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Working Paper

A Bayesian Evaluation of Alternative Models of Trend Inflation

With the concept of trend inflation now widely understood as to be important as a measure of the public’s perception of the inflation goal of the central bank and important to the accuracy of longer-term inflation forecasts, this paper uses Bayesian methods to assess alternative models of trend inflation. Reflecting models common in reduced-form inflation modeling and forecasting, we specify a range of models of inflation, including: AR with constant trend; AR with trend equal to last period’s inflation rate; local level model; AR with random walk trend; AR with trend equal to the long-run expectation from the Survey of Professional Forecasters; and AR with time-varying parameters. We consider versions of the models with constant shock variances and with stochastic volatility. We first use Bayesian metrics to compare the fits of the alternative models. We then use Bayesian methods of model averaging to account for uncertainty surrounding the model of trend inflation, to obtain an alternative estimate of trend inflation in the U.S. and to generate medium-term, model-average forecasts of inflation. Our analysis yields two broad results. First, in model fit and density forecast accuracy, models with stochastic volatility consistently dominate those with constant volatility. Second, for the specification of trend inflation, it is difficult to say that one model of trend inflation is the best. Among alternative models of the trend in core PCE inflation, the local level specification of Stock and Watson (2007) and the survey-based trend specification are about equally good. Among competing models of trend GDP inflation, several trend specifications seem to be about equally good.

Working Papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views expressed in this paper are those of the authors and do not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

Suggested Citation

Clark, Todd E., and Taeyoung Doh. 2011. “A Bayesian Evaluation of Alternative Models of Trend Inflation .” Federal Reserve Bank of Cleveland, Working Paper No. 11-34.