"Thermometers" of speculative frenzy

Establishing unambiguously the existence of speculative bubbles is an on-go ing controversy complicated by the need of defining a model of fundamental prices. Here, we present a novel empirical method which bypasses all the di fficulties of the previous approaches by monitoring external indicators of an anomalously growing interest in the public at times of bubbles. From the definition of a bubble as a self fulfilling reinforcing price change, we i dentify indicators of a possible self-reinforcing imitation between agents in the market. We show that during the build-up phase of a bubble, there is a growing interest in the public for the commodity in question, whether it consists in stocks, diamonds or coins. That interest can be estimated thro ugh different indicators: increase in the number of books published on the topic, increase in the subscriptions to specialized journals. Moreover, the well-known empirical rule according to which the volume of sales is growin g during a bull market finds a natural interpretation in this framework: sa les increases in fact reveal and pinpoint the progress of the bubble's diff usion throughout society. We also present a simple model of rational expect ation which maps exactly onto the Ising model on a random graph. The indica tors are then interpreted as "thermometers", measuring the balance between idiosyncratic information (noise temperature) and imitation (coupling) stre ngth. In this context, bubbles are interpreted as low or critical temperatu re phases, where the imitation strength carries market prices up essentiall y independently of fundamentals. Contrary to the naive conception of a bubb le and a crash as times of disorder, on the contrary, we show that bubbles and crashes are times where the concensus is too strong!.