Rational vs. irrational beliefs in a complex world

How do rational and boundedly rational agents interact in a competitive asset market? To answer this question, we build a highly nonlinear asset pricing model where agents hold heterogeneous beliefs. Our model features fully rational forward looking agents versus boundedly rational backward looking agents whose market shares evolve endogenously. This gives rise to chaotic model dynamics which are characterized by complex bubble and crash dynamics, even without any exogenous fluctuations. We show that computational methods can be applied to numerically analyze models combining agents forming rational expectations and agents forming extrapolative expectations, with the possibility of transition between one type of behavior and the other. Not only do we find that boundedly rational agents remain in the market, but document that their effect on price dynamics is even amplified by the behavior of fully rational agents. In their interaction, trend-extrapolators amplify small deviations from fundamentals, while rational agents eventually anticipate market crashes after large bubbles and drive prices back to the fundamental.