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 the estimated trend displays some serial correlation in first differences. Possible sources of misspecification that would otherwise be hard to detect and correct for include a small amount of measurement error, omitted variables, or minor approximation errors in model dynamics when estimating trend. Our proposed correction is conducted via application of a univariate Beveridge-Nelson decomposition to the preliminary estimated trend and we show with Monte Carlo analysis that our approach can work as well as if the original model used to estimate trend were correctly specified. We demonstrate the empirical relevance of the correction in an application to estimating r* as the trend of a risk-free short-term real interest rate. We find that 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 at least a small amount of measurement error in some of the variables included in the multivariate model.