This paper presents a Bayesian vector autoregression model with time-varying coefficients to analyze the evolution of U.S. inflation and unemployment dynamics after World War II. The model incorporates random walks for coefficients with reflecting barriers to ensure stability. It allows for arbitrary correlations between coefficient innovations and observable innovations, enabling the detection of features emphasized in theoretical analyses of inflation-unemployment dynamics. The model is used to examine how changing monetary authority views about the Phillips curve influenced inflation trends, particularly the rise in inflation during the 1960s and 1970s and the subsequent reduction in inflation following the 1970s. The paper also explores the role of the natural rate of unemployment in shaping inflation dynamics, as suggested by Parkin and Ireland. It discusses the implications of the natural-rate hypothesis, the evolution of the natural rate of unemployment, and the impact of policy changes on inflation. The paper uses a Bayesian framework to estimate the model, incorporating prior beliefs about the stability of the system and the evolution of parameters over time. It also examines the implications of the model for forecasting and policy, highlighting the importance of understanding the persistence and predictability of inflation. The results show that inflation became more persistent and variable in the 1970s, while it became less persistent and variable in the 1980s and 1990s. The paper also discusses the implications of these findings for monetary policy and the role of the natural-rate hypothesis in shaping economic outcomes.This paper presents a Bayesian vector autoregression model with time-varying coefficients to analyze the evolution of U.S. inflation and unemployment dynamics after World War II. The model incorporates random walks for coefficients with reflecting barriers to ensure stability. It allows for arbitrary correlations between coefficient innovations and observable innovations, enabling the detection of features emphasized in theoretical analyses of inflation-unemployment dynamics. The model is used to examine how changing monetary authority views about the Phillips curve influenced inflation trends, particularly the rise in inflation during the 1960s and 1970s and the subsequent reduction in inflation following the 1970s. The paper also explores the role of the natural rate of unemployment in shaping inflation dynamics, as suggested by Parkin and Ireland. It discusses the implications of the natural-rate hypothesis, the evolution of the natural rate of unemployment, and the impact of policy changes on inflation. The paper uses a Bayesian framework to estimate the model, incorporating prior beliefs about the stability of the system and the evolution of parameters over time. It also examines the implications of the model for forecasting and policy, highlighting the importance of understanding the persistence and predictability of inflation. The results show that inflation became more persistent and variable in the 1970s, while it became less persistent and variable in the 1980s and 1990s. The paper also discusses the implications of these findings for monetary policy and the role of the natural-rate hypothesis in shaping economic outcomes.