We propose a novel econometric approach to estimating time-varying policy effects using external instruments in the presence of time-varying instrument relevance in a factor-augmented VAR model with data on the U.S., Canada, Germany, Japan, and the U.K. We find that U.S. monetary policy shocks are an important driver of the exchange rate movements, with no delayed overshooting. We show that estimates of spillover effects of U.S. monetary policy shocks on the inflation and real economic activity would be distorted without considering time variation in instrument relevance, and time variation in policy effects reflects primarily varying shock size, not their transmission.