Parameter Instability, Superexogeneity and the Monetary Model of the Exchange Rate. — This paper argues that failure to test for parameter time invariance yields misleading results. Time heterogeneity other than unit roots will make the parameters of the unrestricted system unstable and statistical inference invalid. However, if the instability stems from a particular subset of variables (superexogenous with respect to the parameters of interest), conditioning on them results in a partial model with stable parameters, and standard inferential procedures can then be used. We apply this methodology to test the monetary model of the exchange rate and find that both system and single-equation estimates support it in the case of yen-dollar exchange rate.