A Bayesian evaluation of alternative models of trend inflation

The concept of trend inflation is important in making accurate inflation forecasts. However, there is little consensus on how the trend in inflation should be modeled. While some studies suggest a survey-based measure of long-run inflation expectations as a good empirical proxy for trend inflation, others have argued for a statistical exercise of decomposing inflation data into trend and cycle components. In this paper, we assess alternative models of trend inflation based on the accuracy of medium-term inflation forecasts. To incorporate recent evidence on the time-varying macroeconomic volatility, we consider models with both constant volatility and time-varying volatility. For all the models, we compare not only point predictions but also density forecasts, such as deflation probability. Our analysis yields two broad results. First, models with time-varying volatility consistently dominate those with constant volatility. Second, once time-varying volatility is incorporated, it is difficult to say that one model of trend inflation is better. Simply averaging forecasts with time-varying volatility is as good as forecasts from the best-fitting model. In addition, the relative performance of each model varies greatly over time. Overall, our results suggest that it is important to consider predictions from a range of models with time-varying volatility.