Well, if so, they might be "doin' it rong!". On September 4th 2007 the Dow stood at 13,400 and the Funds target was 5.25. On March 19, 2008 (yesterday) the Dow kneeled at 12,099 and the Funds target was 2.25. The raw correlation between the Funds target and the Dow from 8/15/07 - 3/19/08 is .75!!
It could just be the Fed is cutting for whatever reason and that's driving the market down. Which would be weird but not a case of the Fed targeting the Dow. However, if the market declines are driving the Fed to cut, that would be targeting. Note that these are not mutually exclusive hypotheses.
To sort them out, lets turn to our friend, the Granger causality test!!
At short lags (2, 3 or 4 days), changes in the funds target Granger cause the Dow (to go down!!!) but changes in the Dow do not Granger cause the funds rate (so no targeting). However at longer lags (which kind of make sense for the stock market feeding into monetary policy) the story changes. At lags of 5, 6, or 7 days each series Granger causes the other! And at lags of 8 or 9 days, the Dow Granger causes the funds target but the target does not Granger cause the Dow (I am using a 10% significance level here, but the results are broadly similar at 5%).
So yes, there is some very crude evidence that the Fed is targeting the Stock Market when looking at lags of between 5-9 days. Of course they are totally failing in these efforts as their cuts are "causing" the market to fall further.
If I've left out another relevant variable, then my tests are misspecified and biased. Also, to match up the interest rate data to the Dow data requires adjusting for the fact that the Dow data is on a 5 day week along with a few holidays missing, and Fred II reports the Funds target on a 7 day week basis. I filled in the holidays for the Dow by repeating the previous days close and matched the 5 day week to the 7 day week by hand.
Here is a graph of the Dow with vertical lines marking the dates of rate cuts: