A bounded model of time variation in trend inflation, NAIRU and the Phillips curve

In this paper, we develop a bivariate unobserved components model for in‡ation and unemployment. The unobserved components
are trend in‡ation and the non-accelerating in‡ation rate of unemployment (NAIRU). Our model also incorporates a time-varying Phillips curve and time-varying in‡ation 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, NAIRU is assumed to evolve within bounds. Our empirical work shows the importance of bounding. We …nd 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 in‡ation, NAIRU, in‡ation persistence and the slope of the Phillips curve.