If you have a classical view of the world, you would argue that nominal shocks should affect the nominal, not the real exchange rate: the real exchange rate is a real phenomenon, and money is a veil. Specifically, you’d expect any nominal shock to move the price level by the same amount that they move the exchange rate.Moreover, Krugman explains:
Now, a classical economist could (and some did) try to explain away this observation by arguing that what’s going on here is that there are real shocks, and that monetary policy was used to stabilize each country’s price level. But then you run into another problem, highlighted in a classic paper by Mike Mussa (haven’t found the original online, but he summarized the argument here (pdf)). Mussa pointed out that the behavior of both nominal and real exchange rates changed dramatically when the exchange rate regime changed, becoming vastly more volatile with the end of Bretton Woods....A paper of mine in the October 2010 issue of Economic Inquiry adds to the "and there's more" evidence. It looks at the US-UK real exchange rate over 1794-2005, during which the nominal exchange rate switches from fixed to floating and back a number of times (5 floating periods and 4 fixed periods). In this graph of the rolling average of the absolute monthly change, one can see that the real exchange rate is more volatile in floating (shaded) periods than in the adjacent fixed rate periods (the dashed lines denote the periods of government controls around the two world wars).
You can, if you’re desperate, try to explain this away by saying that there was some fundamental structural change in the early 1970s, but at that point you’re deep into epicycle territory. And there’s more — for example, Ireland went abruptly from having a stable real exchange rate against the UK to having a stable rate against Germany when it joined the European exchange rate mechanism, etc..
Incidentally, I believe the Mussa paper Krugman is referring to is in the Carnegie-Rochester Conference Series in 1986 (vol. 25) (subscription required).