Agent-Based Modelling in Economics

In Tesfatsion [2006] a framework (“constructive approach”) is formulated for Agent- Based Computational Economics (ACE). This is derived from the Walrasian equi- librium framework, but with the “auctioneer” removed. Four major strands of ACE work are identified:

1. Empirical understanding: why do global regularities persist despite lack of central control and planning.

3. Qualitative insight and theory generation: economic systems can be more fully understood through systematic examination of potential dynamical be- haviours.

4. Methodological advancement: programming, visualisation and validation tools will have to be carefully considered.

Tesfatsion argues that agent-based tools allow for more realistic models of cognitive agents than in ‘homo economus’ models. Events are wholly endogenous and driven purely by agent interactions. But we need to construct dynamically complete eco- nomic model, that is start with full initial conditions and then continue without further exogenous events; to do this we must look at wide range of plausible ini- tial specifications. Models are difficult to verify against empirical data due to the contingency of empirical events.

Tesfatsion describes the general process by which we may replace Walrasian “auctioneer” (or equivalents) by agent-based process. Something like the following circular flow required:

1. Terms of Trade 2. Buyer-Seller matching 3. Rationing 4. Trade 5. Settlement 6. Shake-Out

We then must consider what concept of equilibrium or solution concept should be used. A stationary-state is likely to be too strong for interesting models. Possible alternatives include: unchanging carrying capacity, continual market clearing, un- changing structure, fixed trade network, unchanging belief pattern and steady-state growth pattern (constant rates of growth). However we may want a weakened form of the one or more of the above.

This kind of constructive approach will have several key steps (an example of procurement processes is given in section 4 of Tesfatsion [2006]):

1. Select as benchmark case an equilibrium economic model from literature that is clearly presented and addresses some important issue

3. Dynamically complete model by introducing trading/interactions between agents in model

4. Define “equilibrium” for this complete model

We don’t have to impose rational expectations, but can incorporate realistic models of learning. May introduce conventions and organisations to provide “scaffolding”.

In Axelrod [2006] examples are given where Agent-Based Modelling has been used to facilitate interdisciplinary work, to look at problems which are mathemat- ically intractable and where it has revealed unity across disciplines. Of particu- lar interest are remarks on the difficulties of “selling” Agent-Based Modelling and tentative standards for using this kind of technique, such as parameter values to investigate.

In Judd [2006] some computational issues related to ACE are explored. The main appeal of computational approaches is outlined: the elements previously sac- rificed for simplicity can be investigated. He looks at two objections to numerical approaches. Lack of generality: to which he argues that theories (really) look at a “continuum of examples” (but perhaps a measure zero set of plausible/interesting examples). Viewed this way, Judd argues that the relevance and robustness of ex- amples is more important than the number. A second common objection, errors, is dismissed, as when handled carefully these are negligible. But how can we system- atically do computational (economic) research? We can’t (currently at least) prove theorems using computers, but we can:

1. Search for counter examples to a proposition.

2. Use Monte Carlo sampling methods (which can be clearly expressed in terms of classical or Bayesian statistics)

3. Use regression methods to obtain “shape” of some distribution.

4. Replication and generalisation – can perhaps straightforwardly adapt a com- puter model to a new case, something which is often not at all straightforward for a theorem.

How agents learn is a key aspect of Agent-Based Modelling. In Brenner [2006] various learning processes are surveyed. The assumption is that we wish to model, in an agent-based way, human behaviour as closely as possible; with a categorisation adapted from the psychological literature. Economists are typically divided into two camps vis `a vis learning: a desire that learning should converge towards optimal

behaviour and those not so interested in optimality. Human learning, it is claimed, can be split roughly into reinforcement learning and cognitive learning.

Three frequently used reinforcement learning models are: Bush-Moteller model, the principle of melioration and the Roth-Erev model. In all models the frequency of behaviours that lead to better results increases. Melioration works by average past behaviour. The others assume change is determined by current out- come together with previously determined frequency distribution; they only store frequencies, not the entire past.

We can model routine based learning using techniques such as experimenta- tion (trial and error), melioration/experience collection, imitation, satisficing (meet an aspirational level), replicator dynamics and selection mutation equation, evolu- tionary algorithms and combined models (for example experience weighted attrac- tion, variation-imitation-decision).

And we can model beliefs via Fictitious Play (see section 2.6.2), Bayesian Learning (the oldest and most prominent ‘optimal’ model), Least Squares Learn- ing, Genetic Programming, Classifier Systems, Neural Networks, Rule Learning (i.e. cognitive learning following same kind of process as reinforcement learning) and Stochastic Belief Learning (information from own experience or communication, when contradictory information obtained stochastically stick to old belief or not).

Brenner argues that in relation to routine versus belief learning the choice is difficult and related to choice of realistic versus simple model which may be more tractable. In choosing a model we should be capturing real learning process, obtain- ing an outcome matching stylised facts and, perhaps, converging to equilibrium. In assessing validity he argues experimental studies should provide main criteria, but evidence not always available and laboratory results may not apply to real world. We want effective description of resultant behaviour, even if details contradict psy- chology. Simple models are generally good (not over-fitted) but bad (as learning processes can be complicated) and unnecessary as current computer power means that we may be able to look at large number of parameters.

His practical recommendations include the suggestion that evolutionary ap- proaches are good for population level results though perhaps not individual dynam- ics. Fictitious Play (see above) is both simple and supported by evidence and thus recommended. In terms of belief learning he suggests that more research needed. It seems like Fictitious Play and rule learning recommended as simpler solutions; stochastic belief learning is good if more information about beliefs is available.

In LeBaron and Tesfatsion [2008] the idea of modelling macroeconomic pro- cesses via systems of interacting agents is surveyed. Emphasis is placed on work

which carries out some kind of empirical validation, through for example matching agent-level behaviour with people’s behaviour.

In LeBaron [2001] specific guidance is given for the construction of models of financial markets; these are well organised, centralised and dynamic. To design a model one must think about the key areas of trade (do we assume simple response to excess demand, build market such that local equilibrium price can be found easily or explicitly model dynamics of trading in attempt to approximate real world?), securities, evolution, calibration and time (there are problems with how to deal with the past, the relative rates of change and the issue of concurrency).