A fixed rate limits the actions of central bankers because monetary policy must be aimed at protecting the fixed level of the exchange rate. Under a regime of fixed nominal exchange rates, the economy is forced to absorb the full effect of changes in world prices through changes in domestic nominal wages and prices.
To bring this about, the burden initially falls on output and employment and, eventually, spreads to most wages and prices. And because domestic wages in particular tend to be "sticky," changes in output and employment need to be quite large.