It is impossible to come to the end of the last chapter's review without a sense that something – perhaps many things – in this long trail of studies has gone seriously awry. At a minimum, a viable approach would require that bubble characteristics be made statistically comparable without resort to arcane technical methods or obscure model specifications. And such descriptions probably ought to include fractal and exponential features, be consistent with the concepts of probability and entropy (described below), and be consistent with the ways in which people actually behave.

Economists have instead tried to find and to test a wide array of fundamental features; perhaps dividends ought to be discounted differently or various measures of earnings or operating revenues of some sorts might provide better proxies in modeling for bubble behavior. Indeed, a whole zoology of bubbles has been proposed: rational bubbles, intrinsic bubbles, collapsing bubbles, and so on. Even with all of this, however, financial economists have not arrived at a point where bubbles can be described with much statistical confidence, consistency, or clarity.

As Sornette (2003, p. 285) admits, it is difficult to identify speculative bubbles because they “are model specific and generally defined from a rather restrictive framework.” Indeed, “model specific” is an ideal way to summarize the literature that has already been reviewed.