Does the Fed Control Interest Rates?

To what extent does TF, the target Federal funds rate set by the Fed, influence other rates? There is lots of variation in rates unrelated to TF, and any effects of TF on rates dissipate quickly for longer maturities. For short rates, all the tests have interpretations in terms of: (i) a Fed that has the power to control rates and uses it, and (ii) a Fed that has little power over rates or chooses not to exercise its power. In the end, there is no conclusive evidence (here or elsewhere) on the role of the Fed versus market forces in the long-term path of interest rates.