  We study a generic model for self-referential behaviour in financial markets,
where agents attempt to use some (possibly fictitious) causal correlations
between a certain quantitative information and the price itself. This
correlation is estimated using the past history itself, and is used by a
fraction of agents to devise active trading strategies. The impact of these
strategies on the price modify the observed correlations. A potentially
unstable feedback loop appears and destabilizes the market from an efficient
behaviour. For large enough feedbacks, we find a `phase transition' beyond
which non trivial correlations spontaneously set in and where the market
switches between two long lived states, that we call conventions. This
mechanism leads to overreaction and excess volatility, which may be
considerable in the convention phase. A particularly relevant case is when the
source of information is the price itself. The two conventions then correspond
then to either a trend following regime or to a contrarian (mean reverting)
regime. We provide some empirical evidence for the existence of these
conventions in real markets, that can last for several decades.
