A Simple Correction for Misspecification in Trend-Cycle Decompositions with an Application to Estimating r*

Abstract

We propose a simple correction for misspecification in trend-cycle decompositions when the stochastic trend is assumed to be a random walk process but its estimated path displays serial correlation in its first differences. Possible sources of this misspecification, which might otherwise be hard to detect, include unaccounted for measurement error in the data, omitted variables, or incorrect assumptions about dynamics in the original model used to estimate trend. Our proposed correction is conducted via application of a univariate Beveridge-Nelson decomposition to the preliminary estimated trend and we show in Monte Carlo analysis that this approach can work as well as if the model used to estimate trend were correctly specified. We demonstrate the empirical relevance of our proposed correction in an application to estimating the trend path of the short-term risk-free real interest rate, r* (a.k.a. “r*-star”). Our corrected estimate of r* is considerably smoother than the preliminary estimate from a multivariate Beveridge-Nelson decomposition based on a vector error correction model, consistent with the presence of measurement error in at least some of the variables in the model.


(*Note:The working paper was originally published in January 2022 as 'The Decline in r* according to a Robust Multivariate Trend-Cycle Decomposition'.)

Keywords: trend-cycle decomposition, misspecification, natural rate of interest

JEL Classification: C13, C53, E43