Looking at these figures, taken from Liz Ann Sonders at Schwab, it is clear that market dips and economic dips occur at the same time. It seems that the stock market is just another co-incident indicator.
On the other hand, the economic data shown below was constructed after-the-fact by the BLS -- the stock market is not predicting the economy, but it is a rapid indicator of where it is today.
It is interesting to think about whether it is predicting the US economy or the world economy or some weighted average. Clearly European financial problems rock the stock market, but is that because people believe it will affect the US?
Stock Market at Economic Inflection Points
Source: FactSet, as of March 31, 2013. Y-axis of upper chart in logarithmic scale. Y-axis of lower chart represents year-over-year percentage change in US GDP.