This paper argues that international parity conditions should be tested using an econometric approach, which allows for possible interactions in the determination of prices, interest rates, and exchange rates, and also for different short- and long-run dynamics. Failure to do so might account for the apparent lack of empirical success of exchange rate models based on the purchasing power parity (PPP) and uncovered interest rate parity (UIP) hypotheses. By focusing on the German mark and the Japanese yen (both nominal effective rates and bilateral rates vis-à-vis the U.S. dollar), we show that empirical support for PPP and UIP can be found within a full-information maximum-likelihood (FIML) framework. This confirms that such structural hypotheses are to be tested in a multivariate cointegration system in order to draw valid inference.