To identify a bubble in real time, policymakers would need to judge whether a valuation metric, such as the price-earnings (P/E) ratio for the aggregate stock market, has crossed into bubble territory. But rendering such a judgment may be difficult in practice, particularly if the bubble is triggered by investor overreaction to an actual fundamental improvement in the underlying economy. For example, a pickup in measured productivity growth during the late 1990s appeared to offer to some fundamental justification for the rise in the market P/E ratio. Others have countered that the difficulties in identifying bubbles do not justify ignoring them altogether. Central banks routinely apply judgment to a whole host of issues affecting monetary policy. One example is the size of the so-called “output gap,” defined as the difference between actual GDP and potential GDP. The output gap is notoriously difficult to measure in real time, yet it remains an important input to central bank inflation forecasts.