Part of my research focus in the last decade has been on building flexible unobserved components models for trend inflation. Trend inflation estimates from these models are naturally of interest; these unobserved components models also forecast inflation well. For beginners in this area, Section 6.1 of my teaching notes on unobserved components models would be a good place to start. Below I outline my papers in this area.

Univariate Trend Inflation Models

The models below are all univariate and all you need is inflation data. They do, however, differ in their autocovariance structures and stochastic volatility specifications.

1. The unobserved components stochastic volatility (UCSV) model in Stock and Watson (2007) is the first of this class of univariate trend inflation models; the paper basically started this whole literature. Chan (2018) considers a reparameterization of this classic UCSV model so that one can conveniently test whether stochastic volatility is needed in the trend component and/or the transitionary component.

2. In the original UCSV model, the cyclical component is assumed to have no persistence. This is a curious modeling assumption as one would expect the cyclical component, or the inflation gap, to be autocorrelated. Chan (2013) introduces a class of unobserved components model with stochastic volatility and moving average errors. These moving average models forecast inflation better than the original UCSV.

3. The trend inflation in unobserved components models is typically assumed to be a random walk. However, in successful inflation targeting countries, one would expect the trend inflation to evolve within a narrow band (related to the country's inflation target or target band), not a random walk. Motivated by this observation, Chan, Koop and Potter (2013) introduce a new model of trend inflation with two novel features: 1) the trend inflation is constrained to lie in an interval; and 2) it allows for a time-varying degree of persistence in the transitory component of inflation.

Multivariate Trend Inflation Models

Often this is additional information that can help us better estimate the trend inflation. The following multivariate unobserved components models incorporate other sources of information related to inflation.

1. The Phillips curve is the empirical relationship between inflation gap and some measure of economic slack. Chan, Koop and Potter (2016) propose a bivariate unobserved components model for inflation and unemployment with two new features: 1) both the trend inflation and NAIRU are assumed to evolve within bounds; and 2) it has time-varying Phillips curve and time-varying inflation persistence.

2. Short-horizon inflation forecasts from professional forecasters are generally accurate and informative, but longer-horizon forecasts are more mixed. This raises the question of whether one can still make use of the long-horizon forecasts to refine trend inflation estimates. Motivated by this question, Chan, Clark and Koop (2018) introduce a new model of trend inflation using both inflation data and long-run inflation expectations. It also allows for a time-varying degree of persistence in the transitory component of inflation and stochastic volatility.