  Following our previous investigation of the USA Standard and Poor index
anti-bubble that started in August 2000, we analyze thirty eight world stock
market indices and identify 21 anti-bubble. An ``anti-bubble'' is defined as a
self-fulfilling decreasing price created by positive price-to-price feedbacks
feeding overall pessimism and negative market sentiment further strengthened by
inter-personal interactions. We mathematically characterize anti-bubbles by a
power law decrease of the price (or of the logarithm of the price) as a
function of time and by decelerating/expanding log-periodic oscillations. The
majority of European and Western stock market indices as well as other stock
indices exhibit practically the same log-periodic power law anti-bubble
structure as found for the USA S&P500 index. These anti-bubbles are found to
start approximately at the same time, August 2000, in all these markets. This
shows a remarkable degree of synchronization worldwide. The descent of the
worldwide stock markets since 2000 is thus an international event, suggesting
the strengthening of globalization.
