Rational and Near‐Rational Bubbles Without Drift

Abstract

This article derives a general class of intrinsic rational bubble solutions in a Lucas‐type asset pricing model. I show that the rational bubble component of the price–dividend ratio can evolve as a geometric random walk without drift, such that the mean of the bubble growth rate is zero. Driftless bubbles are part of a continuum of equilibrium solutions that satisfy a period‐by‐period no‐arbitrage condition. I also derive a near‐rational solution in which the agent’s forecast rule is under‐parameterised. The near‐rational solution generates intermittent bubbles and other behaviour that is quantitatively similar to that observed in long‐run US stock market data.