This paper examines the factors behind long-run movements of the dollar. Most recent work has concluded that structural exchange rate models explain only a small proportion of exchange rate movements. However, many economists still find the theory that links exchange rates and interest rates persuasive. We investigate the relationship between exchange rates, prices, and interest rates using multivariate maximum likelihood cointegration tests. In particular, we explicitly test for purchasing power parity and uncovered interest rate parity when using nominal exchange rates, and implicitly test for these two hypothesis when using real exchange rates. The conclusion that emerges from this study is that we almost always identify at least one cointegrating vector among the variables, but we can not verify the theoretical models that show how exchange rates and interest rates are linked.