We study the exchange rate effects of monetary policy in a balanced macroeconometric two-country model for the United States and United Kingdom. In contrast to the empirical literature, which consistently treats the domestic and foreign countries unequally in the modeling process, we consider full model feedback, allowing for a thorough analysis of the system dynamics. The problem of model dimensionality is tackled by invoking the approach by Aoki (1981). Assuming country symmetry in the long run allows to decouple the two-country macrodynamics of country averages and differences such that the cointegration analysis can be applied to smaller systems. Second, the econometric modeling is general-to-specific, a graph-theoretic approach for the contemporaneous effects combined with automatic general-to-specific model selection. We find delayed overshooting of the exchange rate in the case of a Bank of England monetary shock but instantaneous response to a Fed shock. Altogether the response is more pronounced in the former case.