Evidence of excess volatilities of asset prices compared with those of market fundamentals is often attributed to speculative bubbles. This study demonstrates that bubbles could in theory lead to excess volatility, but it shows that certain variance bounds tests preclude bubbles as an explanation. The evidence ought to be attributed to model misspecification or inappropriate statistical tests. One important misspecification occurs if a researcher incorrectly specifies the time series properties of market fundamentals. A bubble-free example economy characterized by a potential switch in government policies produces asset prices that would appear, to an unwary researcher, to contain bubbles.