Speculative dynamics with bounded rationality learning

Abstract

We study a linear model for a future market characterized by the presence of different classes of traders. In the market there are three classes of traders: rational traders, feedback traders and fundamentalist traders. Each class of traders is described by a trading strategy and by an information set about the fundamental. The analysis is developed under bounded rationality, rational traders forming expectations do not know the “true” model but believe in a misspecified model. The convergence of the learning activity to the Rational Expectations Equilibria of the model is analyzed. Two different learning mechanisms are studied: the Ordinary Least Squares algorithm and the Least Mean Squares algorithm. The main goal of the study is to analyze how the presence of different classes of traders in the market affects the robustness of the Rational Expectations Equilibria of the model with respect to bounded rationality learning. Moreover we verify the claim that bubbles and erratic behavior in the stock price dynamics may arise because of learning non-convergence to Rational Expectations Equilibria. The results show that if the Ordinary Least Squares algorithm is used by the agents to update beliefs, convergence to one of the two Rational Expectations Equilibria of the model is ensured only if there are positive feedback traders in the market. On the contrary, the Least Mean Squares algorithm guarantees convergence to the Rational Expectations Equilibria given an appropriate initial belief.