This paper develops a stochastic endogenous growth model that exhibits “excess volatility” of equity prices because speculative agents overreact to observed technology shocks. When making forecasts about the future, speculative agents behave like rational agents with very low risk aversion. The speculative forecast rule alters the dynamics of the model in a way that tends to confirm the stronger technology response. For moderate levels of risk aversion, the forecast errors observed by the speculative agent are close to white noise, making it difficult for the agent to detect a misspecification of the forecast rule. In model simulations, I show that this type of behavior gives rise to intermittent asset price bubbles that coincide with improvements in technology, investment and consumption booms, and faster trend growth, reminiscent of the U.S. economy during the late 1920s and late 1990s. The model can also generate prolonged periods where the price-dividend ratio remains in the vicinity of the fundamental value. The welfare cost of speculation (relative to rational behavior) depends crucially on parameter values. Speculation can improve welfare if actual risk aversion is low and agents underinvest relative to the socially-optimal level. But for higher levels of risk aversion, the welfare cost of speculation is large, typically exceeding one percent of per-period consumption.