A bubble is a runaway effect that takes place when the lid, a limiting factor, the balancing feedback loop, is temporary taken away from the system and only a reinforcing feedback loop remains. Examples are the removal of the mortgage ceiling for the housing market and Clinton allowing savings banks to merge with investment banks if people get rewarded for taking risk and the balancing loop of downward consequences is gone, a bubble will result.   This is now under repair by the Volcker Rule

Ponzi schemes (e.g. Madoff) are bubbles where the feedback loop (loss due to bad investment) is artificially  and maliciously hidden for the participants. Hypes like the Dutch Tulip mania of the 1630s, the South Sea Bubble the 1720s, the Florida real estate boom in the 1920s or the Bitcoin bubble of the 2010s have a lot in common with Ponzi schemes, except that the participants themselves unknowingly hide the feedback loop for a while. When the hype cools down, the feedback loop comes in with a vengeance and the value collapses. 

If government applies a new ceiling, thus a so-called balancing feedback loop, into a system when the wave is at the bottom, it will slow down the recovery of the wave. This happened after the 1930 crisis and this happened in Japan in the nineties. Instead it would be wiser to activate new feed-back mechanisms when a wave is really taking off and before it reaches its inflexion point, that is before it goes through its equilibrium. Restricting the availability of credit at the bottom of the cycle is a pro-cyclic action. The Basel-III accords in this view are somewhat pro-cyclic, as is cancelling the mortgage deduction in Dutch tax system. Alas the very nature of people is to respond pro-cyclic. Governments are almost like real people.

How can you see the difference between a Bubble, a Wave and an S-curve? Good question, and there is no easy answer, but let me try.  A bubble is characterized by an uncontrolled, stimulating, exponential feed-back loop, but sometimes it is difficult to identify this loop. You could also say it is the absence of a regulating, balancing feed-back loop. A bubble bursts when in some variable the limit is reached, but that variable can be different from the immediate feed-back loop . In most bubbles, people involved are exceptionally positive and confident without good cause.

A Wave by definition has an equilibrium, and the things that are increasing in an upswing have the characteristic that they also can  go down, without an external push and without bursting. Most waves are dampened. As long as the variable in question is within the amplitude of an earlier wave peak, it should be ok.  The upward peak in the Lehman Wave for example was not a bubble, because it was caused by the same variable (inventory) that had gone down in the dip: so it was a wave. Otherwise we should have called it the Lehman Bubble, shouldn’t we?  Only in some industries there was an additional bubble, when suppliers were sold out and panic ordering took place.

An S-curve in the beginning is similar to a bubble, but it reaches a stable plateau . When the plateau comes closer, it puts a limit to the growth, i.e. it introduces a balancing feedback loop. For this reason a Ponzi-scheme is never an S-curve. For Bitcoins I have difficulty imagining the plateau, so for the time being I consider Bitcoins a bubble.