In this paper, we develop a bivariate unobserved components model for inflation and unemployment. The unobserved components are trend inflation and the nonaccelerating inflation rate of unemployment (NAIRU). Our model also incorporates a time-varying Phillips curve and time-varying inflation persistence. What sets this paper apart from the existing literature is that we do not use unbounded random walks for the unobserved components, but rather use bounded random walks. For instance, trend inflation is assumed to evolve within bounds. Our empirical work shows the importance of bounding. We find that our bounded bivariate model forecasts better than many alternatives, including a version of our model with unbounded unobserved components. Our model also yields sensible estimates of trend inflation, NAIRU, inflation persistence and the slope of the Phillips curve.