The literature on uncovered interest rate parity (UIP) shows two empirical puzzles. One is the failure of UIP, and the other is the unstable coefficients in the UIP regression. We propose a time-varying coefficients model with stochastic volatility and US structural shocks (TVC-SVX) to study how US structural shocks affect time-variation in the bilateral UIP relation for twelve countries. An unconditional test and a conditional test for UIP are developed. The former tests if UIP coefficients mean-revert to their theoretical values, whereas the latter tests coefficients at each point in time. Our findings suggest that the failure of UIP results from omitted US factors, in particular US monetary policy, productivity and preference shocks, which are also found to Granger cause local movements of UIP coefficients.