Procedural rationality
A number of modellers, mainly associated with the Santa Fe Institute, have been using algorithms from artificial intelligence and artificial life programs to represent heterogeneous agents. The clearest statement of the reasons for so doing is probably Sargent's ([17], pp. 2-3):
Rational expectations imposes two requirements on economic models: individual rationality, and mutual consistency of perceptions. When implemented numerically or econometrically, rational expectations models impute much more knowledge to the agents within the model (who use the equilibrium probability distributions in evaluating their Euler equations) than is possessed by an econometrician, who faces estimation and inference problems that the agents in the model have somehow solved. I interpret a proposal to build models with boundedly `rational agents' as a call to retreat from the second piece of rational expectations (mutual consistence of expectations) by expelling rational agents from our model environments and replacing them with `artificially intelligent' agents who behave like econometricians. These `econometricians' theorize, estimate and adapt in attempting to learn about probability distributions which, under rational expectations, they already know.
The point of this exercise is to demonstrate than it is not necessary to impose mutual consistency of expectations on all agents in order to get simulation results which approximate the rational expectations outcomes. As Marcet and Sargent [10] put it, "the notion of a rational expectations equilibrium would be a more attractive one if there were plausible and undemanding learning schemes which would drive the system towards a rational expectations equilibrium. Even though not all models with heterogeneous agents yield approximately rational-expectations results, where they do, the features of the learning process are frequently (for example Timmermann, 1994) adduced as evidence that volatile prices and sales volumes are part of the convergence to rational-expectations equilibria.
Two recent papers yield some insight into the circumstances in which rational-expectations equilibria are likely to arise in computational models with heterogeneous agents. In one of these papers, Arthur, Holland, LeBaron, Palmer and Tayler [3] represent the traders in an artificial stock market as classifier systems which update their expectations by means of genetic algorithms. Each classifier is of the standard Holland type and represents a linear forecasting model with a limited domain. Over time, the population of classifiers converges to a piece-wise linear forecasting model. If learning takes place at a sufficiently slow rate (because the genetic algorithm is applied relatively infrequently -- in their reported simulations, once in every 1,000 transactions), rational expectations equilibria always emerge as agents' expectations converge to a common norm. Faster rates of learning (once in every 250 transactions) generate a market regime "in which psychological behaviour emerges, there are significant deviations from the r.e.e. benchmark, and statistical "signatures" of real financial markets are observed.
The other paper in this vein, Darley and Kaufman [6] find two similar regimes in dynamic non-cooperative games in which agents learn from more or less local interaction with their neighbours. States resembling rational-expectations equilibria (with shared agent perceptions) arise when prediction is easy (because each agent looks at the behaviour of a small number of neighbours so there is not much feedback but) not when prediction is difficult (because each agent notices the behaviour of a lot of other agents and, so there is a lot of feedback). When the model does not generate rational-expectations equilibria marketed by mutually consistent models or perceptions, then the output is meta-stable in the sense that it is marked by periods of stasis interspersed with periods of turbulence. Darley and Kaufman call these punctuated equilibria by analogy with evolutionary biology.
The suggestion here is that, in general, rational expectations equilibria can emerge from computational models in which heterogeneous agents develop models endogenously. The circumstances in which such equilibria emerge are likely to be characterized by slow rates of learning and low feedback. The faster agents develop their models, perhaps because of high feedback, the less likely is mutual consistency of perceptions as defined by commonality of predictive agent models.
While these results look interesting, they are generated by computational models with unknown analytical properties. Moreover, the learning procedures assumed for agents are arbitrary in the sense that there is no reason to believe that actual decision-makers learn in a manner which is described by those assumptions. Certainly, Herbert Simon, the inventor of the notion of bounded rationality rejects the Sargent view. Sent [18] describes the difference between the Sargent and Simon approaches to representations of cognition as one which turns on the descriptive accuracy of the representation of cognition as behaviour. Whereas Sargent justifies the use of genetic algorithms to represent cognition on their effective parallelism in computation, Simon argues that cognition depends on symbol processing. In effect, Sargent appeals to current views of the physiological basis of all mental activity while Simon appeals to experimental evidence about the epiphenomena of decision-making and learning as observed by experimental psychologists.
This difference is important for economists if either (a) the two approaches imply different theoretical and modelling structures yielding different relationships between actions such as policy measures on the one hand and the consequences of those actions or (b) one approach more usefully supports policy analyses than does the other. In the remainder of this paper, we consider only the second of these criteria.
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