Holston-Laubach-Williams (HLW) is the canonical econometric framework for estimating the natural rate of interest (r-star) using a state-space Kalman filter that jointly extracts r-star, trend growth, and the output gap from data on GDP, inflation, and the real interest rate.
HLW casts the economy as a state-space system: an IS curve linking the output gap to the real-rate gap, a Phillips curve linking inflation to the output gap, and laws of motion for unobserved trend growth and r-star. A Kalman filter backs out the latent natural rate consistent with output at potential and stable inflation. It extends the original 2003 Laubach-Williams setup to multiple economies.
With the FOMC's 2025-2026 r-star debate central to how restrictive policy actually is, HLW estimates anchor the market's view that the long-run neutral rate has drifted higher post-pandemic; the New York Fed publishes updated HLW r-star series that desks read against the dot plot's longer-run rate.
The New York Fed's HLW estimates put US r-star near 0.5% in real terms through much of the 2010s, implying a nominal neutral rate around 2.5% at a 2% inflation target — broadly consistent with the FOMC's longer-run dot. Post-2022, market and model debate centered on whether r-star had risen toward 1-1.5% real, materially changing how restrictive a 4.25-4.5% funds rate truly is.
r* ≈ c·g + z, where g = trend growth of potential output and z = other persistent demand/savings factors; jointly filtered with the output gap and trend growth via a Kalman filter.