Learning and Contagion Effects in Trasitions Between Regimes: A Schematic Model of Bank Runs

D. Heymann, R. P. J. Perazzo, and Andres Schuschny - University of Buenos Aires

The behavior of economic agents sometimes appears to undergo sudden changes. Although this can happen in quite different contexts, the case of bank runs seems a particularly noticeable one. Bank panics have been explained in two ways: as "informationally based" events, caused by revisions of beliefs about the profitability of intermediaries, or as pure coordination phenomena in a system with multiple equilibria. However, both types of explanations are not necessarily disjoint: it maybe the case for example, that some macroeconomic new, which "fundamentally" affect the returns on deposits, induce a response which in turn triggers a self-reinforcing panic. In this instance, the panic is not simply generated by a "sunspot" (since in "normal times" agents would disregard the possibility of multiple equilibria) but it does have a component whereby the observation that people are withdrawing their assets leads to a cascade of withdrawals.

We want to study in a simple setting the interplay of two influences on behavior: the beliefs of agents about the "fundamental state of the system" and the effect of what other individuals are seen to be doing. We model the first mechanism through a learning procedure (a genetic algorithm) based on commonly shared economy-wide information; even so, each agent adapts to that information starting from different initial "interpretations" of the data. Therefore, some diversity in decisions is to be expected. In addition, agents may react to "local" information provided by the obseved behavior of their nearest neighbors. We may interpret this reaction (when it occurs) as a contagion effect.

The model has a large number $N$ of agents who have one unit of resources and can decide whether or not to deposit them in a "bank". This choice is renewed every market "day". The agents bear a cost if the aggregate level of deposits is too low (e.g. the bank cannot meet its contractual obligations) or too high (e.g. due to congestion costs). This scheme is analogous to B. Arthur's "El Farol" model. We find that, except in some particular situations where the system gets locked into a suboptimal deposit pattern, the systems tends to self-organize so that the daily deposits of individuals are near the upper bound. We incorporate the "local" coordination mechanism by allowing agents to choose to imitate their neighbors instead of using the strategy derived from their own learning. We find that both influences (learning and contagion) operate when the level of deposits is high; when deposits fall "too much", the local effect is able to lead the system to a new "ordered" state (similar to the magnetic phase of a ferromagnet).

The system is now disturbed by shocking (exogenously) the lower bound: now, a lesser amount of potential withdrawal demands can be satisfied. We find that the "local" component takes over after a few periods; giving rise to a short transient which can be interpreted as the diffusion of an "awareness of a dangerous state". If the exogenous shock is reversed soon, no major consequences arise. However, if it lasts, there is a "panic", with a large fall in the supply of funds to the bank. If now the exogenous parameter returns to its initial level, a slower reorganization of the system take place. The model lso generates the possibility that, if the "fundamentals" remain in a "bad state" for a long lapse of time, ll clients abandon the system, leading to a collapse.

Although the model is extremely stylized, we may try to "calibrate" its parameters to describe the qualitative features of some concrete episodes, like the recent (1995) banking crisis in Argentina.

Scheduled for Session 1.5 Financial Models - I