All emerging market currencies have been falling since taper-talk first surfaced last Spring. But it's a mistake to say that the prospect of Fed tapering has created a crisis for emerging market countries, and/or that the problems of emerging market economies pose some existential threat to the U.S.
The chart above shows the dollar value of eight emerging market currencies, indexed to 100 as of the end of January, 2007. All of these currencies have been declining since last May, when the Fed began floating the idea of tapering its bond purchases. But as the chart shows, all of these currencies have been falling against the dollar since mid-2011. In short, the weakness of emerging market currencies is nothing new, and it didn't start with taper talk. There is no unifying story that explains what is happening here. Argentina's peso has been clobbered, but the weakness of Chilean peso and the Brazilian real since mid-2011 has only served to reverse the gains these currencies made against the dollar in the four previous years. Over the course of the past seven years, these currencies have pursued widely diverging paths.
The currencies of Russia, Indonesia, India, So. Africa, and Turkey have all moved rather closely in recent years. Not surprisingly, these countries have all had higher inflation than in the U.S. Consider the annual inflation rates for these countries over the past 2-3 years: So. Africa 6%, Russia 7-8%, India 8-9%, Turkey 8%, Indonesia 6-7%. Argentina's annual inflation rate has been at least 25%, so its not surprising that the Argentine peso has been the weakest of the emerging market currencies. If inflation in country A is much higher than inflation in country B, then it is reasonable to expect that the currency of country A will decline relative to the currency of country B. It's therefore not surprising that Chile's inflation rate has been only marginally higher than the U.S. (2-3% since 2011, vs. 2% in the U.S.), and the Chilean peso has been the strongest of the emerging market group.
It's a mistake to pin the problems of these countries and their currencies on the Fed, and it's a mistake to lump them all together.