Determining price bubbles - Harder than you think

Some many investors and market watchers will throw around the term bubble that most would assume these individuals have a good definition of what is a bubble. I have been doing some work with former professor friend to measure or identify housing bubbles. This is not as easy as most would think. 

A conclusion of our research is that defining a bubble is a joint hypothesis of a price dislocation and the model used to define the bubble. If a bubble is an extreme deviation from fair value, then you must have a definition of fair value. One model may show there is a bubble, but another model may justify a high price. One man's bubble is another man's strong move based on fundamentals. 

For example, many of the highflyers of the pandemic have fallen significantly. Does that signify these stocks were in a bubble? If new stocks with limited profits get bid higher and then fall to earth after cash flows are unrealized, does that signify a bubble? If prices move higher versus some regression model, is that a bubble or a misspecified model? 

Rates do not tell us about the likelihood of bubbles. We have had some of the largest bubbles when interest rates were higher than in the last decade. Whether the 1920's, the Japan property bubble, the dot-com bubble, and the housing bubble before the GFC, rates were not abnormally low, so rates by themselves may not tell us about bubbles. Credit availability and herding are not easy to measure. 

I believe there are bubbles and I believe that there is irrationality that can take prices to extremes that are unjustified by data, but proving this proposal is not easy. Higher volatility or range does not constitute a bubble. A large drawdown does not signify a past bubble. Identifying bubbles requires deep knowledge of market structure. Hence, true bubble hunting is not often easy.