Sami Al-Suwailem IRTI - IDB

Coined by Brian Arthur (1999) Attracting more attention Promising with great potential Still needs more precise characterization

Probably the most fundamental property of Neoclassical Economics (NE) Convexity can be viewed as an organizing principle of the comparison between NE and CE Any combination of two points in the set belongs to the same set

Convexity precludes novelty by design: combinations always belong to the same set No innovations or creativity No learning or R&D No entrepreneurship

Convexity allows only negative feedback; positive feedback is not allowed Equilibrium, static system No dynamics, no self-organization

Maximization requires convexity Path-independence: Choice process or act of choice is ignored No place for emotions, ethics, values, and social relations

NE assumes perfectly divisible commodities Real numbers exclude Diophantine problems But if commodities are indivisible, we cannot use real numbers Rational numbers are non-convex Diophantine problems are not decidable

Neoclassical Economics Complexity Economics Novelty not allowed Negative feedback Maximization Path-independent Decidable Perpetual novelty Negative and positive Satisficing Path-dependent Undecidable

Institutions can be seen as factors for “convexifying” the choice set Convexity might not be always bad! A promising line of research

Self-organization—structure Emergence—function

Global order via local interactions Implies positive-feedback—excluded by convexity Examples: Bird flocks Fireflies

“The whole is greater than the sum” Self-organizing system is able to perform functions the sum cannot Implies novelty—excluded by convexity

“Swarm Intelligence” “Group Genius” “Wisdom of the Crowds”

Both exhibit nonlinear dynamics and universality Different nature and properties

Chaotic Systems Complex Systems Indistinguishable from random behavior Ergodic Non-adaptive Basin of attraction computable Not capable of universal computation Path-independent Recognizable patterns and order Non-ergodic Adaptive Basin of attraction not computable Capable of universal computation Path-dependent

Fireflies, bird flocks, fish schools, … Agents react to two sources of information: Environment—exogenous variables Local neighbors—endogenous variables

Each agent has a piece of knowledge regarding target or objective Relative variables communicate the knowledge to neighbors As each agent adjusts to its neighbors, the whole group synchronizes to the environment Knowledge therefore becomes integrated

“The problem is thus in no way solved if we can show that all of the facts, if they were known to a single mind … would uniquely determine the solution; instead, we must show how a solution is produced by the interactions of people, each of whom possesses only partial knowledge”

Dispersed information zi must be consistent An aggregator function must exist: F need not be computable Agents need not know F but they need to know it does exist

If independent variables dominate: stagnant order If relative variables dominate: chaos Complexity lies at the edge between order and chaos

Relative variables: the “self” part Independent variables: “organization” part

Missing from mainstream NE Supported by behavioral and social studies Also by physical sciences (spin glass) A point of departure of CE from NE But can be a point for extending NE

Consumption is presented as a function of income (and wealth) How about consumption of local neighbors? “Social capital” “Social multiplier”

As agents get different incomes, they cannot have equal consumption How to react to “consumption gap”? Move to different neighbors—Schelling model Trade—labor market Borrow—different modes of finance Donate—philanthropic institutions

Simple (NE): Complex: How this affects economic variables?

NetLogo 3.1.4 1225 patches (agents); 8 neighbors 1500 periods 30 runs Income is exogenous, uniformly distributed across agents; normally distributed across time Gap is closed using interest-free lending

Surpluses are managed centrally Deficits are financed from accumulated surpluses Loans are extended based on available funds 27

Total assets = total cash + total credit Total cash = cum (total-surplus + total-principal- payment – total-loans) Net wealth (i) = share in total assets – debt Share (i) = (acc. surplus) / sum (acc. surplus) Total credit = total debt loan-funds = loan-funds + total-surplus + total-principal-payment - total-loan ; this is a measure of cash-stock available for lending before consumption is decided. 28

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surplus Loanable funds Loans Consumption, wealth deficit Desired Consumption

Sum (net-wealth) = total cash Sum (shares) = 1 Income + loan – consumption – surplus – installment = 0 If there is interest or markup, then the equation for income becomes: Income + loan + (interest or markup) – consumption – surplus – installment = 0 31

More efficient fund utilization Smoother consumption Higher wealth More efficient fund utilization 33

Consumption Simple  = 0 Complex  > 0 Mean 74.5 74.3 Median 73.4 74.0 Std/Mean 0.22 0.19 Max. 127 112 No. below .5 max 354 126

Net-wealth Simple  = 0 Complex  > 0 Mean 1,316 1,855 Median 1,245 1,746 Std/Mean 0.55 1.02 Max. No. below .5 max 972 1,102

Wealth and Debt Simple  = 0 Complex  > 0 Wealth 1,439 2,446 Debt 123 591 Net 1,316 1,855

Flow of Funds Simple  = 0 Complex  > 0 Acc. surplus 1,439 2,446 Acc. loans 1,838 10,534 Acc. no. of loans 940 1,112 Average loan size 1.96 9.48 Turnover 1.28 4.31

Relative behavior smoothes out consumption Smoothing reduces excessive consumption, thus adding to wealth Connectedness facilitates channeling funds to deficit agents Higher net-worth and higher efficiency

Relative behavior deserves more attention Agent-based simulation provides a rich environment for research Extensions to investment and capital markets