If floating exchange rates stabilize shocks rather than create shocks, a country that joins a monetary union or fixes its exchange rate looses a stabilizing mechanism. We use a first difference structural VAR on trade weighted macroeconomic data to study the role of floating exchange rates for five small open economies with inflation targets. By including both domestic and foreign variables and using a combination of long and short-run restrictions, we identify asymmetric shocks more carefully than previous studies. Only in Sweden and Canada does the nominal exchange rate appreciate significantly in response to asymmetric demand shocks and depreciate to asymmetric supply shocks. Most exchange rate movements are caused by speculation and are not responses to fundamental shocks. However, these exchange rate shocks have negligible effects on output and inflation. Our findings indicate that exchange rates are neither stabilizing nor destabilizing but may be loosely characterized as disconnected from the rest of the economy.