Fleming (1962) and Mundell (1963) pioneered the idea of impossible trinity or Trilemma. The impossible trinity doctrine suggests that a country can't have fixed exchange rate, capital mobility and independent monetary policy all at a time. As with free flow of capital, the exchange rate would be decided by interest rate parity and so exchange rate can't be fixed, if interest rates are different. To keep exchange rate fixed the interest rate has to equal to concerned country and thus no independent monetary policy. Thus flexible exchange rate are necessary to have independent monetary policy in case of capital mobility. With capital controls we can have fixed exchange rate and independent monetary policy as China has been doing since long.
In an interesting paper presented at Jackson Hole, however, Professor Hélène Rey of the London Business School argued that in todays world where global credit cycles and capital flows are largely dependent on the Federal Reserve’s monetary policy the Trilemma has reduced to dilemma. A country can't have independent monetary policy even in case of flexible exchange rates. Since the capital flows are often dependent on the economic condition in the US, the flows are quite volatile and central banks across the world has to sacrifice some degree of independence in monetary policy. Thus what matters is capital control. Only with capital controls one can have independent monetary policy.
The recent capital outflows from India and pursuant drag on Rupee is an example of Dilemma. With economic condition improving in US the funds are moving back to US, leading to sharp fall in Rupee. To arrest the fall in Rupee, RBI has intervened in the market in the manner that's not warranted by our domestic economic condition( if we exclude the capital flows and exchange rate). If capital outflows flows have been not so bad, RBI would have certainly thought of lowering interest rate and increasing liquidity in the system to boost the falling growth, but with capital outflows it's working in opposite manner.
The problem of Trilemma was solved in most of the emerging economies either by adopting fixed exchange rate and capital control or by flexible exchange rate and varying degree of capital mobility. But all countries opted for independent monetary policy. The challenges from Dilemma are more severe in nature,as it suggest that with free capital flows you can't have independent monetary policy even with flexible exchange rates, only with capital controls one can have independent monetary policy. Since no country would like to sacrifice its independence of monetary policy, Professor Hélène Rey argument suggest that we will move towards a world having more capital controls and not less capital controls. Recent move by RBI in which they tried to reduce the outflows from India are well in line with the hypothesis. Thus, the world is moving towards more capital control and not less capital control whether the exchange rate is fixed or floating.