tmed Test statistic for stationarity of the median (permutation), see page177.
W T Pd,iactive Same asW T Pd,ibut only active consumers, see page127.
WConv Reasonable period of time, see page182.
Y1Q First quantile of ordered statisticY, see page167.
Y3Q Third quantile of ordered statisticY, see page167.
YC:IQR Inter-quartile range convergence of statisticY, see page168.
YC:med Median convergence of statisticY, see page168.
YMAE Mean-absolute error of statisticY, see page167.
YRMSE Root-mean-square error of statisticY, see page167.
Ymax Maximum value of statisticY, see page167.
Ymean Arithmetic average of statisticY, see page167.
Ymed Median of statisticY, see page167.
Ymin Minimum value of statisticY, see page167.
ˇ
y The check symbol (ˇy) indicates that the variable is normalised as specified in section4.1.3.
on page 164.
ˆ
pIRQ P-value forHI,0: The IQR is not constant. See page178.
ˆ
pmed P-value forHII,0: The median is not constant. See page178.
IIRQ Indicates if the single permutation IQR test statistic is more extreme than the original com- position, see page177.
Imed Indicates if the single permutation median test statistic is more extreme than the original composition, see page177.
σ The standard deviation.
d∗ Truncation point, marks the end of the warm-up phase, see page174.
dCohen Cohen’s d, see page178.
g The maximal number of random permutation tests conducted. See page178.
h Constant that defines thepowerof the sequential monte carlo test. See page178.
l The actual number of random permutation tests conducted. See page178.
Prices vs. Quantities
Seepart IIIsection3.1.1. on page 278in addition to part IIsection2.3. on page 91for the general notation.
Miscellaneous
d∗ The day when pre-policy warm-up phase is at an end, see page 278 but also part II, sec- tion4.3.2. on page 173.
d0 The very first day of the simulation experiment, see page278.
dI The day the policy is introduced, see page278.
dII The day the post-policy adjustment process is at an end, see page278.
dIII The day when the simulation stops, see page278.
ΥI(I) The pre-policy non-transient phase. In general the superscriptIdenotes this period of time, see page278.
ΥII(II) The intermediate (or adjustment) phase, just after the policy has been introduced but be- fore the adjustment is complete. See page278.
ΥIII(III) The post-policy phase, when the adjustment is complete. See page278.
∈ {I, . . .} Indicator for the phase, see page278.
d∈ {I, . . .} Superscript for the number of days that passed since the policy has been introduced (sincedI). See page279.
Variables / Response Factors
Q0 The ex-ante level of aggregate production/emissions, see page269
Qq(Q) The conditional standard in the quota regime which might differ from the target standard Q, see page269.
Qz(Q, ρ) The conditional standard in the tax regime which might differ from the target standardQ, see page270
Qˆz(z, n, ρ) Estimate of the conditional standard function, see page269
IP Indicates if the cost increased and such that an increase of the price may be warranted, see page273.
qMCP,constr.(P,q)ˉ AlteredqMCPsuch that the additional quota obligation is considered. See page272 Parameters / Input Factors
ˆ
zQ(Q, n, ρ) Empirical tax function (estimate) to reach the target standardQ, see page270.
Q The target standard (aggregate Emissions/Production), see table18 on page 270.
Q The targetStandardon industry level, see page269.
ρ∈[0,1] Burden sharing, table18 on page 270.
q Individualquotain thecommand-and-controlsetting, see page269.
z Thetaxlevel, see page269.
EP ∈ {0,1,2} Determines the type of policy which is active, see table18 on page 270.
Statistics / Response Factor Analysis
P olicy_P rof itBrT hrDays_mean The average time necessary for a company to break-through.
Only those are covered which regain profitability. See page281.
P olicy_P rof itBrT hrDays_stderr The standard error of the break-through time. See page281.
P olicy_P rof itBrT hr_rate The share of companies that successfully recovered into a profitable zone after the policy had been introduced (if necessary). See page281.
P olicy_T urnOverRate∈[0,1] The share of companies that would have left the market, if allowed to. See page281.
Qμ The average production inter alia pollution for the respective phase, see page279.
Wcv The coefficient of variation for the respective phase, see page279.
Wμ The average welfare for the respective phase, see page279.
ΔQ The relative stringency of the standard, see page282.
Δn The relative competitive level, see page282.
κW,d Punishment factor for the calculation of the relative welfarewd, see page279.
qr∈N>0 The individual target emissions reduction level (i.e. absolute abatement target),P olicy_- IndivReductionLvl. See page287.
wd Relative welfare at dayd, see page279.
WII ∈[−1,1] Smoothness of the adjustment process. See page280.
Wμd Average (conditional) welfareddays after the policy has been introduced measured since it had been introduced. See page279.
Preface
When I began my time as a research assistant at Prof. Alfred Endres’ Chair of Economic Theory at the University in Hagen in September 2009, I had never even heard of the terms “agent-based modelling” (ABM) or “agent-based computational economics” (ACE). A few month after I started in Hagen, I defined my area of interest around a relatively new tool in the environmental econom- ics tool-box: Eco-Labelling (which in the end did not find its way into this thesis). I found that traditional neoclassical models cannot address endogenous preferences and came across this new approach of agent-based computational economics, which provided all the flexibility I needed.
However, my mentor and principal constantly asked me why exactly this thing which I wanted to show (I only had a vague idea at that point) could not be done with established methods, thus amp- lifying my already grown desire to understand the nature of the neoclassical methodology (NCM) and its limits beyond what I had learned during my studies at the University of Trier (Treves). His insisting that I should not simply join the credo of many heterodox economists that “equilibrium makes no sense, ever”; but instead needed to point out when thepure agent-based computational economics may not be substituted by an equilibrium (NCM) approach helped me to find the right arguments. He gave me all the help and opportunity to do research in a direction that diverted from his work in many ways and was so utterly clustered with both, uncertainty and risk regarding the outcome –which is all but to be expected. And he never ever got tired of hearing or reading just another version of mybakerymodel –or at least he did not tell me!
When I envisaged the need to learn how to make use of this so called agent-based computa- tional economics, I found that nobody I knew worked with this methodology and most people had never ever heard of it. Fortunately, I was encouraged by Prof. Alfred Endres to build a network of people working in that direction by visiting plenty of summer schools, conferences and work- shops. At the very first event I met Prof. Klaus Troitzsch. He provided a lecture at the ABM summer school of the European Social Simulation Association (ESSA) in 2011 (located at the University of Surrey, Guildford, UK). Eventually Prof. Klaus Troitzsch became my second mentor and supervisor for the PhD project. He gave me valuable input and reassurance in all kind of questions related to the simulation methodology and beyond. When I got unsure of whether the endeavor was worth the trouble, he reassured me.
Besides my two mentors, a lot of people helped me directly or indirectly during the long period of research cumulating in this thesis. I wish to thank all my colleagues at the Chair of Economic Theory, especially Sven Höfer, Malte Martin and PD Dr. Bianca Rundshagen, who read most of what I have written here in detail and provided me with useful comments. A special thank you goes to Annette from Heede, our chair’s secretary who, with her profound knowledge of the English lan- guage, proofread the complete thesis. Needlessly to say: All remaining errors are mine. In addition, I want to thank Andreas Rudert with whom I made the very first steps on the way to the bakery
model and whose technical advice (being a computer scientist), long discussions and intensively shared work phases have been an invaluable help in this most critical phase: The Beginning.
I also wish to thank the participants of the essa@work sessions (European Social Simulation As- sociation workshop series), the AURÖ young academics workshops (Ausschuss für Ressourcen und Umweltökonomie des Verein für Socialpolitik), and the GENED annual meetings (German Network for New Economic Dynamics) for valuable feedback and reassurance.
Finally, I would like to present my gratitude to the writers of a handful of monographs that where most welcome: The Economics of Time and Ignorance by O’Driscoll, Rizzo and Garrison (1985) should be mentioned first, for the close proximity to the title of the thesis is not a coincidence. The others are Analytical Economics by Georgescu-Roegen (1967), The Invisible Hand by Ingrao and Israel (1990),More heat than lightby Mirowski (1989) andFoundations for New Economic Thinking by Dow (2012); altogether, these books helped me to understand what the limits of the neoclassical approach are and when these may become a problem. It is due to the nature of secondary literature that the number of their citations does not resemble their importance in finding the answers to my questions.
If you didn’t grow it, you didn’t explain its emergence.
— Joshua M. Epstein (1999,Complexity)
Introduction and Purpose
By preferring the support of domestic to that of foreign industry, he intends only his own secur- ity; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. (Adam Smith, 1904 [1776], Book IV, Chapter II, paragraph IX ofAn Inquiry into the Nature and Causes of the Wealth of Nations)
This perhaps most famous quote of Adam Smith refers to the invisible hand that coordinates economic action of selfish individuals in such a manner that an efficient allocationemerges. The neoclassical methodology (NCM) incorporates this metaphor by presuming efficient organisation from the outset (the equilibrium). The relatively new approach of agent-based computational eco- nomics (ACE), however, allows to build models that provide explanations that are explicitly based on the actions of an individual. All these (inter-)actions are simulated. This is why it is called agen- erativeapproach in contrast to analytical approaches. The metaphor of the invisible hand is then reinterpreted through the lens of self-organisation, well known from, e.g., biochemical processes like those that constitute the patterns of a zebra’s hide (see below). The difference to those more simple models of biochemical processes (or other natural processes) is that two additional traits of the single entities need to be accounted for: intentionality and autonomy. Hence, we speak of agentsand complex adaptive systems (CAS). The intention of the current work is to provide a bridge between NCM and ACE, but without compromising the methodological options ACE provides: A maximal absence of exogenous explanation and related simplifications, like the abstraction from time and discrete numbers. Such an approach will be calledpureagent-based computational eco- nomics (pACE).
”In a self-organizing system order is not imposed from the outside, by external influences. No archi- tect or foreman holds the blue-print or has a pre- conceived idea about what patterns will evolve. The patterns that arise are emergent properties, proper- ties that cannot be predicted simply by examining the subunits in isolation. To understand them, the dynamic and often remarkably complex interactions among the subunits must be taken into account”
(Camazine, 2003,Natural History)
Neoclassical Methodology
In today’s high-tech age, one naturally assumes that US President Barack Obama’s economic team and its international counterparts are using sophisticated quantitative computer models to guide us out of the current economic crisis. They are not.
The best models they have are of two types, both with fatal flaws. Type one is econometric:
empirical statistical models that are fitted to past data. These successfully forecast a few quarters ahead as long as things stay more or less the same, but fail in the face of great change. Type two goes by the name of ‘dynamic stochastic general equilibrium’. These models assume a perfect world, and by their very nature rule out crises of the type we are experiencing now. (Farmer and Foley, 2009)
The above quotation by two leading economists in the growing field ofcomputational econom- icsis taken from theopinionsection of the interdisciplinary and renowned journalNature. It hints at a central problem in the economic profession, a problem that gained momentum with the finan- cial crisis of 2008 and the following great recession: The nature of most models that are employed in the profession is not suitable to represent important economic aspects in an unbiased way. These models are nonetheless used to gain an understanding of the working of the economy and help politicians in their everyday decisions. This class of models is constituted upon what I call theneo- classical methodology (NCM). These models are analytical in nature and strongly emphasise the role of equilibrium; at least this is the core of the models. The archetypes are general and partial equilibrium models, and non-cooperative game theory (which is another form of an equilibrium approach).1
(Non-cooperative) game theory and general equilibrium can be seen as two sides of the same coin, in the one case (game theory) operating on the level of individual agents and in the other case (general equilibrium or partial equilibrium) working with aggregate representations. The reader might object to placing both under the same umbrella at this stage, but it will become obvious - so I hope - that both currents in the mainstream of economics have something in common, that there exists an overarchingneoclassical methodology. Anticipating the first part of this thesis, these com- mon properties can be seen in the kind of mathematics that is used and the concept of equilibrium that constitutes the method. But every formalism comes at a cost. In case of the neoclassical form- alism, the cost is an unrealistic and oftentimes insufficient account of uncertainty, time, ration- ality, interaction, heterogeneity and indivisibility. In addition, the concept of equilibrium merely describes under which circumstances a stable organisation will persist. It cannot provide an ex- planation for Adam Smith’s notion of theinvisible hand. There is no description of a process that
1These models date back to ideas and concepts of the famous economists like Antoine Augustin Cournot (*1801-
†1877), Léon Walras (*1834-†1910), Alfred Marshall (*1842-†1924) and Francis Ysidro Edgeworth (*1845-†1926), to name but a few prominentmarginalists. They have been shaped into an axiomatic theory by the work of John von Neumann (*1903-†1953), Oskar Morgenstern (*1902-†1977) and John Forbes Nash, Jr. (*1928-†2015) (Game Theory); as well as Kenneth Joseph Arrow (*1921), Gérard Debreu (*1921-†2004), and Lionel Wilfred McKenzie (*1919-†2010) (General Equi- librium). This list is necessarily and deliberately incomplete. There is no general agreement on what constitutesneoclas- sical economics(Lawson, 2013), which is why I introduce the term neoclassical methodology (NCM) instead.
not only sustains, but also leads to, a stable organisation of economic activity in NCM. This kind of critique of the standard approach to economic theorising is both too important and too funda- mental to be treated casually. Therefore, I dedicate the first half of the first part of the thesis to it.
The novelty of the argument will be the perspective that is chosen by asking:Does the neoclassical methodology put limits to the representation of economic phenomena?
Pure Agent-based Computational Economics
The modern digital computer has changed the situation radically. It provides us with a tool of research-for formulating and testing theories-whose power is commensurate with the complex- ity of the phenomena we seek to understand. [. . . ] As economics finds it more and more neces- sary to understand and explain disequilibrium as well as equilibrium, it will find an increasing use for this new tool and for communication with its sister sciences of psychology and sociology.
(Simon, 1959, p. 280)
Before personal computers were widely applicable, a high level of abstraction and an analytical approach to economics had been necessary in order to get to any solution. With the advent of com- putational economics, a lot of the technical reasons for employing NCM models ceased to exist.
The core idea behind computer simulation is that one does not need to solve any problem at all. Of- ten computer simulation is simply used to find solutions where the analytical approach is imprac- tical (numerical analysis). But it is also possible to use computer simulation as a genuine method.
Computer simulation only necessitates that the problem at hand can be represented (formalised) by a set of variables that hold numerical content (numbers) and a set of procedures (algorithms) that describe what happens with these variables. The single algorithms need to be connected by another algorithm in such a way that the computer can always decide which (sub-)procedure it followsnext. This enveloping algorithm is commonly referred to as the updating scheme, and I will later introduce a methodological agent calledscheduler that is in charge of this updating scheme.
Since the updating scheme is itself nothing but an algorithm in which the other ones are nested, a computer itself simulation is but a single algorithm.2 The complexity of the algorithmic descrip- tion makes it in general impossible to analyse the simulation model “by hand”, i.e., it would be too time-consuming to carry out all the instructions (for all initialisations) and neither can the prob- lem (always) be refined in such a way that an analytical solution can be derived.3 Instead, it is sufficient to provide a set of initial conditions, run the algorithm and analyse the output. This step is purely deductive. But a singlerunis barely representative for the whole structure. Therefore, an- other step is necessary. The researcher decides for adesign of experiment(DOE), not uncommon to that of any classical experiment, in which the sample, i.e. a set of initial conditions and stopping
2The main difference between a mathematical model and a simulation model in these terms is the presence of al- gorithms instead of a system of equations, although we may also state that the solution concept employed to solve the system of equations, if explicitly provided, makes the mathematical model nothing but a specific simulation problem. It should be noted that any algorithm can be formulated as a recursive function, but this would be very hard to interpret and nothing would be won.
3Even if possible, any refinement that goes beyond the deletion of redundancies would change the model.
conditions, is defined. For practical and numerical reasons, this sample can never be complete, hence the selection of the sample is one aspect that constitutes the experimental character of sim- ulation analysis - although the control is higher than in classical experiments in the social and/or natural sciences.4 The simulation is carried out for each single instance of the sample and the data is gathered. At that point a second, inductive element enters the stage. Since the data does sel- dom “speaks for itself”, the researcher will make use of statistical methods to analyse it. Based on the analysis of the sample the scientist interprets the model itself. Supported by this interpretation and accompanied by deductive reasoning frompartsof the model, the researcher will then derive conclusions for the topic of interest in a last step ofabduction.
This definition of computer simulation is quite universal and can be employed for simple nu- merical analysis, system dynamics, microsimulation, cellular automata oragent-based modelling (ABM)5,6all the same. The differences between these methods are the concepts of representation in the simulation model. The current avant-guard method in computational economics is agent- based computational economics(ACE), which is the application of agent-based modelling to eco- nomic problems (a prominent subfield is agent-based finance, ABF). The defining characteristic of ABM is that the relevant individuals are described by single (sets of) algorithms, including their own set of variables and specific protocols for interaction between these individuals. It is the tech- nique which allows the greatest freedom in modelling, but also the most demanding one. Hamill and Gilbert (2015, p. 4) define agent-based modelling as follows:
An agent-based model is a computer program that creates an artificial world of heterogeneous agents and enables investigation into how interactions between these agents, and between agents and other factors such as time and space, add up to form the patterns seen in the real world. The program creates agents located with different characteristics and tells them what they can do under different circumstances.
A more technical definition is that of Cioffi-Revilla (2014, p. 288):
A social agent-based model (ABM) is an object-oriented computational model for analyzing a social system consisting of autonomous, interacting, goal-oriented, bounded-rationalset of act- orsAthat use a givenrule setRand are situated in anenvironmentE.
As such, the technique of ABM does not provide a guideline for the representation of real phe- nomena within a model (i.e, formalised theory), except that it emphasises the role of individual ac- tion and interaction. Agent-based computational economics, it seems, is often used to overcome
4Another aspect has to do with the model design itself. Guided by intuition, experimentation and feedback, the mod- eller has already taken numerous ambiguous decisions in the modelling-cycle before the final model has been finished.
In this respect, the simulation experiment lacks regarding real experiments, for we always need to provide a model of the decision processes. But the same is true for any (mathematical) model.
5Sometimes called individual-based modelling (IBM), agent-based simulation (ABS), multi agent systems (MAS) or similar.
6For a historical introduction to, and overview of, different simulation methodologies, see for example Gilbert and Troitzsch (2005), chapter 1.
