On the possibility of long lasting speculative bubbles in a learning environment

The paper provides a theoretical insight into the possibility of a long lasting speculative trade in asset markets, driven purely by heterogeneous prior beliefs about the relevant dividend process. The analysis of speculative trade is undertaken by focusing on the behavior of market bubbles. A bubble is defined as the departure of an asset price from its fundamental value, which is defined as buy-and-hold forever valuation of the asset. I analyze bubbles in the context of a dynamic general equilibrium dynamic model with risk neutral agents having heterogeneous beliefs, and facing short selling constraints. In this risk neutral environment any trade must be driven by disagreement about the probability assessment to future events by the agents. This justifies the name speculative trade, and speculative bubble. I assume that the dividend process follows a hidden Markov chain and I allow for arbitrarily spread prior beliefs to account for the possibility of Bayesian learning. I use recursive techniques to characterize the equilibrium prices in such environments and to show that under certain conditions any disagreement among the agents might lead to the speculative bubbles. This leads to a natural question whether the bubble can be persistent if agents who start with heterogenous beliefs are allowed to learn. The celebrated Blackwell-Dubins theorem suggests that as long as agents are sufficiently agnostic in their priors learning asymptotically removes any disagreement, which would suggest the bubble would also be removed. On the other hand, Freedman`s theorem states that in infinitely complex non-parametric environments learning is a highly non-generic pattern. This means that to obtain rational justification for long lasting bubbles one need to increase complexity. I provide numerical examples to illustrate these issues. In particular I will show that mere moving from a Markov learning environment to the hidden Markov environment (without increasing the number of states) constitutes a significant increase in complexity, which is reflected in the time it takes for learning to remove the initial disagreement and the bubble.