In this article we employ the Pesaran and Shin (1999) structural cointegrating VAR methodology to reassess the monetary approach to exchange rate determination. This recently developed technique allows us to test directly the over-identifying restrictions of the long-run structural relations underlying the flexible price monetary model of the exchange rate. Using data for the German Mark-U.S. dollar and the Japanese Yen-U.S. dollar, we find for both exchange rates, that structural identification is rejected by the data, results that raise further doubts about the long-run validity of the monetary model.