Among the Fed's International Finance Discussion Papers is the paper "Currency Crashes in Industrial Countries: Much Ado About Nothing?" by Joseph E. Gagnon (2009-966) Feb 2009. Here is the abstract (bold is mine):
Sharp exchange rate depreciations, or currency crashes, are associated with poor economic outcomes in industrial countries only when they are caused by inflationary macroeconomic policies. Moreover, the poor outcomes are attributable to inflationary policies in general and not the currency crashes in particular. On the other hand, crashes caused by rising unemployment or external deficits have always had good economic consequences with stable or falling inflation rates.
When you add up all the policies, fiscal and monetary, and the economy it is hard to come to any conclusion other than that the dollar is going to weaken. Key though is not the dollar/euro or dollar/pound exchange rate -- it is the rate with those countries where the U.S. has big trade deficits. Eco 101 teaches us that, and now Bernanke has confidence that we have nothing to fear of the outcome. There is a geopolitical aspect to it, considering the dollar is the world's reserve currency, and you can bet that this subject came up when Obama and Hu got together yesterday for their one-on-one.