It just happens to be the case that in the reverse situation -- if there is a lack of convergence -- the exchange rate system plays a major role. If exchange rates are flexible, divergence in anti-inflationary policy can increase volatility but it is less dramatic overall. In turn, the degree of convergence is also lower, of course.
The degree of convergence tends to be BIS Review 97/1997  -8-  higher with fixed but adjustable exchange rates. If there is, nevertheless, no adequate convergence, costs will depend on whether there is a timely realignment. If prompt action is taken, the consequences will be contained.