Uncovered interest parity (UIP) has been almost universally rejected in studies of exchange rate movements, although there is little consensus on why it fails. In contrast to previous studies, which have used relatively short-horizon data, we test UIP using interest rates on longer-maturity bonds for the G-7 countries. These long-horizon regressions yield much more support for UIP -- all the coefficients on interest differentials are of the correct sign, and almost all are closer to the UIP value of unity than to the zero coefficient implied by the random walk hypothesis. We then use a small macroeconomic model to explain the differences between the short- and long-horizon results. Regressions run on data generated by stochastic simulations replicate the important regularities in the actual data, including the sharp differences between short- and long-horizon parameters. In the short run from risk premium shocks in the face of endogenous monetary policy. In the long run, in contrast, exchange rate movements are driven by the "fundamentals," leading to a relationship between interest rates and exchange rates that is more consistent with UIP.