Self-fulfilling chaotic mistakes: Some examples and implications

Abstract

In talks given early in the 1990s, Jean-Michel Grandmont (1998) introduced the concept of the self-fulfilling mistake. This phenomenon can emerge when economic agents cannot distinguish between randomness and determinism, a situation that can occur when the underlying true dynamics are chaotic (Radunskaya, 1994), although such a situation could arise with other forms of complex nonlinear dynamics besides those involving chaotic dynamics. In such a situation, agents may be unable to discern the true dynamics and may adopt simple, boundedly rational “rules of thumb” based on some kind of backward-looking adaptive expectations (Bullard, 1994). For certain kinds of underlying processes, agents may be able to mimic the actual dynamics with such an “incorrect” behavioral rule, an outcome known as a consistent expectations equilibrium (CEE), a concept formalized by Hommes (1998) as meaning that the two processes have identical means and also autocorrelation coefficients at all leads and lags. Sorger (1998) and Hommes and Sorger (1998) have shown how in some cases agents can learn to converge on such CEEs, or self-fulfillingly mistaken behavior. These models all involve discrete dynamics. The first realization that a discrete chaotic dynamic could be mimicked by a simple linear autocorrelation function is due to Bunow and Weiss (1979) and Sakai and Tokumaru (1980), the latter demonstrating the possibility for the case of the asymmetric tent map, a result studied in more depth by Brock and Dechert (1991) and Radunskaya (1994).

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