Comparing Apples to Apples: “Synthetic Real‑Time” Estimates of R‑Star

Sophia Cho and John Williams

No 20250303, Liberty Street Economics from Federal Reserve Bank of New York

Abstract: Estimates of the natural rate of interest, commonly called “r-star,” garner a great deal of attention among economists, central bankers, and financial market participants. The natural interest rate is the real (inflation-adjusted) interest rate expected to prevail when supply and demand in the economy are in balance and inflation is stable. The natural rate cannot be measured directly but must be inferred from other data. When assessing estimates of r-star, it is important to distinguish between real-time estimates and retrospective estimates. Real-time estimates answer the question: “What is the value of r-star based on the information available at the time?” Meanwhile, retrospective estimates answer the question: “What was r-star at some point in the past, based on the information available today?” Although the latter question may be of historical interest, the former question is typically more relevant in practice, whether in financial markets or central banks. Thus, given their different nature, comparing real-time and retrospective estimates is like comparing apples to oranges. In this Liberty Street Economics post, we address this issue by creating new “synthetic real-time” estimates of r-star in the U.S. for the Laubach-Williams (2003) and Holston-Laubach-Williams (2017) models, using vintage datasets. These estimates enable apples-to-apples comparisons of the behavior of real-time r-star estimates over the past quarter century.

Keywords: natural rate of interest; real time estimation; Laubach-Williams model; Holston-Laubach-Williams model; R-Star (search for similar items in EconPapers)
JEL-codes: C32 E43 (search for similar items in EconPapers)
Date: 2025-03-03
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