We introduce the ``reflexivity'' index that quantifies the relative importance of short-term endogeneity for financial markets (financial indices, future commodity markets) from mid-2000s to October 2012. Our reflexivity index is defined as the average ratio of the number of price moves that are due to endogenous interactions to the total number of all price changes, which also include exogenous events. It is obtained by calibrating the Hawkes self-excited conditional Poisson model on time series of price changes. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact of news and the endogenous mechanism by which past price changes may influence future price changes. Our robustness tests show that our index provides a 'pure' measure of endogeneity that is independent of the rate of activity, order size, volume or volatility. We find an overall increase of the reflexivity index since the mid-2000s to October 2012, which implies that at least 60-70 percent of financial price changes are now due to self-generated activities rather than novel information, compared to 20-30 percent earlier. While our reflexivity index is defined on short-time windows (10-30 minutes) and thus does not capture long-term memory, we discover striking coincidence between its dynamics and that of the price hikes and abrupt falls that developed during financial bubble regimes. We also show that the ``reflexivity'' index allows one to disentangle the internal dynamics from exogenous factors within the Autoregressive Conditional Duration (ACD) model. We provide a direct comparison of the Hawkes and ACD models based on numerical simulations and show that our effective measure of endogeneity for the ACD can be mapped onto the ``branching ratio'' of the Hawkes model. This opens the road to quantify the degree of endogeneity in the large class of auto-regressive models such as GARCH and extensions. The talk will provide an opportunity to present results of the Financial Crisis Observatory (www.er.ethz.ch/fco) at ETH Zurich, which aims at testing and quantifying rigorously, in a systematic way and on a large scale the hypothesis that financial bubbles can diagnosed with a rigorous scientific methodology before they burst.