One of the curious elements of the politics of monetary policy is that even though monetary stimulus often seems very politically fraught and people at times profess to believe that it's impossible, everyone seems to agree that exchange rate policy works. And indeed this is one reason that small open economies such as Switzerland, Sweden, and Israel all managed to weather the crisis relatively well. Instead of a huge collective national freakout in which they revisited the first principles of short-term macroeconomic stabilization policy they devalued their currencies. Even crisis-ravaged Iceland has managed to use devaluation to bounce back. And from time to time various officials have talked about "currency wars," implicitly acknowledging that large countries too have the ability to bolster their economy through currency devaluation. So maybe everyone just needs to devalue their currency, right?
The problem, as Paul Krugman points out, is that this is mathematically impossible.
But a basically parallel situation arose during the Great Depression. The trick in that case is that since when the Depression started currencies were pegged to gold, each individual country could devalue its currency by leaving the gold standard. So even though it was logically impossible for every country to devalue its currency relative to other currencies it was possible for each currency to devalue relative to gold.
Scott Sumner, discussing other matters, observed that in some respects the practice of imposing a two percent ceiling on consumer price inflation resembles the operation of the interwar gold standard.
I would say the analogy carries over to this target as well. The dollar, the euro, the yen, and the pound can't all get cheaper relative to each other but they can all become cheaper relative to the CPI basket. Which is a long way of saying that if you believe one country with a large output gap can increase real output by devaluing its currency relative to other currencies (which everyone seems to) then you ought to believe that the large depressed economies of the world can collectively boost their real ouput by relaxing the inflation target.